Looks like a good overview of Clojure and functional programming. Anyone have a review?
How many ways can a reasonable programmer write the factorial function imperatively (without using the closed form formula or any dynamic programming). A maximum of two. A for loop or use recursion.
But just look at how many ways you could write factorial in a functional programming language. http://www.willamette.edu/~fruehr/haskell/evolution.html
It is truly unfortunate when your ability to program functionally is directly proportional to how much of the standard library you have memorised. This makes functional programming much harder to learn.
edit: I don't really care if you downvote. I come here discuss programming.
This page is a terrible example. Most of these are not not what a "reasonable programmer" would do.
An unreasonable programmer would be able to screw up on any paradigm. You'd probably have even more ways to screw up like this with an OO language, creating classes for recursive functions, trampolines, a pattern matching class, implement an language interpreter inside your factorial implementation, etc.
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.
I didn't mean to use to imply any of those methods were bad. I have revised my post so people can't miss the point.
That is
> It is unfortunate when your ability to program functionally is directly proportional to how much of the standard library you have memorised. This makes functional programming much harder to learn.
Now, addressing your concerns.
> This page is a terrible example. Most of these are not not what a "reasonable programmer" would do.
All of the examples except for few particularly egregious ones seems reasonable to me.
For example
-- one, need n+k patterns but so what
fac 0 = 1
fac (n+1) = (n+1) * fac n
-- two
fac 0 = 1
fac n = n * fac (n-1)
-- three
fac n = foldl (*) 1 [1..n]
-- four
facs = scanl (*) 1 [1..]
fac n = facs !! n
-- five
fac = foldr (*) 1 . enumFromTo 1
-- six
fac n = product [1..n]
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.
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.
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)))
(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
What would actually be foldl is this:
(define (foldl fn accum lst)
(if (null? lst)
accum
(foldl (fn accum (car lst)) (cdr lst))
)
)
(foldl * 1 '(1 2 3))
(foldl * 1 '(2 3))
(foldl * 2 '(3))
(foldl * 6 '())
6
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))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.
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...
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:
Where as in an imperative language often learning the syntax is enough to get the ball rolling.
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.
The number of ways you can write something is a horrible metric to evaluate languages on. Any sufficiently clever programmer can come up with a number of bad solutions. The useful imperative techniques are more obvious to you because you have more experience with that framework. Experienced functional programmers would just as quickly narrow their list of useful solutions.
In order to be productive in a functional style, you don't need to know much of the language's standard library. You simply write small functions that can be applied in a number of areas. You'll probably end up re-inventing the wheel though, as most functional languages come with most of the essential functional constructs included in the standard library. If anything, functional programming is more beginner friendly, because you don't end up dealing with mutable state and you can easily work on the level of abstraction that you're most comfortable with (you're just composing ever more advanced functions from simpler ones).
having said that, in my experience (perhaps i am just dumb, or old) fp takes a while to get used to. i first looked at haskell some 16 years ago (i can still remember reading the intro while staying in a b+b in edinburgh), before using sml and ocaml, but the first time it really felt natural to me was with clojure this year. i don't think that's much to do with clojure - it just took multiple attempts before things really stuck. perhaps the biggest help was python's slow drift (despite gvr) towards fp idioms.