「counterexample」の検索結果

Automatically repair code violations of temporal properties using model-checking counterexamples as guidance. Use when working with formal verification results, temporal logic property violations (LTL, CTL), model checking counterexamples, or when asked to repair property violations, fix counterexamples, repair temporal properties, fix model checking violations, or repair code based on counterexamples. Applicable to concurrent systems, state machines, synchronization issues, safety/liveness properties, and resource management violations.

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Debug proof failures using counterexamples from Nitpick (Isabelle) or QuickChick (Coq) to identify specification errors, missing preconditions, and proof strategy issues. Use when: (1) A proof attempt fails and you need to understand why, (2) Counterexamples are generated by Nitpick or QuickChick, (3) Specifications may be incorrect or incomplete, (4) Theorems need validation before proving, (5) Missing preconditions or lemmas need identification, or (6) Proof failures need explanation and correction suggestions. Supports both Isabelle/HOL and Coq equally.

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Explain why counterexamples violate specifications by analyzing formal specifications (temporal logic, invariants, pre/postconditions, code contracts), informal requirements (user stories, acceptance criteria), test specifications (assertions, property-based tests), and providing step-by-step traces showing state changes, comparing expected vs actual behavior, identifying root causes, and assessing violation impact. Use when debugging test failures, understanding model checker output, explaining runtime assertion violations, analyzing static analysis warnings, or teaching specification concepts. Produces structured markdown explanations with traces, comparisons, state diagrams, and cause chains. Triggers when users ask why something failed, explain a violation, understand a counterexample, debug a specification, or analyze why a test fails.

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Automatically generates executable test cases from model checking counterexample traces. Translates abstract counterexample states and transitions into concrete test inputs, execution steps, and assertions that reproduce property violations. Use when working with model checker outputs (SPIN, CBMC, NuSMV, TLA+, Java PathFinder, etc.) and needing to create regression tests, validate bug fixes, or reproduce verification failures in executable test suites.

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Automatically repair C/C++ code violations detected by TLA+ model checking. Takes a program, TLA+ specification, and TLC counterexample trace as input, then generates minimal code modifications to eliminate the violation. Use when: (1) TLC model checker reports an invariant violation, deadlock, or temporal property failure, (2) You have a counterexample trace and need to fix the corresponding code, (3) You need to understand how a TLA+ violation maps to program-level bugs, (4) You want to validate repairs by re-running TLC. Supports safety properties (invariants), liveness properties (temporal logic), and deadlock detection.

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Generate concrete counterexamples when formal verification, assertions, or specifications fail. Use this skill when debugging failed proofs, understanding why verification fails, creating minimal reproducing examples, analyzing assertion violations, investigating invariant breaks, or diagnosing specification mismatches. Produces concrete input values, execution traces, and state information that demonstrate the failure.

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Refute-before-prove research discipline: automated counterexample sweeps before any formalization, meter-integrity audits for information-bound experiments, mutation-tested model checkers, pre-registered commit-or-cut gates for speculative directions, wrong-turn reporting, and numeric-claim provenance. Use when validating any new theorem, bound, equilibrium, or security claim; when building or trusting a checker, simulator, or experiment; or when deciding whether a speculative research direction lives or dies. NOT for exploratory brainstorming, product prioritization, writing style, or literature review.

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Solve competition math problems (IMO, Putnam, USAMO, AIME) with adversarial verification that catches the errors self-verification misses. Activates when asked to 'solve this IMO problem', 'prove this olympiad inequality', 'verify this competition proof', 'find a counterexample', 'is this proof correct', or for any problem with 'IMO', 'Putnam', 'USAMO', 'olympiad', or 'competition math' in it. Uses pure reasoning (no tools) — then a fresh-context adversarial verifier attacks the proof using specific failure patterns, not generic 'check logic'. Outputs calibrated confidence — will say 'no confident solution' rather than bluff. If LaTeX is available, produces a clean PDF after verification passes.

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Hardens LifeOS tests via property/mutation testing. USE WHEN harden, hardening, property test, property based testing, PBT, fast-check, mutation test, mutation testing, Stryker, CRAP score, CRAP analysis, DRY scan, jscpd, acceptance test mutation, strengthen tests, sharpen ISCs, find bugs example tests miss, universal quantified claim, shrink counterexample, what bugs am I missing, test the tests, test of the test. NOT FOR writing new feature tests (use bun test directly), grading agent output quality (use Evals), UI verification with real Chrome (use Interceptor), finding security vulnerabilities, or building new functionality.

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Writes, reviews, and debugs property-based tests — Hypothesis, fast-check, proptest, jqwik, rapid, and Echidna or Medusa for Solidity invariants. Use whenever tests should cover a whole input domain instead of a hand-picked list of examples: encode/decode and serialize/deserialize pairs, parsers, canonicalizers and normalizers, validators, numeric and Decimal types, comparators and sort order, data structures, and smart-contract state invariants. Also use when adding cases to an existing @given, fast-check, or proptest suite, when judging whether existing property tests assert anything real, and when a generator has shrunk a counterexample and you need to tell a wrong property from a genuine bug. Not for coverage-guided binary fuzzing (libFuzzer, AFL), mutation-testing campaigns, static analysis, benchmarking, or end-to-end UI tests.

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Role profile — a reviewer who is fact-seeking, bedrock-seeking, honest, and rejecting. Demands that arguments rest on small facts that cannot be wrong (not on stacked assumptions dressed up as foundation), and that deliberately-unclear concepts be quarantined — never leaked into solid layers, never mixed with each other. Catches the failure mode where designs ship after partial grounding: most of the spec researched, the design feels finished, and the unresearched remainder holds the deal-breaker. Invoke with `/pedantic <target>` (e.g. `/pedantic review this design doc`, `/pedantic review the SDK design`, `/pedantic review this PR`). Probes cover logical structure (definitions, assumptions, boundaries, contradictions, unfalsifiability, vague quantifiers, counterexamples), epistemic honesty (researchable vs. discoverable-only-by-doing), bedrock integrity (assumed-bedrock, leaked uncertainty, mixed unclarity), and design pathology (YAGNI, wrong-layer abstraction, unclear responsibility, fragmentation, over-engineering). Use when you want a hard critique of a plan, design doc, technical doc, code change, or PR description — not a copy edit, not a vibe check.

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Teaches how to reason from a transaction protocol’s rules to a working model. Use when analyzing a concurrency-control paper, spec, or algorithm to identify state, metadata, invariants, operation rules, examples, counterexamples, guarantees, false aborts, unsafe commits, or tradeoffs before inspecting concrete traces.

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Hardware verification tool for checking functional equivalence between two RTL designs (Verilog). Use when users need to: (1) Verify if two RTL versions are functionally equivalent, (2) Compare original vs. refactored RTL code, (3) Validate design changes or optimizations, (4) Identify semantic vs. cosmetic differences, (5) Generate counterexamples for non-equivalent designs. Analyzes interface alignment, state variables, logic differences, and produces detailed equivalence verdicts with plain language explanations. Particularly effective for design verification, code reviews, and regression testing of RTL modifications.

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Think and work like an expert Algorithms Researcher. Use when a task calls for Algorithms Researcher judgment. Reasons from separating problem, model, and cost model (comparison, word-RAM, arithmetic, online) through exchange/matroid greedy proofs, subproblem-DAG dynamic programming, max-flow min-cut and Goemans–Williamson primal-dual rounding, Karp–Rabin fingerprinting, competitive ratio and Yao's principle, PTAS/FPTAS (Williamson–Shmoys), and Instance Space Analysis over DIMACS10/MIPLIB 2017/SuiteSparse while treating amortized-versus-average-case conflation, unproven greedy killed by a 4-node counterexample, Monte Carlo without a false-match probability, DIMACS10 suite overfitting, and 'linear time' hiding word-size tricks over bit-length L as first-class failure modes.

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Proof writing and verification techniques for mathematical reasoning. Covers 13 proof strategies with canonical worked examples — direct, contrapositive, contradiction, cases, WLOG, vacuous/trivial, biconditional, counterexample, existence (constructive and non-constructive), uniqueness, induction (weak, strong, structural), pigeonhole/double-counting, and diagonal argument/invariants. Use when writing, verifying, or selecting proof strategies for any mathematical claim.

日本語の概要は準備中です。原文の説明を表示しています。

Solve competition math problems (IMO, Putnam, USAMO, AIME) with adversarial verification that catches the errors self-verification misses. Activates when asked to 'solve this IMO problem', 'prove this olympiad inequality', 'verify this competition proof', 'find a counterexample', 'is this proof correct', or for any problem with 'IMO', 'Putnam', 'USAMO', 'olympiad', or 'competition math' in it. Uses pure reasoning (no tools) — then a fresh-context adversarial verifier attacks the proof using specific failure patterns, not generic 'check logic'. Outputs calibrated confidence — will say 'no confident solution' rather than bluff. If LaTeX is available, produces a clean PDF after verification passes.

日本語の概要は準備中です。原文の説明を表示しています。