formal-methods

name	formal-methods
description	Verify proofs, check theorem correctness, and solve satisfiability problems using Lean 4, Coq, and Z3 SMT solver. Use when the user asks to prove theorems, verify mathematical proofs, check logical satisfiability, or work with proof assistants.

formal-methods

Formal verification tools for the academic workspace. Type-check Lean 4 proofs, verify Coq theories, and solve SMT satisfiability problems with Z3.

Description

This skill wraps locally installed formal verification provers (lean, coqc, z3) via subprocess. No Docker or external services required.

Usage Examples

• "Check if this Lean 4 proof type-checks"
• "Verify my Coq induction proof"
• "Is this SMT formula satisfiable?"
• "What provers are available?"

Process

1. Check availability — Use prover_status to see which provers are installed
2. Write proof — Draft your Lean/Coq code or SMT formula
3. Verify — Use lean_check, coq_check, or z3_solve to verify
4. Iterate — Fix errors based on output and re-check. Common patterns: "type mismatch" in Lean means type annotations need fixing; "unsat" from Z3 means no satisfying assignment exists (formula is a tautology when negated); "unknown" means Z3 couldn't determine satisfiability within limits

Tools

lean_check

Type-check Lean 4 code.

Parameters:

• code (string, required): Lean 4 source code
• filename (string, optional): Source filename (default: check.lean)

Returns: { success, output, errors, returncode }

Example:

{ "code": "theorem add_comm (a b : Nat) : a + b = b + a := Nat.add_comm a b" }

coq_check

Check a Coq proof for correctness.

Parameters:

• code (string, required): Coq source code
• filename (string, optional): Source filename (default: check.v)

Returns: { success, compiled, output, errors, returncode }

Example:

{ "code": "Theorem plus_comm : forall n m : nat, n + m = m + n.\nProof. intros. lia. Qed." }

coq_compile

Compile a Coq file to a .vo object file.

Parameters:

• code (string, required): Coq source code
• filename (string, optional): Source filename (default: compile.v)

Returns: { success, compiled, output, errors, returncode }

z3_solve

Solve a satisfiability problem using Z3 with SMT-LIB2 format.

Parameters:

• formula (string, required): SMT-LIB2 formula

Returns: { success, result, model }

Example:

{ "formula": "(declare-const x Int)\n(assert (> x 5))\n(check-sat)\n(get-model)" }

prover_status

Check which formal provers are available and their versions.

Parameters: None

Returns: { provers: { lean4: { available, version }, coq: { available, version }, z3: { available, version } } }

Notes

• Requires provers installed locally (lean, coqc, z3)
• Z3 only accepts SMT-LIB2 format (declarative, no arbitrary code execution)
• Execution timeout is 60 seconds per invocation