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A Complete Characterization of Complete Intersection-Type Preorders
 

Summary: A Complete Characterization of Complete
Intersection-Type Preorders
M. DEZANI-CIANCAGLINI
Universita di Torino
and
F. HONSELL and F. ALESSI
Universita di Udine
We characterize those type preorders which yield complete intersection-type assignment systems
for -calculi, with respect to the three canonical set-theoretical semantics for intersection-types:
the inference semantics, the simple semantics and the F-semantics. These semantics arise by taking
as interpretation of types subsets of applicative structures, as interpretation of the preorder rela-
tion, , set-theoretic inclusion, as interpretation of the intersection constructor, \, set-theoretic
intersection, and by taking the interpretation of the arrow constructor, ! a la Scott, with respect
to either any possible functionality set, or the largest one, or the least one.
These results strengthen and generalize signi cantly all earlier results in the literature, to our
knowledge, in at least three respects. First of all the inference semantics had not been considered
before. Secondly, the characterizations are all given just in terms of simple closure conditions on
the preorder relation, , on the types, rather than on the typing judgments themselves. The task
of checking the condition is made therefore considerably more tractable. Lastly, we do not restrict
attention just to -models, but to arbitrary applicative structures which admit an interpretation

  

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

 

Collections: Computer Technologies and Information Sciences