Intersection types and lambda models

Authors:
Fabio Alessi;Franco Barbanera;Mariangiola Dezani-Ciancaglini
Affiliations:
Dip. di Matematica e Informatica, Università di Udine, Udine, Italy;Dip. di Matematica e Informatica, Università di Catania, Catania, Italy;Dip. di Informatica, Università di Torino, Torino, Italy
Venue:
Theoretical Computer Science - Logic, language, information and computation
Year:
2006

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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.