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Recursive Domain Equations of Filter Models Fabio Alessi and Paula Severi

Summary: Recursive Domain Equations of Filter Models
Fabio Alessi and Paula Severi
Universit`a degli Studi di Udine
Dipartimento di Matematica ed Informatica
via delle Scienze 208, 33100 Udine, Italy
Abstract. Filter models and (solutions of) recursive domain equations
are two different ways of constructing lambda models. Many partial re-
sults have been shown about the equivalence between these two con-
structions (in some specific cases). This paper deepens the connection by
showing that the equivalence can be shown in a general framework. We
will introduce the class of disciplined intersection type theories and its
four subclasses: natural split, lazy split, natural equated and lazy equated.
We will prove that each class corresponds to a different recursive domain
equation. For this result, we are extracting the essence of the specific
proofs for the particular cases of intersection type theories and making
one general construction that encompasses all of them. This general ap-
proach puts together all these results which may appear scattered and
sometimes with incomplete proofs in the literature.
1 Introduction
This paper is concerned with two different ways of constructing models of the


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


Collections: Computer Technologies and Information Sciences