--- a/doc-src/TutorialI/Recdef/document/Nested1.tex Tue Aug 28 13:15:15 2012 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,75 +0,0 @@
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-\begin{isabellebody}%
-\def\isabellecontext{Nested{\isadigit{1}}}%
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-\isadelimtheory
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-\endisadelimtheory
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-\isatagtheory
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-\endisatagtheory
-{\isafoldtheory}%
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-\isadelimtheory
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-\endisadelimtheory
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-\begin{isamarkuptext}%
-\noindent
-Although the definition of \isa{trev} below is quite natural, we will have
-to overcome a minor difficulty in convincing Isabelle of its termination.
-It is precisely this difficulty that is the \textit{raison d'\^etre} of
-this subsection.
-
-Defining \isa{trev} by \isacommand{recdef} rather than \isacommand{primrec}
-simplifies matters because we are now free to use the recursion equation
-suggested at the end of \S\ref{sec:nested-datatype}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{recdef}\isamarkupfalse%
-\ trev\ {\isachardoublequoteopen}measure\ size{\isachardoublequoteclose}\isanewline
-\ {\isachardoublequoteopen}trev\ {\isacharparenleft}Var\ x{\isacharparenright}\ \ \ \ {\isacharequal}\ Var\ x{\isachardoublequoteclose}\isanewline
-\ {\isachardoublequoteopen}trev\ {\isacharparenleft}App\ f\ ts{\isacharparenright}\ {\isacharequal}\ App\ f\ {\isacharparenleft}rev{\isacharparenleft}map\ trev\ ts{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent
-Remember that function \isa{size} is defined for each \isacommand{datatype}.
-However, the definition does not succeed. Isabelle complains about an
-unproved termination condition
-\begin{isabelle}%
-\ \ \ \ \ t\ {\isasymin}\ set\ ts\ {\isasymlongrightarrow}\ size\ t\ {\isacharless}\ Suc\ {\isacharparenleft}term{\isacharunderscore}list{\isacharunderscore}size\ ts{\isacharparenright}%
-\end{isabelle}
-where \isa{set} returns the set of elements of a list
-and \isa{term{\isacharunderscore}list{\isacharunderscore}size\ {\isacharcolon}{\isacharcolon}\ term\ list\ {\isasymRightarrow}\ nat} is an auxiliary
-function automatically defined by Isabelle
-(while processing the declaration of \isa{term}). Why does the
-recursive call of \isa{trev} lead to this
-condition? Because \isacommand{recdef} knows that \isa{map}
-will apply \isa{trev} only to elements of \isa{ts}. Thus the
-condition expresses that the size of the argument \isa{t\ {\isasymin}\ set\ ts} of any
-recursive call of \isa{trev} is strictly less than \isa{size\ {\isacharparenleft}App\ f\ ts{\isacharparenright}},
-which equals \isa{Suc\ {\isacharparenleft}term{\isacharunderscore}list{\isacharunderscore}size\ ts{\isacharparenright}}. We will now prove the termination condition and
-continue with our definition. Below we return to the question of how
-\isacommand{recdef} knows about \isa{map}.
-
-The termination condition is easily proved by induction:%
-\end{isamarkuptext}%
-\isamarkuptrue%
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-\isadelimtheory
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-\endisadelimtheory
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-\isatagtheory
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-\endisatagtheory
-{\isafoldtheory}%
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-\isadelimtheory
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-\endisadelimtheory
-\end{isabellebody}%
-%%% Local Variables:
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