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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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Approach engineering problems by checking assumptions, defining performance constraints, and choosing suitable tools before implementation. The skill guides algorithm analysis, complete code, performance optimization, and correctness checks through tests, assertions, or formal verification, meaning mathematical checks of correctness.

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• Checking algorithm complexity and design assumptions
• Choosing languages for numerical or distributed systems
• Implementing concurrent code with explicit error handling

Review Apache Pinot changes for correctness in null handling, numeric types, type-based processing, and resource lifecycles. Use it to examine changes to calculations, aggregations, window functions, and segment cleanup or persistence.

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• Reviewing changes to null handling
• Checking branches based on data or index types
• Reviewing numeric processing in aggregations and window functions

await 漏れ・floating promise・並行競合など、非同期処理の correctness バグを検出する。並列化の効率提案（SIMPLIFY Efficiency）や配線断点（e2e-wiring）ではなく、「await を忘れて結果・順序・エラー伝播が壊れる」実装バグに限定する

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Review code changes or a repository for actionable bugs by tracing how components interact. Findings explain reachable triggers, incorrect behavior, consequences, and checked counterarguments. Correctness is the default focus; performance and security can also be selected.

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• Reviewing changes for bugs before integration
• Investigating state mismatches across components
• Checking whether a fix introduces another defect

Review Apache ShardingSphere pull requests or authorized downstream changes using repository evidence. Assess code correctness, merge readiness, or CI failures, then produce consolidated findings or a ready-to-copy reply to a review discussion.

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• Review code changes for correctness and regression risks
• Assess whether a pull request is ready to merge
• Investigate CI failures

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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Reviews audio DSP code for numerical correctness. Use when the user asks to review, audit, or check DSP code for correctness issues — filters, feedback loops, fixed-point arithmetic, accumulation loops, or any numeric computation in audio code. Trigger on "check this filter for NaN", "why does my reverb blow up?", "is this numerically stable?", "why do I hear DC in my output?". Pairs with audio-dsp-review (realtime safety); this skill covers numeric correctness. Flag issues proactively.

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将性能优化拆解为现状测量、单个假设的方案比较和正确性验证，在时间与费用上限内选出测得最快且安全的方案，并保留可重复执行的命令、配置和记录。

• 通过测量优化缓慢操作
• 在相同输入条件下比较实现
• 评估响应时间、吞吐量和执行费用

Prepare GRPO reinforcement learning configurations for tasks with programmatically checkable answers, such as math, code, and structured output. Design and inspect reward functions, then select training variants when runs show instability or exploit flaws in scoring.

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• Preparing GRPO training for tasks with automatic correctness checks
• Designing rewards for output format and correctness
• Inspecting reward scores before training

Create and run evaluations in Arize using an LLM as the judge. Define scoring criteria, connect them to actual data fields, evaluate recorded operations or experiment results, and set up continuous scoring for new data.

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• Check answers for unsupported claims
• Score experiment results for correctness
• Continuously evaluate new production records

Review code changes for security, performance, correctness, and maintainability. Get findings tied to files and lines, severity ratings, practical suggestions with code examples, and a recommendation to approve, request changes, or discuss further.

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• Reviewing a pull request before merging
• Checking authentication and injection risks
• Finding excessive database queries and resource leaks

Verify a local OpenSEO MCP server, which exposes tools to AI agents, through real DataForSEO calls and a headless Claude trial. Check protocol correctness alongside tool discovery, input rules, response size, errors, and asynchronous task recovery.

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• Checking an MCP tool after adding or changing it
• Testing whether an agent can choose tools from their descriptions
• Verifying queued tasks and recovery using taskId

Review code changes for correctness, readable names, clear interfaces, and design problems. Examine duplication, hidden assumptions, and unnecessary abstractions, then report actionable findings with file locations, explanations, and concrete suggestions for fixes.

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• Review pull request changes
• Check names and function interfaces
• Find duplication and unclear responsibilities

Develop or port CPU kernels, the low-level calculation routines used by MNN. Follow staged implementation guidance, check data layout agreements, register functions, and verify correctness across processor instruction sets and numerical precision settings.

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• Implementing or porting an MNN CPU kernel
• Adding support for a processor instruction set
• Changing packed data layouts or tile sizes

Improve MNN's Vulkan backend by separating CPU scheduling bottlenecks from GPU computation costs. It guides operator and shader changes, new feature integration with compatibility fallbacks, and device testing to verify both correctness and end-to-end performance.

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• Finding CPU or GPU bottlenecks in Vulkan inference
• Optimizing a specific operator or shader
• Integrating cooperative matrix or subgroup features

Run TVM's TIRx compiler tests alongside tirx-kernels import and correctness checks. It verifies the local build, selects GPUs, runs parallel tests, saves full logs, and guides failure investigation and result reporting.

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• Testing TIRx compiler and kernel changes
• Checking tirx-kernels imports and registry entries
• Running parallel tests across selected GPUs

Fine-tune language models with TRL using GRPO, a method that compares scored responses to the same prompt. Covers training data, scoring functions, GPU-conscious settings, and monitoring for tasks with measurable correctness or required output formats.

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• Train models to follow JSON or XML output formats
• Reward correct answers in math or coding tasks
• Balance correctness, format, and style during training

Review code changes for security, performance, correctness, and maintainability. Get findings tied to files and lines, severity ratings, practical suggestions with code examples, and a recommendation to approve, request changes, or discuss further.

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• Reviewing a pull request before merging
• Checking authentication and injection risks
• Finding excessive database queries and resource leaks

Review a pull request using repository checks, verified code references, and current official documentation. Assess correctness, security, structure, and unnecessary code, then post one consolidated GitHub review with inline findings and an evidence-based verdict.

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• Review a pull request before merging
• Check code structure and unnecessary comments
• Verify dependency changes against official documentation

Write and review GitHub Actions workflows for syntax and structural correctness. Check quoting around expressions and special characters, then validate with actionlint, a workflow checker, to catch errors that ordinary YAML parsing can miss.

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• Reviewing new or edited GitHub Actions workflow files
• Checking quotes around expressions containing special characters
• Investigating workflow failures before any jobs start

Review MSBuild project files and build definitions for correctness and maintainability. Get prioritized findings with concrete recommendations, distinguishing confirmed defects from conditional risks and valid exceptions such as F# source ordering or required imports.

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• Reviewing build files for maintainability
• Checking path portability across operating systems
• Reviewing import safety and required-file assumptions

Review database access built with Entity Framework Core to find slow queries, excessive database calls, memory costs, and correctness issues. It traces application code and uses available SQL logs or execution plans to support targeted fixes.

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• Reviewing slow EF Core queries and excessive database calls
• Investigating memory use in imports and background jobs
• Checking search filters, pagination, and index coverage

Review GitHub agentic workflows, automated workflows guided by AI agents, for security and correctness. Compile changes, inspect permissions and safeguards, and use available run logs to identify supported improvements to cost and execution time.

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• Reviewing workflow permissions and security safeguards
• Checking workflow compilation and security scan results
• Finding cost and runtime improvements in execution logs