fromMaybe is Just a fold
fromMaybe is a useful function.
Maybe is not guaranteed to hold a value, but you can always get one by providing a default to fallback on:
fromMaybe :: a -> Maybe a -> a = case m_x of fromMaybe dfault m_x Just x -> x Nothing -> dfault
At the interactive Haskell shell, it behaves exactly as intended:
ghci> fromMaybe "default" (Just "a string") "a string" ghci> fromMaybe "default" Nothing "default"
It’s a bit wordy. If I am working with
Maybe-heavy code, I sometimes alias this function to the operator
// y = fromMaybe y xx
or the point-free style:
//) = flip fromMaybe(
ghci> :type (//) (//) :: Maybe c -> c -> c ghci> Just "one little fox" // "no animals here!" "one little fox" ghci> Nothing // "no animals here!" "no animals here!"
Well today I was converting some
Maybe code to use
Either ErrorCode. This is not difficult — the strong type system makes it a pretty mechanical process. I replaced
fromMaybe with this definition of
fromEitherE :: a -> Either e a -> a = case e_x of fromEitherE dfault e_x Right x -> x Left _ -> dfault
Normally this would entail replacing the calls to
fromMaybe all over the place, but since I had been using the
// alias everywhere, that was all I needed to change:
//) = flip fromEitherE(
To show that it works:
ghci> Right "my cool home page" // "server error" "my cool home page" ghci> Left 418 // "server error" "server error"
We get the
Right value if there is one, and if not, ignore the error code and use the provided fallback value.
Sure, this works, but somehow I am dissatisfied. I expected to find a polymorphic solution that can handle both cases cleanly. After all, look at the similarities in their types:
fromMaybe :: a -> Maybe a -> a fromEitherE :: a -> Either e a -> a
I wondered whether there were any other functors which exhibit the same pattern.
We can imagine extracting the first element of a list, or using a fallback if the list is empty!3
fromList :: a -> [a] -> a = case l of fromList dfault l :rest -> first first-> dfault  //) = flip fromList(
ghci>  // "no trains :v(" "no trains :v(" ghci> ["3pm"] // "no trains :v(" "3pm" ghci> ["3pm","7pm"] // "no trains :v(" "3pm"
It is in this form that a solution becomes the most clear. We are reducing a list to a single element, an operation which shares its name with a certain bread-making technique.
fold, in the Lisp tradition, is a function which takes a combining function, a starting value, and a list. It uses the function and starting value to walk through the list, accumulating as it goes along.
fold :: (a -> a -> a) -> a -> [a] -> a = recurse list fold f start list where = case l of recurse l -> start  :rest -> f first (recurse rest) first
ghci> fold (+) 0 [1,2,3,4,5] 15
We could use
fold to implement our
fromList function — we just need a function which always returns its first argument!
const :: a -> b -> a const x y = x
ghci> fold const 0 [1,2,3] 1 ghci> fold const 0  0
But lists are far from the only structures that we can fold. The
Foldable type-class exists to capture the pattern of types which can be folded in some way using a function. Common examples include lists, trees, and sets.
The general version is called
foldr and looks like this:
ghci> :info Foldable class Foldable t where foldr :: (a -> b -> b) -> b -> t a -> b length :: t a -> Int -- and many more... instance Foldable Set -- Defined in ‘Data.Set.Internal’ instance Foldable  -- Defined in ‘Data.Foldable’ instance Foldable NonEmpty -- Defined in ‘Data.Foldable’ instance Foldable Maybe -- Defined in ‘Data.Foldable’ instance Foldable (Either a) -- Defined in ‘Data.Foldable’
Instance Foldable Maybe? Yes!
ghci> length Nothing 0 ghci> length (Just undefined) 1 ghci> foldr (+) 2 (Just 2) 4
It’s true! We can fold both
Either as. This suggests a polymorphic solution to our puzzle:
(//) :: Foldable f => f a -> a -> a //) = flip (foldr const)(
ghci> Just "ok" // "otherwise" "ok" ghci> Right "ok" // "otherwise" "ok" ghci> ["ok"] // "otherwise" "ok"
And there was much rejoicing.
One more thing.
(//) does not make sense for every
NonEmpty lists, for example, are guaranteed to hold at least one value. If we want to get the first value out of a
NonEmpty, we always can! There’s no need for an “otherwise” value.
We can avoid
(//) on such types by defining our own sub-class of
class Foldable f => Optional f where (//) :: f a -> a -> a //) = flip (foldr const) ( instance Optional Maybe instance Optional (Either e) instance Optional 
cool, that’s it
This post was inspired by a discussion in the #haskell irc channel on libera.chat, with special thanks to geekosaur and hpc. I hope you found it interesting too.
All the code examples above are available on GitLab and GitHub.
I would prefer to use
||, in the style of Unix shell. Unfortunately, Haskell copied
||from the C tradition and uses it for Boolean disjunction. If you really want to, you could
import Prelude hiding ((||))and then redefine
(||)to whatever you like. In this post, we will instead use
//as a tribute to Perl.↩︎
fromRightin the base package.↩︎
This function is commonly called “head”, except that the
headfunction in base is partial and will crash your program if passed an empty list.↩︎