> I just don't get the idea that "sequential" is somehow a bad thing?
and this:
> The whole concept of an algorithm/procedure to perform a computation is about performing a series of operations in a specific order.
are different manifestations of the one thing: you are thinking about programming in a sequential terms only. When you think about programming problem you are trying to solve it by a sequence of operations. You should try something like Haskell, something that force your mind to think differently, it would help you to teach your mind to see programming other way.
Such a "sequential thinking" is acceptable, but you probably not as good as you might be at thinking about programming problems. Functional programming helps to think about code one level higher, without distractions and compications caused by "linearization" of your thoughts to fit them into imperative paradigm. The main reason behind functional paradigm is an ability to prove statements about code, to be able to reason about code.
To throw out idea of sequence from reasoning of code is a futher abstraction from underlying machinery like transistors or machine instruction set. As any abstraction it gives you both benefits (you can think about more complex problems using the same amount of computational power of your brains) and downsides -- you become more restricted by paradigm itself, though I cannot explain what these restrictions are, because I can feel them sometimes, but do not know how to verbalize that feelings.
You can reason about code even if you think that any program is a sequence of operations, but you can do it better, if your idea of program is wider than a "series of operations in a specific order". Moreover some of that reasoning you can do by special program, like compiler or static analyzer.
Can you provide a concrete example of this? Otherwise it is just a hand wavy thing to say (which are way too many in programming world).
I should use an artifical task as an example, but the trouble is if someone thinks in imperative terms only, then when he tried to think about a task he would frame the task in imperative terms and he would see it as an imperative problem and would fail to see it as a functional one. It is not because he is stupid or he posess some other disabilities, it is just the way human mind works. It is like people saying "what is so good about language X, if you can do all in Y"? "Why one needs OOP languages, if you can do OOP in C?" The way we think about problems defines how we see problems, and what we see as a problems.
But let us try.
qsort [] = []
qsort (x:xs) = qsort [ y | y <- xs, y < x ] ++ [x] ++ qsort [ y | y <- xs, y > x ]
quicksort of empty sequence is an empty sequence. quicksort of sequence starting with x is a concatenation (operator ++) of three lists: quicksorted list of items from the rest of sequence (sequence without the first element which is designated as x) that are lesser then x, list of one element x, and quicksorted list of elements that are greater than x.
Of course, if you want quicksort to be sorting in place, you would need to think about small details like traversing two pointers, one from the front of the sequence, second from the back, swapping elements, and not forgetting about the choosen one... Yeah, reality is more complicated than that, sometimes you cannot get rid of complexity.
Functional compilers are constantly searching for optimizing techniques to get rid of all these small details, and in some ways they are succeeding. Though no one is good enough to generate machine code for sorting in place by compiling high level code above. But I tried to demonstrate the idea of abstraction of details and how it helps to understand code and to reason about it, and I believe the example is showing it.
As far as imperative vs functional goes: Remove the assignment operator from an imperative language and you will end up with functional language without bell and whistles (then you will have to make conditionals as expressions and instead of loops you will need to use recursion).
Yes, and no. For example B(A(x)), haskell can call A(x), get result, then call B passing result as argument. Or it can call B, passing closure as argument, and when it comes to a point, when calculation of B cannot be continued if we do not know value of A(x) only then A(x) would be calculated. In some sense A(x) was done before B -- before B was finished, but from other hand calculation of A(x) was started after starting calculation of B.
> My question was about "sequence of things to do", which is different concept than "imperative programming".
I'm not sure, that I can see a difference, but nevertheless, in example above there is not sequence of operations. There is almost declarative definition of a quicksorted list. There are multiple ways to linearize it into sequence of operations and even if there was single way I don't mind. It is the task of a compilator to make this linearization, not mine.
Sequential: you deal with one item at a time, you can deal with an infinite amount of data with a finite amount of memory. Cons: can't parralellize, early eval of things you don't need, you might need to go through the loop more than once.
Async/await is sequential where the operations are asynchronous (you don't move to next async operation until the previous async operation is done, given that the second async operation have dependency on the first operation's result).
See the out of the tar pit paper https://blog.acolyer.org/2015/03/20/out-of-the-tar-pit/
Quoted: > The problem with control is that very often we do not want to have to be concerned with this. Obviously — given that we want to construct a real system in which things will actually happen — at some point order is going to be relevant to someone, but there are significant risks in concerning ourselves with this issue unnecessarily.
a = 1;
b = 2;
If you model it sequentially, it takes a lot of work to make sure the right data is calculated in the right order. But you can also model it as a set of lazily evaluated streams, and that makes life a lot easier – because order of evaluation isn't part of the domain, it's essentially an implementation detail.
ETA: another way to think about it is that this lets the compiler manage evaluation order by default, while you're free to focus on other stuff (with the option to manage manually if you need to.) This is a similar type of benefit to garbage collection.
foo :: Int -> Int
foo a = let
z = a * c
b = 10
c = 20
in
b + c + z
(Not that I didn't like Prolog -- I did -- I just felt far from freed of mundane concerns of execution order.)
If the computation truly is one that is most practically described as a sequence of steps, that is easy to do. In fact, in some sense this is what the infamous "Monad" concept is all about.
Getting rid of order gets rid of the bugs. Like how restricting types with type checking gets rid of all type errors.