5a0423cb36
* feat(derivation): Gate A2b case 0002 fractional rest composition Add fraction_portion operation for "gives N/M of that" and "half of the rest" subtract semantics chained after unit_partition, plus keep-on-hand question binding with partition-noun unit inference. Live train_sample moves 6/44/0 to 7/43/0 with wrong=0 preserved; confuser-v1-0007 still refuses without "of that". * test(derivation): add A2b sibling and confuser anti-overfit cases Cover Bob/Alice partition+fraction chains, slash-without-referent refusal, partition-less "of that", and multi-actor pronoun ambiguity. * chore(derivation): normalize A2b fraction test EOF
630 lines
24 KiB
Python
630 lines
24 KiB
Python
"""ADR-0115 — Typed proposition graph for grade-school math word problems.
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This module defines the structural target of the parser added under ADR-0115.
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Parsing a natural-language problem produces a :class:`MathProblemGraph`; the
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solver (ADR-0116) and verifier (ADR-0117) consume the same structure.
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Determinism guarantees:
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- Every dataclass is ``frozen=True, slots=True`` and hashes by value.
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- :meth:`MathProblemGraph.canonical_bytes` is sorted-keys, compact-separators
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JSON — same graph object → byte-identical SHA-256.
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- Field order on ``entities``, ``initial_state``, ``operations`` is
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**order-of-introduction** in the source text. Two graphs that disagree on
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introduction order are NOT equal; this matches CORE's general "preserve
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source-text ordering" doctrine.
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"""
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from __future__ import annotations
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import json
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from dataclasses import dataclass
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from typing import Any, Final, Literal, Mapping
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# Operation kinds correspond to math-pack lemma vocabulary (en_mathematics_logic_v1).
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# A future solver under ADR-0116 dispatches on this string.
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VALID_OPERATION_KINDS: Final[frozenset[str]] = frozenset(
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{
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"add",
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"subtract",
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"transfer",
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"multiply",
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"divide",
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"apply_rate",
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"compare_additive",
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"compare_multiplicative",
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"unit_partition",
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"fraction_portion",
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}
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)
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VALID_FRACTION_REFERENTS: Final[frozenset[str]] = frozenset(
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{"that", "it", "them", "rest", "the_rest"}
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)
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VALID_COMPARISON_DIRECTIONS: Final[frozenset[str]] = frozenset(
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{"more", "fewer", "times", "fraction"}
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)
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class MathGraphError(ValueError):
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"""Raised on schema violations in math-problem-graph construction."""
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@dataclass(frozen=True, slots=True)
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class Quantity:
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"""A numeric value paired with a textual unit.
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The unit is the canonical noun (lowercase). Equality is exact:
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``Quantity(5, 'apples')`` != ``Quantity(5, 'apple')``. Authors and
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parsers must canonicalize units before constructing.
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"""
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value: int | float
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unit: str
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def __post_init__(self) -> None:
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if not isinstance(self.value, (int, float)) or isinstance(self.value, bool):
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raise MathGraphError(
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f"Quantity.value must be int or float, got "
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f"{type(self.value).__name__}"
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)
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if not isinstance(self.unit, str) or not self.unit:
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raise MathGraphError(
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f"Quantity.unit must be a non-empty string, got {self.unit!r}"
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)
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def as_json(self) -> dict[str, Any]:
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return {"unit": self.unit, "value": self.value}
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@dataclass(frozen=True, slots=True)
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class Rate:
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"""A per-unit rate connecting two units (ADR-0122).
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``Rate(2.0, "dollars", "apple")`` means "2 dollars per apple". The
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rate consumes a quantity in ``denominator_unit`` and produces a
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quantity in ``numerator_unit`` via scalar multiplication. ``value``
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must be strictly positive — zero or negative rates are refused at
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construction (illegal states made hard to represent).
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"""
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value: int | float
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numerator_unit: str
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denominator_unit: str
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def __post_init__(self) -> None:
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if not isinstance(self.value, (int, float)) or isinstance(self.value, bool):
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raise MathGraphError(
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f"Rate.value must be int or float, got "
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f"{type(self.value).__name__}"
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)
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if self.value <= 0:
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raise MathGraphError(
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f"Rate.value must be strictly positive; got {self.value!r}"
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)
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if not isinstance(self.numerator_unit, str) or not self.numerator_unit:
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raise MathGraphError(
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f"Rate.numerator_unit must be a non-empty string, got "
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f"{self.numerator_unit!r}"
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)
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if not isinstance(self.denominator_unit, str) or not self.denominator_unit:
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raise MathGraphError(
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f"Rate.denominator_unit must be a non-empty string, got "
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f"{self.denominator_unit!r}"
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)
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if self.numerator_unit == self.denominator_unit:
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raise MathGraphError(
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f"Rate.numerator_unit and Rate.denominator_unit must differ; "
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f"got {self.numerator_unit!r} for both"
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)
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def as_json(self) -> dict[str, Any]:
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return {
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"denominator_unit": self.denominator_unit,
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"numerator_unit": self.numerator_unit,
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"value": self.value,
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}
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@dataclass(frozen=True, slots=True)
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class PartitionChunk:
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"""Fixed-size chunk measure for unit_partition (Gate A2a).
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``PartitionChunk(25, "feet", "sections")`` means "split the actor's
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total in ``unit`` into chunks of size 25, writing the integer chunk
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count under ``result_unit``". ``value`` is the chunk size (divisor);
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``unit`` is the measure unit shared with the prior total; ``result_unit``
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is the count noun for the quotient (not the dividend unit).
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"""
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value: int | float
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unit: str
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result_unit: str
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def __post_init__(self) -> None:
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if not isinstance(self.value, (int, float)) or isinstance(self.value, bool):
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raise MathGraphError(
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f"PartitionChunk.value must be int or float, got "
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f"{type(self.value).__name__}"
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)
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if self.value <= 0:
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raise MathGraphError(
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f"PartitionChunk.value must be strictly positive; got {self.value!r}"
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)
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if not isinstance(self.unit, str) or not self.unit:
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raise MathGraphError(
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f"PartitionChunk.unit must be a non-empty string, got {self.unit!r}"
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)
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if not isinstance(self.result_unit, str) or not self.result_unit:
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raise MathGraphError(
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f"PartitionChunk.result_unit must be a non-empty string, got "
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f"{self.result_unit!r}"
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)
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if self.unit == self.result_unit:
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raise MathGraphError(
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f"PartitionChunk.unit and PartitionChunk.result_unit must differ; "
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f"got {self.unit!r} for both"
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)
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def as_json(self) -> dict[str, Any]:
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return {
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"result_unit": self.result_unit,
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"unit": self.unit,
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"value": self.value,
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}
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@dataclass(frozen=True, slots=True)
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class FractionPortion:
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"""Fraction of an actor's prior count state (Gate A2b).
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``FractionPortion(1, 4, "that")`` on a give surface means subtract
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one quarter of the actor's partition-derived count unit from the actor
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(not a transfer to a recipient). ``referent="rest"`` means the same
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count unit after prior fraction steps.
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"""
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numerator: int
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denominator: int
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referent: Literal["that", "it", "them", "rest", "the_rest"]
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def __post_init__(self) -> None:
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if not isinstance(self.numerator, int) or isinstance(self.numerator, bool):
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raise MathGraphError(
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f"FractionPortion.numerator must be int, got "
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f"{type(self.numerator).__name__}"
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)
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if not isinstance(self.denominator, int) or isinstance(self.denominator, bool):
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raise MathGraphError(
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f"FractionPortion.denominator must be int, got "
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f"{type(self.denominator).__name__}"
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)
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if self.numerator <= 0 or self.denominator <= 0:
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raise MathGraphError(
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f"FractionPortion requires positive numerator/denominator; "
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f"got {self.numerator}/{self.denominator}"
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)
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if self.referent not in VALID_FRACTION_REFERENTS:
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raise MathGraphError(
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f"FractionPortion.referent must be one of "
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f"{sorted(VALID_FRACTION_REFERENTS)}; got {self.referent!r}"
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)
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def as_json(self) -> dict[str, Any]:
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return {
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"denominator": self.denominator,
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"numerator": self.numerator,
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"referent": self.referent,
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}
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@dataclass(frozen=True, slots=True)
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class Comparison:
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"""A comparison between two actors' quantities (ADR-0123).
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Two modes, discriminated by ``direction``:
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- ``direction='more'`` / ``direction='fewer'``: additive — actor's
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quantity is ``reference_actor``'s quantity ± ``delta`` (Quantity).
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``factor`` must be ``None``.
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- ``direction='times'`` / ``direction='fraction'``: multiplicative —
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actor's quantity is ``factor`` × ``reference_actor``'s quantity.
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``delta`` must be ``None``. ``factor`` must be strictly positive.
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Self-reference is refused at the Operation boundary, not here.
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"""
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reference_actor: str
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delta: "Quantity | None"
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factor: float | None
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direction: Literal["more", "fewer", "times", "fraction"]
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def __post_init__(self) -> None:
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if not isinstance(self.reference_actor, str) or not self.reference_actor:
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raise MathGraphError(
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"Comparison.reference_actor must be a non-empty string"
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)
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if self.direction not in VALID_COMPARISON_DIRECTIONS:
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raise MathGraphError(
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f"Comparison.direction must be one of "
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f"{sorted(VALID_COMPARISON_DIRECTIONS)}; got {self.direction!r}"
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)
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if self.direction in ("more", "fewer"):
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if not isinstance(self.delta, Quantity):
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raise MathGraphError(
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"Comparison.delta must be a Quantity when "
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f"direction={self.direction!r}; got "
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f"{type(self.delta).__name__}"
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)
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if self.factor is not None:
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raise MathGraphError(
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"Comparison.factor must be None when "
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f"direction={self.direction!r}; got {self.factor!r}"
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)
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else:
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if self.delta is not None:
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raise MathGraphError(
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"Comparison.delta must be None when "
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f"direction={self.direction!r}; got {self.delta!r}"
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)
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if not isinstance(self.factor, (int, float)) or isinstance(
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self.factor, bool
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):
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raise MathGraphError(
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"Comparison.factor must be int or float when "
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f"direction={self.direction!r}; got "
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f"{type(self.factor).__name__}"
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)
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if self.factor <= 0:
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raise MathGraphError(
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f"Comparison.factor must be strictly positive; "
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f"got {self.factor!r}"
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)
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def as_json(self) -> dict[str, Any]:
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d: dict[str, Any] = {
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"direction": self.direction,
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"reference_actor": self.reference_actor,
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}
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if self.delta is not None:
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d["delta"] = self.delta.as_json()
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if self.factor is not None:
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d["factor"] = self.factor
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return d
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@dataclass(frozen=True, slots=True)
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class InitialPossession:
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"""Some entity holds some quantity at the start of the problem."""
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entity: str
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quantity: Quantity
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def __post_init__(self) -> None:
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if not isinstance(self.entity, str) or not self.entity:
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raise MathGraphError(
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"InitialPossession.entity must be a non-empty string"
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)
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def as_json(self) -> dict[str, Any]:
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return {"entity": self.entity, "quantity": self.quantity.as_json()}
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@dataclass(frozen=True, slots=True)
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class Operation:
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"""A state-mutating event applied in story order.
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``transfer`` denotes ``actor → target`` movement of ``operand``. The
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solver (ADR-0116) decomposes ``transfer`` into ``subtract`` from actor
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plus ``add`` to target; the parser emits ``transfer`` to stay close to
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natural-language surface ("gives X to Y").
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For ``multiply`` / ``divide`` the ``operand`` is the scalar (e.g. a
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factor of 3). Unit handling for these kinds is delegated to the solver.
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"""
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actor: str
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kind: str
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operand: "Quantity | Rate | Comparison | PartitionChunk | FractionPortion"
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target: str | None = None
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def __post_init__(self) -> None:
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if not isinstance(self.actor, str) or not self.actor:
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raise MathGraphError("Operation.actor must be a non-empty string")
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if self.kind not in VALID_OPERATION_KINDS:
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raise MathGraphError(
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f"Operation.kind must be one of {sorted(VALID_OPERATION_KINDS)}, "
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f"got {self.kind!r}"
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)
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if self.kind == "apply_rate":
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if not isinstance(self.operand, Rate):
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raise MathGraphError(
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"Operation.operand must be a Rate when kind='apply_rate'; "
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f"got {type(self.operand).__name__}"
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)
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elif self.kind == "unit_partition":
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if not isinstance(self.operand, PartitionChunk):
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raise MathGraphError(
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"Operation.operand must be a PartitionChunk when "
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f"kind='unit_partition'; got {type(self.operand).__name__}"
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)
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elif self.kind == "fraction_portion":
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if not isinstance(self.operand, FractionPortion):
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raise MathGraphError(
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"Operation.operand must be a FractionPortion when "
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f"kind='fraction_portion'; got {type(self.operand).__name__}"
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)
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elif self.kind in ("compare_additive", "compare_multiplicative"):
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if not isinstance(self.operand, Comparison):
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raise MathGraphError(
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"Operation.operand must be a Comparison when "
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f"kind={self.kind!r}; got {type(self.operand).__name__}"
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)
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if self.kind == "compare_additive" and self.operand.direction not in (
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"more",
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"fewer",
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):
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raise MathGraphError(
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"Operation.kind='compare_additive' requires "
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"Comparison.direction in {'more','fewer'}; got "
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f"{self.operand.direction!r}"
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)
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if self.kind == "compare_multiplicative" and self.operand.direction not in (
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"times",
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"fraction",
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):
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raise MathGraphError(
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"Operation.kind='compare_multiplicative' requires "
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"Comparison.direction in {'times','fraction'}; got "
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f"{self.operand.direction!r}"
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)
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if self.operand.reference_actor == self.actor:
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raise MathGraphError(
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"Operation.operand.reference_actor must differ from "
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f"Operation.actor; both are {self.actor!r}"
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)
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else:
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if not isinstance(self.operand, Quantity):
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raise MathGraphError(
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"Operation.operand must be a Quantity when "
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f"kind={self.kind!r}; got {type(self.operand).__name__}"
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)
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if self.kind == "transfer":
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if not self.target:
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raise MathGraphError(
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"Operation.target required when kind='transfer'"
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)
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if self.target == self.actor:
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raise MathGraphError(
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"Operation.target must differ from Operation.actor for "
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"kind='transfer'"
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)
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elif self.target is not None:
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raise MathGraphError(
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f"Operation.target only valid for kind='transfer'; got "
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f"kind={self.kind!r}"
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)
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def as_json(self) -> dict[str, Any]:
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d: dict[str, Any] = {
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"actor": self.actor,
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"kind": self.kind,
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"operand": self.operand.as_json(),
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}
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if self.target is not None:
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d["target"] = self.target
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return d
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@dataclass(frozen=True, slots=True)
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class Unknown:
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"""The quantity the question is asking for.
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``entity=None`` means "total across every entity holding ``unit``"
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(e.g. "How many apples do they have in total?"). For a single-entity
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question ("How many apples does Sam have?") set ``entity='Sam'``.
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"""
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entity: str | None
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unit: str
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def __post_init__(self) -> None:
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if not isinstance(self.unit, str) or not self.unit:
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raise MathGraphError("Unknown.unit must be a non-empty string")
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if self.entity is not None and (
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not isinstance(self.entity, str) or not self.entity
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):
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raise MathGraphError(
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"Unknown.entity must be a non-empty string or None"
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)
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def as_json(self) -> dict[str, Any]:
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return {"entity": self.entity, "unit": self.unit}
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@dataclass(frozen=True, slots=True)
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class MathProblemGraph:
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"""Typed graph produced by the ADR-0115 parser.
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Field order on tuples is **order of introduction in the source text**,
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not alphabetical. ``MathProblemGraph`` equality is element-wise tuple
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equality; reordering changes the graph identity.
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"""
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entities: tuple[str, ...]
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initial_state: tuple[InitialPossession, ...]
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operations: tuple[Operation, ...]
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unknown: Unknown
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def __post_init__(self) -> None:
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if not self.entities:
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raise MathGraphError(
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"MathProblemGraph.entities must contain at least one entity"
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)
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seen: set[str] = set()
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for e in self.entities:
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if not isinstance(e, str) or not e:
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raise MathGraphError(
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"MathProblemGraph.entities must be non-empty strings"
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)
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if e in seen:
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raise MathGraphError(
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f"MathProblemGraph.entities contains duplicate {e!r}"
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)
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seen.add(e)
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entity_set = set(self.entities)
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# ADR-0174 Phase 3 diagnostic — refuse contradictory initial
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# possessions for the same (entity, unit). Surfaced 2026-05-28
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# by post-merge diagnostic: prior behavior silently overwrote
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# earlier with later in math_solver.solve()'s state dict, so
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# 'Sam has 5 marbles. Sam has 3 marbles.' returned 3.0 — a
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# wrong=0 violation (definite answer from contradictory input).
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# Refuse at construction; admit duplicates only when the value
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# matches (redundant but not contradictory).
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seen_initial: dict[tuple[str, str], int | float] = {}
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for p in self.initial_state:
|
||
if p.entity not in entity_set:
|
||
raise MathGraphError(
|
||
f"initial_state references unknown entity {p.entity!r}"
|
||
)
|
||
key = (p.entity, p.quantity.unit)
|
||
if key in seen_initial and seen_initial[key] != p.quantity.value:
|
||
raise MathGraphError(
|
||
f"initial_state contains contradictory possessions for "
|
||
f"({p.entity!r}, {p.quantity.unit!r}): "
|
||
f"{seen_initial[key]} vs {p.quantity.value}"
|
||
)
|
||
seen_initial[key] = p.quantity.value
|
||
for op in self.operations:
|
||
if op.actor not in entity_set:
|
||
raise MathGraphError(
|
||
f"operation references unknown actor {op.actor!r}"
|
||
)
|
||
if op.target is not None and op.target not in entity_set:
|
||
raise MathGraphError(
|
||
f"operation references unknown target {op.target!r}"
|
||
)
|
||
if isinstance(op.operand, Comparison):
|
||
if op.operand.reference_actor not in entity_set:
|
||
raise MathGraphError(
|
||
"operation Comparison references unknown "
|
||
f"reference_actor {op.operand.reference_actor!r}"
|
||
)
|
||
if self.unknown.entity is not None and self.unknown.entity not in entity_set:
|
||
raise MathGraphError(
|
||
f"unknown references unknown entity {self.unknown.entity!r}"
|
||
)
|
||
|
||
def as_json(self) -> dict[str, Any]:
|
||
return {
|
||
"entities": list(self.entities),
|
||
"initial_state": [p.as_json() for p in self.initial_state],
|
||
"operations": [o.as_json() for o in self.operations],
|
||
"unknown": self.unknown.as_json(),
|
||
}
|
||
|
||
def canonical_bytes(self) -> bytes:
|
||
"""Deterministic JSON for hashing/byte-equality comparison."""
|
||
return json.dumps(
|
||
self.as_json(), sort_keys=True, separators=(",", ":")
|
||
).encode("utf-8")
|
||
|
||
|
||
def graph_from_dict(d: Mapping[str, Any]) -> MathProblemGraph:
|
||
"""Deserialize a graph from its canonical JSON dict.
|
||
|
||
The reverse of :meth:`MathProblemGraph.as_json`. Raises
|
||
:class:`MathGraphError` on any schema violation surfaced by the
|
||
dataclass constructors.
|
||
"""
|
||
if not isinstance(d, Mapping):
|
||
raise MathGraphError(f"graph payload must be a mapping; got {type(d).__name__}")
|
||
for required in ("entities", "initial_state", "operations", "unknown"):
|
||
if required not in d:
|
||
raise MathGraphError(f"graph payload missing required field {required!r}")
|
||
|
||
entities = tuple(d["entities"])
|
||
initial_state = tuple(
|
||
InitialPossession(
|
||
entity=p["entity"],
|
||
quantity=Quantity(value=p["quantity"]["value"], unit=p["quantity"]["unit"]),
|
||
)
|
||
for p in d["initial_state"]
|
||
)
|
||
operations = tuple(
|
||
Operation(
|
||
actor=o["actor"],
|
||
kind=o["kind"],
|
||
operand=_operand_from_dict(o["kind"], o["operand"]),
|
||
target=o.get("target"),
|
||
)
|
||
for o in d["operations"]
|
||
)
|
||
unk = d["unknown"]
|
||
unknown = Unknown(entity=unk.get("entity"), unit=unk["unit"])
|
||
return MathProblemGraph(
|
||
entities=entities,
|
||
initial_state=initial_state,
|
||
operations=operations,
|
||
unknown=unknown,
|
||
)
|
||
|
||
|
||
def _operand_from_dict(
|
||
kind: str, operand: Mapping[str, Any]
|
||
) -> "Quantity | Rate | Comparison | PartitionChunk | FractionPortion":
|
||
"""Reconstruct an Operation.operand from its canonical JSON form.
|
||
|
||
Dispatches on ``kind``:
|
||
|
||
- ``apply_rate`` → ``Rate`` (ADR-0122)
|
||
- ``compare_additive`` / ``compare_multiplicative`` → ``Comparison`` (ADR-0123)
|
||
- ``unit_partition`` → ``PartitionChunk`` (Gate A2a)
|
||
- every other kind → ``Quantity``
|
||
|
||
Payload shapes are structurally distinct (``Rate`` has
|
||
``numerator_unit``/``denominator_unit``; ``Comparison`` has
|
||
``reference_actor``/``direction``; ``Quantity`` has ``unit``) but
|
||
we dispatch on ``kind`` rather than sniffing keys so a mismatch
|
||
between ``kind`` and operand shape raises loudly in the dataclass
|
||
constructor.
|
||
"""
|
||
if not isinstance(operand, Mapping):
|
||
raise MathGraphError(
|
||
f"Operation.operand must be a mapping; got {type(operand).__name__}"
|
||
)
|
||
if kind == "apply_rate":
|
||
return Rate(
|
||
value=operand["value"],
|
||
numerator_unit=operand["numerator_unit"],
|
||
denominator_unit=operand["denominator_unit"],
|
||
)
|
||
if kind in ("compare_additive", "compare_multiplicative"):
|
||
delta_payload = operand.get("delta")
|
||
delta = (
|
||
Quantity(value=delta_payload["value"], unit=delta_payload["unit"])
|
||
if delta_payload is not None
|
||
else None
|
||
)
|
||
return Comparison(
|
||
reference_actor=operand["reference_actor"],
|
||
delta=delta,
|
||
factor=operand.get("factor"),
|
||
direction=operand["direction"],
|
||
)
|
||
if kind == "unit_partition":
|
||
return PartitionChunk(
|
||
value=operand["value"],
|
||
unit=operand["unit"],
|
||
result_unit=operand["result_unit"],
|
||
)
|
||
if kind == "fraction_portion":
|
||
return FractionPortion(
|
||
numerator=operand["numerator"],
|
||
denominator=operand["denominator"],
|
||
referent=operand["referent"],
|
||
)
|
||
return Quantity(value=operand["value"], unit=operand["unit"])
|