Schröder, Lutz - Bootstrapping Inductive and Coinductive Types in HasCASL

lmcs:1166 - Logical Methods in Computer Science, December 25, 2008, Volume 4, Issue 4
Bootstrapping Inductive and Coinductive Types in HasCASL

Authors: Schröder, Lutz

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 generalising corresponding results from topos theory. Moreover, we present similar constructions in categories of internal complete partial orders in quasitoposes.


Source : oai:arXiv.org:0812.3836
DOI : 10.2168/LMCS-4(4:17)2008
Volume: Volume 4, Issue 4
Published on: December 25, 2008
Submitted on: December 15, 2007
Keywords: Computer Science - Logic in Computer Science,Computer Science - Software Engineering,D.2.1,E.1,F.3.1,F.3.2,F.4.1


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