Abstract canonical presentations

Nachum Dershowitz*, Claude Kirchner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Solving goals-like proving properties, deciding word problems or resolving constraints-is much easier with some presentations of the underlying theory than with others. Typically, what have been called "completion processes", in particular in the study of equational logic, involve finding appropriate presentations of a given theory to more easily solve a given class of problems. We provide a general proof-theoretic setting that relies directly on the fundamental concept of "good", that is, normal-form, proofs, itself defined using well-founded orderings on proof objects. This foundational framework allows for abstract definitions of canonical presentations and very general characterizations of saturation and redundancy criteria.

Original languageEnglish
Pages (from-to)53-69
Number of pages17
JournalTheoretical Computer Science
Issue number1-3
StatePublished - 25 Jul 2006


  • Canonical rewriting
  • Canonicity
  • Completion
  • Proof orderings
  • Redundancy
  • Saturation


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