2009/3/19 Jens Blanck <jens.blanck@gmail.com>

Hi,

I found myself writing the following

leastFixedPoint :: (Eq a) => (a -> a) -> a -> a
leastFixedPoint f x = fst . head . dropWhile (uncurry (/=)) $ zip l (tail l)
where l = iterate f x

and was a bit surprised that I couldn't get any matches on hoogle for the type above. The closest one is fix :: (a -> a) -> a but that sort of assumes that we're starting the fixed point search from the bottom element (undefined).

Anyway, is there a nicer way of doing the above?

Well, it's probably not what you're looking for, but to remain true to the domain-theoretical roots of "fix", the "least fixed point above" can be implemented as:

fixAbove f x = fix f `lub` x

Where lub is from the "lub" package on Hackage. This function has the proof obligation that there is in fact any least fixed point above x (otherwise results are non-deterministic).

It still needs to be proven that fixAbove always returns a fixed point (given the precondition). I can kinda see how it would, but I can't be sure that it does.

Luke