diff -r 619531d87ce4 -r 4e2ee88276d2 doc-src/TutorialI/document/Tree2.tex --- /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: