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Summary: Intersection Types and Domain Operators ?
Fabio Alessi a , Mariangiola DezaniCiancaglini b , Stefania Lusin c
a Dipartimento di Matematica e Informatica, Universit‘ a di Udine, via delle Scienze 208,
33100 Udine, Italy alessi@dimi.uniud.it
b Dipartimento di Informatica, Universit‘ a di Torino, Corso Svizzera 185, 10149 Torino,
Italy dezani@di.unito.it
c Dipartimento di Informatica, Universit‘ a di Venezia, via Torino 153, 30170 Venezia, Italy
slusin@dsi.unive.it
Research Report UDMI/07/2004/RR
Abstract
We use intersection types as a tool for obtaining models. Relying on the notion of easy
intersection type theory we successfully build a model in which the interpretation of an
arbitrary simple easy term is any filter which can be described by a continuous predicate.
This allows us to prove two results. The first gives a proof of consistency of the theory
where the term (x:xx)(x:xx) is forced to behave as the join operator. This result has
interesting consequences on the algebraic structure of the lattice of theories. The second
result is that for any simple easy term there is a model where the interpretation of the
term is the minimal fixed point operator.
Introduction
Intersection types were introduced in the late 70's by Dezani and Coppo [8, 10, 6],
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