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vBBdL-2014 (Unpublished)
Author(s) Steffen van Bakel, Franco Barbanera and Ugo de' Liguoro
Title« Intersection Types for the lambda-mu Calculus »
Abstract
We introduce an intersection type system for the pure lambda-mu calculus, which is invariant under subject reduction and expansion. The system is obtained by describing Streicher and ReusÕs denotational model of continuations in the category of omega-algebraic lattices via AbramskyÕs do- main logic approach. This provides at the same time an interpretation of the type system and a proof of the completeness of the system with respect to the continuation models by means of a filter model construction. We then define a restriction of ours system, such that a lambda-mu term is typeable if and only if it is strongly normalising. We also show that ParigotÕs typing of lambda-mu terms with classically valid propositional formulas can be translated into the restricted system, which then provides an alternative proof of strong normalisability for the typed lambda-mu calculus.

Download the complete article: lmcs-IntTypeLmu.pdf

BibTeX code

@unpublished{vBBdL-2014,
  localfile = {http://www.di.unito.it/~deligu/papers/lmcs-IntTypeLmu.pdf},
  abstract = {We introduce an intersection type system for the pure lambda-mu
              calculus, which is invariant under subject reduction and
              expansion. The system is obtained by describing Streicher and
              ReusÕs denotational model of continuations in the category of
              omega-algebraic lattices via AbramskyÕs do- main logic approach.
              This provides at the same time an interpretation of the type
              system and a proof of the completeness of the system with respect
              to the continuation models by means of a filter model
              construction. We then define a restriction of ours system, such
              that a lambda-mu term is typeable if and only if it is strongly
              normalising. We also show that ParigotÕs typing of lambda-mu terms
              with classically valid propositional formulas can be translated
              into the restricted system, which then provides an alternative
              proof of strong normalisability for the typed lambda-mu
              calculus.},
  title = {{Intersection Types for the lambda-mu Calculus}},
  author = {Steffen van Bakel and Franco Barbanera and Ugo de' Liguoro},
  year = {2014},
}


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