[Haskell-cafe] The maximum/minimum asymmetry

[Daniel Fischer]

On Monday 05 September 2011, 08:35:30, Alexander Dunlap wrote:
> On 4 September 2011 21:44, Mario Blažević <blamario at acanac.net> wrote:
> >    I was recently surprised to discover that the maximum and maximumBy
> > functions always return the *last* maximum, while minimum and
> > minimumBy return the *first* minimum in the list. The following GHCi
> > session demonstrates this:
> > 
> > $ ghci
> > GHCi, version 7.2.1: http://www.haskell.org/ghc/  :? for help
> > Loading package ghc-prim ... linking ... done.
> > Loading package integer-gmp ... linking ... done.
> > Loading package base ... linking ... done.
> > Loading package ffi-1.0 ... linking ... done.
> > Prelude> :module +Data.List Data.Ord
> > Prelude Data.List Data.Ord> let list = [(1, 'B'), (1, 'A')]
> > Prelude Data.List Data.Ord> maximumBy (comparing fst) list
> > (1,'A')
> > Prelude Data.List Data.Ord> minimumBy (comparing fst) list
> > (1,'B')
> > 
> >    I would normally consider this kind of gratuitous asymmetry a bug,
> > but seeing that these functions' implementations have been specified
> > in the Haskell 98 Library Report, I guess they are now a permanent
> > feature of the language. Can anybody explain the reason for this
> > behaviour?

> 
> The asymmetry is a result of EQ and LT being treated as equivalent in
> both the minBy and maxBy helper functions in the report's definition
> of the two functions, which has opposite effects for minimumBy and
> maximumBy. Since the documentation doesn't specify a behavior for
> equal values, I could guess that it was just an oversight or that it
> was considered unimportant. But maybe someone more knowledgeable will
> correct me.
> 
> Alexander Dunlap

The default methods for min and max already have this:

    max x y = if x <= y then y else x
    min x y = if x <= y then x else y

I think the reason for this is that if you have

(a, b) = (min x y, max x y),

you'll get both values even if they compare equal (and not everybody thinks 
that if two values compare equal, they shouldn't be distinguishable by any 
other means, so it might matter).

Probably, the behaviour of minimum[By] and maximum[By] is intentional as an 
extension of this.