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BakelBdL17 (Article)
Author(s) Steffen van Bakel, Franco Barbanera and Ugo de' Liguoro
Title« Intersection Types for the lambda-mu Calculus »
JournalCoRR
Volumeabs/1704.00272
Year2017
URLhttp://arxiv.org/abs/1704.00272
Abstract
We introduce an intersection type system for the lambda-mu calculus that is invariant under subject reduction and expansion. The system is obtained by describing Streicher and Reus's denotational model of continuations in the category of omega-algebraic lattices via Abramsky's domain-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 our system, such that a lambda-mu term is typeable if and only if it is strongly normalising. We also show that Parigot's 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.

BibTeX code

@article{BakelBdL17,
  volume = {abs/1704.00272},
  author = {Steffen van Bakel and Franco Barbanera and Ugo de' Liguoro},
  timestamp = {Wed, 07 Jun 2017 14:40:56 +0200},
  url = {http://arxiv.org/abs/1704.00272},
  tag = {to appear in LMCS},
  title = {Intersection Types for the lambda-mu Calculus},
  abstract = {We introduce an intersection type system for the lambda-mu
              calculus that is invariant under subject reduction and expansion.
              The system is obtained by describing Streicher and Reus's
              denotational model of continuations in the category of
              omega-algebraic lattices via Abramsky's domain-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 our system, such
              that a lambda-mu term is typeable if and only if it is strongly
              normalising. We also show that Parigot's 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.
              },
  journal = {CoRR},
  year = {2017},
}


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