Syntactically and Semantically Regular Languages of λ-Terms Coincide Through Logical Relations - Archive ouverte HAL Access content directly
Conference Papers Year : 2024

Syntactically and Semantically Regular Languages of λ-Terms Coincide Through Logical Relations

Abstract

A fundamental theme in automata theory is regular languages of words and trees, and their many equivalent definitions. Salvati has proposed a generalization to regular languages of simply typed λ-terms, defined using denotational semantics in finite sets. We provide here some evidence for its robustness. First, we give an equivalent syntactic characterization that naturally extends the seminal work of Hillebrand and Kanellakis connecting regular languages of words and syntactic λ-definability. Second, we show that any finitary extensional model of the simply typed λ-calculus, when used in Salvati’s definition, recognizes exactly the same class of languages of λ-terms as the category of finite sets does. The proofs of these two results rely on logical relations and can be seen as instances of a more general construction of a categorical nature, inspired by previous categorical accounts of logical relations using the gluing construction.
Fichier principal
Vignette du fichier
article.pdf (713.39 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04447910 , version 1 (08-02-2024)

Licence

Attribution

Identifiers

Cite

Vincent Moreau, Lê Thành Dũng Nguyễn. Syntactically and Semantically Regular Languages of λ-Terms Coincide Through Logical Relations. 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024), Feb 2024, Naples, Italy. pp.40:1-40:22, ⟨10.4230/LIPIcs.CSL.2024.40⟩. ⟨hal-04447910⟩
36 View
14 Download

Altmetric

Share

Gmail Facebook X LinkedIn More