Please use this identifier to cite or link to this item:
doi:10.22028/D291-26058
Title: | On the interpretation of recursive program schemes |
Author(s): | Nivat, Maurice |
Language: | English |
Year of Publication: | 1974 |
OPUS Source: | Saarbrücken, 1974 |
DDC notations: | 004 Computer science, internet |
Publikation type: | Report |
Abstract: | This paper extends a previous paper [8] where we described a semantics for monadic recursive program schemes (also called Scott-de Bakker schemes). The method consists in considering program schemes as rewriting systems which generate subsets of a free magma and defining a mapping of such subsets in a proper domain of functions. In our previous paper, dealing with a simple case, the combinatorial properties on which the whole construction relies were well known or at least immediate corollaries of wellknown results in the theory of context-free languages. In the present case, the rewriting systems which we are led to consider, and which in a very naturalway could be called algebraic rewriting systems or grammars on a free magma, have been little considered in the literature and we need establish first a number of results concerning such systems. This is done in a first part of this paper. Afterwards we establish the link between such rewriting systems and recursive program schemes, define the function computed by such a scheme under a given discrete interpretation and apply the results of part I to show the equivalence of one definition of this function with the classical definitions : the operational semantics as described for example in [3], Kleene's definition of recursive function [2], the fix-point semantics as it can be found in [5], [6] or [10]. |
Link to this record: | urn:nbn:de:bsz:291-scidok-39571 hdl:20.500.11880/26114 http://dx.doi.org/10.22028/D291-26058 |
Series name: | Bericht / A / Fachbereich Angewandte Mathematik und Informatik, Universität des Saarlandes |
Series volume: | 1974/09 |
Date of registration: | 13-Jul-2011 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Informatik |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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fb14_1974_09.pdf | 5,13 MB | Adobe PDF | View/Open |
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