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Rewrite Systems
TLDR
This chapter focuses on rewrite systems, which are directed equations used to compute by repeatedly replacing sub-terms of a given formula with equal terms until the simplest form possible is obtained.
Termination of Rewriting
  • N. Dershowitz
  • Mathematics, Computer Science
    J. Symb. Comput.
  • 1 February 1987
TLDR
Methods for proving that systems of rewrite rules are terminating programs are described, including polynomial interpretations and path orderings, which are used in termination proofs of various kinds of orderings on terms.
Orderings for Term-Rewriting Systems
Methods of proving that a term-rewriting system terminates are presented. They are based on the notion of "simplification orderings", orderings in which any term that is homeomorphically embeddable
Orderings for term-rewriting systems
  • N. Dershowitz
  • Mathematics
    20th Annual Symposium on Foundations of Computer…
  • 1979
Methods of proving that a term-rewriting system terminates are presented. They are based on the notion of "simplification orderings", orderings in which any term that is homeomorphically embeddable
Proving termination with Multiset Orderings
TLDR
By providing more sophisticated well-founded sets, the corresponding termination functions can be simplified.
Proving termination with multiset orderings
TLDR
The multiset ordering enables the use of relatively simple and intuitive termination functions in otherwise difficult termination proofs, and is used to prove the termination of production systems, programs defined in terms of sets of rewriting rules.
Commutation, Transformation, and Termination
TLDR
This paper outlines the application of transforms—mappings from terms to terms—to termination in general, and describes various specific transforms, including transforms for associative-commutative rewrite systems.
Equational inference, canonical proofs, and proof orderings
TLDR
The application of proof orderings to various rewrite-based theorem-proving methods, including refinements of the standard Knuth-Bendix completion procedure based on critical pair criteria, and Huet's procedure for rewriting modulo a congruence are described.
A Note on Simplification Orderings
  • N. Dershowitz
  • Mathematics, Computer Science
    Inf. Process. Lett.
  • 16 December 1979
TLDR
A term-rewriting system P over a set of terms T is a finite set of rewrite rules of the form Q,(g) + ri(@, u here the & are variables ranging over I’.
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