Parameterisation is an important mechanism for structuring programs and specifications into modular units. The interplay between parameterisation (of programs and of specifications) and specification (of parameterised and of non-parameterised programs) is analysed, exposing important semantic and methodological differences between specifications of parameterised programs and parameterised specifications. The extension of parameterisation mechanisms to the higher-order case is considered, both for parameterised programs and parameterised specifications, and the methodological consequences of such an extension are explored. A specification formalism with parameterisation of an arbitrary order is presented. Its denotational-style semantics is accompanied by an inference system for proving that an object satisfies a specification. The formalism includes the basic specification-building operations of the ASL specification language and is institution independent. 1
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