Semantics of signum

[Marcin 'Qrczak' Kowalczyk]

Sat, 10 Feb 2001 11:25:46 -0500, Dylan Thurston <dpt@math.harvard.edu> pisze:

> Can you elaborate?  What do you mean by signum for functions?
> The pointwise signum?

Yes.

> Then abs would be the pointwise abs as well, right?

Yes.

> That might work, but I'm nervous because I don't know the semantics
> for signum/abs in such generality.

For example signum x * abs x == x, where (==) is not Haskell's
equality but equivalence. Similarly to (x + y) + z == x + (y + z).

If (+) can be implicitly lifted to functions, then why not signum?

Note that I would lift neither signum nor (+). I don't feel the need.
It can't be uniformly applied to e.g. (<) whose result is Bool and
not some lifted Bool, so better be consistent and lift explicitly.

-- 
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