2015-03-09 15:42:21 +00:00
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open bool nat
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open function
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inductive univ :=
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| ubool : univ
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| unat : univ
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| uarrow : univ → univ → univ
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open univ
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2015-10-13 22:39:03 +00:00
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definition interp [reducible] : univ → Type₁
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2015-03-09 15:42:21 +00:00
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| ubool := bool
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| unat := nat
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| (uarrow fr to) := interp fr → interp to
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definition foo : Π (u : univ) (el : interp u), interp u
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| ubool tt := ff
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| ubool ff := tt
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| unat n := succ n
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| (uarrow fr to) f := λ x : interp fr, f (foo fr x)
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definition is_even : nat → bool
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| zero := tt
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| (succ n) := bnot (is_even n)
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2015-10-13 22:39:03 +00:00
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example : foo unat (10:nat) = 11 := rfl
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2015-03-09 15:42:21 +00:00
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example : foo ubool tt = ff := rfl
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example : foo (uarrow unat ubool) (λ x : nat, is_even x) 3 = tt := rfl
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example : foo (uarrow unat ubool) (λ x : nat, is_even x) 4 = ff := rfl
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