mirror of
https://github.com/edwinb/Idris2-boot.git
synced 2024-11-28 14:06:26 +03:00
80 lines
1.6 KiB
Idris
80 lines
1.6 KiB
Idris
|
module IFace
|
||
|
|
|
||
|
|
import Stuff
|
||
|
|
|
||
|
|
infixl 5 ==, /=
|
||
|
|
|
||
|
|
interface Eq b where
|
||
|
|
(==) : b -> b -> Bool
|
||
|
|
(/=) : b -> b -> Bool
|
||
|
|
|
||
|
|
Eq Nat where
|
||
|
|
(==) Z Z = True
|
||
|
|
(==) (S j) (S k) = j == k
|
||
|
|
(==) _ _ = False
|
||
|
|
|
||
|
|
(/=) x y = not (x == y)
|
||
|
|
|
||
|
|
[silly] Eq Nat where
|
||
|
|
(==) Z Z = False
|
||
|
|
(==) (S j) (S k) = j == k
|
||
|
|
(==) _ _ = True
|
||
|
|
|
||
|
|
(/=) x y = not (x == y)
|
||
|
|
|
||
|
|
Eq a => Eq (List a) where
|
||
|
|
(==) [] [] = True
|
||
|
|
(==) (x :: xs) (y :: ys) = x == y && xs == ys
|
||
|
|
(==) _ _ = False
|
||
|
|
|
||
|
|
(/=) x y = not (x == y)
|
||
|
|
|
||
|
|
(Eq a, Eq b) => Eq (a, b) where
|
||
|
|
(==) (x, y) (x', y') = x == x' && y == y'
|
||
|
|
|
||
|
|
[alsoSilly] Eq a => Eq (List a) where
|
||
|
|
(==) [] [] = False
|
||
|
|
(==) (x :: xs) (y :: ys) = x == y && xs == ys
|
||
|
|
(==) _ _ = True
|
||
|
|
|
||
|
|
(/=) x y = not (x == y)
|
||
|
|
|
||
|
|
test : ((Eq b, Eq b, Eq a), Eq b) => a -> a -> Bool
|
||
|
|
test x y = x == y
|
||
|
|
|
||
|
|
interface DecEq a where
|
||
|
|
decEq : (x : a) -> (y : a) -> Dec (x = y)
|
||
|
|
|
||
|
|
-- partial!
|
||
|
|
eqNat : (x : Nat) -> (y : Nat) -> Dec (x = y)
|
||
|
|
eqNat (S x) (S y)
|
||
|
|
= case eqNat x y of
|
||
|
|
Yes Refl => Yes Refl
|
||
|
|
eqNat Z Z = Yes Refl
|
||
|
|
|
||
|
|
DecEq Nat where
|
||
|
|
decEq = eqNat
|
||
|
|
|
||
|
|
data Vect : _ -> Type -> Type where
|
||
|
|
Nil : Vect Z a
|
||
|
|
(::) : a -> Vect k a -> Vect (S k) a
|
||
|
|
|
||
|
|
Eq a => Eq (Vect n a) where
|
||
|
|
(==) [] [] = True
|
||
|
|
(==) (x :: xs) (y :: ys) = x == y && xs == ys
|
||
|
|
(==) _ _ = False
|
||
|
|
|
||
|
|
(/=) xs ys = not (xs == ys)
|
||
|
|
|
||
|
|
v1 : DPair Nat (\n => Vect n Nat)
|
||
|
|
v1 = MkDPair _ [Z, S Z]
|
||
|
|
|
||
|
|
v2 : DPair Nat (\n => Vect n Nat)
|
||
|
|
v2 = MkDPair _ [Z, Z]
|
||
|
|
|
||
|
|
(DecEq a, {t : a} -> Eq (p t)) => Eq (DPair a p) where
|
||
|
|
(==) (MkDPair l r) (MkDPair l' r')
|
||
|
|
= case decEq l l' of
|
||
|
|
Yes Refl => r == r'
|
||
|
|
No _ => False
|