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A kernel specification language called ASL is presented. ASL comprises five fundamental but powerful specification-building operations and has a simple semantics. Behavioural abstraction with respect to a set of observable sorts can be expressed, and (recursive) parameterised specifications can be defined using a more powerful and more expressive parameterisation mechanism than usual. A simple notion of implementation permitting vertical and horizontal composition (i.e. it is transitive and monotonic) is adopted and compared with previous more elaborate notions. A collection of identities is given which can provide a foundation for the development of programs by transformation.