# The ∆-calculus: syntax and types

1 KAIROS - Logical Time for Formal Embedded System Design
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : We present the $∆$-calculus, an explicitly typed $λ$-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T , e.g. the Coppo-Dezani, the Coppo-Dezani-Sall ́e, the Coppo- Dezani-Venneri and the Barendregt-Coppo-Dezani ones, producing a family of $∆$-calculi with related intersection typed systems. We prove the main properties like Church-Rosser, unicity of type, subject reduction, strong normalization, decidability of type checking and type reconstruction. We state the relationship between the intersection type assignment systems a la Curry and the corresponding intersection typed systems a la Church by means of an essence function translating an explicitly typed $∆$-term into a pure $λ$-term one. We finally translate a $∆$-term with type coercions into an equivalent one without them; the translation is proved to be coherent because its essence is the identity. The generic $∆$- calculus can be parametrized to take into account other intersection type theories as the ones in the Barendregt et al. book.
Type de document :
Rapport
[Research Report] Inria & Université Nice Sophia Antipolis, CNRS, I3S, Sophia Antipolis, France. 2018
Domaine :

https://hal.archives-ouvertes.fr/hal-01963662
Contributeur : Luigi Liquori <>
Soumis le : vendredi 21 décembre 2018 - 14:42:20
Dernière modification le : jeudi 7 février 2019 - 15:37:15
Document(s) archivé(s) le : vendredi 22 mars 2019 - 17:04:13

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delta-calculus.pdf
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• HAL Id : hal-01963662, version 1
• ARXIV : 1803.09660

### Citation

Luigi Liquori, Claude Stolze. The ∆-calculus: syntax and types. [Research Report] Inria & Université Nice Sophia Antipolis, CNRS, I3S, Sophia Antipolis, France. 2018. 〈hal-01963662〉

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