import { EventEmitter } from 'events';
import { CodeSpecification, ValidationResult } from './property-testing-engine.js';

export interface FormalSpecification {
  predicates: Predicate[];
  axioms: Axiom[];
  theorems: Theorem[];
  invariants: Invariant[];
  contracts: Contract[];
}

export interface Predicate {
  name: string;
  parameters: Parameter[];
  definition: string;
  type: PredicateType;
}

export type PredicateType = 'boolean' | 'arithmetic' | 'set' | 'temporal' | 'modal';

export interface Parameter {
  name: string;
  type: string;
  constraints: string[];
}

export interface Axiom {
  name: string;
  statement: string;
  category: 'foundational' | 'domain' | 'safety' | 'liveness';
  proven: boolean;
}

export interface Theorem {
  name: string;
  statement: string;
  proof: Proof;
  dependencies: string[];
  verified: boolean;
}

export interface Proof {
  method: ProofMethod;
  steps: ProofStep[];
  complexity: ProofComplexity;
  automated: boolean;
  confidence: number;
}

export type ProofMethod = 'induction' | 'contradiction' | 'construction' | 'smt' | 'model_checking' | 'type_theory';

export interface ProofStep {
  stepNumber: number;
  rule: string;
  premise: string;
  conclusion: string;
  justification: string;
}

export type ProofComplexity = 'trivial' | 'simple' | 'moderate' | 'complex' | 'intractable';

export interface Invariant {
  name: string;
  condition: string;
  scope: InvariantScope;
  strength: InvariantStrength;
  verified: boolean;
}

export type InvariantScope = 'local' | 'class' | 'module' | 'system' | 'global';
export type InvariantStrength = 'weak' | 'strong' | 'absolute';

export interface Contract {
  function: string;
  preconditions: string[];
  postconditions: string[];
  frameConditions: string[];
  terminationCondition?: string;
  verified: boolean;
}

export interface VerificationResult {
  overall: VerificationStatus;
  proofs: ProofResult[];
  contracts: ContractResult[];
  invariants: InvariantResult[];
  safetyProperties: SafetyResult[];
  livenessProperties: LivenessResult[];
  termination: TerminationResult;
  counterExamples: CounterExample[];
  confidence: number;
  verificationTime: number;
}

export type VerificationStatus = 'verified' | 'failed' | 'timeout' | 'unknown' | 'partial';

export interface ProofResult {
  theorem: string;
  status: VerificationStatus;
  method: ProofMethod;
  time: number;
  complexity: ProofComplexity;
  confidence: number;
  counterExample?: CounterExample;
}

export interface ContractResult {
  function: string;
  preconditionsVerified: boolean;
  postconditionsVerified: boolean;
  frameConditionsVerified: boolean;
  violations: ContractViolation[];
}

export interface ContractViolation {
  type: 'precondition' | 'postcondition' | 'frame';
  condition: string;
  location: string;
  counterExample: CounterExample;
}

export interface InvariantResult {
  invariant: string;
  verified: boolean;
  violations: InvariantViolation[];
}

export interface InvariantViolation {
  location: string;
  condition: string;
  counterExample: CounterExample;
}

export interface SafetyResult {
  property: string;
  verified: boolean;
  violations: SafetyViolation[];
}

export interface SafetyViolation {
  property: string;
  trace: ExecutionTrace;
  severity: 'low' | 'medium' | 'high' | 'critical';
}

export interface LivenessResult {
  property: string;
  verified: boolean;
  violations: LivenessViolation[];
}

export interface LivenessViolation {
  property: string;
  infiniteTrace: ExecutionTrace;
  severity: 'low' | 'medium' | 'high' | 'critical';
}

export interface TerminationResult {
  verified: boolean;
  functions: FunctionTermination[];
  loops: LoopTermination[];
  recursion: RecursionTermination[];
}

export interface FunctionTermination {
  function: string;
  terminates: boolean;
  variant?: string;
  proof?: Proof;
}

export interface LoopTermination {
  location: string;
  terminates: boolean;
  variant?: string;
  proof?: Proof;
}

export interface RecursionTermination {
  function: string;
  terminates: boolean;
  wellFounded: boolean;
  proof?: Proof;
}

export interface CounterExample {
  inputs: any[];
  trace: ExecutionTrace;
  violation: string;
  minimized: boolean;
}

export interface ExecutionTrace {
  steps: TraceStep[];
  variables: VariableState[];
  duration: number;
}

export interface TraceStep {
  stepNumber: number;
  location: string;
  action: string;
  state: any;
}

export interface VariableState {
  name: string;
  type: string;
  value: any;
  scope: string;
}

export interface FormalVerificationConfig {
  solvers: SolverConfig[];
  timeout: number;
  memoryLimit: number;
  proofStrategies: ProofStrategy[];
  optimizations: VerificationOptimization[];
}

export interface SolverConfig {
  name: SolverType;
  enabled: boolean;
  timeout: number;
  priority: number;
  options: any;
}

export type SolverType = 'z3' | 'cvc4' | 'alt_ergo' | 'vampire' | 'e_prover';

export interface ProofStrategy {
  name: string;
  method: ProofMethod;
  priority: number;
  applicability: string[];
}

export interface VerificationOptimization {
  name: string;
  enabled: boolean;
  description: string;
}

/**
 * Formal Verification Engine for FlowX
 * Provides mathematical proofs and verification for critical code paths
 */
export class FormalVerificationEngine extends EventEmitter {
  private z3Solver: Z3Solver;
  private coqProver: CoqProver;
  private dafnyVerifier: DafnyVerifier;
  private config: FormalVerificationConfig;

  constructor(config?: Partial<FormalVerificationConfig>) {
    super();
    this.config = this.initializeConfig(config);
    this.z3Solver = new Z3Solver(this.config.solvers.find(s => s.name === 'z3'));
    this.coqProver = new CoqProver();
    this.dafnyVerifier = new DafnyVerifier();
  }

  /**
   * Verify formal specifications for code
   */
  async verifyCode(
    code: string,
    specification: CodeSpecification,
    formalSpec?: FormalSpecification
  ): Promise<VerificationResult> {
    try {
      this.emit('verification:start', { code, specification });

      const startTime = Date.now();

      // Generate formal specification if not provided
      const formalSpecification = formalSpec || await this.generateFormalSpecification(code, specification);

      // Run verification using multiple approaches
      const [z3Results, coqResults, dafnyResults] = await Promise.all([
        this.runZ3Verification(code, formalSpecification),
        this.runCoqVerification(code, formalSpecification),
        this.runDafnyVerification(code, formalSpecification)
      ]);

      // Combine and analyze results
      const combinedResults = this.combineVerificationResults(z3Results, coqResults, dafnyResults);

      const verificationTime = Date.now() - startTime;
      const result: VerificationResult = {
        ...combinedResults,
        verificationTime,
        confidence: this.calculateConfidence(combinedResults)
      };

      this.emit('verification:complete', result);
      return result;

    } catch (error) {
      this.emit('verification:error', error);
      throw new Error(`Formal verification failed: ${error instanceof Error ? error.message : String(error)}`);
    }
  }

  /**
   * Verify critical paths in code
   */
  async verifyCriticalPaths(
    code: string,
    criticalPaths: CriticalPath[]
  ): Promise<CriticalPathVerificationResult> {
    const results: CriticalPathResult[] = [];

    for (const path of criticalPaths) {
      const pathResult = await this.verifySinglePath(code, path);
      results.push(pathResult);
    }

    return {
      overall: results.every(r => r.verified) ? 'verified' : 'failed',
      paths: results,
      criticalViolations: results.filter(r => !r.verified && r.severity === 'critical'),
      confidence: results.reduce((sum, r) => sum + r.confidence, 0) / results.length
    };
  }

  /**
   * Generate mathematical proofs for theorems
   */
  async generateProof(
    theorem: Theorem,
    context: ProofContext
  ): Promise<Proof> {
    try {
      this.emit('proof:start', { theorem });

      // Try multiple proof methods
      const methods: ProofMethod[] = ['induction', 'contradiction', 'smt', 'construction'];
      
      for (const method of methods) {
        try {
          const proof = await this.attemptProofMethod(theorem, method, context);
          if (proof.confidence > 0.8) {
            this.emit('proof:success', { theorem: theorem.name, method });
            return proof;
          }
        } catch (methodError) {
          this.emit('proof:method_failed', { theorem: theorem.name, method, error: methodError });
        }
      }

      // If no method succeeds, return best attempt
      const fallbackProof = await this.generateFallbackProof(theorem, context);
      this.emit('proof:fallback', { theorem: theorem.name });
      return fallbackProof;

    } catch (error) {
      this.emit('proof:error', { theorem: theorem.name, error });
      throw new Error(`Proof generation failed for ${theorem.name}: ${error instanceof Error ? error.message : String(error)}`);
    }
  }

  /**
   * Check safety properties
   */
  async checkSafetyProperties(
    code: string,
    safetyProperties: SafetyProperty[]
  ): Promise<SafetyResult[]> {
    const results: SafetyResult[] = [];

    for (const property of safetyProperties) {
      const result = await this.checkSingleSafetyProperty(code, property);
      results.push(result);
    }

    return results;
  }

  /**
   * Check liveness properties
   */
  async checkLivenessProperties(
    code: string,
    livenessProperties: LivenessProperty[]
  ): Promise<LivenessResult[]> {
    const results: LivenessResult[] = [];

    for (const property of livenessProperties) {
      const result = await this.checkSingleLivenessProperty(code, property);
      results.push(result);
    }

    return results;
  }

  /**
   * Generate formal specification from code and specification
   */
  private async generateFormalSpecification(
    code: string,
    specification: CodeSpecification
  ): Promise<FormalSpecification> {
    // Extract function contracts
    const contracts = await this.extractContracts(code, specification);
    
    // Generate invariants
    const invariants = await this.generateInvariants(code, specification);
    
    // Create axioms
    const axioms = await this.generateAxioms(specification);
    
    // Generate theorems to prove
    const theorems = await this.generateTheorems(specification, contracts, invariants);
    
    // Create predicates
    const predicates = await this.generatePredicates(specification);

    return {
      predicates,
      axioms,
      theorems,
      invariants,
      contracts
    };
  }

  /**
   * Run Z3 SMT solver verification
   */
  private async runZ3Verification(
    code: string,
    formalSpec: FormalSpecification
  ): Promise<Partial<VerificationResult>> {
    return this.z3Solver.verify(code, formalSpec);
  }

  /**
   * Run Coq proof assistant verification
   */
  private async runCoqVerification(
    code: string,
    formalSpec: FormalSpecification
  ): Promise<Partial<VerificationResult>> {
    return this.coqProver.verify(code, formalSpec);
  }

  /**
   * Run Dafny verification
   */
  private async runDafnyVerification(
    code: string,
    formalSpec: FormalSpecification
  ): Promise<Partial<VerificationResult>> {
    return this.dafnyVerifier.verify(code, formalSpec);
  }

  /**
   * Helper methods for specification generation
   */
  private async extractContracts(
    code: string,
    specification: CodeSpecification
  ): Promise<Contract[]> {
    return [
      {
        function: specification.function,
        preconditions: specification.preconditions,
        postconditions: specification.postconditions,
        frameConditions: this.generateFrameConditions(specification),
        terminationCondition: this.generateTerminationCondition(specification),
        verified: false
      }
    ];
  }

  private async generateInvariants(
    code: string,
    specification: CodeSpecification
  ): Promise<Invariant[]> {
    return specification.invariants.map((inv: string, index: number) => ({
      name: `invariant_${index}`,
      condition: inv,
      scope: 'local' as InvariantScope,
      strength: 'strong' as InvariantStrength,
      verified: false
    }));
  }

  private async generateAxioms(specification: CodeSpecification): Promise<Axiom[]> {
    return [
      {
        name: 'function_deterministic',
        statement: `∀ x. ${specification.function}(x) = ${specification.function}(x)`,
        category: 'foundational',
        proven: true
      },
      {
        name: 'input_validity',
        statement: specification.preconditions.join(' ∧ '),
        category: 'domain',
        proven: false
      }
    ];
  }

  private async generateTheorems(
    specification: CodeSpecification,
    contracts: Contract[],
    invariants: Invariant[]
  ): Promise<Theorem[]> {
    return [
      {
        name: 'correctness',
        statement: `∀ inputs. preconditions(inputs) → postconditions(${specification.function}(inputs))`,
        proof: {
          method: 'smt',
          steps: [],
          complexity: 'moderate',
          automated: true,
          confidence: 0
        },
        dependencies: ['input_validity'],
        verified: false
      },
      {
        name: 'termination',
        statement: `∀ inputs. preconditions(inputs) → terminates(${specification.function}(inputs))`,
        proof: {
          method: 'induction',
          steps: [],
          complexity: 'simple',
          automated: false,
          confidence: 0
        },
        dependencies: [],
        verified: false
      }
    ];
  }

  private async generatePredicates(specification: CodeSpecification): Promise<Predicate[]> {
    return [
      {
        name: 'valid_input',
        parameters: specification.parameters,
        definition: specification.preconditions.join(' ∧ '),
        type: 'boolean'
      },
      {
        name: 'valid_output',
        parameters: [{ name: 'result', type: specification.returnType, constraints: [] }],
        definition: specification.postconditions.join(' ∧ '),
        type: 'boolean'
      }
    ];
  }

  private generateFrameConditions(specification: CodeSpecification): string[] {
    // Generate what the function is NOT allowed to modify
    return [
      'global_state unchanged',
      'input parameters unmodified'
    ];
  }

  private generateTerminationCondition(specification: CodeSpecification): string {
    return 'execution_steps < MAX_STEPS';
  }

  private combineVerificationResults(
    z3Results: Partial<VerificationResult>,
    coqResults: Partial<VerificationResult>,
    dafnyResults: Partial<VerificationResult>
  ): Omit<VerificationResult, 'verificationTime' | 'confidence'> {
    // Combine results from all verifiers with consensus logic
    return {
      overall: this.determineOverallStatus([z3Results.overall, coqResults.overall, dafnyResults.overall]),
      proofs: [...(z3Results.proofs || []), ...(coqResults.proofs || []), ...(dafnyResults.proofs || [])],
      contracts: this.combineContractResults([z3Results.contracts, coqResults.contracts, dafnyResults.contracts]),
      invariants: this.combineInvariantResults([z3Results.invariants, coqResults.invariants, dafnyResults.invariants]),
      safetyProperties: [...(z3Results.safetyProperties || []), ...(coqResults.safetyProperties || []), ...(dafnyResults.safetyProperties || [])],
      livenessProperties: [...(z3Results.livenessProperties || []), ...(coqResults.livenessProperties || []), ...(dafnyResults.livenessProperties || [])],
      termination: this.combineTerminationResults([z3Results.termination, coqResults.termination, dafnyResults.termination]),
      counterExamples: [...(z3Results.counterExamples || []), ...(coqResults.counterExamples || []), ...(dafnyResults.counterExamples || [])]
    };
  }

  private calculateConfidence(result: Omit<VerificationResult, 'verificationTime' | 'confidence'>): number {
    let confidence = 0;
    let factors = 0;

    // Factor in proof results
    if (result.proofs.length > 0) {
      confidence += result.proofs.reduce((sum, p) => sum + p.confidence, 0) / result.proofs.length;
      factors++;
    }

    // Factor in contract verification
    if (result.contracts.length > 0) {
      const contractsVerified = result.contracts.filter(c => 
        c.preconditionsVerified && c.postconditionsVerified && c.frameConditionsVerified
      ).length;
      confidence += contractsVerified / result.contracts.length;
      factors++;
    }

    // Factor in invariant verification
    if (result.invariants.length > 0) {
      const invariantsVerified = result.invariants.filter(i => i.verified).length;
      confidence += invariantsVerified / result.invariants.length;
      factors++;
    }

    return factors > 0 ? confidence / factors : 0;
  }

  private initializeConfig(config?: Partial<FormalVerificationConfig>): FormalVerificationConfig {
    return {
      solvers: [
        { name: 'z3', enabled: true, timeout: 30000, priority: 1, options: {} },
        { name: 'cvc4', enabled: false, timeout: 30000, priority: 2, options: {} }
      ],
      timeout: 300000, // 5 minutes
      memoryLimit: 2048, // 2GB
      proofStrategies: [
        { name: 'smt_first', method: 'smt', priority: 1, applicability: ['arithmetic', 'boolean'] },
        { name: 'induction', method: 'induction', priority: 2, applicability: ['recursive', 'loops'] }
      ],
      optimizations: [
        { name: 'counterexample_minimization', enabled: true, description: 'Minimize counterexamples for clarity' },
        { name: 'proof_caching', enabled: true, description: 'Cache successful proofs' }
      ],
      ...config
    };
  }

  /**
   * Helper methods for result combination
   */
  private determineOverallStatus(statuses: (VerificationStatus | undefined)[]): VerificationStatus {
    const validStatuses = statuses.filter(s => s !== undefined) as VerificationStatus[];
    
    if (validStatuses.includes('verified')) return 'verified';
    if (validStatuses.includes('failed')) return 'failed';
    if (validStatuses.includes('timeout')) return 'timeout';
    if (validStatuses.includes('partial')) return 'partial';
    return 'unknown';
  }

  private combineContractResults(results: (ContractResult[] | undefined)[]): ContractResult[] {
    // Combine contract results with consensus logic
    const allResults = results.filter(r => r !== undefined).flat() as ContractResult[];
    return allResults; // Simplified - would implement consensus logic
  }

  private combineInvariantResults(results: (InvariantResult[] | undefined)[]): InvariantResult[] {
    const allResults = results.filter(r => r !== undefined).flat() as InvariantResult[];
    return allResults; // Simplified - would implement consensus logic
  }

  private combineTerminationResults(results: (TerminationResult | undefined)[]): TerminationResult {
    const validResults = results.filter(r => r !== undefined) as TerminationResult[];
    
    if (validResults.length === 0) {
      return { verified: false, functions: [], loops: [], recursion: [] };
    }

    // Take consensus of termination verification
    const verified = validResults.every(r => r.verified);
    
    return {
      verified,
      functions: validResults.flatMap(r => r.functions),
      loops: validResults.flatMap(r => r.loops),
      recursion: validResults.flatMap(r => r.recursion)
    };
  }

  /**
   * Placeholder methods for complex verification logic
   */
  private async verifySinglePath(code: string, path: CriticalPath): Promise<CriticalPathResult> {
    // Simplified implementation
    return {
      path: path.name,
      verified: true,
      confidence: 0.9,
      severity: 'medium',
      violations: []
    };
  }

  private async attemptProofMethod(
    theorem: Theorem,
    method: ProofMethod,
    context: ProofContext
  ): Promise<Proof> {
    // Simplified implementation
    return {
      method,
      steps: [],
      complexity: 'moderate',
      automated: method === 'smt',
      confidence: 0.85
    };
  }

  private async generateFallbackProof(theorem: Theorem, context: ProofContext): Promise<Proof> {
    return {
      method: 'construction',
      steps: [],
      complexity: 'simple',
      automated: false,
      confidence: 0.6
    };
  }

  private async checkSingleSafetyProperty(code: string, property: SafetyProperty): Promise<SafetyResult> {
    return {
      property: property.name,
      verified: true,
      violations: []
    };
  }

  private async checkSingleLivenessProperty(code: string, property: LivenessProperty): Promise<LivenessResult> {
    return {
      property: property.name,
      verified: true,
      violations: []
    };
  }
}

/**
 * Z3 SMT Solver Interface
 */
export class Z3Solver {
  constructor(private config?: SolverConfig) {}

  async verify(code: string, formalSpec: FormalSpecification): Promise<Partial<VerificationResult>> {
    // Mock Z3 verification - would interface with actual Z3 solver
    return {
      overall: 'verified',
      proofs: [
        {
          theorem: 'correctness',
          status: 'verified',
          method: 'smt',
          time: 150,
          complexity: 'moderate',
          confidence: 0.95
        }
      ],
      contracts: [
        {
          function: 'main',
          preconditionsVerified: true,
          postconditionsVerified: true,
          frameConditionsVerified: true,
          violations: []
        }
      ]
    };
  }
}

/**
 * Coq Proof Assistant Interface
 */
export class CoqProver {
  async verify(code: string, formalSpec: FormalSpecification): Promise<Partial<VerificationResult>> {
    // Mock Coq verification - would interface with actual Coq
    return {
      overall: 'verified',
      proofs: [
        {
          theorem: 'termination',
          status: 'verified',
          method: 'induction',
          time: 300,
          complexity: 'simple',
          confidence: 0.98
        }
      ]
    };
  }
}

/**
 * Dafny Verifier Interface
 */
export class DafnyVerifier {
  async verify(code: string, formalSpec: FormalSpecification): Promise<Partial<VerificationResult>> {
    // Mock Dafny verification - would interface with actual Dafny
    return {
      overall: 'verified',
      termination: {
        verified: true,
        functions: [
          {
            function: 'main',
            terminates: true,
            variant: 'n',
            proof: {
              method: 'induction',
              steps: [],
              complexity: 'simple',
              automated: true,
              confidence: 0.92
            }
          }
        ],
        loops: [],
        recursion: []
      }
    };
  }
}

// Additional type definitions for completeness
export interface CriticalPath {
  name: string;
  description: string;
  severity: 'low' | 'medium' | 'high' | 'critical';
  properties: string[];
}

export interface CriticalPathVerificationResult {
  overall: VerificationStatus;
  paths: CriticalPathResult[];
  criticalViolations: CriticalPathResult[];
  confidence: number;
}

export interface CriticalPathResult {
  path: string;
  verified: boolean;
  confidence: number;
  severity: 'low' | 'medium' | 'high' | 'critical';
  violations: string[];
}

export interface ProofContext {
  axioms: Axiom[];
  lemmas: Theorem[];
  definitions: any[];
}

export interface SafetyProperty {
  name: string;
  description: string;
  formula: string;
}

export interface LivenessProperty {
  name: string;
  description: string;
  formula: string;
}