regenerate ToyList2/ToyList.thy during raw make *after* session build, to ensure that it is updated sporadically (NB: isabelle build does not support generated sources);
theory ToyList
imports Datatype
begin
datatype 'a list = Nil ("[]")
| Cons 'a "'a list" (infixr "#" 65)
(* This is the append function: *)
primrec app :: "'a list => 'a list => 'a list" (infixr "@" 65)
where
"[] @ ys = ys" |
"(x # xs) @ ys = x # (xs @ ys)"
primrec rev :: "'a list => 'a list" where
"rev [] = []" |
"rev (x # xs) = (rev xs) @ (x # [])"
lemma app_Nil2 [simp]: "xs @ [] = xs"
apply(induct_tac xs)
apply(auto)
done
lemma app_assoc [simp]: "(xs @ ys) @ zs = xs @ (ys @ zs)"
apply(induct_tac xs)
apply(auto)
done
lemma rev_app [simp]: "rev(xs @ ys) = (rev ys) @ (rev xs)"
apply(induct_tac xs)
apply(auto)
done
theorem rev_rev [simp]: "rev(rev xs) = xs"
apply(induct_tac xs)
apply(auto)
done
end