Initiality for Typed Syntax and Semantics

Abstract : We give an algebraic characterization of the syntax and semantics of a class of simply-typed languages, such as the language PCF: we characterize simply-typed binding syntax equipped with reduction rules via a universal property, namely as the initial object of some category. For this purpose, we employ techniques developed in two previous works: in [2], we model syntactic translations between languages over different sets of types as initial morphisms in a category of models. In [1], we characterize untyped syntax with reduction rules as initial object in a category of models. In the present work, we show that those techniques are modular enough to be combined: we thus characterize simply-typed syntax with reduction rules as initial object in a category. The universal property yields an operator which allows to specify translations - that are semantically faithful by construction - between languages over possibly different sets of types. We specify a language by a 2-signature, that is, a signature on two levels: the syntactic level specifies the types and terms of the language, and associates a type to each term. The semantic level specifies, through inequations, reduction rules on the terms of the language. To any given 2-signature we associate a category of models. We prove that this category has an initial object, which integrates the types and terms freely generated by the 2-signature, and the reduction relation on those terms generated by the given inequations. We call this object the (programming) language generated by the 2-signature. [1] Ahrens, B.: Modules over relative monads for syntax and semantics (2011), arXiv:1107.5252, to be published in Math. Struct. in Comp. Science [2] Ahrens, B.: Extended Initiality for Typed Abstract Syntax. Logical Methods in Computer Science 8(2), 1-35 (2012)
Type de document :
Chapitre d'ouvrage
Logic, Language, Information and Computation, 7456, 2012, Lecture Notes in Computer Science, 978-3-642-32621-9. 〈10.1007/978-3-642-32621-9_10〉. 〈http://link.springer.com/chapter/10.1007%2F978-3-642-32621-9_10〉
Liste complète des métadonnées

https://hal.univ-cotedazur.fr/hal-01329607
Contributeur : Jean-Louis Thomin <>
Soumis le : jeudi 9 juin 2016 - 14:11:23
Dernière modification le : jeudi 3 mai 2018 - 13:32:58

Lien texte intégral

Identifiants

Collections

Citation

Benedikt Ahrens. Initiality for Typed Syntax and Semantics. Logic, Language, Information and Computation, 7456, 2012, Lecture Notes in Computer Science, 978-3-642-32621-9. 〈10.1007/978-3-642-32621-9_10〉. 〈http://link.springer.com/chapter/10.1007%2F978-3-642-32621-9_10〉. 〈hal-01329607〉

Partager

Métriques

Consultations de la notice

77