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This is a proposal to add Foldable1 (non-empty Foldable) to base

-- Data.Semigroup.Foldable
class Foldable f => Foldable1 f where
  fold1    :: Semigroup m => f m -> m
  foldMap1 :: Semigroup m => (a -> m) -> (f a -> m)

  -- Possible methods
  head1      :: f a -> a
  last1      :: f a -> a
  toNonEmpty :: f a -> NonEmpty a 

along with instances and function that are only valid for non-empty structures (details: semigroupoids issue #49, github)

import qualified Data.Semigroup as S

minimum1, maximum1 :: (Ord a, Foldable1 f) => f a -> a
minimum1 = S.getMin . foldMap1 S.Min
maximum1 = S.getMax . foldMap1 S.Max

head1, last1 :: Foldable1 f => f a -> a
head1 = S.getFirst . foldMap1 S.First
last1 = S.getLast  . foldMap1 S.Last

foldr1, foldl1 :: Foldable1 f => (a -> a -> a) -> (f a -> a)
foldr1 f = unimprove . foldMap1 (\a -> Diff (f a) a)
foldl1 f = unimprove . getDual . foldMap1 (\a -> Dual $ Diff (flip f a) a)

Adding foldM, foldM_, foldrM and foldlM for non-empty structures is also a possibility.

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Currently these are partial functions in Foldable. This proposal does not propose replacing partial Foldable functions.

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I wanted to test the waters before submitting it to the libraries mailing list. This may be controversial but it gives us a path to avoid partial functions in Foldable.