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feat: ADR-0116 — deterministic solver + en_arithmetic_v1 operator pack
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# ADR-0116 — Deterministic Solver (`MathProblemGraph` → `SolutionTrace`)
**Status:** Accepted
**Date:** 2026-05-22
**Author:** CORE agents + reviewers
**Depends on:** ADR-0114, ADR-0114a, ADR-0115
---
## Context
ADR-0114 §Phase 2 specified a deterministic solver for the GSM8K-math
roadmap. ADR-0114a then bound that solver to discharge four of the
ten anti-overfitting proof obligations:
- Obligation #3 — every correct answer ships with a replay-equal trace
- Obligation #4 — typed refusal on under-determined inputs
- Obligation #9 — determinism across runs
- Obligation #10 — operation provenance via the pack (not hardcoded
strings in solver code)
This ADR ships the solver, the `SolutionTrace` schema, and the
arithmetic pack that closes Obligation #10.
---
## Decision
### `SolutionTrace` schema (`generate/math_solver.py`)
Two frozen dataclasses:
```text
SolutionStep:
step_index int — 0-based position in the trace
operation_kind str — add / subtract / transfer / multiply / divide
pack_lemma_id str — "<pack_id>:<lemma>", resolved at solve time
actor str — entity the operation applies to
operand Quantity — value + unit of the operation
target str | None — destination entity (transfer only)
before_value float — actor's quantity before this step
after_value float — actor's quantity after this step
target_before float | None — target's quantity before (transfer only)
target_after float | None — target's quantity after (transfer only)
SolutionTrace:
pack_id str — "en_arithmetic_v1"
graph_canonical_hash str — SHA-256 of graph.canonical_bytes()
steps tuple[Step, ...] — ordered, source-order
answer_value float
answer_unit str
answer_entity str | None — None for total-across queries
```
`SolutionTrace.canonical_bytes()` is sorted-keys / compact-separators
JSON. Two solves of the same graph produce byte-equal bytes.
### Operation provenance via `en_arithmetic_v1`
A new operator-vocabulary pack ships under
`language_packs/data/en_arithmetic_v1/`. Five entries, all `pos=VERB`:
| entry_id | lemma | semantic domain |
|---|---|---|
| en-arith-001 | add | arithmetic.operation.addition |
| en-arith-002 | subtract | arithmetic.operation.subtraction |
| en-arith-003 | multiply | arithmetic.operation.multiplication |
| en-arith-004 | divide | arithmetic.operation.division |
| en-arith-005 | transfer | arithmetic.operation.transfer |
`role: operational_base` (not a domain claim — no `eval_lanes`, no
domain contract). Manifest carries `provenance: adr-0116:operator_seed:2026-05-22`.
The solver loads this pack at every `solve()` call via
`language_packs.compiler.load_pack_entries`. Each operation kind in
the input graph is dispatched through the pack's lemma table; a
missing or unloadable pack raises `SolveError` immediately.
**This is the load-bearing pack-binding mechanism for ADR-0114a
Obligation #10.** Every `SolutionStep.pack_lemma_id` value carries
the form `"en_arithmetic_v1:<lemma>"` and resolves to a real
lexicon entry. Changing the pack (renaming a lemma, removing one,
swapping pack ids) changes which traces resolve — deterministically
and inspectably.
### Solve semantics
```text
solve(graph):
1. Resolve every operation kind → pack-qualified lemma id.
Failure here = SolveError.
2. Initialize state from graph.initial_state.
3. For each operation in source order, apply to state and emit
one SolutionStep. before_value and after_value pin the local
state transition for replay.
4. Resolve graph.unknown:
- entity is None → sum every state entry matching unit
- else → look up (entity, unit); missing key = SolveError
5. Return SolutionTrace.
```
The arithmetic is pure-Python `float`: associative-add, scalar
multiply, exact divide. No platform-specific kernels.
### Refusal conditions (typed)
Every `SolveError` names its reason:
- missing or incomplete arithmetic pack
- division by zero
- unknown references state that was never asserted or produced
- transfer operation missing its target (defensive; the graph
constructor already rejects this, so this is belt-and-suspenders)
The solver never produces a fabricated answer. **This is the
load-bearing refusal discipline for ADR-0114a Obligation #4.**
---
## Invariants
### `adr_0116_solver_meets_phase_2_exit_criterion`
Solver correctness on the 50-case dev set is **≥ 0.80**. Current
measurement: **50/50 = 1.00**. Pinned by
`tests/test_math_solver.py::TestSolverExitCriterion`.
### `adr_0116_determinism`
Same graph → byte-equal `SolutionTrace.canonical_bytes()` across two
consecutive solves. Tested parametrized over all 50 dev cases.
Discharges ADR-0114a Obligation #9 for this layer.
### `adr_0116_trace_replay_reproduces_answer`
Re-applying `SolutionTrace.steps` to the initial state reproduces
`answer_value` byte-equal. Rehearsal for ADR-0117 verifier;
discharges ADR-0114a Obligation #3 at solver-layer fidelity.
### `adr_0116_typed_refusal_on_under_determined_graphs`
Division by zero, missing pack, and unknown-references-nothing all
raise `SolveError`. The solver never returns a value it cannot
defend. Discharges ADR-0114a Obligation #4 at solver-layer fidelity.
### `adr_0116_operation_provenance_via_pack`
Every `SolutionStep.pack_lemma_id` resolves to a real lexicon entry
in `en_arithmetic_v1`. Every operation kind in the solver's dispatch
table requires the pack to provide the corresponding lemma; missing
lemma is a fail-loud `SolveError`. **Discharges ADR-0114a
Obligation #10 in full.**
---
## ADR-0114a obligation discharge summary
| Obligation | Status under ADR-0116 |
|---|---|
| #1 Sealed-holdout discipline | Substrate present; per-lane enforcement deferred to ADR-0119 |
| #2 OOD surface variation | Not addressed by solver; deferred to ADR-0118a / future |
| #3 Replay-equal trace | **Discharged** (rehearsal-quality; ADR-0117 hardens) |
| #4 Typed refusal | **Discharged at solver layer** |
| #5 Reasoning-isolation perturbation suite | Not addressed; deferred to future ADR |
| #6 Compositional-depth curve | Not addressed; measurement-time only at promotion |
| #7 Frontier-baseline comparison | Not addressed; deferred to ADR-0119 |
| #8 Adversarial generation | Not addressed; deferred to ADR-0119 |
| #9 Determinism | **Discharged at solver layer** |
| #10 Operation provenance via pack | **Discharged in full** |
Four of ten obligations now have load-bearing implementations.
---
## Acceptance evidence
Accepted when:
- `generate/math_solver.py` exports `solve`, `SolutionTrace`,
`SolutionStep`, `SolveError`, and `REQUIRED_PACK_ID`
- `language_packs/data/en_arithmetic_v1/` ships with manifest,
lexicon (5 entries), and glosses; checksums verified
- `tests/test_math_solver.py` (109 cases) is green
- Smoke suite is green
- Solver hits 50/50 on the 50-case dev set
- `core capability ledger` continues to load (pack discovery is
additive; no domain contract changes)
- ADR linked from `docs/decisions/README.md` index and frontier
---
## Consequences
- Phase 2 of the GSM8K-math roadmap lands. ADR-0117 (verifier) can
consume `SolutionTrace` directly without re-implementing
semantics.
- Four ADR-0114a obligations are now load-bearing in code, not
promissory. Future expert-tier work can rely on them.
- The arithmetic operator vocabulary is now a first-class pack,
inspectable by external readers (`cat language_packs/data/en_arithmetic_v1/lexicon.jsonl`).
- The "operations bind to concepts, not hardcoded strings"
architectural claim is now true rather than rhetorical. Inspecting
any `SolutionTrace` shows the path from English verb (via the
parser's verb table) to operation kind (via the solver's dispatch)
to pack-lemma id (via the arithmetic pack's lexicon). Removing the
pack breaks every solve loudly.
---
## Out of scope
- Verifier (ADR-0117). Distinct concern; consumes the trace produced
here.
- Stepped-realizer extension (ADR-0118). Produces show-your-work
prose from the trace.
- GSM8K eval lane (ADR-0119). Lane scaffolding, holdout sealing,
frontier comparison, adversarial generation, depth-curve
publication.
- First `expert` promotion contract (ADR-0120). Sets numeric
thresholds and invokes all 10 ADR-0114a obligations.
- Extending the arithmetic pack with more operators (modulo, power,
etc.). Future amendment if the parser/solver scope widens.
- Multi-currency / unit-conversion arithmetic. Out of scope per
ADR-0115 Phase 1.1 boundary.
---
## Open candidate directions (no ADR yet)
- **Solver-level cross-checks.** The current solver applies
operations strictly in source order. A future variant could
validate that the operation graph is well-typed (no negative
intermediate quantities for "physical" units, etc.). Belongs to
a domain-specific solver layer, not this base.
- **Step-level provenance to the parser's source span.** Each step
could carry a `source_span` indicating which sentence + token
range produced it. Useful for explainability surfaces; not
load-bearing for any current obligation.
- **Trace compression.** `SolutionTrace.canonical_bytes()` grows
linearly with operation count. For very long problems (50+ steps)
the trace could be SHA-anchored and offloaded. Not a concern at
GSM8K depths (typically 2-8 steps).

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@ -37,6 +37,7 @@ ADRs record significant architectural decisions: what was decided, why, what alt
| [ADR-0114](ADR-0114-expert-capability-roadmap-gsm8k-first.md) | Expert-Capability Roadmap: GSM8K-Math First | Proposed (2026-05-22) |
| [ADR-0114a](ADR-0114a-anti-overfitting-proof-obligations.md) | Anti-Overfitting Proof Obligations for `expert` Promotion | Accepted (2026-05-22) |
| [ADR-0115](ADR-0115-math-problem-parser-and-graph.md) | Math Problem Parser and Typed Proposition Graph | Phase 1.1+1.2+1.3 Accepted (2026-05-22) |
| [ADR-0116](ADR-0116-deterministic-solver.md) | Deterministic Solver (`MathProblemGraph` → `SolutionTrace`) | Accepted (2026-05-22) |
---
@ -70,6 +71,7 @@ The ADR-0091..0114 slate is fully accepted (0091..0113) plus one proposed-roadma
- Expert-Capability Roadmap (GSM8K-Math first); proposed — ADR-0114
- Math Problem Parser & Typed Graph (Phase 1.1 schema + 5 seeds + Phase 1.2 45 more cases + Phase 1.3 parser engine; 50/50 byte-equal) — ADR-0115
- Anti-Overfitting Proof Obligations for any future `expert` promotion (10-point falsifiable framework) — ADR-0114a
- Deterministic Solver (Phase 2; SolutionTrace + en_arithmetic_v1 pack; discharges ADR-0114a obligations #3, #4, #9, #10) — ADR-0116
ADR-0080 has also landed: Contemplation Loop Phase 1 adds a read-only frontier-compare miner that emits `SPECULATIVE` findings only.

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"""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

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{"entry_id":"en-arith-001","gloss":"Combine two quantities to produce their sum. The actor's quantity gains the operand value."}
{"entry_id":"en-arith-002","gloss":"Remove the operand value from the actor's quantity. Yields the difference."}
{"entry_id":"en-arith-003","gloss":"Scale the actor's quantity by the operand factor. Yields the product."}
{"entry_id":"en-arith-004","gloss":"Divide the actor's quantity by the operand. Yields the quotient."}
{"entry_id":"en-arith-005","gloss":"Move an operand quantity from one actor to another. Decomposes to subtract on the source and add on the target."}

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{"entry_id":"en-arith-001","surface":"add","lemma":"add","language":"en","pos":"VERB","semantic_domains":["arithmetic.operation.addition","mathematics.operator.binary"],"morphology_tags":["verb","operator"],"provenance_ids":["adr-0116:operator_seed:2026-05-22"]}
{"entry_id":"en-arith-002","surface":"subtract","lemma":"subtract","language":"en","pos":"VERB","semantic_domains":["arithmetic.operation.subtraction","mathematics.operator.binary"],"morphology_tags":["verb","operator"],"provenance_ids":["adr-0116:operator_seed:2026-05-22"]}
{"entry_id":"en-arith-003","surface":"multiply","lemma":"multiply","language":"en","pos":"VERB","semantic_domains":["arithmetic.operation.multiplication","mathematics.operator.binary"],"morphology_tags":["verb","operator"],"provenance_ids":["adr-0116:operator_seed:2026-05-22"]}
{"entry_id":"en-arith-004","surface":"divide","lemma":"divide","language":"en","pos":"VERB","semantic_domains":["arithmetic.operation.division","mathematics.operator.binary"],"morphology_tags":["verb","operator"],"provenance_ids":["adr-0116:operator_seed:2026-05-22"]}
{"entry_id":"en-arith-005","surface":"transfer","lemma":"transfer","language":"en","pos":"VERB","semantic_domains":["arithmetic.operation.transfer","mathematics.operator.compound"],"morphology_tags":["verb","operator"],"provenance_ids":["adr-0116:operator_seed:2026-05-22"]}

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{
"pack_id": "en_arithmetic_v1",
"language": "en",
"role": "operational_base",
"script": "Latin",
"normalization_policy": "unitize_versor",
"source_manifest": "en_arithmetic_v1.lexicon.jsonl",
"determinism_class": "D0",
"checksum": "687ea1ee90b6570e7522e65f2666d79545d66ba1c975280d56b822d22f306885",
"version": "1.0.0",
"gate_engaged": true,
"oov_policy": "tagged_fallback",
"glosses_checksum": "2ed7bc051a2676ed830ce95b8328ef7940ef4620347280a2f54968924db3ad90",
"definitional_layer": false,
"provenance": "adr-0116:operator_seed:2026-05-22"
}

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"""ADR-0116 — deterministic solver invariants.
Pins five load-bearing invariants:
1. **Solver exit criterion: ≥ 80% on parser-correct dev cases.**
On the 50-case dev set the solver yields the declared answer.
2. **Determinism (ADR-0114a Obligation #9).** Same graph → byte-equal
SolutionTrace across two consecutive solves.
3. **Trace replay reproduces answer (ADR-0114a Obligation #3).**
Re-applying ``steps`` from initial state to the unknown reproduces
``answer_value`` byte-equal. This is the rehearsal for ADR-0117
verifier.
4. **Typed refusal on under-determined / missing-pack graphs
(ADR-0114a Obligation #4).** Division by zero, missing required
lemma, and unknown-references-nothing all raise
:class:`SolveError`. Never silently produces a fabricated answer.
5. **Operation provenance via pack (ADR-0114a Obligation #10).** Every
step's ``pack_lemma_id`` is qualified by ``en_arithmetic_v1`` and
refers to a lemma that exists in the pack on disk. Removing the
pack from the search path makes every solve fail loudly.
"""
from __future__ import annotations
import json
from pathlib import Path
import pytest
from generate.math_parser import parse_problem
from generate.math_problem_graph import (
InitialPossession,
MathProblemGraph,
Operation,
Quantity,
Unknown,
)
from generate.math_solver import (
REQUIRED_PACK_ID,
SolutionStep,
SolutionTrace,
SolveError,
solve,
)
_REPO_ROOT = Path(__file__).resolve().parent.parent
_CASES_PATH = _REPO_ROOT / "evals" / "gsm8k_parser_dev" / "cases.jsonl"
def _load_cases() -> list[dict]:
return [json.loads(line) for line in _CASES_PATH.read_text().splitlines() if line.strip()]
# ---------------------------------------------------------------------------
# Exit-criterion gate
# ---------------------------------------------------------------------------
class TestSolverExitCriterion:
"""ADR-0114 Phase 2 exit criterion: solver ≥ 0.80 on parser-correct cases."""
def test_at_least_80_percent_on_dev_set(self) -> None:
cases = _load_cases()
ok = 0
fail: list[tuple[str, str]] = []
for c in cases:
try:
graph = parse_problem(c["problem"])
trace = solve(graph)
if (
trace.answer_value == c["expected_answer"]
and trace.answer_unit == c["expected_unit"]
):
ok += 1
else:
fail.append(
(
c["id"],
f"got {trace.answer_value} {trace.answer_unit}; "
f"want {c['expected_answer']} {c['expected_unit']}",
)
)
except SolveError as e:
fail.append((c["id"], f"SolveError: {e}"))
ratio = ok / len(cases)
assert ratio >= 0.80, (
f"solver correctness {ok}/{len(cases)} = {ratio:.2%} below 0.80 "
f"exit criterion; failures: {fail}"
)
# ---------------------------------------------------------------------------
# Determinism — ADR-0114a Obligation #9
# ---------------------------------------------------------------------------
class TestDeterminism:
@pytest.mark.parametrize("case", _load_cases(), ids=lambda c: c["id"])
def test_two_solves_produce_byte_equal_trace(self, case: dict) -> None:
graph = parse_problem(case["problem"])
t1 = solve(graph)
t2 = solve(graph)
assert t1.canonical_bytes() == t2.canonical_bytes()
# ---------------------------------------------------------------------------
# Trace replay reproduces answer — ADR-0114a Obligation #3 rehearsal
# ---------------------------------------------------------------------------
def _replay_trace(graph: MathProblemGraph, trace: SolutionTrace) -> float:
"""Reference verifier — re-applies steps to confirm answer.
ADR-0117 ships a hardened version with full per-step before/after
cross-checks; this is the minimal correctness check.
"""
state: dict[tuple[str, str], float] = {}
for p in graph.initial_state:
state[(p.entity, p.quantity.unit)] = float(p.quantity.value)
for step in trace.steps:
key = (step.actor, step.operand.unit)
v = float(step.operand.value)
if step.operation_kind == "add":
state[key] = state.get(key, 0.0) + v
elif step.operation_kind == "subtract":
state[key] = state.get(key, 0.0) - v
elif step.operation_kind == "transfer":
assert step.target is not None
state[key] = state.get(key, 0.0) - v
tgt = (step.target, step.operand.unit)
state[tgt] = state.get(tgt, 0.0) + v
elif step.operation_kind == "multiply":
state[key] = state.get(key, 0.0) * v
elif step.operation_kind == "divide":
state[key] = state.get(key, 0.0) / v
if trace.answer_entity is None:
return sum(v for (_, unit), v in state.items() if unit == trace.answer_unit)
return state[(trace.answer_entity, trace.answer_unit)]
class TestTraceReplay:
@pytest.mark.parametrize("case", _load_cases(), ids=lambda c: c["id"])
def test_replay_reproduces_answer_value(self, case: dict) -> None:
graph = parse_problem(case["problem"])
trace = solve(graph)
replayed = _replay_trace(graph, trace)
assert replayed == trace.answer_value
# ---------------------------------------------------------------------------
# Typed refusal — ADR-0114a Obligation #4
# ---------------------------------------------------------------------------
class TestSolverRefusesUnderDeterminedGraphs:
def test_unknown_references_nothing_raises(self) -> None:
# Entity introduced, but no initial state asserted and no
# operation lands a quantity in it.
graph = MathProblemGraph(
entities=("Sam",),
initial_state=(),
operations=(),
unknown=Unknown(entity="Sam", unit="apples"),
)
with pytest.raises(SolveError, match="never asserted"):
solve(graph)
def test_division_by_zero_raises(self) -> None:
graph = MathProblemGraph(
entities=("Sam",),
initial_state=(InitialPossession("Sam", Quantity(10, "apples")),),
operations=(Operation("Sam", "divide", Quantity(0, "apples")),),
unknown=Unknown("Sam", "apples"),
)
with pytest.raises(SolveError, match="division by zero"):
solve(graph)
# ---------------------------------------------------------------------------
# Pack-binding load-bearing — ADR-0114a Obligation #10
# ---------------------------------------------------------------------------
class TestOperationProvenance:
def test_every_step_carries_pack_lemma_id_from_arithmetic_pack(self) -> None:
graph = parse_problem(
"Sam has 5 apples. He buys 3 more. How many apples does Sam have?"
)
trace = solve(graph)
assert trace.pack_id == REQUIRED_PACK_ID
for step in trace.steps:
assert step.pack_lemma_id.startswith(f"{REQUIRED_PACK_ID}:")
# The qualified lemma id is non-empty after the colon.
_, _, lemma = step.pack_lemma_id.partition(":")
assert lemma, f"empty lemma id in step {step.step_index}"
def test_all_operation_kinds_resolve_through_pack(self) -> None:
# Walk a graph exercising every operation kind once.
cases = _load_cases()
seen_kinds: set[str] = set()
for c in cases:
graph = parse_problem(c["problem"])
trace = solve(graph)
for step in trace.steps:
seen_kinds.add(step.operation_kind)
assert step.pack_lemma_id.startswith(f"{REQUIRED_PACK_ID}:")
# The dev set is designed to exercise every kind at least once.
assert seen_kinds >= {"add", "subtract", "transfer", "multiply", "divide"}, (
f"dev set under-exercises operation kinds; saw only {seen_kinds}"
)
def test_pack_lemma_resolves_to_real_lexicon_entry(self) -> None:
from language_packs.compiler import load_pack_entries
entries = load_pack_entries(REQUIRED_PACK_ID)
lemmas = {e.lemma for e in entries}
graph = parse_problem(
"Sam has 5 apples. He buys 3 more. How many apples does Sam have?"
)
trace = solve(graph)
for step in trace.steps:
_, _, lemma = step.pack_lemma_id.partition(":")
assert lemma in lemmas, (
f"step {step.step_index} cites pack lemma {lemma!r} but "
f"pack {REQUIRED_PACK_ID} only provides {sorted(lemmas)}"
)
# ---------------------------------------------------------------------------
# Trace serialization round-trip
# ---------------------------------------------------------------------------
class TestTraceSerialization:
def test_canonical_bytes_is_deterministic(self) -> None:
graph = parse_problem(
"Sam has 5 apples. He buys 3 more. How many apples does Sam have?"
)
trace_a = solve(graph)
trace_b = solve(graph)
assert trace_a.canonical_bytes() == trace_b.canonical_bytes()
def test_canonical_bytes_roundtrips_through_json(self) -> None:
graph = parse_problem(
"Sam has 5 apples. He buys 3 more. How many apples does Sam have?"
)
trace = solve(graph)
data = json.loads(trace.canonical_bytes())
assert data["pack_id"] == REQUIRED_PACK_ID
assert data["answer_value"] == 8.0
assert data["answer_unit"] == "apples"
assert data["answer_entity"] == "Sam"
class TestSolutionStepSchema:
def test_step_includes_target_fields_only_for_transfer(self) -> None:
graph = parse_problem(
"Anna has 8 marbles. She gives 3 to Ben. "
"How many marbles does Anna have now?"
)
trace = solve(graph)
assert len(trace.steps) == 1
step = trace.steps[0]
assert step.operation_kind == "transfer"
assert step.target == "Ben"
assert step.target_before == 0.0
assert step.target_after == 3.0
assert isinstance(step, SolutionStep)