name: soundness-proof-assistant description: Assist in constructing type soundness proofs using progress and preservation theorems allowed-tools:

• Bash
• Read
• Write
• Edit
• Glob
• Grep metadata: specialization: computer-science domain: science category: programming-language-theory phase: 6

Soundness Proof Assistant

Purpose

Provides expert guidance on constructing type soundness proofs for programming language type systems.

Capabilities

• Progress theorem proof templates
• Preservation theorem proof templates
• Substitution lemma generation
• Canonical forms lemma derivation
• Proof case enumeration
• Mechanization guidance

Usage Guidelines

1. Lemma Identification: Identify required supporting lemmas
2. Progress Proof: Prove progress theorem by cases
3. Preservation Proof: Prove preservation theorem
4. Substitution Lemmas: Prove substitution preserves typing
5. Mechanization: Translate to proof assistant

Tools/Libraries

• Coq
• Agda
• Lean
• Twelf