So, what's going on here? First you have the declaration of the function - in this case, you have a list of items of type A which can be compared to another one (Ord means "I can use <, <= and so on over this element"), and you'll return a list of type A.
Then you have the base case - if the list is empty, you'll return an empty list.
After that you have the case "item++[list of items]" (note that the second one can be an empty list), where you return [list of smaller items]++item++[list of larger items] (the two lists are defined under the "where" - filter removes elements from a list).
Note however that, instead of "(lesser) ++ item ++ (larger)" you have "(quicksort lesser) ++ item ++ (quicksort larger)" - this will call the algorithm recursively over smaller lists, but I bet you already knew that.
Both pieces of code do the same thing, but I think mine is what you'd expect from a typical piece of Haskell code - the one you have is closer to "see how small I can make this function".
Interesting question -- in Haskell that means something else (some would say "nothing"). The language is designed around making sure that you only specify the function that the code is supposed to accomplish, and all implementation decisions are left to the compiler -- just as it would be for the RHS of a statement like `x = 3 + 4*(5 + 1);` in C.
In this case, as in all others, the Haskell compiler would decide what is the optimal way to implement it, given whatever other constraints you've placed on the program.
You can add additional constraints that ensure the compiled code turns out to be in-place, at a cost of verbosity.
If there is an example where such an optimization has actually been implemented and correctly chosen, that is news to me.
I mean, to a very large extent, this is the reason why classical imperative languages are so easy to understand and reason about. The programmers directions are much more straight forwardly executed than in examples like these hypotheticals.
Oh, I just got to your last sentence. Basically, that this would be a lot more verbose if written in such a way that it would be in place. Which is kind of the point of this criticism. Isn't it?
Don't get me wrong, the power of Haskell is not really in question. Just that example.
Your criticisms are all from the perspective of "it keeps me from telling it how to implement the functionality", which is true, but not what Haskell's design (or pure FP language design in general) optimizes for.
Sometimes, you really do want to make commands to the bare metal regarding exactly how you want the program implemented. For general use, however, you don't: compilers are (at least these days) a lot better at finding optimizations than the typical user.
It comes down to abstraction levels: pick the one that matches the problem you're working on. The FP philosophy is "speaking about specific memory cells is way too low" in most cases, like telling it you want a sorted list.
In fact, it would probably be even better (from that selfsame philosophy) to define a sort in terms of the conditions the final list would meet (as opposed to nested, recursing conditions like in the example). Something like, "return a list where every element is <= the one after it, and where every element is also in the original list, as many times as it occurs there".
If you want to see the examples of quicksort in Haskell to enforce in-place and other requirements, see this discussion here, with links:
I understand what you are saying. I'm arguing that when quick sort was first contrived, the speed aspect that you can achieve with the in place variant was not just a lucky by product. It was the bloody point. To such an extent that if you are lucky enough -- which most of us are -- to be in a place where that is not a consideration, then sure, go for the higher level abstractions.
That said, it is highly telling that none of the actual implementations of quick sort in any of these languages are that succinct. To the point that it is still a truism to "use a library" for something such as sorting. Because that isn't easy. Do not be fooled by such a quaint example.
It's interesting to see is how very similar Haskel and C sources fundamentally become once they really solve the same problem and not the different ones.
The "direct compare" in Haskell isn't. The Ord constraint effectively passes a dictionary, and even if that were inlined in a particular case you could always apply a newtype for a different ordering.
I'd really like to learn, can you please explain where the Ord constraint is, and where the dictionary is passed in the link I've given (with the STUArray -- isn't that really an array in a C sense)? To give you an idea how little I know: I understand the basic ideas of Haskell (that is, what I as a C programmer who made some compilers understand as basic: the type inference and the illusion of the infinite memory by not doing things in place but lazily with the GC unless unsafe or when it is possible to optimize the laziness out) but I don't really know the language. Thanks in advance.
Ah, my bad, the STUArray example is specialized and probably does not pass an Ord around (though there's implicitly one present because of the less-then). Certainly, the function does not meaningfully allow the user to pick it.
Has anyone ever bothered to ask Tony Hoare what he thinks on this topic? I know SPJ and him both work for MS Research, maybe he can get on that and settle this for us.
I would be curious to know the answer. Though, I should have added in my original post that I am far from the originator of this view. I see a sibling post elaborated. I think the crux is simply that without the "in place" nature, it loses a lot of its speed advantage. Cache localities and such.
The list is the sorted list of lesser items, then the pivot, then the sorted list of greater items. But since the list of greater items is defined with ">=" rather than just ">", the list of greater items will also contain the pivot. That will put the pivot in the sorted list twice (for each recursive call).
Thanks for the insightful reply! I can understand most of the code but I still do not understand how should I know what "p" and "xs" is. Is it something you get when you declare the function as being "possible" to order (I believe that's what "Ord" means based on your explanation)?
One last thing I'll add to the other replies, the example shown is a bit unusual, like indexing a for loop with "q" instead of "i". The traditional pattern is this:
(x:xs)
And that reads "x and the rest of the x-es", that is, the "xs" is not "ex ess", but "plural x", whatever remainder remains of the list of "things" in that list. (p:xs) is a bit weird, but if I saw (p:ps) I'd understand.
Also, Haskellers often use "x" here because they write a lot of functions that operate on "anything"; for instance, in this case, you don't really know what you're sorting, so, call it x because what other name is any better? There's a set of about 10 of these conventional one-letter variable names. (A few more than conventional imperative languages, but not obscenely so; imperative has i, j, and k for iteration, a and b in sorting, sometimes f for function, and p for pointer.)
I assume here it's p for pivot, xs because the rest of the list is just items, not pivots (as ps would imply). I'm not sure I love the naming choice, but it has a logic to it.
Those are pattern matches [1]. In Haskell, you have a very powerful pattern matching system for describing and deconstructing function arguments. So quicksort here is defined as
quicksort [] = []
quicksort (p:xs) = ...
The first pattern, [], matches an empty list. The second pattern, (p:xs), matches a list of length 1 or greater, and binds the first element of the list to the variable p, and the rest of the list to the variable xs. In other words, p is the head, xs is the tail. Note that in the case of a 1-element list, the tail will be empty.
This is a valid pattern match because AFAIK the colon (:) is a type constructor in Haskell, and it's used to create lists. For instance, 1 : [] == [1], and 1 : 2 : [3, 4] = [1, 2, 3, 4].
Because (:) is a type constructor, and not an operator (unlike (+) for instance), you can use it in pattern matching expressions to deconstruct lists. This is quite useful for many things, as you might imagine.
No, it's pattern matching (it's a bit warty because that's the only case I can think of where the pattern matching part doesn't look like the way you build the data structure).
Normal pattern matching:
-- a Foo record, with a data constructor Foo and a single field
data Foo = Foo { bar :: String }
-- takes an instance of Foo, returns "prefix:" + the value of the bar field
prefixBarInFoo :: Foo -> String
-- Pattern matches on Foo, tells Haskell to bind 'valueOfBar' to the 'bar' field of the instance of Foo
prefixBarInFoo (Foo valueOfBar) = "prefix:" ++ valueOfBar
List pattern matching:
myList = [1,2,3,4,5]
addOne :: [Integer] -> [Integer]
addOne [] = []
-- when called with 'myList', binds x to 1 and xs to [2,3,4,5] (the rest of the list)
addOne (x:xs) = (x+1) : (addOne xs)
Then you have the base case - if the list is empty, you'll return an empty list.
After that you have the case "item++[list of items]" (note that the second one can be an empty list), where you return [list of smaller items]++item++[list of larger items] (the two lists are defined under the "where" - filter removes elements from a list).
Note however that, instead of "(lesser) ++ item ++ (larger)" you have "(quicksort lesser) ++ item ++ (quicksort larger)" - this will call the algorithm recursively over smaller lists, but I bet you already knew that.
Both pieces of code do the same thing, but I think mine is what you'd expect from a typical piece of Haskell code - the one you have is closer to "see how small I can make this function".