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Conference Papers Year : 2019

The Delta-calculus: syntax and types

Luigi Liquori
Claude Stolze
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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-Salle', 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.
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Dates and versions

hal-01963662 , version 1 (21-12-2018)

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Luigi Liquori, Claude Stolze. The Delta-calculus: syntax and types. FSCD 2019 - 4th International Conference on Formal Structures for Computation and Deduction, Jun 2019, Dortmund, Germany. ⟨10.1007/978-3-030-44411-2\_6⟩. ⟨hal-01963662⟩
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