Safe Haskell	None
Language	Haskell98

Control.Scanl

Contents

Scan Types
Scanning
Utilities

Description

This module provides efficient and streaming left map-with-accumulator that you can combine using Applicative style.

Import this module qualified to avoid clashing with the Prelude:

>>> import qualified Control.Scanl as SL

Use scan to apply a Fold to a list (or other Traversable structures) from left to right, and scanr to do so from right to left.

Synopsis

data Scan a b = Scan (a -> State x b) x
data ScanM m a b = ScanM (a -> StateT x m b) (m x)
scan :: Traversable t => Scan a b -> t a -> t b
scanM :: (Traversable t, Monad m) => ScanM m a b -> t a -> m (t b)
scanr :: Traversable t => Scan a b -> t a -> t b
prescan :: Fold a b -> Scan a b
postscan :: Fold a b -> Scan a b
purely :: (forall x. (a -> State x b) -> x -> r) -> Scan a b -> r
purely_ :: (forall x. (x -> a -> (x, b)) -> x -> r) -> Scan a b -> r
impurely :: (forall x. (a -> StateT x m b) -> m x -> r) -> ScanM m a b -> r
impurely_ :: Monad m => (forall x. (x -> a -> m (x, b)) -> m x -> r) -> ScanM m a b -> r
generalize :: Monad m => Scan a b -> ScanM m a b
simplify :: ScanM Identity a b -> Scan a b
hoists :: (forall x. m x -> n x) -> ScanM m a b -> ScanM n a b
arrM :: Monad m => (b -> m c) -> ScanM m b c
premap :: (a -> b) -> Scan b r -> Scan a r
premapM :: Monad m => (a -> m b) -> ScanM m b r -> ScanM m a r

Scan Types

data Scan a b Source #

Efficient representation of a left map-with-accumulator that preserves the scan's step function and initial accumulator.

This allows the Applicative instance to assemble derived scans that traverse the container only once

A 'Scan a b' processes elements of type a replacing each with a value of type b.

Constructors

Scan (a -> State x b) x

Scan step initial

Instances

Arrow Scan Source #
Instance details Defined in Control.Scanl Methods arr :: (b -> c) -> Scan b c # first :: Scan b c -> Scan (b, d) (c, d) # second :: Scan b c -> Scan (d, b) (d, c) # (***) :: Scan b c -> Scan b' c' -> Scan (b, b') (c, c') # (&&&) :: Scan b c -> Scan b c' -> Scan b (c, c') #
Profunctor Scan Source #
Instance details Defined in Control.Scanl Methods dimap :: (a -> b) -> (c -> d) -> Scan b c -> Scan a d # lmap :: (a -> b) -> Scan b c -> Scan a c # rmap :: (b -> c) -> Scan a b -> Scan a c # (#.) :: Coercible c b => q b c -> Scan a b -> Scan a c # (.#) :: Coercible b a => Scan b c -> q a b -> Scan a c #
Functor (Scan a) Source #
Instance details Defined in Control.Scanl Methods fmap :: (a0 -> b) -> Scan a a0 -> Scan a b # (<$) :: a0 -> Scan a b -> Scan a a0 #
Applicative (Scan a) Source #
Instance details Defined in Control.Scanl Methods pure :: a0 -> Scan a a0 # (<>) :: Scan a (a0 -> b) -> Scan a a0 -> Scan a b # liftA2 :: (a0 -> b -> c) -> Scan a a0 -> Scan a b -> Scan a c # (>) :: Scan a a0 -> Scan a b -> Scan a b # (<*) :: Scan a a0 -> Scan a b -> Scan a a0 #
Category Scan Source #
Instance details Defined in Control.Scanl Methods id :: Scan a a # (.) :: Scan b c -> Scan a b -> Scan a c #
Floating b => Floating (Scan a b) Source #
Instance details Defined in Control.Scanl Methods pi :: Scan a b # exp :: Scan a b -> Scan a b # log :: Scan a b -> Scan a b # sqrt :: Scan a b -> Scan a b # (**) :: Scan a b -> Scan a b -> Scan a b # logBase :: Scan a b -> Scan a b -> Scan a b # sin :: Scan a b -> Scan a b # cos :: Scan a b -> Scan a b # tan :: Scan a b -> Scan a b # asin :: Scan a b -> Scan a b # acos :: Scan a b -> Scan a b # atan :: Scan a b -> Scan a b # sinh :: Scan a b -> Scan a b # cosh :: Scan a b -> Scan a b # tanh :: Scan a b -> Scan a b # asinh :: Scan a b -> Scan a b # acosh :: Scan a b -> Scan a b # atanh :: Scan a b -> Scan a b # log1p :: Scan a b -> Scan a b # expm1 :: Scan a b -> Scan a b # log1pexp :: Scan a b -> Scan a b # log1mexp :: Scan a b -> Scan a b #
Fractional b => Fractional (Scan a b) Source #
Instance details Defined in Control.Scanl Methods (/) :: Scan a b -> Scan a b -> Scan a b # recip :: Scan a b -> Scan a b # fromRational :: Rational -> Scan a b #
Num b => Num (Scan a b) Source #
Instance details Defined in Control.Scanl Methods (+) :: Scan a b -> Scan a b -> Scan a b # (-) :: Scan a b -> Scan a b -> Scan a b # (*) :: Scan a b -> Scan a b -> Scan a b # negate :: Scan a b -> Scan a b # abs :: Scan a b -> Scan a b # signum :: Scan a b -> Scan a b # fromInteger :: Integer -> Scan a b #
Semigroup b => Semigroup (Scan a b) Source #
Instance details Defined in Control.Scanl Methods (<>) :: Scan a b -> Scan a b -> Scan a b # sconcat :: NonEmpty (Scan a b) -> Scan a b # stimes :: Integral b0 => b0 -> Scan a b -> Scan a b #
Monoid b => Monoid (Scan a b) Source #
Instance details Defined in Control.Scanl Methods mempty :: Scan a b # mappend :: Scan a b -> Scan a b -> Scan a b # mconcat :: [Scan a b] -> Scan a b #

data ScanM m a b Source #

Like Scan, but monadic.

A 'ScanM m a b' processes elements of type a and results in a monadic value of type m b.

Constructors

ScanM (a -> StateT x m b) (m x)

ScanM step initial extract

Instances

Monad m => Arrow (ScanM m) Source #
Instance details Defined in Control.Scanl Methods arr :: (b -> c) -> ScanM m b c # first :: ScanM m b c -> ScanM m (b, d) (c, d) # second :: ScanM m b c -> ScanM m (d, b) (d, c) # (***) :: ScanM m b c -> ScanM m b' c' -> ScanM m (b, b') (c, c') # (&&&) :: ScanM m b c -> ScanM m b c' -> ScanM m b (c, c') #
Functor m => Profunctor (ScanM m) Source #
Instance details Defined in Control.Scanl Methods dimap :: (a -> b) -> (c -> d) -> ScanM m b c -> ScanM m a d # lmap :: (a -> b) -> ScanM m b c -> ScanM m a c # rmap :: (b -> c) -> ScanM m a b -> ScanM m a c # (#.) :: Coercible c b => q b c -> ScanM m a b -> ScanM m a c # (.#) :: Coercible b a => ScanM m b c -> q a b -> ScanM m a c #
Monad m => Category (ScanM m :: * -> * -> *) Source #
Instance details Defined in Control.Scanl Methods id :: ScanM m a a # (.) :: ScanM m b c -> ScanM m a b -> ScanM m a c #
Functor m => Functor (ScanM m a) Source #
Instance details Defined in Control.Scanl Methods fmap :: (a0 -> b) -> ScanM m a a0 -> ScanM m a b # (<$) :: a0 -> ScanM m a b -> ScanM m a a0 #
Applicative m => Applicative (ScanM m a) Source #
Instance details Defined in Control.Scanl Methods pure :: a0 -> ScanM m a a0 # (<>) :: ScanM m a (a0 -> b) -> ScanM m a a0 -> ScanM m a b # liftA2 :: (a0 -> b -> c) -> ScanM m a a0 -> ScanM m a b -> ScanM m a c # (>) :: ScanM m a a0 -> ScanM m a b -> ScanM m a b # (<*) :: ScanM m a a0 -> ScanM m a b -> ScanM m a a0 #
(Monad m, Floating b) => Floating (ScanM m a b) Source #
Instance details Defined in Control.Scanl Methods pi :: ScanM m a b # exp :: ScanM m a b -> ScanM m a b # log :: ScanM m a b -> ScanM m a b # sqrt :: ScanM m a b -> ScanM m a b # (**) :: ScanM m a b -> ScanM m a b -> ScanM m a b # logBase :: ScanM m a b -> ScanM m a b -> ScanM m a b # sin :: ScanM m a b -> ScanM m a b # cos :: ScanM m a b -> ScanM m a b # tan :: ScanM m a b -> ScanM m a b # asin :: ScanM m a b -> ScanM m a b # acos :: ScanM m a b -> ScanM m a b # atan :: ScanM m a b -> ScanM m a b # sinh :: ScanM m a b -> ScanM m a b # cosh :: ScanM m a b -> ScanM m a b # tanh :: ScanM m a b -> ScanM m a b # asinh :: ScanM m a b -> ScanM m a b # acosh :: ScanM m a b -> ScanM m a b # atanh :: ScanM m a b -> ScanM m a b # log1p :: ScanM m a b -> ScanM m a b # expm1 :: ScanM m a b -> ScanM m a b # log1pexp :: ScanM m a b -> ScanM m a b # log1mexp :: ScanM m a b -> ScanM m a b #
(Monad m, Fractional b) => Fractional (ScanM m a b) Source #
Instance details Defined in Control.Scanl Methods (/) :: ScanM m a b -> ScanM m a b -> ScanM m a b # recip :: ScanM m a b -> ScanM m a b # fromRational :: Rational -> ScanM m a b #
(Monad m, Num b) => Num (ScanM m a b) Source #
Instance details Defined in Control.Scanl Methods (+) :: ScanM m a b -> ScanM m a b -> ScanM m a b # (-) :: ScanM m a b -> ScanM m a b -> ScanM m a b # (*) :: ScanM m a b -> ScanM m a b -> ScanM m a b # negate :: ScanM m a b -> ScanM m a b # abs :: ScanM m a b -> ScanM m a b # signum :: ScanM m a b -> ScanM m a b # fromInteger :: Integer -> ScanM m a b #
(Monad m, Semigroup b) => Semigroup (ScanM m a b) Source #
Instance details Defined in Control.Scanl Methods (<>) :: ScanM m a b -> ScanM m a b -> ScanM m a b # sconcat :: NonEmpty (ScanM m a b) -> ScanM m a b # stimes :: Integral b0 => b0 -> ScanM m a b -> ScanM m a b #
(Monad m, Monoid b) => Monoid (ScanM m a b) Source #
Instance details Defined in Control.Scanl Methods mempty :: ScanM m a b # mappend :: ScanM m a b -> ScanM m a b -> ScanM m a b # mconcat :: [ScanM m a b] -> ScanM m a b #

Scanning

scan :: Traversable t => Scan a b -> t a -> t b Source #

Apply a strict left Scan to a Traversable container

scanM :: (Traversable t, Monad m) => ScanM m a b -> t a -> m (t b) Source #

Like scan but monadic

scanr :: Traversable t => Scan a b -> t a -> t b Source #

Like scan but start scanning from the right

prescan :: Fold a b -> Scan a b Source #

Convert a Fold into a prescan

"Prescan" means that the last element of the scan is not included

postscan :: Fold a b -> Scan a b Source #

Convert a Fold into a postscan

"Postscan" means that the first element of the scan is not included

Utilities

purely :: (forall x. (a -> State x b) -> x -> r) -> Scan a b -> r Source #

Upgrade a scan to accept the Scan type

purely_ :: (forall x. (x -> a -> (x, b)) -> x -> r) -> Scan a b -> r Source #

Upgrade a more traditional scan to accept the Scan type

impurely :: (forall x. (a -> StateT x m b) -> m x -> r) -> ScanM m a b -> r Source #

Upgrade a monadic scan to accept the ScanM type

impurely_ :: Monad m => (forall x. (x -> a -> m (x, b)) -> m x -> r) -> ScanM m a b -> r Source #

Upgrade a more traditional monadic scan to accept the ScanM type

generalize :: Monad m => Scan a b -> ScanM m a b Source #

Generalize a Scan to a ScanM

generalize (pure r) = pure r

generalize (f <*> x) = generalize f <*> generalize x

simplify :: ScanM Identity a b -> Scan a b Source #

Simplify a pure ScanM to a Scan

simplify (pure r) = pure r

simplify (f <*> x) = simplify f <*> simplify x

hoists :: (forall x. m x -> n x) -> ScanM m a b -> ScanM n a b Source #

Shift a ScanM from one monad to another with a morphism such as lift or liftIO; the effect is the same as hoist.

arrM :: Monad m => (b -> m c) -> ScanM m b c Source #

premap :: (a -> b) -> Scan b r -> Scan a r Source #

(premap f scaner) returns a new Scan where f is applied at each step

scan (premap f scaner) list = scan scaner (map f list)

premap id = id

premap (f . g) = premap g . premap f

premap k (pure r) = pure r

premap k (f <*> x) = premap k f <*> premap k x

premapM :: Monad m => (a -> m b) -> ScanM m b r -> ScanM m a r Source #

(premapM f scaner) returns a new ScanM where f is applied to each input element

premapM return = id

premapM (f <=< g) = premap g . premap f

premapM k (pure r) = pure r

premapM k (f <*> x) = premapM k f <*> premapM k x