I have written several times before about using the Haskell programming language as a tool for exploring mathematics, but until now I had no good recommendation for people who were interested in learning it for that purpose (Real World Haskell is a great book if you are already a programmer and want to Get Things Done with Haskell, but not so great if you just want to have fun with it).

I am therefore happy to report that No Starch Press has just published Learn You a Haskell for Great Good! A Beginner’s Guide by Miran Lipovača. It’s a fantastic, fun, thorough introduction to Haskell, spiced up by Miran’s great sense of humor and zany illustrations. You can buy a paper copy or read it on the web for free!

Just for fun, in honor of the occasion:

> -- @powmod base exp m@ efficiently computes (base^exp (mod m)).
> powmod :: Integer -> Integer -> Integer -> Integer
> powmod _ 0 _      = 1
> powmod base exp m | even exp  = (x * x) `mod` m
>                   | otherwise = (x * x * base) `mod` m
>   where x = powmod base (exp `div` 2) m
>
> f n = powmod 2 n n
>
> -- http://oeis.org/A015910
> a015910 = map f [1..]
>
> -- http://oeis.org/A050259
> test = all (==3)
>        (map f [ 4700063497
>               , 3468371109448915
>               , 8365386194032363
>               , 10991007971508067
>               , 63130707451134435989380140059866138830623361447484274774099906755
>               ]
>        )

*Main> take 50 a015910 
[0,0,2,0,2,4,2,0,8,4,2,4,2,4,8,0,2,10,2,16,8,4,2,16,7,4,26,16,2,4,2,0,8,4,18,28,2,4,8,16,2,22,2,16,17,4,2,16,30,24]
*Main> :set +s
*Main> test
True
(0.01 secs, 1110184 bytes)