Results 1 
9 of
9
InductiveDataType Systems
, 2002
"... In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schem ..."
Abstract

Cited by 821 (23 self)
 Add to MetaCart
In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schema", whichgeneral39I theusual recursor definitions fornatural numbers and simil9 "basic inductive types". This combined lmbined was shown to bestrongl normalIk39f The purpose of this paper is toreformul33 and extend theGeneral Schema in order to make it easil extensibl3 to capture a more general cler of inductive types, cals, "strictly positive", and to ease the strong normalgAg9Ik proof of theresulGGg system. Thisresul provides a computation model for the combination of anal"DAfGI specification language based on abstract data types and of astrongl typed functional language with strictly positive inductive types.
Completion Without Failure
, 1989
"... We present an "unfailing" extension of the standard KnuthBendix completion procedure that is guaranteed to produce a desired canonical system, provided certain conditions are met. Weprove that this unfailing completion method is refutationally complete for theorem proving in equational the ..."
Abstract

Cited by 140 (21 self)
 Add to MetaCart
We present an "unfailing" extension of the standard KnuthBendix completion procedure that is guaranteed to produce a desired canonical system, provided certain conditions are met. Weprove that this unfailing completion method is refutationally complete for theorem proving in equational theories. The method can also be applied to Horn clauses with equality, in which case it corresponds to positive unit resolution plus oriented paramodulation, with unrestricted simplification.
Equational Inference, Canonical Proofs, And Proof Orderings
 Journal of the ACM
, 1992
"... We describe the application of proof orderingsa technique for reasoning about inference systemsto various rewritebased theoremproving methods, including re#nements of the standard KnuthBendix completion procedure based on critical pair criteria; Huet's procedure for rewriting modulo a ..."
Abstract

Cited by 30 (10 self)
 Add to MetaCart
(Show Context)
We describe the application of proof orderingsa technique for reasoning about inference systemsto various rewritebased theoremproving methods, including re#nements of the standard KnuthBendix completion procedure based on critical pair criteria; Huet's procedure for rewriting modulo a congruence; ordered completion #a refutationally complete extension of standard completion#; and a proof by consistency procedure for proving inductive theorems. # This is a substantially revised version of the paper, #Orderings for equational proofs," coauthored with J. Hsiang and presented at the Symp. on Logic in Computer Science #Boston, Massachusetts, June 1986#. It includes material from the paper #Proof by consistency in equational theories," by the #rst author, presented at the ThirdAnnual Symp. on Logic in Computer Science #Edinburgh, Scotland, July 1988#. This researchwas supported in part by the National Science Foundation under grants CCR8901322, CCR9007195, and CCR9024271. 1 ...
A maximalliteral unit strategy for Horn clauses
 In Proc. CTRS90
, 1991
"... A new positiveunit theoremproving procedure for equational Horn clauses is presented. It uses a term ordering to restrict paxamodulation to potentially maximal sides of equations. Completeness is shown using proof orderings. 1. ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
A new positiveunit theoremproving procedure for equational Horn clauses is presented. It uses a term ordering to restrict paxamodulation to potentially maximal sides of equations. Completeness is shown using proof orderings. 1.
Rewriting Methods for Word Problems
 Words, Languages & Combinatorics (Proceedings of the International Colloquium, Kyoto
, 1992
"... This paper outlines various recent approaches to solving word problems. Term orderings are used to define a terminating rewrite relation. When confluent, that relation defines unique normal forms that can be used to decide word problems. Some results obtained by these methods are summarized. 1. Intr ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
This paper outlines various recent approaches to solving word problems. Term orderings are used to define a terminating rewrite relation. When confluent, that relation defines unique normal forms that can be used to decide word problems. Some results obtained by these methods are summarized. 1. Introduction The central idea of rewriting is to impose directionality on the use of equations in proofs. A rewrite rule is an ordered pair of terms, written l ! r. Like equations, rules are used to replace instances of l by corresponding instances of r; unlike equations, rules are not used to replace instances of the righthand side r. For any given set R of rules, the rewrite relation !R is the closure of R (viewed as a binary relation) under the "replacement" property (within any context) and "fully invariant property" (under any substitution). In other words, s !R t if s contains a subterm that is an instance loe of l, for some rule l ! r in R, and t is s with that subterm replaced by roe...
OrderingBased Strategies for Horn Clauses*
"... Two new theoremproving procedures for equational Horn clauses are presented. The largest literal is selected for paramodulation in both strategies, except that one method treats positive literals as larger than negative ones and results in a unit strategy. Both use term orderings to restrict paramo ..."
Abstract
 Add to MetaCart
Two new theoremproving procedures for equational Horn clauses are presented. The largest literal is selected for paramodulation in both strategies, except that one method treats positive literals as larger than negative ones and results in a unit strategy. Both use term orderings to restrict paramodulation to potentially maximal sides of equations and to increase the amount of allowable simplification (demodulation). Completeness is shown using proof orderings. 1