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%
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\begin{isabellebody}%
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%
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\begin{isamarkuptext}%
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\noindent In Exercise~\ref{ex:Tree} we defined a function
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\isa{flatten} from trees to lists. The straightforward version of
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\isa{flatten} is based on \isa{\at} and is thus, like \isa{rev}, quadratic.
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A linear time version of \isa{flatten} again reqires an extra
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argument, the accumulator:%
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\end{isamarkuptext}%
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\isacommand{consts}\ flatten\isadigit{2}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ tree\ {\isacharequal}{\isachargreater}\ {\isacharprime}a\ list\ {\isacharequal}{\isachargreater}\ {\isacharprime}a\ list{\isachardoublequote}%
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\begin{isamarkuptext}%
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\noindent Define \isa{flatten2} and prove%
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\end{isamarkuptext}%
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\isacommand{lemma}\ {\isachardoublequote}flatten\isadigit{2}\ t\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ flatten\ t{\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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