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