--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/doc-src/TutorialI/document/Tree2.tex	Thu Jul 26 19:59:06 2012 +0200
@@ -0,0 +1,75 @@
+%
+\begin{isabellebody}%
+\def\isabellecontext{Tree{\isadigit{2}}}%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+%
+\isatagtheory
+%
+\endisatagtheory
+{\isafoldtheory}%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+%
+\begin{isamarkuptext}%
+\noindent In Exercise~\ref{ex:Tree} we defined a function
+\isa{flatten} from trees to lists. The straightforward version of
+\isa{flatten} is based on \isa{{\isaliteral{40}{\isacharat}}} and is thus, like \isa{rev},
+quadratic. A linear time version of \isa{flatten} again reqires an extra
+argument, the accumulator. Define%
+\end{isamarkuptext}%
+\isamarkuptrue%
+flatten{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ tree\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}%
+\begin{isamarkuptext}%
+\noindent and prove%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+\isacommand{lemma}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}flatten{\isadigit{2}}\ t\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ flatten\ t{\isaliteral{22}{\isachardoublequoteclose}}%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isadelimtheory
+%
+\endisadelimtheory
+%
+\isatagtheory
+%
+\endisatagtheory
+{\isafoldtheory}%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+\end{isabellebody}%
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "root"
+%%% End: