FA-4286 / Collection algebra / Open access

Subsequence not subset · case 01

The operation returns a result or retained state that violates this contract: Return whether right is an order-preserving, multiplicity-respecting subsequence of left.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Independent membership tests reuse positions and ignore order.

VERIFIED REPAIR

Return whether right is an order-preserving, multiplicity-respecting subsequence of left.

Unsuccessful approach: Contiguous-window search rejects valid gapped subsequences.

Case contract

Return whether right is an order-preserving, multiplicity-respecting subsequence of left. Inputs are the finite Python values shown by the executable fixtures; no concurrent execution is assumed.

Why this case matters

A controlled local-runtime regression for collection APIs, language semantics, or ownership wrappers. Fixtures include boundary and interaction cases.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x, y=None):
    return all(v in x for v in y)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('both empty', solve([], []), True)
check('empty right operand', solve(['a'], []), True)
check('empty left operand', solve([], ['b']), False)
check('overlap and multiplicity', solve(['b', 'a', 'b'], ['b', 'c', 'c']), False)
check('gapped subsequence succeeds', solve(['a','b','c'], ['a','c']), True)
check('reusing occurrence is forbidden', solve(['a'], ['a','a']), False)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
both empty	`True`	`True`	Passed
empty right operand	`True`	`True`	Passed
empty left operand	`False`	`False`	Passed
overlap and multiplicity	`False`	`False`	Passed
gapped subsequence succeeds	`True`	`True`	Passed
reusing occurrence is forbidden	`True`	`False`	Failed

SHA-256 / 048819b09a83277988b25072648e9ee9d8b826b97a8d3e02256d90f080a6b6db

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x, y=None):
    return any(x[i:i+len(y)]==y for i in range(len(x)+1))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('both empty', solve([], []), True)
check('empty right operand', solve(['a'], []), True)
check('empty left operand', solve([], ['b']), False)
check('overlap and multiplicity', solve(['b', 'a', 'b'], ['b', 'c', 'c']), False)
check('gapped subsequence succeeds', solve(['a','b','c'], ['a','c']), True)
check('reusing occurrence is forbidden', solve(['a'], ['a','a']), False)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
both empty	`True`	`True`	Passed
empty right operand	`True`	`True`	Passed
empty left operand	`False`	`False`	Passed
overlap and multiplicity	`False`	`False`	Passed
gapped subsequence succeeds	`False`	`True`	Failed
reusing occurrence is forbidden	`False`	`False`	Passed

SHA-256 / f020cb2a87059e3bdf6c1829f2e787deb7297aad1d5feef39ba62626dfdf2a7d

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x, y=None):
    return (lambda it: all(any(v==a for a in it) for v in y))(iter(x))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('both empty', solve([], []), True)
check('empty right operand', solve(['a'], []), True)
check('empty left operand', solve([], ['b']), False)
check('overlap and multiplicity', solve(['b', 'a', 'b'], ['b', 'c', 'c']), False)
check('gapped subsequence succeeds', solve(['a','b','c'], ['a','c']), True)
check('reusing occurrence is forbidden', solve(['a'], ['a','a']), False)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
both empty	`True`	`True`	Passed
empty right operand	`True`	`True`	Passed
empty left operand	`False`	`False`	Passed
overlap and multiplicity	`False`	`False`	Passed
gapped subsequence succeeds	`True`	`True`	Passed
reusing occurrence is forbidden	`False`	`False`	Passed

SHA-256 / e60defdbec8dd5d60086d157986efb4bce3679d509fa90da4bc82a6d14ff3f7a

Verification & scope

This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:37:37.566268+00:00.

Case digest / 8912b6bdf5622743059ebf0cfefbee4dcd13ef092192f5ed0e3729610549d50a