Haskell: Find the minimum in custom data type

Question

So I have a custom data type, let's call it Struct , defined like this:

data Struct = Struct  [SubStruct] deriving (Read, Show)
data SubStruct = SubStruct (Int, Int) deriving (Read, Show)

What I need to do is to go through all the elements in Struct and find the minimum based on fst and then based on the snd . How do I do that? More specifically, I want to get another SubStruct such as:

SubStruct (-2,-5) , based on the example in the code.

Currently, i started by doing this:

import Data.List
import Data.Function (on)
import Data.List (sortBy)

data Struct = Struct  [SubStruct] deriving (Read, Show)
data SubStruct = SubStruct (Int, Int) deriving (Read, Show  )

struct s sx = Struct(s:sx)

subStruct :: (Int, Int) -> SubStruct
subStruct (x, y) = SubStruct (x, y)

substructs = Struct $ [subStruct (0,1), subStruct (-2, 3), subStruct (4,-5)]

results xs = sortBy (compare `on` fst) (substructs xs)

But I get this error:

Couldn't match expected type `t -> [(a, b)]'
            with actual type `Struct'
Relevant bindings include
  xs :: t (bound at bbox.hs:15:9)
  results :: t -> [(a, b)] (bound at file.hs:15:1)
The function `substructs' is applied to one argument,
but its type `Struct' has none
In the second argument of `sortBy', namely `(substructs xs)'
In the expression: sortBy (compare `on` fst) (substructs xs)

Answer 1

Why not use the unzip function. If we define an auxiliary function:

unSubStruct :: SubStruct -> (Int, Int)
unSubStruct (SubStruct p) = p

Then the function that returns the element that you want can be written as:

getMin :: Struct -> SubStruct
getMin (Struct l) = SubStruct (minimum xs, minimum ys)
  where
    (xs, ys) = unzip $ map unSubStruct l

Note that this will traverse the list twice. You can avoid that if you define your own version minimum that works on pairs:

getMin :: Struct -> SubStruct
getMin (Struct l) =
    SubStruct $ foldr1 minPair $ map unSubStruct l
  where
    minPair (x0, y0) (x, y) = (min x0 x, min y0 y)

Answer 2

You have a list of SubStruct , which is basically the same as a list of tuples.

So, one solution using only common functions would be:

result = SubStruct (min1, min2) where
    min1 = minimum (map fst . list)
    min2 = minimum (map snd . list)
    list = case substructs of
         Struct this -> map (\(SubStruct t) -> t) this