A Rewriting Approach to the Combination of Data Structures with Bridging Theories
Abstract
We introduce a combination method à la Nelson-Oppen to solve the
satisfiability problem modulo a non-disjoint union of theories
connected with bridging functions. The combination method is
particularly useful to handle verification conditions involving
functions defined over inductive data structures. We investigate the
problem of determining the data structure theories for which this
combination method is sound and complete. Our completeness proof is
based on a rewriting approach where the bridging function is defined
as a term rewrite system, and the data structure theory is given by
a basic congruence relation. Our contribution is to introduce a
class of data structure theories that are combinable with a disjoint
target theory via an inductively defined bridging function. This
class includes the theory of equality, the theory of absolutely free
data structures, and all the theories in between. Hence, our
non-disjoint combination method applies to many classical data
structure theories admitting a rewrite-based satisfiability
procedure.
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