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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
|
