Intersection types and lambda models
Fabio Alessi,Franco Barbanera,Mariangiola Dezani-Ciancaglini +2 more
- 11 Apr 2006
- Vol. 355, Iss: 2, pp 108-126
TL;DR: The present paper provides a (syntactic) characterisation of the above mentioned requirement in terms of characterisation results Ibr intersection-type assignment systems by considering conversion as a whole and reduction and expansion separately.
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Abstract: Invariance of interpretation by β-conversion is one of the minimal requirements for any standard model for the λ-calculus. With the intersection-type systems being a general framework for the study of semantic domains for the λ-calculus, the present paper provides a (syntactic) characterisation of the above mentioned requirement in terms of characterisation results Ibr intersection-type assignment systems.Instead of considering conversion as a whole, reduction and expansion will be considered separately. Not only for usual computational rules like β η, but also for a number of relevant restrictions of those. Characterisations will be also provided for (intersection) filter structures that are indeed λ-models.
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Citations
Non-idempotent intersection types and strong normalisation
TL;DR: In this paper, a typing system with non-idempotent intersection types is presented, where a term is typable if and only if it is strongly normalising, as it is the case in (many) systems with idempotent intersections.
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Inhabitation of Low-Rank Intersection Types
Paweł Urzyczyn
- 29 Jun 2009
TL;DR: It is proved that the inhabitation problem ("Does there exist a closed term of a given type?") is undecidable for intersection types of rank 3 and exponential space complete for intersectiontypes of rank 2.
22
•Posted Content
Intersection Type Distributors
TL;DR: A family of distributors-induced bicategorical models of λ-calculus are studied, proving that they can be syntactically presented via intersection type systems and proving that their model characterize solvability, adapting reducibility techniques to the authors' setting.
A filter model for the λµ-calculus
Steffen van Bakel,Franco Barbanera,Ugo de'Liguoro +2 more
- 01 Jun 2011
TL;DR: In this article, an intersection type assignment system for the pure λµ-calculus, which is invariant under subject reduction and expansion, is introduced by describing Streicher and Reus's denotational model of continuations in the category of ωalgebraic lattices via Abramsky's domain logic approach.
15
References
•Book
The Lambda Calculus. Its Syntax and Semantics
Henk Barendregt
- 30 Apr 2012
TL;DR: In this article, the Lambda-Calculus has been studied as a theory of composition and reduction, and the theory of reduction has been used to construct models of Lambda Theories.
2.9K
Call-by-name, call-by-value and the λ-calculus
TL;DR: This paper examines the old question of the relationship between ISWIM and the λ-calculus, using the distinction between call-by-value and call- by-name, and finds that operational equality is not preserved by either of the simulations.
1.3K
A filter lambda model and the completeness of type assignment
TL;DR: On etend syntaxe et semantique de types Curry de facon que des filtres dans the structure type resultante forment un domaine au sens de Scott.
Domain theory in logical form
TL;DR: Abramsky as discussed by the authors introduced a notion of universes of discourse for various computational situations, and a standard denotational interpretation of the metalanguage is given, assigning domains to types and domain elements to terms.
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