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Infinitary Initial Algebra Specifications For Stream Algebras (1998)
| Venue: | CONFORMATIONAL SELFASSEMBLY, PACI SYMPOSIUM ON BIOCOMPUTING'98 |
| Citations: | 4 - 4 self |
BibTeX
@INPROCEEDINGS{Tucker98infinitaryinitial,
author = {J. V. Tucker and J. I. Zucker},
title = {Infinitary Initial Algebra Specifications For Stream Algebras},
booktitle = {CONFORMATIONAL SELFASSEMBLY, PACI SYMPOSIUM ON BIOCOMPUTING'98},
year = {1998},
pages = {609--620},
publisher = {}
}
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Abstract
A stream is an in nite sequence of data from a set A. A wide variety of algorithms and architectures operate continuously in time, processing streams of data, for example: hardware systems, embedded systems and emergent systems. Also many models of real number computation use streams. In this paper we study the construction of an algebra A of streams over a many-sorted algebra A of data. In particular, we show how an initial algebra specification for A can be constructed from one for A. One problem is that A is uncountable even when A is finite. To handle this, we work with infinitary terms called stream terms, and infinitary formulae that generalise conditional equations, called !-conditional stream equations. We state a Birkhoff-Mal'cev type theorem that shows conservativity for the many-sorted stream version of full infinitary first-order logic L! 1 ! over an !-conditional equational logic, and also that certain !-conditional stream equational theories have initial model...
Keyphrases
infinitary initial algebra specification stream algebra conditional equational logic many model conditional equation many-sorted algebra certain conditional stream equational theory infinitary formula infinitary term stream term initial model conditional stream equation wide variety emergent system cev type theorem nite sequence real number computation use stream many-sorted stream version hardware system full infinitary first-order logic initial algebra specification
