Shallow confluence of conditional term rewriting systems

Claus-Peter Wirth
2009 Journal of symbolic computation  
Recursion can be conveniently modeled with left-linear positive/ negative-conditional term rewriting systems, provided that nontermination, non-trivial critical overlaps, non-right-stability, nonnormality, and extra variables are admitted. For such systems we present novel sufficient criteria for shallow confluence and arrive at the first decidable confluence criterion admitting nontrivial critical overlaps. To this end, we restrict the introduction of extra variables of right-hand sides to
more » ... ing equations and require the critical pairs to have somehow complementary literals in their conditions. Shallow confluence implies [level] confluence, has applications in functional logic programming, and guarantees the object-level consistency of the underlying data types in the inductive theorem prover QuodLibet.
doi:10.1016/j.jsc.2008.05.005 fatcat:zjp4ce43onbfxbt3sv5g5wndoq