9722
|
1 |
%
|
|
2 |
\begin{isabellebody}%
|
10267
|
3 |
\def\isabellecontext{Tree{\isadigit{2}}}%
|
17056
|
4 |
%
|
|
5 |
\isadelimtheory
|
|
6 |
%
|
|
7 |
\endisadelimtheory
|
|
8 |
%
|
|
9 |
\isatagtheory
|
|
10 |
%
|
|
11 |
\endisatagtheory
|
|
12 |
{\isafoldtheory}%
|
|
13 |
%
|
|
14 |
\isadelimtheory
|
|
15 |
%
|
|
16 |
\endisadelimtheory
|
9493
|
17 |
%
|
|
18 |
\begin{isamarkuptext}%
|
|
19 |
\noindent In Exercise~\ref{ex:Tree} we defined a function
|
|
20 |
\isa{flatten} from trees to lists. The straightforward version of
|
9792
|
21 |
\isa{flatten} is based on \isa{{\isacharat}} and is thus, like \isa{rev},
|
|
22 |
quadratic. A linear time version of \isa{flatten} again reqires an extra
|
27015
|
23 |
argument, the accumulator. Define%
|
9493
|
24 |
\end{isamarkuptext}%
|
17175
|
25 |
\isamarkuptrue%
|
27015
|
26 |
flatten{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ tree\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}%
|
9493
|
27 |
\begin{isamarkuptext}%
|
27015
|
28 |
\noindent and prove%
|
9493
|
29 |
\end{isamarkuptext}%
|
17175
|
30 |
\isamarkuptrue%
|
17056
|
31 |
%
|
|
32 |
\isadelimproof
|
|
33 |
%
|
|
34 |
\endisadelimproof
|
|
35 |
%
|
|
36 |
\isatagproof
|
|
37 |
%
|
|
38 |
\endisatagproof
|
|
39 |
{\isafoldproof}%
|
|
40 |
%
|
|
41 |
\isadelimproof
|
|
42 |
%
|
|
43 |
\endisadelimproof
|
17175
|
44 |
\isacommand{lemma}\isamarkupfalse%
|
|
45 |
\ {\isachardoublequoteopen}flatten{\isadigit{2}}\ t\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ flatten\ t{\isachardoublequoteclose}%
|
17056
|
46 |
\isadelimproof
|
|
47 |
%
|
|
48 |
\endisadelimproof
|
|
49 |
%
|
|
50 |
\isatagproof
|
|
51 |
%
|
|
52 |
\endisatagproof
|
|
53 |
{\isafoldproof}%
|
|
54 |
%
|
|
55 |
\isadelimproof
|
|
56 |
%
|
|
57 |
\endisadelimproof
|
|
58 |
%
|
|
59 |
\isadelimtheory
|
|
60 |
%
|
|
61 |
\endisadelimtheory
|
|
62 |
%
|
|
63 |
\isatagtheory
|
|
64 |
%
|
|
65 |
\endisatagtheory
|
|
66 |
{\isafoldtheory}%
|
|
67 |
%
|
|
68 |
\isadelimtheory
|
|
69 |
%
|
|
70 |
\endisadelimtheory
|
11866
|
71 |
\end{isabellebody}%
|
9493
|
72 |
%%% Local Variables:
|
|
73 |
%%% mode: latex
|
|
74 |
%%% TeX-master: "root"
|
|
75 |
%%% End:
|