| Ale+Dez+Lus:TCS-2004 (Article)
|
| Author(s) | Fabio Alessi, Mariangiola Dezani-Ciancaglini and Stefania Lusin |
| Title | « Intersection Types and Domain Operators » |
| Journal | Theoret. Comput. Sci. |
| Volume | 316 |
| Number | 1--3 |
| Page(s) | 25--47 |
| Year | 2004 |
| URL | http://www.di.unito.it/~dezani/papers/adl.pdf |
| Abstract |
| 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 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. |
@article{Ale+Dez+Lus:TCS-2004,
volume = {316},
number = {1--3},
author = {Alessi, Fabio and Dezani-Ciancaglini, Mariangiola and Lusin,
Stefania},
fjournal = {Theoretical Compututer Science},
url = {http://www.di.unito.it/~dezani/papers/adl.pdf},
title = {{Intersection Types and Domain Operators}},
abstract = {We use intersection types as a tool for obtaining
$\lambda$-models. Relying on the notion of {\em easy intersection
type theory} we successfully build a $\lambda$-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 $\lambda$-theory where the $\lambda$-term $(\lambda
x.xx)(\lambda x.xx)$ is forced to behave as the join operator.
This result has interesting consequences on the algebraic
structure of the lattice of $\lambda$-theories. The second result
is that for any simple easy term there is a $\lambda$-model where
the interpretation of the term is the {\em minimal} fixed point
operator. },
year = {2004},
journal = {Theoret. Comput. Sci.},
pages = {25--47},
}
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