hyper-abstracted R contest

[gustavolacerda]

(originally posted December 02, 2009, 21:44)

## `*` is the hyper of `+`, `^` is the hyper of `*`
> hyper <- function(fn) function(a,b) Reduce(fn, rep(a,b))

> compose <- function(fn1,fn2) function(x) fn1(fn2(x))

> hyperoperation <- function(n) Reduce(compose,listRep(hyper,n))(`+`)

('rep(obj,n)' and 'listRep(obj,n)' just return a list containing

Comments

[wjl]

woohoo, functional programming! except *real* FPLs actually support recursion :P

P.S. that essay is great!

[gustavolacerda]

yes it is. As of last week, he's my hero. Check out his other writings: http://www.scottaaronson.com/writings/

Have you seen the Gödel CAPTCHA: http://www.scottaaronson.com/writings/captcha.html

[gustavolacerda]

R supports recursion:

> fact <- function(n) ifelse(n==1,1,n*fact(n-1))
> fact(7)
[1] 5040

I honestly don't know why it breaks down here.

[wjl]

my off-the-cuff guess was that it has a far-too-conservative recursion depth limit to cut off "infinite looping". my tongue-in-cheek comment about supporting recursion is just to say that in a functional programming language, such deep recursion is *expected* :) it's really funny to me how some language designers have such a limited idea of how deep recursion can be and still be useful.

[gustavolacerda]

um, I think I need to use:

hyper <- function(fn) function(a,b) Reduce(fn, rep(a,b), right=TRUE)

foldr, not foldl.

[wjl]

i don't see why it shouldn't work with either -- i just tried it in SML and both work fine

[wjl]

or anyway, neither loops infinitely.. i think hyper is indeed incorrect if it's not a fold right

[gustavolacerda]

yeah, that's what I was saying.