Nicta course types summary

gistfile1.hs

data Id a
      runId :: Id a -> a
      mapId :: (a -> b) -> Id a -> Id b
      bindId :: (a -> Id b) -> Id a -> Id b

data List t = Nil | t :. (List t)
      infinity :: List Integer
      foldRight :: (a -> b -> b) -> b -> List a -> b
      foldLeft :: (b -> a -> b) -> b -> List a -> b
      headOr :: a -> List a -> a
      product :: List Int -> Int
      sum :: List Int -> Int
      length :: List a -> Int
      map :: (a -> b) -> List a -> List b
      filter :: (a -> Bool) -> List a -> List a
      (++) :: List a -> List a -> List a
      flatten :: List (List a) -> List a
      flatMap :: (a -> List b) -> List a -> List b
      seqOptional :: List (Optional a) -> Optional (List a)
      find :: (a -> Bool) -> List a -> Optional a
      lengthGT4 :: List a -> Bool
      reverse :: List a -> List a
      ...

class Functor f where
      (<$>) :: (a -> b) -> f a -> f b

    (<$) :: Functor f => a -> f b -> f a

class Functor f => Apply f where
      (<*>) :: f (a -> b) -> f a -> f b

    lift2 :: Apply f => (a -> b -> c) -> f a -> f b -> f c
    (*>) :: Apply f => f a -> f b -> f b
    (<*) :: Apply f => f b -> f a -> f b

class Apply f => Applicative f where
      pure :: a -> f a

    sequence :: Applicative f => List (f a) -> f (List a)
    replicateA :: Applicative f => Int -> f a -> f (List a)
    filtering :: Applicative f => (a -> f Bool) -> List a -> f (List a)