The quest for program correctness has long been a central concern in computer science. In this post, I explore how we can leverage TLA+ specifications alongside Scheme implementations to build systems with strong correctness guarantees.

Why Scheme for Verified Systems?

Scheme's minimalist design and powerful metaprogramming capabilities make it an ideal candidate for formal verification:

  1. Small Core Language: The R7RS-small specification is remarkably concise, making it feasible to formally specify the entire language semantics.

  2. Homoiconicity: Code-as-data enables powerful program analysis and transformation techniques.

  3. Functional Paradigm: Immutability and referential transparency simplify reasoning about program behavior.

Bridging TLA+ and Scheme

My recent work on the scheme-formal-verification project demonstrates a practical approach to bridging these worlds:

;; Scheme implementation
(define (merge-sort lst)
  (cond
    [(null? lst) '()]
    [(null? (cdr lst)) lst]
    [else
     (let* ([mid (quotient (length lst) 2)]
            [left (take lst mid)]
            [right (drop lst mid)])
       (merge (merge-sort left)
              (merge-sort right)))]))

The corresponding TLA+ specification captures the essential properties:

MergeSort(lst) ==
  IF Len(lst) <= 1
  THEN lst
  ELSE LET mid == Len(lst) \div 2
           left == SubSeq(lst, 1, mid)
           right == SubSeq(lst, mid + 1, Len(lst))
       IN Merge(MergeSort(left), MergeSort(right))

Property-Based Testing as a Bridge

Rather than attempting full formal proofs, I've found property-based testing to be an effective middle ground. By generating test cases from TLA+ specifications, we can achieve high confidence in correctness while maintaining practical development velocity.

Future Directions

The integration of neural approaches through LLMs opens exciting possibilities for automated verification. Tools that can suggest invariants, generate test properties, or even produce proof sketches could dramatically lower the barrier to building verified systems.

The goal isn't to verify every line of code, but rather to apply formal methods judiciously where correctness is critical—and Scheme's elegant design makes this eminently achievable.