List functions - "Under" operations

[Ross Paterson]

On Fri, Jan 16, 2004 at 11:03:21AM +0100, Tomasz Zielonka wrote:
> On Fri, Jan 16, 2004 at 01:43:40AM -0800, Brandon Michael Moore wrote:
> > I think it would often be useful if the list functions with class
> > constraints had versions paramaterized on a function mapping your element
> > type into an instance of the classes, in addition to the "By" forms that
> > take an implementation for the required class method.
> > 
> > Almost all of the times I use the "By" functions follow that pattern:
> > e.g.
> > sortFoos :: [Foo] -> [Foo]
> > sortFoos = sortBy (\x y -> compare (f x) (f y))
> 
> No need for so many new functions. Just write a function:
> 
>   composeFGxGy :: (b -> b -> c) -> (a -> b) -> a -> a -> c
>   composeFGxGy f g x y = f (g x) (g y)
> 
> Then you can:
> 
>   sortFoos = sortBy (composeFGxGy compare f)

The special case may be useful if f is expensive:

  -- sortImage f = sortBy (\x y -> compare (f x) (f y))
  sortImage :: Ord b => (a -> b) -> [a] -> [a]
  sortImage f xs = map snd (sortBy cmp_fst [(f x, x) | x <- xs])
   where cmp_fst (x,_) (y,_) = compare x y