How do you use two mappings to traverse a 2-tuple in Haskell?-CodePudding

I have a monad m that supports the following operation:

someName :: (t1 -> m u1) -> (t2 -> m u2) -> ((t1, t2) -> m (u1, u2))

In something more like English: given a mapping that could be used with bind to turn an m t1 into m u1 and another mapping for another pair of types, return such a mapping for pairs of the two types.

Does this concept have a name? Is it well-defined for all monads? Only some? None, and I have my facts wrong for the one I'm working on?

This is reminiscent of the traverse operation on Traversables, except there are two mappings involved. Plus, traverse for 2-tuples only seems to apply the mapping to the second element:

ghci> f a = Just (a   1)
ghci> traverse f (0, 1)
Just (0,2)
ghci> traverse f ("Hello", 1)
Just ("Hello",2)

CodePudding user response：

It's called bitraverse and comes standard with your favorite compiler.

CodePudding user response：

All monads have this operation. In fact, all applicative functors have this operation:

someName :: Applicative m => (t1 -> m u1) -> (t2 -> m u2) -> ((t1, t2) -> m (u1, u2))
someName f1 f2 = \(t1, t2) -> (,) <$> f1 t1 <*> f2 t2

For this reason, I doubt it has any special name, or any interesting properties beyond those of Applicative more generally.