Skills-4-SE

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.

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.

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.

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.

Automatically generate TLA+ specifications from program code, repositories, or system implementations. Use when asked to generate TLA+ spec, create TLA+ specification from code, convert program to TLA+, formalize system in TLA+, extract TLA+ model from code, or when working with formal specification of concurrent systems, distributed systems, protocols, algorithms, or state machines that need to be verified.

Extract abstract mathematical models from functional code (Haskell, OCaml, F#) for formal reasoning in Isabelle/HOL. Use when users need to: (1) Convert functional programs to Isabelle definitions, (2) Extract high-level algorithm essence from implementation code, (3) Generate formal specifications and properties from code, (4) Create verification-ready models that capture mathematical properties while abstracting away implementation details. Focuses on structural recursion, algebraic data types, higher-order functions, and invariant extraction.

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.

Transforms natural language requirements (user stories, verbal descriptions, business rules) into formal specifications and constraints. Use when converting informal requirements into structured, testable specifications with explicit constraints. Outputs in multiple formats including BDD-style Given-When-Then, JSON Schema, and structured plain text requirements documents.

Optimize test suites using mutation testing to maximize mutation kill rate with minimal tests. Use when you need to reduce test suite size while maintaining quality, identify redundant tests, improve mutation coverage, or validate test effectiveness. The skill analyzes test coverage, execution intervals, and redundancy using mutation operators, selects or generates a minimal subset of tests that maximizes mutation kill rate, and outputs an optimized test suite with detailed reports showing killed and surviving mutants. Supports multiple programming languages and mutation testing frameworks.

Compare behavior across multiple versions of programs or repositories. Use when you need to analyze how functionality changes between versions, identify regressions, compare outputs and exceptions, or validate upgrades. The skill compares execution behavior, test results, outputs, exceptions, and observable states across versions, generating detailed reports showing behavioral divergences, potential regressions, added/removed functionality, and areas requiring validation. Supports multiple programming languages and can work with test suites or execution traces.

Translate source code between programming languages at function, class, and module levels while preserving behavior and generating verification tests. Use when translating code from one language to another (e.g., "translate this Python module to JavaScript", "convert this Java class to C#", "port this code to Go and generate tests"), migrating codebases between languages, or creating equivalent implementations across different technology stacks. Handles idiom adaptation, standard library mappings, and test generation.

Generates complete modules and components from interface contracts and specifications. Use when Claude needs to build larger software components, implement interfaces, create service layers, or generate complete modules with multiple related classes. Supports Python (with type hints and protocols) and Java (with interfaces and abstract classes). Trigger when users request "implement this interface", "generate a module for", "create a service layer", "build a component that implements", or provide interface definitions that need implementation.

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.

Generate unit tests with proper mocking for Python (unittest.mock/pytest) or Java (Mockito/JUnit) code. Use when users request test generation, unit tests with mocks, or testing code that has external dependencies like database calls, API requests, file I/O, or network operations. Automatically identifies dependencies to mock and creates executable, maintainable test code.

Generate test cases using metamorphic testing by applying transformations based on metamorphic properties. Use when you need to expand test suites, test programs without oracles, validate mathematical or algorithmic properties, or detect subtle bugs through input-output relationships. The skill takes a program, original test cases, and metamorphic properties as input, generates new test cases by applying transformations, executes tests, verifies outputs satisfy properties, reports violations and anomalies, and outputs an expanded test suite with property coverage summary. Supports multiple programming languages and property types.

Automatically identify metamorphic properties (symmetry, linearity, additivity, input invariances) from programs or functions. Use when generating metamorphic tests, discovering program properties, validating transformations, or creating test oracles without explicit specifications. Analyzes control flow, data flow, and sample executions to output structured properties for metamorphic test generation and verification.

Reorganizes markdown documents into well-structured, consistent format while preserving content and improving readability. Use when Claude needs to: (1) Fix heading hierarchy issues (skipped levels, multiple h1s), (2) Generate or update table of contents, (3) Standardize formatting (lists, code blocks, emphasis, links), (4) Improve grammar and spelling, (5) Add missing standard sections (installation, usage, etc.), (6) Remove redundant or duplicate content, (7) Restructure technical docs, READMEs, or long-form content for better organization and flow.

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.

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.

Produces comprehensive summaries and insights about legacy codebases to help understand unfamiliar code. Use when onboarding to a new project, planning refactoring efforts, assessing code for acquisition/migration, or generating documentation for undocumented systems. Analyzes architecture, dependencies, code quality issues, and test coverage. Creates high-level overviews with architecture diagrams, key components, entry points, and actionable insights for understanding and improving legacy code.

Update Java test classes and methods to work with new code versions after refactoring or modifications. Use when code changes break existing tests due to signature changes, refactoring, or behavior modifications. Takes old and new code versions plus old tests as input, and outputs updated tests that compile and pass against the new code. Handles method signature changes, class refactoring, assertion updates, and mock modifications.

Automatically generate regression tests for Java codebases by analyzing changes between old and new code versions. Use when users need to: (1) Generate tests after refactoring or code changes, (2) Ensure previously tested behavior still works in new versions, (3) Cover modified or newly added code paths, (4) Migrate existing tests to work with updated APIs or signatures, (5) Maintain test coverage during code evolution. Supports JUnit and TestNG frameworks with unit tests, parameterized tests, and exception testing patterns.

Validate API consistency between two versions of Java libraries. Use when you need to compare API behavior, signatures, and exceptions between Java library versions to identify breaking changes, incompatible modifications, and behavior differences. The skill performs static analysis of Java code, compares method signatures, class definitions, interface changes, parameter types, return types, exception declarations, and generates a detailed JSON report with breaking changes, warnings, and migration guidance. Supports Java libraries and packages.

Automatically generate clear, actionable issue reports from failing tests and repository analysis. Analyze test failures to understand expected vs. actual behavior, identify affected code components, and produce well-structured Markdown reports suitable for GitHub Issues or similar trackers. Use when a test fails, when debugging issues, or when the user asks to create an issue report, generate a bug report, or document a test failure.

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.