Typechecking in the lambda-Pi-Calculus Modulo: Theory and Practice

R Saillard - 2015 - pastel.hal.science
… of the dependently-typed lambda-calculus with first-order rewrite … The lambda-Pi-Calculus
Modulo is a very expressive … a new definition of the lambda-Pi-Calculus Modulo that takes into …

Proofs for Free in the -Calculus Modulo Theory

T Traversié - arXiv preprint arXiv:2407.06627, 2024 - arxiv.org
… The lambdaPi-calculus modulo theory is an extension of the lambda-calculus with … We
define an interpretation of theories of the lambdaPi-calculus modulo theory, inspired by …

Embedding pure type systems in the lambda-pi-calculus modulo

D Cousineau, G Dowek - Typed Lambda Calculi and Applications: 8th …, 2007 - Springer
… The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be
extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calculus

The undecidability of typability in the lambda-pi-calculus

G Dowek - International Conference on Typed Lambda Calculi …, 1993 - Springer
… in a A-calculus with dependent types (M/-calculus [8]). Since this calculus verifies the …
But in order to prove the undecidability of typability in the ~//-calculus we need to prove that …

A functional presentation of Pi calculus

Y Fu - Science in China Series F Information Sciences, 2001 - Springer
calculus which has only one class of entities---the lambda terms. We introduce in this paper
a process calculus … We will call this language Lamp, where Lamp is for Lambda Pi. We will …

Safe, fast, concurrent proof checking for the lambda-pi calculus modulo rewriting

M Färber - Proceedings of the 11th ACM SIGPLAN International …, 2022 - dl.acm.org
… This design is implemented in a new proof checker called Kontroli for the lambda-Pi calculus
… Kontroli is faster than the reference proof checker for this calculus, Dedukti, on all of five …

[PDF][PDF] Checking the type safety of rewrite rules in the -calculus modulo rewriting

JH Wu - 2019 - inria.hal.science
calculus is an extension of the simply typed lambda calculus (λ →) with dependent types. In
this calculus… just terms of type Type in the λΠ-calculus. Some terms have the type A → Type, …

Kuroda's Translation for the -Calculus Modulo Theory and Dedukti

T Traversié - arXiv preprint arXiv:2407.06626, 2024 - arxiv.org
… of the λn-calculus modulo theory that … -calculus modulo theory and we detail an encoding
of higher-order logic in it. In Section 3, we define Kuroda’s translation for theories of λn-calculus

Conservativity of embeddings in the lambda pi calculus modulo rewriting

A Assaf - 13th International Conference on Typed Lambda …, 2015 - drops.dagstuhl.de
The lambda Pi calculus can be extended with rewrite rules to embed any functional pure
type system. In this paper, we show that the embedding is conservative by proving a relative …

Rewriting Modulo\beta in the\lambda\Pi-Calculus Modulo

R Saillard - arXiv preprint arXiv:1507.08055, 2015 - arxiv.org
… of rewriting modulo beta for the lambda-Pi-calculus Modulo. We prove … We achieve our goal
by encoding the lambda-Pi-calculus … for HRSs available for the lambda-Pi-calculus Modulo. …