Automated merge with bundle:/var/folders/9z/l1x9y3bd16x9_70pdp4703jr0000gp/T/SourceTreeTemp.VldMQI
(*<*)
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
(*>*)