85 lines
1.9 KiB
Agda
85 lines
1.9 KiB
Agda
module TypeClass
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data Monad : (U -> U) -> U where
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MkMonad : { M : U -> U } ->
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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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Monad M
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infixl 1 _>>=_ _>>_
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_>>=_ : ∀ m a b. {{Monad m}} -> (m a) -> (a -> m b) -> m b
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_>>=_ {{MkMonad bind' _}} 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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pure : ∀ m a. {{Monad m}} -> a -> m a
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pure {{MkMonad _ pure'}} a = pure' a
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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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bindEither : ∀ A B C. (Either A B) -> (B -> Either A C) -> Either A C
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bindEither (Left a) amb = Left a
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bindEither (Right b) amb = amb b
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EitherMonad : {A : U} -> Monad (Either A)
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EitherMonad = MkMonad {Either A} bindEither Right
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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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bindMaybe : ∀ A B. Maybe A -> (A -> Maybe B) -> Maybe B
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bindMaybe Nothing amb = Nothing
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bindMaybe (Just a) amb = amb a
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MaybeMonad : Monad Maybe
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MaybeMonad = MkMonad bindMaybe Just
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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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bindList : ∀ A B. List A -> (A -> List B) -> List B
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bindList Nil f = Nil
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bindList (x :: xs) f = f x ++ bindList xs f
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singleton : ∀ A. A -> List A
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singleton a = a :: Nil
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-- TODO need better error when the monad is not defined
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ListMonad : Monad List
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ListMonad = MkMonad bindList singleton
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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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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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