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Abstract: . We define Higher Order Recursive Program Schemes (HRPSs) by allowing metasubstitutions (as in the -calculus) in righthand sides of function and quantifier definitions. A study of several kinds of similarity of redexes makes it possible to lift properties of (first order) Recursive Program Schemes to the higher order case. The main result is the decidability of weak normalization in HRPSs, which immediately implies that HRPSs do not have full computational power. We analyze the structural... (Update)
Context of citations to this paper: More
...is required. The theory of neededness has already been generalised to the second order framework of Expression Reduction Systems (ERSs [Kha]) and we expect no difficulties in extending those results to HRSs. Concerning sequentiality, we expect that the methods and results of...
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BibTeX entry: (Update)
Zurab Khasidashvily. On higher order recursive program schemes. In [Tis94, pp. 172--186]. http://citeseer.ist.psu.edu/88625.html More
@inproceedings{ khasidashvili94higher,
author = "Zurab Khasidashvili",
title = "On Higher Order Recursive Program Schemes",
booktitle = "Colloquium on Trees in Algebra and Programming",
pages = "172-186",
year = "1994",
url = "citeseer.ist.psu.edu/88625.html" }
Citations (may not include all citations):788 Rewrite Systems - Dershowitz, Jouannaud - 1990
474 Term Rewriting Systems - Klop - 1992
210 its Syntax and Semantics (context) - Lambda - 1984
174 Combinatory Reduction Systems (context) - Klop - 1980
102 Computations in Orthogonal Rewriting Systems (context) - Huet, L'evy - 1991
63 Optimal Reduction in the Lambda-Calculus (context) - L'evy - 1980
62 Combinatory reduction Systems: introduction and survey - Klop, van Oostrom et al. - 1993
38 Recursive Applicative Program Schemes (context) - Courcelle - 1990
27 The Church-Rosser theorem in Orthogonal Combinatory Reductio.. (context) - Khasidashvili - 1992
25 Optimal normalization in orthogonal term rewriting systems - Khasidashvili - 1993
13 Some problems of the Notation Theory (context) - Sh - 1977
11 La strat'egie paresseuse (context) - Maranget - 1992
4 Perpetual reductions in orthogonal combinatory reduction sys.. (context) - Khasidashvili - 1993
2 Higher order recursive program schemes are Turing incomplete - Khasidashvili - 1993
1 The theory of optimal reductions (context) - Asperti, Laneve - 1992
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