The Maybe data is used with functions that might be unsuccessful. The full description is in Maybe monad chapter.
Definition
The Standard Prelude defines the Maybe type as follows:
data Maybe a = Nothing | Just a
Recall that the type a is polymorphic and can contain complex types or even other monads (such as IO () types).
Library functions
The module Data.Maybe, in the standard hierarchical libraries, contains a wealth of functions for working with Maybe values.
Querying
Two obvious functions give you information about a Maybe value:
isJust
isJust returns True if when given an argument in the form Just _.
isJust :: Maybe a -> Bool
isJust (Just _) = True
isJust Nothing = False
isNothing
isNothing returns True if its argument is Nothing.
isNothing :: Maybe a -> Bool
isNothing (Just _) = False
isNothing Nothing = True
Getting out
There are a handful of functions for converting Maybe values to non-Maybe values.
maybe
maybe applies a given function to the internal value passed by a Just but otherwise returns a default value when given Nothing.
maybe :: b -> (a -> b) -> Maybe a -> b
maybe _ f (Just x) = f x
maybe z _ Nothing = z
fromMaybe
We might want to use maybe without applying any function to the Just. We can do that by calling maybe with the function id. Data.Maybe already has this as fromMaybe:
fromMaybe :: a -> Maybe a -> a
fromMaybe z = maybe z id
Note the use of point-free style. maybe z id evaluates to a function that is ready to take a Maybe value.
Lists and Maybe
The many similarities between lists and Maybe are discussed in the List monad chapter. Given the connections, there are a couple of functions for converting between one and the other:
listToMaybe
Failed computations return [] for lists and Nothing for Maybe. listToMaybe converts from the list to the Maybe monad. As Maybe can only hold one value, listToMaybe only takes the first solution from a list.
listToMaybe :: [a] -> Maybe a
listToMaybe [] = Nothing
listToMaybe (x:_) = Just x
maybeToList
The reverse listToMaybe is, of course, maybeToList:
maybeToList :: Maybe a -> [a]
maybeToList Nothing = []
maybeToList (Just x) = [x]
Lists manipulation
There are a couple of functions which are analogues of the normal Prelude list manipulation functions but are specialized to Maybe values.
Continue on some failures
We might want an OR function that won't make a whole computation fail just because one part failed.
catMaybes
Given a list of Maybe values, catMaybes extracts all the values in the form Just _, and strips off the Just constructors. List comprehension does the job here (as we showed in the pattern matching chapter):
catMaybes :: [Maybe a] -> [a]
catMaybes ms = [ x | Just x <- ms ]
mapMaybe
mapMaybe applies a function to a list and collects the successes. It can be understood as a composition of functions you already know:
mapMaybe :: (a -> Maybe b) -> [a] -> [b]
mapMaybe f xs = catMaybes (map f xs)
However, the actual definition in Data.Maybe traverses the list is potentially more efficient:
mapMaybe :: (a -> Maybe b) -> [a] -> [b]
mapMaybe _ [] = []
mapMaybe f (x:xs) =
case f x of
Just y -> y : mapMaybe f xs
Nothing -> mapMaybe f xs
Stop on failure
Rather than OR, we might want to collect values if and only if all succeed.
sequence
sequence :: [Maybe a] -> Maybe [a]
sequence [] = Just []
sequence (Nothing:xs) = Nothing
sequence (Just x:xs) = case sequence xs of
Just xs' -> Just (x:xs')
_ -> Nothing