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The recent development of abstract algebraic logic has led to a reconsideration of the universal algebraic theory of ordered algebras from a new perspective. The familiar equational logic of Birkhoff can be naturally viewed as one of the deductive systems that constitute the main object of study in abstract algebraic logic; technically it is a deductive(More)
Lambda abstraction algebras (LAAs) are designed to algebraize the untyped lambda calculus in the same way cylindric and polyadic algebras algebraize the first-order predicate logic. Like combinatory algebras they can be defined by true identities and thus form a variety in the sense of universal algebra, but they differ from combinatory algebras in several(More)
A slightly abbreviated version will appear in Theoretical Computer Science. Abstract. A model theory for proving correctness of abstract data types is developed within the framework of the behavior-realization adjunction. To allow for incomplete speciications, proof-of-correctness is based on comparison to one of several paradigmatic models. For making such(More)