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After the first 2, the rest are based on common and very useful abstractions. You could translate those to an OO language quite easily too, though with a lot more code.

For example, what foldl does, from my understanding, is to recursively apply a function to both a starting value and the first element of a list, and then the same thing again, where the result from the last call becomes the starting value and the rest of the list becomes the list we're working on, up until the list is empty. Not sure if I've explained this well but I've not been into this long.

If you see the second function, that's what it's doing, except it's working just with numbers and not a list. Since foldl works on lists, you need an enumerator, which in this case is just 1 through to n.

The sixth example is great here. Product could easily be an abstraction on something quite similar to three, which itself could very well be an abstraction quite similar to two (using lists, functions to deal with lists and a given function).

Please correct me if I'm wrong at any point here. I'm looking to improve these skills quite a lot so it'd be very, very welcome.

You got the core, I will correct your edges.

The [1..3] is just sugar for 1:2:3:[]

Product is not actually an abstraction as it's restricted to work on number types.

And no foldl is not an abstraction of (2) because foldl is tail recursive while (2) is not. foldr is not tail recursive however and combined with haskell's laziness can make short work of infinite lists. But you are right in that any tail recursive function on a list can be rewritten using foldl. What is particular to haskell vs a strict language like say F# is that foldl can still pop a stack due to haskell's laziness. You want foldl' as it will force the initial argument. Fold is also a fundamental operation on any algebraic data structure such as trees , lists, and natural numbers. You can write filter, map, filtermap etc in terms of it for example. There is so much to say about fold - they are like the cupboard which leads to narnia.. but I will stop now so as not to turn this into an infodump.

Oh wow, thanks! I should have also noted I have no experience with the language in the examples so please ignore any ignorance there (probably should have read up on it).

Interesting! All well noted and I'll look into this more.

I'm vaguely aware of fold's power and can definitely see how filter, map and the likes would be implemented in terms of it but I would be really interested in the infodump!

I'm just wondering, ignoring laziness and typing (or any language-specifics), if foldl could be written similar to (2)? Obviously it wouldn't be very good. I've written an example in Racket of what I have in mind:

  (define (foldl fn initial lst)
    (if (null? lst) 
        initial
        (fn (car lst) (foldl fn initial (cdr lst)))))

  (define (fac n)
    (if (= n 0)
        1
        (* n (fac (- n 1)))))

  (= (fac 3)
     (foldl * 1 '(1 2 3)))

Thanks again for the info, really appreciated. :)

Also ignoring tail recursion for the purpose of the above piece of code, haha.

Actually, what you have written is not foldl, it's foldr. Why is it going right to left? Let's expand your example:

    (foldl * 1 '(1 2 3))
    (* 1 (foldl * 1 '(2 3))
    (* 1 (* 2 (foldl * 1 '(3))))
    (* 1 (* 2 (* 3 (foldl 1 '()))))
    (* 1 (* 2 (* 3 1)))
    ...
    6

Basically, the calls to * start nesting into each other, so the one that actually gets evaluated first is the rightmost one.

What would actually be foldl is this:

    (define (foldl fn accum lst)
       (if (null? lst)
            accum
            (foldl (fn accum (car lst)) (cdr lst))
       )
    )

Now if you expand this (dropping the tail recursion):

    (foldl * 1 '(1 2 3))
    (foldl * 1 '(2 3))
    (foldl * 2 '(3))
    (foldl * 6 '())
    6

And even though you think that such a tiny thing can't be a good implementations, it actually is super efficient. The tail recursion is automatically optimized for you (and you can assume that for any functional language - it's a very crucial optimization for this style of code, after all). That's what the core of it will be in an actual implementation, though with added error handling, type checking and so on.

P.S. unlike haskell, in Racket you don't really need to fold the basic operators, they take variable arguments, so you can just:

    (apply * (list 1 2 3))

in order to get it to run on a list.

Ivo's answered so I'll just say the main trick to turning a function tail recursive is to have the function lug its state around. So always look to see if you can rewrite your function so it passes the current value explicitly to the next iteration. Non tail recursion is like winding a spring and then having it unwind, a jack in a box. Tail recursion is like a snowball rolling down a hill. You should always try to make a recursive function tail recursive if you can.

As for fold it's a bit involved and has a lot of scary sounding jargon on the way to understanding it. You can write a fold for a tree and then code depth first search in a couple lines. Folds follow some basic properties that allow for program derivation. I rarely use those but it does inform my programming. It's kind of like how knowing Lisp informs your python. There is also an opposite or dual to fold called unfold. You can write many algorithms efficiently just using fold and unfold and a couple techniques to prune inefficiencies. Fold is the same kind of object to your initial tree as say a matrix is to a vector, or a derivative is to a polynomial.

Yes, functional programming does give you more options, and that's the point. Each style of programming -- functional, object-oriented, relational, imperative, etc. -- has its strengths and weaknesses. It's up to the programmer to choose which one best fits the problem at hand.

In some languages, like Java, you're stuck in the OO style of programming because its syntax and features make anything else too cumbersome. Clojure actually works the other way around: though the most common style is functional, it's easy to work in terms of objects. It might not look the same as Java OO, but that's for the better.

Here's a good book about switching between programming styles within a single program: http://www.amazon.com/Concepts-Techniques-Models-Computer-Pr...

Well, to nitpick, the first, fourth and fifth example are just variations of the other ones, and they're (ab)using Haskell features - respectively n+k patterns, laziness and point-free programming.

Those features aren't available on every functional language, and they're not really used indiscriminately as shown here on most Haskell code bases, so yeah, I maintain that this page is a terrible example (albeit a very educational and fun one).

Here's a Python version, showing that even on an imperative language there's a lot of ways of doing the same things:

https://gist.github.com/289467

One would still need to know the majority of the functions in Prelude write a useful program, and even more to write an elegant program, since they are abstracted as concepts.

Where as in an imperative language often learning the syntax is enough to get the ball rolling.

> My example was about imperative languages. You assertion on how many ways one could screw up on OO is irrelevant and besides, you'd really need a good understanding of OO to even try implementing those.

Isn't OOP languages also imperative, at least most of those languages (java, C++, .Net, etc)?

I thought that OO was mostly an "structural" paradigm, where you organize your code as objects and methods that apply to those data structures, and you got inheritance and stuff like that.

Imperative programming on the other hand is about programming with statements, no matter if you are using gotos, routines, objects, etc. You just instruct the computer how to change from state to state.

I'm not qualified to judge the merits of the language, but as a manager I'd want something where the idioms are commonly understood. Writing new code is easy in almost any language. The real test is whether new hire can re-write it 12-18 months later when a bug or new requirement emerges.