From signatures to monads in UniMath

Benedikt Ahrens 1 Ralph Matthes 2 Anders Mörtberg 3
1 ASCOLA - Aspect and composition languages
LINA - Laboratoire d'Informatique de Nantes Atlantique, Département informatique - EMN, Inria Rennes – Bretagne Atlantique
3 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The term UniMath refers both to a formal system for mathematics, as well as a computer-checked library of mathematics formalized in that system. The UniMath system is a core dependent type theory, augmented by the univalence axiom. The system is kept as small as possible in order to ease verification of it—in particular, general inductive types are not part of the system. In this work, we partially remedy the lack of inductive types by constructing some datatypes and their associated induction principles from other type constructors. This involves a formaliza-tion of a category-theoretic result on the construction of initial algebras, as well as a mechanism to conveniently use the datatypes obtained. We also connect this construction to a previous formalization of substitution for languages with variable binding. Altogether, we construct a framework that allows us to concisely specify, via a simple notion of binding signature, a language with variable binding. From such a specification we obtain the datatype of terms of that language, equipped with a certified monadic substitution operation and a suitable recursion scheme. Using this we formalize the untyped lambda calculus and the raw syntax of Martin-Löf type theory.
Type de document :
Article dans une revue
Journal of Automated Reasoning, Springer Verlag, 2018, 〈10.1007/s10817-018-9474-4〉
Liste complète des métadonnées

https://hal.inria.fr/hal-01410487
Contributeur : Yves Bertot <>
Soumis le : vendredi 11 janvier 2019 - 11:16:11
Dernière modification le : samedi 12 janvier 2019 - 01:21:24

Fichier

Identifiants

Citation

Benedikt Ahrens, Ralph Matthes, Anders Mörtberg. From signatures to monads in UniMath. Journal of Automated Reasoning, Springer Verlag, 2018, 〈10.1007/s10817-018-9474-4〉. 〈hal-01410487v2〉

Partager

Métriques

Consultations de la notice

39

Téléchargements de fichiers

102