* small * useful * demonstrate Haskell's power * preferably something that might be a bit tricky in another language
Something I like: A finite (binary) relation
data Rel q = Rel { elems :: [(q,q)] }
We do not export constructors, hence
rel xs = Rel { elems = xs }
Now, the function mirror
mirror r = rel [ (p,q) | (q,p) <- elems r ]
is an involution, that is mirror . mirror == id. Okay, how to exploit that? Nothing easier than that in Haskell: Just make mirror a field of Rel
data Rel q = Rel { elems :: [(q,q)], mirror :: Rel q }
and change the construction function to
rel xs = r where r = Rel { elems = xs , mirror = let m = rel [ (p,q) | (q,p) <- elems r ] in m { mirror = r } }
Note that the signatures of mirror and rel are the same as before. Try this in your favorite language! Regards, -- -- Mirko Rahn -- Tel +49-721 608 7504 -- --- http://liinwww.ira.uka.de/~rahn/ ---