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On abstract data types presented by multiequations

Summary: On abstract data types presented by
J. Ad'amek 1
Technical University Braunschweig, Postfach 3329, 38023 Braunschweig,
M. H'ebert
The American University in Cairo, Box 2511, Cairo 11511, Egypt
J. Rosick'y 1
Masaryk University, Jan'aŸckovo n'am. 2a, 662 95 Brno, Czech Republic
Equational presentation of abstract data types is generalized to presentation by
multiequations, i.e., exclusive­or's of equations, in order to capture parametric data
types such as array or set. Multiinitial­algebra semantics for such data types is
introduced. Classes of algebras described by multiequations are characterized.
A number of important data types, e.g., stack, list, tree, have an abstract
specifications using equational logic: for a given many­sorted signature \Sigma one
considers a set E of equations, and the loose semantics of the data type is then
the whole variety of \Sigma­algebras satisfying E, whereas the initial semantics
works with the initial algebras of that variety. There are, however, basic data


Source: Adámek, Jiri - Institut für Theoretische Informatik, Fachbereich Mathematik und Informatik, Technische Universität Braunschweig
Rosický, Jirí - Department of Mathematics and Statistics, Masaryk University


Collections: Computer Technologies and Information Sciences; Mathematics