Modeling abstract types in modules with open existential types

  • Authors:

  • Benoît Montagu;Didier Rémy

  • Affiliations:

  • INRIA, Paris, France;INRIA, Paris, France

  • Venue:
  • Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

We propose F-zip, a calculus of open existential types that is an extension of System F obtained by decomposing the introduction and elimination of existential types into more atomic constructs. Open existential types model modular type abstraction as done in module systems. The static semantics of F-zip adapts standard techniques to deal with linearity of typing contexts, its dynamic semantics is a small-step reduction semantics that performs extrusion of type abstraction as needed during reduction, and the two are related by subject reduction and progress lemmas. Applying the Curry-Howard isomorphism, F-zip can be also read back as a logic with the same expressive power as second-order logic but with more modular ways of assembling partial proofs. We also extend the core calculus to handle the double vision problem as well as type-level and term-level recursion. The resulting language turns out to be a new formalization of (a minor variant of) Dreyer's internal language for recursive and mixin modules.