proper support for "isabelle update -D DIR": avoid accidental exclusion of select_dirs (amending e5dafe9e120f);
theory Reverse
imports Define_Time_Function
begin
time_fun append
time_fun rev
lemma T_append: "T_append xs ys = length xs + 1"
by(induction xs) auto
lemma T_rev: "T_rev xs \<le> (length xs + 1)^2"
by(induction xs) (auto simp: T_append power2_eq_square)
fun itrev :: "'a list \<Rightarrow> 'a list \<Rightarrow> 'a list" where
"itrev [] ys = ys" |
"itrev (x#xs) ys = itrev xs (x # ys)"
lemma itrev: "itrev xs ys = rev xs @ ys"
by(induction xs arbitrary: ys) auto
lemma itrev_Nil: "itrev xs [] = rev xs"
by(simp add: itrev)
time_fun itrev
lemma T_itrev: "T_itrev xs ys = length xs + 1"
by(induction xs arbitrary: ys) auto
end