73 lines
1.4 KiB
Agda
73 lines
1.4 KiB
Agda
module TypeClass
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class Monad (m : U → U) where
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bind : ∀ a b. m a → (a → m b) → m b
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pure : ∀ a. a → m a
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infixl 1 _>>=_ _>>_
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_>>=_ : {0 m} {{Monad m}} {0 a b} -> (m a) -> (a -> m b) -> m b
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ma >>= amb = bind ma amb
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_>>_ : ∀ m a b. {{Monad m}} -> m a -> m b -> m b
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ma >> mb = mb
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data Either : U -> U -> U where
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Left : ∀ A B. A -> Either A B
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Right : ∀ A B. B -> Either A B
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instance {a} -> Monad (Either a) where
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bind (Left a) amb = Left a
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bind (Right b) amb = amb b
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pure a = Right a
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data Maybe : U -> U where
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Just : ∀ A. A -> Maybe A
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Nothing : ∀ A. Maybe A
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instance Monad Maybe where
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bind Nothing amb = Nothing
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bind (Just a) amb = amb a
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pure a = Just a
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infixr 7 _::_
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data List : U -> U where
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Nil : ∀ A. List A
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_::_ : ∀ A. A -> List A -> List A
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infixl 7 _++_
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_++_ : ∀ A. List A -> List A -> List A
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Nil ++ ys = ys
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(x :: xs) ++ ys = x :: (xs ++ ys)
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instance Monad List where
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bind Nil f = Nil
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bind (x :: xs) f = f x ++ bind xs f
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pure x = x :: Nil
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infixr 1 _,_
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data Pair : U -> U -> U where
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_,_ : ∀ A B. A -> B -> Pair A B
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ptype Int
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test : Maybe Int
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test = pure 10
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foo : Int -> Maybe Int
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foo x = Just 42 >> Just x >>= (\ x => pure 10)
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bar : Int -> Maybe Int
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bar x = do
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let y = x
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z <- Just x
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pure z
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baz : ∀ A B. List A -> List B -> List (Pair A B)
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baz xs ys = do
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x <- xs
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y <- ys
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pure (x , y)
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