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soundness-proof-assistant

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Assist in constructing type soundness proofs using progress and preservation theorems

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Source SKILL.md: https://github.com/a5c-ai/babysitter/blob/HEAD/library/specializations/domains/science/computer-science/skills/soundness-proof-assistant/SKILL.md

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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