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Abstract: In this paper two formats of higher-order rewriting are compared: Combinatory Reduction Systems introduced by Klop and Higher-order Rewrite Systems defined by Nipkow. Although it always has been obvious that both formats are closely related to each other, up to now the exact relationship between them has not been clear. This was an unsatisfying situation since it meant that proofs for much related frameworks were given twice. We present two translations, one from Combinatory Reduction Systems... (Update)
Context of citations to this paper: More
.... like Coq [10] or Lego [17] Although CRSs and HRSs seem quite different, they have been precisely compared by van Oostrom and van Raamsdonk [31], and shown to have the same expressive power, CRSs using a more lazy evaluation strategy than HRSs. On the other hand, although...
...an abstraction. In a certain sense, ISABST checks for the presence of the symbol introduced by the translation from CRSs into HRSs, see [6, 15]. exec (CHECK vs) let fun check n (Var k) k n orelse not(member vs (k n) check n (Sym( bs) all (check n) bs check...
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1.2: Comparing Combinatory Reduction Systems and.. - van Oostrom, van.. (1993) (Correct)
0.2: Combinatory Reduction Systems: introduction and survey - Klop, van Oostrom, al. (1993) (Correct)
0.2: Information Extraction & Object Views - Lacroix (Correct)
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0.9: Compilation of Combinatory Reduction Systems - Kahrs (1993) (Correct)
0.7: Termination and Confluence of Higher-Order Rewrite Systems - Blanqui (Correct)
0.5: Higher-Order Rewriting - van Raamsdonk (1999) (Correct)
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4: Higher-order critical pairs (context) - Nipkow - 1991
3: A logic programming language with lambda-abstraction - Miller - 1991
2: Polymorphic rewriting conserves algebraic strong normalization (context) - Breazu-Tannen, Gallier - 1991
BibTeX entry: (Update)
V. van Oostrom and F. van Raamsdonk. Comparing combinatory reduction systems and higher-order rewrite systems, 1994. This proceedings. http://citeseer.ist.psu.edu/vanoostrom93comparing.html More
@inproceedings{ vanoostrom93comparing,
author = "Vincent van Oostrom and Femke van Raamsdonk",
title = "Comparing Combinatory Reduction Systems and Higher-order Rewrite Systems",
booktitle = "{HOA}",
pages = "276-304",
year = "1993",
url = "citeseer.ist.psu.edu/vanoostrom93comparing.html" }
Citations (may not include all citations):251 A logic programming language with lambda-abstraction - Miller
174 Combinatory reduction systems (context) - Klop, van Oostrom et al. - 1993
174 Combinatory Reduction Systems (context) - Klop - 1980
166 An overview of Prolog (context) - Nadathur, Miller - 1988
145 Isabelle: The next 700 theorem provers (context) - Paulson - 1990
126 Higher-order critical pairs (context) - Nipkow
109 Interaction nets (context) - Lafont - 1990
92 Explicit substitutions - Abadi, Cardelli et al. - 1990
54 Tree-manipulating systems and Church-Rosser theorems (context) - Rosen - 1973
54 Polymorphic rewriting conserves algebraic strong normalizati.. (context) - Breazu-Tannen, Gallier - 1989
46 Orthogonal Higher-Order Rewrite Systems are Confluent (context) - Nipkow
41 Interaction systems I: the theory of optimal reductions - Asperti - 1992
39 Transactions of the American Mathematical Society (context) - Hindley, residuals - 1978
37 A general Church-Rosser theorem (context) - Aczel - 1978
20 Expression reduction systems - Khasidashvili - 1990
19 volume 21 of Cambridge Tracts in Theoretical Computer Scienc.. (context) - Wolfram, Theory - 1993
19 Confluence and superdevelopments (context) - van Raamsdonk - 1993
19 calculi with conditional rules (context) - Takahashi
10 Confluence by decreasing diagrams (context) - van Oostrom - 1993
7 Context rewriting (context) - Kahrs - 1992
4 volume 475 of Lecture Notes in Artificial Intelligence (context) - Siekmann, of et al. - 1991
2 dipartimento di informatica universit`a di pisa (context) - Laneve, Concurrency et al. - 1993
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