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| 1 | +/** |
| 2 | + * Format proof steps for validation logs in the same way the student sees them in the frontend. |
| 3 | + * Mirrors client/proof/statements.ts statementToString and client/proof/reasons.ts REASONS names. |
| 4 | + */ |
| 5 | + |
| 6 | +import type { ProofStepLogEntry } from './types.js'; |
| 7 | + |
| 8 | +/** Human-readable string for a statement (same as client/proof/statements statementToString). */ |
| 9 | +function statementToString(s: { kind: string; pointNames: string[]; constant?: number }): string { |
| 10 | + const n = s.pointNames; |
| 11 | + switch (s.kind) { |
| 12 | + case 'points-distinct': |
| 13 | + return `${n[0]} ≠ ${n[1]}`; |
| 14 | + case 'point-on-line': |
| 15 | + return `${n[0]} ∈ line ${n[1]}${n[2]}`; |
| 16 | + case 'point-on-segment': |
| 17 | + return `${n[0]} ∈ ${n[1]}${n[2]}`; |
| 18 | + case 'point-on-ray': |
| 19 | + return `${n[0]} ∈ ray ${n[1]}${n[2]}`; |
| 20 | + case 'line-equals-line': |
| 21 | + return `line ${n[0]}${n[1]} = line ${n[2]}${n[3]}`; |
| 22 | + case 'rays-form-line': |
| 23 | + return `ray ${n[0]}${n[1]} ∪ ray ${n[2]}${n[1]} = line ${n[0]}${n[1]}`; |
| 24 | + case 'unique-line': |
| 25 | + return `∃₁ line through ${n[0]}, ${n[1]}`; |
| 26 | + case 'intersection-equals': |
| 27 | + return `${n[0]} = line ${n[1]}${n[2]} ∩ line ${n[3]}${n[4]}`; |
| 28 | + case 'intersection-segment-equals': |
| 29 | + return `${n[1]}${n[0]} ∩ ${n[2]}${n[3]} = ${n[0]}`; |
| 30 | + case 'angle-equals-constant': |
| 31 | + return `∠${n[0]}${n[1]}${n[2]} = ${(s as { constant?: number }).constant ?? '·'}°`; |
| 32 | + case 'angle-equals-angle': |
| 33 | + return `∠${n[0]}${n[1]}${n[2]} = ∠${n[3]}${n[4]}${n[5]}`; |
| 34 | + case 'angle-less-than-angle': |
| 35 | + return `∠${n[0]}${n[1]}${n[2]} < ∠${n[3]}${n[4]}${n[5]}`; |
| 36 | + case 'angle-greater-than-angle': |
| 37 | + return `∠${n[0]}${n[1]}${n[2]} > ∠${n[3]}${n[4]}${n[5]}`; |
| 38 | + case 'angle-leq-angle': |
| 39 | + return `∠${n[0]}${n[1]}${n[2]} ≤ ∠${n[3]}${n[4]}${n[5]}`; |
| 40 | + case 'angle-geq-angle': |
| 41 | + return `∠${n[0]}${n[1]}${n[2]} ≥ ∠${n[3]}${n[4]}${n[5]}`; |
| 42 | + case 'segment-equals-segment': |
| 43 | + return `${n[0]}${n[1]} = ${n[2]}${n[3]}`; |
| 44 | + case 'segment-perpendicular': |
| 45 | + return `${n[0]}${n[1]} ⊥ ${n[2]}${n[3]}`; |
| 46 | + case 'triangles-congruent': |
| 47 | + return `Δ${n[0]}${n[1]}${n[2]} ≅ Δ${n[3]}${n[4]}${n[5]}`; |
| 48 | + case 'triangle-angles-sum-180': |
| 49 | + return `angles of Δ${n[0]}${n[1]}${n[2]} sum to 180°`; |
| 50 | + case 'point-midpoint-of-segment': |
| 51 | + return `${n[0]} is midpoint of ${n[1]}${n[2]}`; |
| 52 | + default: |
| 53 | + return String(s.kind); |
| 54 | + } |
| 55 | +} |
| 56 | + |
| 57 | +/** Reason id -> display name (same as client/proof/reasons REASONS[].name). */ |
| 58 | +const REASON_NAMES: Record<string, string> = { |
| 59 | + given: 'Given in task statement', |
| 60 | + definition: 'New Definition', |
| 61 | + 'perpendicular-definition': 'Perpendicular definition', |
| 62 | + 'line-determination': 'Incidence axiom I1 (two points determine a unique line)', |
| 63 | + 'point-on-line-same-line': 'By I1 (point on line: line AC = line AB)', |
| 64 | + 'opposite-rays-form-line': 'Theorem: opposite rays lie on one line', |
| 65 | + reflexivity: 'Reflexivity (AB = AB or ∠A = ∠A)', |
| 66 | + 'reflexivity-segment': 'Reflexivity (AB = AB or ∠A = ∠A)', |
| 67 | + 'transitivity-equals': 'Transitivity (=)', |
| 68 | + 'transitivity-less': 'Transitivity (<)', |
| 69 | + 'transitivity-greater': 'Transitivity (>)', |
| 70 | + 'transitivity-leq': 'Transitivity (≤)', |
| 71 | + 'transitivity-geq': 'Transitivity (≥)', |
| 72 | + sas: 'Triangle congruence (SAS)', |
| 73 | + asa: 'Triangle congruence (ASA)', |
| 74 | + aas: 'Triangle congruence (AAS)', |
| 75 | + sss: 'Triangle congruence (SSS)', |
| 76 | + hl: 'Triangle congruence (HL)', |
| 77 | + 'from-congruence': 'From congruence (CPCTC): corresponding sides equal', |
| 78 | + 'sum-triangle-angles': 'Sum of triangle angles', |
| 79 | + thales: 'Thales theorem', |
| 80 | +}; |
| 81 | + |
| 82 | +/** |
| 83 | + * Format one proof step as shown in the frontend: "1. statement (Reason name) [from: Given, Step 2]" |
| 84 | + */ |
| 85 | +export function formatProofStep(step: ProofStepLogEntry, index: number): string { |
| 86 | + const statement = step.outcome ? statementToString(step.outcome) : '?'; |
| 87 | + const reasonName = (step.reasonId && REASON_NAMES[step.reasonId]) || step.reasonId || '?'; |
| 88 | + const refs = Array.isArray(step.prerequisiteRefs) && step.prerequisiteRefs.length; |
| 89 | + const prereqStr = refs |
| 90 | + ? ` [from: ${step.prerequisiteRefs.map((r) => (r === 'given' ? 'Given' : `Step ${r}`)).join(', ')}]` |
| 91 | + : ''; |
| 92 | + return `${index + 1}. ${statement} (${reasonName})${prereqStr}`; |
| 93 | +} |
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