Superposition modulo a Shostak theory (2003)
| Venue: | AUTOMATED DEDUCTION (CADE-19), VOLUME 2741 OF LNAI |
| Citations: | 2 - 0 self |
BibTeX
@INPROCEEDINGS{Ganzinger03superpositionmodulo,
author = {Harald Ganzinger and Thomas Hillenbrand and Uwe Waldmann},
title = {Superposition modulo a Shostak theory},
booktitle = {AUTOMATED DEDUCTION (CADE-19), VOLUME 2741 OF LNAI},
year = {2003},
pages = {182--196},
publisher = {Springer-Verlag}
}
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Abstract
We investigate superposition modulo a Shostak theory T in order to facilitate reasoning in the amalgamation of T and a free theory F. Free operators occur naturally for instance in program verication problems when abstracting over subroutines. If their behaviour in addition can be specied axiomatically, much more of the program semantics can be captured. Combining the Shostak-style components for deciding the clausal validity problem with the ordering and saturation techniques developed for equational reasoning, we derive a refutationally complete calculus on mixed ground clauses which result for example from CNF transforming arbitrary universally quantied formulae. The calculus works modulo a Shostak theory in the sense that it operates on canonizer normalforms. For the Shostak solvers that we study, coherence comes for free: no coherence pairs need to be considered.
