Homomorphism preserving algebraic specifications require hidden sorts:

Abstract: "Although every computable data type has an initial algebra specification with hidden functions, it may happen that some of the homomorphic images of the data type are not models of the specification. The latter are reducts of algebras that would be models of the specification if all...

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Bibliographic Details
Main Authors: Bergstra, Jan A. 1951- (Author), Heering, Jürgen (Author)
Format: Book
Language:English
Published: Amsterdam 1993
Series:Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS 93,44
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Summary:Abstract: "Although every computable data type has an initial algebra specification with hidden functions, it may happen that some of the homomorphic images of the data type are not models of the specification. The latter are reducts of algebras that would be models of the specification if all its functions were visible, whereas the homomorphic images of the data type are independent of the specification and need not be compatible with the hidden functions used in it. A hidden function specification 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 specification, homomorphism preserving initial algebra specification of computable data types requires both hidden sorts and hidden functions.
Physical Description:12 S.

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