Design and implementation of a proof verifying kernel for the λΠ-calculus modulo
type: Dataset
description: In recent years, the emergence of feature rich and mature interactive proof assistants has enabled large formalization efforts of high-profile conjectures and results previously established only by pen and paper. A medley of incompatible and philosophically diverging logics are at the core of all these proof assistants. Cousineau and Dowek (2007) have proposed the λΠ-calculus modulo as a universal target framework for other front-end proof languages and environments. We explain in this thesis how this particularly simple formalism allows for a small, modular and efficient proof checker upon which the consistency of entire systems can be made to rely upon. Proofs increasingly rely on computation both in the large, as exemplified by the proof of the four colour theorem by Gonthier (2007), and in the small following the SSReflect methodoly and supporting tools. Encoding proofs from other systems in the λΠ-calculus modulo bakes yet more computation into the proof terms. We show how to make the proof checking problem manageable by turning entire proof terms into functional programs and compiling them in one go using off-the-shelf compilers for standard programming languages. We use untyped normalization by evaluation (NbE) as an enabling technology and show how to optimize previous instances of it found in the literature. Through a single change to the interpretation of proof terms, we arrive at a representation of proof terms using higher order abstract syntax (HOAS) allowing for a proof checking algorithm devoid of any explicit typing context for all Pure Type Systems (PTS). We observe that this novel algorithm is a generalization to dependent types of a type checking algorithm found in the HOL proof assistants enabling on-the-fly checking of proofs. We thus arrive at a purely functional system with no explicit state, where all proofs are checked by construction. We formally verify in Coq the correspondence of the type system on higher order terms lying behind this alg…
landing page: https://theses.hal.science/tel-00672699
keyword: compilation
keyword: formal-proof
keyword: infoeu-reposemanticsdoctoralthesis
keyword: infoinfo-locomputer-science-cslogic-in-computer-science-cslo
keyword: infoinfo-plcomputer-science-csprogramming-languages-cspl
keyword: preuve-formelle
keyword: reecriture
keyword: rewriting
keyword: theorie-des-types
keyword: theses
keyword: type-theory
issued: 2026-05-27T16:10:12.673523
modified: 2026-05-27T16:10:12.673529
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Design and implementation of a proof verifying kernel for the λΠ-calculus modulo
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00672699
issued: 2026-05-27T16:10:12.699664
modified: 2026-05-27T16:10:12.643742