Task Error [String] instead of [Task Error String]. That way, we'd have one future value holding all the results, which is much more amenable to our async needs than several future values arriving at their leisure.IOs longing to be together. It'd be just lovely to join them, let them dance cheek to cheek, but alas a Maybe stands between them like a chaperone at prom. Our best move here would be to shift their positions next to one another, that way each type can be together at last and our signature can be simplified to IO (Maybe Node).sequence and traverse.sequence:sequence is bit particular about its arguments. It looks like this:t (f a) which gets turned into a f (t a). Isn't that expressive? It's clear as day the two types do-si-do around each other. That first argument there is merely a crutch and only necessary in an untyped language. It is a type constructor (our of) provided so that we can invert map-reluctant types like Left - more on that in a minute.sequence, we can shift types around with the precision of a sidewalk thimblerigger. But how does it work? Let's look at how a type, say Either, would implement it:$value is a functor (it must be an applicative, in fact), we can simply map our constructor to leap frog the type.of entirely. It is passed in for the occasion where mapping is futile, as is the case with Left:Left who don't actually hold our inner applicative to get a little help in doing so. The Applicative interface requires that we first have a Pointed Functor so we'll always have a of to pass in. In a language with a type system, the outer type can be inferred from the signature and does not need to be explicitly given.[Maybe a], that's a collection of possible values whereas if I have a Maybe [a], that's a possible collection of values. The former indicates we'll be forgiving and keep "the good ones", while the latter means it's an "all or nothing" type of situation. Likewise, Either Error (Task Error a) could represent a client side validation and Task Error (Either Error a) could be a server side one. Types can be swapped to give us different effects.map or traverse. The first, partition will give us an array of Lefts and Rights according to the predicate function. This is useful to keep precious data around for future use rather than filtering it out with the bathwater. validate instead will give us the first item that fails the predicate in Left, or all the items in Right if everything is hunky dory. By choosing a different type order, we get different behavior.traverse function of List, to see how the validate method is made.reduce on the list. The reduce function is (f, a) => fn(a).map(b => bs => bs.concat(b)).ap(f), which looks a bit scary, so let's step through it.reduce(..., ...)reduce :: [a] -> (f -> a -> f) -> f -> f. The first argument is actually provided by the dot-notation on $value, so it's a list of things. Then we need a function from a f (the accumulator) and a a (the iteree) to return us a new accumulator.of(new List([]))of(new List([])), which in our case is Right([]) :: Either e [a]. Notice that Either e [a] will also be our final resulting type!fn :: Applicative f => a -> f afn is actually fromPredicate(f) :: a -> Either e a..map(b => bs => bs.concat(b))Right, Either.map passes the right value to the function and returns a new Right with the result. In this case the function has one parameter (b), and returns another function (bs => bs.concat(b), where b is in scope due to the closure). When Left, the left value is returned.ap(f)f is an Applicative here, so we can apply the function bs => bs.concat(b) to whatever value bs :: [a] is in f. Fortunately for us, f comes from our initial seed and has the following type: f :: Either e [a] which is by the way, preserved when we apply bs => bs.concat(b). When f is Right, this calls bs => bs.concat(b), which returns a Right with the item added to the list. When Left, the left value (from the previous step or previous iteration respectively) is returned.List.traverse, and is accomplished with of, map and ap, so will work for any Applicative Functor. This is a great example of how those abstraction can help to write highly generic code with only a few assumptions (that can, incidentally, be declared and checked at the type level!).traverse instead of map, we've successfully herded those unruly Tasks into a nice coordinated array of results. This is like Promise.all(), if you're familiar, except it isn't just a one-off, custom function, no, this works for any traversable type. These mathematical apis tend to capture most things we'd like to do in an interoperable, reusable way, rather than each library reinventing these functions for a single type.map(map($)) we have chain(traverse(IO.of, $)) which inverts our types as it maps then flattens the two IOs via chain.Identity in our functor, then turn it inside out with sequence that's the same as just placing it on the outside to begin with. We chose Right as our guinea pig as it is easy to try the law and inspect. An arbitrary functor there is normal, however, the use of a concrete functor here, namely Identity in the law itself might raise some eyebrows. Remember a category is defined by morphisms between its objects that have associative composition and identity. When dealing with the category of functors, natural transformations are the morphisms and Identity is, well identity. The Identity functor is as fundamental in demonstrating laws as our compose function. In fact, we should give up the ghost and follow suit with our Compose type:true, Right, Identity, and Array to test it out. Libraries like quickcheck or jsverify can help us test the law by fuzz testing the inputs.joining them down. Next, we'll take a bit of a detour to see one of the most powerful interfaces of functional programming and perhaps even algebra itself: Monoids bring it all together​getJsons to Map Route Route → Task Error (Map Route JSON)validate function, update startGame (and its signature) to only start the game if all players are valid