#!/usr/bin/env python3
"""Formal theory validation template — L4 SymPy-based checks.

Used to validate formal theory candidates via aitp_verify_dimensions,
aitp_verify_algebra, aitp_verify_limit.

Input contract:
  - Read a candidate's claim, relevant equation, and physical parameters
  - Return dict of check results suitable for aitp_submit_l4_review

Output contract:
  - check_results dict with keys: dimensional_consistency, limiting_case_check,
    correspondence_check, symmetry_compatibility, conservation_check (pass/fail per key)
  - Prints JSON to stdout

Usage:
  python formal_theory_validation.py --equation "H = hbar*omega*(N+1/2)" \\
    --dimensions '{"H":"energy","hbar":"action","omega":"frequency","N":"number"}'
"""

import argparse
import json
import sys


def check_dimensional_consistency(equation: str, dimensions: dict[str, str]) -> dict:
    """Check that all terms have consistent physical dimensions.

    Uses simple dimensional analysis by mapping symbols to SI base dimensions.
    """
    # SI base dimension mapping (mass, length, time, current, temperature)
    dim_map = {
        "energy":       (1, 2, -2, 0, 0),
        "action":       (1, 2, -1, 0, 0),
        "frequency":    (0, 0, -1, 0, 0),
        "time":         (0, 0, 1, 0, 0),
        "length":       (0, 1, 0, 0, 0),
        "mass":         (1, 0, 0, 0, 0),
        "velocity":     (0, 1, -1, 0, 0),
        "momentum":     (1, 1, -1, 0, 0),
        "force":        (1, 1, -2, 0, 0),
        "charge":       (0, 0, 0, 1, 0),
        "number":       (0, 0, 0, 0, 0),
        "temperature":  (0, 0, 0, 0, 1),
    }

    # Parse which symbols have which dimensions
    symbol_dims = {}
    for sym, dim_name in dimensions.items():
        if dim_name.lower() in dim_map:
            symbol_dims[sym] = dim_map[dim_name.lower()]
        else:
            return {"status": "error", "detail": f"Unknown dimension: {dim_name}"}

    # Check for dimensional consistency: all terms should have same dimension
    # For now, report symbols and their assigned dimensions
    lhs_rhs = equation.split("=")
    if len(lhs_rhs) != 2:
        return {"status": "error", "detail": "Equation must have exactly one '='"}

    lhs = lhs_rhs[0].strip()
    rhs = lhs_rhs[1].strip()

    # Find which symbols appear on each side
    lhs_symbols = [s for s in symbol_dims if s in lhs]
    rhs_symbols = [s for s in symbol_dims if s in rhs]

    # Check: LHS dimension should match RHS dimension
    lhs_dim = tuple(sum(symbol_dims[s][d] for s in lhs_symbols) for d in range(5))
    rhs_dim = tuple(sum(symbol_dims[s][d] for s in rhs_symbols) for d in range(5))

    consistent = lhs_dim == rhs_dim
    return {
        "status": "pass" if consistent else "fail",
        "detail": f"LHS dim {lhs_dim} {'==' if consistent else '!='} RHS dim {rhs_dim}",
        "symbol_dimensions": {s: d for s, d in symbol_dims.items()},
    }


def check_limiting_case(equation: str, limit_var: str, limit_val: str, expected: str) -> dict:
    """Check that the equation reduces to expected form in a limit.

    Uses sympy.limit() if sympy is available, otherwise returns a manual-review flag.
    """
    try:
        import sympy
    except ImportError:
        return {
            "status": "manual_review",
            "detail": "SymPy not available — manually verify limit behavior",
        }

    try:
        e_expr = sympy.sympify(equation.replace("=", "-(") + ")")
        var = sympy.Symbol(limit_var)
        limit_result = sympy.limit(e_expr, var, sympy.oo if limit_val == "oo" else sympy.sympify(limit_val))
        expected_expr = sympy.sympify(expected)
        diff = sympy.simplify(limit_result - expected_expr)
        is_eq = diff == 0
        return {
            "status": "pass" if is_eq else "fail",
            "detail": f"lim({limit_var}->{limit_val}) = {limit_result}, expected {expected}",
            "difference": str(diff),
        }
    except Exception as e:
        return {"status": "error", "detail": str(e)}


def main() -> int:
    parser = argparse.ArgumentParser(description="Formal theory validation")
    parser.add_argument("--equation", required=True, help="Equation to validate")
    parser.add_argument("--dimensions", default="{}", help='JSON dict: {"symbol":"dimension", ...}')
    parser.add_argument("--limit-var", default="", help="Variable to take limit of")
    parser.add_argument("--limit-val", default="", help="Limit value")
    parser.add_argument("--limit-expected", default="", help="Expected limiting form")
    args = parser.parse_args()

    dimensions = json.loads(args.dimensions)
    check_results = {}

    # 1. Dimensional consistency
    check_results["dimensional_consistency"] = check_dimensional_consistency(
        args.equation, dimensions
    )

    # 2. Limiting case
    if args.limit_var and args.limit_val and args.limit_expected:
        check_results["limiting_case_check"] = check_limiting_case(
            args.equation, args.limit_var, args.limit_val, args.limit_expected
        )

    all_pass = all(
        c.get("status") == "pass"
        for c in check_results.values()
    )

    output = {
        "equation": args.equation,
        "check_results": check_results,
        "verdict": "pass" if all_pass else "manual_review",
        "timestamp": __import__("datetime").datetime.now().isoformat(),
    }

    print(json.dumps(output, indent=2, ensure_ascii=False))
    return 0


if __name__ == "__main__":
    raise SystemExit(main())
