Higher-Order Order-Sorted Algebras

The aim of this paper is to present a new semantics of higher-order order-sorted types for functional programming, data type specification and program transformation. Our type discipline unifies higher-order functions, overloading and subtype polymorphism in a very simple way. The new approach can be considered as an extension of order-sorted algebra with higher-order functions. We show the existence of initial algebras and give a sound and complete equational deduction system.

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