Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A Decision Procedure for an Extensional Theory of Arrays
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Combining Nonstably Infinite Theories
Journal of Automated Reasoning
Combined satisfiability modulo parametric theories
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Combining data structures with nonstably infinite theories using many-sorted logic
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Sharing is caring: combination of theories
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Being careful about theory combination
Formal Methods in System Design
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The classic method of Nelson and Oppen for combining decision procedures requires the theories to be stably-infinite. Unfortunately, some important theories do not fall into this category (e.g. the theory of bit-vectors). To remedy this problem, previous work introduced the notion of polite theories. Polite theories can be combined with any other theory using an extension of the Nelson-Oppen approach. In this paper we revisit the notion of polite theories, fixing a subtle flaw in the original definition. We give a new combination theorem which specifies the degree to which politeness is preserved when combining polite theories. We also give conditions under which politeness is preserved when instantiating theories by identifying two sorts. These results lead to a more general variant of the theorem for combining multiple polite theories.