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Author, Editor(s)

Author(s):

Waldmann, Uwe

dblp



BibTeX cite key*:

Waldmann92a

Title

Title*:

Semantics of Order-Sorted Specifications

Journal

Journal Title*:

Theoretical Computer Science

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Language:

English

Publisher

Publisher's
Name:

North-Holland Publishing Co.

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Address:


ISSN:

0304-3975

Vol, No, pp, Date

Volume*:

94

Number:

1

Publishing Date:

1992

Pages*:

1-35

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VG Pages:


Page Start:


Page End:


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DOI:


Note, Abstract, ©

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(LaTeX) Abstract:

Order-sorted specifications (i.e., many-sorted specifications with subsort relations) have been proved to be a useful tool for the description of partially defined functions and error handling in abstract data types. \par Several definitions for order-sorted algebras have been proposed. In some papers an operator symbol, which may be multiply declared, is interpreted by a family of functions (``overloaded'' algebras), in other papers it is always interpreted by a single function (``non-overloaded'' algebras). On the one hand, we try to demonstrate the differences between these two approaches with respect to equality, rewriting, and completion; on the other hand, we prove that in fact both theories can be studied parallelly, provided that certain notions are suitably defined. \par The overloaded approach differs from the many-sorted and the non-overloaded case, in that the overloaded term algebra is not necessarily initial. We give a decidable sufficient criterion for the initiality of the term algebra, which is less restrictive than GJM-regularity as proposed by Goguen, Jouannaud, and Meseguer. \par Sort decreasingness is an important property of rewrite system, since it ensures that confluence and Church-Rosser property are equivalent, that the overloaded and non-overloaded rewrite relations agree, and that variable overlaps do not yield critical pairs. We prove that it is decidable whether or not a rewrite rule is sort decreasing, even if the signature is not regular. \par Finally we demonstrate that every overloaded completion procedure may also be used in the non-overloaded world, but not conversely, and that specifications exist that can only be completed using the non-overloaded semantics.

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MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Programming Logics Group

Audience:

experts only

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BibTeX Entry:

@ARTICLE{Waldmann92a,
AUTHOR = {Waldmann, Uwe},
TITLE = {Semantics of Order-Sorted Specifications},
JOURNAL = {Theoretical Computer Science},
PUBLISHER = {North-Holland Publishing Co.},
YEAR = {1992},
NUMBER = {1},
VOLUME = {94},
PAGES = {1--35},
ISBN = {0304-3975},
}


Entry last modified by Uwe Brahm, 03/12/2010
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Editor(s)
Uwe Brahm
Created
05/07/1997 10:50:51 AM
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Editor(s)
Uwe Brahm
Uwe Brahm
Uwe Brahm
Uwe Brahm
Uwe Brahm
Edit Dates
01.10.98 20:16:53
25/03/98 10:16:36
03/05/98 07:33:00 PM
16/03/97 00:48:01
21/01/95 20:57:01