37 lines
880 B
Agda
37 lines
880 B
Agda
module Order
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data Nat : U where
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Z : Nat
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S : Nat -> Nat
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plus : Nat -> Nat -> Nat
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plus Z y = y
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plus (S x) y = S (plus x y)
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data Pair : U -> U -> U where
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_,_ : {A B : U} -> A -> B -> Pair A B
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infix 1 _,_
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foo : Pair Nat Nat
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-- vscode plugin issue: Without the space the info is rendered on Z...
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foo = (Z , S Z)
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-- So I was going to force a (a + b, a) =?= (3,0) unification problem
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-- as an example of needing _dynamic_ pattern unification
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data Eq : {A : U} -> A -> A -> U where
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Refl : {A : U} -> {x : A} -> Eq x x
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-- but hold up here. This doesn't solve either.
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-- Oh, because I can't reduce case.
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-- And the FC is useless.
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-- these go into caseeval.newt test
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two : Eq (plus Z (S (S Z))) (S (S Z))
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two = Refl
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two' : Eq (plus (S Z) (S Z)) (S (S Z))
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two' = Refl {Nat} {S (S Z)}
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three : Eq (plus (S Z) (S (S Z))) (plus (S (S Z)) (S Z))
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three = Refl {Nat} {S (S (S Z))}
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