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**11 - 19**of**19**### A Survey of Rewriting Strategies in Program Transformation Systems

"... Many systems for program transformation exist that are often specialized for a specific object language and/or kind of transformation. All these systems share many ideas about program transformation and use similar techniques, but are often ad-hoc in many respects. The ultimate goal is to achieve a ..."

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Many systems for program transformation exist that are often specialized for a specific object language and/or kind of transformation. All these systems share many ideas about program transformation and use similar techniques, but are often ad-hoc in many respects. The ultimate goal is to achieve a specification language or family of specification languages for the high-level, declarative specification of program transformation systems in which generic, language independent schemas of transformation can be captured, and which admits efficient implementation of those transformations that can scale up to large programs.

### Free Variables and Subexpressions in Higher-Order Meta Logic

"... This paper addresses the problem of how to represent free variables and subexpressions involving -bindings. The aim is to apply what is known as higher-order abstract syntax to higher-order term rewriting systems. Directly applying fi-reduction for the purpose of subtermreplacement is incompatib ..."

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This paper addresses the problem of how to represent free variables and subexpressions involving -bindings. The aim is to apply what is known as higher-order abstract syntax to higher-order term rewriting systems. Directly applying fi-reduction for the purpose of subtermreplacement is incompatible with the requirements of term-rewriting. A new meta-level representation of subterms is developed that will allow term-rewriting systems to be formulated in a higher-order meta logic.

### A Functional Logic Language Based on Higher Order Narrowing

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©Copyright in this paper belongs to the author(s) Published in collaboration with the

### Higher-Order Conditional Term Rewriting in the L lambda Logic Programming Language

"... In this paper, we extend the notions of first-order conditional rewrite systems and higher-order rewrite systems to obtain higher-order conditional rewriting. Such rewrite systems can be used to directly express many operations in theorem proving and functional programming. We then illustrate that t ..."

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In this paper, we extend the notions of first-order conditional rewrite systems and higher-order rewrite systems to obtain higher-order conditional rewriting. Such rewrite systems can be used to directly express many operations in theorem proving and functional programming. We then illustrate that these rewrite systems can be naturally specified and implemented in a higher-order logic programming language. This paper was presented at the Third International Workshop on Extensions of Logic Programming, February 1992. 1 Introduction Higher-order rewrite systems extend first-order rewrite systems and provide a mechanism for reasoning about equality in languages that include notions of bound variables [1, 9, 12, 5]. First-order conditional rewrite systems extend firstorder rewrite systems, providing more expressive power by allowing conditions to be placed on rewrite rules [2, 8]. Such conditions must be satisfied before a particular rewrite can be applied. In this paper, we extend these ...

### ElfRW: A Tool for Higher-Order Dependently Typed Rewriting (System Description)

, 1997

"... We report on an extension of the SML implementationofthe logic programminglanguage Elf [Pfe94] to support thecheckofconvergence for higher-order critical pairs. Since Elf is based on the Edinburgh Logical Framework [HHP93] it utilizes dependenttypes. Therefore in the implementation a generalization ..."

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We report on an extension of the SML implementationofthe logic programminglanguage Elf [Pfe94] to support thecheckofconvergence for higher-order critical pairs. Since Elf is based on the Edinburgh Logical Framework [HHP93] it utilizes dependenttypes. Therefore in the implementation a generalization of thecritical pair lemmatothis case as done in [Vir96]had to be employed. 2 1 Motivation Higher-order rewrite systems (HRS) as an extension of term rewritingto simply typed -terms were introduced by Nipkow [Nip91]. Several confluence and local confluence results could be generalized tothe higher-order case [MN94]. In particular the convergence of all critical pairs implies local confluence and (weak) orthogonality implies confluence. Since the logic programming language Elf [Pfe94] provides a higher-order setting it can be used in a similar way as -Prolog [Mil91]asdonebyFeltyin[Fel92]to implement higher-order rewriting. Nevertheless Elf and -Prolog differ in several aspects. Additionally it is desirable toprovidethe user withmeans e.g. tocheck (local) confluence bycritical pair criteria. Elf is based on thetheEdinburgh Logical Framework [HHP93]. Therefore unlikethesetting of Nipkow [Nip91] Elf additionally supportsdependenttypes. This is also reflected bythe implementation. Here we report by example on the followingworkdone: -- the extension of the SML implementation of Elf -- allowingtheautomatic checkofhigher-order critical pairs -- takingdependenttypes into account. The used generalization of thecritical pair criterion todependenttypes follows [Vir96]. Attheendwe concludeand suggest future work.

### Term Rewriting with Traversal Functions

"... Term rewriting is an appealing technique for performing program analysis and program transfor-mation. Tree (term) traversal is frequently used but is not supported by standard term rewriting. We extend many-sorted, first-order term rewriting with traversal functions that automate tree traversal in a ..."

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Term rewriting is an appealing technique for performing program analysis and program transfor-mation. Tree (term) traversal is frequently used but is not supported by standard term rewriting. We extend many-sorted, first-order term rewriting with traversal functions that automate tree traversal in a simple and type safe way. Traversal functions can be bottom-up or top-down traver-sals and can either traverse all nodes in a tree or can stop the traversal at a certain depth as soon as a matching node is found. They can either define sort preserving transformations or mappings to a fixed sort. We give small and somewhat larger examples of traversal functions and describe their operational semantics and implementation. An assessment of various applications and a discussion conclude the paper.

### door

, 2005

"... Copyright It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content licence (like ..."

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Copyright It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content licence (like

### Higher-Order Conditional Term Rewriting in the L Logic Programming Language Preliminary Results

"... In this paper, we extend the notions of rst-order conditional rewrite systems and higher-order rewrite systems to obtain higher-order conditional rewriting. Such rewrite systems can be used to directly express many operations in theo-rem proving and functional programming. We then illustrate that th ..."

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In this paper, we extend the notions of rst-order conditional rewrite systems and higher-order rewrite systems to obtain higher-order conditional rewriting. Such rewrite systems can be used to directly express many operations in theo-rem proving and functional programming. We then illustrate that these rewrite systems can be naturally specied and implemented in a higher-order logic pro-gramming language. This paper was presented at the Third International Work-shop on Extensions of Logic Programming, February 1992. 1