# Models and Termination of Proof Reduction in the lambda Pi-Calculus Modulo Theory

@inproceedings{Dowek2015ModelsAT, title={Models and Termination of Proof Reduction in the lambda Pi-Calculus Modulo Theory}, author={Gilles Dowek}, booktitle={International Colloquium on Automata, Languages and Programming}, year={2015} }

We define a notion of model for the λΠ-calculus modulo theory, a notion of superconsistent theory, and prove that proof-reduction terminates in the λΠ-calculus modulo a super-consistent theory. We prove this way the termination of proof-reduction in two theories in the λΠ-calculus modulo theory, and their consistency: an embedding of Simple type theory and an embedding of the Calculus of constructions.

## 7 Citations

### Encoding of Predicate Subtyping with Proof Irrelevance in the lambda Pi-Calculus Modulo Theory

- Computer Science
- 2021

This paper shows how to encode predicate subtyping and proof irrelevance, two important features of the PVS proof assistant, and proves that this encoding is correct and that encoded proofs can be mechanically checked by Dedukti, a type checker for the λΠ-calculus modulo theory using rewriting.

### Encoding of Predicate Subtyping with Proof Irrelevance in the λΠ-Calculus Modulo Theory

- Computer ScienceTYPES
- 2020

This paper shows how to encode predicate subtyping and proof irrelevance, two important features of the PVS proof assistant, and proves that this encoding is correct and that encoded proofs can be mechanically checked by Dedukti, a type checker for the λΠ-calculus modulo theory using rewriting.

### A framework for defining computational higher-order logics. (Un cadre de définition de logiques calculatoires d'ordre supérieur)

- Computer Science
- 2015

The main aim of this thesis is to make formal proofs more universal by expressing them in a common logical framework. More specifically, we use the lambda-Pi-calculus modulo rewriting, a lambda…

### Termination checking in the λΠ-calculus modulo theory.From a practical and a theoretical viewpoint

- Computer Science
- 2017

A type-checker for the λΠ-calculus modulo theory, which has the particularity to allow the user to declare rewrite rules, to develop an automatic tool for the termination of a rewrite rule system.

### Importing SMT and Connection proofs as expansion trees

- Computer Science, MathematicsPxTP@CADE
- 2015

An implementation that takes SMT and Connection proof objects from two different provers and imports them both as expansion trees so that all the algorithms and tools available for expansion trees can be employed uniformly.

### Mixing HOL and Coq in Dedukti (Extended Abstract)

- Computer SciencePxTP@CADE
- 2015

We use Dedukti as a logical framework for interoperability. We use automated tools to translate different developments made in HOL and in Coq to Dedukti, and we combine them to prove new results. We…

### Adequate and computational encodings in the logical framework Dedukti

- Computer ScienceFSCD
- 2022

This work is the first to present and prove correct an approach allowing for encodings that are both adequate and computational in Dedukti and is computational – that is, represents computation directly as computation.

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