We introduce CoCasl as a simple coalgebraic extension of the algebraic specification language Casl. CoCasl allows the nested combination of algebraic datatypes and coalgebraic process types. We show that the well-known coalgebraic modal logic can be expressed in CoCasl. We present sufficient criteria for the existence of cofree models, also for several variants of nested cofree and free specifications. Moreover, we describe an extension of the existing proof support for Casl (in the shape of an encoding into higher-order logic) to CoCasl.

Abstract not found

The development of programs in modern functional languages such as Haskell calls for a wide-spectrum specification formalism that supports the type system of such languages, in particular higher order types, type constructors, and polymorphism, and that contains a functional language as an executable subset in order to facilitate rapid prototyping. We lay out the design of HasCasl, a higher order extension of Casl that is geared towards precisely this purpose. Its semantics is tuned to allow program development by specification refinement, while at the same time staying close to the set-theoretic semantics of first order Casl. The number of primitive concepts in the logic has been kept as small as possible; advanced concepts, in particular general recursion, can be formulated within the language itself. This document provides a detailed definition of the HasCasl syntax and an informal description of the semantics, building on the existing Casl Summary [CoF].