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Report (Bericht) zugänglich unter
URN: urn:nbn:de:bsz:291-scidok-39571

On the interpretation of recursive program schemes

Nivat, Maurice

Quelle: (1974) Saarbr├╝cken, 1974
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Institut: Fachrichtung 6.2 - Informatik
DDC-Sachgruppe: Informatik
Dokumentart: Report (Bericht)
Schriftenreihe: Bericht / A / Fachbereich Angewandte Mathematik und Informatik, Universit├Ąt des Saarlandes
Bandnummer: 1974/09
Sprache: Englisch
Erstellungsjahr: 1974
Publikationsdatum: 13.07.2011
Kurzfassung auf Englisch: 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].
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