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Essential and relational models†

Published online by Cambridge University Press:  23 July 2015

LUCA PAOLINI ,
MAURO PICCOLO  and
SIMONA RONCHI DELLA ROCCA
LUCA PAOLINI
Affiliation:
Dipartimento di Informatica, Università degli Studi di Torino, Corso Svizzera 185, 10149 Torino, Italy Emails: paolini@di.unito.it, piccolo@di.unito.it
MAURO PICCOLO
Affiliation:
Dipartimento di Informatica Scienze ed Ingegneria, Università di Bologna, Mura Anteo Zamboni 7, Bologna, Italy Email: ronchi@di.unito.it
SIMONA RONCHI DELLA ROCCA
Affiliation:
Dipartimento di Informatica, Università degli Studi di Torino, Corso Svizzera 185, 10149 Torino, Italy Emails: paolini@di.unito.it, piccolo@di.unito.it
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Abstract

Intersection type assignment systems can be used as a general framework for building logical models of λ-calculus that allow to reason about the denotation of terms in a finitary way. We define essential models (a new class of logical models) through a parametric type assignment system using non-idempotent intersection types. Under an interpretation of terms based on typings instead than the usual one based on types, every suitable instance of the parameters induces a λ-model, whose theory is sensible. We prove that this type assignment system provides a logical description of a family of λ-models arising from a category of sets and relations.

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Footnotes

‡

Dedicated to Corrado Böhm for his 90th birthdays.

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