Compositional pre-processing for automated reasoning in dependent type theory

TL;DR

This paper introduces a set of compositional pre-processing techniques for enhancing automation in dependent type theory, specifically within the Coq proof assistant, enabling more flexible and powerful proof automation.

Contribution

It presents the design and implementation of atomic goal transformations that can be composed to improve automation in dependent type theory proof assistants.

Findings

Expanded automation capabilities in Coq through new pre-processing operations

Demonstrated effectiveness with diverse proof examples

Enhanced flexibility of automation tactics in dependent type theory

Abstract

In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical fragment. This very often prevents users from applying these tactics in other contexts, even similar ones. This paper discusses the design and the implementation of pre-processing operations for automating formal proofs in the Coq proof assistant. It presents the implementation of a wide variety of predictible, atomic goal transformations, which can be composed in various ways to target different backends. A gallery of examples illustrates how it helps to expand significantly the power of automation engines.