The Deltacalculus: syntax and types
Abstract
We present the Deltacalculus, an explicitly typed lambdacalculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the CoppoDezani, the CoppoDezaniSalle', the CoppoDezaniVenneri and the BarendregtCoppoDezani ones, producing a family of Deltacalculi with related intersection type systems. We prove the main properties like ChurchRosser, 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 type systems a` la Church by means of an essence function translating an explicitly typed Deltaterm into a pure lambdaterm one. We finally translate a Deltaterm with type coercions into an equivalent one without them; the translation is proved to be coherent because its essence is the identity. The generic Deltacalculus can be parametrized to take into account other intersection type theories as the ones in the Barendregt et al. book.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 arXiv:
 arXiv:1803.09660
 Bibcode:
 2018arXiv180309660L
 Keywords:

 Computer Science  Logic in Computer Science