Re: [Haskell-cafe] Fixed points

FWIW, what you have written is equivalent to equivalenceClosure = fix (const (reflexivity . symmetry . transitivity)) and because the fixed point of `const a` is `a`, equivalenceClosure = reflexivity . symmetry . transitivity which obviously only performs a single pass on its input On Fri, Jun 10, 2011 at 12:10:16PM -0700, Alexander Solla wrote:

On Fri, Jun 10, 2011 at 12:05 PM, Alexander Solla wrote:

...

On Thu, Jun 9, 2011 at 6:04 PM, Felipe Almeida Lessa < felipe.lessa@gmail.com> wrote:

...

Something like this?

equivalenceClosure = fix $ \f e -> let e' = reflexivity . symmetry . transitivity $ e in if e' == e then e else f e'

Cheers,

-- Felipe.

I managed something even "clearer". I still have very little intuition about what's going on, but I had an aha moment -- which I promptly forgot :0( -- and at least there's a mechanical translation from the iterate version to the fix one.

equivalenceClosure :: (Ord a) => Relation a -> Relation a equivalenceClosure = fix (\f -> reflexivity . symmetry . transitivity)

Cancel that, it's not passing my tests.

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