---
name: soundness-proof-assistant-602789e15498
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
graph:
  domains: [domain:computer-science]
  specializations: [specialization:theoretical-computer-science]
  skillAreas: [skill-area:compiler-implementation, skill-area:language-design, skill-area:graph-algorithms]
  workflows: [workflow:research-grant-lifecycle]
  roles: [role:research-engineer, role:computational-scientist]
---

# 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


---
Source attribution: a5c-ai
Original project: https://github.com/a5c-ai/babysitter/blob/feb68abe397acc14f32b34984975c48fedba2b33/library/specializations/domains/science/computer-science/skills/soundness-proof-assistant/SKILL.md
License: MIT
License information: https://opensource.org/license/mit
Original upstream instructions; downloaded from Mega AI Hub.

## Upstream license notice

# MIT License

Copyright (c) 2025 A5C AI

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.



# Mega AI Hub resource metadata

Creator / publisher: a5c-ai
Original project: https://github.com/a5c-ai/babysitter/blob/feb68abe397acc14f32b34984975c48fedba2b33/library/specializations/domains/science/computer-science/skills/soundness-proof-assistant/SKILL.md
Attribution basis: Source repository record

Fields of work: Data & Analytics, Development & Engineering, Education & Research
Roles: Data Scientist, ML / AI Engineer, Researcher
Specialties: Specialty not specified
Tools: Agda, Bash, Coq, Lean, Twelf
Country applicability: Country not specified
Classification basis: Source catalog labels
Instruction SHA-256: 9e0244af98780ed3d8b3ed0be00c13fcf6d440caf35720206f9fa446df11d4ef