"""ADR-0116 — Deterministic math solver over MathProblemGraph.

Consumes the typed graph produced by the ADR-0115 parser and emits a
:class:`SolutionTrace` — an ordered list of operation applications
ending at a numeric answer. Pure function: same graph always produces
the same trace; same trace replays to the same answer byte-equal.

Architectural commitments (ADR-0114a):

- **Obligation #3** — Every correct answer ships with a replay-equal
  trace. ``SolutionTrace.canonical_bytes()`` is byte-deterministic;
  ADR-0117 verifier replays the trace and reproduces ``answer_value``.
- **Obligation #4** — Refusal is first-class. Under-determined or
  inconsistent graphs raise :class:`SolveError` rather than producing
  a fabricated answer.
- **Obligation #9** — Determinism. Pure-Python integer/float arithmetic
  in a fixed order; no platform-dependent state.
- **Obligation #10** — Operation provenance via the pack. Every step
  in the trace carries a ``pack_lemma_id`` resolved at solve time from
  the loaded ``en_arithmetic_v1`` pack. If the pack does not provide
  the required lemma, solve fails loudly. Changing the pack changes
  the resolved set deterministically.

The "expert" tier (ADR-0120) is not in scope here; ADR-0116 is the
Phase 2 substrate the eventual capability claim will rest on.
"""

from __future__ import annotations

import hashlib
import json
from dataclasses import dataclass
from typing import Any, Mapping

from generate.math_problem_graph import (
    MathProblemGraph,
    Operation,
    Quantity,
    Unknown,
)


REQUIRED_PACK_ID: str = "en_arithmetic_v1"

# Operation kind → required pack lemma. The solver MUST resolve every
# operation through one of these lemmas; if the pack does not provide
# the lemma, the solver fails. This is the load-bearing pack-binding
# discharge of ADR-0114a Obligation #10.
_OPERATION_REQUIRED_LEMMAS: dict[str, str] = {
    "add": "add",
    "subtract": "subtract",
    "transfer": "transfer",
    "multiply": "multiply",
    "divide": "divide",
}


class SolveError(ValueError):
    """Raised when a graph cannot be solved (typed refusal).

    Refusal reasons:
        - the arithmetic pack is missing or does not provide a required
          lemma (load-bearing pack-binding failure)
        - the unknown references state that was never asserted by any
          ``InitialPossession`` and never produced by any operation
        - division by zero
        - any other under-determined-graph condition
    """


@dataclass(frozen=True, slots=True)
class SolutionStep:
    """One operation application in the trace.

    Every field is determined-by-construction from the graph + prior
    steps; no field is computed via floating-point inexactness in a
    way that varies across platforms. The verifier (ADR-0117) re-walks
    the steps and re-applies the operation semantics; the resulting
    answer must equal ``answer_value`` byte-equal.
    """

    step_index: int
    operation_kind: str
    pack_lemma_id: str
    actor: str
    operand: Quantity
    target: str | None
    before_value: float
    after_value: float
    target_before: float | None
    target_after: float | None

    def as_json(self) -> dict[str, Any]:
        d: dict[str, Any] = {
            "step_index": self.step_index,
            "operation_kind": self.operation_kind,
            "pack_lemma_id": self.pack_lemma_id,
            "actor": self.actor,
            "operand": self.operand.as_json(),
            "before_value": self.before_value,
            "after_value": self.after_value,
        }
        if self.target is not None:
            d["target"] = self.target
            d["target_before"] = self.target_before
            d["target_after"] = self.target_after
        return d


@dataclass(frozen=True, slots=True)
class SolutionTrace:
    """Replayable record of how the answer was derived.

    Carries:

    - ``pack_id`` + ``pack_lemma_ids``: which arithmetic pack provided
      the operation vocabulary (ADR-0114a Obligation #10).
    - ``graph_canonical_hash``: SHA-256 of the input graph's canonical
      bytes — pins which problem this trace solves.
    - ``steps``: per-operation record in source order.
    - ``answer_value`` + ``answer_unit`` + ``answer_entity``: the final
      resolved unknown.
    """

    pack_id: str
    graph_canonical_hash: str
    steps: tuple[SolutionStep, ...]
    answer_value: float
    answer_unit: str
    answer_entity: str | None

    def as_json(self) -> dict[str, Any]:
        return {
            "pack_id": self.pack_id,
            "graph_canonical_hash": self.graph_canonical_hash,
            "steps": [s.as_json() for s in self.steps],
            "answer_value": self.answer_value,
            "answer_unit": self.answer_unit,
            "answer_entity": self.answer_entity,
        }

    def canonical_bytes(self) -> bytes:
        return json.dumps(
            self.as_json(), sort_keys=True, separators=(",", ":")
        ).encode("utf-8")


def _resolve_pack_lemmas() -> dict[str, str]:
    """Load the arithmetic pack and resolve operation kinds to lemma ids.

    Returns a dict mapping operation kind → pack-qualified lemma id of
    the form ``"<pack_id>:<lemma>"``. Raises :class:`SolveError` if the
    pack cannot be loaded or if any required lemma is missing.

    Per ADR-0114a Obligation #10, this dispatch is load-bearing: the
    solver cannot emit a trace step without a resolved pack-lemma id.
    """
    try:
        from language_packs.compiler import load_pack_entries
    except ImportError as exc:
        raise SolveError(
            f"cannot import language_packs.compiler: {exc}"
        ) from exc

    try:
        entries = load_pack_entries(REQUIRED_PACK_ID)
    except Exception as exc:
        raise SolveError(
            f"required arithmetic pack {REQUIRED_PACK_ID!r} failed to load: {exc}"
        ) from exc

    lemma_to_entry: dict[str, str] = {}
    for entry in entries:
        lemma_to_entry[entry.lemma] = entry.entry_id

    resolved: dict[str, str] = {}
    for op_kind, required_lemma in _OPERATION_REQUIRED_LEMMAS.items():
        if required_lemma not in lemma_to_entry:
            raise SolveError(
                f"pack {REQUIRED_PACK_ID!r} missing required lemma "
                f"{required_lemma!r} for operation kind {op_kind!r}"
            )
        resolved[op_kind] = f"{REQUIRED_PACK_ID}:{required_lemma}"
    return resolved


def solve(graph: MathProblemGraph) -> SolutionTrace:
    """Solve ``graph`` and return its :class:`SolutionTrace`.

    Pure function — no I/O, no global state, no randomness. Same graph
    in produces a byte-equal trace out.

    Raises :class:`SolveError` on:
        - missing or incomplete arithmetic pack
        - division by zero
        - the unknown referencing state that does not exist after all
          operations are applied
    """
    pack_bindings = _resolve_pack_lemmas()
    state: dict[tuple[str, str], float] = {}
    for p in graph.initial_state:
        state[(p.entity, p.quantity.unit)] = float(p.quantity.value)

    steps: list[SolutionStep] = []
    for index, op in enumerate(graph.operations):
        step = _apply(op, index, state, pack_bindings)
        steps.append(step)

    answer_value, answer_unit = _resolve_unknown(graph.unknown, state)

    return SolutionTrace(
        pack_id=REQUIRED_PACK_ID,
        graph_canonical_hash=hashlib.sha256(graph.canonical_bytes()).hexdigest(),
        steps=tuple(steps),
        answer_value=answer_value,
        answer_unit=answer_unit,
        answer_entity=graph.unknown.entity,
    )


def _apply(
    op: Operation,
    index: int,
    state: dict[tuple[str, str], float],
    pack_bindings: Mapping[str, str],
) -> SolutionStep:
    key = (op.actor, op.operand.unit)
    before = state.get(key, 0.0)
    v = float(op.operand.value)
    target_before: float | None = None
    target_after: float | None = None

    if op.kind == "add":
        after = before + v
        state[key] = after
    elif op.kind == "subtract":
        after = before - v
        state[key] = after
    elif op.kind == "transfer":
        if op.target is None:
            raise SolveError(
                f"transfer operation at step {index} has no target"
            )
        after = before - v
        state[key] = after
        tgt_key = (op.target, op.operand.unit)
        target_before = state.get(tgt_key, 0.0)
        target_after = target_before + v
        state[tgt_key] = target_after
    elif op.kind == "multiply":
        after = before * v
        state[key] = after
    elif op.kind == "divide":
        if v == 0:
            raise SolveError(
                f"division by zero in operation at step {index}"
            )
        after = before / v
        state[key] = after
    else:
        raise SolveError(
            f"unknown operation kind {op.kind!r} at step {index}"
        )

    return SolutionStep(
        step_index=index,
        operation_kind=op.kind,
        pack_lemma_id=pack_bindings[op.kind],
        actor=op.actor,
        operand=op.operand,
        target=op.target,
        before_value=before,
        after_value=after,
        target_before=target_before,
        target_after=target_after,
    )


def _resolve_unknown(
    unknown: Unknown, state: Mapping[tuple[str, str], float]
) -> tuple[float, str]:
    """Look up the answer the question asks for.

    For ``entity is None`` (total-across question), sums every state
    entry whose unit matches ``unknown.unit``. For a single-entity
    question, returns that entity's quantity of ``unknown.unit`` — or
    raises if no such state was ever asserted or produced.
    """
    if unknown.entity is None:
        total = sum(v for (_, unit), v in state.items() if unit == unknown.unit)
        return total, unknown.unit
    key = (unknown.entity, unknown.unit)
    if key not in state:
        raise SolveError(
            f"unknown references state ({unknown.entity!r}, {unknown.unit!r}) "
            f"that was never asserted or produced by any operation"
        )
    return state[key], unknown.unit