{
"meta": {
"name": "tpc_form_corpus",
"version": "0.5.1",
"status": "increment 8 phase E, every slot of tpm_increment_8_phase_F 0.1.0 at Option 1 (2026-09-24); VERIFIED (both residences)",
"conforms_tps": "0.1.0 revision 4 (kernel tests T3, T4, T6 of TPS 2.2.3 and guide 3.6 over the D108.1 declared form; IC4 (a) of TPS 2.3.14 and guide 4.6, syntactic), with the bounds of D186.1 as drafted for TPS revision 6, 2.2.13 (proposed), and D177.1 as taken 2026-09-26 (TPS revision 6 text pending)",
"module": "tpc_form 0.2.1, proposed with TPC-PY 0.2.0, carrying D186.1, S14, D177.1, S32 and C-MS-5 (tpc_zone 0.5.1, schema 0.5.0; tpc_units 0.1.1; tpc_strike 0.2.1)",
"note": "Every expectation is hand-derived. The spring fixture is the zone corpus's toy with a DOF t, an entry E_t, and the forms of S1, S3 and S8; a test fixture, not physics under research. Evaluated values are IEEE doubles compared through canon() at twelve significant digits. Both residences MUST reproduce every expect. 0.2.0 adds the DEPTH cases (tpc_form 0.1.1): nesting to 10,000 and chains to 2,000 terms, each expectation hand-derived and matched to TPC-PHP's answer before it was first written. 0.3.0 (tpc_form 0.2.0, D186.1) adds the BOUNDS cases - an integer of at most 4 digits, a form of at most 4096 code points and 64 nested parentheses, refused beyond in that order before the grammar reads the form - and moves 30 DEPTH cases that lie beyond the bounds to the refusal, each noting its 0.1.1 answer; and the S14 cases - the exponent a form composes under nested powers and roots at most 9999 in lowest terms (T1), every exponent the dimension and KIND walks read or compute within -9999..9999, and a zero base under a negative rational exponent refused. 0.4.0 (D177.1, 2026-09-26; schema 0.5.0): the D variable is any DOF that no CONSTRAINT targets, one per TPK under D_VARIABLES ONE (the default) and any number under SEVERAL (T1: d_variable_check; the list: d_variables); T4 reads D(x, s, n) as dim(x) less n times dim(s); two earlier cases moved (dim/derivative-not-T1, t4/derivative-variable-not-T1), each noting its former answer; every fixture LAW carries a ROLE. 0.5.0 (S32, 2026-09-26): form_tree, the public parse tree the checks walk, as parsed, with parse_form's refusals; and S33: a LAW restating the motion of a FIXed DOF carries ROLE CONSTRAINT (no answer moves). 0.5.1 (C-MS-5, increment 11, 2026-09-28): 16 decode/ cases, a JSON {} and [] and an object keyed 0 read as written in both residences, with their list controls; no earlier answer moves."
},
"cases": [
{
"id": "parse/law-N2",
"fn": "parse_form",
"input": {
"text": "m * D(v, t) = -k_s * x",
"mode": "equation"
},
"expect": "[OK,m*D(v,t)=-k_s*x]"
},
{
"id": "parse/law-KIN",
"fn": "parse_form",
"input": {
"text": "D(x, t) = v",
"mode": "equation"
},
"expect": "[OK,D(x,t)=v]"
},
{
"id": "parse/law-FREE_Z",
"fn": "parse_form",
"input": {
"text": "D(z, t, 2) = 0",
"mode": "equation"
},
"expect": "[OK,D(z,t,2)=0]"
},
{
"id": "parse/boundary-B_small",
"fn": "parse_form",
"input": {
"text": "abs(x) < x_max",
"mode": "predicate"
},
"expect": "[OK,abs(x)<x_max]"
},
{
"id": "parse/signature-form",
"fn": "parse_form",
"input": {
"text": "D(x, t) = v",
"mode": "form"
},
"expect": "[OK,D(x,t)=v]"
},
{
"id": "parse/signature-operation",
"fn": "parse_form",
"input": {
"text": "D(x, t)",
"mode": "form"
},
"expect": "[OK,D(x,t)]"
},
{
"id": "parse/assoc-minus",
"fn": "parse_form",
"input": {
"text": "a-b-c",
"mode": "expression"
},
"expect": "[OK,a-b-c]"
},
{
"id": "parse/assoc-minus-paren",
"fn": "parse_form",
"input": {
"text": "a-(b-c)",
"mode": "expression"
},
"expect": "[OK,a-(b-c)]"
},
{
"id": "parse/assoc-div-mul",
"fn": "parse_form",
"input": {
"text": "a/b*c",
"mode": "expression"
},
"expect": "[OK,a/b*c]"
},
{
"id": "parse/assoc-div-paren",
"fn": "parse_form",
"input": {
"text": "a/(b*c)",
"mode": "expression"
},
"expect": "[OK,a/(b*c)]"
},
{
"id": "parse/unary-minus-power",
"fn": "parse_form",
"input": {
"text": "-a^2",
"mode": "expression"
},
"expect": "[OK,-a^2]"
},
{
"id": "parse/paren-neg-power",
"fn": "parse_form",
"input": {
"text": "(-a)^2",
"mode": "expression"
},
"expect": "[OK,(-a)^2]"
},
{
"id": "parse/power-chained-refused",
"fn": "parse_form",
"input": {
"text": "a^2^3",
"mode": "expression"
},
"expect": "[REFUSED,chained ^ needs parentheses at 4]"
},
{
"id": "parse/power-non-literal-refused",
"fn": "parse_form",
"input": {
"text": "a^b^c",
"mode": "expression"
},
"expect": "[REFUSED,^ takes an integer or a parenthesized rational exponent at 2]"
},
{
"id": "parse/power-paren",
"fn": "parse_form",
"input": {
"text": "(a^2)^3",
"mode": "expression"
},
"expect": "[OK,(a^2)^3]"
},
{
"id": "parse/precedence-mul",
"fn": "parse_form",
"input": {
"text": "a+b*c",
"mode": "expression"
},
"expect": "[OK,a+b*c]"
},
{
"id": "parse/precedence-paren",
"fn": "parse_form",
"input": {
"text": "(a+b)*c",
"mode": "expression"
},
"expect": "[OK,(a+b)*c]"
},
{
"id": "parse/outer-parens-dropped",
"fn": "parse_form",
"input": {
"text": "((a+b))",
"mode": "expression"
},
"expect": "[OK,a+b]"
},
{
"id": "parse/outer-parens-each-side",
"fn": "parse_form",
"input": {
"text": "(a)=(b)",
"mode": "equation"
},
"expect": "[OK,a=b]"
},
{
"id": "parse/outer-parens-argument",
"fn": "parse_form",
"input": {
"text": "sqrt((x))",
"mode": "expression"
},
"expect": "[OK,sqrt(x)]"
},
{
"id": "parse/outer-parens-predicate",
"fn": "parse_form",
"input": {
"text": "(x<1)",
"mode": "predicate"
},
"expect": "[OK,x<1]"
},
{
"id": "parse/outer-parens-comparison-side",
"fn": "parse_form",
"input": {
"text": "(x+1)<2",
"mode": "predicate"
},
"expect": "[OK,x+1<2]"
},
{
"id": "parse/inner-parens-kept",
"fn": "parse_form",
"input": {
"text": "a*((b))",
"mode": "expression"
},
"expect": "[OK,a*((b))]"
},
{
"id": "parse/inner-parens-kept-not",
"fn": "parse_form",
"input": {
"text": "not ((x<1))",
"mode": "predicate"
},
"expect": "[OK,not ((x<1))]"
},
{
"id": "parse/literal-fraction",
"fn": "parse_form",
"input": {
"text": "0.50*x",
"mode": "expression"
},
"expect": "[OK,5e-1*x]"
},
{
"id": "parse/literal-hundred",
"fn": "parse_form",
"input": {
"text": "100*x",
"mode": "expression"
},
"expect": "[OK,1e2*x]"
},
{
"id": "parse/literal-exponent",
"fn": "parse_form",
"input": {
"text": "1e5",
"mode": "expression"
},
"expect": "[OK,1e5]"
},
{
"id": "parse/literal-two",
"fn": "parse_form",
"input": {
"text": "2.0",
"mode": "expression"
},
"expect": "[OK,2]"
},
{
"id": "parse/literal-zero",
"fn": "parse_form",
"input": {
"text": "0.0",
"mode": "expression"
},
"expect": "[OK,0]"
},
{
"id": "parse/exponent-leading-zero",
"fn": "parse_form",
"input": {
"text": "x^02",
"mode": "expression"
},
"expect": "[OK,x^2]"
},
{
"id": "parse/exponent-negative",
"fn": "parse_form",
"input": {
"text": "x^(-1)",
"mode": "expression"
},
"expect": "[OK,x^(-1)]"
},
{
"id": "parse/exponent-rational",
"fn": "parse_form",
"input": {
"text": "x^(1/2)",
"mode": "expression"
},
"expect": "[OK,x^(1/2)]"
},
{
"id": "parse/exponent-rational-as-written",
"fn": "parse_form",
"input": {
"text": "x^(2/4)",
"mode": "expression"
},
"expect": "[OK,x^(2/4)]"
},
{
"id": "parse/exponent-zero",
"fn": "parse_form",
"input": {
"text": "x^0",
"mode": "expression"
},
"expect": "[OK,x^0]"
},
{
"id": "parse/derivative-n1-dropped",
"fn": "parse_form",
"input": {
"text": "D(x, t, 1)",
"mode": "expression"
},
"expect": "[OK,D(x,t)]"
},
{
"id": "parse/derivative-n2",
"fn": "parse_form",
"input": {
"text": "D(x,t,2)",
"mode": "expression"
},
"expect": "[OK,D(x,t,2)]"
},
{
"id": "parse/whitespace",
"fn": "parse_form",
"input": {
"text": "m *\tD(v,\nt) = x",
"mode": "equation"
},
"expect": "[OK,m*D(v,t)=x]"
},
{
"id": "parse/keywords-precedence",
"fn": "parse_form",
"input": {
"text": "x<1 or y>2 and z=3",
"mode": "predicate"
},
"expect": "[OK,x<1 or y>2 and z=3]"
},
{
"id": "parse/keywords-paren",
"fn": "parse_form",
"input": {
"text": "(x<1 or y>2) and z=3",
"mode": "predicate"
},
"expect": "[OK,(x<1 or y>2) and z=3]"
},
{
"id": "parse/not-binds-tighter",
"fn": "parse_form",
"input": {
"text": "not x<1 and y>2",
"mode": "predicate"
},
"expect": "[OK,not x<1 and y>2]"
},
{
"id": "parse/not-paren",
"fn": "parse_form",
"input": {
"text": "not (x<1 and y>2)",
"mode": "predicate"
},
"expect": "[OK,not (x<1 and y>2)]"
},
{
"id": "parse/not-not",
"fn": "parse_form",
"input": {
"text": "not not x<1",
"mode": "predicate"
},
"expect": "[OK,not not x<1]"
},
{
"id": "parse/paren-lookahead-double",
"fn": "parse_form",
"input": {
"text": "((x<1))",
"mode": "predicate"
},
"expect": "[OK,x<1]"
},
{
"id": "parse/paren-lookahead-nested",
"fn": "parse_form",
"input": {
"text": "((x+1)<2)",
"mode": "predicate"
},
"expect": "[OK,x+1<2]"
},
{
"id": "parse/comparison-ops",
"fn": "parse_form",
"input": {
"text": "a<=1 and a>=0 and a!=1 and a=0 and a>0",
"mode": "predicate"
},
"expect": "[OK,a<=1 and a>=0 and a!=1 and a=0 and a>0]"
},
{
"id": "parse/functions",
"fn": "parse_form",
"input": {
"text": "exp(a)+ln(a)+sin(a)+cos(a)+tan(a)+abs(a)+sqrt(a)",
"mode": "expression"
},
"expect": "[OK,exp(a)+ln(a)+sin(a)+cos(a)+tan(a)+abs(a)+sqrt(a)]"
},
{
"id": "parse/function-name-as-identifier",
"fn": "parse_form",
"input": {
"text": "exp+1",
"mode": "expression"
},
"expect": "[OK,exp+1]"
},
{
"id": "parse/equation-without-equals",
"fn": "parse_form",
"input": {
"text": "a",
"mode": "equation"
},
"expect": "[REFUSED,the equation has no =]"
},
{
"id": "parse/expression-with-equals",
"fn": "parse_form",
"input": {
"text": "a=b",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token = at 2]"
},
{
"id": "parse/two-equals",
"fn": "parse_form",
"input": {
"text": "a=b=c",
"mode": "equation"
},
"expect": "[REFUSED,unexpected token = at 4]"
},
{
"id": "parse/unbalanced-open",
"fn": "parse_form",
"input": {
"text": "x+(",
"mode": "expression"
},
"expect": "[REFUSED,unexpected end]"
},
{
"id": "parse/unbalanced-close",
"fn": "parse_form",
"input": {
"text": "x+)",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token ) at 3]"
},
{
"id": "parse/unclosed",
"fn": "parse_form",
"input": {
"text": "(x",
"mode": "expression"
},
"expect": "[REFUSED,unexpected end]"
},
{
"id": "parse/stray-close",
"fn": "parse_form",
"input": {
"text": "x)",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token ) at 2]"
},
{
"id": "parse/unknown-function",
"fn": "parse_form",
"input": {
"text": "f(x)",
"mode": "expression"
},
"expect": "[REFUSED,unknown function f at 1]"
},
{
"id": "parse/two-operators-minus",
"fn": "parse_form",
"input": {
"text": "a--b",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token - at 3]"
},
{
"id": "parse/two-operators-mul-minus",
"fn": "parse_form",
"input": {
"text": "a*-b",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token - at 3]"
},
{
"id": "parse/two-operators-plus-mul",
"fn": "parse_form",
"input": {
"text": "a+*b",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token * at 3]"
},
{
"id": "parse/empty",
"fn": "parse_form",
"input": {
"text": "",
"mode": "expression"
},
"expect": "[REFUSED,empty form]"
},
{
"id": "parse/blank",
"fn": "parse_form",
"input": {
"text": " \t\n",
"mode": "expression"
},
"expect": "[REFUSED,empty form]"
},
{
"id": "parse/empty-operand-end",
"fn": "parse_form",
"input": {
"text": "a+",
"mode": "expression"
},
"expect": "[REFUSED,unexpected end]"
},
{
"id": "parse/empty-operand-start",
"fn": "parse_form",
"input": {
"text": "*a",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token * at 1]"
},
{
"id": "parse/two-operands",
"fn": "parse_form",
"input": {
"text": "a b",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token b at 3]"
},
{
"id": "parse/implicit-multiplication",
"fn": "parse_form",
"input": {
"text": "2x",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token x at 2]"
},
{
"id": "parse/unit-inside",
"fn": "parse_form",
"input": {
"text": "0.05 m",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token m at 6]"
},
{
"id": "parse/hidden-code-point",
"fn": "parse_form",
"input": {
"text": "x\u202e",
"mode": "expression"
},
"expect": "[REFUSED,unexpected character <U+202E> at 2]"
},
{
"id": "parse/non-ascii",
"fn": "parse_form",
"input": {
"text": "x\u00d7y",
"mode": "expression"
},
"expect": "[REFUSED,unexpected character \u00d7 at 2]"
},
{
"id": "parse/literal-leading-point",
"fn": "parse_form",
"input": {
"text": ".5",
"mode": "expression"
},
"expect": "[REFUSED,unexpected character . at 1]"
},
{
"id": "parse/literal-trailing-point",
"fn": "parse_form",
"input": {
"text": "5.",
"mode": "expression"
},
"expect": "[REFUSED,unexpected character . at 2]"
},
{
"id": "parse/literal-comma",
"fn": "parse_form",
"input": {
"text": "1,5",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token , at 2]"
},
{
"id": "parse/literal-exponent-too-long",
"fn": "parse_form",
"input": {
"text": "1e12345",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token e12345 at 2]"
},
{
"id": "parse/literal-two-points",
"fn": "parse_form",
"input": {
"text": "1.5.2",
"mode": "expression"
},
"expect": "[REFUSED,unexpected character . at 4]"
},
{
"id": "parse/comparison-in-equation",
"fn": "parse_form",
"input": {
"text": "a<b",
"mode": "equation"
},
"expect": "[REFUSED,unexpected token < at 2]"
},
{
"id": "parse/chained-comparison",
"fn": "parse_form",
"input": {
"text": "a<b<c",
"mode": "predicate"
},
"expect": "[REFUSED,unexpected token < at 4]"
},
{
"id": "parse/predicate-without-comparison",
"fn": "parse_form",
"input": {
"text": "x",
"mode": "predicate"
},
"expect": "[REFUSED,unexpected end]"
},
{
"id": "parse/keyword-as-operand",
"fn": "parse_form",
"input": {
"text": "and",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token and at 1]"
},
{
"id": "parse/keyword-dangling",
"fn": "parse_form",
"input": {
"text": "x and",
"mode": "predicate"
},
"expect": "[REFUSED,unexpected token and at 3]"
},
{
"id": "parse/keyword-after-comparison",
"fn": "parse_form",
"input": {
"text": "x<1 and",
"mode": "predicate"
},
"expect": "[REFUSED,unexpected end]"
},
{
"id": "parse/derivative-one-argument",
"fn": "parse_form",
"input": {
"text": "D(x)",
"mode": "expression"
},
"expect": "[REFUSED,D is written D(x,t) or D(x,t,n) at 1]"
},
{
"id": "parse/derivative-order-zero",
"fn": "parse_form",
"input": {
"text": "D(x,t,0)",
"mode": "expression"
},
"expect": "[REFUSED,D is written D(x,t) or D(x,t,n) at 1]"
},
{
"id": "parse/derivative-literal-variable",
"fn": "parse_form",
"input": {
"text": "D(x,2)",
"mode": "expression"
},
"expect": "[REFUSED,D is written D(x,t) or D(x,t,n) at 1]"
},
{
"id": "parse/derivative-in-condition",
"fn": "parse_form",
"input": {
"text": "D(x,t)<1",
"mode": "predicate"
},
"expect": "[REFUSED,D is not permitted in a CONDITION at 1]"
},
{
"id": "parse/exponent-identifier",
"fn": "parse_form",
"input": {
"text": "x^y",
"mode": "expression"
},
"expect": "[REFUSED,^ takes an integer or a parenthesized rational exponent at 2]"
},
{
"id": "parse/exponent-decimal",
"fn": "parse_form",
"input": {
"text": "x^1.5",
"mode": "expression"
},
"expect": "[REFUSED,^ takes an integer or a parenthesized rational exponent at 2]"
},
{
"id": "parse/exponent-unparenthesized-negative",
"fn": "parse_form",
"input": {
"text": "x^-1",
"mode": "expression"
},
"expect": "[REFUSED,^ takes an integer or a parenthesized rational exponent at 2]"
},
{
"id": "parse/exponent-zero-denominator",
"fn": "parse_form",
"input": {
"text": "x^(1/0)",
"mode": "expression"
},
"expect": "[REFUSED,a rational exponent needs a positive denominator at 2]"
},
{
"id": "parse/not-a-string",
"fn": "parse_form",
"input": {
"text": 7,
"mode": "expression"
},
"expect": "[REFUSED,the form is not a string]"
},
{
"id": "parse/unknown-mode",
"fn": "parse_form",
"input": {
"text": "x",
"mode": "law"
},
"expect": "[REFUSED,unknown mode law]"
},
{
"id": "parse/grammar-witnesses",
"fn": "grammar_witness_count",
"input": {},
"note": "the count of witnesses both residences assert when loaded (S2: unambiguity as a vector)",
"expect": "33"
},
{
"id": "names/law-N2",
"fn": "form_names",
"input": {
"text": "m * D(v, t) = -k_s * x",
"mode": "equation"
},
"expect": "[OK,[k_s,m,t,v,x]]"
},
{
"id": "names/functions-excluded",
"fn": "form_names",
"input": {
"text": "exp(x)+sqrt(y)+exp",
"mode": "expression"
},
"note": "exp( is the function; a bare exp is an identifier",
"expect": "[OK,[exp,x,y]]"
},
{
"id": "names/predicate",
"fn": "form_names",
"input": {
"text": "x<1 and not y>2",
"mode": "predicate"
},
"expect": "[OK,[x,y]]"
},
{
"id": "names/refused",
"fn": "form_names",
"input": {
"text": "x+",
"mode": "expression"
},
"expect": "[REFUSED,unexpected end]"
},
{
"id": "dim/plus-pass",
"fn": "form_dimension",
"input": {
"text": "x+z",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1]"
},
{
"id": "dim/plus-fail",
"fn": "form_dimension",
"input": {
"text": "x+v",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,+ joins L1 and L1 T-1]"
},
{
"id": "dim/minus-pass",
"fn": "form_dimension",
"input": {
"text": "x-z",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1]"
},
{
"id": "dim/minus-fail",
"fn": "form_dimension",
"input": {
"text": "x-t",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,- joins L1 and T1]"
},
{
"id": "dim/times",
"fn": "form_dimension",
"input": {
"text": "m*x",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1 M1]"
},
{
"id": "dim/divide",
"fn": "form_dimension",
"input": {
"text": "x/t",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1 T-1]"
},
{
"id": "dim/divide-cancels",
"fn": "form_dimension",
"input": {
"text": "x/x",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/divide-by-zero",
"fn": "form_dimension",
"input": {
"text": "x/0",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,divides by zero]"
},
{
"id": "dim/divide-by-zero-expression",
"fn": "form_dimension",
"input": {
"text": "x/(0*x)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,divides by zero]"
},
{
"id": "dim/power-integer",
"fn": "form_dimension",
"input": {
"text": "x^2",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L2]"
},
{
"id": "dim/power-negative",
"fn": "form_dimension",
"input": {
"text": "x^(-1)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L-1]"
},
{
"id": "dim/power-zero",
"fn": "form_dimension",
"input": {
"text": "x^0",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/power-rational-pass",
"fn": "form_dimension",
"input": {
"text": "(x^2)^(1/2)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1]"
},
{
"id": "dim/power-rational-fail",
"fn": "form_dimension",
"input": {
"text": "x^(1/2)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,^ (1/2) of L1 is not a dimension]"
},
{
"id": "dim/power-rational-frequency",
"fn": "form_dimension",
"input": {
"text": "(k_s/m)^(1/2)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,T-1]"
},
{
"id": "dim/sqrt-pass",
"fn": "form_dimension",
"input": {
"text": "sqrt(x^2)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1]"
},
{
"id": "dim/sqrt-fail",
"fn": "form_dimension",
"input": {
"text": "sqrt(x)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,sqrt of L1 is not a dimension]"
},
{
"id": "dim/sqrt-frequency",
"fn": "form_dimension",
"input": {
"text": "sqrt(k_s/m)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,T-1]"
},
{
"id": "dim/exp-pass",
"fn": "form_dimension",
"input": {
"text": "exp(theta)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/exp-fail",
"fn": "form_dimension",
"input": {
"text": "exp(x)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,exp needs a dimensionless argument, not L1]"
},
{
"id": "dim/ln-ratio",
"fn": "form_dimension",
"input": {
"text": "ln(x/z)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/sin",
"fn": "form_dimension",
"input": {
"text": "sin(theta)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/cos-ratio",
"fn": "form_dimension",
"input": {
"text": "cos(x/x_max)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/tan-fail",
"fn": "form_dimension",
"input": {
"text": "tan(x)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,tan needs a dimensionless argument, not L1]"
},
{
"id": "dim/abs",
"fn": "form_dimension",
"input": {
"text": "abs(x)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1]"
},
{
"id": "dim/literal",
"fn": "form_dimension",
"input": {
"text": "2*x",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1]"
},
{
"id": "dim/literal-alone",
"fn": "form_dimension",
"input": {
"text": "2",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/zero-any",
"fn": "form_dimension",
"input": {
"text": "0",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,ANY]"
},
{
"id": "dim/zero-times",
"fn": "form_dimension",
"input": {
"text": "0*x",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,ANY]"
},
{
"id": "dim/zero-plus",
"fn": "form_dimension",
"input": {
"text": "x+0",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1]"
},
{
"id": "dim/zero-plus-zero",
"fn": "form_dimension",
"input": {
"text": "0+0",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,ANY]"
},
{
"id": "dim/zero-over",
"fn": "form_dimension",
"input": {
"text": "0/x",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,ANY]"
},
{
"id": "dim/zero-function",
"fn": "form_dimension",
"input": {
"text": "exp(0)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/zero-abs",
"fn": "form_dimension",
"input": {
"text": "abs(0)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,ANY]"
},
{
"id": "dim/equation-N2",
"fn": "form_dimension",
"input": {
"text": "m*D(v,t)=-k_s*x",
"mode": "equation",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1 M1 T-2]"
},
{
"id": "dim/equation-KIN",
"fn": "form_dimension",
"input": {
"text": "D(x,t)=v",
"mode": "equation",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1 T-1]"
},
{
"id": "dim/equation-FREE_Z",
"fn": "form_dimension",
"input": {
"text": "D(z,t,2)=0",
"mode": "equation",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1 T-2]"
},
{
"id": "dim/equation-zero-left",
"fn": "form_dimension",
"input": {
"text": "0=x",
"mode": "equation",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1]"
},
{
"id": "dim/equation-fail",
"fn": "form_dimension",
"input": {
"text": "m*x=v",
"mode": "equation",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,sides have dimensions L1 M1 and L1 T-1]"
},
{
"id": "dim/equation-inner-fail",
"fn": "form_dimension",
"input": {
"text": "x+v=v",
"mode": "equation",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,+ joins L1 and L1 T-1]"
},
{
"id": "dim/derivative",
"fn": "form_dimension",
"input": {
"text": "D(x,t)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1 T-1]"
},
{
"id": "dim/derivative-second",
"fn": "form_dimension",
"input": {
"text": "D(z,t,2)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1 T-2]"
},
{
"id": "dim/derivative-not-T1",
"fn": "form_dimension",
"input": {
"text": "D(x,m)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "D177.1: dim(x) less n times dim(m); tpc_form 0.2.0 before D177.1 answered [REFUSED,D needs a T1 variable, not m of M1]",
"expect": "[OK,L1 M-1]"
},
{
"id": "dim/derivative-unknown-operand",
"fn": "form_dimension",
"input": {
"text": "D(q,t)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,q has no DIMENSION]"
},
{
"id": "dim/derivative-unknown-variable",
"fn": "form_dimension",
"input": {
"text": "D(x,q)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,q has no DIMENSION]"
},
{
"id": "dim/unknown-name",
"fn": "form_dimension",
"input": {
"text": "q+1",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,q has no DIMENSION]"
},
{
"id": "dim/predicate-pass",
"fn": "form_dimension",
"input": {
"text": "abs(x)<x_max",
"mode": "predicate",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/predicate-fail",
"fn": "form_dimension",
"input": {
"text": "x<v",
"mode": "predicate",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,< compares L1 and L1 T-1]"
},
{
"id": "dim/predicate-zero",
"fn": "form_dimension",
"input": {
"text": "x!=0",
"mode": "predicate",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/predicate-literal-fail",
"fn": "form_dimension",
"input": {
"text": "x<1",
"mode": "predicate",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,< compares L1 and 1]"
},
{
"id": "dim/predicate-ratio",
"fn": "form_dimension",
"input": {
"text": "x/x_max<1",
"mode": "predicate",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/form-expression",
"fn": "form_dimension",
"input": {
"text": "D(x,t)",
"mode": "form",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1 T-1]"
},
{
"id": "dim/unparsable-dimension",
"fn": "form_dimension",
"input": {
"text": "q",
"mode": "expression",
"dimensions": {
"q": "bogus"
}
},
"expect": "[REFUSED,q has no DIMENSION]"
},
{
"id": "dim/parse-refused",
"fn": "form_dimension",
"input": {
"text": "x+",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,unexpected end]"
},
{
"id": "total/B_small",
"fn": "form_totality",
"input": {
"text": "abs(x)<x_max",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/divide-unguarded",
"fn": "form_totality",
"input": {
"text": "1/a<2",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses / on a with no guard a != 0]]"
},
{
"id": "total/divide-guarded",
"fn": "form_totality",
"input": {
"text": "a!=0 and 1/a<2",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/divide-guarded-mirror",
"fn": "form_totality",
"input": {
"text": "0!=a and 1/a<2",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/divide-guarded-after",
"fn": "form_totality",
"input": {
"text": "1/a<2 and a!=0",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/divide-guard-under-or",
"fn": "form_totality",
"input": {
"text": "a!=0 or 1/a<2",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses / on a with no guard a != 0]]"
},
{
"id": "total/divide-guard-wrong-form",
"fn": "form_totality",
"input": {
"text": "a>0 and 1/a<2",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "the guard table is closed: a > 0 is not the fixed form a != 0",
"expect": "[OK,[uses / on a with no guard a != 0]]"
},
{
"id": "total/ln-guarded",
"fn": "form_totality",
"input": {
"text": "ln(a)<1 and a>0",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/ln-guarded-mirror",
"fn": "form_totality",
"input": {
"text": "ln(a)<1 and 0<a",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/ln-unguarded",
"fn": "form_totality",
"input": {
"text": "ln(a)<1",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses ln on a with no guard a > 0]]"
},
{
"id": "total/ln-guard-wrong-form",
"fn": "form_totality",
"input": {
"text": "ln(a)<1 and a>=0",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses ln on a with no guard a > 0]]"
},
{
"id": "total/sqrt-guarded",
"fn": "form_totality",
"input": {
"text": "sqrt(a)<1 and a>=0",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/sqrt-guarded-mirror",
"fn": "form_totality",
"input": {
"text": "sqrt(a)<1 and 0<=a",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/sqrt-unguarded",
"fn": "form_totality",
"input": {
"text": "sqrt(a)<1",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses sqrt on a with no guard a >= 0]]"
},
{
"id": "total/power-negative-guarded",
"fn": "form_totality",
"input": {
"text": "a^(-1)<1 and a!=0",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/power-negative-unguarded",
"fn": "form_totality",
"input": {
"text": "a^(-1)<1",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses ^ with a negative exponent on a with no guard a != 0]]"
},
{
"id": "total/power-rational-guarded",
"fn": "form_totality",
"input": {
"text": "a^(1/2)<1 and a>=0",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/power-rational-unguarded",
"fn": "form_totality",
"input": {
"text": "a^(1/2)<1",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses ^ with a rational exponent on a with no guard a >= 0]]"
},
{
"id": "total/power-integer-total",
"fn": "form_totality",
"input": {
"text": "a^2<1 and a^0<1",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/tan-refused",
"fn": "form_totality",
"input": {
"text": "tan(theta)<1",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses tan on theta, which is not total]]"
},
{
"id": "total/tan-refused-even-guarded",
"fn": "form_totality",
"input": {
"text": "tan(theta)<1 and theta!=0",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses tan on theta, which is not total]]"
},
{
"id": "total/total-functions",
"fn": "form_totality",
"input": {
"text": "exp(a)+sin(a)+cos(a)+abs(a)<1",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/guards-nested-left",
"fn": "form_totality",
"input": {
"text": "(a>=0 and b!=0) and sqrt(a)/b<1",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/guards-nested-right",
"fn": "form_totality",
"input": {
"text": "a>=0 and (b!=0 and sqrt(a)/b<1)",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/guard-lost-across-or",
"fn": "form_totality",
"input": {
"text": "b!=0 and (a>=0 or sqrt(a)/b<1)",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses sqrt on a with no guard a >= 0]]"
},
{
"id": "total/guard-inside-not",
"fn": "form_totality",
"input": {
"text": "not (a!=0 and 1/a<2)",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/guard-negated",
"fn": "form_totality",
"input": {
"text": "not (a!=0) and 1/a<2",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses / on a with no guard a != 0]]"
},
{
"id": "total/guard-canonical-spelling",
"fn": "form_totality",
"input": {
"text": "1/(a+1)<2 and (a+1)!=0",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/guard-canonical-spelling-2",
"fn": "form_totality",
"input": {
"text": "1/(a+1)<2 and a+1!=0",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/guard-other-spelling",
"fn": "form_totality",
"input": {
"text": "1/(a+1)<2 and (1+a)!=0",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "guards match by canonical spelling: a+1 and 1+a are different spellings (S10)",
"expect": "[OK,[uses / on a+1 with no guard a+1 != 0]]"
},
{
"id": "total/guard-must-itself-be-total",
"fn": "form_totality",
"input": {
"text": "a!=0 and 1/a!=0 and 1/(1/a)<2",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/guard-not-total",
"fn": "form_totality",
"input": {
"text": "1/a!=0 and 1/(1/a)<2",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses / on a with no guard a != 0]]"
},
{
"id": "total/two-problems-sorted",
"fn": "form_totality",
"input": {
"text": "1/a<2 and ln(b)<1",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[uses / on a with no guard a != 0,uses ln on b with no guard b > 0]]"
},
{
"id": "total/dimension-pass",
"fn": "form_totality",
"input": {
"text": "x<y",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,[]]"
},
{
"id": "total/dimension-fail",
"fn": "form_totality",
"input": {
"text": "x<a",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,< compares L1 and 1]"
},
{
"id": "total/dimension-inner-fail",
"fn": "form_totality",
"input": {
"text": "x+a<y",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,+ joins L1 and 1]"
},
{
"id": "total/parse-refused",
"fn": "form_totality",
"input": {
"text": "x<",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,unexpected end]"
},
{
"id": "total/derivative-refused",
"fn": "form_totality",
"input": {
"text": "D(x,t)<1",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,D is not permitted in a CONDITION at 1]"
},
{
"id": "eval/N2-bound-true",
"fn": "eval_form",
"input": {
"text": "m * D(v, t) = -k_s * x",
"mode": "equation",
"bindings": {
"m": {
"VALUE": "2",
"UNIT": "kg"
},
"v": {
"VALUE": "1",
"UNIT": "m s-1"
},
"k_s": {
"VALUE": "3",
"UNIT": "N m-1"
},
"x": {
"VALUE": "0",
"UNIT": "m"
}
}
},
"note": "D of a bound identifier is 0; -k_s*x is -0.0, written 0",
"expect": "[OK,0,0,none]"
},
{
"id": "eval/scaled-cm",
"fn": "eval_form",
"input": {
"text": "2*x=1",
"mode": "equation",
"bindings": {
"x": {
"VALUE": "50",
"UNIT": "cm"
}
}
},
"expect": "[OK,1,1,none]"
},
{
"id": "eval/scaled-m",
"fn": "eval_form",
"input": {
"text": "2*x=1",
"mode": "equation",
"bindings": {
"x": {
"VALUE": "0.5",
"UNIT": "m"
}
}
},
"expect": "[OK,1,1,none]"
},
{
"id": "eval/two-units-agree",
"fn": "eval_form",
"input": {
"text": "x=x_max",
"mode": "equation",
"bindings": {
"x": {
"VALUE": "0.05",
"UNIT": "m"
},
"x_max": {
"VALUE": "5",
"UNIT": "cm"
}
}
},
"expect": "[OK,0.05,0.05,none]"
},
{
"id": "eval/false",
"fn": "eval_form",
"input": {
"text": "x=x_max",
"mode": "equation",
"bindings": {
"x": {
"VALUE": "0.06",
"UNIT": "m"
},
"x_max": {
"VALUE": "5",
"UNIT": "cm"
}
}
},
"expect": "[OK,0.06,0.05,none]"
},
{
"id": "eval/kind-difference",
"fn": "eval_form",
"input": {
"text": "f=w",
"mode": "equation",
"bindings": {
"f": {
"VALUE": "1",
"UNIT": "Hz"
},
"w": {
"VALUE": "6.283185307179586",
"UNIT": "rad s-1"
}
}
},
"expect": "[CONVENTION,units of different kind: Hz1 and rad1]"
},
{
"id": "eval/kind-difference-sum",
"fn": "eval_form",
"input": {
"text": "f+w",
"mode": "expression",
"bindings": {
"f": {
"VALUE": "1",
"UNIT": "Hz"
},
"w": {
"VALUE": "6.283185307179586",
"UNIT": "rad s-1"
}
}
},
"expect": "[CONVENTION,units of different kind: Hz1 and rad1]"
},
{
"id": "eval/kind-product",
"fn": "eval_form",
"input": {
"text": "f*w",
"mode": "expression",
"bindings": {
"f": {
"VALUE": "1",
"UNIT": "Hz"
},
"w": {
"VALUE": "6.283185307179586",
"UNIT": "rad s-1"
}
}
},
"expect": "[OK,6.28318530718,rad1 Hz1]"
},
{
"id": "eval/kind-ratio-cancels",
"fn": "eval_form",
"input": {
"text": "theta/theta",
"mode": "expression",
"bindings": {
"theta": {
"VALUE": "90",
"UNIT": "deg"
}
}
},
"expect": "[OK,1,none]"
},
{
"id": "eval/kind-square",
"fn": "eval_form",
"input": {
"text": "theta*theta",
"mode": "expression",
"bindings": {
"theta": {
"VALUE": "90",
"UNIT": "deg"
}
}
},
"expect": "[OK,2.46740110027,rad2]"
},
{
"id": "eval/kind-sqrt",
"fn": "eval_form",
"input": {
"text": "sqrt(theta*theta)",
"mode": "expression",
"bindings": {
"theta": {
"VALUE": "90",
"UNIT": "deg"
}
}
},
"expect": "[OK,1.57079632679,rad1]"
},
{
"id": "eval/kind-sqrt-odd",
"fn": "eval_form",
"input": {
"text": "sqrt(theta)",
"mode": "expression",
"bindings": {
"theta": {
"VALUE": "90",
"UNIT": "deg"
}
}
},
"expect": "[REFUSED,sqrt of kind rad1 is not a kind]"
},
{
"id": "eval/kind-rational-odd",
"fn": "eval_form",
"input": {
"text": "theta^(1/2)",
"mode": "expression",
"bindings": {
"theta": {
"VALUE": "90",
"UNIT": "deg"
}
}
},
"expect": "[REFUSED,^ (1/2) of kind rad1 is not a kind]"
},
{
"id": "eval/angle-in-rad",
"fn": "eval_form",
"input": {
"text": "theta",
"mode": "expression",
"bindings": {
"theta": {
"VALUE": "90",
"UNIT": "deg"
}
}
},
"expect": "[OK,1.57079632679,rad1]"
},
{
"id": "eval/sin",
"fn": "eval_form",
"input": {
"text": "sin(theta)",
"mode": "expression",
"bindings": {
"theta": {
"VALUE": "90",
"UNIT": "deg"
}
}
},
"expect": "[OK,1,none]"
},
{
"id": "eval/cos",
"fn": "eval_form",
"input": {
"text": "cos(theta)",
"mode": "expression",
"bindings": {
"theta": {
"VALUE": "90",
"UNIT": "deg"
}
}
},
"expect": "[OK,6.12323399574e-17,none]"
},
{
"id": "eval/tan",
"fn": "eval_form",
"input": {
"text": "tan(theta)",
"mode": "expression",
"bindings": {
"theta": {
"VALUE": "45",
"UNIT": "deg"
}
}
},
"expect": "[OK,1,none]"
},
{
"id": "eval/sqrt-frequency",
"fn": "eval_form",
"input": {
"text": "sqrt(k_s/m)",
"mode": "expression",
"bindings": {
"k_s": {
"VALUE": "8",
"UNIT": "N m-1"
},
"m": {
"VALUE": "2",
"UNIT": "kg"
}
}
},
"expect": "[OK,2,none]"
},
{
"id": "eval/exp",
"fn": "eval_form",
"input": {
"text": "exp(a)",
"mode": "expression",
"bindings": {
"a": {
"VALUE": "1",
"UNIT": "1"
}
}
},
"expect": "[OK,2.71828182846,none]"
},
{
"id": "eval/exp-overflow",
"fn": "eval_form",
"input": {
"text": "exp(a)",
"mode": "expression",
"bindings": {
"a": {
"VALUE": "1000",
"UNIT": "1"
}
}
},
"expect": "[REFUSED,not a finite double]"
},
{
"id": "eval/product-overflow",
"fn": "eval_form",
"input": {
"text": "x*x",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1e200",
"UNIT": "m"
}
}
},
"expect": "[REFUSED,not a finite double]"
},
{
"id": "eval/divide-by-zero",
"fn": "eval_form",
"input": {
"text": "1/x",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "0",
"UNIT": "m"
}
}
},
"expect": "[REFUSED,division by zero]"
},
{
"id": "eval/rational-negative-base",
"fn": "eval_form",
"input": {
"text": "x^(1/2)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "-4",
"UNIT": "1"
}
}
},
"expect": "[REFUSED,a negative base under a rational exponent]"
},
{
"id": "eval/rational",
"fn": "eval_form",
"input": {
"text": "x^(1/2)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "4",
"UNIT": "1"
}
}
},
"expect": "[OK,2,none]"
},
{
"id": "eval/integer-power",
"fn": "eval_form",
"input": {
"text": "x^3",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "2",
"UNIT": "m"
}
}
},
"expect": "[OK,8,none]"
},
{
"id": "eval/negative-power",
"fn": "eval_form",
"input": {
"text": "x^(-2)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "4",
"UNIT": "1"
}
}
},
"expect": "[OK,0.0625,none]"
},
{
"id": "eval/negative-power-of-zero",
"fn": "eval_form",
"input": {
"text": "x^(-1)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "0",
"UNIT": "1"
}
}
},
"expect": "[REFUSED,0 under a negative exponent]"
},
{
"id": "eval/ln",
"fn": "eval_form",
"input": {
"text": "ln(a)",
"mode": "expression",
"bindings": {
"a": {
"VALUE": "1",
"UNIT": "1"
}
}
},
"expect": "[OK,0,none]"
},
{
"id": "eval/ln-non-positive",
"fn": "eval_form",
"input": {
"text": "ln(a)",
"mode": "expression",
"bindings": {
"a": {
"VALUE": "0",
"UNIT": "1"
}
}
},
"expect": "[REFUSED,ln of a non-positive value]"
},
{
"id": "eval/sqrt-negative",
"fn": "eval_form",
"input": {
"text": "sqrt(a)",
"mode": "expression",
"bindings": {
"a": {
"VALUE": "-1",
"UNIT": "1"
}
}
},
"expect": "[REFUSED,sqrt of a negative value]"
},
{
"id": "eval/abs",
"fn": "eval_form",
"input": {
"text": "abs(x)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "-3",
"UNIT": "m"
}
}
},
"expect": "[OK,3,none]"
},
{
"id": "eval/negation",
"fn": "eval_form",
"input": {
"text": "-x",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "-3",
"UNIT": "m"
}
}
},
"expect": "[OK,3,none]"
},
{
"id": "eval/literal-hundred",
"fn": "eval_form",
"input": {
"text": "100*x",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "2",
"UNIT": "cm"
}
}
},
"expect": "[OK,2,none]"
},
{
"id": "eval/unbound",
"fn": "eval_form",
"input": {
"text": "x+y",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "4",
"UNIT": "1"
}
}
},
"expect": "[UNBOUND,y]"
},
{
"id": "eval/unbound-derivative",
"fn": "eval_form",
"input": {
"text": "D(y,t)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "4",
"UNIT": "1"
}
}
},
"expect": "[UNBOUND,y]"
},
{
"id": "eval/derivative-bound",
"fn": "eval_form",
"input": {
"text": "D(x,t)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "4",
"UNIT": "m"
}
}
},
"note": "the derivative variable t need not be bound",
"expect": "[OK,0,none]"
},
{
"id": "eval/derivative-plus",
"fn": "eval_form",
"input": {
"text": "D(x,t,2)+x",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "4",
"UNIT": "m"
}
}
},
"expect": "[OK,4,none]"
},
{
"id": "eval/binding-not-normalizable",
"fn": "eval_form",
"input": {
"text": "x",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1e9999",
"UNIT": "m"
}
}
},
"expect": "[REFUSED,VALUE 1e9999 in UNIT m is not a finite double]"
},
{
"id": "eval/binding-unit-refused",
"fn": "eval_form",
"input": {
"text": "x",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "furlong"
}
}
},
"expect": "[REFUSED,UNIT furlong: furlong is not a unit symbol]"
},
{
"id": "eval/predicate-not-evaluated",
"fn": "eval_form",
"input": {
"text": "x<1",
"mode": "predicate",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "1"
}
}
},
"expect": "[REFUSED,a predicate is not evaluated]"
},
{
"id": "eval/parse-refused",
"fn": "eval_form",
"input": {
"text": "x+",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "1"
}
}
},
"expect": "[REFUSED,unexpected end]"
},
{
"id": "eval/form-mode",
"fn": "eval_form",
"input": {
"text": "D(x,t)=v",
"mode": "form",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "m"
},
"v": {
"VALUE": "0",
"UNIT": "m s-1"
}
}
},
"expect": "[OK,0,0,none]"
},
{
"id": "names_check/spring",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "names_check/derivative-variable-not-in-refs",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:KIN: EQUATION names t, which is not in REFS]]"
},
{
"id": "names_check/refs-member-unused",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t",
"z"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:N2: REFS z is not named in EQUATION]]"
},
{
"id": "names_check/condition-names-nonmember",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[BOUNDARY:B_small: CONDITION names x_max, which is not in REFS]]"
},
{
"id": "names_check/does-not-parse",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) ="
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:N2: EQUATION does not parse: unexpected end]]"
},
{
"id": "names_check/hidden-left-to-T1",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x\u202e"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "names_check/wrong-type-left-to-T1",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": 7
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "names_check/not-an-object",
"fn": "names_check",
"input": {
"tpk": "x"
},
"expect": "[true,[]]"
},
{
"id": "coverage/spring-with-forms",
"fn": "form_coverage",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[[],[]]"
},
{
"id": "coverage/no-forms",
"fn": "form_coverage",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
]
}
]
}
},
"expect": "[[FREE_Z,KIN,N2],[B_small]]"
},
{
"id": "coverage/partial",
"fn": "form_coverage",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[[KIN],[]]"
},
{
"id": "t4/spring",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "t4/sides-differ",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = k_s"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:N2: EQUATION sides have dimensions L1 M1 T-2 and M1 T-2 (T4)]]"
},
{
"id": "t4/inner-sum",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) + x = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:KIN: EQUATION + joins L1 T-1 and L1 (T4)]]"
},
{
"id": "t4/derivative-variable-not-T1",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"m"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, m) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"note": "D177.1: D(x,m) is L1 M-1 (that m is no DOF is T1's refusal, d_variable_check); tpc_form 0.2.0 before D177.1 answered [false,[LAW:KIN: EQUATION D needs a T1 variable, not m of M1 (T4)]]",
"expect": "[false,[LAW:KIN: EQUATION sides have dimensions L1 M-1 and L1 T-1 (T4)]]"
},
{
"id": "t4/two-laws-one-fails",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x,t) = x"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:KIN: EQUATION sides have dimensions L1 T-1 and L1 (T4)]]"
},
{
"id": "t4/parse-left-to-T1",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) ="
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "t4/law-without-form-not-checked",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "t4/constant-without-value-allowed",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"note": "m and k_s carry no VALUE: T4 reads DIMENSION only (V3)",
"expect": "[true,[]]"
},
{
"id": "t6/spring",
"fn": "t6_totality",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "t6/unguarded-divide",
"fn": "t6_totality",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "x / x_max < 1"
}
]
}
},
"expect": "[false,[BOUNDARY:B_small: CONDITION uses / on x_max with no guard x_max != 0 (T6)]]"
},
{
"id": "t6/guarded-divide",
"fn": "t6_totality",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "x_max != 0 and x / x_max < 1"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "t6/comparison-dimensions",
"fn": "t6_totality",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"v"
],
"CONDITION": "x < v"
}
]
}
},
"expect": "[false,[BOUNDARY:B_small: CONDITION < compares L1 and L1 T-1 (T6)]]"
},
{
"id": "t6/tan-refused",
"fn": "t6_totality",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max and tan(x / x_max) < 1"
}
]
}
},
"expect": "[false,[BOUNDARY:B_small: CONDITION uses / on x_max with no guard x_max != 0 (T6),BOUNDARY:B_small: CONDITION uses tan on x/x_max, which is not total (T6)]]"
},
{
"id": "t6/parse-left-to-T1",
"fn": "t6_totality",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) <"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "t6/boundary-without-form-not-checked",
"fn": "t6_totality",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
]
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "t3laws/spring-nothing-claimed",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"note": "N2 and KIN name unbound identifiers; FREE_Z evaluates 0 = 0 through the FIXed z",
"expect": "[true,[]]"
},
{
"id": "t3laws/bound-true",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "a",
"DIMENSION": "L1",
"VALUE": "1",
"UNIT": "m"
},
{
"NAME": "b",
"DIMENSION": "L1",
"VALUE": "2",
"UNIT": "m"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "a + a = b",
"REFS": [
"a",
"b"
],
"ROLE": "DEFINITION",
"EQUATION": "a + a = b"
}
],
"CONSTRAINT": []
}
},
"expect": "[true,[]]"
},
{
"id": "t3laws/bound-false",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "a",
"DIMENSION": "L1",
"VALUE": "1",
"UNIT": "m"
},
{
"NAME": "b",
"DIMENSION": "L1",
"VALUE": "2",
"UNIT": "m"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "a = b",
"REFS": [
"a",
"b"
],
"ROLE": "DEFINITION",
"EQUATION": "a = b"
}
],
"CONSTRAINT": []
}
},
"expect": "[false,[LAW:L: L evaluates 1 = 2 under the declared values (T3)]]"
},
{
"id": "t3laws/bound-true-other-unit",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "a",
"DIMENSION": "L1",
"VALUE": "1",
"UNIT": "m"
},
{
"NAME": "b",
"DIMENSION": "L1",
"VALUE": "100",
"UNIT": "cm"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "a = b",
"REFS": [
"a",
"b"
],
"ROLE": "DEFINITION",
"EQUATION": "a = b"
}
],
"CONSTRAINT": []
}
},
"expect": "[true,[]]"
},
{
"id": "t3laws/fixed-dof",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "a",
"DIMENSION": "L1",
"VALUE": "1",
"UNIT": "m"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "z = a",
"REFS": [
"z",
"a"
],
"ROLE": "CONSTRAINT",
"EQUATION": "z = a"
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "z = 0"
}
]
}
},
"expect": "[false,[LAW:L and CONSTRAINT:C_NOZ: L evaluates 0 = 1 under the fixed values (T3)]]"
},
{
"id": "t3laws/derivative-of-fixed-dof",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "a",
"DIMENSION": "L1 T-1",
"VALUE": "1",
"UNIT": "m s-1"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "D(z, t) = a",
"REFS": [
"z",
"t",
"a"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t) = a"
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "z = 0"
}
]
}
},
"expect": "[false,[LAW:L and CONSTRAINT:C_NOZ: L evaluates 0 = 1 under the fixed values (T3)]]"
},
{
"id": "t3laws/free-identifier-not-evaluated",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "a",
"DIMENSION": "L1",
"VALUE": "1",
"UNIT": "m"
},
{
"NAME": "b",
"DIMENSION": "L1"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "a = b",
"REFS": [
"a",
"b"
],
"ROLE": "DEFINITION",
"EQUATION": "a = b"
}
],
"CONSTRAINT": []
}
},
"expect": "[true,[]]"
},
{
"id": "t3laws/kind-difference",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "f",
"DIMENSION": "T-1",
"VALUE": "1",
"UNIT": "Hz"
},
{
"NAME": "w",
"DIMENSION": "T-1",
"VALUE": "6.283185307179586",
"UNIT": "rad s-1"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "f = w",
"REFS": [
"f",
"w"
],
"ROLE": "DEFINITION",
"EQUATION": "f = w"
}
],
"CONSTRAINT": []
}
},
"expect": "[false,[LAW:L: the two sides of EQUATION cannot be compared: units of different kind: Hz1 and rad1 (T3)]]"
},
{
"id": "t3laws/overflow",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "big",
"DIMENSION": "L1",
"VALUE": "1e200",
"UNIT": "m"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "big * big = big",
"REFS": [
"big"
],
"ROLE": "DEFINITION",
"EQUATION": "big * big = big"
}
],
"CONSTRAINT": []
}
},
"expect": "[false,[LAW:L: EQUATION cannot be evaluated under the declared values: not a finite double (T3)]]"
},
{
"id": "t3laws/binding-not-normalizable",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "a",
"DIMENSION": "L1",
"VALUE": "1e9999",
"UNIT": "m"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "a = a",
"REFS": [
"a"
],
"ROLE": "DEFINITION",
"EQUATION": "a = a"
}
],
"CONSTRAINT": []
}
},
"expect": "[false,[LAW:L: EQUATION cannot be evaluated: VALUE 1e9999 in UNIT m is not a finite double (T3)]]"
},
{
"id": "t3laws/division-by-zero",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "a",
"DIMENSION": "L1",
"VALUE": "0",
"UNIT": "m"
},
{
"NAME": "b",
"DIMENSION": "L1",
"VALUE": "1",
"UNIT": "m"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "b / a = b",
"REFS": [
"a",
"b"
],
"ROLE": "DEFINITION",
"EQUATION": "b / a = b"
}
],
"CONSTRAINT": []
}
},
"expect": "[false,[LAW:L: EQUATION cannot be evaluated under the declared values: division by zero (T3)]]"
},
{
"id": "t3laws/two-laws-one-left-side",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
}
],
"LAW": [
{
"NAME": "KIN",
"STATEMENT": "D(x, t) = v",
"REFS": [
"x",
"t",
"v"
],
"ROLE": "DEFINITION",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "KIN2",
"STATEMENT": "D(x,t) = 2 * v",
"REFS": [
"x",
"t",
"v"
],
"ROLE": "DEFINITION",
"EQUATION": "D(x,t) = 2 * v"
}
],
"CONSTRAINT": []
}
},
"expect": "[false,[LAW:KIN and LAW:KIN2: the left side D(x,t) is equated to v and to 2*v (T3)]]"
},
{
"id": "t3laws/two-laws-same-right-side",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
}
],
"LAW": [
{
"NAME": "KIN",
"STATEMENT": "D(x, t) = v",
"REFS": [
"x",
"t",
"v"
],
"ROLE": "DEFINITION",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "KIN2",
"STATEMENT": "D(x,t) = (v)",
"REFS": [
"x",
"t",
"v"
],
"ROLE": "DEFINITION",
"EQUATION": "D(x,t) = (v)"
}
],
"CONSTRAINT": []
}
},
"note": "redundant, not contradictory: one canonical right side",
"expect": "[true,[]]"
},
{
"id": "t3laws/three-laws-one-left-side",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1"
}
],
"LAW": [
{
"NAME": "A",
"STATEMENT": "x = v",
"REFS": [
"x",
"v"
],
"ROLE": "DEFINITION",
"EQUATION": "x = v"
},
{
"NAME": "B",
"STATEMENT": "x = 2*v",
"REFS": [
"x",
"v"
],
"ROLE": "DEFINITION",
"EQUATION": "x = 2*v"
},
{
"NAME": "C",
"STATEMENT": "x = v",
"REFS": [
"x",
"v"
],
"ROLE": "DEFINITION",
"EQUATION": "x = v"
}
],
"CONSTRAINT": []
}
},
"expect": "[false,[LAW:A and LAW:B: the left side x is equated to v and to 2*v (T3),LAW:B and LAW:C: the left side x is equated to 2*v and to v (T3)]]"
},
{
"id": "t3laws/parse-left-to-T1",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) ="
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "t3laws/not-an-object",
"fn": "t3_laws",
"input": {
"tpk": "x"
},
"expect": "[true,[]]"
},
{
"id": "ic4a/spring",
"fn": "ic4a_signature",
"input": {
"trm": {
"HEADER": {
"ENVIRONMENT_INVENTORY": [
{
"ENVIRONMENT_QUANTITY": "position",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "velocity",
"DIMENSION": "L1 T-1"
},
{
"ENVIRONMENT_QUANTITY": "height",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "time",
"DIMENSION": "T1"
}
],
"SIGNATURE": [
{
"NAME": "time_derivative",
"OVER": [
"x",
"v",
"t"
],
"IMAGE": "d/dt maps position to velocity",
"FORM": "D(x, t) = v",
"IMAGE_FORM": "D(position, time) = velocity"
}
],
"TRANSFORMATIONS": [
{
"NAME": "time_translation",
"STATEMENT": "t -> t + t0"
}
]
},
"ENTRIES": [
{
"NAME": "E_x",
"DOF": "x",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "position",
"IDENTIFICATION": "x is the displacement from equilibrium along the spring axis",
"FALSIFIER": "a measured restoring force not proportional to x inside the domain",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"N2",
"KIN"
],
"DIMENSION": "L1"
},
{
"NAME": "E_v",
"DOF": "v",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "velocity",
"IDENTIFICATION": "v is the time derivative of x",
"FALSIFIER": "a measured velocity differing from dx/dt beyond uncertainty",
"FALSIFIER_CLASS": "F2",
"BEARS": [
"KIN"
],
"DIMENSION": "L1 T-1"
},
{
"NAME": "E_z",
"DOF": "z",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "height",
"IDENTIFICATION": "z is the height above the track",
"FALSIFIER": "any measured z different from 0",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"FREE_Z",
"C_NOZ"
],
"DIMENSION": "L1"
},
{
"NAME": "E_t",
"DOF": "t",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "time",
"IDENTIFICATION": "t is the laboratory clock reading",
"FALSIFIER": "two laboratory clocks that disagree beyond their stated uncertainty",
"FALSIFIER_CLASS": "F3",
"BEARS": [],
"DIMENSION": "T1"
}
]
},
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[],[]]"
},
{
"id": "ic4a/image-differs",
"fn": "ic4a_signature",
"input": {
"trm": {
"HEADER": {
"ENVIRONMENT_INVENTORY": [
{
"ENVIRONMENT_QUANTITY": "position",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "velocity",
"DIMENSION": "L1 T-1"
},
{
"ENVIRONMENT_QUANTITY": "height",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "time",
"DIMENSION": "T1"
}
],
"SIGNATURE": [
{
"NAME": "time_derivative",
"OVER": [
"x",
"v",
"t"
],
"IMAGE": "d/dt maps position to velocity",
"FORM": "D(x, t) = v",
"IMAGE_FORM": "D(position, time) = speed"
}
],
"TRANSFORMATIONS": [
{
"NAME": "time_translation",
"STATEMENT": "t -> t + t0"
}
]
},
"ENTRIES": [
{
"NAME": "E_x",
"DOF": "x",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "position",
"IDENTIFICATION": "x is the displacement from equilibrium along the spring axis",
"FALSIFIER": "a measured restoring force not proportional to x inside the domain",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"N2",
"KIN"
],
"DIMENSION": "L1"
},
{
"NAME": "E_v",
"DOF": "v",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "velocity",
"IDENTIFICATION": "v is the time derivative of x",
"FALSIFIER": "a measured velocity differing from dx/dt beyond uncertainty",
"FALSIFIER_CLASS": "F2",
"BEARS": [
"KIN"
],
"DIMENSION": "L1 T-1"
},
{
"NAME": "E_z",
"DOF": "z",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "height",
"IDENTIFICATION": "z is the height above the track",
"FALSIFIER": "any measured z different from 0",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"FREE_Z",
"C_NOZ"
],
"DIMENSION": "L1"
},
{
"NAME": "E_t",
"DOF": "t",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "time",
"IDENTIFICATION": "t is the laboratory clock reading",
"FALSIFIER": "two laboratory clocks that disagree beyond their stated uncertainty",
"FALSIFIER_CLASS": "F3",
"BEARS": [],
"DIMENSION": "T1"
}
]
},
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[IC4(a): SIGNATURE:time_derivative: FORM under the entries reads D(position,time)=velocity, not IMAGE_FORM D(position,time)=speed],[]]"
},
{
"id": "ic4a/image-respelled",
"fn": "ic4a_signature",
"input": {
"trm": {
"HEADER": {
"ENVIRONMENT_INVENTORY": [
{
"ENVIRONMENT_QUANTITY": "position",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "velocity",
"DIMENSION": "L1 T-1"
},
{
"ENVIRONMENT_QUANTITY": "height",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "time",
"DIMENSION": "T1"
}
],
"SIGNATURE": [
{
"NAME": "time_derivative",
"OVER": [
"x",
"v",
"t"
],
"IMAGE": "d/dt maps position to velocity",
"FORM": "D(x, t) = v",
"IMAGE_FORM": "D( position , time ) = velocity"
}
],
"TRANSFORMATIONS": [
{
"NAME": "time_translation",
"STATEMENT": "t -> t + t0"
}
]
},
"ENTRIES": [
{
"NAME": "E_x",
"DOF": "x",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "position",
"IDENTIFICATION": "x is the displacement from equilibrium along the spring axis",
"FALSIFIER": "a measured restoring force not proportional to x inside the domain",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"N2",
"KIN"
],
"DIMENSION": "L1"
},
{
"NAME": "E_v",
"DOF": "v",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "velocity",
"IDENTIFICATION": "v is the time derivative of x",
"FALSIFIER": "a measured velocity differing from dx/dt beyond uncertainty",
"FALSIFIER_CLASS": "F2",
"BEARS": [
"KIN"
],
"DIMENSION": "L1 T-1"
},
{
"NAME": "E_z",
"DOF": "z",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "height",
"IDENTIFICATION": "z is the height above the track",
"FALSIFIER": "any measured z different from 0",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"FREE_Z",
"C_NOZ"
],
"DIMENSION": "L1"
},
{
"NAME": "E_t",
"DOF": "t",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "time",
"IDENTIFICATION": "t is the laboratory clock reading",
"FALSIFIER": "two laboratory clocks that disagree beyond their stated uncertainty",
"FALSIFIER_CLASS": "F3",
"BEARS": [],
"DIMENSION": "T1"
}
]
},
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[],[]]"
},
{
"id": "ic4a/untied-dof-undecided",
"fn": "ic4a_signature",
"input": {
"trm": {
"HEADER": {
"ENVIRONMENT_INVENTORY": [
{
"ENVIRONMENT_QUANTITY": "position",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "velocity",
"DIMENSION": "L1 T-1"
},
{
"ENVIRONMENT_QUANTITY": "height",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "time",
"DIMENSION": "T1"
}
],
"SIGNATURE": [
{
"NAME": "time_derivative",
"OVER": [
"x",
"v",
"t"
],
"IMAGE": "d/dt maps position to velocity",
"FORM": "D(x, t) = v",
"IMAGE_FORM": "D(position, time) = velocity"
}
],
"TRANSFORMATIONS": [
{
"NAME": "time_translation",
"STATEMENT": "t -> t + t0"
}
]
},
"ENTRIES": [
{
"NAME": "E_x",
"DOF": "x",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "position",
"IDENTIFICATION": "x is the displacement from equilibrium along the spring axis",
"FALSIFIER": "a measured restoring force not proportional to x inside the domain",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"N2",
"KIN"
],
"DIMENSION": "L1"
},
{
"NAME": "E_v",
"DOF": "v",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "velocity",
"IDENTIFICATION": "v is the time derivative of x",
"FALSIFIER": "a measured velocity differing from dx/dt beyond uncertainty",
"FALSIFIER_CLASS": "F2",
"BEARS": [
"KIN"
],
"DIMENSION": "L1 T-1"
},
{
"NAME": "E_z",
"DOF": "z",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "height",
"IDENTIFICATION": "z is the height above the track",
"FALSIFIER": "any measured z different from 0",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"FREE_Z",
"C_NOZ"
],
"DIMENSION": "L1"
}
]
},
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[],[IC4(a): SIGNATURE:time_derivative: DOF t untied, not decided]]"
},
{
"id": "ic4a/no-form",
"fn": "ic4a_signature",
"input": {
"trm": {
"HEADER": {
"ENVIRONMENT_INVENTORY": [
{
"ENVIRONMENT_QUANTITY": "position",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "velocity",
"DIMENSION": "L1 T-1"
},
{
"ENVIRONMENT_QUANTITY": "height",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "time",
"DIMENSION": "T1"
}
],
"SIGNATURE": [
{
"NAME": "time_derivative",
"OVER": [
"x",
"v",
"t"
],
"IMAGE": "d/dt maps position to velocity"
}
],
"TRANSFORMATIONS": [
{
"NAME": "time_translation",
"STATEMENT": "t -> t + t0"
}
]
},
"ENTRIES": [
{
"NAME": "E_x",
"DOF": "x",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "position",
"IDENTIFICATION": "x is the displacement from equilibrium along the spring axis",
"FALSIFIER": "a measured restoring force not proportional to x inside the domain",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"N2",
"KIN"
],
"DIMENSION": "L1"
},
{
"NAME": "E_v",
"DOF": "v",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "velocity",
"IDENTIFICATION": "v is the time derivative of x",
"FALSIFIER": "a measured velocity differing from dx/dt beyond uncertainty",
"FALSIFIER_CLASS": "F2",
"BEARS": [
"KIN"
],
"DIMENSION": "L1 T-1"
},
{
"NAME": "E_z",
"DOF": "z",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "height",
"IDENTIFICATION": "z is the height above the track",
"FALSIFIER": "any measured z different from 0",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"FREE_Z",
"C_NOZ"
],
"DIMENSION": "L1"
},
{
"NAME": "E_t",
"DOF": "t",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "time",
"IDENTIFICATION": "t is the laboratory clock reading",
"FALSIFIER": "two laboratory clocks that disagree beyond their stated uncertainty",
"FALSIFIER_CLASS": "F3",
"BEARS": [],
"DIMENSION": "T1"
}
]
},
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
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},
{
"id": "parse/depth-chain-D-2000",
"fn": "parse_form",
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"mode": "equation"
},
"note": "D186.1; 14,001 code points; tpc_form 0.1.1 answered the text unchanged",
"expect": "[REFUSED,the form is longer than 4096 code points]"
},
{
"id": "parse/depth-chain-and-2000",
"fn": "parse_form",
"input": {
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x<1",
"mode": "predicate"
},
"note": "D186.1; 15,995 code points; tpc_form 0.1.1 answered the text unchanged",
"expect": "[REFUSED,the form is longer than 4096 code points]"
},
{
"id": "parse/depth-not-1000",
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"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "every divisor needs its own guard; the fifty problems in code point order",
"expect": "[OK,[uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(a)))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(a)))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(a))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(a))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(a)))))) with no guard 1/(1/(1/(1/(1/(1/(a)))))) != 0,uses / on 1/(1/(1/(1/(1/(a))))) with no guard 1/(1/(1/(1/(1/(a))))) != 0,uses / on 1/(1/(1/(1/(a)))) with no guard 1/(1/(1/(1/(a)))) != 0,uses / on 1/(1/(1/(a))) with no guard 1/(1/(1/(a))) != 0,uses / on 1/(1/(a)) with no guard 1/(1/(a)) != 0,uses / on 1/(a) with no guard 1/(a) != 0,uses / on a with no guard a != 0]]"
},
{
"id": "eval/depth-paren-1000",
"fn": "eval_form",
"input": {
"text": "((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))*2=1",
"mode": "equation",
"bindings": {
"x": {
"VALUE": "0.5",
"UNIT": "m"
}
}
},
"note": "D186.1; tpc_form 0.1.1 answered [OK,1,1,none]",
"expect": "[REFUSED,more than 64 nested parentheses at 65]"
},
{
"id": "eval/depth-chain-2000",
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}
},
"note": "D186.1: the form does not parse, so T3 skips it and T1 reports it; tpc_form 0.1.1 answered [false,[LAW:L: L evaluates 1 = 2 under the declared values (T3)]]",
"expect": "[true,[]]"
},
{
"id": "ic4a/depth-1000",
"fn": "ic4a_signature",
"input": {
"trm": {
"HEADER": {
"ENVIRONMENT_INVENTORY": [
{
"ENVIRONMENT_QUANTITY": "position",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "velocity",
"DIMENSION": "L1 T-1"
},
{
"ENVIRONMENT_QUANTITY": "height",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "time",
"DIMENSION": "T1"
}
],
"SIGNATURE": [
{
"NAME": "time_derivative",
"OVER": [
"x",
"v",
"t"
],
"IMAGE": "d/dt maps position to velocity",
"FORM": "D(x, t) = 2*((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((v))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"IMAGE_FORM": "D(position, time) = 2*((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((velocity))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))"
}
],
"TRANSFORMATIONS": [
{
"NAME": "time_translation",
"STATEMENT": "t -> t + t0"
}
]
},
"ENTRIES": [
{
"NAME": "E_x",
"DOF": "x",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "position",
"IDENTIFICATION": "x is the displacement from equilibrium along the spring axis",
"FALSIFIER": "a measured restoring force not proportional to x inside the domain",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"N2",
"KIN"
],
"DIMENSION": "L1"
},
{
"NAME": "E_v",
"DOF": "v",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "velocity",
"IDENTIFICATION": "v is the time derivative of x",
"FALSIFIER": "a measured velocity differing from dx/dt beyond uncertainty",
"FALSIFIER_CLASS": "F2",
"BEARS": [
"KIN"
],
"DIMENSION": "L1 T-1"
},
{
"NAME": "E_z",
"DOF": "z",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "height",
"IDENTIFICATION": "z is the height above the track",
"FALSIFIER": "any measured z different from 0",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"FREE_Z",
"C_NOZ"
],
"DIMENSION": "L1"
},
{
"NAME": "E_t",
"DOF": "t",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "time",
"IDENTIFICATION": "t is the laboratory clock reading",
"FALSIFIER": "two laboratory clocks that disagree beyond their stated uncertainty",
"FALSIFIER_CLASS": "F3",
"BEARS": [],
"DIMENSION": "T1"
}
]
},
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"note": "D186.1: the forms do not parse, so IC4 (a) skips them and the structural check reports them",
"expect": "[true,[],[]]"
},
{
"id": "parse/bounds-exp-9999",
"fn": "parse_form",
"input": {
"text": "x^9999",
"mode": "expression"
},
"expect": "[OK,x^9999]"
},
{
"id": "parse/bounds-exp-10000",
"fn": "parse_form",
"input": {
"text": "x^10000",
"mode": "expression"
},
"expect": "[REFUSED,an integer of more than 4 digits at 3]"
},
{
"id": "parse/bounds-exp-neg-9999",
"fn": "parse_form",
"input": {
"text": "x^(-9999)",
"mode": "expression"
},
"expect": "[OK,x^(-9999)]"
},
{
"id": "parse/bounds-exp-neg-10000",
"fn": "parse_form",
"input": {
"text": "x^(-10000)",
"mode": "expression"
},
"expect": "[REFUSED,an integer of more than 4 digits at 5]"
},
{
"id": "parse/bounds-rational-p-4",
"fn": "parse_form",
"input": {
"text": "x^(9999/2)",
"mode": "expression"
},
"expect": "[OK,x^(9999/2)]"
},
{
"id": "parse/bounds-rational-p-5",
"fn": "parse_form",
"input": {
"text": "x^(10000/2)",
"mode": "expression"
},
"expect": "[REFUSED,an integer of more than 4 digits at 4]"
},
{
"id": "parse/bounds-rational-q-4",
"fn": "parse_form",
"input": {
"text": "x^(1/9999)",
"mode": "expression"
},
"expect": "[OK,x^(1/9999)]"
},
{
"id": "parse/bounds-rational-q-5",
"fn": "parse_form",
"input": {
"text": "x^(1/10000)",
"mode": "expression"
},
"expect": "[REFUSED,an integer of more than 4 digits at 6]"
},
{
"id": "parse/bounds-rational-both-4",
"fn": "parse_form",
"input": {
"text": "x^(-9999/9999)",
"mode": "expression"
},
"expect": "[OK,x^(-9999/9999)]"
},
{
"id": "parse/bounds-D-order-9999",
"fn": "parse_form",
"input": {
"text": "D(x, t, 9999)",
"mode": "expression"
},
"expect": "[OK,D(x,t,9999)]"
},
{
"id": "parse/bounds-D-order-10000",
"fn": "parse_form",
"input": {
"text": "D(x, t, 10000)",
"mode": "expression"
},
"expect": "[REFUSED,an integer of more than 4 digits at 9]"
},
{
"id": "parse/bounds-leading-zero-4",
"fn": "parse_form",
"input": {
"text": "x^0009",
"mode": "expression"
},
"expect": "[OK,x^9]"
},
{
"id": "parse/bounds-leading-zero-5",
"fn": "parse_form",
"input": {
"text": "x^00009",
"mode": "expression"
},
"expect": "[REFUSED,an integer of more than 4 digits at 3]"
},
{
"id": "parse/bounds-leading-zero-rational-4",
"fn": "parse_form",
"input": {
"text": "x^(0009/0002)",
"mode": "expression"
},
"expect": "[OK,x^(9/2)]"
},
{
"id": "parse/bounds-leading-zero-rational-5",
"fn": "parse_form",
"input": {
"text": "x^(9/00002)",
"mode": "expression"
},
"expect": "[REFUSED,an integer of more than 4 digits at 6]"
},
{
"id": "parse/bounds-leading-zero-D-4",
"fn": "parse_form",
"input": {
"text": "D(x,t,0002)",
"mode": "expression"
},
"expect": "[OK,D(x,t,2)]"
},
{
"id": "parse/bounds-leading-zero-D-5",
"fn": "parse_form",
"input": {
"text": "D(x,t,00002)",
"mode": "expression"
},
"expect": "[REFUSED,an integer of more than 4 digits at 7]"
},
{
"id": "parse/bounds-D-order-zero-4",
"fn": "parse_form",
"input": {
"text": "D(x,t,0000)",
"mode": "expression"
},
"expect": "[REFUSED,D is written D(x,t) or D(x,t,n) at 1]"
},
{
"id": "parse/bounds-D-order-zero-5",
"fn": "parse_form",
"input": {
"text": "D(x,t,00000)",
"mode": "expression"
},
"note": "the digits are checked before the order's value",
"expect": "[REFUSED,an integer of more than 4 digits at 7]"
},
{
"id": "parse/bounds-rational-zero-q-4",
"fn": "parse_form",
"input": {
"text": "x^(1/0000)",
"mode": "expression"
},
"expect": "[REFUSED,a rational exponent needs a positive denominator at 2]"
},
{
"id": "parse/bounds-exp-20-digits",
"fn": "parse_form",
"input": {
"text": "x^99999999999999999999",
"mode": "expression"
},
"note": "tpc_form 0.1.1: TPC-PY x^99999999999999999999, TPC-PHP x^9223372036854775807",
"expect": "[REFUSED,an integer of more than 4 digits at 3]"
},
{
"id": "parse/bounds-D-20-digits",
"fn": "parse_form",
"input": {
"text": "D(x,t,99999999999999999999)",
"mode": "expression"
},
"note": "tpc_form 0.1.1: TPC-PHP spelled the order 9223372036854775807",
"expect": "[REFUSED,an integer of more than 4 digits at 7]"
},
{
"id": "parse/bounds-rational-20-digits",
"fn": "parse_form",
"input": {
"text": "x^(1/99999999999999999999)",
"mode": "expression"
},
"expect": "[REFUSED,an integer of more than 4 digits at 6]"
},
{
"id": "parse/bounds-exp-4094-digits",
"fn": "parse_form",
"input": {
"text": "x^99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
"mode": "expression"
},
"note": "4,096 code points; tpc_form 0.1.1: TPC-PHP x^9223372036854775807",
"expect": "[REFUSED,an integer of more than 4 digits at 3]"
},
{
"id": "parse/bounds-exp-5000-digits",
"fn": "parse_form",
"input": {
"text": "x^99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
"mode": "expression"
},
"note": "tpc_form 0.1.1: TPC-PY raised ValueError (int of more than 4300 digits), TPC-PHP answered x^0",
"expect": "[REFUSED,the form is longer than 4096 code points]"
},
{
"id": "parse/bounds-literal-mantissa-30",
"fn": "parse_form",
"input": {
"text": "123456789012345678901234567890*x",
"mode": "expression"
},
"expect": "[OK,12345678901234567890123456789e1*x]"
},
{
"id": "dim/bounds-exp-9999",
"fn": "form_dimension",
"input": {
"text": "x^9999",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L9999]"
},
{
"id": "dim/bounds-rational-9999",
"fn": "form_dimension",
"input": {
"text": "(x^9999)^(1/9999)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1]"
},
{
"id": "dim/bounds-D-order-9999",
"fn": "form_dimension",
"input": {
"text": "D(x,t,9999)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1 T-9999]"
},
{
"id": "dim/bounds-exp-10000",
"fn": "form_dimension",
"input": {
"text": "x^10000",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,an integer of more than 4 digits at 3]"
},
{
"id": "eval/bounds-exp-9999-one",
"fn": "eval_form",
"input": {
"text": "x^9999",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "m"
}
}
},
"expect": "[OK,1,none]"
},
{
"id": "eval/bounds-exp-neg-9999-one",
"fn": "eval_form",
"input": {
"text": "x^(-9999)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "m"
}
}
},
"expect": "[OK,1,none]"
},
{
"id": "eval/bounds-exp-9999-overflow",
"fn": "eval_form",
"input": {
"text": "x^9999",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "2",
"UNIT": "m"
}
}
},
"note": "2^9999 by repeated multiplication overflows to +inf",
"expect": "[REFUSED,not a finite double]"
},
{
"id": "eval/bounds-exp-10000",
"fn": "eval_form",
"input": {
"text": "x^10000",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "m"
}
}
},
"expect": "[REFUSED,an integer of more than 4 digits at 3]"
},
{
"id": "parse/bounds-size-4096",
"fn": "parse_form",
"input": {
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{
"id": "parse/bounds-size-4097-whitespace",
"fn": "parse_form",
"input": {
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"mode": "expression"
},
"note": "whitespace counts toward the length; the spelling would be 4,095 code points",
"expect": "[REFUSED,the form is longer than 4096 code points]"
},
{
"id": "parse/bounds-size-4097",
"fn": "parse_form",
"input": {
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"mode": "expression"
},
"expect": "[REFUSED,the form is longer than 4096 code points]"
},
{
"id": "parse/bounds-size-4096-cp-4097-bytes",
"fn": "parse_form",
"input": {
"text": " \u00e9",
"mode": "expression"
},
"note": "4,096 code points, 4,097 UTF-8 bytes: within the length bound, refused by the tokens",
"expect": "[REFUSED,unexpected character \u00e9 at 4096]"
},
{
"id": "parse/bounds-size-4096-cp-16384-bytes",
"fn": "parse_form",
"input": {
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"mode": "expression"
},
"note": "U+1D465 (NFC-stable), 4 UTF-8 bytes each: 4,096 code points pass the length bound",
"expect": "[REFUSED,unexpected character \ud835\udc65 at 1]"
},
{
"id": "parse/bounds-size-4097-cp-16388-bytes",
"fn": "parse_form",
"input": {
"text": 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"mode": "expression"
},
"expect": "[REFUSED,the form is longer than 4096 code points]"
},
{
"id": "parse/bounds-size-nfc-4098-raw",
"fn": "parse_form",
"input": {
"text": 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"mode": "expression"
},
"note": "4,098 code points as given, 2,049 after NFC: the canonical text is measured",
"expect": "[REFUSED,unexpected character \u00e9 at 1]"
},
{
"id": "parse/bounds-size-crlf-4096",
"fn": "parse_form",
"input": {
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"mode": "expression"
},
"note": "5,461 code points as given, 4,096 after CRLF becomes LF: accepted",
"expect": "[OK,x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x+x]"
},
{
"id": "parse/bounds-size-crlf-4097",
"fn": "parse_form",
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",
"mode": "expression"
},
"expect": "[REFUSED,the form is longer than 4096 code points]"
},
{
"id": "parse/bounds-nest-paren-64",
"fn": "parse_form",
"input": {
"text": "((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"expect": "[OK,x]"
},
{
"id": "parse/bounds-nest-paren-65",
"fn": "parse_form",
"input": {
"text": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"expect": "[REFUSED,more than 64 nested parentheses at 65]"
},
{
"id": "parse/bounds-nest-function-64",
"fn": "parse_form",
"input": {
"text": "abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"expect": "[OK,abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]"
},
{
"id": "parse/bounds-nest-function-65",
"fn": "parse_form",
"input": {
"text": "abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(abs(x)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"note": "the k-th ( at 4k",
"expect": "[REFUSED,more than 64 nested parentheses at 260]"
},
{
"id": "parse/bounds-nest-D-64",
"fn": "parse_form",
"input": {
"text": "sqrt(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((D(x, t))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"note": "sqrt's ( is level 1, D's level 64; the spelling drops the argument's parentheses",
"expect": "[OK,sqrt(D(x,t))]"
},
{
"id": "parse/bounds-nest-D-65",
"fn": "parse_form",
"input": {
"text": "sqrt((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((D(x, t)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"note": "sqrt( at 1-5, 63 ( at 6-68, D at 69, its ( level 65 at 70",
"expect": "[REFUSED,more than 64 nested parentheses at 70]"
},
{
"id": "parse/bounds-nest-exponent-64",
"fn": "parse_form",
"input": {
"text": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x^(1/2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"expect": "[OK,x^(1/2)]"
},
{
"id": "parse/bounds-nest-exponent-65",
"fn": "parse_form",
"input": {
"text": "((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x^(1/2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"expect": "[REFUSED,more than 64 nested parentheses at 67]"
},
{
"id": "parse/bounds-nest-predicate-64",
"fn": "parse_form",
"input": {
"text": "((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x < 1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "predicate"
},
"expect": "[OK,x<1]"
},
{
"id": "parse/bounds-nest-predicate-65",
"fn": "parse_form",
"input": {
"text": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x < 1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "predicate"
},
"expect": "[REFUSED,more than 64 nested parentheses at 65]"
},
{
"id": "parse/bounds-nest-reopen-64",
"fn": "parse_form",
"input": {
"text": "((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x)+(y))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"note": "a closed level is reopened, never added to: the depth stays 64",
"expect": "[OK,(x)+(y)]"
},
{
"id": "parse/bounds-nest-sequential",
"fn": "parse_form",
"input": {
"text": "(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)",
"mode": "expression"
},
"expect": "[OK,(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)+(x)]"
},
{
"id": "parse/bounds-nest-stray-close-65",
"fn": "parse_form",
"input": {
"text": ")(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"note": "a ) with none open closes none",
"expect": "[REFUSED,more than 64 nested parentheses at 66]"
},
{
"id": "parse/bounds-nest-stray-close-64",
"fn": "parse_form",
"input": {
"text": ")((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token ) at 1]"
},
{
"id": "names/bounds-nest-65",
"fn": "form_names",
"input": {
"text": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = v",
"mode": "equation"
},
"expect": "[REFUSED,more than 64 nested parentheses at 65]"
},
{
"id": "total/bounds-divisors-64",
"fn": "form_totality",
"input": {
"text": "1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))<2",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "64 nested divisors, the most the depth bound admits: 64 problems in code point order",
"expect": "[OK,[uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))))))))))))))))))))))))))))))) with no guard 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guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))))))))))))))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))))))))))))))))))))) != 0,uses / on 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!= 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(1/(a)))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(1/(a))))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(1/(a)))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(1/(a)))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(1/(a))))))) with no guard 1/(1/(1/(1/(1/(1/(1/(a))))))) != 0,uses / on 1/(1/(1/(1/(1/(1/(a)))))) with no guard 1/(1/(1/(1/(1/(1/(a)))))) != 0,uses / on 1/(1/(1/(1/(1/(a))))) with no guard 1/(1/(1/(1/(1/(a))))) != 0,uses / on 1/(1/(1/(1/(a)))) with no guard 1/(1/(1/(1/(a)))) != 0,uses / on 1/(1/(1/(a))) with no guard 1/(1/(1/(a))) != 0,uses / on 1/(1/(a)) with no guard 1/(1/(a)) != 0,uses / on 1/(a) with no guard 1/(a) != 0,uses / on a with no guard a != 0]]"
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{
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"x": "L1",
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"x_max": "L1",
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"note": "the k-th ( at 3k",
"expect": "[REFUSED,more than 64 nested parentheses at 195]"
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"x": "L1",
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"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
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"note": "4,003 code points; refused before the guard walk",
"expect": "[REFUSED,more than 64 nested parentheses at 195]"
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"text": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((",
"mode": "expression"
},
"expect": "[REFUSED,the form is longer than 4096 code points]"
},
{
"id": "parse/bounds-order-depth-before-integer",
"fn": "parse_form",
"input": {
"text": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x^10000)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"expect": "[REFUSED,more than 64 nested parentheses at 65]"
},
{
"id": "parse/bounds-order-tokens-before-integer",
"fn": "parse_form",
"input": {
"text": "x^10000+@",
"mode": "expression"
},
"expect": "[REFUSED,unexpected character @ at 9]"
},
{
"id": "parse/bounds-order-integers-as-read",
"fn": "parse_form",
"input": {
"text": "x^10000 + D(x,t,00000)",
"mode": "expression"
},
"expect": "[REFUSED,an integer of more than 4 digits at 3]"
},
{
"id": "parse/bounds-order-grammar-before-integer",
"fn": "parse_form",
"input": {
"text": "x^^10000",
"mode": "expression"
},
"expect": "[REFUSED,^ takes an integer or a parenthesized rational exponent at 2]"
},
{
"id": "names_check/bounds-integer",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t, 10000) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:KIN: EQUATION does not parse: an integer of more than 4 digits at 9]]"
},
{
"id": "names_check/bounds-nest-64",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((D(x, t)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "t4/bounds-nest-64",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((D(x, t)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "names_check/bounds-nest-65",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((D(x, t))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:KIN: EQUATION does not parse: more than 64 nested parentheses at 66]]"
},
{
"id": "t6/bounds-nest-64",
"fn": "t6_totality",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((abs(x) < x_max)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "names_check/bounds-size-4097",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max "
}
]
}
},
"expect": "[false,[BOUNDARY:B_small: CONDITION does not parse: the form is longer than 4096 code points]]"
},
{
"id": "t3laws/bounds-chain-true",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "a",
"DIMENSION": "L1",
"VALUE": "1",
"UNIT": "m"
},
{
"NAME": "b",
"DIMENSION": "L1",
"VALUE": "2000",
"UNIT": "m"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a = b",
"REFS": [
"a",
"b"
],
"ROLE": "DEFINITION",
"EQUATION": "a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a = b"
}
],
"CONSTRAINT": []
}
},
"note": "4,003 code points; a chain of 2,000 terms is exact in binary64",
"expect": "[true,[]]"
},
{
"id": "t3laws/bounds-chain-false",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "a",
"DIMENSION": "L1",
"VALUE": "1",
"UNIT": "m"
},
{
"NAME": "b",
"DIMENSION": "L1",
"VALUE": "1999",
"UNIT": "m"
}
],
"LAW": [
{
"NAME": "L",
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"REFS": [
"a",
"b"
],
"ROLE": "DEFINITION",
"EQUATION": "a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a+a = b"
}
],
"CONSTRAINT": []
}
},
"expect": "[false,[LAW:L: L evaluates 2000 = 1999 under the declared values (T3)]]"
},
{
"id": "ic4a/bounds-nest-64",
"fn": "ic4a_signature",
"input": {
"trm": {
"HEADER": {
"ENVIRONMENT_INVENTORY": [
{
"ENVIRONMENT_QUANTITY": "position",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "velocity",
"DIMENSION": "L1 T-1"
},
{
"ENVIRONMENT_QUANTITY": "height",
"DIMENSION": "L1"
},
{
"ENVIRONMENT_QUANTITY": "time",
"DIMENSION": "T1"
}
],
"SIGNATURE": [
{
"NAME": "time_derivative",
"OVER": [
"x",
"v",
"t"
],
"IMAGE": "d/dt maps position to velocity",
"FORM": "D(x, t) = 2*((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((v))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"IMAGE_FORM": "D(position, time) = 2*((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((velocity))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))"
}
],
"TRANSFORMATIONS": [
{
"NAME": "time_translation",
"STATEMENT": "t -> t + t0"
}
]
},
"ENTRIES": [
{
"NAME": "E_x",
"DOF": "x",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "position",
"IDENTIFICATION": "x is the displacement from equilibrium along the spring axis",
"FALSIFIER": "a measured restoring force not proportional to x inside the domain",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"N2",
"KIN"
],
"DIMENSION": "L1"
},
{
"NAME": "E_v",
"DOF": "v",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "velocity",
"IDENTIFICATION": "v is the time derivative of x",
"FALSIFIER": "a measured velocity differing from dx/dt beyond uncertainty",
"FALSIFIER_CLASS": "F2",
"BEARS": [
"KIN"
],
"DIMENSION": "L1 T-1"
},
{
"NAME": "E_z",
"DOF": "z",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "height",
"IDENTIFICATION": "z is the height above the track",
"FALSIFIER": "any measured z different from 0",
"FALSIFIER_CLASS": "F3",
"BEARS": [
"FREE_Z",
"C_NOZ"
],
"DIMENSION": "L1"
},
{
"NAME": "E_t",
"DOF": "t",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "time",
"IDENTIFICATION": "t is the laboratory clock reading",
"FALSIFIER": "two laboratory clocks that disagree beyond their stated uncertainty",
"FALSIFIER_CLASS": "F3",
"BEARS": [],
"DIMENSION": "T1"
}
]
},
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"note": "64 levels in FORM and IMAGE_FORM: the rename walks them",
"expect": "[true,[],[]]"
},
{
"id": "parse/s14-nested-power-5",
"fn": "parse_form",
"input": {
"text": "((((x^9999)^9999)^9999)^9999)^9999",
"mode": "expression"
},
"note": "the second ^ composes 99980001; before S14 TPC-PY spelled it and TPC-PHP raised in the dimension walk",
"expect": "[REFUSED,a computed exponent beyond 9999 at 12]"
},
{
"id": "parse/s14-composed-9999",
"fn": "parse_form",
"input": {
"text": "(x^99)^101",
"mode": "expression"
},
"expect": "[OK,(x^99)^101]"
},
{
"id": "parse/s14-composed-10000",
"fn": "parse_form",
"input": {
"text": "(x^100)^100",
"mode": "expression"
},
"expect": "[REFUSED,a computed exponent beyond 9999 at 8]"
},
{
"id": "parse/s14-composed-neg-9999",
"fn": "parse_form",
"input": {
"text": "(x^(-99))^101",
"mode": "expression"
},
"expect": "[OK,(x^(-99))^101]"
},
{
"id": "parse/s14-composed-neg-10000",
"fn": "parse_form",
"input": {
"text": "(x^(-100))^100",
"mode": "expression"
},
"expect": "[REFUSED,a computed exponent beyond 9999 at 11]"
},
{
"id": "parse/s14-rational-reduced-1",
"fn": "parse_form",
"input": {
"text": "(x^(9999/2))^(2/9999)",
"mode": "expression"
},
"note": "19998/19998 in lowest terms is 1",
"expect": "[OK,(x^(9999/2))^(2/9999)]"
},
{
"id": "parse/s14-rational-reduced-9999",
"fn": "parse_form",
"input": {
"text": "(x^(9999/3))^3",
"mode": "expression"
},
"note": "29997/3 is 9999",
"expect": "[OK,(x^(9999/3))^3]"
},
{
"id": "parse/s14-rational-num-after-mult",
"fn": "parse_form",
"input": {
"text": "(x^(5000/3))^2",
"mode": "expression"
},
"note": "every written part within 4 digits; 10000/3 past the bound only after the product",
"expect": "[REFUSED,a computed exponent beyond 9999 at 13]"
},
{
"id": "parse/s14-rational-den",
"fn": "parse_form",
"input": {
"text": "(x^(1/9999))^(1/2)",
"mode": "expression"
},
"note": "1/19998",
"expect": "[REFUSED,a computed exponent beyond 9999 at 13]"
},
{
"id": "parse/s14-rational-den-reduced",
"fn": "parse_form",
"input": {
"text": "(x^(2/9999))^(1/2)",
"mode": "expression"
},
"note": "2/19998 is 1/9999",
"expect": "[OK,(x^(2/9999))^(1/2)]"
},
{
"id": "parse/s14-sqrt-counts-half",
"fn": "parse_form",
"input": {
"text": "(sqrt(x^9998))^2",
"mode": "expression"
},
"note": "9998 x 1/2 x 2",
"expect": "[OK,(sqrt(x^9998))^2]"
},
{
"id": "parse/s14-sqrt-then-power",
"fn": "parse_form",
"input": {
"text": "(sqrt(x^9999))^3",
"mode": "expression"
},
"note": "29997/2",
"expect": "[REFUSED,a computed exponent beyond 9999 at 15]"
},
{
"id": "parse/s14-sqrt-nested-13",
"fn": "parse_form",
"input": {
"text": "sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(x)))))))))))))",
"mode": "expression"
},
"note": "1/8192",
"expect": "[OK,sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(x)))))))))))))]"
},
{
"id": "parse/s14-sqrt-nested-14",
"fn": "parse_form",
"input": {
"text": "sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(x))))))))))))))",
"mode": "expression"
},
"note": "1/16384 at the outermost sqrt, which completes last",
"expect": "[REFUSED,a computed exponent beyond 9999 at 1]"
},
{
"id": "parse/s14-abs-passes",
"fn": "parse_form",
"input": {
"text": "(abs(x^9999))^2",
"mode": "expression"
},
"expect": "[REFUSED,a computed exponent beyond 9999 at 14]"
},
{
"id": "parse/s14-function-ends",
"fn": "parse_form",
"input": {
"text": "(sin(x^9999)^9999)^9999",
"mode": "expression"
},
"note": "sin yields a pure number: the outer powers compose no exponent of x",
"expect": "[OK,(sin(x^9999)^9999)^9999]"
},
{
"id": "parse/s14-exp-ln-end",
"fn": "parse_form",
"input": {
"text": "(exp(x)^9999*ln(x)^9999)^9999",
"mode": "expression"
},
"expect": "[OK,(exp(x)^9999*ln(x)^9999)^9999]"
},
{
"id": "parse/s14-literal-no-leaf",
"fn": "parse_form",
"input": {
"text": "(2^9999)^9999",
"mode": "expression"
},
"expect": "[OK,(2^9999)^9999]"
},
{
"id": "parse/s14-D-leaf",
"fn": "parse_form",
"input": {
"text": "(D(x,t,9999)^9999)^2",
"mode": "expression"
},
"expect": "[REFUSED,a computed exponent beyond 9999 at 19]"
},
{
"id": "parse/s14-leaves-mixed",
"fn": "parse_form",
"input": {
"text": "((x^9999*y)^1)^2",
"mode": "expression"
},
"note": "y composes 2, x 19998",
"expect": "[REFUSED,a computed exponent beyond 9999 at 15]"
},
{
"id": "parse/s14-zero-exponent",
"fn": "parse_form",
"input": {
"text": "((x^9999)^0)^9999",
"mode": "expression"
},
"expect": "[OK,((x^9999)^0)^9999]"
},
{
"id": "parse/s14-order-chained-first",
"fn": "parse_form",
"input": {
"text": "(x^9999)^9999^2",
"mode": "expression"
},
"note": "the grammar refuses the chained ^ before the power is complete",
"expect": "[REFUSED,chained ^ needs parentheses at 14]"
},
{
"id": "dim/s14-nested-power-5",
"fn": "form_dimension",
"input": {
"text": "((((x^9999)^9999)^9999)^9999)^9999",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,a computed exponent beyond 9999 at 12]"
},
{
"id": "eval/s14-nested-power-kind",
"fn": "eval_form",
"input": {
"text": "(((a)^9999)^9999)",
"mode": "expression",
"bindings": {
"a": {
"VALUE": "1",
"UNIT": "rad"
}
}
},
"expect": "[REFUSED,a computed exponent beyond 9999 at 12]"
},
{
"id": "names_check/s14-composed",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = (v^100)^100"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:KIN: EQUATION does not parse: a computed exponent beyond 9999 at 18]]"
},
{
"id": "dim/s14-value-9999",
"fn": "form_dimension",
"input": {
"text": "f^9999",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,T-9999]"
},
{
"id": "dim/s14-value-10000-mul",
"fn": "form_dimension",
"input": {
"text": "f^9999*f",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,an exponent is out of range]"
},
{
"id": "dim/s14-value-9999-mul",
"fn": "form_dimension",
"input": {
"text": "f^9998*f",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,T-9999]"
},
{
"id": "dim/s14-value-10000-div",
"fn": "form_dimension",
"input": {
"text": "x^9999/x^(-1)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,an exponent is out of range]"
},
{
"id": "dim/s14-value-10000-D",
"fn": "form_dimension",
"input": {
"text": "D(v,t,9999)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "tpc_form 0.2.0 before S14 answered [OK,L1 T-10000]",
"expect": "[REFUSED,an exponent is out of range]"
},
{
"id": "dim/s14-value-D-sum",
"fn": "form_dimension",
"input": {
"text": "D(x,t,9999)*D(x,t,1)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,an exponent is out of range]"
},
{
"id": "dim/s14-value-D-9999",
"fn": "form_dimension",
"input": {
"text": "D(x,t,9998)*D(x,t,1)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L2 T-9999]"
},
{
"id": "dim/s14-value-pow-10000",
"fn": "form_dimension",
"input": {
"text": "k_s^5000",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,an exponent is out of range]"
},
{
"id": "dim/s14-value-pow-9998",
"fn": "form_dimension",
"input": {
"text": "k_s^4999",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,M4999 T-9998]"
},
{
"id": "dim/s14-value-rational",
"fn": "form_dimension",
"input": {
"text": "(k_s*k_s)^(5001/2)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "composes 5001/2 (T1 passes); T -4 x 5001/2 = -10002",
"expect": "[REFUSED,an exponent is out of range]"
},
{
"id": "dim/s14-value-rational-9998",
"fn": "form_dimension",
"input": {
"text": "(k_s*k_s)^(4999/2)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,M4999 T-9998]"
},
{
"id": "dim/s14-read-19998",
"fn": "form_dimension",
"input": {
"text": "x",
"mode": "expression",
"dimensions": {
"x": "L9999 L9999"
}
},
"note": "the exponents add to 19998: under S15 tpc_zone refuses the DIMENSION, so x has none (under S14 alone, an exponent is out of range; before S14, [OK,L19998])",
"expect": "[REFUSED,x has no DIMENSION]"
},
{
"id": "dim/s14-read-9999",
"fn": "form_dimension",
"input": {
"text": "x",
"mode": "expression",
"dimensions": {
"x": "L9999"
}
},
"expect": "[OK,L9999]"
},
{
"id": "dim/s14-mul-19998",
"fn": "form_dimension",
"input": {
"text": "x*x",
"mode": "expression",
"dimensions": {
"x": "L9999"
}
},
"expect": "[REFUSED,an exponent is out of range]"
},
{
"id": "t4/s14-value",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [],
"LAW": [
{
"NAME": "L",
"STATEMENT": "D(z, t, 9999)*D(z, t, 1) = D(z, t, 9999)*D(z, t, 1)",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTITUTIVE",
"EQUATION": "D(z, t, 9999)*D(z, t, 1) = D(z, t, 9999)*D(z, t, 1)"
}
],
"CONSTRAINT": []
}
},
"expect": "[false,[LAW:L: EQUATION an exponent is out of range (T4)]]"
},
{
"id": "t6/s14-value",
"fn": "t6_totality",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x)^9999*x < x_max"
}
]
}
},
"expect": "[false,[BOUNDARY:B_small: CONDITION an exponent is out of range (T6)]]"
},
{
"id": "eval/s14-kind-read-10000",
"fn": "eval_form",
"input": {
"text": "x",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "sr5000"
}
}
},
"note": "sr counts as rad2; tpc_form 0.2.0 before S14 answered [OK,1,rad10000]",
"expect": "[REFUSED,a kind exponent is out of range]"
},
{
"id": "eval/s14-kind-mul-19998",
"fn": "eval_form",
"input": {
"text": "x*x",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "rad9999"
}
}
},
"expect": "[REFUSED,a kind exponent is out of range]"
},
{
"id": "eval/s14-kind-mul-9999",
"fn": "eval_form",
"input": {
"text": "x*y",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "rad9998"
},
"y": {
"VALUE": "1",
"UNIT": "rad"
}
}
},
"expect": "[OK,1,rad9999]"
},
{
"id": "eval/s14-kind-pow-10000",
"fn": "eval_form",
"input": {
"text": "x^2",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "rad5000"
}
}
},
"expect": "[REFUSED,a kind exponent is out of range]"
},
{
"id": "eval/s14-kind-div-10000",
"fn": "eval_form",
"input": {
"text": "x/y",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "1",
"UNIT": "rad9999"
},
"y": {
"VALUE": "1",
"UNIT": "rad-1"
}
}
},
"expect": "[REFUSED,a kind exponent is out of range]"
},
{
"id": "t3laws/s14-kind",
"fn": "t3_laws",
"input": {
"tpk": {
"DOF": [
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "a",
"DIMENSION": "1",
"VALUE": "1",
"UNIT": "rad9999"
},
{
"NAME": "b",
"DIMENSION": "1",
"VALUE": "1",
"UNIT": "rad9999"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "a*a = b",
"REFS": [
"a",
"b"
],
"ROLE": "DEFINITION",
"EQUATION": "a*a = b"
}
],
"CONSTRAINT": []
}
},
"expect": "[false,[LAW:L: EQUATION cannot be evaluated under the declared values: a kind exponent is out of range (T3)]]"
},
{
"id": "eval/s14-zero-neg-rational",
"fn": "eval_form",
"input": {
"text": "x^(-1/2)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "0",
"UNIT": "m"
}
}
},
"note": "tpc_form 0.2.0 before S14: TPC-PY raised ValueError (math domain error); TPC-PHP answered not a finite double",
"expect": "[REFUSED,0 under a negative exponent]"
},
{
"id": "eval/s14-negzero-neg-rational",
"fn": "eval_form",
"input": {
"text": "(-x)^(-1/2)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "0",
"UNIT": "m"
}
}
},
"note": "-0.0 is a zero base",
"expect": "[REFUSED,0 under a negative exponent]"
},
{
"id": "eval/s14-zero-neg-integral-rational",
"fn": "eval_form",
"input": {
"text": "x^(-4/2)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "0",
"UNIT": "m"
}
}
},
"expect": "[REFUSED,0 under a negative exponent]"
},
{
"id": "eval/s14-zero-neg-rational-downstream",
"fn": "eval_form",
"input": {
"text": "1/x^(-1/2)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "0",
"UNIT": "m"
}
}
},
"note": "tpc_form 0.2.0 before S14: TPC-PHP answered [OK,0,none]",
"expect": "[REFUSED,0 under a negative exponent]"
},
{
"id": "eval/s14-zero-pos-rational",
"fn": "eval_form",
"input": {
"text": "x^(1/2)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "0",
"UNIT": "m"
}
}
},
"expect": "[OK,0,none]"
},
{
"id": "eval/s14-zero-zero-rational",
"fn": "eval_form",
"input": {
"text": "x^(0/2)",
"mode": "expression",
"bindings": {
"x": {
"VALUE": "0",
"UNIT": "m"
}
}
},
"expect": "[OK,1,none]"
},
{
"id": "dim/d177-scaled-variable",
"fn": "form_dimension",
"input": {
"text": "D(x,theta)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "a dimensionless variable: L1 less 1",
"expect": "[OK,L1]"
},
{
"id": "dim/d177-scaled-variable-order-2",
"fn": "form_dimension",
"input": {
"text": "D(x,theta,2)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,L1]"
},
{
"id": "dim/d177-length-variable",
"fn": "form_dimension",
"input": {
"text": "D(v,x)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "L1 T-1 less L1",
"expect": "[OK,T-1]"
},
{
"id": "dim/d177-length-variable-order-2",
"fn": "form_dimension",
"input": {
"text": "D(x,y,2)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "L1 less 2 x L1",
"expect": "[OK,L-1]"
},
{
"id": "dim/d177-frequency-variable",
"fn": "form_dimension",
"input": {
"text": "D(x,f)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "L1 less T-1",
"expect": "[OK,L1 T1]"
},
{
"id": "dim/d177-self",
"fn": "form_dimension",
"input": {
"text": "D(f,f)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[OK,1]"
},
{
"id": "dim/d177-time-order-3",
"fn": "form_dimension",
"input": {
"text": "D(x,t,3)",
"mode": "expression",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "the time variable reads as before",
"expect": "[OK,L1 T-3]"
},
{
"id": "dim/d177-equation-length-variable",
"fn": "form_dimension",
"input": {
"text": "D(v,x)*v=D(v,t)",
"mode": "equation",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"note": "dv/dx times v is dv/dt: T-1 times L1 T-1 against L1 T-2",
"expect": "[OK,L1 T-2]"
},
{
"id": "dim/d177-equation-mixed-fail",
"fn": "form_dimension",
"input": {
"text": "D(x,theta)=v",
"mode": "equation",
"dimensions": {
"x": "L1",
"v": "L1 T-1",
"z": "L1",
"t": "T1",
"m": "M1",
"k_s": "M1 T-2",
"x_max": "L1",
"theta": "1",
"a": "1",
"b": "1",
"y": "L1",
"f": "T-1"
}
},
"expect": "[REFUSED,sides have dimensions L1 and L1 T-1]"
},
{
"id": "dim/d177-product-past-bound-result-within",
"fn": "form_dimension",
"input": {
"text": "D(x,s,9999)",
"mode": "expression",
"dimensions": {
"x": "L9999",
"s": "L2"
}
},
"note": "n times dim(s) is L19998, not a result of any step; the result L9999 less L19998 is L-9999, within the bound",
"expect": "[OK,L-9999]"
},
{
"id": "dim/d177-result-out-of-range",
"fn": "form_dimension",
"input": {
"text": "D(x,s,2)",
"mode": "expression",
"dimensions": {
"x": "L1",
"s": "L-5000"
}
},
"note": "L1 less 2 x L-5000 is L10001",
"expect": "[REFUSED,an exponent is out of range]"
},
{
"id": "dim/d177-result-out-of-range-negative",
"fn": "form_dimension",
"input": {
"text": "D(x,s,9999)",
"mode": "expression",
"dimensions": {
"x": "L-1",
"s": "L1"
}
},
"note": "L-1 less 9999 x L1 is L-10000",
"expect": "[REFUSED,an exponent is out of range]"
},
{
"id": "dim/d177-result-at-bound",
"fn": "form_dimension",
"input": {
"text": "D(x,s,9999)",
"mode": "expression",
"dimensions": {
"x": "L0",
"s": "L1 T-1"
}
},
"expect": "[OK,L-9999 T9999]"
},
{
"id": "dim/d177-variable-read-out-of-range",
"fn": "form_dimension",
"input": {
"text": "D(x,s)",
"mode": "expression",
"dimensions": {
"x": "L1",
"s": "L9999 L1"
}
},
"note": "a DIMENSION tpc_zone refuses (S15) is none",
"expect": "[REFUSED,s has no DIMENSION]"
},
{
"id": "t4/d177-scaled-time-A21",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "X",
"DIMENSION": "1"
},
{
"NAME": "V",
"DIMENSION": "1"
},
{
"NAME": "tau",
"DIMENSION": "1"
}
],
"LAW": [
{
"NAME": "KIN",
"STATEMENT": "dX/dtau = V",
"REFS": [
"X",
"V",
"tau"
],
"ROLE": "EOM(X)",
"EQUATION": "D(X, tau) = V"
},
{
"NAME": "N2",
"STATEMENT": "dV/dtau = -X",
"REFS": [
"X",
"V",
"tau"
],
"ROLE": "EOM(V)",
"EQUATION": "D(V, tau) = -X"
}
]
}
},
"note": "out/A/suite/A21 with ROLEs added; before D177.1: [false,[LAW:KIN: EQUATION D needs a T1 variable, not tau of 1 (T4),LAW:N2: EQUATION D needs a T1 variable, not tau of 1 (T4)]]",
"expect": "[true,[]]"
},
{
"id": "t4/d177-scaled-time-second-order",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "X",
"DIMENSION": "1"
},
{
"NAME": "V",
"DIMENSION": "1"
},
{
"NAME": "tau",
"DIMENSION": "1"
}
],
"LAW": [
{
"NAME": "KIN",
"STATEMENT": "dX/dtau = V",
"REFS": [
"X",
"V",
"tau"
],
"ROLE": "EOM(X)",
"EQUATION": "D(X, tau) = V"
},
{
"NAME": "N2",
"STATEMENT": "dV/dtau = -X",
"REFS": [
"X",
"V",
"tau"
],
"ROLE": "EOM(V)",
"EQUATION": "D(V, tau, 2) = -X"
}
]
}
},
"note": "a dimensionless variable: every order has the operand's DIMENSION",
"expect": "[true,[]]"
},
{
"id": "t4/d177-beam-arc-length",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "w",
"DIMENSION": "L1"
},
{
"NAME": "s",
"DIMENSION": "L1"
}
],
"CONSTANT": [
{
"NAME": "M_b",
"DIMENSION": "L2 M1 T-2"
},
{
"NAME": "E_y",
"DIMENSION": "L-1 M1 T-2"
},
{
"NAME": "I_a",
"DIMENSION": "L4"
}
],
"LAW": [
{
"NAME": "BEAM",
"STATEMENT": "d2w/ds2 = M_b / (E_y I_a)",
"REFS": [
"w",
"s",
"M_b",
"E_y",
"I_a"
],
"ROLE": "EOM(w)",
"EQUATION": "D(w, s, 2) = M_b / (E_y * I_a)"
}
]
}
},
"note": "D(w,s,2): L1 less 2 x L1 = L-1; M_b/(E_y*I_a): L2 M1 T-2 less L-1 M1 T-2 less L4 = L-1",
"expect": "[true,[]]"
},
{
"id": "t4/d177-beam-wrong-order",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "w",
"DIMENSION": "L1"
},
{
"NAME": "s",
"DIMENSION": "L1"
}
],
"CONSTANT": [
{
"NAME": "M_b",
"DIMENSION": "L2 M1 T-2"
},
{
"NAME": "E_y",
"DIMENSION": "L-1 M1 T-2"
},
{
"NAME": "I_a",
"DIMENSION": "L4"
}
],
"LAW": [
{
"NAME": "BEAM",
"STATEMENT": "d2w/ds2 = M_b / (E_y I_a)",
"REFS": [
"w",
"s",
"M_b",
"E_y",
"I_a"
],
"ROLE": "EOM(w)",
"EQUATION": "D(w, s) = M_b / (E_y * I_a)"
}
]
}
},
"expect": "[false,[LAW:BEAM: EQUATION sides have dimensions 1 and L-1 (T4)]]"
},
{
"id": "dvars/spring",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[t]"
},
{
"id": "dvars/two-clocks",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[t,tau]"
},
{
"id": "dvars/scaled-time-A21",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "X",
"DIMENSION": "1"
},
{
"NAME": "V",
"DIMENSION": "1"
},
{
"NAME": "tau",
"DIMENSION": "1"
}
],
"LAW": [
{
"NAME": "KIN",
"STATEMENT": "dX/dtau = V",
"REFS": [
"X",
"V",
"tau"
],
"ROLE": "EOM(X)",
"EQUATION": "D(X, tau) = V"
},
{
"NAME": "N2",
"STATEMENT": "dV/dtau = -X",
"REFS": [
"X",
"V",
"tau"
],
"ROLE": "EOM(V)",
"EQUATION": "D(V, tau) = -X"
}
]
}
},
"expect": "[tau]"
},
{
"id": "dvars/beam",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "w",
"DIMENSION": "L1"
},
{
"NAME": "s",
"DIMENSION": "L1"
}
],
"CONSTANT": [
{
"NAME": "M_b",
"DIMENSION": "L2 M1 T-2"
},
{
"NAME": "E_y",
"DIMENSION": "L-1 M1 T-2"
},
{
"NAME": "I_a",
"DIMENSION": "L4"
}
],
"LAW": [
{
"NAME": "BEAM",
"STATEMENT": "d2w/ds2 = M_b / (E_y I_a)",
"REFS": [
"w",
"s",
"M_b",
"E_y",
"I_a"
],
"ROLE": "EOM(w)",
"EQUATION": "D(w, s, 2) = M_b / (E_y * I_a)"
}
]
}
},
"expect": "[s]"
},
{
"id": "dvars/heat-one-law-two-variables",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "u",
"DIMENSION": "TH1"
},
{
"NAME": "X",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "alpha_d",
"DIMENSION": "L2 T-1"
}
],
"LAW": [
{
"NAME": "HEAT",
"STATEMENT": "du/dt = alpha d2u/dX2",
"REFS": [
"u",
"t",
"alpha_d",
"X"
],
"ROLE": "EOM(u)",
"EQUATION": "D(u, t) = alpha_d * D(u, X, 2)"
}
]
}
},
"note": "code point order: X before t",
"expect": "[X,t]"
},
{
"id": "dvars/no-forms",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[]"
},
{
"id": "dvars/unparsed-form-uses-none",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) ="
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[t]"
},
{
"id": "dvars/hidden-character-uses-none",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) = v\u202e"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[t]"
},
{
"id": "dvars/wrong-type-uses-none",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": 7
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[t]"
},
{
"id": "dvars/nested",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "abs(D(x, tau)) + 0*D(v, t, 2) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[t,tau]"
},
{
"id": "dvars/condition-holds-none",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "D(x,tau)<1"
}
]
}
},
"note": "a CONDITION cannot hold D (it does not parse); only LAW EQUATIONs are read",
"expect": "[t]"
},
{
"id": "dvars/not-an-object",
"fn": "d_variables",
"input": {
"tpk": "x"
},
"expect": "[]"
},
{
"id": "dvars/laws-not-a-list",
"fn": "d_variables",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": "N2",
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[]"
},
{
"id": "dvar_check/spring",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "dvar_check/two-clocks-default-one",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[TPK: D_VARIABLES is ONE (ONE when absent), but the forms use D variables t (LAW:FREE_Z, LAW:N2), tau (LAW:KIN)]]"
},
{
"id": "dvar_check/two-clocks-explicit-one",
"fn": "d_variable_check",
"input": {
"tpk": {
"PARAMETERS": {
"D_VARIABLES": "ONE"
},
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[TPK: D_VARIABLES is ONE (ONE when absent), but the forms use D variables t (LAW:FREE_Z, LAW:N2), tau (LAW:KIN)]]"
},
{
"id": "dvar_check/two-clocks-empty-parameters",
"fn": "d_variable_check",
"input": {
"tpk": {
"PARAMETERS": {},
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[TPK: D_VARIABLES is ONE (ONE when absent), but the forms use D variables t (LAW:FREE_Z, LAW:N2), tau (LAW:KIN)]]"
},
{
"id": "dvar_check/two-clocks-several",
"fn": "d_variable_check",
"input": {
"tpk": {
"PARAMETERS": {
"D_VARIABLES": "SEVERAL"
},
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "dvar_check/two-clocks-malformed-switch",
"fn": "d_variable_check",
"input": {
"tpk": {
"PARAMETERS": {
"D_VARIABLES": "TWO"
},
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"note": "the count rule reads ONE or SEVERAL only; T1 refuses D_VARIABLES TWO as a field",
"expect": "[true,[]]"
},
{
"id": "dvar_check/two-clocks-parameters-not-object",
"fn": "d_variable_check",
"input": {
"tpk": {
"PARAMETERS": "ONE",
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"note": "T1 refuses the PARAMETERS part; the count rule is not applied under it",
"expect": "[true,[]]"
},
{
"id": "dvar_check/heat-default-one",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "u",
"DIMENSION": "TH1"
},
{
"NAME": "X",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "alpha_d",
"DIMENSION": "L2 T-1"
}
],
"LAW": [
{
"NAME": "HEAT",
"STATEMENT": "du/dt = alpha d2u/dX2",
"REFS": [
"u",
"t",
"alpha_d",
"X"
],
"ROLE": "EOM(u)",
"EQUATION": "D(u, t) = alpha_d * D(u, X, 2)"
}
]
}
},
"expect": "[false,[TPK: D_VARIABLES is ONE (ONE when absent), but the forms use D variables X (LAW:HEAT), t (LAW:HEAT)]]"
},
{
"id": "dvar_check/heat-several",
"fn": "d_variable_check",
"input": {
"tpk": {
"PARAMETERS": {
"D_VARIABLES": "SEVERAL"
},
"DOF": [
{
"NAME": "u",
"DIMENSION": "TH1"
},
{
"NAME": "X",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "alpha_d",
"DIMENSION": "L2 T-1"
}
],
"LAW": [
{
"NAME": "HEAT",
"STATEMENT": "du/dt = alpha d2u/dX2",
"REFS": [
"u",
"t",
"alpha_d",
"X"
],
"ROLE": "EOM(u)",
"EQUATION": "D(u, t) = alpha_d * D(u, X, 2)"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "dvar_check/scaled-time-A21",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "X",
"DIMENSION": "1"
},
{
"NAME": "V",
"DIMENSION": "1"
},
{
"NAME": "tau",
"DIMENSION": "1"
}
],
"LAW": [
{
"NAME": "KIN",
"STATEMENT": "dX/dtau = V",
"REFS": [
"X",
"V",
"tau"
],
"ROLE": "EOM(X)",
"EQUATION": "D(X, tau) = V"
},
{
"NAME": "N2",
"STATEMENT": "dV/dtau = -X",
"REFS": [
"X",
"V",
"tau"
],
"ROLE": "EOM(V)",
"EQUATION": "D(V, tau) = -X"
}
]
}
},
"note": "a DOF of DIMENSION 1 is a D variable (the DIMENSION T1 requirement removed)",
"expect": "[true,[]]"
},
{
"id": "dvar_check/constant-under-several",
"fn": "d_variable_check",
"input": {
"tpk": {
"PARAMETERS": {
"D_VARIABLES": "SEVERAL"
},
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"m"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, m) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:KIN: EQUATION's D variable m is not a DOF]]"
},
{
"id": "dvar_check/constant-under-one",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"m"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, m) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:KIN: EQUATION's D variable m is not a DOF,TPK: D_VARIABLES is ONE (ONE when absent), but the forms use D variables m (LAW:KIN), t (LAW:FREE_Z, LAW:N2)]]"
},
{
"id": "dvar_check/unresolved",
"fn": "d_variable_check",
"input": {
"tpk": {
"PARAMETERS": {
"D_VARIABLES": "SEVERAL"
},
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, q) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"note": "REFS are not read here: T1 reports them",
"expect": "[false,[LAW:KIN: EQUATION's D variable q is not a DOF]]"
},
{
"id": "dvar_check/names-a-law",
"fn": "d_variable_check",
"input": {
"tpk": {
"PARAMETERS": {
"D_VARIABLES": "SEVERAL"
},
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, N2) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:KIN: EQUATION's D variable N2 is not a DOF]]"
},
{
"id": "dvar_check/fix-target",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
},
{
"NAME": "C_T",
"TARGET": "t",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "s",
"STATEMENT": "t = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:FREE_Z: EQUATION's D variable t is the TARGET of CONSTRAINT:C_T,LAW:KIN: EQUATION's D variable t is the TARGET of CONSTRAINT:C_T,LAW:N2: EQUATION's D variable t is the TARGET of CONSTRAINT:C_T]]"
},
{
"id": "dvar_check/two-targets",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_TR",
"TARGET": "t",
"ACTION": "REMOVE",
"STATEMENT": "no t"
},
{
"NAME": "C_TF",
"TARGET": "t",
"ACTION": "FIX",
"VALUE": "1",
"UNIT": "s",
"STATEMENT": "t = 1"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[LAW:KIN: EQUATION's D variable t is the TARGET of CONSTRAINT:C_TF,LAW:KIN: EQUATION's D variable t is the TARGET of CONSTRAINT:C_TR]]"
},
{
"id": "dvar_check/any-action-counts",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
},
{
"NAME": "C_T",
"TARGET": "t",
"ACTION": "fix",
"STATEMENT": "t held"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"note": "a CONSTRAINT's TARGET counts whatever its ACTION; T1 refuses ACTION fix separately",
"expect": "[false,[LAW:FREE_Z: EQUATION's D variable t is the TARGET of CONSTRAINT:C_T,LAW:KIN: EQUATION's D variable t is the TARGET of CONSTRAINT:C_T,LAW:N2: EQUATION's D variable t is the TARGET of CONSTRAINT:C_T]]"
},
{
"id": "dvar_check/malformed-constraints-ignored",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_X",
"TARGET": [
"t"
],
"ACTION": "FIX"
},
"C_T",
5
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"note": "a TARGET that is not a string targets nothing; T1 reports the shapes",
"expect": "[true,[]]"
},
{
"id": "dvar_check/constraints-not-a-list",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": "C_T",
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "dvar_check/unnamed-and-hidden-escaped",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "K\u202eIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
},
{
"TARGET": "t",
"ACTION": "REMOVE",
"STATEMENT": "no t"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"note": "a quoted NAME escapes disallowed code points; an unnamed entry shows as ?",
"expect": "[false,[LAW:K<U+202E>IN: EQUATION's D variable t is the TARGET of CONSTRAINT:?]]"
},
{
"id": "dvar_check/unparsed-form-uses-none",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) ="
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "dvar_check/hidden-character-uses-none",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) = v\u202e"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "dvar_check/unnamed-law",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "tau",
"DIMENSION": "T1"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"tau"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, tau) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[false,[TPK: D_VARIABLES is ONE (ONE when absent), but the forms use D variables t (LAW:FREE_Z, LAW:N2), tau (LAW:?)]]"
},
{
"id": "dvar_check/input-dof",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "v",
"DIMENSION": "L1 T-1"
},
{
"NAME": "z",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1",
"ROLE": "INPUT"
}
],
"CONSTANT": [
{
"NAME": "m",
"DIMENSION": "M1"
},
{
"NAME": "k_s",
"DIMENSION": "M1 T-2"
},
{
"NAME": "x_max",
"DIMENSION": "L1",
"VALUE": "0.05",
"UNIT": "m",
"UNCERTAINTY": "0.001"
}
],
"LAW": [
{
"NAME": "N2",
"STATEMENT": "m dv/dt = -k_s x",
"REFS": [
"m",
"v",
"k_s",
"x",
"t"
],
"ROLE": "EOM(v)",
"EQUATION": "m * D(v, t) = -k_s * x"
},
{
"NAME": "KIN",
"STATEMENT": "dx/dt = v",
"REFS": [
"x",
"v",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x, t) = v"
},
{
"NAME": "FREE_Z",
"STATEMENT": "d2z/dt2 = 0",
"REFS": [
"z",
"t"
],
"ROLE": "CONSTRAINT",
"EQUATION": "D(z, t, 2) = 0"
}
],
"ASSUMPTION": [
{
"NAME": "A_lin",
"PROPOSITION": "the restoring force is linear in x (Hooke r\u00e9gime)",
"REFS": [
"x"
]
}
],
"CONSTRAINT": [
{
"NAME": "C_NOZ",
"TARGET": "z",
"ACTION": "FIX",
"VALUE": "0",
"UNIT": "m",
"STATEMENT": "motion confined to z = 0"
}
],
"BOUNDARY": [
{
"NAME": "B_small",
"PREDICATE": "|x| < x_max",
"REFS": [
"x",
"x_max"
],
"CONDITION": "abs(x) < x_max"
}
]
}
},
"expect": "[true,[]]"
},
{
"id": "dvar_check/not-an-object",
"fn": "d_variable_check",
"input": {
"tpk": "x"
},
"expect": "[true,[]]"
},
{
"id": "tree/law-N2",
"fn": "form_tree",
"input": {
"text": "m * D(v, t) = -k_s * x",
"mode": "equation"
},
"note": "unary minus binds to its power, so -k_s * x is (-k_s)*x",
"expect": "[OK,[eq,[bin,*,[id,m],[D,v,t,1]],[bin,*,[neg,[id,k_s]],[id,x]]]]"
},
{
"id": "tree/law-KIN",
"fn": "form_tree",
"input": {
"text": "D(x, t) = v",
"mode": "equation"
},
"expect": "[OK,[eq,[D,x,t,1],[id,v]]]"
},
{
"id": "tree/law-FREE_Z",
"fn": "form_tree",
"input": {
"text": "D(z, t, 2) = 0",
"mode": "equation"
},
"expect": "[OK,[eq,[D,z,t,2],[num,0]]]"
},
{
"id": "tree/law-EOM_Z",
"fn": "form_tree",
"input": {
"text": "m * D(z, t, 2) = 0",
"mode": "equation"
},
"expect": "[OK,[eq,[bin,*,[id,m],[D,z,t,2]],[num,0]]]"
},
{
"id": "tree/boundary-B_small",
"fn": "form_tree",
"input": {
"text": "abs(x) < x_max",
"mode": "predicate"
},
"expect": "[OK,[pred,[cmp,<,[fn,abs,[id,x]],[id,x_max]]]]"
},
{
"id": "tree/signature-form",
"fn": "form_tree",
"input": {
"text": "D(x, t) = v",
"mode": "form"
},
"expect": "[OK,[eq,[D,x,t,1],[id,v]]]"
},
{
"id": "tree/signature-operation",
"fn": "form_tree",
"input": {
"text": "D(x, t)",
"mode": "form"
},
"expect": "[OK,[expr,[D,x,t,1]]]"
},
{
"id": "tree/derivative-order-one-written",
"fn": "form_tree",
"input": {
"text": "D(x,t,1)",
"mode": "expression"
},
"note": "D(x,t,1) and D(x,t) give one tree",
"expect": "[OK,[expr,[D,x,t,1]]]"
},
{
"id": "tree/parens-kept",
"fn": "form_tree",
"input": {
"text": "((a+b))",
"mode": "expression"
},
"note": "parse_form spells it a+b; the tree keeps both parentheses",
"expect": "[OK,[expr,[paren,[paren,[bin,+,[id,a],[id,b]]]]]]"
},
{
"id": "tree/parens-each-side",
"fn": "form_tree",
"input": {
"text": "(a)=(b)",
"mode": "equation"
},
"expect": "[OK,[eq,[paren,[id,a]],[paren,[id,b]]]]"
},
{
"id": "tree/assoc-minus",
"fn": "form_tree",
"input": {
"text": "a-b-c",
"mode": "expression"
},
"expect": "[OK,[expr,[bin,-,[bin,-,[id,a],[id,b]],[id,c]]]]"
},
{
"id": "tree/assoc-div-mul",
"fn": "form_tree",
"input": {
"text": "a/b*c",
"mode": "expression"
},
"expect": "[OK,[expr,[bin,*,[bin,/,[id,a],[id,b]],[id,c]]]]"
},
{
"id": "tree/precedence-mul",
"fn": "form_tree",
"input": {
"text": "a+b*c",
"mode": "expression"
},
"expect": "[OK,[expr,[bin,+,[id,a],[bin,*,[id,b],[id,c]]]]]"
},
{
"id": "tree/unary-minus-power",
"fn": "form_tree",
"input": {
"text": "-a^2",
"mode": "expression"
},
"expect": "[OK,[expr,[neg,[pow,[id,a],[2,1]]]]]"
},
{
"id": "tree/exponents-as-written",
"fn": "form_tree",
"input": {
"text": "x^(-1)+x^(2/4)+x^02",
"mode": "expression"
},
"note": "a rational exponent is kept as written, not reduced; an integer's leading zero is read away",
"expect": "[OK,[expr,[bin,+,[bin,+,[pow,[id,x],[-1,1]],[pow,[id,x],[2,4]]],[pow,[id,x],[2,1]]]]]"
},
{
"id": "tree/exponent-negative-rational",
"fn": "form_tree",
"input": {
"text": "x^(-3/2)",
"mode": "expression"
},
"expect": "[OK,[expr,[pow,[id,x],[-3,2]]]]"
},
{
"id": "tree/literals-canonical",
"fn": "form_tree",
"input": {
"text": "0.50*x+100-2.0+0.0",
"mode": "expression"
},
"expect": "[OK,[expr,[bin,+,[bin,-,[bin,+,[bin,*,[num,5e-1],[id,x]],[num,1e2]],[num,2]],[num,0]]]]"
},
{
"id": "tree/functions",
"fn": "form_tree",
"input": {
"text": "sqrt(x^2)*exp(-t)",
"mode": "expression"
},
"expect": "[OK,[expr,[bin,*,[fn,sqrt,[pow,[id,x],[2,1]]],[fn,exp,[neg,[id,t]]]]]]"
},
{
"id": "tree/keywords-precedence",
"fn": "form_tree",
"input": {
"text": "x<1 or y>2 and z=3",
"mode": "predicate"
},
"expect": "[OK,[pred,[or,[cmp,<,[id,x],[num,1]],[and,[cmp,>,[id,y],[num,2]],[cmp,=,[id,z],[num,3]]]]]]"
},
{
"id": "tree/not-predicate-paren",
"fn": "form_tree",
"input": {
"text": "not (x<1 and y>2)",
"mode": "predicate"
},
"expect": "[OK,[pred,[not,[pparen,[and,[cmp,<,[id,x],[num,1]],[cmp,>,[id,y],[num,2]]]]]]]"
},
{
"id": "tree/expression-paren-in-predicate",
"fn": "form_tree",
"input": {
"text": "(x+1)<2",
"mode": "predicate"
},
"note": "a parenthesis holding no comparison or keyword opens an expression",
"expect": "[OK,[pred,[cmp,<,[paren,[bin,+,[id,x],[num,1]]],[num,2]]]]"
},
{
"id": "tree/nesting-at-bound",
"fn": "form_tree",
"input": {
"text": "((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"note": "64 parentheses deep, the D186.1 bound: admitted, every level a node",
"expect": "[OK,[expr,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[paren,[id,x]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]"
},
{
"id": "tree/refused-unexpected-end",
"fn": "form_tree",
"input": {
"text": "m * D(v, t) =",
"mode": "equation"
},
"expect": "[REFUSED,unexpected end]"
},
{
"id": "tree/refused-chained-power",
"fn": "form_tree",
"input": {
"text": "a^2^3",
"mode": "expression"
},
"expect": "[REFUSED,chained ^ needs parentheses at 4]"
},
{
"id": "tree/refused-equals-in-expression",
"fn": "form_tree",
"input": {
"text": "x = 1",
"mode": "expression"
},
"expect": "[REFUSED,unexpected token = at 3]"
},
{
"id": "tree/refused-no-equals",
"fn": "form_tree",
"input": {
"text": "x",
"mode": "equation"
},
"expect": "[REFUSED,the equation has no =]"
},
{
"id": "tree/refused-D-in-condition",
"fn": "form_tree",
"input": {
"text": "D(x,t)<1",
"mode": "predicate"
},
"expect": "[REFUSED,D is not permitted in a CONDITION at 1]"
},
{
"id": "tree/refused-empty",
"fn": "form_tree",
"input": {
"text": "",
"mode": "expression"
},
"expect": "[REFUSED,empty form]"
},
{
"id": "tree/refused-hidden-character",
"fn": "form_tree",
"input": {
"text": "x\u202e",
"mode": "expression"
},
"note": "the refusal escapes the code point, as parse_form's",
"expect": "[REFUSED,unexpected character <U+202E> at 2]"
},
{
"id": "tree/refused-integer-digits",
"fn": "form_tree",
"input": {
"text": "x^12345",
"mode": "expression"
},
"expect": "[REFUSED,an integer of more than 4 digits at 3]"
},
{
"id": "tree/refused-nesting",
"fn": "form_tree",
"input": {
"text": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((x)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
"mode": "expression"
},
"expect": "[REFUSED,more than 64 nested parentheses at 65]"
},
{
"id": "tree/refused-length",
"fn": "form_tree",
"input": {
"text": "x ",
"mode": "expression"
},
"expect": "[REFUSED,the form is longer than 4096 code points]"
},
{
"id": "tree/refused-computed-exponent",
"fn": "form_tree",
"input": {
"text": "(x^9999)^2",
"mode": "expression"
},
"expect": "[REFUSED,a computed exponent beyond 9999 at 9]"
},
{
"id": "tree/refused-not-a-string",
"fn": "form_tree",
"input": {
"text": 7,
"mode": "expression"
},
"expect": "[REFUSED,the form is not a string]"
},
{
"id": "tree/refused-unknown-mode",
"fn": "form_tree",
"input": {
"text": "x",
"mode": "Equation"
},
"expect": "[REFUSED,unknown mode Equation]"
},
{
"id": "decode/names-check-kind-zero-keyed",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"LAW": {
"0": {
"NAME": "L",
"STATEMENT": "x moves as y",
"REFS": [
"x",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x,t)=y"
}
}
}
},
"note": "the LAW kind is not a list: no form is read (it read L and found y outside REFS)",
"expect": "[true,[]]"
},
{
"id": "decode/names-check-kind-list",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "x moves as y",
"REFS": [
"x",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x,t)=y"
}
]
}
},
"note": "the same law as a list",
"expect": "[false,[LAW:L: EQUATION names y, which is not in REFS]]"
},
{
"id": "decode/names-check-refs-zero-keyed",
"fn": "names_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
}
],
"LAW": [
{
"NAME": "L",
"STATEMENT": "x is zero",
"REFS": {
"0": "x"
},
"ROLE": "CONSTRAINT",
"EQUATION": "x=0"
}
]
}
},
"note": "REFS keyed 0 is not a list of names",
"expect": "[false,[LAW:L: EQUATION names x, which is not in REFS]]"
},
{
"id": "decode/form-coverage-kinds-zero-keyed",
"fn": "form_coverage",
"input": {
"tpk": {
"LAW": {
"0": {
"NAME": "L",
"STATEMENT": "a definition",
"REFS": [],
"ROLE": "DEFINITION"
}
},
"BOUNDARY": {
"0": {
"NAME": "B",
"PREDICATE": "always",
"REFS": []
}
}
}
},
"expect": "[[],[]]"
},
{
"id": "decode/form-coverage-kinds-list",
"fn": "form_coverage",
"input": {
"tpk": {
"LAW": [
{
"NAME": "L",
"STATEMENT": "a definition",
"REFS": [],
"ROLE": "DEFINITION"
}
],
"BOUNDARY": [
{
"NAME": "B",
"PREDICATE": "always",
"REFS": []
}
]
}
},
"expect": "[[L],[B]]"
},
{
"id": "decode/form-coverage-tpk-list",
"fn": "form_coverage",
"input": {
"tpk": []
},
"expect": "[[],[]]"
},
{
"id": "decode/t4-kind-zero-keyed",
"fn": "t4_homogeneity",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
}
],
"LAW": {
"0": {
"NAME": "L",
"STATEMENT": "x grows as x",
"REFS": [
"x",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x,t)=x"
}
}
}
},
"note": "no law is read (it read L, whose sides are L1 T-1 and L1)",
"expect": "[true,[]]"
},
{
"id": "decode/t6-kind-zero-keyed",
"fn": "t6_totality",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
}
],
"BOUNDARY": {
"0": {
"NAME": "B",
"PREDICATE": "x is positive",
"REFS": [
"x"
],
"CONDITION": "1/x>0"
}
}
}
},
"note": "no boundary is read",
"expect": "[true,[]]"
},
{
"id": "decode/t3-laws-kind-zero-keyed",
"fn": "t3_laws",
"input": {
"tpk": {
"CONSTANT": [
{
"NAME": "c",
"DIMENSION": "L1",
"VALUE": "1",
"UNIT": "m"
}
],
"LAW": {
"0": {
"NAME": "L",
"STATEMENT": "c is twice c",
"REFS": [
"c"
],
"ROLE": "DEFINITION",
"EQUATION": "c=2*c"
}
}
}
},
"note": "no law is read (it read L, false under c = 1 m)",
"expect": "[true,[]]"
},
{
"id": "decode/dvar-parameters-list",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "s",
"DIMENSION": "L1"
}
],
"LAW": [
{
"NAME": "L1",
"STATEMENT": "x is still in t",
"REFS": [
"x",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x,t)=0"
},
{
"NAME": "L2",
"STATEMENT": "x is flat in s",
"REFS": [
"x",
"s"
],
"ROLE": "CONSTITUTIVE",
"EQUATION": "D(x,s)=0"
}
],
"PARAMETERS": []
}
},
"note": "PARAMETERS [] is not an object: T1 refuses it, and no D_VARIABLES count applies here",
"expect": "[true,[]]"
},
{
"id": "decode/dvar-parameters-empty-object",
"fn": "d_variable_check",
"input": {
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
},
{
"NAME": "t",
"DIMENSION": "T1"
},
{
"NAME": "s",
"DIMENSION": "L1"
}
],
"LAW": [
{
"NAME": "L1",
"STATEMENT": "x is still in t",
"REFS": [
"x",
"t"
],
"ROLE": "EOM(x)",
"EQUATION": "D(x,t)=0"
},
{
"NAME": "L2",
"STATEMENT": "x is flat in s",
"REFS": [
"x",
"s"
],
"ROLE": "CONSTITUTIVE",
"EQUATION": "D(x,s)=0"
}
],
"PARAMETERS": {}
}
},
"note": "an empty PARAMETERS object: D_VARIABLES absent, so ONE",
"expect": "[false,[TPK: D_VARIABLES is ONE (ONE when absent), but the forms use D variables s (LAW:L2), t (LAW:L1)]]"
},
{
"id": "decode/eval-bindings-list",
"fn": "eval_form",
"input": {
"text": "x",
"mode": "expression",
"bindings": [
{
"VALUE": "q",
"UNIT": "m"
}
]
},
"note": "bindings [] is not an object: nothing is bound (it read a binding 0 and refused its VALUE)",
"expect": "[UNBOUND,x]"
},
{
"id": "decode/eval-binding-entry-list",
"fn": "eval_form",
"input": {
"text": "x",
"mode": "expression",
"bindings": {
"x": []
}
},
"note": "a binding that is not an object binds nothing",
"expect": "[UNBOUND,x]"
},
{
"id": "decode/eval-bindings-empty-object",
"fn": "eval_form",
"input": {
"text": "2",
"mode": "expression",
"bindings": {}
},
"expect": "[OK,2,none]"
},
{
"id": "decode/ic4a-signature-zero-keyed",
"fn": "ic4a_signature",
"input": {
"trm": {
"HEADER": {
"ENVIRONMENT_INVENTORY": [
{
"ENVIRONMENT_QUANTITY": "position",
"DIMENSION": "L1"
}
],
"SIGNATURE": {
"0": {
"NAME": "sg",
"OVER": [
"x"
],
"IMAGE": "the position",
"FORM": "x",
"IMAGE_FORM": "pos"
}
},
"TRANSFORMATIONS": []
},
"ENTRIES": [
{
"NAME": "E_x",
"DOF": "x",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "position",
"IDENTIFICATION": "x is the position",
"FALSIFIER": "a position off x",
"FALSIFIER_CLASS": "F2",
"BEARS": [],
"DIMENSION": "L1"
}
]
},
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
}
]
}
},
"note": "the SIGNATURE part is not a list: no signature is read",
"expect": "[true,[],[]]"
},
{
"id": "decode/ic4a-signature-list",
"fn": "ic4a_signature",
"input": {
"trm": {
"HEADER": {
"ENVIRONMENT_INVENTORY": [
{
"ENVIRONMENT_QUANTITY": "position",
"DIMENSION": "L1"
}
],
"SIGNATURE": [
{
"NAME": "sg",
"OVER": [
"x"
],
"IMAGE": "the position",
"FORM": "x",
"IMAGE_FORM": "pos"
}
],
"TRANSFORMATIONS": []
},
"ENTRIES": [
{
"NAME": "E_x",
"DOF": "x",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "position",
"IDENTIFICATION": "x is the position",
"FALSIFIER": "a position off x",
"FALSIFIER_CLASS": "F2",
"BEARS": [],
"DIMENSION": "L1"
}
]
},
"tpk": {
"DOF": [
{
"NAME": "x",
"DIMENSION": "L1"
}
]
}
},
"note": "the same signature as a list",
"expect": "[false,[IC4(a): SIGNATURE:sg: FORM under the entries reads position, not IMAGE_FORM pos],[]]"
}
]
}
