by Lutz Schröder
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.
Reference:
Lutz Schröder: Bootstrapping Types and Cotypes in HasCASL, In Till Mossakowski, Udo Montanari, eds.: Algebra and Coalgebra in Computer Science (CALCO 07), Lecture Notes in Computer Science, vol. 4624, pp. 447–462, Springer, 2007. Extended version available [preprint]
Bibtex Entry:
@InProceedings{Schroder07a,
author = {Lutz Schr{\"o}der},
title = {Bootstrapping Types and Cotypes in HasCASL},
year = {2007},
editor = {Till Mossakowski and Udo Montanari},
booktitle = {Algebra and Coalgebra in Computer Science (CALCO 07)},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
volume = {4624},
pages = {447-462},
keywords = {HasCASL algebra coalgebra process type datatype quasitopos},
url = {http://dx.doi.org/10.1007/978-3-540-73859-6_30},
comment = { <a href = "http://www8.informatik.uni-erlangen.de/~schroeder/papers/HasCASLtypes.pdf"> [preprint] </a>},
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.},
note = {<a href="http://www8.informatik.uni-erlangen.de/~schroeder/papers/HasCASLtypes-ext.pdf">Extended version</a> available},
}