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. We investigate how to add coercive structural subtyping to a type system for simply-typed lambda calculus with Hindley-Milner polymorphism. Coercions allow to convert between different types, and their automatic insertion can greatly increase readability of terms. We present a type inference algorithm that, given a term without type information, computes a type assignment and determines at which positions in the term coercions have to be inserted to make it type-correct according to the standard Hindley-Milner system (without any subtypes). The algorithm is sound and, if the subtype relation on base types is a disjoint union of lattices, also complete. The algorithm has been implemented in the proof assistant Isabelle. 1