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Bootstrapping Types and Cotypes in HasCASL

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Book cover Algebra and Coalgebra in Computer Science (CALCO 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4624))

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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 decribe 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.

This work forms part of the DFG-project HasCASL (KR 1191/7-2).

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Authors and Affiliations

  1. DFKI-Lab Bremen and Department of Computer Science, University of Bremen,  

    Lutz Schröder

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  1. Lutz Schröder
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Till Mossakowski Ugo Montanari Magne Haveraaen

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Schröder, L. (2007). Bootstrapping Types and Cotypes in HasCASL . In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds) Algebra and Coalgebra in Computer Science. CALCO 2007. Lecture Notes in Computer Science, vol 4624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73859-6_30

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  • DOI: https://doi.org/10.1007/978-3-540-73859-6_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73857-2

  • Online ISBN: 978-3-540-73859-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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