Data.Fold.M

Unlike L and R this Comonad is based on a (->) r Comonad for a Monoid r rather than than on the Store r Comonad.

Documentation

data M a b

A foldMap caught in amber. a.k.a. a monoidal reducer

Constructors

M (m -> b) (a -> m) (m -> m -> m) m

Instances

Corepresentable M

Associated Types

type Corep (M :: * -> * -> *) :: * -> *

Methods

cotabulate :: (Corep M d -> c) -> M d c

Profunctor M

Methods

dimap :: (a -> b) -> (c -> d) -> M b c -> M a d

lmap :: (a -> b) -> M b c -> M a c

rmap :: (b -> c) -> M a b -> M a c

(#.) :: Coercible * c b => (b -> c) -> M a b -> M a c

(.#) :: Coercible * b a => M b c -> (a -> b) -> M a c

Choice M

Methods

left' :: M a b -> M (Either a c) (Either b c)

right' :: M a b -> M (Either c a) (Either c b)

Closed M

Methods

closed :: M a b -> M (x -> a) (x -> b)

Costrong M

Methods

unfirst :: M (a, d) (b, d) -> M a b

unsecond :: M (d, a) (d, b) -> M a b

Folding M

efficient prefix, efficient postfix

Methods

prefix :: Foldable t => t a -> M a b -> M a b

prefixOf :: Fold s a -> s -> M a b -> M a b

postfix :: Foldable t => M a b -> t a -> M a b

postfixOf :: Fold s a -> M a b -> s -> M a b

run :: Foldable t => t a -> M a b -> b

runOf :: Fold s a -> s -> M a b -> b

filtering :: (a -> Bool) -> M a b -> M a b

Scan M

Methods

prefix1 :: a -> M a b -> M a b

postfix1 :: M a b -> a -> M a b

run1 :: a -> M a b -> b

interspersing :: a -> M a b -> M a b

AsRM M

We can convert from a monoidal fold to a lazy right fold

Methods

asM :: M a b -> M a b

asR :: M a b -> R a b

AsRM1 M

Methods

asM1 :: M a b -> M1 a b

asR1 :: M a b -> R1 a b

Cosieve M FreeMonoid

Methods

cosieve :: M a b -> FreeMonoid a -> b

Monad (M a)

Methods

(>>=) :: M a a -> (a -> M a b) -> M a b

(>>) :: M a a -> M a b -> M a b

return :: a -> M a a

fail :: String -> M a a

Functor (M a)

Methods

fmap :: (a -> b) -> M a a -> M a b

(<$) :: a -> M a b -> M a a

MonadFix (M a)

Methods

mfix :: (a -> M a a) -> M a a

Applicative (M a)

Methods

pure :: a -> M a a

(<*>) :: M a (a -> b) -> M a a -> M a b

(*>) :: M a a -> M a b -> M a b

(<*) :: M a a -> M a b -> M a a

Distributive (M a)

Methods

distribute :: Functor f => f (M a a) -> M a (f a)

collect :: Functor f => (a -> M a b) -> f a -> M a (f b)

distributeM :: Monad m => m (M a a) -> M a (m a)

collectM :: Monad m => (a -> M a b) -> m a -> M a (m b)

Representable (M a)

Associated Types

type Rep (M a :: * -> *) :: *

Methods

tabulate :: (Rep (M a) -> a) -> M a a

index :: M a a -> Rep (M a) -> a

MonadZip (M a)

Methods

mzip :: M a a -> M a b -> M a (a, b)

mzipWith :: (a -> b -> c) -> M a a -> M a b -> M a c

munzip :: M a (a, b) -> (M a a, M a b)

Comonad (M a)

Methods

extract :: M a a -> a

duplicate :: M a a -> M a (M a a)

extend :: (M a a -> b) -> M a a -> M a b

ComonadApply (M a)

Methods

(<@>) :: M a (a -> b) -> M a a -> M a b

(@>) :: M a a -> M a b -> M a b

(<@) :: M a a -> M a b -> M a a

Apply (M a)

Methods

(<.>) :: M a (a -> b) -> M a a -> M a b

(.>) :: M a a -> M a b -> M a b

(<.) :: M a a -> M a b -> M a a

Bind (M a)

Methods

(>>-) :: M a a -> (a -> M a b) -> M a b

join :: M a (M a a) -> M a a

Extend (M a)

Methods

duplicated :: M a a -> M a (M a a)

extended :: (M a a -> b) -> M a a -> M a b

MonadReader (FreeMonoid a) (M a)

Methods

ask :: M a (FreeMonoid a)

local :: (FreeMonoid a -> FreeMonoid a) -> M a a -> M a a

reader :: (FreeMonoid a -> a) -> M a a

type Corep M

type Corep M = FreeMonoid

type Rep (M a)

type Rep (M a) = FreeMonoid a