Necessity of deep SMT integration for a Sledgehammer-like Lean tactic

Determine whether developing a Lean tactic with ambition and potential impact comparable to Isabelle/HOL’s Sledgehammer necessarily requires integration with proof-producing SMT solvers at a level of depth comparable to Sledgehammer’s SMT integration, i.e., translating goals to SMT-LIB and reconstructing solver proofs within Lean.

Background

Isabelle/HOL’s Sledgehammer tactic achieves strong automation by integrating proof-producing SMT solvers, translating proof goals to SMT-LIB and reconstructing solver proofs back into Isabelle. Lean currently lacks an equivalent ‘hammer’ tactic, motivating efforts to replicate Sledgehammer’s capabilities in Lean.

The paper introduces lean-smt, a tactic that integrates cvc5 with Lean, translating certain Lean goals to SMT problems and reconstructing CPC proofs into Lean. In articulating the broader motivation, the authors explicitly conjecture that a Sledgehammer-level tactic for Lean will require similarly deep SMT integration.