lean2/tests/lean/extra/tree_list_rec.lean

30 lines
928 B
Text
Raw Normal View History

open nat
inductive tree (A : Type) :=
leaf : A → tree A,
node : tree_list A → tree A
with tree_list :=
nil : tree_list A,
cons : tree A → tree_list A → tree_list A
namespace tree
open tree_list
definition size {A : Type} : tree A → nat
with size_l : tree_list A → nat,
size (leaf a) := 1,
size (node l) := size_l l,
size_l !nil := 0,
size_l (cons t l) := size t + size_l l
definition eq_tree {A : Type} : tree A → tree A → Prop
with eq_tree_list : tree_list A → tree_list A → Prop,
eq_tree (leaf a₁) (leaf a₂) := a₁ = a₂,
eq_tree (node l₁) (node l₂) := eq_tree_list l₁ l₂,
eq_tree _ _ := false,
eq_tree_list !nil !nil := true,
eq_tree_list (cons t₁ l₁) (cons t₂ l₂) := eq_tree t₁ t₂ ∧ eq_tree_list l₁ l₂,
eq_tree_list _ _ := false
end tree