Intersection Types for the lambda-mu Calculus

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...

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Veröffentlicht in:Logical methods in computer science Jg. 14, Issue 1
Hauptverfasser: van Bakel, Steffen, Barbanera, Franco, de'Liguoro, Ugo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Logical Methods in Computer Science e.V 01.01.2018
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computer science - logic in computer science
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ISSN:1860-5974, 1860-5974
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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.
AbstractList 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.
Author van Bakel, Steffen
de'Liguoro, Ugo
Barbanera, Franco
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Snippet We introduce an intersection type system for the lambda-mu calculus that is invariant under subject reduction and expansion. The system is obtained by...
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