30 件 ・ 関連度順
概要と使いどころ
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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Use when a proof needs Rocq (formerly Coq), including legacy Coq codebase maintenance and migration through the Coq to Rocq rename. Not for Lean 4: use writing-lean-proofs.
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Analyze proof states in Isabelle or Coq and suggest applicable tactics to make progress. Use when users need help with: (1) Choosing the next tactic in an interactive proof, (2) Understanding what tactics apply to their current goal, (3) Getting unstuck in a proof, (4) Learning which tactics work for specific goal structures (conjunctions, implications, induction, etc.). Provides 3-5 ranked tactic suggestions with explanations for intermediate-level proofs in both Isabelle/Isar and Coq.
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Generate structured proof skeletons with tactics, strategies, and intermediate lemmas for theorems in Isabelle/HOL or Coq. Use when users need to: (1) Create proof outlines for theorem statements, (2) Generate proof structure with tactic placeholders, (3) Identify key lemmas needed for a proof, (4) Plan proof strategies (induction, case analysis, forward/backward reasoning), (5) Scaffold proofs with intermediate steps and subgoals, or (6) Convert theorem statements into detailed proof templates. Supports both Isabelle/HOL and Coq equally.
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Generate Isabelle or Coq proofs establishing partial or total correctness of imperative programs from code and formal specifications. Use when users need to: (1) Prove program correctness using Hoare logic, (2) Generate verification conditions from pre/postconditions, (3) Construct loop invariants and termination arguments, (4) Verify imperative programs with assignments, conditionals, and loops. Supports both partial correctness (if terminates, postcondition holds) and total correctness (terminates and postcondition holds) for both Isabelle/HOL and Coq.
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Summarize long Isabelle or Coq proof scripts into high-level logical steps and reasoning flow. Use when users need to: (1) Understand the structure of a complex proof, (2) Document proof strategies for others, (3) Extract the key reasoning steps from verbose proof scripts, (4) Create readable proof outlines from detailed tactical proofs. Produces hierarchical outlines with moderate detail showing proof structure, main cases, key lemmas, and reasoning flow for both Isabelle/Isar and Coq proofs.
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Analyze and explain why Isabelle or Coq proofs fail, identifying the root cause such as type mismatches, missing assumptions, incorrect goals, unification failures, or inapplicable tactics. Use when the user encounters proof failures, error messages in formal verification, stuck proof states, or asks why their Isabelle/Coq proof doesn't work.
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Recommend relevant Isabelle/HOL or Coq standard library theories, lemmas, and tactics based on proof goals. Use when: (1) Users need library lemmas for their proof, (2) Proof goals match standard library patterns, (3) Users ask what libraries to import, (4) Specific lemmas are needed for list/set/arithmetic operations, (5) Users are stuck and need to know what library support exists, or (6) Guidance on find_theorems/Search commands is needed. Supports both Isabelle/HOL and Coq standard libraries.
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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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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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Machine learning environment for automated theorem proving with Coq.
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Formal verification of Rust programs via translation to Coq/Rocq.
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Mathematical foundations, logical structures, and formal verification guidance. Trigger when: - Designing protocol contracts, formal specifications, verifying state spaces, or using proof assistants. - Tasks involve: TLA+, Alloy, Lean, Coq, model checkers, invariants, temporal logic. - Prompt contains keywords: formal verification, alloy, tla+, lean, coq, invariant, state machine, model checker, liveness, safety.
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Quality control for flow, spectral, and mass cytometry - time-based anomaly cleaning (flowAI, flowCut, PeacoQC, flowClean), margin/boundary event removal, signal-drift detection, dead-cell exclusion, CyTOF Gaussian/DNA/event-length checks, instrument calibration/standardization (MESF, CS&T, peak-2), and batch-level outlier flagging. Use when assessing acquisition quality, choosing a cleaning tool, ordering QC relative to compensation, deciding margin removal before density-based steps, or flagging problematic samples before clustering or differential analysis.
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Establish explicit traceability between formal specifications (preconditions, postconditions, invariants) and verified code components with their correctness proofs. Produce structured Markdown mapping reports showing verification coverage and proof evidence. Use when auditing formal verification, documenting verified systems, establishing traceability for certification, or when the user asks to map specifications to code, generate verification reports, or analyze verification coverage in Coq, Dafny, Isabelle, or other proof assistants.
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Analyze formal verification artifacts (Isabelle, Coq, Dafny, etc.) and produce structured reports identifying the precise boundary between verified, assumed, and unverified components. Use when assessing verification coverage, understanding trust boundaries, auditing formal proofs, or documenting verification scope. Reports explicitly list verified code, assumptions, axioms, trusted computing base, and unverified components. Conservative and explicit about verification status without attempting to repair or mask gaps.
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Extract language-agnostic pseudocode from formally verified programs (Isabelle/HOL, Coq) while preserving verified control flow, data dependencies, and algorithmic logic. Use when: (1) Users have verified code and need readable pseudocode, (2) Documenting verified algorithms for broader audiences, (3) Translating verified implementations to other languages, (4) Creating algorithm specifications from verified code, (5) Preserving verification guarantees in pseudocode form, or (6) Abstracting proof-heavy code to essential logic. Maintains semantic faithfulness to verified implementation.
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Generate systematic refinement steps from high-level specifications to concrete implementations in Isabelle/HOL or Coq, preserving correctness obligations at each step. Use when working with formal verification, program refinement, proof development, or when translating abstract specifications into executable code while maintaining formal guarantees. Supports data refinement (abstract types → concrete structures), algorithmic refinement (specifications → algorithms), and stepwise refinement with proof obligations.
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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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Restructure and improve Isabelle or Coq proofs to enhance readability, modularity, and maintainability without changing semantics. Use when proofs are long and monolithic, have repeated patterns, use unclear naming, lack documentation, or when the user asks to refactor, clean up, improve, or reorganize their formal proofs.
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Analyze failed or stuck proofs and propose auxiliary lemmas to help complete the proof in Isabelle/HOL or Coq. Use when encountering proof failures, stuck proof states, unprovable subgoals, or when needing to strengthen induction hypotheses. Identifies missing lemmas, suggests proof strategies, and generates helper lemmas with appropriate statements and proof sketches. Supports inductive proofs, case analysis, rewriting, and complex proof obligations.
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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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Think and work like an expert Logician. Use when a task calls for Logician judgment. Reasons from syntax-versus-semantics and object-versus-metalanguage discipline, the ⊢/⊨ distinction, and matching each logic to its intended semantics through natural deduction and sequent calculus (cut-elimination, subformula property), compactness and Löwenheim–Skolem, forcing and diagonalization, and proof assistants (Lean 4/mathlib, Coq, Isabelle/HOL, Agda) with Z3/CVC5/Vampire/Mace4 automation while treating use–mention conflation, second-order misuse of compactness, mis-stated incompleteness hypotheses (ω-consistency vs consistency), and Gödel philosophical overreach as first-class failure modes.
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Think and work like an expert Formal Methods Researcher. Use when a task calls for Formal Methods Researcher judgment. Reasons from operational semantics and temporal logics through SPIN/TLA+/PRISM, Coq/Lean/Isabelle, Z3/CVC5, refinement and separation logic, vacuity and false-positive diagnosis, and Dafny/F* versus property-based testing boundaries.
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