Computer Science > Logic in Computer Science
[Submitted on 6 Jul 2021]
Title:General Automation in Coq through Modular Transformations
View PDFAbstract:Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further away from first-order logic, the logic of most automatic theorem provers. In this article, we develop a methodology to transform a subset of Coq goals into first-order statements that can be automatically discharged by automatic provers. The general idea is to write modular, pairwise independent transformations and combine them. Each of these eliminates a specific aspect of Coq logic towards first-order logic. As a proof of concept, we apply this methodology to a set of simple but crucial transformations which extend the local context with proven first-order assertions that make Coq definitions and algebraic types explicit. They allow users of Coq to solve non-trivial goals automatically. This methodology paves the way towards the definition and combination of more complex transformations, making Coq more accessible.
Submission history
From: EPTCS [view email] [via EPTCS proxy][v1] Tue, 6 Jul 2021 02:35:47 UTC (71 KB)
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