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要旨:
We investigate superposition modulo a Shostak theory $T$ in order to
facilitate reasoning in the amalgamation of $T$ and a free
theory~$F$.
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Free operators occur naturally e.\,g.\ in program verification
problems when abstracting over subroutines. If their behaviour in
addition can be specified axiomatically, much more of the program
semantics can be captured.
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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 quantified formulae.
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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.
