Modular pre-processing for automated reasoning in dependent type theory

04/06/2022
by   Valentin Blot, et al.
0

The power of modern automated theorem provers can be put at the service of interactive theorem proving. But this requires in particular bridging the expressivity gap between the logics these provers are respectively based on. This paper presents the implementation of a modular suite of pre-processing transformations, which incrementally bring certain formulas expressed in the Calculus of Inductive Constructions closer to the first-order logic of Satifiability Modulo Theory solvers. These transformations address issues related to the axiomatization of inductive types, to polymorphic definitions or to the different implementations of a same theory signature. This suite is implemented as a plugin for the Coq proof assistant, and integrated to the SMTCoq toolchain.

READ FULL TEXT

page 1

page 5

page 7

page 10

page 11

page 12

page 15

page 17

research
10/11/2017

Consistency of the Predicative Calculus of Cumulative Inductive Constructions (pCuIC)

In order to avoid well-know paradoxes associated with self-referential d...
research
09/21/2020

Synthesizing Lemmas for Inductive Reasoning

Recursively defined structures and properties about them are naturally e...
research
07/06/2021

General Automation in Coq through Modular Transformations

Whereas proof assistants based on Higher-Order Logic benefit from extern...
research
01/11/2021

Object-Level Reasoning with Logics Encoded in HOL Light

We present a generic framework that facilitates object level reasoning w...
research
01/13/2020

Interactive Visualization of Saturation Attempts in Vampire

Many applications of formal methods require automated reasoning about sy...
research
09/15/2023

MetaOCaml Theory and Implementation

Quasi-quotation (or, code templates) has long been used as a convenient ...
research
05/09/2019

Extensions to Justification Theory

Justification theory is a unifying framework for semantics of non-monoto...

Please sign up or login with your details

Forgot password? Click here to reset