Parallel reductions in λ-calculus
Journal of Symbolic Computation
A calculus for overloaded functions with subtyping
Information and Computation
Computational Adequacy via "Mixed" Inductive Definitions
Proceedings of the 9th International Conference on Mathematical Foundations of Programming Semantics
A Semantics for Lambda&-early: A Calculus with Overloading and Early Binding
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
On Typed Calculi with a Merge Operator
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
A domain-theoretic semantics of lax generic functions
Theoretical Computer Science - Category theory and computer science
| Hi-index | 0.00 |
We give a denotational semantics to a calculus λ⊗ with overloading and subtyping. In λ⊗, the interaction between overloading and subtyping causes self application, and non-normalizing terms exist for each type. Moreover, the semantics of a type depends not on that type alone, but also on infinitely many others. Thus, we need to consider infinitely many domains, which are related by an infinite number of mutually recursive equations. We solve this by considering a functor category from the poset of types modulo equivalence to a category in which each type is interpreted. We introduce a categorical constructor corresponding to overloading, and formalize the equations as a single equation in the functor category. A semantics of λ ⊗ is then expressed in terms of the minimal solution of this equation. We prove the adequacy theorem for λ⊗ following the construction in Pitts (1994) and use it to derive some syntactic properties.