doc-src/TutorialI/Misc/document/Tree2.tex
author wenzelm
Tue, 12 Sep 2000 22:13:23 +0200
changeset 9941 fe05af7ec816
parent 9924 3370f6aa3200
child 10187 0376cccd9118
permissions -rw-r--r--
renamed atts: rulify to rule_format, elimify to elim_format;
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
9722
a5f86aed785b *** empty log message ***
nipkow
parents: 9721
diff changeset
     1
%
a5f86aed785b *** empty log message ***
nipkow
parents: 9721
diff changeset
     2
\begin{isabellebody}%
9924
3370f6aa3200 updated;
wenzelm
parents: 9792
diff changeset
     3
\def\isabellecontext{Tree2}%
9493
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
     4
%
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
     5
\begin{isamarkuptext}%
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
     6
\noindent In Exercise~\ref{ex:Tree} we defined a function
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
     7
\isa{flatten} from trees to lists. The straightforward version of
9792
bbefb6ce5cb2 *** empty log message ***
nipkow
parents: 9722
diff changeset
     8
\isa{flatten} is based on \isa{{\isacharat}} and is thus, like \isa{rev},
bbefb6ce5cb2 *** empty log message ***
nipkow
parents: 9722
diff changeset
     9
quadratic. A linear time version of \isa{flatten} again reqires an extra
9493
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
    10
argument, the accumulator:%
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
    11
\end{isamarkuptext}%
9673
1b2d4f995b13 updated;
wenzelm
parents: 9541
diff changeset
    12
\isacommand{consts}\ flatten\isadigit{2}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ tree\ {\isacharequal}{\isachargreater}\ {\isacharprime}a\ list\ {\isacharequal}{\isachargreater}\ {\isacharprime}a\ list{\isachardoublequote}%
9493
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
    13
\begin{isamarkuptext}%
9792
bbefb6ce5cb2 *** empty log message ***
nipkow
parents: 9722
diff changeset
    14
\noindent Define \isa{flatten\isadigit{2}} and prove%
9493
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
    15
\end{isamarkuptext}%
9722
a5f86aed785b *** empty log message ***
nipkow
parents: 9721
diff changeset
    16
\isacommand{lemma}\ {\isachardoublequote}flatten\isadigit{2}\ t\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ flatten\ t{\isachardoublequote}\end{isabellebody}%
9493
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
    17
%%% Local Variables:
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
    18
%%% mode: latex
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
    19
%%% TeX-master: "root"
494f8cd34df7 *** empty log message ***
nipkow
parents:
diff changeset
    20
%%% End: