[Haskell-cafe] constant functions

[Brandon S. Allbery KF8NH]

On Dec 27, 2006, at 22:55 , michael rice wrote:

> By similar reasoning the always function would seem to
> have a signature
>
> a -> (b -> a)
>
> where the first argument is just a value and the
> return value is a function that when given a possibly
> different value just returns the value originally
> given to always?
>
> Is that reasoning OK? Are
>
> a -> (b -> a) and a -> b -> a the same signature?

This is a point that has been glossed over a bit:  Haskell has the  
notion of partial application.  If you want to start with a function  
that takes two values, and return a function that takes one value and  
uses the one previously passed in, you just invoke the function with  
one parameter; Haskell will produce a function which takes a single  
argument to complete the expression.  Using (*) (prefix version of  
multiplication) as an example:

     Prelude> :t ((*) 2)
     ((*) 2) :: (Num t) => t -> t
     Prelude> let x2 = ((*) 2) in x2 5
     10

This shows the equivalence of the type signatures (a -> a -> a) and  
(a -> (a -> a)), and is one of the strengths of Haskell:  you can  
pass a section (a "partially expanded" function") wherever a function  
is expected.

     Prelude> map ((*) 2) [1..5]
     [2,4,6,8,10]

This doesn't only work for prefix functions, by the way; the above  
example is more naturally written as (2*):

     Prelude> :t (2*)
     (2*) :: (Num t) => t -> t
     Prelude> map (2*) [1..5]
     [2,4,6,8,10]

You can also say (*2), which provides the right-hand argument; this  
is useful for non-commutative functions like (/).  But don't try it  
with (-), because you'll trip over an unfortunate parsing hack for  
negative numbers:

     Prelude> :t (-2) -- whoops, it's a number, not a function!
     (-2) :: (Num a) => a

The Prelude provides a workaround for this, though:

     Prelude> :t (subtract 2)
     (subtract 2) :: (Num t) => t -> t

-- 
brandon s. allbery    [linux,solaris,freebsd,perl]     allbery at kf8nh.com
system administrator [openafs,heimdal,too many hats] allbery at ece.cmu.edu
electrical and computer engineering, carnegie mellon university    KF8NH