> 1 ; : : : ; v 6 of them; these will be formulated as we need them. Theorem. 8a 1 ; a 2 (0 ! a 2 ! 9k 1 ; k 2 (abs(k 1 a 1 \Gamma k 2 a 2 )ja 1 abs(k 1 a 1 \Gamma k 2 a 2 )ja 2 0 ! abs(k 1 a 1 \Gamma k 2 a 2 ))): Proof. Let a 1 ; a 2 be given and assume 0 ! a 2 . The ideal (a 1 ; a 2

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), and difficult to optimize (which is necessary to combat the exponential complexity of verification algorithms). In this paper, we describe an integrated collection of program analysis and transformation components, called Bandera, that enables the automatic extraction of safe, compact finite-state models from

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that respects the interpretation of the logical connectives as search instructions. The concept of a uniform proof is used to define the notion of an abstract logic programming language, and it is shown that first-order and higher-order Horn clauses with classical provability are examples of such a language

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