Research-Stack/4-Infrastructure/shim/alphaproof_loop.py

"""
AlphaProof-inspired proof search loop.

Generates Lean proof candidates via a local LLM (Ollama), verifies them
through lake build, and iterates with error feedback until a valid proof
is found or max iterations exhausted.

Logs all iterations to JSONL for replay analysis.
"""

import json
import os
import re
import subprocess
import sys
import tempfile
import time
from datetime import datetime, timezone
from pathlib import Path
from typing import Optional, List, Dict

sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "4-Infrastructure"))
from lib.q16 import Q16_SCALE, q16_mul, to_q16

try:
    import requests
    HAS_REQUESTS = True
except ImportError:
    HAS_REQUESTS = False

# Import pre-filter for copy-if pattern
try:
    from lean_proof_prefilter import analyze_file, classify_theorem, extract_theorems
    HAS_PREFILTER = True
except ImportError:
    HAS_PREFILTER = False


# ---------------------------------------------------------------------------
# Configuration
# ---------------------------------------------------------------------------

OLLAMA_URL = os.environ.get("OLLAMA_URL", "http://localhost:11434")
DEFAULT_MODEL = os.environ.get("ALPHAPROOF_MODEL", "deepseek-coder-v2:16b")
LOG_DIR = Path(__file__).parent / "alphaproof_logs"


# ---------------------------------------------------------------------------
# Ollama LLM interface
# ---------------------------------------------------------------------------

def generate_candidate(prompt: str, model: str = DEFAULT_MODEL,
                       temperature: float = 0.7) -> str:
    """Call Ollama API to generate a candidate Lean proof.

    Args:
        prompt: The problem description + error feedback.
        model: Ollama model name.
        temperature: Sampling temperature.

    Returns:
        Generated Lean code string.
    """
    if not HAS_REQUESTS:
        raise ImportError("requests library required. pip install requests")

    system_prompt = (
        "You are a Lean 4 theorem prover. Given a mathematical problem, "
        "generate a complete, compilable Lean 4 module with all necessary "
        "imports. Use `import Mathlib` for standard library. "
        "Output ONLY the Lean code, no markdown fences or explanations. "
        "The module must compile with `lake build`."
    )

    payload = {
        "model": model,
        "system": system_prompt,
        "prompt": prompt,
        "stream": False,
        "options": {
            "temperature": temperature,
            "num_predict": 4096,
        }
    }

    try:
        resp = requests.post(f"{OLLAMA_URL}/api/generate", json=payload,
                             timeout=120)
        resp.raise_for_status()
        result = resp.json()
        code = result.get("response", "")
        # Strip markdown fences if present
        code = re.sub(r'^```(?:lean|lean4)?\s*\n?', '', code, flags=re.MULTILINE)
        code = re.sub(r'\n?```\s*$', '', code, flags=re.MULTILINE)
        return code.strip()
    except requests.RequestException as e:
        return f"-- ERROR: Ollama request failed: {e}"


# ---------------------------------------------------------------------------
# Lean verification
# ---------------------------------------------------------------------------

def verify_proof(lean_code: str, module_name: str = "Candidate",
                 lake_project: Optional[str] = None,
                 timeout: int = 120) -> dict:
    """Write Lean code to a temp file and verify via lake build.

    Args:
        lean_code: Complete Lean 4 module source.
        module_name: Name for the temp module file.
        lake_project: Path to existing lake project. If None, creates a temp one.
        timeout: Build timeout in seconds.

    Returns:
        {'success': bool, 'errors': list[str], 'warnings': list[str]}
    """
    errors = []
    warnings = []

    with tempfile.TemporaryDirectory(prefix="alphaproof_") as tmpdir:
        tmpdir = Path(tmpdir)

        if lake_project is None:
            # Create a minimal lake project
            lakefile = tmpdir / "lakefile.lean"
            lakefile.write_text(
                'import Lake\n'
                'open Lake DSL in\n'
                'package «candidate» where\n'
                '  leanOptions := #[\n'
                '    ⟨`pp.unicode.fun, true⟩\n'
                '  ]\n\n'
                'require mathlib from git\n'
                '  "https://github.com/leanprover-community/mathlib4" @ "master"\n'
            )
            project_dir = tmpdir
        else:
            project_dir = Path(lake_project)

        # Write candidate file
        candidate_dir = project_dir / "Candidate"
        candidate_dir.mkdir(exist_ok=True)
        candidate_file = candidate_dir / f"{module_name}.lean"
        candidate_file.write_text(lean_code)

        # Run lake build
        try:
            result = subprocess.run(
                ["lake", "build", f"Candidate.{module_name}"],
                cwd=str(project_dir),
                capture_output=True,
                text=True,
                timeout=timeout,
                env={**os.environ, "LAKE_PATH": str(project_dir)}
            )

            if result.returncode == 0:
                return {'success': True, 'errors': [], 'warnings': []}

            # Parse errors from stderr
            stderr = result.stderr
            error_lines = []
            for line in stderr.split('\n'):
                line = line.strip()
                if not line:
                    continue
                if 'error' in line.lower():
                    error_lines.append(line)
                elif 'warning' in line.lower():
                    warnings.append(line)
                elif line.startswith('error:') or 'Error' in line:
                    error_lines.append(line)

            if not error_lines and stderr:
                error_lines = [stderr[:500]]

            return {
                'success': False,
                'errors': error_lines,
                'warnings': warnings
            }

        except subprocess.TimeoutExpired:
            return {
                'success': False,
                'errors': [f'Build timed out after {timeout}s'],
                'warnings': []
            }
        except FileNotFoundError:
            return {
                'success': False,
                'errors': ['lake command not found. Is Lean/Lake installed?'],
                'warnings': []
            }


# ---------------------------------------------------------------------------
# FPGA Q16 acceleration (Python placeholder)
# ---------------------------------------------------------------------------
def q16_to_float(q: int) -> float:
    """Convert Q16.16 to float."""
    return q / Q16_SCALE


def fpga_accelerate(candidates: list[dict]) -> list[dict]:
    """Rank candidates using Q16.16 fixed-point scoring.

    This is a Python placeholder for FPGA Q16 LUT acceleration.
    In production, this would route through UART to the Tang Nano 9K
    or direct memory-mapped LUT access.

    Scoring heuristic:
        - Shorter proofs score higher (fewer tokens)
        - Proofs with fewer sorry/axiom/admit score higher
        - Previous success patterns boost score

    Args:
        candidates: list of {'code': str, 'iteration': int, ...}

    Returns:
        Candidates sorted by Q16 score (descending), with 'q16_score' added.
    """
    scored = []
    for c in candidates:
        code = c.get('code', '')

        # Length penalty (shorter is better)
        length_score = to_q16(1.0 / (1.0 + len(code) / 1000.0))

        # Penalty for incomplete proofs
        penalty = 0
        for bad_word in ['sorry', 'admit', 'axiom', 'by omega']:
            count = code.count(bad_word)
            penalty += to_q16(count * 0.1)

        # Base score from length
        base = length_score

        # Bonus for having structure (def, theorem, proof)
        if 'theorem' in code or 'lemma' in code:
            base = q16_mul(base, to_q16(1.2))

        final_score = max(0, base - penalty)
        c['q16_score'] = final_score
        c['q16_score_float'] = q16_to_float(final_score)
        scored.append(c)

    scored.sort(key=lambda x: x.get('q16_score', 0), reverse=True)
    return scored


# ---------------------------------------------------------------------------
# Proof prioritization (copy-if pre-filter)
# ---------------------------------------------------------------------------


def prioritize_problems(lean_dir: str, max_problems: int = 20) -> List[Dict]:
    """Pre-filter and prioritize proof problems using the copy-if pattern.

    Scans the Lean codebase, classifies theorems as trivial/non-trivial,
    and returns the highest-priority non-trivial problems for the LLM.

    This is the Lean equivalent of the vectorized copy_if:
    - Trivial theorems (zero deltas) = skip
    - Non-trivial theorems (non-zero deltas) = feed to solver

    Args:
        lean_dir: Path to Lean source directory.
        max_problems: Maximum number of problems to return.

    Returns:
        List of prioritized problem dicts with file, theorem, and priority.
    """
    if not HAS_PREFILTER:
        print("[alphaproof] pre-filter not available, using default order")
        return []

    problems = []
    lean_path = Path(lean_dir)

    for lean_file in sorted(lean_path.rglob('*.lean')):
        if '.lake' in str(lean_file):
            continue
        try:
            analysis = analyze_file(str(lean_file))
            for thm in analysis['theorems']:
                if thm['classification'] == 'non_trivial':
                    # Priority: more tactics = harder = higher priority
                    tactic_count = len(thm.get('category', '').split(','))
                    has_sorry = 'sorry' in thm.get('category', '')
                    priority = tactic_count + (10 if has_sorry else 0)

                    problems.append({
                        'file': str(lean_file),
                        'theorem': thm['name'],
                        'kind': thm['kind'],
                        'line': thm['line'],
                        'category': thm['category'],
                        'priority': priority,
                        'block': thm['block'],
                    })
        except Exception:
            continue

    # Sort by priority (highest first = hardest problems first)
    problems.sort(key=lambda p: p['priority'], reverse=True)

    # Deduplicate by theorem name
    seen = set()
    unique = []
    for p in problems:
        if p['theorem'] not in seen:
            seen.add(p['theorem'])
            unique.append(p)

    return unique[:max_problems]


def batch_proof_search(lean_dir: str, max_iterations: int = 10,
                       model: str = DEFAULT_MODEL,
                       lake_project: Optional[str] = None) -> Dict:
    """Run AlphaProof on prioritized non-trivial theorems.

    Uses the copy-if pre-filter to skip trivial theorems and focus
    the LLM solver on the hardest problems first.
    """
    problems = prioritize_problems(lean_dir)

    if not problems:
        print("[alphaproof] no non-trivial problems found")
        return {'problems': [], 'results': []}

    print(f"[alphaproof] found {len(problems)} non-trivial problems")
    print(f"[alphaproof] top 5: {[p['theorem'] for p in problems[:5]]}")

    results = []
    for i, problem in enumerate(problems):
        print(f"\n[alphaproof] [{i+1}/{len(problems)}] {problem['theorem']}"
              f" (priority={problem['priority']}, category={problem['category']})")

        # Build prompt from the theorem block
        prompt = (
            f"Prove this Lean 4 theorem. The file is {problem['file']}, "
            f"line {problem['line']}.\n\n"
            f"```lean\n{problem['block']}\n```\n\n"
            f"Replace the sorry with a complete proof. "
            f"Use omega, simp, decide, norm_num, ring, or linarith as appropriate."
        )

        result = search_loop(
            problem=prompt,
            max_iterations=max_iterations,
            model=model,
            lake_project=lake_project,
        )

        results.append({
            'theorem': problem['theorem'],
            'file': problem['file'],
            'priority': problem['priority'],
            'success': result['success'],
            'iterations': result['iterations'],
            'solution': result.get('solution', ''),
        })

        if result['success']:
            print(f"[alphaproof] SOLVED {problem['theorem']} "
                  f"in {result['iterations']} iterations")
        else:
            print(f"[alphaproof] FAILED {problem['theorem']} "
                  f"after {result['iterations']} iterations")

    # Summary
    solved = sum(1 for r in results if r['success'])
    print(f"\n[alphaproof] summary: {solved}/{len(results)} solved")

    return {
        'problems': problems,
        'results': results,
        'solved': solved,
        'total': len(results),
    }


# Main search loop
# ---------------------------------------------------------------------------

def search_loop(problem: str, max_iterations: int = 50,
                model: str = DEFAULT_MODEL,
                lake_project: Optional[str] = None,
                temperature: float = 0.7,
                build_timeout: int = 120) -> dict:
    """Main AlphaProof search loop: generate → verify → feedback → retry.

    Args:
        problem: Natural language description of the problem to prove.
        max_iterations: Maximum number of generate-verify cycles.
        model: Ollama model to use.
        lake_project: Optional path to existing lake project.
        temperature: LLM temperature.
        build_timeout: Lean build timeout per iteration.

    Returns:
        {'solution': str, 'iterations': int, 'success': bool,
         'candidates': list[dict], 'log_path': str}
    """
    LOG_DIR.mkdir(parents=True, exist_ok=True)
    log_path = LOG_DIR / f"search_{datetime.now(timezone.utc).strftime('%Y%m%d_%H%M%S')}.jsonl"

    candidates = []
    best_solution = ""
    feedback = ""

    with open(log_path, 'w') as log_f:
        for iteration in range(1, max_iterations + 1):
            t0 = time.time()

            # Build prompt with feedback from previous iterations
            if feedback:
                prompt = (
                    f"Problem:\n{problem}\n\n"
                    f"Previous attempt failed with these errors:\n{feedback}\n\n"
                    f"Please fix the Lean code and try again. "
                    f"Iteration {iteration}/{max_iterations}."
                )
            else:
                prompt = f"Problem:\n{problem}\n\nPlease write a Lean 4 proof."

            # Generate candidate
            code = generate_candidate(prompt, model=model,
                                      temperature=temperature)
            gen_time = time.time() - t0

            # Verify
            t1 = time.time()
            result = verify_proof(code, module_name=f"Iter{iteration}",
                                  lake_project=lake_project,
                                  timeout=build_timeout)
            ver_time = time.time() - t1

            candidate = {
                'iteration': iteration,
                'code': code,
                'success': result['success'],
                'errors': result['errors'],
                'warnings': result['warnings'],
                'gen_time': round(gen_time, 2),
                'verify_time': round(ver_time, 2),
                'timestamp': datetime.now(timezone.utc).isoformat(),
            }
            candidates.append(candidate)

            # Log to JSONL
            log_entry = {**candidate, 'code_length': len(code)}
            log_f.write(json.dumps(log_entry) + '\n')
            log_f.flush()

            if result['success']:
                best_solution = code
                # Rank remaining candidates via FPGA Q16 path
                candidates = fpga_accelerate(candidates)
                return {
                    'solution': best_solution,
                    'iterations': iteration,
                    'success': True,
                    'candidates': candidates,
                    'log_path': str(log_path),
                }

            # Build feedback for next iteration
            feedback = '\n'.join(result['errors'][:5])  # Top 5 errors
            print(f"[alphaproof] iter {iteration}/{max_iterations}: "
                  f"FAIL ({len(result['errors'])} errors, "
                  f"gen={gen_time:.1f}s, ver={ver_time:.1f}s)")

    # Exhausted iterations
    candidates = fpga_accelerate(candidates)
    return {
        'solution': best_solution,
        'iterations': max_iterations,
        'success': False,
        'candidates': candidates,
        'log_path': str(log_path),
    }


# ---------------------------------------------------------------------------
# CLI entry point
# ---------------------------------------------------------------------------

if __name__ == '__main__':
    import sys

    if len(sys.argv) < 2:
        print("Usage: python alphaproof_loop.py <problem_file_or_text> "
              "[--max-iter N] [--model MODEL]")
        print("       python alphaproof_loop.py --batch <lean_dir> "
              "[--max-iter N] [--model MODEL]")
        sys.exit(1)

    problem_arg = sys.argv[1]

    # Batch mode: run pre-filter on Lean codebase
    if problem_arg == '--batch':
        lean_dir = sys.argv[2] if len(sys.argv) > 2 else '.'
        max_iter = 10
        model_name = DEFAULT_MODEL

        for i, arg in enumerate(sys.argv[3:], 3):
            if arg == '--max-iter' and i + 1 < len(sys.argv):
                max_iter = int(sys.argv[i + 1])
            elif arg == '--model' and i + 1 < len(sys.argv):
                model_name = sys.argv[i + 1]

        result = batch_proof_search(lean_dir, max_iterations=max_iter,
                                    model=model_name)

        print(f"\n{'='*60}")
        print(f"Solved: {result['solved']}/{result['total']}")
        print(f"{'='*60}")
        sys.exit(0 if result['solved'] > 0 else 1)

    # Single problem mode
    if os.path.isfile(problem_arg):
        problem_text = Path(problem_arg).read_text()
    else:
        problem_text = problem_arg

    max_iter = 50
    model_name = DEFAULT_MODEL

    for i, arg in enumerate(sys.argv[2:], 2):
        if arg == '--max-iter' and i + 1 < len(sys.argv):
            max_iter = int(sys.argv[i + 1])
        elif arg == '--model' and i + 1 < len(sys.argv):
            model_name = sys.argv[i + 1]

    result = search_loop(problem_text, max_iterations=max_iter,
                         model=model_name)

    print(f"\n{'='*60}")
    print(f"Success: {result['success']}")
    print(f"Iterations: {result['iterations']}")
    print(f"Log: {result['log_path']}")
    if result['success']:
        print(f"\nSolution:\n{result['solution']}")