The system F of variable types, fifteen years later
Theoretical Computer Science
Theoretical Computer Science
Proofs and types
Design of the programming language FORSYTHE
ALGOL-like Languages, Volume 1
ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
Towards a theory of type structure
Programming Symposium, Proceedings Colloque sur la Programmation
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Intersection-types à la Church
Information and Computation
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In this work we present a proof-theoretical justification for the intersection type assignment system IT by means of the logical system Intersection Synchronous Logic ISL. ISL builds classes of equivalent deductions of the implicative and conjunctive fragment of the intuitionistic logic NJ. ISL results from decomposing intuitionistic conjunction into two connectives: a synchronous conjunction, that can be used only among equivalent deductions of NJ, and an asynchronous one, that can be applied among any sets of deductions of NJ. A term decoration of ISL exists so that it matches both: the IT assignment system, when only the synchronous conjunction is used, and the simple types assignment with pairs and projections, when the asynchronous conjunction is used. Moreover, the proof of strong normalization property for ISL is a simple consequence of the same property in NJ and hence strong normalization for IT comes for free.