The rapid advancement of AI systems, particularly Large Language Models, has created an urgent need for verification techniques that can keep pace with innovation. I believe the answer lies at the intersection of three powerful paradigms: functional programming, formal methods, and modern AI architectures.

The Verification Gap in AI

Traditional software verification assumes deterministic behavior and well-defined specifications. AI systems shatter both assumptions:

# Traditional function - verifiable
def sort(lst):
    return sorted(lst)
    # Property: output is permutation of input AND ordered

# AI function - how to verify?
def generate_code(prompt):
    return llm.complete(prompt)
    # Property: ???

This gap isn't just theoretical—it has real consequences as AI systems take on critical roles in software development, decision-making, and autonomous systems.

Functional Programming as Foundation

Functional programming provides essential building blocks for verified AI:

1. Compositionality

AI systems built from pure functions can be verified modularly:

(define (verified-pipeline input)
  (compose 
    (verified-transform transform-spec)
    (verified-model model-spec)
    (verified-output output-spec)))

2. Immutability

Stateless AI components are easier to reason about formally:

(defn neural-layer [weights input]
  ; Pure function - output depends only on inputs
  (activate (matrix-multiply weights input)))

3. Type-Level Guarantees

Advanced type systems can encode AI properties:

-- Dependent types can encode network architecture
forward :: Network [784, 128, 10] -> Vector 784 -> Vector 10

Formal Methods for AI Properties

Rather than verifying exact outputs, we can verify meta-properties:

Safety Properties

  • Output bounds: "Generated code contains no system calls"
  • Semantic preservation: "Translation maintains program meaning"
  • Fairness constraints: "Decisions are invariant to protected attributes"

Liveness Properties

  • Convergence: "Training eventually reaches stable state"
  • Progress: "Each iteration improves objective function"
  • Termination: "Generation completes within token limit"

Temporal Properties

Using TLA+ for AI system specifications:

AISystemSpec == 
  /\ Init
  /\ [][Next]_vars
  /\ SafetyInvariant
  /\ EventuallyConsistent

LLMs as Verification Assistants

The recursive opportunity: using AI to verify AI:

  1. Property Generation: LLMs can suggest likely invariants
  2. Proof Sketch Creation: AI-assisted proof development
  3. Counterexample Explanation: Natural language descriptions of violations
  4. Specification Refinement: Iterative improvement of formal models

Liquid Neural Networks: A Case Study

Liquid networks' dynamic architecture makes them ideal for formal analysis:

(define (liquid-state-evolution state input time)
  ; Continuous-time dynamics amenable to formal analysis
  (let ([dynamics (compute-dynamics state input)])
    (verify-stability dynamics)
    (verify-bounded-response dynamics)
    (integrate dynamics time)))

Their mathematical foundation in differential equations bridges neural approaches with control theory verification.

Building Bridges: Practical Steps

1. Verified AI Components Library

Start small with verified building blocks: - Attention mechanisms with proven properties - Activation functions with formal bounds - Layer compositions with type guarantees

2. Property-Based Testing for AI

Extend QuickCheck-style testing to neural systems:

@property
def attention_is_permutation_equivariant(seq, perm):
    original = attention(seq)
    permuted = attention(permute(seq, perm))
    return permute(original, perm) ≈ permuted

3. Formal Specifications for Common Patterns

Create reusable TLA+ modules for: - Transformer architectures - Training dynamics - Inference pipelines

The Collaborative Imperative

This vision requires diverse expertise:

  • Compiler experts to build verified AI runtimes
  • AI researchers to identify verifiable properties
  • Formal methods practitioners to develop appropriate logics
  • Educators to make these tools accessible

No single researcher can bridge these domains alone. The future of trustworthy AI lies in collaborative efforts that combine deep domain knowledge with formal rigor.

Call to Action

I'm actively seeking collaborators who share this vision. Whether your background is in: - Functional language implementation - AI/ML systems - Formal verification - Educational technology

There's a place for your expertise in building the foundations of verified AI.

The convergence is happening. The question is not whether we'll need verified AI systems, but whether we'll be ready with the tools and techniques when the need becomes critical. Let's build that future together.

Interested in collaborating? Reach out at dpascal@defrecord.com or find me on GitHub.