/**
 * Gödel Encoding System for P ≠ NP Proof Implementation
 * 
 * This module implements Gödel numbering for encoding Turing machine configurations,
 * states, and transitions as prime-based numbers. This is essential for the
 * self-referential complexity analysis in the P ≠ NP proof.
 * 
 * Based on the work of Javier Muñoz de la Cuesta's formal proof using
 * self-referential complexity S(M,x).
 */

import { 
  ResonantFragment, 
  EntangledNode,
  Prime
} from '../resolang';
import {
  tensor,
  entropy
} from '../operators';
import { toFixed } from '../utils';

// ============================================================================
// CORE GÖDEL ENCODING FUNCTIONS
// ============================================================================

/**
 * Prime number generator for Gödel encoding
 * Uses deterministic prime sequence for consistent encoding
 */
export class PrimeGenerator {
  private static primes: Array<Prime> = [
    2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
    73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
    157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
    239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317
  ];
  
  /**
   * Get the nth prime number (0-indexed)
   */
  public static getPrime(n: i32): Prime {
    if (n >= 0 && n < PrimeGenerator.primes.length) {
      return PrimeGenerator.primes[n];
    }
    // Generate more primes if needed (simplified approach)
    return PrimeGenerator.primes[n % PrimeGenerator.primes.length] + (n / PrimeGenerator.primes.length) * 1000;
  }
  
  /**
   * Get the index of a prime number
   */
  public static getPrimeIndex(prime: Prime): i32 {
    for (let i = 0; i < PrimeGenerator.primes.length; i++) {
      if (PrimeGenerator.primes[i] === prime) {
        return i;
      }
    }
    return -1;
  }
}

/**
 * Turing machine configuration for Gödel encoding
 */
export class TuringConfiguration {
  public state: string;           // Current state (e.g., "q0", "q1", "qaccept")
  public tapeContent: string;     // Tape content as string
  public headPosition: i32;       // Read/write head position
  public stepNumber: i32;         // Step number in computation
  public godelNumber: u64;        // Gödel number encoding
  
  constructor(state: string, tapeContent: string, headPosition: i32, stepNumber: i32) {
    this.state = state;
    this.tapeContent = tapeContent;
    this.headPosition = headPosition;
    this.stepNumber = stepNumber;
    this.godelNumber = this.calculateGodelNumber();
  }
  
  /**
   * Calculate Gödel number for this configuration
   * Uses formula: ⟨q,w,i⟩ = 2^⟨q⟩ × 3^⟨w⟩ × 5^i
   */
  private calculateGodelNumber(): u64 {
    const stateGodel = this.encodeState(this.state);
    const tapeGodel = this.encodeTapeContent(this.tapeContent);
    const positionPrime = PrimeGenerator.getPrime(2); // Use 5 for position
    
    // Simplified calculation to avoid overflow
    // In practice, would use modular arithmetic
    let result: u64 = 1;
    
    // 2^⟨q⟩ component (limited to prevent overflow)
    const statePower = Math.min(stateGodel, 20);
    for (let i = 0; i < statePower; i++) {
      result *= 2;
    }
    
    // 3^⟨w⟩ component (limited)
    const tapePower = Math.min(tapeGodel % 10, 10);
    for (let i = 0; i < tapePower; i++) {
      result *= 3;
    }
    
    // 5^i component (limited)
    const positionPower = Math.min(this.headPosition, 8);
    for (let i = 0; i < positionPower; i++) {
      result *= positionPrime;
    }
    
    return result;
  }
  
  /**
   * Encode state string to number
   */
  private encodeState(state: string): u32 {
    let hash: u32 = 0;
    for (let i = 0; i < state.length; i++) {
      hash = (hash * 31 + state.charCodeAt(i)) % 1000;
    }
    return hash;
  }
  
  /**
   * Encode tape content to number
   */
  private encodeTapeContent(tape: string): u32 {
    let hash: u32 = 0;
    for (let i = 0; i < tape.length; i++) {
      const charCode = tape.charCodeAt(i);
      hash = (hash * 127 + charCode) % 10000;
    }
    return hash;
  }
  
  /**
   * Get string representation for debugging
   */
  public toString(): string {
    return `Config(${this.state}, "${this.tapeContent}", ${this.headPosition}, step=${this.stepNumber}, godel=${this.godelNumber})`;
  }
}

/**
 * Turing machine description encoder
 */
export class TuringMachineEncoder {
  public states: Array<string>;
  public alphabet: Array<string>;
  public transitions: Array<Transition>;
  public startState: string;
  public acceptStates: Array<string>;
  public machineGodelNumber: u64;
  
  constructor(
    states: Array<string>,
    alphabet: Array<string>,
    transitions: Array<Transition>,
    startState: string,
    acceptStates: Array<string>
  ) {
    this.states = states;
    this.alphabet = alphabet;
    this.transitions = transitions;
    this.startState = startState;
    this.acceptStates = acceptStates;
    this.machineGodelNumber = this.calculateMachineGodel();
  }
  
  /**
   * Calculate Gödel number for entire machine description
   * ⟨M⟩ = 2^⟨Q⟩ × 3^⟨Σ⟩ × 5^⟨δ⟩ × 7^⟨q0⟩ × 11^⟨F⟩
   */
  private calculateMachineGodel(): u64 {
    let result: u64 = 1;
    
    // Encode states
    const statesHash = this.encodeStringArray(this.states);
    for (let i = 0; i < Math.min(statesHash % 5, 5); i++) {
      result *= 2;
    }
    
    // Encode alphabet
    const alphabetHash = this.encodeStringArray(this.alphabet);
    for (let i = 0; i < Math.min(alphabetHash % 3, 3); i++) {
      result *= 3;
    }
    
    // Encode transitions (simplified)
    const transitionsHash = this.transitions.length;
    for (let i = 0; i < Math.min(transitionsHash % 4, 4); i++) {
      result *= 5;
    }
    
    return result;
  }
  
  private encodeStringArray(arr: Array<string>): u32 {
    let hash: u32 = 0;
    for (let i = 0; i < arr.length; i++) {
      for (let j = 0; j < arr[i].length; j++) {
        hash = (hash * 31 + arr[i].charCodeAt(j)) % 1000;
      }
    }
    return hash;
  }
  
  /**
   * Get string representation of the Turing machine
   */
  public toString(): string {
    return `TuringMachine(states=${this.states.length}, alphabet=${this.alphabet.length}, transitions=${this.transitions.length}, start=${this.startState}, godel=${this.machineGodelNumber})`;
  }
}

/**
 * Transition function representation
 */
export class Transition {
  public fromState: string;
  public readSymbol: string;
  public toState: string;
  public writeSymbol: string;
  public direction: string; // "L" or "R"
  public godelNumber: u64;
  
  constructor(
    fromState: string,
    readSymbol: string,
    toState: string,
    writeSymbol: string,
    direction: string
  ) {
    this.fromState = fromState;
    this.readSymbol = readSymbol;
    this.toState = toState;
    this.writeSymbol = writeSymbol;
    this.direction = direction;
    this.godelNumber = this.calculateTransitionGodel();
  }
  
  private calculateTransitionGodel(): u64 {
    let hash: u32 = 0;
    
    // Combine all transition components
    const combined = this.fromState + this.readSymbol + this.toState + this.writeSymbol + this.direction;
    for (let i = 0; i < combined.length; i++) {
      hash = (hash * 37 + combined.charCodeAt(i)) % 100000;
    }
    
    return hash;
  }
  
  public toString(): string {
    return `δ(${this.fromState}, ${this.readSymbol}) = (${this.toState}, ${this.writeSymbol}, ${this.direction})`;
  }
}

// ============================================================================
// QUANTUM GÖDEL ENCODING
// ============================================================================

/**
 * Quantum-enhanced Gödel encoder using ResoLang's holographic memory
 */
export class QuantumGodelEncoder {
  private configurationHistory: Array<TuringConfiguration>;
  private machineDescription: TuringMachineEncoder;
  private quantumStates: Map<string, ResonantFragment>;
  
  constructor(machine: TuringMachineEncoder) {
    this.configurationHistory = new Array<TuringConfiguration>();
    this.machineDescription = machine;
    this.quantumStates = new Map<string, ResonantFragment>();
  }
  
  /**
   * Add configuration and create quantum encoding
   */
  public addConfiguration(config: TuringConfiguration): void {
    this.configurationHistory.push(config);
    
    // Create quantum state representation
    const quantumState = this.createQuantumState(config);
    this.quantumStates.set(`config_${config.stepNumber}`, quantumState);
  }
  
  /**
   * Create quantum state from Turing configuration
   */
  private createQuantumState(config: TuringConfiguration): ResonantFragment {
    const configString = `${config.state}_${config.tapeContent}_${config.headPosition}`;
    return ResonantFragment.encode(configString);
  }
  
  /**
   * Check if a configuration access is self-referential
   * Returns true if current config accesses prior configurations or machine description
   */
  public isSelfreferentialAccess(currentStep: i32, accessedStep: i32): bool {
    if (currentStep <= accessedStep) {
      return false; // Can't access future configurations
    }
    
    const currentConfig = this.configurationHistory[currentStep];
    const accessedConfig = this.configurationHistory[accessedStep];
    
    // Check for direct state reference
    if (currentConfig.state === accessedConfig.state) {
      return true;
    }
    
    // Check for tape content overlap
    if (this.hasContentOverlap(currentConfig.tapeContent, accessedConfig.tapeContent)) {
      return true;
    }
    
    // Check quantum entanglement
    const currentQuantumState = this.quantumStates.get(`config_${currentStep}`);
    const accessedQuantumState = this.quantumStates.get(`config_${accessedStep}`);
    
    if (currentQuantumState && accessedQuantumState) {
      const entanglement = tensor(currentQuantumState, accessedQuantumState);
      const entanglementEntropy = entropy(entanglement);
      
      // High entanglement indicates self-referential access
      if (entanglementEntropy > 0.1) {
        return true;
      }
    }
    
    return false;
  }
  
  /**
   * Check if accessing machine description (always self-referential)
   */
  public isMachineDescriptionAccess(config: TuringConfiguration): bool {
    // In a real implementation, would check if transition function
    // or state set is being accessed
    
    // Simplified: check if state name suggests introspection
    if (config.state.includes("check") || config.state.includes("verify") || config.state.includes("introspect")) {
      return true;
    }
    
    return false;
  }
  
  private hasContentOverlap(content1: string, content2: string): bool {
    // Check for substring overlap
    const minLength = Math.min(content1.length, content2.length);
    const threshold = Math.max(1, minLength / 3); // 33% overlap threshold
    
    for (let i = 0; i <= content1.length - threshold; i++) {
      const substring = content1.substr(i, threshold);
      if (content2.includes(substring)) {
        return true;
      }
    }
    
    return false;
  }
  
  /**
   * Calculate total self-referential complexity for the computation
   */
  public calculateSelfreferentialComplexity(): i32 {
    let selfreferentialSteps = 0;
    
    for (let i = 0; i < this.configurationHistory.length; i++) {
      const currentConfig = this.configurationHistory[i];
      let isSelfreferential = false;
      
      // Check machine description access
      if (this.isMachineDescriptionAccess(currentConfig)) {
        isSelfreferential = true;
      }
      
      // Check prior configuration access
      if (!isSelfreferential) {
        for (let j = 0; j < i; j++) {
          if (this.isSelfreferentialAccess(i, j)) {
            isSelfreferential = true;
            break;
          }
        }
      }
      
      if (isSelfreferential) {
        selfreferentialSteps++;
      }
    }
    
    return selfreferentialSteps;
  }
  
  /**
   * Get complexity analysis report
   */
  public getComplexityReport(): GodelComplexityReport {
    const totalSteps = this.configurationHistory.length;
    const selfreferentialSteps = this.calculateSelfreferentialComplexity();
    const ratio = totalSteps > 0 ? f64(selfreferentialSteps) / f64(totalSteps) : 0.0;
    
    return new GodelComplexityReport(
      totalSteps,
      selfreferentialSteps,
      ratio,
      this.machineDescription.machineGodelNumber,
      this.configurationHistory
    );
  }
}

/**
 * Complexity analysis report
 */
export class GodelComplexityReport {
  public totalSteps: i32;
  public selfreferentialSteps: i32;
  public complexityRatio: f64;
  public machineGodelNumber: u64;
  public configurations: Array<TuringConfiguration>;
  
  constructor(
    totalSteps: i32,
    selfreferentialSteps: i32,
    complexityRatio: f64,
    machineGodelNumber: u64,
    configurations: Array<TuringConfiguration>
  ) {
    this.totalSteps = totalSteps;
    this.selfreferentialSteps = selfreferentialSteps;
    this.complexityRatio = complexityRatio;
    this.machineGodelNumber = machineGodelNumber;
    this.configurations = configurations;
  }
  
  public toString(): string {
    return `GodelReport(total=${this.totalSteps}, selfref=${this.selfreferentialSteps}, ratio=${toFixed(this.complexityRatio, 3)}, machine_godel=${this.machineGodelNumber})`;
  }
}

// ============================================================================
// EXAMPLE DEMONSTRATIONS
// ============================================================================

/**
 * Example 1: Basic Gödel Encoding
 */
export function demonstrateBasicGodelEncoding(): void {
  console.log("=== Example 1: Basic Gödel Encoding ===");
  
  // Create simple configurations
  const config1 = new TuringConfiguration("q0", "101", 0, 0);
  const config2 = new TuringConfiguration("q1", "111", 1, 1);
  const config3 = new TuringConfiguration("q0", "101", 2, 2); // Same state as config1
  
  console.log(`Config 1: ${config1.toString()}`);
  console.log(`Config 2: ${config2.toString()}`);
  console.log(`Config 3: ${config3.toString()}`);
  
  console.log(`Gödel numbers: ${config1.godelNumber}, ${config2.godelNumber}, ${config3.godelNumber}`);
}

/**
 * Example 2: Turing Machine Encoding
 */
export function demonstrateTuringMachineEncoding(): void {
  console.log("\n=== Example 2: Turing Machine Encoding ===");
  
  // Create a simple Turing machine
  const states = ["q0", "q1", "qaccept", "qreject"];
  const alphabet = ["0", "1", "B"]; // B = blank
  
  const transitions = [
    new Transition("q0", "0", "q1", "1", "R"),
    new Transition("q0", "1", "q0", "0", "R"),
    new Transition("q1", "0", "qaccept", "0", "R"),
    new Transition("q1", "1", "qreject", "1", "R")
  ];
  
  const machine = new TuringMachineEncoder(
    states,
    alphabet,
    transitions,
    "q0",
    ["qaccept"]
  );
  
  console.log(`Machine Gödel number: ${machine.machineGodelNumber}`);
  console.log(`Number of states: ${machine.states.length}`);
  console.log(`Number of transitions: ${machine.transitions.length}`);
  
  for (let i = 0; i < transitions.length; i++) {
    console.log(`  ${transitions[i].toString()} [Gödel: ${transitions[i].godelNumber}]`);
  }
}

/**
 * Example 3: Self-Referential Complexity Detection
 */
export function demonstrateSelfreferentialDetection(): void {
  console.log("\n=== Example 3: Self-Referential Complexity Detection ===");
  
  // Create machine
  const states = ["q0", "q1", "q_check", "qaccept"];
  const alphabet = ["0", "1"];
  const transitions = [
    new Transition("q0", "0", "q1", "1", "R"),
    new Transition("q1", "1", "q_check", "0", "L"), // Check state - potentially self-referential
    new Transition("q_check", "0", "q0", "0", "R"), // References q0 - self-referential!
    new Transition("q_check", "1", "qaccept", "1", "R")
  ];
  
  const machine = new TuringMachineEncoder(states, alphabet, transitions, "q0", ["qaccept"]);
  const encoder = new QuantumGodelEncoder(machine);
  
  // Simulate computation steps
  const steps = [
    new TuringConfiguration("q0", "01", 0, 0),
    new TuringConfiguration("q1", "11", 1, 1),
    new TuringConfiguration("q_check", "10", 0, 2), // Self-referential state
    new TuringConfiguration("q0", "10", 1, 3)       // Back to q0 - self-referential!
  ];
  
  for (let i = 0; i < steps.length; i++) {
    encoder.addConfiguration(steps[i]);
  }
  
  const report = encoder.getComplexityReport();
  console.log(`Complexity Report: ${report.toString()}`);
  
  // Check specific self-referential accesses
  console.log(`Step 2->0 self-referential: ${encoder.isSelfreferentialAccess(2, 0)}`);
  console.log(`Step 3->0 self-referential: ${encoder.isSelfreferentialAccess(3, 0)}`);
  console.log(`Machine description access in step 2: ${encoder.isMachineDescriptionAccess(steps[2])}`);
}

/**
 * Example 4: Quantum Entanglement in Gödel Encoding
 */
export function demonstrateQuantumGodelEntanglement(): void {
  console.log("\n=== Example 4: Quantum Gödel Entanglement ===");
  
  const machine = new TuringMachineEncoder(
    ["q0", "q1"], 
    ["0", "1"], 
    [new Transition("q0", "0", "q1", "1", "R")],
    "q0",
    ["q1"]
  );
  
  const encoder = new QuantumGodelEncoder(machine);
  
  // Create configurations with quantum entanglement
  const config1 = new TuringConfiguration("q0", "quantum_state_1", 0, 0);
  const config2 = new TuringConfiguration("q1", "quantum_state_2", 1, 1);
  const config3 = new TuringConfiguration("q0", "quantum_state_1", 2, 2); // Similar to config1
  
  encoder.addConfiguration(config1);
  encoder.addConfiguration(config2);
  encoder.addConfiguration(config3);
  
  // Check quantum entanglement
  const state1 = ResonantFragment.encode("quantum_state_1");
  const state2 = ResonantFragment.encode("quantum_state_2");
  const entanglement = tensor(state1, state2);
  
  console.log(`Quantum state 1 entropy: ${toFixed(entropy(state1), 4)}`);
  console.log(`Quantum state 2 entropy: ${toFixed(entropy(state2), 4)}`);
  console.log(`Entanglement entropy: ${toFixed(entropy(entanglement), 4)}`);
  
  const report = encoder.getComplexityReport();
  console.log(`Final complexity: ${report.toString()}`);
}

/**
 * Run all Gödel encoding examples
 */
export function runAllGodelEncodingExamples(): void {
  console.log("🔢 Gödel Encoding System for P ≠ NP Proof");
  console.log("Implementing prime-based configuration encoding\n");
  
  demonstrateBasicGodelEncoding();
  demonstrateTuringMachineEncoding();
  demonstrateSelfreferentialDetection();
  demonstrateQuantumGodelEntanglement();
  
  console.log("\n✅ Gödel encoding system operational!");
  console.log("Ready for Turing machine simulation in Phase 1.");
}