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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 ..."
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Cited by 821 (23 self)
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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.
Inductive synthesis of equational programs
 In Eighth National Conf. on Arti cial Intelligence
, 1990
"... An equational approach to the synthesis of functional and logic program is taken. In this context, the synthesis task involves nding executable equations such that the given speci cation holds in their standard model. Hence, to synthesize such programs, induction is necessary.We formulate procedures ..."
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Cited by 27 (3 self)
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An equational approach to the synthesis of functional and logic program is taken. In this context, the synthesis task involves nding executable equations such that the given speci cation holds in their standard model. Hence, to synthesize such programs, induction is necessary.We formulate procedures for inductiveproof,aswell as for program synthesis, using the framework of \ordered rewriting". We also propose heuristics for generalizing from a sequence of equational consequences. These heuristics handle cases where the deductive process alone is inadequate for coming up with a program. 1.
Open Problems in Rewriting
 Proceeding of the Fifth International Conference on Rewriting Techniques and Application (Montreal, Canada), LNCS 690
, 1991
"... Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27 ..."
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Cited by 19 (2 self)
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Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27, 28, 44, 56,57,76, 82, 81#; one edited collection of papers #1#; four monographs #3, 12,55,65#; and seven books #four of them still in progress# #8,9, 35, 54, 60,75, 84#. To encourage and stimulate continued progress in this area, wehave collected #with the help of colleagues# a number of problems that appear to us to be of interest and regarding whichwe do not know the answer. Questions on rewriting and other equational paradigms have been included; manyhave not aged su#ciently to be accorded the appellation #open problem". Wehave limited ourselves to theoretical questions, though there are certainly many additional interesting questions relating to applications and implementation
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. ..."
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Cited by 13 (0 self)
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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 ..."
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Cited by 2 (1 self)
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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...