Data/Maybe.hs

    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE NoImplicitPrelude #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Maybe
    -- Copyright   :  (c) The University of Glasgow 2001
    -- License     :  BSD-style (see the file libraries/base/LICENSE)
    --
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  stable
    -- Portability :  portable
    --
    -- The Maybe type, and associated operations.
    --
    -----------------------------------------------------------------------------

    module Data.Maybe
       (
         Maybe(Nothing,Just)

       , maybe

       , isJust
       , isNothing
       , fromJust
       , fromMaybe
       , listToMaybe
       , maybeToList
       , catMaybes
       , mapMaybe
       ) where

    import GHC.Base

    -- ---------------------------------------------------------------------------
    -- The Maybe type, and instances

    -- | The 'Maybe' type encapsulates an optional value.  A value of type
    -- @'Maybe' a@ either contains a value of type @a@ (represented as @'Just' a@),
    -- or it is empty (represented as 'Nothing').  Using 'Maybe' is a good way to
    -- deal with errors or exceptional cases without resorting to drastic
    -- measures such as 'error'.
    --
    -- The 'Maybe' type is also a monad.  It is a simple kind of error
    -- monad, where all errors are represented by 'Nothing'.  A richer
    -- error monad can be built using the 'Data.Either.Either' type.

    data  Maybe a  =  Nothing | Just a
      deriving (Eq, Ord)

    instance  Functor Maybe  where
        fmap _ Nothing       = Nothing
        fmap f (Just a)      = Just (f a)

    instance  Monad Maybe  where
        (Just x) >>= k      = k x
        Nothing  >>= _      = Nothing

        (Just _) >>  k      = k
        Nothing  >>  _      = Nothing

        return              = Just
        fail _              = Nothing

    -- ---------------------------------------------------------------------------
    -- Functions over Maybe

    -- | The 'maybe' function takes a default value, a function, and a 'Maybe'
    -- value.  If the 'Maybe' value is 'Nothing', the function returns the
    -- default value.  Otherwise, it applies the function to the value inside
    -- the 'Just' and returns the result.
    maybe :: b -> (a -> b) -> Maybe a -> b
    maybe n _ Nothing  = n
    maybe _ f (Just x) = f x

    -- | The 'isJust' function returns 'True' iff its argument is of the
    -- form @Just _@.
    isJust         :: Maybe a -> Bool
    isJust Nothing = False
    isJust _       = True

    -- | The 'isNothing' function returns 'True' iff its argument is 'Nothing'.
    isNothing         :: Maybe a -> Bool
    isNothing Nothing = True
    isNothing _       = False

    -- | The 'fromJust' function extracts the element out of a 'Just' and
    -- throws an error if its argument is 'Nothing'.
    fromJust          :: Maybe a -> a
    fromJust Nothing  = error "Maybe.fromJust: Nothing" -- yuck
    fromJust (Just x) = x

    -- | The 'fromMaybe' function takes a default value and and 'Maybe'
    -- value.  If the 'Maybe' is 'Nothing', it returns the default values;
    -- otherwise, it returns the value contained in the 'Maybe'.
    fromMaybe     :: a -> Maybe a -> a
    fromMaybe d x = case x of {Nothing -> d;Just v  -> v}

    -- | The 'maybeToList' function returns an empty list when given
    -- 'Nothing' or a singleton list when not given 'Nothing'.
    maybeToList            :: Maybe a -> [a]
    maybeToList  Nothing   = []
    maybeToList  (Just x)  = [x]

    -- | The 'listToMaybe' function returns 'Nothing' on an empty list
    -- or @'Just' a@ where @a@ is the first element of the list.
    listToMaybe           :: [a] -> Maybe a
    listToMaybe []        =  Nothing
    listToMaybe (a:_)     =  Just a

    -- | The 'catMaybes' function takes a list of 'Maybe's and returns
    -- a list of all the 'Just' values.
    catMaybes              :: [Maybe a] -> [a]
    catMaybes ls = [x | Just x <- ls]

    -- | The 'mapMaybe' function is a version of 'map' which can throw
    -- out elements.  In particular, the functional argument returns
    -- something of type @'Maybe' b@.  If this is 'Nothing', no element
    -- is added on to the result list.  If it just @'Just' b@, then @b@ is
    -- included in the result list.
    mapMaybe          :: (a -> Maybe b) -> [a] -> [b]
    mapMaybe _ []     = []
    mapMaybe f (x:xs) =
     let rs = mapMaybe f xs in
     case f x of
      Nothing -> rs
      Just r  -> r:rs
    {-# NOINLINE [1] mapMaybe #-}

    {-# RULES
    "mapMaybe"     [~1] forall f xs. mapMaybe f xs
                        = build (\c n -> foldr (mapMaybeFB c f) n xs)
    "mapMaybeList" [1]  forall f. foldr (mapMaybeFB (:) f) [] = mapMaybe f
      #-}

    {-# NOINLINE [0] mapMaybeFB #-}
    mapMaybeFB :: (b -> r -> r) -> (a -> Maybe b) -> a -> r -> r
    mapMaybeFB cons f x next = case f x of
      Nothing -> next
      Just r -> cons r next