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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)

- Don Pigozzi
- AMAST
- 1998

An infinite sequence ∆ = ∆n(x0,. .. , xn−1, y, ¯ u) : n < ω of possibly infinite sets of formulas in n + 1 variables x0,. .. , xn−1, y and a possibly infinite system of parameters ¯ u is a parameterized graded deduction-detachment (PGDD) system for a de-ductive system S over a S-theory T if, for every n < ω and for all ϕ0,. ϑ) for every possible system of… (More)

According to Frege's principle the denotation of a sentence coincides with its truth-value. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense. A 2nd-order matrix is an algebra together with an algebraic… (More)

We present a model-theoretic study of correct behavioral subtyping for rst-order, deterministic, abstract data types with immutable objects. For such types, we give a new algebraic criterion for proving correct behavioral subtyping that is both necessary and suucient. This proof technique handles incomplete speciica-tions by allowing proofs of correct… (More)