diff -r 629f3a92863e -r 0ddd8028f98c doc-src/AxClass/Group/document/Semigroups.tex
--- a/doc-src/AxClass/Group/document/Semigroups.tex	Thu Feb 26 10:13:43 2009 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
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-\begin{isabellebody}%
-\def\isabellecontext{Semigroups}%
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-\isamarkupheader{Semigroups%
-}
-\isamarkuptrue%
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-\isadelimtheory
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-\endisadelimtheory
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-\isatagtheory
-\isacommand{theory}\isamarkupfalse%
-\ Semigroups\ \isakeyword{imports}\ Main\ \isakeyword{begin}%
-\endisatagtheory
-{\isafoldtheory}%
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-\isadelimtheory
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-\endisadelimtheory
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-\begin{isamarkuptext}%
-\medskip\noindent An axiomatic type class is simply a class of types
-  that all meet certain properties, which are also called \emph{class
-  axioms}. Thus, type classes may be also understood as type
-  predicates --- i.e.\ abstractions over a single type argument \isa{{\isacharprime}a}.  Class axioms typically contain polymorphic constants that
-  depend on this type \isa{{\isacharprime}a}.  These \emph{characteristic
-  constants} behave like operations associated with the ``carrier''
-  type \isa{{\isacharprime}a}.
-
-  We illustrate these basic concepts by the following formulation of
-  semigroups.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{consts}\isamarkupfalse%
-\isanewline
-\ \ times\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymodot}{\isachardoublequoteclose}\ {\isadigit{7}}{\isadigit{0}}{\isacharparenright}\isanewline
-\isacommand{axclass}\isamarkupfalse%
-\ semigroup\ {\isasymsubseteq}\ type\isanewline
-\ \ assoc{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymodot}\ y{\isacharparenright}\ {\isasymodot}\ z\ {\isacharequal}\ x\ {\isasymodot}\ {\isacharparenleft}y\ {\isasymodot}\ z{\isacharparenright}{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent Above we have first declared a polymorphic constant \isa{{\isasymodot}\ {\isasymColon}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a} and then defined the class \isa{semigroup} of
-  all types \isa{{\isasymtau}} such that \isa{{\isasymodot}\ {\isasymColon}\ {\isasymtau}\ {\isasymRightarrow}\ {\isasymtau}\ {\isasymRightarrow}\ {\isasymtau}} is indeed an
-  associative operator.  The \isa{assoc} axiom contains exactly one
-  type variable, which is invisible in the above presentation, though.
-  Also note that free term variables (like \isa{x}, \isa{y},
-  \isa{z}) are allowed for user convenience --- conceptually all of
-  these are bound by outermost universal quantifiers.
-
-  \medskip In general, type classes may be used to describe
-  \emph{structures} with exactly one carrier \isa{{\isacharprime}a} and a fixed
-  \emph{signature}.  Different signatures require different classes.
-  Below, class \isa{plus{\isacharunderscore}semigroup} represents semigroups \isa{{\isacharparenleft}{\isasymtau}{\isacharcomma}\ {\isasymoplus}\isactrlsup {\isasymtau}{\isacharparenright}}, while the original \isa{semigroup} would
-  correspond to semigroups of the form \isa{{\isacharparenleft}{\isasymtau}{\isacharcomma}\ {\isasymodot}\isactrlsup {\isasymtau}{\isacharparenright}}.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{consts}\isamarkupfalse%
-\isanewline
-\ \ plus\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymoplus}{\isachardoublequoteclose}\ {\isadigit{7}}{\isadigit{0}}{\isacharparenright}\isanewline
-\isacommand{axclass}\isamarkupfalse%
-\ plus{\isacharunderscore}semigroup\ {\isasymsubseteq}\ type\isanewline
-\ \ assoc{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymoplus}\ y{\isacharparenright}\ {\isasymoplus}\ z\ {\isacharequal}\ x\ {\isasymoplus}\ {\isacharparenleft}y\ {\isasymoplus}\ z{\isacharparenright}{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent Even if classes \isa{plus{\isacharunderscore}semigroup} and \isa{semigroup} both represent semigroups in a sense, they are certainly
-  not quite the same.%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\isacommand{end}\isamarkupfalse%
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-\endisatagtheory
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-\endisadelimtheory
-\isanewline
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