36 lines
855 B
Text
36 lines
855 B
Text
open nat
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definition foo : nat → nat
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| foo (0 + x) := x
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definition foo : nat → nat → nat
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| foo 0 _ := 0
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| foo x ⌞y⌟ := x
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definition foo : nat → nat → nat
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| foo 0 _ := 0
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| foo ⌞x⌟ x := x
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inductive tree (A : Type) :=
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| node : tree_list A → tree A
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| leaf : 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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definition is_leaf {A : Type} : tree A → bool
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with is_leaf_aux : tree_list A → bool
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| is_leaf (tree.node _) := bool.ff
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| is_leaf (tree.leaf _) := bool.tt
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| is_leaf_aux tree_list.nil := bool.ff
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| is_leaf_aux (tree_list.cons _ _) := bool.ff
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definition foo : nat → nat
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| foo 0 := 0
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| foo (x+1) := let y := x + 2 in y * y
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example : foo 5 = 36 := rfl
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definition boo : nat → nat
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| boo (x + 1) := boo (x + 2)
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| boo 0 := 0
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