Formal Verification AI

**Category:** Phase 3 Core - Correctness Guarantees **Status:** Skeleton Implementation **Dependencies:** `categorical-composition` (correctness as functoriality)

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SKILL.md

Full skill instructions

Formal Verification AI

Category: Phase 3 Core - Correctness Guarantees Status: Skeleton Implementation Dependencies: categorical-composition (correctness as functoriality)

Overview

Integrates formal verification methods with AI systems: theorem proving for correctness guarantees, interval arithmetic for certified bounds, and categorical proofs for compositional correctness.

Capabilities

Theorem Proving: Automated verification of AI properties
Interval Arithmetic: Certified bounds on network outputs
Categorical Correctness: Functorial preservation guarantees
Adversarial Robustness: Verified defense certificates

Core Components

Theorem Prover Interface (theorem_proving.jl)
- Integration with Z3, Lean, or Coq
- Encode neural networks as logical formulas
- Automated proof search
Interval Arithmetic (interval_arithmetic.jl)
- Interval propagation through networks
- Certified bounds on outputs
- Robustness verification
Categorical Proofs (categorical_correctness.jl)
- Verify functor laws for compositional networks
- Natural transformation diagrams
- Commutativity checking
Verification Examples (verification_examples.jl)
- Adversarial robustness proofs
- Fairness guarantees
- Safety-critical system verification

Integration Points

Input from: All Phase 3 skills (provides verification layer)
Output to: categorical-composition (verified transformations)
Coordinates with: oriented-simplicial-networks (topological invariants)

Usage

using FormalVerificationAI

# Define neural network
network = SimpleNN([Dense(10, 20, relu), Dense(20, 2)])

# Verify robustness using interval arithmetic
input_interval = Interval([0.0, 0.0], [1.0, 1.0])
output_bounds = propagate_intervals(network, input_interval)

# Prove categorical correctness
F = network_to_functor(network)
@assert verify_functor_laws(F)

# Automated theorem proving
property = "∀x. ||x - x'|| < ε ⟹ ||f(x) - f(x')|| < δ"
proof = prove_property(network, property, timeout=60)

References

Katz et al. "Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks" (2017)
Singh et al. "An Abstract Domain for Certifying Neural Networks" (POPL 2019)
Fong & Spivak "Hypergraph Categories" (2019)

Implementation Status

Basic interval arithmetic
Z3 interface skeleton
Full neural network encoding
Categorical correctness verification
Benchmark on standard verification tasks

Install skill

Copy and run in your terminal

npx -y skills add https://github.com/plurigrid/asi --skill formal-verification-ai

View on GitHub

ies/music-topos/.codex/skills/formal-verification-ai/SKILL.md

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