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import Data.Semigroup

pattern ArgMin :: a -> b -> ArgMin a b
pattern ArgMin a b = Min (Arg a b)

pattern ArgMax :: a -> b -> ArgMax a b
pattern ArgMax a b = Max (Arg a b)

Or even record pattern synonyms, à la this

pattern ArgMin :: a -> b -> ArgMin a b
pattern ArgMin {minArg, minValue} = Min (Arg minArg minValue)

pattern ArgMax :: a -> b -> ArgMax a b
pattern ArgMax {maxArg, maxValue} = Max (Arg maxArg maxValue)

and we can define

import Data.Semigroup.Foldable

argmin :: Ord k => Foldable1 f => (a -> k) -> (f a -> a)
argmin f = minValue . foldMap1 (\a -> ArgMin (f a) a)

argmax :: Ord k => Foldable1 f => (a -> k) -> (f a -> a)
argmax f = maxValue . foldMap1 (\a -> ArgMax (f a) a)