Order-sorted algebraic specifications with higher-order functions

This paper gives a proposal for how order-sorted algebraic specification languages can be extended with higher-order functions. The approach taken is a generalisation to the order-sorted case of an approach given by Moller, Tarlecki and Wirsing for the many-sorted case. The main idea in the proposal is to only consider reachable extensional algebras. This leads to a very simple theory, where it is possible to relate the higher-order specifications to first-order specifications.