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| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 | /** * Topology-based proposition detection from free-form construction. * * Detects which proposition the user is attempting based on the construction's * topology (element counts + relational structure). This is the heckler's * activation trigger — when the matcher identifies a known proposition, * Euclid calls the user. * * Matching strategy (two tiers): * 1. Count-based pre-filter — extract a fingerprint from the construction state * 2. Relational structure check — verify graph edges for shortlisted candidates * * Confidence levels: * - 'speculative' — early pattern match (e.g., cross-centered circles, no intersection yet) * - 'likely' — most structure present (e.g., + intersection at circle meeting) * - 'confirmed' — complete match (e.g., full equilateral triangle drawn) */ import type { ConstructionState, ConstructionPoint, ConstructionCircle, ConstructionSegment, } from '../types' import { getAllPoints, getAllCircles, getAllSegments } from '../engine/constructionState' export type MatchConfidence = 'speculative' | 'likely' | 'confirmed' export interface PropositionMatch { propositionId: number confidence: MatchConfidence /** Human-readable description of what was detected. */ description: string } /** Count-based fingerprint of a construction state. */ interface ConstructionFingerprint { points: ConstructionPoint[] circles: ConstructionCircle[] segments: ConstructionSegment[] intersectionPoints: ConstructionPoint[] extendPoints: ConstructionPoint[] freePoints: ConstructionPoint[] givenPoints: ConstructionPoint[] } function fingerprint(state: ConstructionState): ConstructionFingerprint { const points = getAllPoints(state) const circles = getAllCircles(state) const segments = getAllSegments(state) return { points, circles, segments, intersectionPoints: points.filter((p) => p.origin === 'intersection'), extendPoints: points.filter((p) => p.origin === 'extend'), freePoints: points.filter((p) => p.origin === 'free'), givenPoints: points.filter((p) => p.origin === 'given'), } } // --------------------------------------------------------------------------- // Proposition I.1 — Construct an equilateral triangle on a given segment // --------------------------------------------------------------------------- /** * Check if two circles are cross-centered: each centered on one of two points, * with the radius-point being the other. */ function findCrossCenteredCirclePair(circles: ConstructionCircle[]): { circleA: ConstructionCircle circleB: ConstructionCircle ptIdA: string ptIdB: string } | null { for (let i = 0; i < circles.length; i++) { for (let j = i + 1; j < circles.length; j++) { const a = circles[i] const b = circles[j] // a centered at P through Q, b centered at Q through P if (a.centerId === b.radiusPointId && a.radiusPointId === b.centerId) { return { circleA: a, circleB: b, ptIdA: a.centerId, ptIdB: b.centerId } } } } return null } /** * Check if a point lies at a circle-circle intersection. * We don't recompute geometry — we check if the point's origin is 'intersection' * and whether both circles exist with the expected relationship. */ function isCircleCircleIntersection( pt: ConstructionPoint, circleA: ConstructionCircle, circleB: ConstructionCircle, state: ConstructionState ): boolean { if (pt.origin !== 'intersection') return false // The point should lie on both circles geometrically. // Since we can't know the parent elements directly from the state, // we check coordinates: compute the distance from the point to each // circle's center and compare with the circle's radius. const allPts = getAllPoints(state) const centerA = allPts.find((p) => p.id === circleA.centerId) const radPtA = allPts.find((p) => p.id === circleA.radiusPointId) const centerB = allPts.find((p) => p.id === circleB.centerId) const radPtB = allPts.find((p) => p.id === circleB.radiusPointId) if (!centerA || !radPtA || !centerB || !radPtB) return false const radiusA = Math.hypot(radPtA.x - centerA.x, radPtA.y - centerA.y) const radiusB = Math.hypot(radPtB.x - centerB.x, radPtB.y - centerB.y) const distA = Math.hypot(pt.x - centerA.x, pt.y - centerA.y) const distB = Math.hypot(pt.x - centerB.x, pt.y - centerB.y) const tolerance = 0.02 // slightly more generous than the 0.01 in serializeProofState return Math.abs(distA - radiusA) < tolerance && Math.abs(distB - radiusB) < tolerance } /** * Check if a segment connects two specific points (in either order). */ function segmentConnects(seg: ConstructionSegment, ptIdA: string, ptIdB: string): boolean { return ( (seg.fromId === ptIdA && seg.toId === ptIdB) || (seg.fromId === ptIdB && seg.toId === ptIdA) ) } function matchProp1( state: ConstructionState, fp: ConstructionFingerprint ): PropositionMatch | null { // Need at least 2 circles if (fp.circles.length < 2) return null // Find cross-centered pair const crossPair = findCrossCenteredCirclePair(fp.circles) if (!crossPair) return null const { ptIdA, ptIdB, circleA, circleB } = crossPair // Find intersection point at circle-circle meeting const meetingPoints = fp.intersectionPoints.filter((pt) => isCircleCircleIntersection(pt, circleA, circleB, state) ) if (meetingPoints.length === 0) { // Cross-centered circles exist but no intersection placed yet return { propositionId: 1, confidence: 'speculative', description: 'Two cross-centered circles detected — Prop I.1 pattern', } } // At least one intersection point exists at the circle meeting const meetPt = meetingPoints[0] // Check for triangle segments const hasSegAMeet = fp.segments.some((s) => segmentConnects(s, ptIdA, meetPt.id)) const hasSegBMeet = fp.segments.some((s) => segmentConnects(s, ptIdB, meetPt.id)) const hasBaseSeg = fp.segments.some((s) => segmentConnects(s, ptIdA, ptIdB)) if (hasSegAMeet && hasSegBMeet && hasBaseSeg) { return { propositionId: 1, confidence: 'confirmed', description: 'Complete equilateral triangle constructed — Prop I.1', } } // Intersection placed = likely return { propositionId: 1, confidence: 'likely', description: 'Cross-centered circles with intersection point — Prop I.1', } } // --------------------------------------------------------------------------- // Main matcher // --------------------------------------------------------------------------- /** All proposition matchers, ordered by priority. */ const MATCHERS: Array< (state: ConstructionState, fp: ConstructionFingerprint) => PropositionMatch | null > = [ matchProp1, // Future: matchProp2, matchProp3, matchProp4, matchProp5, etc. ] /** * Detect which proposition the user is attempting based on the construction's * topology. Returns the highest-confidence match, or null if no pattern detected. */ export function matchProposition(state: ConstructionState): PropositionMatch | null { const fp = fingerprint(state) // Need at least 2 points and 1 non-point element to match anything if (fp.points.length < 2 || (fp.circles.length === 0 && fp.segments.length === 0)) { return null } console.log( '[heckler-matcher] checking: %d pts, %d circles, %d segs, %d intersections', fp.points.length, fp.circles.length, fp.segments.length, fp.intersectionPoints.length ) let bestMatch: PropositionMatch | null = null const confidenceRank: Record<MatchConfidence, number> = { speculative: 0, likely: 1, confirmed: 2, } for (const matcher of MATCHERS) { const match = matcher(state, fp) if (match) { if (!bestMatch || confidenceRank[match.confidence] > confidenceRank[bestMatch.confidence]) { bestMatch = match } } } if (bestMatch) { console.log( '[heckler-matcher] match: prop I.%d (%s) — %s', bestMatch.propositionId, bestMatch.confidence, bestMatch.description ) } return bestMatch } |