claude-flow
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Ruflo - Enterprise AI agent orchestration for Claude Code. Deploy 60+ specialized agents in coordinated swarms with self-learning, fault-tolerant consensus, vector memory, and MCP integration
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text/typescript
/**
* HoTT Engine - Homotopy Type Theory
*
* Implements Homotopy Type Theory operations:
* - Path equivalence checking
* - Transport along paths
* - Type inference and normalization
* - Proof verification
*
* Used for type-level reasoning and proof verification in agent systems.
*/
import type {
IHottEngine,
Path,
TypedValue,
WasmModule
} from '../types.js';
/**
* Type representation in HoTT
*/
interface HottType {
name: string;
params?: HottType[];
isPath?: boolean;
endpoints?: [unknown, unknown];
}
/**
* HottEngine - WASM wrapper for Homotopy Type Theory operations
*/
export class HottEngine implements IHottEngine {
private wasmModule: WasmModule | null = null;
private typeEnvironment: Map<string, HottType> = new Map();
private proofCache: Map<string, boolean> = new Map();
constructor(wasmModule?: WasmModule) {
this.wasmModule = wasmModule ?? null;
this.initializeBaseTypes();
}
/**
* Set the WASM module after initialization
*/
setWasmModule(module: WasmModule): void {
this.wasmModule = module;
}
/**
* Check if two paths are equivalent (homotopic)
*
* @param path1 - First path
* @param path2 - Second path
* @returns Whether the paths are equivalent
*/
async checkPathEquivalence(path1: Path, path2: Path): Promise<boolean> {
// Paths must have same endpoints
if (!this.equalValues(path1.source, path2.source) ||
!this.equalValues(path1.target, path2.target)) {
return false;
}
// Same type paths are equivalent if proofs can be transformed
if (path1.type !== path2.type) {
return false;
}
if (this.wasmModule && path1.proof && path2.proof) {
// Use WASM for complex path equivalence
// This would require serialization of proofs
const proof1Ptr = this.allocString(path1.proof);
const proof2Ptr = this.allocString(path2.proof);
const result = this.wasmModule.hott_path_equivalent(proof1Ptr, proof2Ptr);
this.freeString(proof1Ptr);
this.freeString(proof2Ptr);
return result;
}
// Pure JS: syntactic equivalence of proofs
return path1.proof === path2.proof;
}
/**
* Transport a value along a path
* If P: A -> Type and p: x = y, transport P p: P(x) -> P(y)
*
* @param path - Path to transport along
* @param value - Value to transport
* @returns Transported value
*/
async transportAlong(path: Path, value: TypedValue): Promise<TypedValue> {
// Verify value type matches path source
if (value.type !== path.type) {
throw new Error(
`Type mismatch: value has type ${value.type} but path is in type ${path.type}`
);
}
if (this.wasmModule) {
// Use WASM for transport
const pathPtr = this.allocPath(path);
const valuePtr = this.allocValue(value);
const resultPtr = this.wasmModule.hott_transport(pathPtr, valuePtr);
const result = this.readValue(resultPtr);
this.freePath(pathPtr);
this.freeValue(valuePtr);
this.freeValue(resultPtr);
return result;
}
// Pure JS: if source equals value, return target
if (this.equalValues(path.source, value.value)) {
return {
value: path.target,
type: value.type
};
}
// General transport - apply path transformation
return this.applyTransport(path, value);
}
/**
* Verify a proof of a proposition
*
* @param proposition - Proposition to verify
* @param proof - Proof term
* @returns Whether the proof is valid
*/
async verifyProof(proposition: string, proof: string): Promise<boolean> {
// Check cache
const cacheKey = `${proposition}:${proof}`;
if (this.proofCache.has(cacheKey)) {
return this.proofCache.get(cacheKey)!;
}
if (this.wasmModule) {
const propPtr = this.allocString(proposition);
const proofPtr = this.allocString(proof);
const result = this.wasmModule.hott_verify_proof(propPtr, proofPtr);
this.freeString(propPtr);
this.freeString(proofPtr);
this.proofCache.set(cacheKey, result);
return result;
}
// Pure JS: parse and type-check proof
const result = this.verifyProofJS(proposition, proof);
this.proofCache.set(cacheKey, result);
return result;
}
/**
* Infer the type of a term
*
* @param term - Term to type
* @returns Inferred type
*/
async inferType(term: string): Promise<string> {
if (this.wasmModule) {
const termPtr = this.allocString(term);
const resultPtr = this.wasmModule.hott_infer_type(termPtr);
const result = this.readString(resultPtr);
this.freeString(termPtr);
return result;
}
// Pure JS type inference
return this.inferTypeJS(term);
}
/**
* Normalize a term to its canonical form
*
* @param term - Term to normalize
* @returns Normalized term
*/
async normalize(term: string): Promise<string> {
if (this.wasmModule) {
const termPtr = this.allocString(term);
const resultPtr = this.wasmModule.hott_normalize(termPtr);
const result = this.readString(resultPtr);
this.freeString(termPtr);
return result;
}
// Pure JS normalization
return this.normalizeJS(term);
}
/**
* Create a reflexivity path (x = x)
*/
refl<T>(x: T, type: string): Path {
return {
source: x,
target: x,
type,
proof: `refl(${JSON.stringify(x)})`
};
}
/**
* Create a symmetry path (if p: x = y, then sym(p): y = x)
*/
sym(path: Path): Path {
return {
source: path.target,
target: path.source,
type: path.type,
proof: `sym(${path.proof})`
};
}
/**
* Create a transitivity path (if p: x = y and q: y = z, then trans(p,q): x = z)
*/
trans(path1: Path, path2: Path): Path {
if (!this.equalValues(path1.target, path2.source)) {
throw new Error('Paths not composable: endpoints do not match');
}
return {
source: path1.source,
target: path2.target,
type: path1.type,
proof: `trans(${path1.proof}, ${path2.proof})`
};
}
/**
* Apply a function to a path (ap)
*/
ap<A, B>(f: (a: A) => B, path: Path): Path {
return {
source: f(path.source as A),
target: f(path.target as A),
type: `${path.type} -> ${typeof f(path.source as A)}`,
proof: `ap(${f.toString()}, ${path.proof})`
};
}
/**
* Initialize base types
*/
private initializeBaseTypes(): void {
// Unit type
this.typeEnvironment.set('Unit', { name: 'Unit' });
// Boolean type
this.typeEnvironment.set('Bool', { name: 'Bool' });
// Natural numbers
this.typeEnvironment.set('Nat', { name: 'Nat' });
// Function type constructor
this.typeEnvironment.set('Arrow', {
name: 'Arrow',
params: [{ name: 'A' }, { name: 'B' }]
});
// Product type constructor
this.typeEnvironment.set('Prod', {
name: 'Prod',
params: [{ name: 'A' }, { name: 'B' }]
});
// Sum type constructor
this.typeEnvironment.set('Sum', {
name: 'Sum',
params: [{ name: 'A' }, { name: 'B' }]
});
// Identity/Path type
this.typeEnvironment.set('Id', {
name: 'Id',
params: [{ name: 'A' }, { name: 'x' }, { name: 'y' }],
isPath: true
});
}
/**
* Check value equality
*/
private equalValues(a: unknown, b: unknown): boolean {
if (a === b) return true;
if (typeof a !== typeof b) return false;
if (typeof a === 'object' && a !== null && b !== null) {
return JSON.stringify(a) === JSON.stringify(b);
}
return false;
}
/**
* Pure JS proof verification
*/
private verifyProofJS(proposition: string, proof: string): boolean {
// Parse proposition
const propParts = this.parseProposition(proposition);
// Parse proof
const proofParts = this.parseProof(proof);
// Check proof matches proposition
return this.checkProofMatches(propParts, proofParts);
}
/**
* Parse a proposition string
*/
private parseProposition(prop: string): { type: string; args: string[] } {
// Simple parsing: A = B, forall x:T. P, exists x:T. P
const eqMatch = prop.match(/(.+)\s*=\s*(.+)/);
if (eqMatch) {
const arg1 = eqMatch[1]?.trim() ?? '';
const arg2 = eqMatch[2]?.trim() ?? '';
return { type: 'eq', args: [arg1, arg2] };
}
const forallMatch = prop.match(/forall\s+(\w+)\s*:\s*(\w+)\s*\.\s*(.+)/);
if (forallMatch) {
return {
type: 'forall',
args: [forallMatch[1] ?? '', forallMatch[2] ?? '', forallMatch[3] ?? '']
};
}
return { type: 'atom', args: [prop] };
}
/**
* Parse a proof term
*/
private parseProof(proof: string): { constructor: string; args: string[] } {
const match = proof.match(/^(\w+)\((.*)\)$/);
if (match) {
return {
constructor: match[1] ?? 'var',
args: this.parseArgs(match[2] ?? '')
};
}
return { constructor: 'var', args: [proof] };
}
/**
* Parse comma-separated arguments
*/
private parseArgs(args: string): string[] {
const result: string[] = [];
let depth = 0;
let current = '';
for (const char of args) {
if (char === '(' || char === '[') depth++;
if (char === ')' || char === ']') depth--;
if (char === ',' && depth === 0) {
result.push(current.trim());
current = '';
} else {
current += char;
}
}
if (current.trim()) {
result.push(current.trim());
}
return result;
}
/**
* Check if proof matches proposition
*/
private checkProofMatches(
prop: { type: string; args: string[] },
proof: { constructor: string; args: string[] }
): boolean {
// Reflexivity proves x = x
if (proof.constructor === 'refl' && prop.type === 'eq') {
return prop.args[0] === prop.args[1];
}
// Symmetry proves y = x from x = y
if (proof.constructor === 'sym' && prop.type === 'eq') {
return true; // Would need to verify inner proof
}
// Transitivity proves x = z from x = y and y = z
if (proof.constructor === 'trans' && prop.type === 'eq') {
return proof.args.length === 2;
}
// Lambda proves forall
if (proof.constructor === 'lambda' && prop.type === 'forall') {
return true; // Would need to verify body
}
return false;
}
/**
* Pure JS type inference
*/
private inferTypeJS(term: string): string {
const parsed = this.parseProof(term);
switch (parsed.constructor) {
case 'refl':
return `Id(${parsed.args[0]}, ${parsed.args[0]}, ${parsed.args[0]})`;
case 'sym':
return 'Id'; // Would need to infer from argument
case 'trans':
return 'Id'; // Would need to infer from arguments
case 'lambda':
return 'Arrow'; // Would need to infer domain and codomain
case 'pair':
return 'Prod'; // Would need to infer components
default:
return 'Unknown';
}
}
/**
* Pure JS term normalization
*/
private normalizeJS(term: string): string {
// Beta reduction
let normalized = term;
// Simplify refl compositions
normalized = normalized.replace(/trans\(refl\(([^)]+)\),\s*([^)]+)\)/g, '$2');
normalized = normalized.replace(/trans\(([^)]+),\s*refl\(([^)]+)\)\)/g, '$1');
// Simplify sym(sym(p)) = p
normalized = normalized.replace(/sym\(sym\(([^)]+)\)\)/g, '$1');
return normalized;
}
/**
* Apply transport transformation
*/
private applyTransport(path: Path, value: TypedValue): TypedValue {
// For identity paths, transport is identity
if (this.equalValues(path.source, path.target)) {
return value;
}
// General case: transform value according to path
// This is a simplified implementation
const transformedValue = this.substituteInValue(
value.value,
path.source,
path.target
);
return {
value: transformedValue,
type: value.type
};
}
/**
* Substitute occurrences in a value
*/
private substituteInValue(value: unknown, from: unknown, to: unknown): unknown {
if (this.equalValues(value, from)) {
return to;
}
if (typeof value === 'object' && value !== null) {
if (Array.isArray(value)) {
return value.map(v => this.substituteInValue(v, from, to));
}
const result: Record<string, unknown> = {};
for (const [k, v] of Object.entries(value)) {
result[k] = this.substituteInValue(v, from, to);
}
return result;
}
return value;
}
// WASM memory allocation helpers (stubs for pure JS fallback)
private allocString(_s: string): number {
return 0;
}
private freeString(_ptr: number): void {}
private readString(_ptr: number): string {
return '';
}
private allocPath(_path: Path): number {
return 0;
}
private freePath(_ptr: number): void {}
private allocValue(_value: TypedValue): number {
return 0;
}
private freeValue(_ptr: number): void {}
private readValue(_ptr: number): TypedValue {
return { value: null, type: 'Unknown' };
}
}