from typing import Dict, Any


def to_canonical(local_problem: Dict[str, Any]) -> Dict[str, Any]:
    """
    Minimal bridge: map a LocalProblem into a canonical representation.
    In a full MVP this would be a richer translation; here we preserve shape.
    """
    # Expect input like: {"id": "...", "objective": ..., "variables": {...}, "domain": "..."}
    canonical = {
        "LocalProblem": {
            "id": local_problem.get("id"),
            "domain": local_problem.get("domain", "unknown"),
            "objective": local_problem.get("objective"),
            "variables": local_problem.get("variables", {}),
        }
    }
    return canonical


def from_canonical(canonical: Dict[str, Any]) -> Dict[str, Any]:
    """
    Inverse mapping from canonical representation back to a LocalProblem-like dict.
    """
    lp = canonical.get("LocalProblem", {})
    # Flatten for compatibility with simple local problem consumer
    return {
        "id": lp.get("id"),
        "domain": lp.get("domain", "unknown"),
        "objective": lp.get("objective"),
        "variables": lp.get("variables", {}),
    }