15-815 Automated Theorem Proving
Lecture 24: Completion

We discuss methods for deciding if a given equation follows from a collection of universally quantified equations. The first idea is that if we a reduction order that orients all equations and the resulting system is confluent, then we can decide equality between two terms by normalizing them and comparing the normal forms for equality.

Often, we cannot directly find such a presentation but we need to complete the set of rewrite rules in order to make the confluent (while still respecting the reduction order, of course). We present completion abstractly as a set of inference rules, to be applied in the forward direction.

[DP01] Nachum Dershowitz and David A. Plaisted.
Handbook of Automated Reasoning, Vol.1, pp 537-610, Elsevier Science and MIT Press, 2001.

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Frank Pfenning