Building Extended Canonizers by Graph-Based Deduction

We consider the problem of efficiently building extended canonizers, which are capable of solving the uniform word problem for some first-order theories. These reasoning artifacts have been introduced in previous work to solve the lack of modularity of Shostak combination schema while retaining its efficiency. It is known that extended canonizers can be modularly combined to solve the uniform word problem in unions of theories. Unfortunately, little is known about efficiently implementing such canonizers for component theories, especially those of interest for verification like, e.g., those of uninterpreted function symbols or lists. In this paper, we investigate this problem by adapting and combining work on rewriting-based decision procedures for satisfiability in first-order theories and SER graphs, a graph-based method defined for abstract congruence closure. Our goal is to build graph-based extended canonizers for theories which are relevant for verification. Based on graphs our approach addresses implementation issues that were lacking in previous rewriting-based decision procedure approaches and which are important to argue the viability of extended canonizers.

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