/**
 * 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' };
  }
}
