How to convert `[[Either String c]]` into `Either String [[c]]`?

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Say I have two functions:

b2c :: B -> Either String C
a2bs :: A -> [[B]]

How to make the following a2cs function using b2c and a2bs such that if there is any Left value in the [[Either String c]] then Either String [[c]] should be a Left value?

a2cs :: A -> Either String [[C]]

You can use sequence for this, but it's not a single step. It commutes one pair of layers of type constructors, but you need to move the Either String constructor out two type layers. Well, our old friend map comes in handy.

foo1 :: [[Either String c]] -> [Either String [c]]
foo1 = map sequence

And then to go the rest of the way:

foo2 :: [Either String [c]] -> Either String [[c]]
foo2 = sequence

If you want to be more compact, you can just put it all together with function composition: sequence . map sequence :: [[Either String c]] -> Either String [[c]]

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I would write this:

a2cs = traverse (traverse b2c) . a2bs

Although this doesn't use exactly your proposed implementation strategy of first producing a [[Either String C]] and then flattening that to Either String [[C]], it has the advantage that it requires only one pass over the nested lists rather than the two required by your strategy.

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first convert your [[Either String c]] into [Either String [c]] then convert it to Either String [[c]] as follows:

func = sequence . map sequence

func [[Right 1, Right 2], [Left "a"]]
> Left "a"

func [[Right 1, Right 2], [Right 3]]
> Right [[1,2][3]]

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Comments
  • When you say the type of b2c is b -> Either String c, it's not really b is it? It's some other more concrete type, not a type var... same for the other function, right?
  • Yes, a, b, c in the type signatures are all concrete types.
  • Also when you say the if there's any Left value then Either String [[c]] should be a Left value, which should it be? What should be on Left? Concatenated strings?
  • @LeoZhang Consider writing them with uppercase letters in the types, then. Lowercase-starting identifers are reserved for type variables.
  • Simple solution will be getCompose <$> sequence (Compose [[Right 10, Right 20]]) Or f = fmap getCompose . sequence . Compose