Haskell/Libraries/Maybe

Libraries Reference 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 Libraries Reference