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Intersection Types and Domain Operators ? Fabio Alessi a , Mariangiola DezaniCiancaglini b , Stefania Lusin c
 

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],

  

Source: Alessi, Fabio - Dipartimento di Matematica e Informatica, Universitŕ degli Studi di Udine

 

Collections: Computer Technologies and Information Sciences