「invariants」の検索結果

Automatically infer loop invariants for code verification and correctness proofs. Use when analyzing loops to identify properties that hold throughout execution, generating assertions for verification, proving loop correctness, or documenting loop behavior. Supports Python, Java, C/C++, and language-agnostic analysis. Generates invariants as code assertions (assert statements). Triggers when users ask to infer invariants, find loop properties, generate loop assertions, prove loop correctness, or verify loop behavior.

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Uses abstract interpretation to automatically infer loop invariants, function preconditions, and postconditions for formal verification. Generates invariants that capture program behavior and support correctness proofs in Dafny, Isabelle, Coq, and other verification systems. Use when adding formal specifications to code, generating verification conditions, inferring contracts for functions, or discovering loop invariants for proofs.

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Find tests that enumerate a domain by copying it, and declare the invariants a codebase depends on. Reports where a parametrize list, for-loop, or it.each iterates a hand-written subset of a dict/set/tuple/Enum that exists in the source, and names the members nothing covers. Use when reviewing tests, when a module gains a name-to-thing table, registry, enum, or dispatch map, before trusting a green suite as evidence a domain is covered, or when asked "is this test actually total", "does anything cover X", "what does this repo guarantee", "which invariants do we declare". Also for vacuous tests that pass over an empty collection, for a domain that has silently NARROWED (an enumeration cannot see that), and for recording the refutation that proves a claim can fail.

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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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Property-based testing with Hypothesis for discovering edge cases and validating invariants. Use when implementing comprehensive test coverage, testing complex logic with many inputs, or validating mathematical properties and invariants across input domains. Triggered by: hypothesis, property-based testing, @given, strategies, generative testing.

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Read-only drift detector. Diffs SPEC.md against current code and reports violations grouped by severity. Writes nothing — suggests remedies via the spec or build skills but never invokes them. Triggers when the user asks to check drift, audit the spec, verify invariants, or ask whether code still matches the spec. Phrasings: "check drift", "audit the spec", "does the code still match §V", "check invariants", "spec vs code".

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Generate formal specifications including preconditions, postconditions, invariants, and contracts from code or requirements. Use this skill when documenting APIs, creating formal verification annotations, defining function contracts, specifying class invariants, writing design-by-contract code, or preparing code for formal verification. Supports multiple specification languages including JML, ACSL, Dafny, Eiffel contracts, and documentation annotations.

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Generates automated test oracles to verify correct software behavior. Creates assertion-based oracles (expected values), property-based oracles (invariants), differential oracles (comparing implementations), and metamorphic oracles (input transformations). Use when you need to generate assertions for test cases, identify invariants that should always hold, compare new vs legacy implementations, create metamorphic test relationships, validate function correctness, or improve test coverage with better verification strategies. Supports Python (pytest, unittest, hypothesis) and Java (JUnit, property testing).

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Generate formal specifications (definitions, predicates, invariants, pre/post-conditions) in Isabelle/HOL or Coq from informal requirements, source code, pseudocode, or mathematical descriptions. Use when users need to: (1) Formalize algorithms or data structures, (2) Create function specifications with contracts, (3) Generate predicates and properties for verification, (4) Translate informal requirements into formal logic, (5) Specify invariants for loops or data structures, or (6) Create formal definitions for mathematical concepts. Supports both Isabelle/HOL and Coq equally.

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Performs abstract interpretation to produce summarized execution traces and high-level program behavior representations. Highlights key control flow paths, variable relationships, loop invariants, function summaries, and potential runtime states using abstract domains (intervals, signs, nullness, etc.). Use when analyzing program behavior, understanding execution paths, computing loop invariants, tracking variable ranges, detecting potential runtime errors, or generating program summaries without concrete execution.

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Applies abstract interpretation using different abstract domains (intervals, octagons, polyhedra, sign, congruence) to statically analyze program variables and infer invariants, value ranges, and relationships. Use when analyzing program properties, inferring loop invariants, detecting potential errors, or understanding variable relationships through static analysis.

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CEO (Chief Executive Officer) — 一家公司「最高操作员」的工艺, 与泛泛「领导力 / 管理学」不同: (a) 设定战略与凝结愿景 (Drucker 的「企业的经营理论」+ Porter 论定位 + Hamilton Helmer 的「七力」+ Andy Grove 的「战略转折点」+ Roger Martin 《Playing to Win》); (b) 资本配置是 CEO 单一最高杠杆的工作 (Buffett/Munger Berkshire 致股东信 + William Thorndike 《The Outsiders 商界局外人》论 8 位非常规 CEO + Michael Mauboussin 论 hurdle rate + Bezos 年度致股东信「invariants vs bets」+ Mark Leonard Constellation Software); (c) 组建与领导高管班子 (Patrick Lencioni 《团队的五大障碍》+ Ben Horowitz 《艰难的事》+ Reed Hastings 《No Rules Rules》人才密度 + Andy Grove HOP《高产出管理》+ Lou Gerstner IBM 转型 + Marshall Goldsmith); (d) 董事会与投资人关系 (Larcker & Tayan 《公司治理重要》+ Bill George 《True North》+ 正式 CEO-董事长 / CEO-独立董事 protocol + 维权投资人 playbook + 资本市场沟通); (e) 企业文化与价值观作为操作系统 (Netflix 文化手册 + Amazon Leadership Principles + Bridgewater 《Principles》Ray Dalio + Schein 论组织文化 + 任正非 灰度 + 张瑞敏 人单合一 + 稻盛和夫 阿米巴); (f) 高不确定下的高风险决策 (Bezos Type 1/Type 2 决策 + premortem Klein + Kahneman 论 executive bias + RAPID/DACI + base rates + 情景规划 + 反思 premortem); (g) 对内对外沟通 (创始人 / CEO 致股东信作为机构构建工具: Bezos / Buffett / Reed Hastings 备忘录 / 任正非 内部讲话 + Town Hall + 危机沟通 Tylenol/Boeing/Wells Fargo + 应对维权投资人); (h) 跨阶段规模化 (创业 0→1 / 扩张 1→100 / 成熟期掌舵 / 危机转型): Steve Blank + Brian Chesky founder-mode + Marc Andreessen + Pierre Lassonde + Lou Gerstner 转型; (i) 创始人 CEO vs 职业经理人 CEO 的差异 (Paul Graham 「Founder Mode」2024 + Brian Chesky + Reed Hastings (创始人→职业过渡) + BCG/McKinsey 的「manager mode」+ 两者各自代价 + 什么时候切换)。诚实处理: 幸存者偏差 (单个 CEO 的打法 ≠ 普适规律, 学术研究显示 CEO 个人方差约 ⅓, 约 70% 来自行业 / 时代 / 运气 / 资本结构), 创始人崇拜, 区分可复制工艺与不可移植个人魅力, 治理与利益相关者责任 (员工 / 股东 / 社会), 反对 CEO 神话与 Welch 退休金扭曲 / Theranos / WeWork / FTX / Uber-Kalanick 时代 / Musk 80h+ / 996 工时崇拜。覆盖 founder-CEO (Bezos/Hastings/黄仁勋/Chesky/Brin/任正非) 与职业 CEO (Nadella/Gerstner/Pichai/Mulally/Lafley)。不含: 泛泛管理理论 (商业书已覆盖, 本 skill 专谈 C-suite 这个具体岗位), 不含: 「领导力」作为个人成长自助 (Robbins/Tracy/Maxwell 励志体裁), 不含: 「如何创业」早期战术 — 一旦有员工 / 董事会 / 资本, CEO 的工艺才开始。 (CEO (Chief Executive Officer) — the craft of being the top operator of a company, distinct from generic 'leadership/management': (a) setting the strategy and crystallizing the vision (Drucker's 'theory of the business' + Porter on positioning + Hamilton Helmer's 7 powers + Andy Grove's strategic inflection points + Roger Martin Playing to Win); (b) capital allocation as the CEO's single highest-leverage job (Buffett/Munger Berkshire letters + William Thorndike 'The Outsiders' on 8 unconventional CEOs + Michael Mauboussin on hurdle rates + Bezos's annual shareholder letter approach to invariants vs bets + Mark Leonard Constellation Software); (c) building and leading the executive team (Patrick Lencioni 'Five Dysfunctions' + Ben Horowitz 'Hard Things About Hard Things' + Reed Hastings 'No Rules Rules' on talent density + Andy Grove HOP + Lou Gerstner IBM turnaround + Marshall Goldsmith); (d) board and investor relations (Larcker & Tayan 'Corporate Governance Matters' + Bill George 'True North' + the formal CEO-Chair / CEO-Lead Director protocols + activist investor playbooks + capital markets communication); (e) culture and values as operating system (Netflix culture deck + Amazon Leadership Principles + Bridgewater 'Principles' Ray Dalio + Schein on org culture + 任正非 Ren Zhengfei 灰度 + 张瑞敏 Zhang Ruimin 人单合一 + 稻盛和夫 阿米巴); (f) high-stakes decision-making under uncertainty (Bezos Type 1 vs Type 2 + premortem Klein + Kahneman 'Thinking Fast and Slow' for executive bias + RAPID/DACI + base rates + scenario planning + premortem); (g) internal and external communication (founder/CEO letters as institution-builders: Bezos shareholder letters / Buffett letters / Reed Hastings memos / 任正非 内部讲话 + Town Halls + crisis communication Tylenol/Boeing/Wells Fargo + activist responses); (h) cross-stage scaling (founder-CEO of 0→1 / scaling 1→100 / mature-stage stewardship / turnaround): Steve Blank + Brian Chesky founder-mode + Marc Andreessen + Pierre Lassonde mining vs steady-state + Lou Gerstner turnaround; (i) the founder-CEO vs professional-manager-CEO distinction (Paul Graham 'Founder Mod

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The crouton mental model for someone who has never seen this repo — what "layer" means (two different things), the two-halves rule, the three app.config registries, team-scoped multi-tenancy, manifest-driven field types, the numbered invariants with the incidents behind them, and the known-weak points. Use when orienting in this codebase for the first time, when a question is shaped like "how does crouton work / why is it built this way / where does X live", when deciding whether a change belongs in a package or a generated layer, when confused by an extends chain or by croutonApps/croutonCollections/croutonLayoutBlocks, or before proposing any structural change. Trigger phrases: "what is a crouton layer", "package vs generated layer", "how does multi-tenancy work here", "why is there a stub component", "where do field types come from", "what invariants must hold".

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Heuristic-first software surgery for proof-backed, minimal-diff implementation: Contract to Invariants to Cut Rationale to inevitable incision to Proof. Use when users say "run /tw-tk", "patch-first", "keep the diff small", "state contract + invariants", "one clear incision", "fix it with a validation signal", or orchestration cues like "workers use /tw-tk" / "internally use /tw-tk".

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Turn 'should never happen' into 'cannot happen' by defining owned inductive invariants and enforcing them at parse/construct/API/DB/lock/txn boundaries with a verification signal. Use when prompts mention invariants, impossible states, validation sprawl, cache/index drift, idempotency/versioning, retries/duplicates/out-of-order events, race/linearization bugs, loop correctness, or hardening another workflow (for example /tw-fix) with invariant checks first.

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Discover conserved quantities and symmetries from trajectory data. Identifies energy, momentum, angular momentum, and custom invariants using neural networks and symbolic methods. Inspired by Noether's theorem.

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Author the project's non-negotiable engineering rules — the constitution that every feature spec, plan, and implementation must satisfy. Load when the user asks to write a constitution, define project rules, set engineering invariants, write project standards, define non-negotiables, capture agent guardrails as policy, or when spec-driven-development orchestrator routes here. Also triggers on "project constitution", "engineering invariants", "non-negotiable rules", "project policy", "set our standards", "/constitution". Output: docs/constitution.md. The third strategic artifact alongside AGENTS.md (agent behavior) and product-soul (strategy).

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製品の要望や企画書を、開発に着手できる具体的な要件へ整理します。業務ルール、データ、サービス間の接点、未決事項を明文化し、次の担当へ引き継ぎます。

• 製品要求書を開発要件に落としたいとき
• 複数サービスにまたがる機能の要件整理
• レビューで繰り返す前提の文書化

Scaffold an aggregate root with entity, value objects, repository interface, domain events, and test stubs. Use when adding a new aggregate to an existing bounded context, modeling a new business concept that owns invariants, or generating the boilerplate for an entity + repo + events triplet.

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This skill should be used when a model gets read-write control over its own live context window instead of a harness-scheduled compaction policy: the context exposed as an editable file the model rewrites with code tools, model-driven eviction and in-place updates, the harness invariants that keep self-editing safe (pinned prefix, edit gate, edit receipts, budget readouts, rollback on overflow), the prefix-cache cost of mid-context edits, and steering or training the model's own context-editing strategy. Route note content and fixed-threshold summarization to context-compression, cache-stable layout under harness control to context-optimization, file offloading to filesystem-context, and loop governance to self-improvement-loops.

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MCP server integrating Slither + Aderyn + SWC patterns into Claude Code for smart contract auditing. Use when analyzing Solidity files, running DeFi-specific detectors, or generating invariants. 10 MCP tools, 86 SWC detectors, DeFi preset pack, CI/CD workflow.

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Identify and verify loop invariants for correctness proofs

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Bug condition/postcondition formalization as testable Behavior Contracts. Defines invariants that must be preserved across fixes.

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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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