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Pré-Publication, Document De Travail Année : 2020

Implicit automata in typed λ-calculi I: aperiodicity in a non-commutative logic

Résumé

We give a characterization of star-free languages in a λ-calculus with support for non-commutative affine types (in the sense of linear logic), via the algebraic characterization of the former using aperiodic monoids. When the type system is made commutative, we show that we get regular languages instead. A key ingredient in our approach – that it shares with higher-order model checking – is the use of Church encodings for inputs and outputs. Our result is, to our knowledge, the first use of non-commutativity to control the expressible functions in a programming language.
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Dates et versions

hal-02476219 , version 1 (12-02-2020)
hal-02476219 , version 2 (22-04-2020)
hal-02476219 , version 3 (13-02-2023)

Identifiants

  • HAL Id : hal-02476219 , version 1

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Lê Thành Dũng Nguyễn, Pierre Pradic. Implicit automata in typed λ-calculi I: aperiodicity in a non-commutative logic. 2020. ⟨hal-02476219v1⟩
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