[Haskell-cafe] Re: what are the points in pointsfree?

Steve Downey sdowney at gmail.com
Thu Dec 14 20:20:17 EST 2006

the wiki wasn't half as clear. other tham covering the first half,
that it doesn't mean the '.' function.

so pointsfree is a step beyond leaving the domain unspecified.

my reading knowledge of haskell at this point far exceeds my ability
to write haskell. but so far, it has seemed to me that functions
written in the pf style are the most reuseable.

from what you just told me, it's not an artifact of the pf style, but
that maximally reusable functions will be expressible in a pointsfree
style. that those functions embody a pattern of computation, without
concern for the details.

On 12/14/06, Donald Bruce Stewart <dons at cse.unsw.edu.au> wrote:
> sdowney:
> > i'm not naive enough to think they are the composition function, and
> > i've gathered it has something to do with free terms, but beyond that
> > i'm not sure. unless it also has something to do with fix points?
> The wiki knows all! :)
>     http://haskell.org/haskellwiki/Pointfree
>     1 But pointfree has more points!
>     A common misconception is that the 'points' of pointfree style are the
> (.)
>     operator (function composition, as an ASCII symbol), which uses the same
>     identifier as the decimal point. This is wrong. The term originated in
>     topology, a branch of mathematics which works with spaces composed of
> points,
>     and functions between those spaces. So a 'points-free' definition of a
> function
>     is one which does not explicitly mention the points (values) of the
> space on
>     which the function acts. In Haskell, our 'space' is some type, and
> 'points' are
>     values.
> -- Don

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