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2 Fundamenta Informaticae

2 1999

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On intuitionistic proof transformations, their complexity, and application to constructive program synthesis

Egly U., Schmitt S.

Fundamenta Informaticae

1999

Vol. 39, Nr 1,2

59-83

We present a translation of intuitionistic sequent proofs from a multi-succedent calculus LJmc into a single-succedent calculus LJ. The former gives a basis for automated proof search whereas the latter is better suited for proof presentation and program construction from proofs in a system for constructive program synthesis. Well-known translations from the literature have a severe drawback; they use cuts in order to establish the transformation with the undesired consequence that the resulting program term is not intuitive. We establish a transformation based on permutation of inferences and discuss the relevant properties with respect to proof complexity and program terms. As an important result we show that LJ cannot polynomially simulate LJmc (both without the cut rule), even in the propositional fragment.

Automating inductive specification proofs

Pientka B., Kreitz Ch.

Fundamenta Informaticae

1999

Vol. 39, Nr 1,2

189-209

We present an automatic method which combines logical proof search and rippling heuristics to prove specifications. The key idea is to instantiate meta-variables in the proof with a simultaneous match based on rippling/reverse rippling heuristic. Underlying our rippling strategy is the rippling distance strategy which introduces a new powerful approach to rippling, as it avoids termination problems of other rippling strategies. Moreover, we are able to synthesize conditional substitutions for meta-variables in the proof. The strength of our approach is illustrated by discussing the specification of the integer square root and automatically synthesizing the corresponding algorithm. The described procedure has been integrated as a tactic into the NUPRL system but it can be combined with other proof methods as well.