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Intersection Types and Domain Operators Fabio Alessi a

Summary: Intersection Types and Domain Operators
Fabio Alessi a
, Mariangiola Dezani-Ciancaglini b
, Stefania Lusin c
aDipartimento di Matematica e Informatica, Universit`a di Udine, via delle Scienze 208,
33100 Udine, Italy alessi@dimi.uniud.it
bDipartimento di Informatica, Universit`a di Torino, Corso Svizzera 185, 10149 Torino,
Italy dezani@di.unito.it
cDipartimento di Informatica, Universit`a di Venezia, via Torino 153, 30170 Venezia, Italy
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.
Key words: Lambda calculus, intersection types, models of lambda calculus, lambda


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


Collections: Computer Technologies and Information Sciences