RAPPORT Homomorphism preserving algebraic specifications require hidden

Although every computable data type has an initial algebra speci-cation with hidden functions, it may happen that some of the homo-morphic images of the data type are not models of the speciication. The latter are reducts of algebras that would be models of the specii-cation if all its functions were visible, whereas the homomorphic images of the data type are independent of the speciication and need not be compatible with the hidden functions used in it. A hidden function speciication that does not exclude any of the homomorphic images of its initial model from its model class will be called homomorphism preserving. It turns out that, unlike unrestricted initial algebra specii-cation, homomorphism preserving initial algebra speciication of computable data types requires both hidden sorts and hidden functions. 1991 Mathematics Subject Classiication: 08A70 Algebraic struc-tures]: Applications of universal algebra in computer science; 68Q65 Theory of computing]: Abstract data types; algebraic speciica-tion.