In Haskell, how can I use the built in sortBy function to sort a list of pairs(tuple)?

Question

I am a beginner in Haskell so please bear with me. (Just started learning yesterday!) How can I sort a list of tuples primarily by their first components (highest to smallest) and secondarily by their second components (smallest to highest)? A sample input/output would be:

[(1, "b"), (1, "a"), (2, "b"), (2, "a")] (input)

[(1, "a"), (2, "a"), (1, "b"), (2, "b")] (middle step)

[(2, "a"), (2, "b"), (1, "a"), (1, "b")] (output)

I tried using the following but it gave wrong output:

sortGT a b = GT  sortBy sortGT lst 

I am sure that I can do this by using sortBy only, but I can't figure it out myself. Any help would be highly appreciated!

Answer 1

You need to construct your function sortGT, so that it compares pairs the way you want it:

sortGT (a1, b1) (a2, b2)   | a1 < a2 = GT   | a1 > a2 = LT   | a1 == a2 = compare b1 b2 

Using this you get the following results (I used ghci):

*Main Data.List> sortBy sortGT [(1, "b"), (1, "a"), (2, "b"), (2, "a")] [(2,"a"),(2,"b"),(1,"a"),(1,"b")] 

Answer 2

May I suggest the following?

import Data.List (sortBy) import Data.Monoid (mconcat)  myPredicate (a1, a2) (b1, b2) = mconcat [compare b1 a1, compare a2 b2] 

You can then sort by writing sortBy myPredicate lst. The function mconcat simply scans through the list and obtains the first non-EQ occurence (or EQ if all elements are EQ and thus both pairs are considered equal).

On second thought, building the list isn't necessary.

import Data.List (sortBy) import Data.Monoid (mappend)  myPredicate (a1, a2) (b1, b2) = compare b1 a1 `mappend` compare a2 b2 

The definition of mappend for Ordering is essentially:

EQ `mappend` x = x x  `mappend` _ = x 

Which is exactly what we need.

Just for fun, generalizing gbacon's answer and making the use a little more flexible:

import Data.Ord import Data.List import Data.Monoid  ascending  = id descending = flip  sortPairs f x g y = f (comparing x) `mappend` g (comparing y)  mySort = sortBy (sortPairs descending fst ascending snd)