Section: Software and Platforms

A New Tactic Engine for Coq

Participant : Arnaud Spiwack [Correspondent] .

Keywords: Coq, Proof assistant, Dependent types, Tactics, Proof search.

Coq is a proof assistant based on dependent type theory developed chiefly at Inria. This project addresses longstanding usability issues when developing proofs interactively: proofs, in Coq, are typically sequences of instructions – called tactics – which transform the proof into further proof obligations. The expressiveness of tactic affects the kind of proofs which can be written realistically in Coq. Two issues have been addressed. First, providing more backtracking primitives: in a typical automated procedure – which a Coq user could write to discharge proof obligations without human effort – there is some amount of non-determinism. It is hence important to be able to devise strategies, and Coq suffered from limited options on that front. The new tactics support further primitives loosely inspired by Prolog, in particular a backtracking choice (like disjunction in Prolog), and a primitive “once” which is akind to Prolog's soft-cut control primitive.

The second issue is more fundamental: since Coq is based on dependent types, a proof can appear in the statement of a proof obligation. As a result, tactics should be able to handle so-called dependent subgoals (where several proof obligations are left to be discharged, and the proof of one of them is mentioned into the statement of another). This was not historically the case in Coq, which had a direct influence on some users.

Both of the backtracking primitive and the dependent subgoals are part of the development version of Coq and will be part of the next release.