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Monadic Endo #110

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Monadic Endo #110

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KEndo monoid
Jan 5, 2024
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Merge branch 'master' of github.com:ndmitchell/extra
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19 changes: 18 additions & 1 deletion src/Data/Monoid/Extra.hs
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Expand Up @@ -3,10 +3,14 @@
module Data.Monoid.Extra(
module Data.Monoid,
-- * Extra operations
mwhen
mwhen,

-- * Kleisli endomorphisms
KEndo(KEndo, appKEndo)
) where

import Data.Monoid
import Control.Monad

-- | Like 'Control.Monad.when', but operating on a 'Monoid'. If the first argument
-- is 'True' returns the second, otherwise returns 'mempty'.
Expand All @@ -15,3 +19,16 @@ import Data.Monoid
-- > mwhen False "test" == ""
mwhen :: Monoid a => Bool -> a -> a
mwhen b x = if b then x else mempty

-- | The intersection of 'Data.Monoid.Endo' and 'Control.Arrow.Kleisli'. This
-- type provides a 'Monoid' instance for composition of monadic actions
-- @a -> m a@.
newtype KEndo m a = KEndo { appKEndo :: a -> m a }
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@Bodigrim Bodigrim Jul 5, 2024 •
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This can be generalized to

newtype Endomorphism k a = Endomorphism (k a a)

instance Category k => Semigroup (Endomorphism k a) where 
  (<>) = coerce (Control.Category..)

instance Category k => Monoid (Endomorphism k a) where 
  mempty = coerce Control.Category.id

Then Endomorphism k a would cover both usual Endo (when k ~ (->)) and monadic endo (when k ~ Kleisli).

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@ndmitchell ndmitchell Jul 28, 2024

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This seems like a great idea. That said, once we have gone this far, I wonder if extra is the right place for it? It seems to be more categorical and less compose a few obvious things?

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@Taneb Taneb Feb 5, 2026

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This exists in monoid-extras: https://hackage-content.haskell.org/package/monoid-extras-0.7.0.1/docs/Data-Monoid-Endomorphism.html


instance (Monad m) => Semigroup (KEndo m a) where
-- | Right-to-left composition
KEndo f <> KEndo g = KEndo (f <=< g)

instance (Monad m) => Monoid (KEndo m a) where
mempty = KEndo pure