Section:
New Results
Union and Intersection constraints
Participants :
Luigi Liquori, Claude Stolze.
In [21], we introduced
an explicitly typed -calculus with strong pairs, projections
and explicit type coercions. The calculus can be parameterized with different
intersection type theories, producing a family of calculi with related
intersection typed systems. We proved the main properties like Church-Rosser,
unicity of type, subject reduction, strong normalization, decidability of type
checking and type reconstruction. We stated the relationship between the
intersection type assignment systems and the corresponding
intersection typed systems by means of an essence function
translating an explicitly typed Delta-term into a pure -term
one. We finally translated a term with type coercions into an
equivalent one without them; the translation is proved to be coherent
because its essence is the identity. The resulting generic calculus can be
parametrized to take into account other intersection type theories as
the ones in the Barendregt et al. book.