'formal' 검색 결과

Generate executable code together with formal proofs certifying safety and correctness properties in Isabelle/HOL or Coq. Use when building verified software, safety-critical systems, or when formal guarantees are required. Produces code with accompanying proofs for memory safety, bounds checking, functional correctness, invariant preservation, and termination. Supports extraction to OCaml/Haskell/SML and integration with existing codebases.

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Extract abstract mathematical models from imperative code (C, C++, Python, Java, etc.) suitable for formal reasoning in Coq. Use when the user asks to model imperative code in Coq, create Coq specifications from imperative programs, extract mathematical models for verification, or translate imperative algorithms to Coq for formal reasoning and proof.

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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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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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台灣正式文件撰寫助手 — 涵蓋政府公文、政府機關其他文件、法律文件、人民對政府文書四類中文正式文件的撰寫（不含學術論文、商業文書、私人書信等，見下方排除清單）。 根據使用者意圖自動判斷文件類別，載入對應的撰寫規範與格式指引。 觸發此 skill 的情境： - 政府公文：簽、函、書函、公告、令、呈、咨、箋函、便簽、行文、發文、簽辦、擬稿、陳核、簽稿併陳、以稿代簽、先簽後稿、上行文、下行文、平行文 - 政府機關其他文件：會議紀錄、開會通知單、新聞稿、聲明稿、施政報告、出國報告、施政計畫書、業務計畫書、裁處書、訴願決定書、聘函、獎狀、證書 - 法律文件：存證信函、律師函、合約書、備忘錄(MOU)、保密協議(NDA)、聲明書、切結書、委託書、授權書 - 人民對政府文書：陳情書、申請書、訴願書、異議書、申覆書 - 描述需要撰寫正式文件的情境（如「幫我寫一封給教育部的公文」「我要寄存證信函」「幫我寫陳情書」） - 詢問任何正式文件的格式或用語規範 - 公務員考試或受訓的公文練習題 - 公文案件後續：催辦、展期、補正、否准、陳述意見通知、陳情答復、原函更正、會辦、會勘、會議異動、公務電話紀錄 不應觸發的情境： - 商業 email、求職信、履歷 - 學術論文、研究計畫書 - 商業計畫書、簡報 - 私人書信、感謝卡 - 翻譯任務 - 純粹的文章潤飾或改寫

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Apply semi-formal certificate reasoning to code analysis — patch verification, fault localization, patch equivalence. Use when reviewing patches, hunting bugs across scopes, comparing fixes, or when code reasoning requires tracing execution across files/modules. Triggers on code review, bug localization, patch comparison, name shadowing, scope analysis, regression checking.

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The logical structure of mathematical proof -- how first-order logic, natural deduction, and semantic reasoning combine to produce rigorous mathematical arguments. Covers the logical skeleton of direct proof, contraposition, contradiction, cases, and induction; the role of definitions, lemmas, and theorems; how informal mathematical prose maps to formal deductive structure; and the difference between proof-as-object and proof-as-activity. Use when the question is "why is this a valid proof?" rather than "what proof technique applies?"

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Musical form and structural analysis covering binary, ternary, rondo, sonata, theme-and-variations, and popular song forms. Covers formal archetypes (AB, ABA, ABACA, sonata-allegro), 12-bar blues, arch form, minimalist process forms, strophic and through-composed designs, and formal analysis methodology for both score study and listening. Use when determining the structural plan of a piece, analyzing sectional relationships, or understanding how form shapes musical narrative.

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Computational thinking as a problem-solving discipline independent of programming languages. Covers the four pillars (decomposition, pattern recognition, abstraction, algorithm design), computational problem-solving methodology (understand, decompose, generalize, formalize, verify), abstraction levels (from hardware through user interface), modeling and simulation, automata and formal languages (DFA, NFA, regular expressions, context-free grammars, Turing machines), computational complexity classes (P, NP, NP-complete, undecidable), and constructionist pedagogy (learning by building, Logo, Scratch, physical computing). Use when approaching unfamiliar problems, teaching problem-solving strategies, analyzing problem complexity, or bridging between domain knowledge and computational solutions.

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Deductive and inductive reasoning, formal and informal logical structure, validity, soundness, and rules of inference. Covers propositional logic, quantified reasoning, syllogisms, common inference patterns (modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism), and the distinction between deductive certainty and inductive probability. Use when the question is not whether a premise is true but whether the reasoning from premises to conclusion is logically valid.

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Conformal Geometric Algebra (CGA) for circles, spheres, and Möbius transformations

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CoSProver framework for translating informal proofs to Lean4 via intermediate formal proof states.

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> Formal oracle for behavioral equivalence via bisimulation games. Triggers: behavioral equivalence check, bisimulation game, are two systems equivalent, did a skill update preserve behavior, attacker-defender game, partition refinement, distinguishing trace. >>>>>>> origin/main

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Draft a project charter that defines scope, stakeholders, success criteria, and initial risk register. Covers problem statement, RACI matrix, milestone planning, and scope boundaries for both agile and classic methodologies. Use when kicking off a new project or initiative, formalizing scope after an informal start, aligning stakeholders before detailed planning begins, or transitioning from discovery to active project work.

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Use this skill during Phase 5 formal hardening. Provides tool selection, proof harness patterns, security/purity audit expectations, and verification result interpretation for Rust (Kani), Python (hypothesis), and TypeScript (fast-check).

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Manage QA release gates - go/no-go decisions, release sign-off reports, defect triage, and release readiness communication. Use this skill whenever a QA lead or manager needs to formally assess whether a build is ready to ship. Trigger on phrases like "release sign-off", "go or no-go", "is this ready to release", "defect triage", "release gate", "approve the release", "block the release", "release readiness", "quality gate", "sign off on this build", "triage these bugs", or any request to make or document a formal release decision. Also trigger when a release manager or PM asks "what's the QA status?" or "can we ship this?".

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Assess the scientific integrity and trustworthiness of publications before relying on their findings. Use this skill whenever evaluating a paper for a workflow, citing a study, building an analysis on published methods, or when a user asks about the reliability of a study. Checks for formal retractions, corrections, expressions of concern, and — critically — informal contradictions where subsequent studies failed to reproduce key findings. Integrates with PubMed, bioRxiv, and Consensus to provide a trust assessment. Use this skill for ANY publication evaluation, retraction checking, author reliability assessment, or when a user says "can I trust this paper", "is this study reliable", "has this been refuted", or "check this publication".

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Expert in formal logic, informal logic, fallacies, and argumentation theory

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Use this skill to configure and manage NPSP Household Accounts: household naming rules, formal/informal greeting formats, primary contact designation, household merges, and household splits. Trigger keywords: NPSP household naming, household account not updating, merge duplicate households NPSP, household greeting customization, primary affiliation NPSP. NOT for FSC (Financial Services Cloud) households — use admin/household-model-configuration. NOT for bulk-loading constituents and households into NPSP — use data/constituent-data-migration.

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Drafts formal appellate mandates that conclude the appeal process and direct trial courts to implement appellate decisions. Extracts disposition language, remand directives, and procedural history from appellate records to construct jurisdiction-specific mandate orders. Use when preparing mandate orders, returning jurisdiction to lower courts, or formalizing appellate dispositions after ruling.

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Structure persuasive speeches and formal arguments in forensic, legal, policy, and competitive debate styles. Use when the user needs to prepare talks, opening or closing arguments, policy pitches, public explanations, debate speeches, or mentions 'forensic speech', 'formal argument', 'persuasive speech structure', 'debate speech', 'opening statement', 'closing argument'. Turns structured claims into audience-tuned persuasive delivery.

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Expert-level complex analysis knowledge. Use when working with complex functions, holomorphic functions, Cauchy's theorem, contour integration, Laurent series, residues, conformal mappings, or analytic continuation. Also use when the user mentions 'holomorphic', 'analytic', 'Cauchy theorem', 'residue', 'contour integral', 'Laurent series', 'conformal map', 'Riemann mapping', 'Mobius transformation', 'harmonic function', 'entire function', or 'meromorphic'.

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Use when work produces a deliverable, factual claim, dataset, code change, decision, publication, deployment, automation, or irreversible action whose failure would matter; when the user asks for a quality gate, acceptance criteria, QA, completeness, validation, audit, evidence, preflight, release readiness, or a definition of done; or before claiming completion on medium- or high-risk work. Automatically decide whether a formal gate is warranted, derive task-specific pass/fail criteria, gather evidence, and block unsupported completion. Make sure to use this skill even when the user does not say "quality gate" if consequential work needs acceptance criteria or completion evidence. Skip formal gating for trivial, reversible, low-impact requests.

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SOP for formal mathematical domain modeling. Trigger when: - Creating new formal models or applying mathematical lenses to analyze existing specifications. - Navigating phases: Identify, Select, Construct, Validate, Record, Connect. - Prompt contains: /form, form workflow, categorical, coalgebraic, linear logic, information-theoretic, validation.

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