Created
March 15, 2013 16:16
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-- General | |
foldl :: (a -> b -> a) -> a -> [b] -> a | |
foldr :: (a -> b -> b) -> b -> [a] -> b | |
curry :: ((a, b) -> c) -> a -> b -> c | |
uncurry :: (a -> b -> c) -> ((a, b) -> c) | |
(.) :: (b -> c) -> (a -> b) -> (a -> c) | |
-- Monoids | |
class Monoid a where | |
mempty :: a | |
mappend :: a -> a -> a | |
-- Law 1. 0 + m == m | |
-- Law 2. m + 0 == m | |
-- Law 3. (m1 + m2) + m3 == m1 + (m2 + m3) | |
-- Functors | |
class Functor f where | |
fmap :: (a -> b) -> f a -> f b | |
-- Identity: fmap id == id | |
-- Composition: fmap (f . g) == fmap f . fmap g | |
-- Applicative functors | |
class Functor f => Applicative f where | |
pure :: a -> f a | |
(<*>) :: f (a -> b) -> f a -> f b | |
(*>) :: f a -> f b -> f b | |
(<*) :: f a -> f b -> f a | |
-- Identity: pure id <*> v = v | |
-- Composition: pure (.) <*> u <*> v <*> w = u <*> (v <*> w) | |
-- Homomorphism: pure f <*> pure x = pure (f x) | |
-- Interchange: u <*> pure y = pure ($ y) <*> u | |
-- Ignore left: u *> v = pure (const id) <*> u <*> v | |
-- Ignore right: u <* v = pure const <*> u <*> v | |
-- Monads | |
class {- Functor m => -} Monad m where | |
(>>=) :: m a -> (a -> m b) -> m b | |
(>>) :: m a -> m b -> m b | |
return :: a -> m a | |
fail :: String -> m a | |
-- Law 1. return x >>= f == f x | |
-- Law 2. m >>= return == m | |
-- Law 3. (m >>= f) >>= g == m >>= (\x -> f x >>= g) | |
Monad composition: f >=> g (same as \x -> f x >>= g) | |
liftM :: (Monad m) => (a -> b) -> (m a -> m b) | |
liftM2 :: (Monad m) => (a -> b -> c) -> (m a -> m b -> m c) | |
liftIO :: MonadIO m => IO a -> m a | |
mapM :: Monad m => (a -> m b) -> [a] -> m [b] | |
foldM :: Monad m => (a -> b -> m a) -> a -> [b] -> m a | |
sequence :: Monad m => [m a] -> m [a] | |
( Suffixed _ makes value type () ) | |
class MonadTrans t where | |
lift :: Monad m => m a -> t a | |
class Monad m => MonadPlus m where | |
mzero :: m a | |
mplus :: m a -> m a -> m a | |
-- Control.Monad.Reader | |
newtype ReaderT r m a = ReaderT { runReaderT :: r -> m a } | |
type Reader r = ReaderT r Identity | |
class (Monad m) => MonadReader r m | m -> r where | |
ask :: m r | |
reader :: (r -> a) -> m a | |
local :: (r -> r) -> m a -> m a | |
asks :: MonadReader r m => (r -> a) -> m a | |
-- Control.Monad.Writer | |
newtype WriterT w m a = WriterT { runWriterT :: m (a, w) } | |
type Writer w = WriterT w Identity | |
instance (Monoid w, Monad m) => Monad (WriterT w m) | |
class (Monoid w, Monad m) => MonadWriter w m | m -> w where | |
tell :: w -> m () | |
listen :: m a -> m (a, w) | |
pass :: m (a, w -> w) -> m a | |
-- Control.Monad.State | |
newtype StateT s m a = StateT { runStateT :: s -> m (a, s) } | |
type State s = StateT s Identity | |
class (Monad m) => MonadState s m | m -> s where | |
get :: m s | |
put :: s -> m () | |
gets :: (MonadState s m) => (s -> a) -> m a | |
modify :: (MonadState s m) => (s -> s) -> m () | |
-- Control.Monad.Error | |
data Either e a = Left e | Right a -- Haskell Prelude | |
-- Either e is already MonadError | |
newtype ErrorT e m a = ErrorT { runErrorT :: m (Either e a) } | |
class (Monad m) => MonadError e m | m -> e where | |
throwError :: e -> m a | |
catchError :: m a -> (e -> m a) -> m a | |
-- Type families | |
class Add a b where -- uses MultiParamTypeClasses | |
type AddTy a b -- uses TypeFamilies; :: * | |
add :: a -> b -> AddTy a b | |
instance Add Double Integer where | |
type AddTy Double Integer = Double | |
add x y = x + fromIntegral y | |
instance (Num a) => Add a a where -- uses FlexibleInstances | |
type AddTy a a = a | |
add x y = x + y | |
instance (Add Integer a) => | |
Add Integer [a] where -- uses FlexibleContexts | |
type AddTy Integer [a] = [AddTy Integer a] | |
add x ys = map (add x) ys |
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