Summary: Intersection Types and Lambda Models
Fabio Alessi a
aDip. di Matematica e Informatica Via delle Scienze, 206 33100 Udine (Italy)
Franco Barbanera b,1
bDip. di Matematica e Informatica Viale A.Doria, 6 95125 Catania (Italy)
Mariangiola Dezani-Ciancaglini c,2
cDip. di Informatica Corso Svizzera, 185 10149 Torino (Italy)
Invariance of interpretation by -conversion is one of the minimal requirements for any
standard model for the -calculus. With the intersection type systems being a general
framework for the study of semantic domains for the -calculus, the present paper provides
a (syntactic) characterisation of the above mentioned requirement in terms of characterisa-
tion results for intersection type assignment systems.
Instead of considering conversion as a whole, reduction and expansion will be consid-
ered separately. Not only for usual computational rules like , , but also for a number of
relevant restrictions of those. Characterisations will be also provided for (intersection) filter
structures that are indeed -models.