lean2/tests/lean/run/interp.lean
2015-03-09 08:42:21 -07:00

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import algebra.function
open bool nat
open function
inductive univ :=
| ubool : univ
| unat : univ
| uarrow : univ → univ → univ
open univ
definition interp : univ → Type₁
| ubool := bool
| unat := nat
| (uarrow fr to) := interp fr → interp to
definition foo : Π (u : univ) (el : interp u), interp u
| ubool tt := ff
| ubool ff := tt
| unat n := succ n
| (uarrow fr to) f := λ x : interp fr, f (foo fr x)
definition is_even : nat → bool
| zero := tt
| (succ n) := bnot (is_even n)
example : foo unat 10 = 11 := rfl
example : foo ubool tt = ff := rfl
example : foo (uarrow unat ubool) (λ x : nat, is_even x) 3 = tt := rfl
example : foo (uarrow unat ubool) (λ x : nat, is_even x) 4 = ff := rfl