# Prefix negation

Brian Boutel brian@boutel.co.nz
Thu, 30 Aug 2001 20:21:02 +1200

```Marcin 'Qrczak' Kowalczyk wrote:
>
> Wed, 29 Aug 2001 16:34:52 +0200, Rijk-Jan van Haaften <rjchaaft@cs.uu.nl> pisze:
>
> > -3 ^ 2 = -9
> >
> > In most programming languages as well as in mathematics
> > it is quite unusual to have infix operators with a higher
> > priority than prefix operators.
>
> In mathematics the prefix negation is handled like in Haskell:
>
>       2
>     -3  = -9
>
> I agree that many languages got it wrong :-)

This is not a simple matter.

Mathematics (and some programming languages) also have postfix
operators. Suppose ! is defined as usual as postfix factorial, and * as
prefix square, then it is not obvious what the value of *5! should be.

Mathematics has some conventions about operator precedence and
associativity, but unfortunately not enough to serve as a model for
programming languages which allow the definition of new operators.

There seem to be two main classes of languages which allow prefix
operators. Languages like C have them all at higher precedence than any
infix operator, and right associative (in the sense that *\$x is *(\$x),
not (*\$)x). This makes good sense for languages with many prefix
operators. Suppose prefix * is bound to square, then *-5 is 25, and -*5
is -25. If instead you use the same precedence as the infix version of
the operator, *-5 is illegal, and -*5 is -25.

Haskell has only the one prefix operator. I remember there being a
discussion about its precedence, but not the reasons for the final
decision. If anyone remembers, it will be Joe Fasel. To my mind, it is
not a big deal. Neither solution is ideal, but neither is a bad as not
having unary -. Sure, that would simplify the syntax, but that is not
necessarily the goal.

--brian

```