Integrating Gandalf and HOL

Abstract

Abstract. Gandalf is a first-order resolution theorem-prover, optimized for speed and specializing in manipulations of large clauses. In this paper I describe GANDALF TAC, a HOL tactic that proves goals by calling Gandalf and mirroring the resulting proofs in HOL. This call can occur over a network, and a Gandalf server may be set up servicing multiple HOL clients. In addition, the translation of the Gandalf proof into HOL fits in with the LCF model and guarantees logical consistency.

Modular SMT Proofs for Fast Reflexive Checking Inside Coq

“…An edge labelled by an equality corresponds to a transitivity: t 6 (18) −−→ z yields [Trans (18, true)]. An edge labelled by two equalities uses congruence: t 3 (1) (2) − −−− → t 5 yields [Trans(1, f alse); Congr(11, 1, true); Trans(2, true)].…”

“…Several approaches have been proposed to integrate new decision procedures in sceptical proof assistants for various theories. First-order provers have been integrated in Isabelle [25], HOL [18] or Coq [9]. These works rely generally on resolution proof trees.…”

Providing Automated Verification in HOL Using MDGs

“…Hurd [10] used PROSPER [5] to combine the Gandalf first-order theorem prover with HOL. A HOL tactic, GANDALF TAC, is used to enable first-order HOL goals to be proven by Gandalf and mirror the resulting proofs in HOL.…”

“…The work in [1,10,11,19] use the same approach as the HOL-MDG hybrid tool in the way they integrate the model checker to the theorem prover. The work in [18] uses the µ-calculus as a medium for communicating between the theorem prover and the model checker.…”

Source-Level Proof Reconstruction for Interactive Theorem Proving

“…He has already shown [4] how difficult it is to harness existing ATPs for this purpose: ambiguities in their output complicate proof reconstruction. Although Metis cannot compete with the best ATPs, it includes a full implementation of the superposition calculus, and its performance is respectable [6].…”