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* Parse chat text for structured geometric entity markers.
*
* The LLM is instructed to use markers like:
* {seg:AB} → segment A–B
* {tri:ABC} → triangle △ABC
* {ang:ABC} → angle ∠ABC (vertex is middle letter)
* {pt:A} → point A
*
* This is far more reliable than guessing from free-form text.
* If the model doesn't use markers, text renders as-is with no highlights.
*/
export type GeometricEntityRef =
| { type: 'segment'; from: string; to: string }
| { type: 'triangle'; vertices: [string, string, string] }
| { type: 'angle'; points: [string, string, string] }
| { type: 'point'; label: string }
export type FoundationEntityRef =
| { type: 'definition'; id: number }
| { type: 'postulate'; id: number }
| { type: 'commonNotion'; id: number }
| { type: 'proposition'; id: number }
/** Union of all entity ref types supported in Euclid chat */
export type EuclidEntityRef = GeometricEntityRef | FoundationEntityRef
export function isGeometricEntity(entity: EuclidEntityRef): entity is GeometricEntityRef {
return (
entity.type === 'segment' ||
entity.type === 'triangle' ||
entity.type === 'angle' ||
entity.type === 'point'
)
}
export function isFoundationEntity(entity: EuclidEntityRef): entity is FoundationEntityRef {
return (
entity.type === 'definition' ||
entity.type === 'postulate' ||
entity.type === 'commonNotion' ||
entity.type === 'proposition'
)
}
/** Convert a FoundationEntityRef to the citation key format used by CitationPopover (e.g. "Def.15", "Post.1") */
export function foundationToCitationKey(entity: FoundationEntityRef): string {
switch (entity.type) {
case 'definition':
return `Def.${entity.id}`
case 'postulate':
return `Post.${entity.id}`
case 'commonNotion':
return `C.N.${entity.id}`
case 'proposition':
return `I.${entity.id}`
}
}
export type TextSegment =
| { kind: 'text'; text: string }
| { kind: 'entity'; text: string; entity: GeometricEntityRef }
/** Display text for each entity type */
function displayText(tag: string, labels: string): string {
switch (tag) {
case 'seg':
return labels // "AB"
case 'tri':
return `△${labels}` // "△ABC"
case 'ang':
return `∠${labels}` // "∠ABC"
case 'pt':
return labels // "A"
default:
return labels
}
}
/** Build entity ref from tag and labels, or null if invalid. */
function buildEntity(tag: string, labels: string): GeometricEntityRef | null {
switch (tag) {
case 'seg':
if (labels.length === 2) {
return { type: 'segment', from: labels[0], to: labels[1] }
}
return null
case 'tri':
if (labels.length === 3) {
return { type: 'triangle', vertices: [labels[0], labels[1], labels[2]] }
}
return null
case 'ang':
if (labels.length === 3) {
return { type: 'angle', points: [labels[0], labels[1], labels[2]] }
}
return null
case 'pt':
if (labels.length === 1) {
return { type: 'point', label: labels[0] }
}
return null
default:
return null
}
}
/**
* Convert LaTeX-style geometric notation from voice transcripts to our marker syntax.
*
* Why post-processing instead of prompting the voice model to use {seg:AB} markers?
* The voice model generates *speech* — the transcript is a byproduct of audio output.
* If we instructed it to use {seg:AB} markers, it would literally say "open brace seg
* colon A B close brace" aloud. The model naturally speaks "segment A B" and its
* transcript formatter renders that as LaTeX: \( AB \). We convert that to our markers
* so the shared chat history gets hoverable entity highlights.
*
* The text chat model CAN be prompted to use {seg:AB} directly because it only produces
* text, never speech.
*
* Patterns handled:
* \( \triangle ABC \) → {tri:ABC}
* \( \angle ABC \) → {ang:ABC}
* \( AB = CD \) → {seg:AB} = {seg:CD}
* \( AB \) → {seg:AB}
* \( A \) → {pt:A}
*/
export function latexToMarkers(text: string): string {
return (
text
// \( \triangle ABC \) → {tri:ABC}
.replace(/\\\(\s*\\triangle\s+([A-Z]{3})\s*\\\)/g, '{tri:$1}')
// \( \angle ABC \) → {ang:ABC}
.replace(/\\\(\s*\\angle\s+([A-Z]{3})\s*\\\)/g, '{ang:$1}')
// \( AB = CD \) → {seg:AB} = {seg:CD} (segment equations)
.replace(/\\\(\s*([A-Z]{2})\s*=\s*([A-Z]{2})\s*\\\)/g, '{seg:$1} = {seg:$2}')
// \( AB \) → {seg:AB} (two uppercase letters = segment)
.replace(/\\\(\s*([A-Z]{2})\s*\\\)/g, '{seg:$1}')
// \( A \) → {pt:A} (single uppercase letter = point)
.replace(/\\\(\s*([A-Z])\s*\\\)/g, '{pt:$1}')
)
}
// Match {tag:LABELS} where tag is seg|tri|ang|pt and LABELS is uppercase letters,
// or {tag:N} where tag is def|post|cn|prop and N is a number
const MARKER_RE = /\{(seg|tri|ang|pt):([A-Z]+)\}|\{(def|post|cn|prop):(\d+)\}/g
/**
* Parse text for structured geometric entity markers.
*
* `knownLabels` is accepted for API compatibility but not used for filtering —
* the LLM explicitly marks entities so we trust its output.
*/
export function parseGeometricEntities(text: string, _knownLabels?: Set<string>): TextSegment[] {
const result: TextSegment[] = []
let lastIndex = 0
let match: RegExpExecArray | null
// Reset regex state
MARKER_RE.lastIndex = 0
while ((match = MARKER_RE.exec(text)) !== null) {
const [full, tag, labels] = match
const entity = buildEntity(tag!, labels!)
if (!entity) continue
// Add preceding text
if (match.index > lastIndex) {
result.push({ kind: 'text', text: text.slice(lastIndex, match.index) })
}
result.push({
kind: 'entity',
text: displayText(tag!, labels!),
entity,
})
lastIndex = match.index + full!.length
}
// Add trailing text
if (lastIndex < text.length) {
result.push({ kind: 'text', text: text.slice(lastIndex) })
}
// If no markers found, return the whole thing as text
if (result.length === 0) {
return [{ kind: 'text', text }]
}
return result
}
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