from __future__ import annotations

import copy

import pytest

from gap_pipeline.models import CanonicalItem


@pytest.fixture
def item() -> CanonicalItem:
    return CanonicalItem(
        item_id="demo-A-1",
        problem=r"Let \(a>0\). Prove that \(a+1/a\ge 2\).",
        solution=(
            r"Since \((a-1)^2\ge0\), expanding gives \(a^2-2a+1\ge0\). "
            r"Divide by \(a>0\) to obtain \(a+1/a\ge2\)."
        ),
        variables=["a"],
        problem_type="proof",
    )


@pytest.fixture
def dag_dict() -> dict:
    return {
        "nodes": [
            {
                "node_id": "n1",
                "claim": "(a-1)^2 >= 0",
                "derivation": "a square is nonnegative",
                "dependencies": [],
                "source_span": "Since (a-1)^2 >= 0",
                "mathematical_objects": ["a", "(a-1)^2"],
            },
            {
                "node_id": "n2",
                "claim": "a+1/a >= 2",
                "derivation": "expand and divide by positive a",
                "dependencies": ["n1"],
                "source_span": "Divide by a>0",
                "mathematical_objects": ["a"],
            },
        ],
        "terminal_node_id": "n2",
    }


@pytest.fixture
def plan_dict() -> dict:
    return {
        "steps": [
            {
                "node_id": "n1",
                "method_label": "use nonnegativity of a square",
                "input_roles": ["positive scalar"],
                "output_role": "nonnegative expression",
                "invariants": ["scalar is real"],
            },
            {
                "node_id": "n2",
                "method_label": "expand and divide by a positive quantity",
                "input_roles": ["nonnegative expression", "positive scalar"],
                "output_role": "target inequality",
                "invariants": ["divisor is positive"],
            },
        ],
        "terminal_node_id": "n2",
    }


@pytest.fixture
def replacement_dict() -> dict:
    return {
        "target_node_id": "n1",
        "original_object": "(a-1)^2",
        "replacement_object": "(x-2)^2",
        "guard_conditions": ["x>0"],
        "guard_evidence": ["choose x in the positive reals"],
        "expected_downstream_changes": ["expand around 2", "divide by x"],
        "rationale": "the same square-nonnegativity plan applies",
    }


@pytest.fixture
def diffused_dict(plan_dict: dict) -> dict:
    return {
        "node_instantiations": [
            {
                "node_id": "n1",
                "method_label": plan_dict["steps"][0]["method_label"],
                "instantiated_claim": "(x-2)^2 >= 0",
                "instantiated_derivation": "a square is nonnegative",
                "dependencies": [],
            },
            {
                "node_id": "n2",
                "method_label": plan_dict["steps"][1]["method_label"],
                "instantiated_claim": "x+4/x >= 4",
                "instantiated_derivation": "expand and divide by positive x",
                "dependencies": ["n1"],
            },
        ],
        "regenerated_proof": (
            "Since (x-2)^2 >= 0, expand and divide by x>0 to get x+4/x >= 4."
        ),
        "terminal_answer": "x+4/x >= 4",
    }


@pytest.fixture
def candidate_dict(replacement_dict: dict, diffused_dict: dict) -> dict:
    return {
        "problem": "Let x>0. Prove that x+4/x >= 4.",
        "proof": diffused_dict["regenerated_proof"],
        "terminal_answer": diffused_dict["terminal_answer"],
        "node_instantiations": diffused_dict["node_instantiations"],
        "replacement": replacement_dict,
    }


def changed_candidate(candidate: dict, suffix: str) -> dict:
    value = copy.deepcopy(candidate)
    value["problem"] = value["problem"] + f" [{suffix}]"
    value["proof"] = value["proof"] + f" Repair {suffix}."
    return value