## Semantic Types: A Fresh Look at the Ideal Model for Types (2004)

Citations: | 24 - 2 self |

### BibTeX

@MISC{Vouillon04semantictypes:,

author = {Jérôme Vouillon and Paul-André Melliès},

title = {Semantic Types: A Fresh Look at the Ideal Model for Types},

year = {2004}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present a generalization of the ideal model for recursive polymorphic types. Types are defined as sets of terms instead of sets of elements of a semantic domain. Our proof of the existence of types (computed by fixpoint of a typing operator) does not rely on metric properties, but on the fact that the identity is the limit of a sequence of projection terms. This establishes a connection with the work of Pitts on relational properties of domains. This also suggests that ideals are better understood as closed sets of terms defined by orthogonality with respect to a set of contexts.