Author(s): Steggles LJ
Abstract: Motivated by the need to address the issue of specification in the large and the problems of specifying a full function space we consider extending the theory of parameterised algebraic specifications to the higher--order case. We develop the notion of a higher--order abstract parameterised data type and a parameterised higher--order equational specification. Due to the nature of the higher--order initial model we cannot extend the results for the first--order free functor semantics to the higher--order case and thus we present a concrete construction of a functor which we take to be the semantics of a parameterised higher--order equational specification. We demonstrate the theory we develop by considering a detailed specification case study of a second--order abstract parameterised data type for convolution.
Keywords: algebraic specification, case studies, higher-order algebra