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Abstract: Isabelle o#ers order-sorted type classes on top of the simple types of plain Higher-Order Logic. The resulting type system is similar to that of the programming language Haskell. Its interpretation within the logic enables further application, though, apart from restricting polymorphism syntactically. In particular, the concept of Axiomatic Type Classes provides a useful light-weight mechanism for hierarchically-structured abstract theories. Subsequently, we demonstrate typical uses of... (Update)
Context of citations to this paper: More
.... The mechanism of defining type classes together with axioms has now become an explicit device of the Isabelle specification language [Wen95] A type class in Isabelle is a device for grouping types. For example, semigroup term defines a type class as a subclass of the built...
.... a proposal [Pau91b] and experiments [Asp91] In addition, Isabelle s polymorphism gives rise to a notion of axiomatic type classes [Nip93, Wen95] that is integrated in the current release. This concept can be seen as a particular case of modules (see Section 2.1.3) A good...
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Studies in Computer Aided Verification of Protocols - Griffioen (2000) (Correct)
Formalizing Integration Theory, with an Application to.. - Richter (2003) (Correct)
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0.9: Using Axiomatic Type Classes in Isabelle - Wenzel (2000) (Correct)
0.3: Miscellaneous Isabelle/Isar examples for Higher-Order Logic - Wenzel (1999) (Correct)
0.3: Some aspects of Unix file-system security - Wenzel (2001) (Correct)
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0.2: A Comparison of the Mathematical Proof Languages Mizar and Isar - Wenzel, Wiedijk (2002) (Correct)
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4: Type classes and overloading in higher-order logic - Wenzel - 1997
3: Isar --- a generic interpretative approach to readable formal proof documents - Wenzel - 1999
3: Computer-assisted mathematics at work --- the Hahn-Banach theorem in Isabelle/Is.. - Bauer, Wenzel - 2000
BibTeX entry: (Update)
Markus Wenzel. Using axiomatic type classes in Isabelle, a tutorial, 1995. http://www4.informatik.tu-muenchen.de/~wenzelm/papers.html. http://citeseer.ist.psu.edu/article/wenzel00using.html More
@misc{ wenzel95using,
author = "M. Wenzel",
title = "Using axiomatic type classes in Isabelle",
text = "Markus Wenzel. Using axiomatic type classes in Isabelle, a tutorial, 1995.
http://www4.informatik.tu-muenchen.de/~wenzelm/papers.html.",
year = "1995",
url = "citeseer.ist.psu.edu/article/wenzel00using.html" }
Citations (may not include all citations):183 Report on the programming language Haskell: A non-strict (context) - Hudak, Jones et al. - 1992
81 Isabelle: A Generic Theorem Prover (context) - Paulson - 1994
28 Type classes and overloading in higher-order logic - Wenzel - 1997
26 Order-sorted polymorphism in Isabelle (context) - Nipkow - 1993
17 Isar --- a generic interpretative approach to readable forma.. - Wenzel - 1999
10 Isabelle's Logics: HOL - Nipkow, Paulson et al.
5 Isar Reference Manual (context) - Wenzel
2 Presentation at the workshop Types for Proof and Programs (context) - Nipkow, classes et al. - 1993
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://isabelle.in.tum.de/Isar/): More
The Isabelle/Isar Reference Manual - Wenzel (1999) (Correct)
The Hahn-Banach Theorem for Real Vector Spaces - Bauer (1999) (Correct)
Miscellaneous Isabelle/Isar examples for Higher-Order Logic - Wenzel (1999) (Correct)
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