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Inverse Limit Models as Filter Models Fabio Alessi 1 , Mariangiola Dezani-Ciancaglini 2? , and Furio Honsell 1
 

Summary: Inverse Limit Models as Filter Models
Fabio Alessi 1 , Mariangiola Dezani-Ciancaglini 2? , and Furio Honsell 1
1 Dipartimento di Matematica e Informatica, Via delle Scienze, 206 33100 Udine (Italy)
alessi,honsell@dimi.uniud.it
2 Dipartimento di Informatica, Corso Svizzera, 125 10149 Torino (Italy)
dezani@di.unito.it
Research Report UDMI/10/2004/RR
Abstract. Natural intersection type preorders are the type structures which
agree with the plain intuition of intersection type constructor as set-theoretic
intersection operation and arrow type constructor as set-theoretic function space
constructor. In this paper we study the relation between natural intersection
type preorders and natural -structures, i.e. !-algebraic lattices D with Galois
connections given by F : D ! [D ! D] and G : [D ! D] ! D. We prove on one
hand that natural intersection type preorders induces natural -structures, on the
other hand that natural -structures admits presentations through intersection
type preorders. Moreover we give a concise presentations of classical D1 models
of untyped -calculus through suitable natural intersection type preorders and
prove that lter models induced by them are isomorphic to D1 .
1 Introduction
Intersection type preorders can be viewed as domain logics for !-algerbraic lat-

  

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

 

Collections: Computer Technologies and Information Sciences