Initial Algebra Specifications for Parametrized Data Types

Ab.stract: We consider parametrized data types <P: Alg(.!') __.. Alg(LI) where <P is a partial functor from the class of all .!'-algebras (the parameter algebras) to the class of LI-algebras (the target algebras), for given signatures :E, LI with L1 extending .!'. Here it is required that the target algebra is generated by a homomorphic image of the parameter algebra. For such parametrized data types a general theorem about the existence of initial algebra specifications with conditional equations is proved. The theorem involves the concept of an effectively_ given parametrized data type.