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%
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\begin{isabellebody}%
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\def\isabellecontext{Nested{\isadigit{0}}}%
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%
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\begin{isamarkuptext}%
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In \S\ref{sec:nested-datatype} we defined the datatype of terms%
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\end{isamarkuptext}%
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\isacommand{datatype}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}b{\isacharparenright}{\isachardoublequote}term{\isachardoublequote}\ {\isacharequal}\ Var\ {\isacharprime}a\ {\isacharbar}\ App\ {\isacharprime}b\ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}b{\isacharparenright}term\ list{\isachardoublequote}%
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\begin{isamarkuptext}%
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\noindent
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and closed with the observation that the associated schema for the definition
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of primitive recursive functions leads to overly verbose definitions. Moreover,
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if you have worked exercise~\ref{ex:trev-trev} you will have noticed that
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you needed to reprove many lemmas reminiscent of similar lemmas about
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\isa{rev}. We will now show you how \isacommand{recdef} can simplify
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definitions and proofs about nested recursive datatypes. As an example we
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choose exercise~\ref{ex:trev-trev}:%
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\end{isamarkuptext}%
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\isacommand{consts}\ trev\ \ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}b{\isacharparenright}term\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}b{\isacharparenright}term{\isachardoublequote}\end{isabellebody}%
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "root"
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%%% End:
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