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 parametric polymorphism, and 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 the algebraic specification language 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; we demonstrate how various extensions to the logic, in particular general recursion, can be formulated within the language itself.

Abstract not found

Along the lines of classical categorical type theory for total functions, we establish equivalence results between certain classes of partial equational theories on the one hand and corresponding classes of categories on the other hand, staying close to standard categorical notions.

If is a formula then we denote by x [c] the formula obtained from by replacing every free occurrence of x by c. If c is the name of an element of a set O then x [c] is called O-instance of . In order to omit parentheses, we assume that the one-place operators bind closer that the two place operators and ^, _ bind closer than !, (i.e. ^ ! _ is ( ^ ) ! ( _ ), and a sequence of ! is parenthesized to the right (i.e. ! ! ! i