doc-src/TutorialI/Misc/Tree2.thy
author wenzelm
Wed, 08 Jun 2011 20:58:51 +0200
changeset 43284 04d473e883df
parent 27015 f8537d69f514
permissions -rw-r--r--
build jedit as part of regular startup script (in that case depending on jedit_build component); misc tuning and simplification;

(*<*)
theory Tree2 imports Tree begin
(*>*)

text{*\noindent In Exercise~\ref{ex:Tree} we defined a function
@{term"flatten"} from trees to lists. The straightforward version of
@{term"flatten"} is based on @{text"@"} and is thus, like @{term"rev"},
quadratic. A linear time version of @{term"flatten"} again reqires an extra
argument, the accumulator. Define *}
(*<*)primrec(*>*)flatten2 :: "'a tree \<Rightarrow> 'a list \<Rightarrow> 'a list"(*<*)where
"flatten2 Tip xs = xs" |
"flatten2 (Node l x r) xs = flatten2 l (x#(flatten2 r xs))"
(*>*)

text{*\noindent and prove*}
(*<*)
lemma [simp]: "!xs. flatten2 t xs = flatten t @ xs"
apply(induct_tac t)
by(auto);
(*>*)
lemma "flatten2 t [] = flatten t"
(*<*)
by(simp)

end
(*>*)