more efficient Markup_Tree, based on branches sorted by quasi-order;
renamed markup_node.scala to markup_tree.scala and classes/objects accordingly;
Position.Range: produce actual Text.Range;
Symbol.Index.decode: convert 1-based Isabelle offsets here;
added static Command.range;
simplified Command.markup;
Document_Model.token_marker: flatten markup at most once;
tuned;
(*<*)
theory Tree imports Main begin
(*>*)
text{*\noindent
Define the datatype of \rmindex{binary trees}:
*}
datatype 'a tree = Tip | Node "'a tree" 'a "'a tree";(*<*)
primrec mirror :: "'a tree \<Rightarrow> 'a tree" where
"mirror Tip = Tip" |
"mirror (Node l x r) = Node (mirror r) x (mirror l)";(*>*)
text{*\noindent
Define a function @{term"mirror"} that mirrors a binary tree
by swapping subtrees recursively. Prove
*}
lemma mirror_mirror: "mirror(mirror t) = t";
(*<*)
apply(induct_tac t);
by(auto);
primrec flatten :: "'a tree => 'a list" where
"flatten Tip = []" |
"flatten (Node l x r) = flatten l @ [x] @ flatten r";
(*>*)
text{*\noindent
Define a function @{term"flatten"} that flattens a tree into a list
by traversing it in infix order. Prove
*}
lemma "flatten(mirror t) = rev(flatten t)";
(*<*)
apply(induct_tac t);
by(auto);
end
(*>*)