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Observational Proofs with Critical Contexts
 In Fundamental Approaches to Software Engineering
, 1998
"... Observability concepts contribute to a better understanding of software correctness. In order to prove observational properties, the concept of Context Induction has been developed by Hennicker [10]. We propose in this paper to embed Context Induction in the implicit induction framework of [8]. The ..."
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Observability concepts contribute to a better understanding of software correctness. In order to prove observational properties, the concept of Context Induction has been developed by Hennicker [10]. We propose in this paper to embed Context Induction in the implicit induction framework of [8]. The proof system we obtain applies to conditional specifications. It allows for many rewriting techniques and for the refutation of false observational conjectures. Under reasonable assumptions our method is refutationally complete, i.e. it can refute any conjecture which is not observationally valid. Moreover this proof system is operational: it has been implemented within the Spike prover and interesting computer experiments are reported.
Inductive Theorem Proving by Consistency for FirstOrder Clauses
 The Third International Workshop on Conditional Term Rewriting Systems, Extended Abstracts
, 1993
"... . We show how the method of proof by consistency can be extended to proving properties of the perfect model of a set of firstorder clauses with equality. Technically proofs by consistency will be similar to proofs by case analysis over the term structure. As our method also allows to prove sufficie ..."
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. We show how the method of proof by consistency can be extended to proving properties of the perfect model of a set of firstorder clauses with equality. Technically proofs by consistency will be similar to proofs by case analysis over the term structure. As our method also allows to prove sufficientcompleteness of function definitions in parallel with proving an inductive theorem we need not distinguish between constructors and defined functions. Our method is linear and refutationally complete with respect to the perfect model, it supports lemmas in a natural way, and it provides for powerful simplification and elimination techniques. 1 Introduction For proving inductive theorems of equational theories "proof by consistency" is a particularly powerful method. The method has been engineered during the last decade by gradually removing restrictions on the specification side, by reducing the search space for inferences, and by including methods from term rewriting for the simplificat...