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Publication type: Article in Proceedings
Author: Lutz Schröder
Editor: Till Mossakowski, Udo Montanari
Title: Bootstrapping Types and Cotypes in HasCASL
Book / Collection title: Algebra and Coalgebra in Computer Science (CALCO 07)
Volume: 4624
Page(s): 447 – 462
Series: Lecture Notes in Computer Science
Year published: 2007
Publisher: Springer
Abstract: We discuss the treatment of initial datatypes and final process types in the wide-spectrum language HasCASL. In particular, we present specifications that illustrate how datatypes and process types arise as bootstrapped concepts using HasCASL's type class mechanism, and we describe constructions of types of finite and infinite trees that establish the conservativity of datatype and process type declarations adhering to certain reasonable formats. The latter amounts to modifying known constructions from HOL to avoid unique choice; in categorical terminology, this means that we establish that quasitoposes with an internal natural numbers object support initial algebras and final coalgebras for a range of polynomial functors, thereby partially generalizing corresponding results from topos theory.
Internet: http://dx.doi.org/10.1007/978-3-540-73859-6_30
PDF Version: http://www.informatik.uni-bremen.de/~lschrode/papers/HasCASLtypes.pdf
Keywords: HasCASL algebra coalgebra process type datatype quasitopos
Note / Comment: Extended version available
Status: Reviewed
Last updated: 18. 06. 2008

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