Abstractions of uniform proofs
In this paper we analyze a framework for abstract interpretation of programs written in abstract logic programming languages in the sense of . The framework is based on the sequent calculus formulation of the class of considered languages. Two systems of inductive definitions to model the bottom-up and the top-down constructions of proof trees in a sequent system are introduced. These constructions are then abstracted on domains in which a possible less precise yet correct description of computations is given. In the abstract domain, the meaning of a program is still characterized by sets of inference rules and by the induced operators. Anyway the abstract operators we define this way are the most precise approximations of the concrete ones.
Some properties of the abstraction function with respect to the sequent system are given that allow to restate in the abstract domain the equivalence of the bottom-up and top-down approaches and the compositionality of the semantic operators.
Keywordsuniform proofs abstract interpretation inference rule systems
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