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Lazy rewriting on eager machinery
 ACM Transactions on Programming Languages and Systems
, 2000
"... The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives a ..."
Abstract

Cited by 23 (1 self)
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The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as an implementation of eager rewriting. 1
Origin Tracking for HigherOrder Term Rewriting Systems
 Proceedings of the International Workshop on HigherOrder Algebra, Logic and Term Rewriting HOA93
, 1993
"... Origin Tracking is a technique which, in the framework of firstorder term rewriting systems, establishes relations between each subterm t of a normal form and a set of subterms, the origins of t, in the initial term. Origin tracking is based on the notion of residuals. It has been used successfully ..."
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Cited by 3 (2 self)
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Origin Tracking is a technique which, in the framework of firstorder term rewriting systems, establishes relations between each subterm t of a normal form and a set of subterms, the origins of t, in the initial term. Origin tracking is based on the notion of residuals. It has been used successfully for the generation of error handlers and debuggers from algebraic specifications of programming languages. Recent experiments with the use of higherorder algebraic specifications for the definition of programming languages revealed a need to extend origin tracking for higherorder term rewriting systems. In this paper, we discuss how origin information can be maintained for fij reductions and expansions, during higherorder rewriting. We give a definition of higherorder origin tracking. The suitability of this definition is illustrated with a small, existing specification. AMS Subject Classification (1991): 68N20, 68Q55, 68Q65. CR Subject Classification (1991): D.2.5, D.2.6, D.3.4, F.3...
Origin Tracking in Primitive Recursive Schemes
 CONFERENCE PROCEEDINGS COMPUTING SCIENCE IN THE NETHERLANDS CSN'93
, 1993
"... Algebraic specifications of programming languages can be used to generate languagespecific programming support tools. Some of these can be obtained in a straightforward way by executing language specifications as term rewriting systems. More advanced tools can be obtained if the term rewriting ma ..."
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Cited by 1 (1 self)
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Algebraic specifications of programming languages can be used to generate languagespecific programming support tools. Some of these can be obtained in a straightforward way by executing language specifications as term rewriting systems. More advanced tools can be obtained if the term rewriting machinery is extended with origin tracking . Origin tracking is a technique which automatically establishes a relation between subterms of the result value (normal form) and their origins , which are subterms of the initial term. For specifications having a syntaxdirected nature, as formalized by the class of socalled primitive recursive schemes, highquality origins can be established. The definition, properties, extensions, and implementation of these socalled syntaxdirected origins are discussed.
Four Equivalent Equivalences of Reductions
, 2002
"... Two coinitial reductions in a term rewriting system are said to be equivalent if they perform the same steps, albeit maybe in a di#erent order. We present four characterisations of such a notion of equivalence, based on permutation, standardisation, labelling and projection, respectively. We prove ..."
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Two coinitial reductions in a term rewriting system are said to be equivalent if they perform the same steps, albeit maybe in a di#erent order. We present four characterisations of such a notion of equivalence, based on permutation, standardisation, labelling and projection, respectively. We prove that the characterisations all yield the same notion of equivalence, for the class of firstorder leftlinear term rewriting systems. A crucial role in our development is played by the notion of a proof term. 1