# Semantics of signum

**Marcin 'Qrczak' Kowalczyk
**
qrczak@knm.org.pl

*10 Feb 2001 17:55:32 GMT*

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.
--
__("< Marcin Kowalczyk * qrczak@knm.org.pl http://qrczak.ids.net.pl/
\__/
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QRCZAK