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\\[4ex] Using Axiomatic Type Classes in Isabelle}
\author{\emph{Markus Wenzel} \\ TU M\"unchen}
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\begin{document}
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\begin{abstract}
Isabelle offers 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 \emph{Axiomatic Type Classes}
provides a useful light-weight mechanism for hierarchically-structured
abstract theories. Subsequently, we demonstrate typical uses of Isabelle's
axiomatic type classes to model basic algebraic structures.
Note that this document describes axiomatic type classes using Isabelle/Isar
theories, with proofs expressed via Isar proof language elements. The new
theory format greatly simplifies the arrangement of the overall development,
since definitions and proofs may be freely intermixed. Users who prefer
tactic scripts over structured proofs do not need to fall back on separate
ML scripts, but may refer to Isar's tactic emulation commands.
\end{abstract}
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\nocite{nipkow-types93}
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\nocite{Wenzel:1997:TPHOL}
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\nocite{Wenzel:1999:TPHOL}
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