Nonequivalence of categories for equational algebraic specifications
Four different alternatives for the definition of standard equational algebraic specifications and the corresponding specification morphisms are studied and compared. Although intuitively the definitions may appear equivalent, they lead to three different equivalence classes of categories. It is shown, in fact, that the construction of pushouts and pullbacks is significantly different in these three cases. Although the corresponding specification logics are all semantical equivalent in a weak sense, three of them are semantical inconsistent with respect to pullback constructions. The nonequivalence of the equational categories has also significant implications for the corresponding high-level-replacement (HLR) system.
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