parcadei

Find lemmas, reusable mathematical results, in Mathlib by matching the type signature you need for a Lean proof. Search with type variables, related terms, or exact names to identify candidates you can apply.

• Finding a lemma when its name is unknown
• Exploring lemmas associated with a particular type
• Finding list functions from their input and output types

Guide framework, language, database, and infrastructure migrations through research, impact analysis, phased planning, implementation, and review. Specialized agents produce reports and code changes, with testing steps and a rollback strategy included in the workflow.

• Upgrading a framework or language version
• Moving to a different database
• Planning a move between cloud platforms

Delegate implementation, file reading, and testing to separate agents, then bring concise summaries back to the main conversation. The rules explain when delegation helps and when a small edit is better handled directly.

• Implementing a feature across multiple files
• Completing a specific phase of an implementation plan
• Delegating feature development and testing

Investigate problems during implementation or manual testing by examining logs, database records, Git history, and service status. It produces an evidence-based report with likely causes and suggested next steps, without editing files.

• Investigating errors found during manual testing
• Tracing problems after recent code changes
• Checking database records for unexpected states

Find the right tool for equations, calculus, numerical calculations, proof checks, or math practice. The guide connects tasks to commands for computing results, verifying steps, requesting hints, and plotting functions.

• Solving equations and checking the answers
• Learning with practice problems and progressive hints
• Choosing tools for proofs and constraint problems

Create a structured YAML handoff before clearing a conversation. It records completed work, decisions, findings, blockers, and next steps so a later session has the information needed to resume, with an outcome recorded from user feedback.

• Saving progress before running /clear
• Handing off implementation work across multiple days
• Recording decisions and blockers during a complex refactor

Handle equations, calculus, matrices, unit conversions, and mathematical explanations through one entry point. The skill selects a suitable calculation tool or topic guide, including symbolic math tools that work directly with expressions.

• Solve equations and calculate integrals
• Find matrix eigenvalues
• Convert between units

Verify that infrastructure code is connected to the system and actually runs. Trace execution paths, check hook registration and database configuration, and test the full workflow to identify unused code or duplicate implementations before declaring completion.

• Checking that new infrastructure is actually invoked
• Verifying hook registration and configuration
• Confirming the intended database backend is used

Follow execution rules when testing in Agentica’s asynchronous REPL, an interactive code environment. Await tools that return pending results, and keep computation and the return statement in one code block so both execute in the same response.

• Checking tool calls in Agentica’s asynchronous REPL
• Waiting for file-reading results before processing them
• Combining computation and result return in one code block

Connect Agentica SDK agents to Claude Code CLI through a proxy, an intermediary server. Use setup and debugging guidance to address file permissions, streamed responses, result formatting, and agents reporting success without performing the requested operations.

• Connecting Agentica agents to Claude Code tools
• Investigating file write and edit permission errors
• Debugging streaming and REPL response formats

Guide Claude Code hook development with shell wrappers and TypeScript handlers. It covers event timing, JSON input and output, hook registration, and manual testing, including handlers that can block tool execution.

• Add a check before tool execution
• Process events when a session starts
• Standardize hook registration and manual testing