Data.Group.Combinators

[initialized documentation ekmett@gmail.com**20090329044124] { adddir ./doc adddir ./doc/html adddir ./doc/html/monoids adddir ./doc/html/monoids/src addfile ./doc/html/monoids/Data-Group-Combinators.html hunk ./doc/html/monoids/Data-Group-Combinators.html 1 + + +Data.Group.Combinators

Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Description

Utilities for working with Groups that conflict with names from the Prelude. +

Intended to be imported qualified. +

 import Data.Group.Combinators as Group (replicate)
+

Documentation

module Data.Group

replicate :: (Group m, Integral n) => m -> n -> m

Source

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Group-Sugar.html hunk ./doc/html/monoids/Data-Group-Sugar.html 1 + + +Data.Group.Sugar

Data.Group.Sugar

Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Description

Syntactic sugar for working with groups that conflicts with names from the Prelude. +

 import Prelude hiding ((-), (+), negate, subtract)
+ import Data.Group.Sugar
+

Documentation

module Data.Monoid.Additive.Sugar

module Data.Group

(-) :: Group g => g -> g -> g

Source

negate :: Group g => g -> g

Source

subtract :: Group g => g -> g -> g

Source

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Group.html hunk ./doc/html/monoids/Data-Group.html 1 + + +Data.Group

monoids-0.1.8: Lots of Monoids

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Data.Group

Portability	portable
Stability	experimental
Maintainer	Edward Kmett <ekmett@gmail.com>

Description

Extends Monoid to support Group operations +

Synopsis

module Data.Monoid.Additive

class Monoid a => Group a where

gnegate :: a -> a

minus :: a -> a -> a

gsubtract :: a -> a -> a

gnegate :: Group a => a -> a

gsubtract :: Group a => a -> a -> a

minus :: Group a => a -> a -> a

Documentation

module Data.Monoid.Additive

class Monoid a => Group a where

Source

Minimal complete definition: gnegate or minus +

Methods

gnegate :: a -> a

Source

minus :: a -> a -> a

Source

gsubtract :: a -> a -> a

Source

Instances

Group BoolRing

Group a => Group (Dual a)

Num a => Group (Sum a)

Fractional a => Group (Product a)

Group a => Group (Self a)

Group a => Group (FromString a)

Num a => Group (FromNum a)

(Group m, Applicative f) => Group (TraversalWith f m)

(Group m, Monad f) => Group (ActionWith f m)

(Group r, Module r m, Group m) => Group (D r m)

gnegate :: Group a => a -> a

Source

gsubtract :: Group a => a -> a -> a

Source

minus :: Group a => a -> a -> a

Source

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Additive-Sugar.html hunk ./doc/html/monoids/Data-Monoid-Additive-Sugar.html 1 + + +Data.Monoid.Additive.Sugar

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Data.Monoid.Additive.Sugar

Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Description

Syntactic sugar for working with a Monoid that conflicts with names from the Prelude. +

 import Prelude hiding ((+))
+ import Data.Monoid.Additive.Sugar
+

Documentation

module Data.Monoid.Additive

(+) :: Monoid m => m -> m -> m

Source

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addfile ./doc/html/monoids/Data-Monoid-Additive.html hunk ./doc/html/monoids/Data-Monoid-Additive.html 1 + + +Data.Monoid.Additive

Data.Monoid.Additive

Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Description

More easily understood aliases for mappend and mempty +

 import Data.Monoid.Additive
+

Documentation

plus :: Monoid m => m -> m -> m

Source

zero :: Monoid m => m

Source

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addfile ./doc/html/monoids/Data-Monoid-Applicative.html hunk ./doc/html/monoids/Data-Monoid-Applicative.html 1 + + +Data.Monoid.Applicative

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Data.Monoid.Applicative

Portability	non-portable (MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

Monoids for working with an Applicative Functor. +

Synopsis

module Data.Monoid.Reducer

module Data.Ring.Semi.Near

module Data.Ring.Module

newtype Traversal f = Traversal {

getTraversal :: f ()

}

newtype WrappedApplicative f a = WrappedApplicative {

getWrappedApplicative :: f a

}

newtype TraversalWith f m = TraversalWith {

getTraversalWith :: f m

}

snocTraversal :: Reducer (f ()) (Traversal f) => Traversal f -> f () -> Traversal f

Documentation

module Data.Monoid.Reducer

module Data.Ring.Semi.Near

module Data.Ring.Module

newtype Traversal f

Source

A Traversal uses an glues together Applicative actions with (*>) + in the manner of traverse_ from Data.Foldable. Any values returned by + reduced actions are discarded. +

Constructors

Traversal

getTraversal :: f ()

Instances

Applicative f => Monoid (Traversal f)

Applicative f => Reducer (f a) (Traversal f)

newtype WrappedApplicative f a

Source

A WrappedApplicative turns any Alternative instance into a Monoid. + It also provides a Multiplicative instance for an Applicative functor wrapped around a Monoid + and asserts that any Alternative applied to a Monoid forms a LeftSemiNearRing + under these operations. +

Constructors

WrappedApplicative

getWrappedApplicative :: f a

Instances

(Alternative f, Reducer c a) => Reducer c (WrappedApplicative f a)

Functor f => Functor (WrappedApplicative f)

Applicative f => Applicative (WrappedApplicative f)

Alternative f => Alternative (WrappedApplicative f)

Pointed f => Pointed (WrappedApplicative f)

Copointed f => Copointed (WrappedApplicative f)

Eq (f a) => Eq (WrappedApplicative f a)

Ord (f a) => Ord (WrappedApplicative f a)

Read (f a) => Read (WrappedApplicative f a)

Show (f a) => Show (WrappedApplicative f a)

Alternative f => Monoid (WrappedApplicative f a)

(Alternative f, Monoid a) => Multiplicative (WrappedApplicative f a)

(Alternative f, Monoid a) => LeftSemiNearRing (WrappedApplicative f a)

newtype TraversalWith f m

Source

if m is a Module and f is a Applicative then f TraversalWith m is a Module as well +

Constructors

TraversalWith

getTraversalWith :: f m

Instances

(Reducer c m, Applicative f) => Reducer c (TraversalWith f m)

(Module r m, Applicative f) => Module r (TraversalWith f m)

(RightModule r m, Applicative f) => RightModule r (TraversalWith f m)

(LeftModule r m, Applicative f) => LeftModule r (TraversalWith f m)

Functor f => Functor (TraversalWith f)

Applicative f => Applicative (TraversalWith f)

Alternative f => Alternative (TraversalWith f)

Pointed f => Pointed (TraversalWith f)

Copointed f => Copointed (TraversalWith f)

Eq (f m) => Eq (TraversalWith f m)

Ord (f m) => Ord (TraversalWith f m)

Read (f m) => Read (TraversalWith f m)

Show (f m) => Show (TraversalWith f m)

(Monoid m, Applicative f) => Monoid (TraversalWith f m)

(Group m, Applicative f) => Group (TraversalWith f m)

snocTraversal :: Reducer (f ()) (Traversal f) => Traversal f -> f () -> Traversal f

Source

Efficiently avoid needlessly rebinding when using snoc on an action that already returns () + A rewrite rule automatically applies this when possible +

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Categorical.html hunk ./doc/html/monoids/Data-Monoid-Categorical.html 1 + + +Data.Monoid.Categorical

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Data.Monoid.Categorical

Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Contents

Generalized Endo +
Monoids as Categories +

Description

Synopsis

module Data.Monoid.Reducer

data GEndo k a = GEndo {

getGEndo :: k a a

}

data Mon m n o where

Mon :: Monoid m => m -> Mon m a a

getMon :: Mon m m m -> m

Documentation

module Data.Monoid.Reducer

Generalized Endo +

data GEndo k a

Source

The Monoid of the endomorphisms over some object in an arbitrary Category. +

Constructors

GEndo

getGEndo :: k a a

Instances

Category k => Monoid (GEndo k a)

Monoids as Categories +

data Mon m n o where

Source

A Monoid is just a Category with one object. +

Constructors

Mon :: Monoid m => m -> Mon m a a

Instances

Reducer c m => Reducer c (Mon m m m)

Monoid m => Category (Mon m)

Monoid m => Monoid (Mon m m m)

getMon :: Mon m m m -> m

Source

Extract the Monoid from its representation as a Category +

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Combinators.html hunk ./doc/html/monoids/Data-Monoid-Combinators.html 1 + + +Data.Monoid.Combinators

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Data.Monoid.Combinators

Portability	non-portable (type families, MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Contents

Monadic Reduction +
Applicative Reduction +
Logical Reduction +
Monoidal Reduction +
List-Like Reduction +
List-Like Monoid Generation +

Description

Utilities for working with Monoids that conflict with names from the Prelude, + Data.Foldable, Control.Monad or elsewhere. Intended to be imported qualified. +

 import Data.Group.Combinators as Monoid 
+

Synopsis

module Data.Monoid.Generator

mapM_ :: (Generator c, Monad m) => (Elem c -> m b) -> c -> m ()

forM_ :: (Generator c, Monad m) => c -> (Elem c -> m b) -> m ()

traverse_ :: (Generator c, Applicative f) => (Elem c -> f b) -> c -> f ()

for_ :: (Generator c, Applicative f) => c -> (Elem c -> f b) -> f ()

and :: (Generator c, Elem c ~ Bool) => c -> Bool

or :: (Generator c, Elem c ~ Bool) => c -> Bool

any :: Generator c => (Elem c -> Bool) -> c -> Bool

all :: Generator c => (Elem c -> Bool) -> c -> Bool

foldMap :: (Monoid m, Generator c) => (Elem c -> m) -> c -> m

fold :: (Monoid m, Generator c, Elem c ~ m) => c -> m

concatMap :: Generator c => (Elem c -> [b]) -> c -> [b]

elem :: (Generator c, Eq (Elem c)) => Elem c -> c -> Bool

filter :: (Generator c, Reducer (Elem c) m) => (Elem c -> Bool) -> c -> m

find :: Generator c => (Elem c -> Bool) -> c -> Maybe (Elem c)

sum :: (Generator c, Num (Elem c)) => c -> Elem c

product :: (Generator c, Num (Elem c)) => c -> Elem c

notElem :: (Generator c, Eq (Elem c)) => Elem c -> c -> Bool

repeat :: Reducer e m => e -> m

replicate :: (Monoid m, Integral n) => m -> n -> m

cycle :: Monoid m => m -> m

Documentation

module Data.Monoid.Generator

Monadic Reduction +

mapM_ :: (Generator c, Monad m) => (Elem c -> m b) -> c -> m ()

Source

Efficiently mapReduce a Generator using the Action monoid. A specialized version of its namesake from Data.Foldable and Control.Monad +

forM_ :: (Generator c, Monad m) => c -> (Elem c -> m b) -> m ()

Source

flipped mapM_ as in Data.Foldable and Control.Monad +

Applicative Reduction +

traverse_ :: (Generator c, Applicative f) => (Elem c -> f b) -> c -> f ()

Source

Efficiently mapReduce a Generator using the Traversal monoid. A specialized version of its namesake in Data.Foldable +

for_ :: (Generator c, Applicative f) => c -> (Elem c -> f b) -> f ()

Source

flipped traverse_ as in Data.Foldable +

Logical Reduction +

and :: (Generator c, Elem c ~ Bool) => c -> Bool

Source

Efficiently reduce a Generator that contains values of type Bool +

or :: (Generator c, Elem c ~ Bool) => c -> Bool

Source

Efficiently reduce a Generator that contains values of type Bool +

any :: Generator c => (Elem c -> Bool) -> c -> Bool

Source

Efficiently mapReduce any Generator checking to see if any of its values match the supplied predicate +

all :: Generator c => (Elem c -> Bool) -> c -> Bool

Source

Efficiently mapReduce any Generator checking to see if all of its values match the supplied predicate +

Monoidal Reduction +

foldMap :: (Monoid m, Generator c) => (Elem c -> m) -> c -> m

Source

Efficiently mapReduce a Generator using the Self monoid. A specialized version of its namesake from Data.Foldable +

fold :: (Monoid m, Generator c, Elem c ~ m) => c -> m

Source

Efficiently reduce a Generator using the Self monoid. A specialized version of its namesake from Data.Foldable +

List-Like Reduction +

concatMap :: Generator c => (Elem c -> [b]) -> c -> [b]

Source

A further specialization of foldMap +

elem :: (Generator c, Eq (Elem c)) => Elem c -> c -> Bool

Source

Check to see if any member of the Generator matches the supplied value +

filter :: (Generator c, Reducer (Elem c) m) => (Elem c -> Bool) -> c -> m

Source

Efficiently mapReduce a subset of the elements in a Generator +

find :: Generator c => (Elem c -> Bool) -> c -> Maybe (Elem c)

Source

A specialization of filter using the First Monoid, analogous to Data.List.find +

sum :: (Generator c, Num (Elem c)) => c -> Elem c

Source

Efficiently mapReduce any Generator using the Sum Monoid +

product :: (Generator c, Num (Elem c)) => c -> Elem c

Source

Efficiently mapReduce any Generator using the Product Monoid +

notElem :: (Generator c, Eq (Elem c)) => Elem c -> c -> Bool

Source

Check to make sure that the supplied value is not a member of the Generator +

List-Like Monoid Generation +

repeat :: Reducer e m => e -> m

Source

A generalization of Data.List.repeat to an arbitrary Monoid. May fail to terminate for some values in some monoids. +

replicate :: (Monoid m, Integral n) => m -> n -> m

Source

A generalization of Data.List.replicate to an arbitrary Monoid. Adapted from + http://augustss.blogspot.com/2008/07/lost-and-found-if-i-write-108-in.html +

cycle :: Monoid m => m -> m

Source

A generalization of Data.List.cycle to an arbitrary Monoid. May fail to terminate for some values in some monoids. +

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-FromString.html hunk ./doc/html/monoids/Data-Monoid-FromString.html 1 + + +Data.Monoid.FromString

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Data.Monoid.FromString

Portability	non-portable (overloaded strings, MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

Transform any Char Reducer into an IsString instance so it can be + used directly with overloaded string literals. +

Documentation

module Data.Monoid.Reducer

data FromString m

Source

Constructors

FromString

getFromString :: m

Instances

Functor FromString

Pointed FromString

Copointed FromString

Reducer Char m => Reducer Char (FromString m)

Reducer Char m => IsString (FromString m)

Monoid m => Monoid (FromString m)

Multiplicative m => Multiplicative (FromString m)

LeftSemiNearRing m => LeftSemiNearRing (FromString m)

RightSemiNearRing m => RightSemiNearRing (FromString m)

Group a => Group (FromString a)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Generator-LZ78.html hunk ./doc/html/monoids/Data-Monoid-Generator-LZ78.html 1 + + +Data.Monoid.Generator.LZ78

Data.Monoid.Generator.LZ78

Documentation

module Data.Monoid.Generator

newtype LZ78 a

Source

Constructors

LZ78

getLZ78 :: [(Int, a)]

Instances

Generator (LZ78 a)

decode :: LZ78 a -> [a]

Source

encode :: Ord a => [a] -> LZ78 a

Source

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Generator.html hunk ./doc/html/monoids/Data-Monoid-Generator.html 1 + + +Data.Monoid.Generator

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Data.Monoid.Generator

Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Description

A Generator c is a possibly-specialized container, which contains values of + type Elem c, and which knows how to efficiently apply a Reducer to extract + an answer. +

Since a Generator is not polymorphic in its contents, it is more specialized + than Data.Foldable.Foldable, and a Reducer may supply efficient left-to-right + and right-to-left reduction strategies that a Generator may avail itself of. +

Synopsis

module Data.Monoid.Reducer

class Generator c where

type Elem c :: *

mapReduce :: Reducer e m => (Elem c -> e) -> c -> m

mapTo :: Reducer e m => (Elem c -> e) -> m -> c -> m

mapFrom :: Reducer e m => (Elem c -> e) -> c -> m -> m

mapReduce :: (Generator c, Reducer e m) => (Elem c -> e) -> c -> m

mapTo :: (Generator c, Reducer e m) => (Elem c -> e) -> m -> c -> m

mapFrom :: (Generator c, Reducer e m) => (Elem c -> e) -> c -> m -> m

reduce :: (Generator c, Reducer (Elem c) m) => c -> m

newtype Keys c = Keys {

getKeys :: c

}

newtype Values c = Values {

getValues :: c

}

newtype Char8 c = Char8 {

getChar8 :: c

}

Documentation

module Data.Monoid.Reducer

class Generator c where

Source

minimal definition mapReduce or mapTo +

Associated Types

type Elem c :: *

Source

Methods

mapReduce :: Reducer e m => (Elem c -> e) -> c -> m

Source

mapTo :: Reducer e m => (Elem c -> e) -> m -> c -> m

Source

mapFrom :: Reducer e m => (Elem c -> e) -> c -> m -> m

Source

Instances

Generator ByteString

Generator IntSet

Generator Text

Generator ([] c)

Generator (IntMap v)

Generator (Seq c)

Generator (Set a)

Generator (Char8 ByteString)

Ix i => Generator (Values (Array i e))

Generator (Values (IntMap v))

Generator (Values (Map k v))

Ix i => Generator (Keys (Array i e))

Generator (Keys (IntMap v))

Generator (Keys (Map k v))

Generator (LZ78 a)

Ix i => Generator (Array i e)

Generator (Map k v)

Measured v e => Generator (FingerTree v e)

mapReduce :: (Generator c, Reducer e m) => (Elem c -> e) -> c -> m

Source

mapTo :: (Generator c, Reducer e m) => (Elem c -> e) -> m -> c -> m

Source

mapFrom :: (Generator c, Reducer e m) => (Elem c -> e) -> c -> m -> m

Source

reduce :: (Generator c, Reducer (Elem c) m) => c -> m

Source

Apply a Reducer directly to the elements of a Generator +

newtype Keys c

Source

a Generator transformer that asks only for the keys of an indexed container +

Constructors

Keys

getKeys :: c

Instances

Ix i => Generator (Keys (Array i e))

Generator (Keys (IntMap v))

Generator (Keys (Map k v))

newtype Values c

Source

a Generator transformer that asks only for the values contained in an indexed container +

Constructors

Values

getValues :: c

Instances

Ix i => Generator (Values (Array i e))

Generator (Values (IntMap v))

Generator (Values (Map k v))

newtype Char8 c

Source

a Generator transformer that treats Word8 as Char + This lets you use a ByteString as a Char source without going through a Monoid transformer like UTF8 +

Constructors

Char8

getChar8 :: c

Instances

Generator (Char8 ByteString)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Instances.html hunk ./doc/html/monoids/Data-Monoid-Instances.html 1 + + +Data.Monoid.Instances

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Data.Monoid.Instances

Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Description

A collection of orphan instance declarations for Monoids that should + eventually be pushed back down to the source packages. +

Every package that uses these instances includes this package internally. +

Includes: +

Monoid instances for the Monad transformers from the mtl package +
A Monoid instance for the ParsecT Monad from parsec-3. +
IsString instances for tuples of IsString for overloaded string support. +
A Monoid instance for the FingerTree in the fingertree package +
Monoid instances for Int, Integer, and Ratio using (+,0) +

This module is automatically included everywhere this functionality is required + within this package. You should only have to import this module yourself if you + want these instances for your own purposes. +

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Lexical-RunLengthEncoding.html hunk ./doc/html/monoids/Data-Monoid-Lexical-RunLengthEncoding.html 1 + + +Data.Monoid.Lexical.RunLengthEncoding

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Data.Monoid.Lexical.RunLengthEncoding

Portability	non-portable (MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

A simple Monoid transformer that turns any monoidal Reducer into a + a reducer that expects to be supplied both a run length n with each item + and which efficiently exponentiates the result of unit n times through + replicate. +

Documentation

module Data.Monoid.Reducer

newtype RLE n m

Source

Constructors

RLE

getRLE :: m

Instances

(Integral n, Monoid m) => Monoid (RLE n m)

(Integral n, Reducer c m) => Reducer ((,) n c) (RLE n m)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Lexical-SourcePosition.html hunk ./doc/html/monoids/Data-Monoid-Lexical-SourcePosition.html 1 + + +Data.Monoid.Lexical.SourcePosition

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Data.Monoid.Lexical.SourcePosition

Portability	non-portable (MPTCs, OverloadedStrings)
Stability	experimental
Maintainer	libraries@haskell.org

Description

Incrementally determine locations in a source file through local information + This allows for efficient recomputation of line #s and token locations + while the file is being interactively updated by storing this as a supplemental + measure on a FingerTree. +

The general idea is to use this as part of a measure in a FingerTree so you can + use mappend to prepend a startOfFile with the file information. +

Synopsis

module Data.Monoid.Reducer.Char

nextTab :: Int -> Int

data SourcePosition file

type SourceLine = Int

type SourceColumn = Int

sourceLine :: SourcePosition f -> Maybe SourceLine

sourceColumn :: SourcePosition f -> Maybe SourceColumn

startOfFile :: f -> SourcePosition f

showSourcePosition :: SourcePosition String -> String

Documentation

module Data.Monoid.Reducer.Char

nextTab :: Int -> Int

Source

Compute the location of the next standard 8-column aligned tab +

data SourcePosition file

Source

A Monoid of partial information about locations in a source file. + This is polymorphic in the kind of information you want to maintain about each source file. +

Instances

Functor SourcePosition

Pointed SourcePosition

FunctorZero SourcePosition

FunctorPlus SourcePosition

Reducer Char (SourcePosition file)

Eq file => Eq (SourcePosition file)

Read file => Read (SourcePosition file)

Show file => Show (SourcePosition file)

IsString (SourcePosition file)

Monoid (SourcePosition file)

CharReducer (SourcePosition file)

type SourceLine = Int

Source

type SourceColumn = Int

Source

sourceLine :: SourcePosition f -> Maybe SourceLine

Source

extract partial information about the current line number if possible +

sourceColumn :: SourcePosition f -> Maybe SourceColumn

Source

extract partial information about the current column, even in the absence of knowledge of the source file +

startOfFile :: f -> SourcePosition f

Source

lift information about a source file into a starting SourcePosition for that file +

showSourcePosition :: SourcePosition String -> String

Source

extract the standard format for an absolute source position +

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Lexical-UTF8-Decoder.html hunk ./doc/html/monoids/Data-Monoid-Lexical-UTF8-Decoder.html 1 + + +Data.Monoid.Lexical.UTF8.Decoder

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Data.Monoid.Lexical.UTF8.Decoder

Portability	non-portable (MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

UTF8 encoded unicode characters can be parsed both forwards and backwards, + since the start of each Char is clearly marked. This Monoid accumulates + information about the characters represented and reduces that information + using a CharReducer, which is just a Reducer Monoid that knows what + it wants to do about an invalidChar -- a string of Word8 values that + don't form a valid UTF8 character. +

As this monoid parses chars it just feeds them upstream to the underlying + CharReducer. Efficient left-to-right and right-to-left traversals are + supplied so that a lazy ByteString can be parsed efficiently by + chunking it into strict chunks, and batching the traversals over each + before stitching the edges together. +

Because this needs to be a Monoid and should return the exact same result + regardless of forward or backwards parsing, it chooses to parse only + canonical UTF8 unlike most Haskell UTF8 parsers, which will blissfully + accept illegal alternative long encodings of a character. +

This actually fixes a potential class of security issues in some scenarios: +

http://prowebdevelopmentblog.com/content/big-overhaul-java-utf-8-charset +

NB: Due to naive use of a list to track the tail of an unfinished character + this may exhibit O(n^2) behavior parsing backwards along an invalid sequence + of a large number of bytes that all claim to be in the tail of a character. +

Documentation

module Data.Monoid.Reducer.Char

data UTF8 m

Source

Instances

Functor UTF8

Pointed UTF8

CharReducer m => Reducer Word8 (UTF8 m)

CharReducer m => Monoid (UTF8 m)

runUTF8 :: CharReducer m => UTF8 m -> m

Source

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Lexical-Words.html hunk ./doc/html/monoids/Data-Monoid-Lexical-Words.html 1 + + +Data.Monoid.Lexical.Words

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Data.Monoid.Lexical.Words

Portability	non-portable (MPTCs, OverloadedStrings)
Stability	experimental
Maintainer	libraries@haskell.org

Contents

Words +
Lines +

Description

A simple demonstration of tokenizing a Generator into distinct words + and/or lines using a word-parsing Monoid that accumulates partial + information about words and then builds up a token stream. +

Synopsis

module Data.Monoid.Reducer.Char

data Words m

runWords :: Words m -> [m]

data Unspaced m

wordsFrom :: (Generator c, Elem c ~ Char, Reducer Char m, Reducer Char n, Reducer Char o) => m -> c -> [(m, n, o)]

data Lines m

runLines :: Lines m -> [m]

data Unlined m

linesFrom :: (Generator c, Elem c ~ Char, Reducer Char m, Reducer Char n, Reducer Char o) => m -> c -> [(m, n, o)]

Documentation

module Data.Monoid.Reducer.Char

Words +

data Words m

Source

A CharReducer transformer that breaks a Char Generator into distinct words, feeding a Char Reducer each line in turn +

Instances

Functor Words

Reducer Char m => Reducer Char (Words m)

Read m => Read (Words m)

Show m => Show (Words m)

Reducer Char m => IsString (Words m)

Monoid m => Monoid (Words m)

CharReducer m => CharReducer (Words m)

runWords :: Words m -> [m]

Source

Extract the matched words from the Words Monoid +

data Unspaced m

Source

A CharReducer transformer that strips out any character matched by isSpace +

Instances

Functor Unspaced

Pointed Unspaced

Copointed Unspaced

Reducer Char m => Reducer Char (Unspaced m)

Eq m => Eq (Unspaced m)

Ord m => Ord (Unspaced m)

Read m => Read (Unspaced m)

Show m => Show (Unspaced m)

Reducer Char m => IsString (Unspaced m)

Monoid m => Monoid (Unspaced m)

CharReducer m => CharReducer (Unspaced m)

wordsFrom :: (Generator c, Elem c ~ Char, Reducer Char m, Reducer Char n, Reducer Char o) => m -> c -> [(m, n, o)]

Source

Utility function to extract words using accumulator, inside-word, and until-next-word monoids +

Lines +

data Lines m

Source

A CharReducer transformer that breaks a Char Generator into distinct lines, feeding a Char Reducer each line in turn. +

Instances

Functor Lines

Reducer Char m => Reducer Char (Lines m)

Read m => Read (Lines m)

Show m => Show (Lines m)

Reducer Char m => IsString (Lines m)

Monoid m => Monoid (Lines m)

CharReducer m => CharReducer (Lines m)

runLines :: Lines m -> [m]

Source

Extract the matched lines from the Lines Monoid +

data Unlined m

Source

A CharReducer transformer that strips out newlines +

Instances

Functor Unlined

Pointed Unlined

Copointed Unlined

Reducer Char m => Reducer Char (Unlined m)

Eq m => Eq (Unlined m)

Ord m => Ord (Unlined m)

Read m => Read (Unlined m)

Show m => Show (Unlined m)

Reducer Char m => IsString (Unlined m)

Monoid m => Monoid (Unlined m)

CharReducer m => CharReducer (Unlined m)

linesFrom :: (Generator c, Elem c ~ Char, Reducer Char m, Reducer Char n, Reducer Char o) => m -> c -> [(m, n, o)]

Source

Utility function to extract lines using accumulator, inside-line, and until-next-line monoids +

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Monad.html hunk ./doc/html/monoids/Data-Monoid-Monad.html 1 + + +Data.Monoid.Monad

monoids-0.1.8: Lots of Monoids

Source code

Contents

Index

Data.Monoid.Monad

Portability	non-portable (MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Contents

Actions +
Lifting Modules +
Wrapped Monads +

Description

Monoid instances for working with a Monad +

Synopsis

module Data.Monoid.Reducer

module Data.Ring.Semi.Near

newtype Action m = Action {

getAction :: m ()

}

snocAction :: Reducer (m ()) (Action m) => Action m -> m () -> Action m

newtype ActionWith f m = ActionWith {

getActionWith :: f m

}

newtype WrappedMonad m a = WrappedMonad {

getWrappedMonad :: m a

}

Documentation

module Data.Monoid.Reducer

module Data.Ring.Semi.Near

Actions +

newtype Action m

Source

An Action uses glues together Monad actions with (>>) + in the manner of mapM_ from Data.Foldable. Any values returned by + reduced actions are discarded. +

Constructors

Action

getAction :: m ()

Instances

Monad m => Monoid (Action m)

Monad m => Reducer (m a) (Action m)

snocAction :: Reducer (m ()) (Action m) => Action m -> m () -> Action m

Source

Efficiently avoid needlessly rebinding when using snoc on an action that already returns () + A rewrite rule automatically applies this when possible +

Lifting Modules +

newtype ActionWith f m

Source

if m is a Module over r and f is a Monad then f ActionWith m is a Module as well +

Constructors

ActionWith

getActionWith :: f m

Instances

(Reducer c m, Monad f) => Reducer c (ActionWith f m)

(Module r m, Monad f) => Module r (ActionWith f m)

(RightModule r m, Monad f) => RightModule r (ActionWith f m)

(LeftModule r m, Monad f) => LeftModule r (ActionWith f m)

Monad f => Monad (ActionWith f)

Functor f => Functor (ActionWith f)

MonadPlus f => MonadPlus (ActionWith f)

Pointed f => Pointed (ActionWith f)

Eq (f m) => Eq (ActionWith f m)

Ord (f m) => Ord (ActionWith f m)

Read (f m) => Read (ActionWith f m)

Show (f m) => Show (ActionWith f m)

(Monoid m, Monad f) => Monoid (ActionWith f m)

(Group m, Monad f) => Group (ActionWith f m)

Wrapped Monads +

newtype WrappedMonad m a

Source

A WrappedMonad turns any MonadPlus instance into a Monoid. + It also provides a Multiplicative instance for a Monad wrapped around a Monoid + and asserts that any MonadPlus applied to a Monoid forms a LeftSemiNearRing + under these operations. +

Constructors

WrappedMonad

getWrappedMonad :: m a

Instances

(MonadPlus m, Reducer c a) => Reducer c (WrappedMonad m a)

Monad m => Monad (WrappedMonad m)

Functor m => Functor (WrappedMonad m)

MonadPlus m => MonadPlus (WrappedMonad m)

Pointed m => Pointed (WrappedMonad m)

Eq (m a) => Eq (WrappedMonad m a)

Ord (m a) => Ord (WrappedMonad m a)

Read (m a) => Read (WrappedMonad m a)

Show (m a) => Show (WrappedMonad m a)

MonadPlus m => Monoid (WrappedMonad m a)

(Monad m, Monoid a) => Multiplicative (WrappedMonad m a)

(MonadPlus m, Monoid a) => LeftSemiNearRing (WrappedMonad m a)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Multiplicative-Sugar.html hunk ./doc/html/monoids/Data-Monoid-Multiplicative-Sugar.html 1 + + +Data.Monoid.Multiplicative.Sugar

monoids-0.1.8: Lots of Monoids

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Index

Data.Monoid.Multiplicative.Sugar

Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Description

Syntactic sugar for working with a Multiplicative monoids that conflicts with names from the Prelude. +

 import Prelude hiding ((+),(*))
+ import Data.Monoid.Multiplicative.Sugar
+

Documentation

module Data.Monoid.Additive.Sugar

module Data.Monoid.Multiplicative

(*) :: Multiplicative r => r -> r -> r

Source

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Multiplicative.html hunk ./doc/html/monoids/Data-Monoid-Multiplicative.html 1 + + +Data.Monoid.Multiplicative

monoids-0.1.8: Lots of Monoids

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Index

Data.Monoid.Multiplicative

Portability	portable (but instances use MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Contents

Multiplicative Monoids +
Multiplicative to Monoid +
Monoid to Multiplicative +

Description

When dealing with a Ring or other structure, you often need a pair of + Monoid instances that are closely related. Making a newtype for one + is unsatisfying and yields an unnatural programming style. +

A Multiplicative is a Monoid that is intended for use in a scenario + that can be extended to have another Monoid slot in for addition. This + enables one to use common notation. +

Any Multiplicative can be turned into a Monoid using the Log wrapper. +

Any Monoid can be turned into a Multiplicative using the Exp wrapper. +

Instances are supplied for common Monads of Monoids, in a fashion + which can be extended if the Monad is a MonadPlus to yield a LeftSemiNearRing +

Instances are also supplied for common Applicatives of Monoids, in a + fashion which can be extended if the Applicative is Alternative to + yield a LeftSemiNearRing +

Synopsis

module Data.Monoid.Additive

class Multiplicative m where

one :: m

times :: m -> m -> m

one :: Multiplicative m => m

times :: Multiplicative m => m -> m -> m

data Log m = Log {

getLog :: m

}

data Exp m = Exp {

getExp :: m

}

Documentation

module Data.Monoid.Additive

Multiplicative Monoids +

class Multiplicative m where

Source

Methods

one :: m

Source

times :: m -> m -> m

Source

Instances

Multiplicative Int

Multiplicative Integer

Multiplicative BoolRing

Monoid m => Multiplicative ([] m)

Integral m => Multiplicative (Ratio m)

Monoid n => Multiplicative (IO n)

Monoid m => Multiplicative (Maybe m)

Monoid n => Multiplicative (ZipList n)

Monoid n => Multiplicative (STM n)

Monoid m => Multiplicative (Seq m)

Monoid m => Multiplicative (Identity m)

Multiplicative m => Multiplicative (Self m)

Multiplicative m => Multiplicative (FromString m)

Monoid m => Multiplicative (Exp m)

Num a => Multiplicative (Tropical a)

Ord a => Multiplicative (Priority a)

(Bounded a, Ord a) => Multiplicative (Order a)

Num a => Multiplicative (FromNum a)

Monoid m => Multiplicative (Const m a)

Monoid n => Multiplicative (ST s n)

Monoid m => Multiplicative (Cont r m)

(Monoid w, Monoid m) => Multiplicative (Writer w m)

Monoid m => Multiplicative (State s m)

Monoid m => Multiplicative (Reader e m)

(Measured v m, Monoid m) => Multiplicative (FingerTree v m)

(Alternative f, Monoid a) => Multiplicative (WrappedApplicative f a)

(Monad m, Monoid a) => Multiplicative (WrappedMonad m a)

Module r m => Multiplicative (D r m)

(Monad m, Monoid n) => Multiplicative (ContT r m n)

(Monad m, Monoid w, Monoid n) => Multiplicative (WriterT w m n)

(Monad m, Monoid n) => Multiplicative (StateT s m n)

(Monad m, Monoid n) => Multiplicative (ReaderT e m n)

(Monoid w, Monoid m) => Multiplicative (RWS r w s m)

(Stream s m t, Monoid n) => Multiplicative (ParsecT s u m n)

(Monad m, Monoid w, Monoid n) => Multiplicative (RWST r w s m n)

one :: Multiplicative m => m

Source

times :: Multiplicative m => m -> m -> m

Source

Multiplicative to Monoid +

data Log m

Source

Convert a Multiplicative into a Monoid. Mnemonic: Log a + Log b = Log (a * b) +

Constructors

Log

getLog :: m

Instances

Multiplicative m => Monoid (Log m)

Monoid to Multiplicative +

data Exp m

Source

Convert a Monoid into a Multiplicative. Mnemonic: Exp a * Exp b = Exp (a + b) +

Constructors

Exp

getExp :: m

Instances

Monoid m => Multiplicative (Exp m)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Ord.html hunk ./doc/html/monoids/Data-Monoid-Ord.html 1 + + +Data.Monoid.Ord

monoids-0.1.8: Lots of Monoids

Source code

Contents

Index

Data.Monoid.Ord

Contents

Max +
Min +
MaxPriority: Max semigroup w/ added bottom +
MinPriority: Min semigroup w/ added top +

Synopsis

module Data.Monoid.Reducer

newtype Max a = Max {

getMax :: a

}

newtype Min a = Min {

getMin :: a

}

newtype MaxPriority a = MaxPriority {

getMaxPriority :: Maybe a

}

minfinity :: MaxPriority a

newtype MinPriority a = MinPriority {

getMinPriority :: Maybe a

}

infinity :: MinPriority a

Documentation

module Data.Monoid.Reducer

Max +

newtype Max a

Source

The Monoid (max,minBound) +

Constructors

Max

getMax :: a

Instances

Functor Max

Pointed Max

Copointed Max

(Ord a, Bounded a) => Reducer a (Max a)

Bounded a => Bounded (Max a)

Eq a => Eq (Max a)

Ord a => Ord (Max a)

Read a => Read (Max a)

Show a => Show (Max a)

(Ord a, Bounded a) => Monoid (Max a)

Min +

newtype Min a

Source

The Monoid given by (min,maxBound) +

Constructors

Min

getMin :: a

Instances

Functor Min

Pointed Min

Copointed Min

(Ord a, Bounded a) => Reducer a (Min a)

Bounded a => Bounded (Min a)

Eq a => Eq (Min a)

Ord a => Ord (Min a)

Read a => Read (Min a)

Show a => Show (Min a)

(Ord a, Bounded a) => Monoid (Min a)

MaxPriority: Max semigroup w/ added bottom +

newtype MaxPriority a

Source

The Monoid (max,Nothing) over Maybe a where Nothing is the bottom element +

Constructors

MaxPriority

getMaxPriority :: Maybe a

Instances

Functor MaxPriority

Pointed MaxPriority

Eq a => Eq (MaxPriority a)

Ord a => Ord (MaxPriority a)

Read a => Read (MaxPriority a)

Show a => Show (MaxPriority a)

Ord a => Monoid (MaxPriority a)

Ord a => Reducer (Maybe a) (MaxPriority a)

Ord a => Reducer (MaxPriority a) (Priority a)

minfinity :: MaxPriority a

Source

MinPriority: Min semigroup w/ added top +

newtype MinPriority a

Source

The Monoid (min,Nothing) over Maybe a where Nothing is the top element +

Constructors

MinPriority

getMinPriority :: Maybe a

Instances

Functor MinPriority

Pointed MinPriority

Eq a => Eq (MinPriority a)

Ord a => Ord (MinPriority a)

Read a => Read (MinPriority a)

Show a => Show (MinPriority a)

Ord a => Monoid (MinPriority a)

Ord a => Reducer (Maybe a) (MinPriority a)

Ord a => Reducer (MinPriority a) (Tropical a)

Ord a => Reducer (MinPriority a) (Priority a)

infinity :: MinPriority a

Source

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Reducer-Char.html hunk ./doc/html/monoids/Data-Monoid-Reducer-Char.html 1 + + +Data.Monoid.Reducer.Char

monoids-0.1.8: Lots of Monoids

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Index

Data.Monoid.Reducer.Char

Portability	non-portable (MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

Synopsis

module Data.Monoid.Reducer

class Reducer Char m => CharReducer m where

fromChar :: Char -> m

invalidChar :: [Word8] -> m

invalidChar :: CharReducer m => [Word8] -> m

fromChar :: CharReducer m => Char -> m

Documentation

module Data.Monoid.Reducer

class Reducer Char m => CharReducer m where

Source

Provides a mechanism for the UTF8 Monoid to report invalid characters to one or more monoids. +

Methods

fromChar :: Char -> m

Source

invalidChar :: [Word8] -> m

Source

Instances

CharReducer ([] Char)

CharReducer (SourcePosition file)

CharReducer m => CharReducer (Unlined m)

CharReducer m => CharReducer (Unspaced m)

CharReducer m => CharReducer (Lines m)

CharReducer m => CharReducer (Words m)

(CharReducer m, CharReducer m') => CharReducer ((,) m m')

(CharReducer m, CharReducer m', CharReducer m'') => CharReducer ((,,) m m' m'')

(CharReducer m, CharReducer m', CharReducer m'', CharReducer m''') => CharReducer ((,,,) m m' m'' m''')

invalidChar :: CharReducer m => [Word8] -> m

Source

fromChar :: CharReducer m => Char -> m

Source

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Reducer-With.html hunk ./doc/html/monoids/Data-Monoid-Reducer-With.html 1 + + +Data.Monoid.Reducer.With

monoids-0.1.8: Lots of Monoids

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Data.Monoid.Reducer.With

Portability	non-portable (MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

Synopsis

module Data.Monoid.Reducer

newtype WithReducer c m = WithReducer {

withoutReducer :: c

}

Documentation

module Data.Monoid.Reducer

newtype WithReducer c m

Source

If m is a c-Reducer, then m is (c WithReducer m)-Reducer + This can be used to quickly select a Reducer for use as a FingerTree + measure. +

Constructors

WithReducer

withoutReducer :: c

Instances

Reducer c m => Measured m (WithReducer c m)

Reducer c m => Reducer (WithReducer c m) m

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Reducer.html hunk ./doc/html/monoids/Data-Monoid-Reducer.html 1 + + +Data.Monoid.Reducer

monoids-0.1.8: Lots of Monoids

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Data.Monoid.Reducer

Portability	non-portable (MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

A c-Reducer is a Monoid with a canonical mapping from c to the Monoid. + This unit acts in many ways like return for a Monad but is limited + to a single type. +

Synopsis

class Monoid m => Reducer c m where

unit :: c -> m

snoc :: m -> c -> m

cons :: c -> m -> m

unit :: Reducer c m => c -> m

snoc :: Reducer c m => m -> c -> m

cons :: Reducer c m => c -> m -> m

foldMapReduce :: (Foldable f, Reducer e m) => (a -> e) -> f a -> m

foldReduce :: (Foldable f, Reducer e m) => f e -> m

pureUnit :: (Applicative f, Reducer c n) => c -> f n

returnUnit :: (Monad m, Reducer c n) => c -> m n

Documentation

class Monoid m => Reducer c m where

Source

This type may be best read infix. A c Reducer m is a Monoid m that maps + values of type c through unit to values of type m. A c-Reducer may also + supply operations which tack-on another c to an existing Monoid m on the left + or right. These specialized reductions may be more efficient in some scenarios + and are used when appropriate by a Generator. The names cons and snoc work + by analogy to the synonymous operations in the list monoid. +

This class deliberately avoids functional-dependencies, so that () can be a c-Reducer + for all c, and so many common reducers can work over multiple types, for instance, + First and Last may reduce both a and Maybe a. Since a Generator has a fixed element + type, the input to the reducer is generally known and extracting from the monoid usually + is sufficient to fix the result type. Combinators are available for most scenarios where + this is not the case, and the few remaining cases can be handled by using an explicit + type annotation. +

Minimal definition: unit or snoc +

Methods

unit :: c -> m

Source

Convert a value into a Monoid +

snoc :: m -> c -> m

Source

Append a value to a Monoid for use in left-to-right reduction +

cons :: c -> m -> m

Source

Prepend a value onto a Monoid for use during right-to-left reduction +

Instances

Reducer Bool All

Reducer Bool Any

Reducer Bool BoolRing

Reducer Int IntSet

Reducer c ()

Reducer Char (SourcePosition file)

Reducer Char m => Reducer Char (Unlined m)

Reducer Char m => Reducer Char (Unspaced m)

Reducer Char m => Reducer Char (Lines m)

Reducer Char m => Reducer Char (Words m)

Reducer Char m => Reducer Char (FromString m)

Num a => Reducer Integer (FromNum a)

CharReducer m => Reducer Word8 (UTF8 m)

Ord a => Reducer a (Set a)

Reducer a (Seq a)

Reducer a (Last a)

Reducer a (First a)

Num a => Reducer a (Product a)

Num a => Reducer a (Sum a)

Monoid a => Reducer a (Dual a)

Reducer c ([] c)

HasUnion f => Reducer f (Union f)

Monoid m => Reducer m (Self m)

(Ord a, Bounded a) => Reducer a (Min a)

(Ord a, Bounded a) => Reducer a (Max a)

Ord a => Reducer a (Tropical a)

Ord a => Reducer a (Priority a)

(Bounded a, Ord a) => Reducer a (Order a)

Measured v a => Reducer a (FingerTree v a)

(Reducer c m, Reducer c n) => Reducer c ((,) m n)

(Reducer c m, Applicative f) => Reducer c (TraversalWith f m)

(Alternative f, Reducer c a) => Reducer c (WrappedApplicative f a)

(Reducer c m, Monad f) => Reducer c (ActionWith f m)

(MonadPlus m, Reducer c a) => Reducer c (WrappedMonad m a)

(Reducer c r, Reducer c m) => Reducer c (D r m)

(Reducer c m, Reducer c n, Reducer c o) => Reducer c ((,,) m n o)

Reducer c m => Reducer c (Mon m m m)

(Stream s m t, Reducer c a) => Reducer c (ParsecT s u m a)

(Reducer c m, Reducer c n, Reducer c o, Reducer c p) => Reducer c ((,,,) m n o p)

Applicative f => Reducer (f a) (Traversal f)

Monad m => Reducer (m a) (Action m)

Reducer (Maybe a) (Last a)

Reducer (Maybe a) (First a)

Ord a => Reducer (Maybe a) (MinPriority a)

Ord a => Reducer (Maybe a) (MaxPriority a)

Ord a => Reducer (Maybe a) (Tropical a)

Ord a => Reducer (MinPriority a) (Tropical a)

Ord a => Reducer (MinPriority a) (Priority a)

Ord a => Reducer (MaxPriority a) (Priority a)

(HasUnionWith f, Monoid m) => Reducer (f m) (UnionWith f m)

Reducer c m => Reducer (WithReducer c m) m

Reducer (a -> a) (Endo a)

Reducer ((,) Int v) (IntMap v)

Ord k => Reducer ((,) k v) (Map k v)

(Integral n, Reducer c m) => Reducer ((,) n c) (RLE n m)

unit :: Reducer c m => c -> m

Source

Convert a value into a Monoid +

snoc :: Reducer c m => m -> c -> m

Source

Append a value to a Monoid for use in left-to-right reduction +

cons :: Reducer c m => c -> m -> m

Source

Prepend a value onto a Monoid for use during right-to-left reduction +

foldMapReduce :: (Foldable f, Reducer e m) => (a -> e) -> f a -> m

Source

Apply a Reducer to a Foldable container, after mapping the contents into a suitable form for reduction. +

foldReduce :: (Foldable f, Reducer e m) => f e -> m

Source

Apply a Reducer to a Foldable mapping each element through unit +

pureUnit :: (Applicative f, Reducer c n) => c -> f n

Source

returnUnit :: (Monad m, Reducer c n) => c -> m n

Source

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Self.html hunk ./doc/html/monoids/Data-Monoid-Self.html 1 + + +Data.Monoid.Self

monoids-0.1.8: Lots of Monoids

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Data.Monoid.Self

Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Description

A simple Monoid transformer that takes a Monoid m and produces a new m-Reducer named Self m +

This is useful when you have a generator that already contains monoidal values or someone supplies + the map to the monoid in the form of a function rather than as a Reducer instance. You can just + getSelf . reduce or getSelf . mapReduce f in those scenarios. These behaviors are encapsulated + into the fold and foldMap combinators in Data.Monoid.Combinators respectively. +

Documentation

module Data.Monoid.Reducer

newtype Self m

Source

Constructors

Self

getSelf :: m

Instances

Functor Self

Pointed Self

Copointed Self

Monoid m => Reducer m (Self m)

Monoid m => Monoid (Self m)

Multiplicative m => Multiplicative (Self m)

LeftSemiNearRing m => LeftSemiNearRing (Self m)

RightSemiNearRing m => RightSemiNearRing (Self m)

Group a => Group (Self a)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Monoid-Union.html hunk ./doc/html/monoids/Data-Monoid-Union.html 1 + + +Data.Monoid.Union

monoids-0.1.8: Lots of Monoids

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Index

Data.Monoid.Union

Contents

Unions of Containers +
Unions of Containers of Monoids +

Synopsis

module Data.Monoid.Reducer

class HasUnion f where

empty :: f

union :: f -> f -> f

empty :: HasUnion f => f

union :: HasUnion f => f -> f -> f

newtype Union f = Union {

getUnion :: f

}

class HasUnionWith f where

unionWith :: (a -> a -> a) -> f a -> f a -> f a

emptyWith :: f a

emptyWith :: HasUnionWith f => f a

unionWith :: HasUnionWith f => (a -> a -> a) -> f a -> f a -> f a

newtype UnionWith f m = UnionWith {

getUnionWith :: f m

}

Documentation

module Data.Monoid.Reducer

Unions of Containers +

class HasUnion f where

Source

A Container suitable for the Union Monoid +

Methods

empty :: f

Source

union :: f -> f -> f

Source

Instances

HasUnion IntSet

Eq a => HasUnion ([] a)

HasUnion (IntMap a)

Ord a => HasUnion (Set a)

Ord k => HasUnion (Map k a)

empty :: HasUnion f => f

Source

union :: HasUnion f => f -> f -> f

Source

newtype Union f

Source

The Monoid (union,empty) +

Constructors

Union

getUnion :: f

Instances

Functor Union

Pointed Union

Copointed Union

HasUnion f => Reducer f (Union f)

Eq f => Eq (Union f)

Ord f => Ord (Union f)

Read f => Read (Union f)

Show f => Show (Union f)

HasUnion f => Monoid (Union f)

Unions of Containers of Monoids +

class HasUnionWith f where

Source

Polymorphic containers that we can supply an operation to handle unions with +

Methods

unionWith :: (a -> a -> a) -> f a -> f a -> f a

Source

emptyWith :: f a

Source

Instances

HasUnionWith IntMap

Ord k => HasUnionWith (Map k)

emptyWith :: HasUnionWith f => f a

Source

unionWith :: HasUnionWith f => (a -> a -> a) -> f a -> f a -> f a

Source

newtype UnionWith f m

Source

The Monoid ('unionWith mappend',empty) for containers full of monoids. +

Constructors

UnionWith

getUnionWith :: f m

Instances

Monad f => Monad (UnionWith f)

Functor f => Functor (UnionWith f)

Pointed f => Pointed (UnionWith f)

(HasUnionWith f, Monoid m) => Reducer (f m) (UnionWith f m)

Eq (f m) => Eq (UnionWith f m)

Ord (f m) => Ord (UnionWith f m)

Read (f m) => Read (UnionWith f m)

Show (f m) => Show (UnionWith f m)

(HasUnionWith f, Monoid m) => Monoid (UnionWith f m)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Ring-Boolean.html hunk ./doc/html/monoids/Data-Ring-Boolean.html 1 + + +Data.Ring.Boolean

monoids-0.1.8: Lots of Monoids

Source code

Contents

Index

Data.Ring.Boolean

Portability	non-portable (MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

A Boolean Ring over Bool. Note well that the mappend of this ring is + symmetric difference and not disjunction like you might expect. To get that + you should use use Ord from Data.Ring.Semi.Ord.Order on Bool to get the '&&'/'||'-based + distributive-lattice SemiRing +

Documentation

module Data.Ring

newtype BoolRing

Source

Constructors

BoolRing

getBoolRing :: Bool

Instances

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Ring-FromNum.html hunk ./doc/html/monoids/Data-Ring-FromNum.html 1 + + +Data.Ring.FromNum

monoids-0.1.8: Lots of Monoids

Source code

Contents

Index

Data.Ring.FromNum

Portability	non-portable (MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

A wrapper that lies for you and claims any instance of Num is a Ring. + Who knows, for your type it might even be telling the truth! +

Documentation

module Data.Ring

newtype FromNum a

Source

Constructors

FromNum

getFromNum :: a

Instances

Num a => Reducer Integer (FromNum a)

Eq a => Eq (FromNum a)

Num a => Num (FromNum a)

Show a => Show (FromNum a)

Num a => Monoid (FromNum a)

Num a => Multiplicative (FromNum a)

Num a => LeftSemiNearRing (FromNum a)

Num a => RightSemiNearRing (FromNum a)

Num a => SemiRing (FromNum a)

Num a => Group (FromNum a)

Num a => Ring (FromNum a)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Ring-Module-AutomaticDifferentiation.html hunk ./doc/html/monoids/Data-Ring-Module-AutomaticDifferentiation.html 1 + + +Data.Ring.Module.AutomaticDifferentiation

Data.Ring.Module.AutomaticDifferentiation

Documentation

module Data.Ring.Module

data D r m

Source

Instances

(Reducer c r, Reducer c m) => Reducer c (D r m)

(Monoid r, Monoid m) => Monoid (D r m)

Module r m => Multiplicative (D r m)

(LeftSemiNearRing r, Module r m) => LeftSemiNearRing (D r m)

(RightSemiNearRing r, Module r m) => RightSemiNearRing (D r m)

(SemiRing r, Module r m) => SemiRing (D r m)

(Group r, Module r m, Group m) => Group (D r m)

(Ring r, Module r m, Group m) => Ring (D r m)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Ring-Module.html hunk ./doc/html/monoids/Data-Ring-Module.html 1 + + +Data.Ring.Module

monoids-0.1.8: Lots of Monoids

Source code

Contents

Index

Data.Ring.Module

Portability	non-portable (MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

Left- and right- modules over rings, semirings, and Seminearrings. + To avoid a proliferation of classes. These only require that there + be an addition and multiplication operation for the Ring +

Synopsis

module Data.Ring

class (Monoid r, Multiplicative r, Monoid m) => LeftModule r m where

(*.) :: r -> m -> m

(*.) :: LeftModule r m => r -> m -> m

class (Monoid r, Multiplicative r, Monoid m) => RightModule r m where

(.*) :: m -> r -> m

(.*) :: RightModule r m => m -> r -> m

class (LeftModule r m, RightModule r m) => Module r m

Documentation

module Data.Ring

class (Monoid r, Multiplicative r, Monoid m) => LeftModule r m where

Source

 (x * y) *. m = x * (y *. m)

Methods

(*.) :: r -> m -> m

Source

Instances

(LeftModule r m, Applicative f) => LeftModule r (TraversalWith f m)

(LeftModule r m, Monad f) => LeftModule r (ActionWith f m)

(*.) :: LeftModule r m => r -> m -> m

Source

class (Monoid r, Multiplicative r, Monoid m) => RightModule r m where

Source

 (m .* x) * y = m .* (x * y)

Methods

(.*) :: m -> r -> m

Source

Instances

(RightModule r m, Applicative f) => RightModule r (TraversalWith f m)

(RightModule r m, Monad f) => RightModule r (ActionWith f m)

(.*) :: RightModule r m => m -> r -> m

Source

class (LeftModule r m, RightModule r m) => Module r m

Source

 (x *. m) .* y = x *. (m .* y)

Instances

(Module r m, Applicative f) => Module r (TraversalWith f m)

(Module r m, Monad f) => Module r (ActionWith f m)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Ring-Semi-Near.html hunk ./doc/html/monoids/Data-Ring-Semi-Near.html 1 + + +Data.Ring.Semi.Near

monoids-0.1.8: Lots of Monoids

Source code

Contents

Index

Data.Ring.Semi.Near

Portability	portable (instances use MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

Defines left- and right- seminearrings. Every MonadPlus wrapped around + a Monoid qualifies due to the distributivity of (>>=) over mplus. +

See http://conway.rutgers.edu/~ccshan/wiki/blog/posts/WordNumbers1/ +

Synopsis

module Data.Monoid.Multiplicative

class (Multiplicative m, Monoid m) => LeftSemiNearRing m

class (Multiplicative m, Monoid m) => RightSemiNearRing m

Documentation

module Data.Monoid.Multiplicative

class (Multiplicative m, Monoid m) => LeftSemiNearRing m

Source

a * (b + c) = (a * b) + (a * c)

Instances

LeftSemiNearRing BoolRing

Monoid m => LeftSemiNearRing ([] m)

Monoid m => LeftSemiNearRing (Maybe m)

Monoid m => LeftSemiNearRing (Seq m)

LeftSemiNearRing m => LeftSemiNearRing (Self m)

LeftSemiNearRing m => LeftSemiNearRing (FromString m)

(Ord a, Num a) => LeftSemiNearRing (Tropical a)

Ord a => LeftSemiNearRing (Priority a)

(Bounded a, Ord a) => LeftSemiNearRing (Order a)

Num a => LeftSemiNearRing (FromNum a)

(Measured v m, Monoid m) => LeftSemiNearRing (FingerTree v m)

(Alternative f, Monoid a) => LeftSemiNearRing (WrappedApplicative f a)

(MonadPlus m, Monoid a) => LeftSemiNearRing (WrappedMonad m a)

(LeftSemiNearRing r, Module r m) => LeftSemiNearRing (D r m)

(MonadPlus m, Monoid w, Monoid n) => LeftSemiNearRing (WriterT w m n)

(MonadPlus m, Monoid n) => LeftSemiNearRing (StateT s m n)

(MonadPlus m, Monoid n) => LeftSemiNearRing (ReaderT e m n)

(Stream s m t, Monoid a) => LeftSemiNearRing (ParsecT s u m a)

(MonadPlus m, Monoid w, Monoid n) => LeftSemiNearRing (RWST r w s m n)

class (Multiplicative m, Monoid m) => RightSemiNearRing m

Source

(a + b) * c = (a * c) + (b * c)

Instances

RightSemiNearRing BoolRing

RightSemiNearRing m => RightSemiNearRing (Self m)

RightSemiNearRing m => RightSemiNearRing (FromString m)

(Ord a, Num a) => RightSemiNearRing (Tropical a)

Ord a => RightSemiNearRing (Priority a)

(Bounded a, Ord a) => RightSemiNearRing (Order a)

Num a => RightSemiNearRing (FromNum a)

(RightSemiNearRing r, Module r m) => RightSemiNearRing (D r m)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Ring-Semi-Ord.html hunk ./doc/html/monoids/Data-Ring-Semi-Ord.html 1 + + +Data.Ring.Semi.Ord

monoids-0.1.8: Lots of Monoids

Source code

Contents

Index

Data.Ring.Semi.Ord

Stability	experimental
Maintainer	ekmett@gmail.com

Description

Turn an instance of Ord into a SemiRing over max and min +

Synopsis

module Data.Ring.Semi

newtype Order a = Order {

getOrder :: a

}

data Priority a

= MinBound

| Priority a

| MaxBound

Documentation

module Data.Ring.Semi

newtype Order a

Source

A SemiRing using a type's built-in Bounded instance. +

Constructors

Order

getOrder :: a

Instances

Functor Order

Pointed Order

Copointed Order

(Bounded a, Ord a) => Reducer a (Order a)

Bounded a => Bounded (Order a)

Eq a => Eq (Order a)

Ord a => Ord (Order a)

Read a => Read (Order a)

Show a => Show (Order a)

Arbitrary a => Arbitrary (Order a)

(Bounded a, Ord a) => Monoid (Order a)

(Bounded a, Ord a) => Multiplicative (Order a)

(Bounded a, Ord a) => LeftSemiNearRing (Order a)

(Bounded a, Ord a) => RightSemiNearRing (Order a)

(Bounded a, Ord a) => SemiRing (Order a)

data Priority a

Source

A SemiRing which adds minBound and maxBound to a pre-existing type. +

Constructors

MinBound
Priority a
MaxBound

Instances

Functor Priority

Pointed Priority

Ord a => Reducer a (Priority a)

Bounded (Priority a)

Eq a => Eq (Priority a)

Ord a => Ord (Priority a)

Read a => Read (Priority a)

Show a => Show (Priority a)

Arbitrary a => Arbitrary (Priority a)

Ord a => Monoid (Priority a)

Ord a => Multiplicative (Priority a)

Ord a => LeftSemiNearRing (Priority a)

Ord a => RightSemiNearRing (Priority a)

Ord a => SemiRing (Priority a)

Ord a => Reducer (MinPriority a) (Priority a)

Ord a => Reducer (MaxPriority a) (Priority a)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Ring-Semi-Tropical.html hunk ./doc/html/monoids/Data-Ring-Semi-Tropical.html 1 + + +Data.Ring.Semi.Tropical

monoids-0.1.8: Lots of Monoids

Source code

Contents

Index

Data.Ring.Semi.Tropical

Contents

Tropical Semirings +

Synopsis

module Data.Monoid.Reducer

module Data.Ring.Semi

infinity :: Tropical a

newtype Tropical a = Tropical {

getTropical :: Maybe a

}

Documentation

module Data.Monoid.Reducer

module Data.Ring.Semi

Tropical Semirings +

infinity :: Tropical a

Source

newtype Tropical a

Source

The SemiRing (min,+) over a extended with infinity. + When a has a Num instance with an addition that respects order, then this is + transformed into a tropical semiring. It is assumed that 0 is the least element + of a. +

http://hal.archives-ouvertes.fr/docs/00/11/37/79/PDF/Tropical.pdf +

Constructors

Tropical

getTropical :: Maybe a

Instances

Functor Tropical

Pointed Tropical

Ord a => Reducer a (Tropical a)

Eq a => Eq (Tropical a)

Ord a => Ord (Tropical a)

Read a => Read (Tropical a)

Show a => Show (Tropical a)

Ord a => Monoid (Tropical a)

Num a => Multiplicative (Tropical a)

(Ord a, Num a) => LeftSemiNearRing (Tropical a)

(Ord a, Num a) => RightSemiNearRing (Tropical a)

(Ord a, Num a) => SemiRing (Tropical a)

Ord a => Reducer (Maybe a) (Tropical a)

Ord a => Reducer (MinPriority a) (Tropical a)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Ring-Semi.html hunk ./doc/html/monoids/Data-Ring-Semi.html 1 + + +Data.Ring.Semi

monoids-0.1.8: Lots of Monoids

Source code

Contents

Index

Data.Ring.Semi

Portability	non-portable (MPTCs)
Stability	experimental
Maintainer	libraries@haskell.org

Description

Synopsis

module Data.Ring.Semi.Near

class (RightSemiNearRing a, LeftSemiNearRing a) => SemiRing a

Documentation

module Data.Ring.Semi.Near

class (RightSemiNearRing a, LeftSemiNearRing a) => SemiRing a

Source

A SemiRing is an instance of both Multiplicative and Monoid where + times distributes over plus. +

Instances

SemiRing BoolRing

(Ord a, Num a) => SemiRing (Tropical a)

Ord a => SemiRing (Priority a)

(Bounded a, Ord a) => SemiRing (Order a)

Num a => SemiRing (FromNum a)

(SemiRing r, Module r m) => SemiRing (D r m)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Ring-Sugar.html hunk ./doc/html/monoids/Data-Ring-Sugar.html 1 + + +Data.Ring.Sugar

Data.Ring.Sugar

Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Description

Syntactic sugar for working with rings that conflicts with names from the Prelude. +

 import Prelude hiding ((-), (+), (*), negate, subtract)
+ import Data.Ring.Sugar
+

Documentation

module Data.Monoid.Multiplicative.Sugar

module Data.Ring.Semi.Near

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/Data-Ring.html hunk ./doc/html/monoids/Data-Ring.html 1 + + +Data.Ring

Data.Ring

Documentation

module Data.Group

module Data.Ring.Semi

class (Group a, SemiRing a) => Ring a

Source

Instances

Ring BoolRing

Num a => Ring (FromNum a)

(Ring r, Module r m, Group m) => Ring (D r m)

Produced by Haddock version 2.3.0

addfile ./doc/html/monoids/doc-index.html hunk ./doc/html/monoids/doc-index.html 1 + + +monoids-0.1.8: Lots of Monoids (Index)

*	Data.Monoid.Multiplicative.Sugar, Data.Ring.Sugar
*.	Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation
+	Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative.Sugar, Data.Ring.Sugar, Data.Group.Sugar
-	Data.Group.Sugar
.	Data.Monoid.Categorical
.*	Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation
<<<	Data.Monoid.Categorical
>>>	Data.Monoid.Categorical
Action
1 (Type/Class)	Data.Monoid.Monad
2 (Data Constructor)	Data.Monoid.Monad
ActionWith
1 (Type/Class)	Data.Monoid.Monad
2 (Data Constructor)	Data.Monoid.Monad
All
1 (Data Constructor)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
2 (Type/Class)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
all	Data.Monoid.Combinators
and	Data.Monoid.Combinators
Any
1 (Data Constructor)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
2 (Type/Class)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
any	Data.Monoid.Combinators
appEndo	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
BoolRing
1 (Type/Class)	Data.Ring.Boolean
2 (Data Constructor)	Data.Ring.Boolean
Category	Data.Monoid.Categorical
Char8
1 (Type/Class)	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
2 (Data Constructor)	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
CharReducer	Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words
concatMap	Data.Monoid.Combinators
cons	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Union, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding
cycle	Data.Monoid.Combinators
D	Data.Ring.Module.AutomaticDifferentiation
decode	Data.Monoid.Generator.LZ78
Dual
1 (Data Constructor)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
2 (Type/Class)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
Elem	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
elem	Data.Monoid.Combinators
empty	Data.Monoid.Union
emptyWith	Data.Monoid.Union
encode	Data.Monoid.Generator.LZ78
Endo
1 (Data Constructor)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
2 (Type/Class)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
Exp
1 (Type/Class)	Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
2 (Data Constructor)	Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
filter	Data.Monoid.Combinators
find	Data.Monoid.Combinators
First
1 (Data Constructor)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
2 (Type/Class)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
fold	Data.Monoid.Combinators
foldMap	Data.Monoid.Combinators
foldMapReduce	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding
foldReduce	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding
forM_	Data.Monoid.Combinators
for_	Data.Monoid.Combinators
fromChar	Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words
FromNum
1 (Type/Class)	Data.Ring.FromNum
2 (Data Constructor)	Data.Ring.FromNum
FromString
1 (Type/Class)	Data.Monoid.FromString
2 (Data Constructor)	Data.Monoid.FromString
GEndo
1 (Type/Class)	Data.Monoid.Categorical
2 (Data Constructor)	Data.Monoid.Categorical
Generator	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
getAction	Data.Monoid.Monad
getActionWith	Data.Monoid.Monad
getAll	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
getAny	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
getBoolRing	Data.Ring.Boolean
getChar8	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
getDual	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
getExp	Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
getFirst	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
getFromNum	Data.Ring.FromNum
getFromString	Data.Monoid.FromString
getGEndo	Data.Monoid.Categorical
getKeys	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
getLast	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
getLog	Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
getLZ78	Data.Monoid.Generator.LZ78
getMax	Data.Monoid.Ord
getMaxPriority	Data.Monoid.Ord
getMin	Data.Monoid.Ord
getMinPriority	Data.Monoid.Ord
getMon	Data.Monoid.Categorical
getOrder	Data.Ring.Semi.Ord
getProduct	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
getRLE	Data.Monoid.Lexical.RunLengthEncoding
getSelf	Data.Monoid.Self
getSum	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
getTraversal	Data.Monoid.Applicative
getTraversalWith	Data.Monoid.Applicative
getTropical	Data.Ring.Semi.Tropical
getUnion	Data.Monoid.Union
getUnionWith	Data.Monoid.Union
getValues	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
getWrappedApplicative	Data.Monoid.Applicative
getWrappedMonad	Data.Monoid.Monad
gnegate	Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation
Group	Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation
gsubtract	Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation
HasUnion	Data.Monoid.Union
HasUnionWith	Data.Monoid.Union
id	Data.Monoid.Categorical
infinity
1 (Function)	Data.Monoid.Ord
2 (Function)	Data.Ring.Semi.Tropical
invalidChar	Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words
Keys
1 (Type/Class)	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
2 (Data Constructor)	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
Last
1 (Data Constructor)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
2 (Type/Class)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
LeftModule	Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation
LeftSemiNearRing	Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
Lines	Data.Monoid.Lexical.Words
linesFrom	Data.Monoid.Lexical.Words
Log
1 (Type/Class)	Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
2 (Data Constructor)	Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
LZ78
1 (Type/Class)	Data.Monoid.Generator.LZ78
2 (Data Constructor)	Data.Monoid.Generator.LZ78
mapFrom	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
mapM_	Data.Monoid.Combinators
mappend	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Union, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Monoid.Ord, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
mapReduce	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
mapTo	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
Max
1 (Type/Class)	Data.Monoid.Ord
2 (Data Constructor)	Data.Monoid.Ord
MaxBound	Data.Ring.Semi.Ord
MaxPriority
1 (Type/Class)	Data.Monoid.Ord
2 (Data Constructor)	Data.Monoid.Ord
mconcat	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
mempty	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Union, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Monoid.Ord, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
Min
1 (Type/Class)	Data.Monoid.Ord
2 (Data Constructor)	Data.Monoid.Ord
MinBound	Data.Ring.Semi.Ord
minfinity	Data.Monoid.Ord
MinPriority
1 (Type/Class)	Data.Monoid.Ord
2 (Data Constructor)	Data.Monoid.Ord
minus	Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation
Module	Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation
Mon
1 (Type/Class)	Data.Monoid.Categorical
2 (Data Constructor)	Data.Monoid.Categorical
Monoid	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Union, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Monoid.Ord, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
Multiplicative	Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
negate	Data.Group.Sugar
nextTab	Data.Monoid.Lexical.SourcePosition
notElem	Data.Monoid.Combinators
one	Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
or	Data.Monoid.Combinators
Order
1 (Type/Class)	Data.Ring.Semi.Ord
2 (Data Constructor)	Data.Ring.Semi.Ord
plus	Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
Priority
1 (Type/Class)	Data.Ring.Semi.Ord
2 (Data Constructor)	Data.Ring.Semi.Ord
Product
1 (Data Constructor)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
2 (Type/Class)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
product	Data.Monoid.Combinators
pureUnit	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding
reduce	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
Reducer	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Union, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Ord, Data.Ring.Semi.Tropical, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding
repeat	Data.Monoid.Combinators
replicate
1 (Function)	Data.Group.Combinators
2 (Function)	Data.Monoid.Combinators
returnUnit	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding
RightModule	Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation
RightSemiNearRing	Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
Ring	Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation
RLE
1 (Type/Class)	Data.Monoid.Lexical.RunLengthEncoding
2 (Data Constructor)	Data.Monoid.Lexical.RunLengthEncoding
runLines	Data.Monoid.Lexical.Words
runUnlined	Data.Monoid.Lexical.Words
runUnspaced	Data.Monoid.Lexical.Words
runUTF8	Data.Monoid.Lexical.UTF8.Decoder
runWords	Data.Monoid.Lexical.Words
Self
1 (Type/Class)	Data.Monoid.Self
2 (Data Constructor)	Data.Monoid.Self
SemiRing	Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation
showSourcePosition	Data.Monoid.Lexical.SourcePosition
snoc	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Union, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding
snocAction	Data.Monoid.Monad
snocTraversal	Data.Monoid.Applicative
SourceColumn	Data.Monoid.Lexical.SourcePosition
sourceColumn	Data.Monoid.Lexical.SourcePosition
SourceLine	Data.Monoid.Lexical.SourcePosition
sourceLine	Data.Monoid.Lexical.SourcePosition
SourcePosition	Data.Monoid.Lexical.SourcePosition
startOfFile	Data.Monoid.Lexical.SourcePosition
subtract	Data.Group.Sugar
Sum
1 (Data Constructor)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
2 (Type/Class)	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding, Data.Ring.Module.AutomaticDifferentiation
sum	Data.Monoid.Combinators
times	Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
Traversal
1 (Type/Class)	Data.Monoid.Applicative
2 (Data Constructor)	Data.Monoid.Applicative
TraversalWith
1 (Type/Class)	Data.Monoid.Applicative
2 (Data Constructor)	Data.Monoid.Applicative
traverse_	Data.Monoid.Combinators
Tropical
1 (Type/Class)	Data.Ring.Semi.Tropical
2 (Data Constructor)	Data.Ring.Semi.Tropical
Union
1 (Type/Class)	Data.Monoid.Union
2 (Data Constructor)	Data.Monoid.Union
union	Data.Monoid.Union
UnionWith
1 (Type/Class)	Data.Monoid.Union
2 (Data Constructor)	Data.Monoid.Union
unionWith	Data.Monoid.Union
unit	Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Reducer.With, Data.Monoid.Union, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Ord, Data.Ring.Semi.Tropical, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Lexical.RunLengthEncoding
Unlined	Data.Monoid.Lexical.Words
Unspaced	Data.Monoid.Lexical.Words
UTF8	Data.Monoid.Lexical.UTF8.Decoder
Values
1 (Type/Class)	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
2 (Data Constructor)	Data.Monoid.Generator, Data.Monoid.Generator.LZ78, Data.Monoid.Combinators
withoutReducer	Data.Monoid.Reducer.With
WithReducer
1 (Type/Class)	Data.Monoid.Reducer.With
2 (Data Constructor)	Data.Monoid.Reducer.With
Words	Data.Monoid.Lexical.Words
wordsFrom	Data.Monoid.Lexical.Words
WrappedApplicative
1 (Type/Class)	Data.Monoid.Applicative
2 (Data Constructor)	Data.Monoid.Applicative
WrappedMonad
1 (Type/Class)	Data.Monoid.Monad
2 (Data Constructor)	Data.Monoid.Monad
zero	Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Tropical, Data.Ring.Semi.Ord, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation

addfile ./doc/html/monoids/haddock-util.js hunk ./doc/html/monoids/haddock-util.js 1 +// Haddock JavaScript utilities +function toggle(button,id) +{ + var n = document.getElementById(id).style; + if (n.display == "none") + { + button.src = "minus.gif"; + n.display = "block"; + } + else + { + button.src = "plus.gif"; + n.display = "none"; + } +} + + +var max_results = 75; // 50 is not enough to search for map in the base libraries +var shown_range = null; +var last_search = null; + +function quick_search() +{ + perform_search(false); +} + +function full_search() +{ + perform_search(true); +} + + +function perform_search(full) +{ + var text = document.getElementById("searchbox").value.toLowerCase(); + if (text == last_search && !full) return; + last_search = text; + + var table = document.getElementById("indexlist"); + var status = document.getElementById("searchmsg"); + var children = table.firstChild.childNodes; + + // first figure out the first node with the prefix + var first = bisect(-1); + var last = (first == -1 ? -1 : bisect(1)); + + if (first == -1) + { + table.className = ""; + status.innerHTML = "No results found, displaying all"; + } + else if (first == 0 && last == children.length - 1) + { + table.className = ""; + status.innerHTML = ""; + } + else if (last - first >= max_results && !full) + { + table.className = ""; + status.innerHTML = "More than " + max_results + ", press Search to display"; + } + else + { + // decide what you need to clear/show + if (shown_range) + setclass(shown_range[0], shown_range[1], "indexrow"); + setclass(first, last, "indexshow"); + shown_range = [first, last]; + table.className = "indexsearch"; + status.innerHTML = ""; + } + + + function setclass(first, last, status) + { + for (var i = first; i <= last; i++) + { + children[i].className = status; + } + } + + + // do a binary search, treating 0 as ... + // return either -1 (no 0's found) or location of most far match + function bisect(dir) + { + var first = 0, finish = children.length - 1; + var mid, success = false; + + while (finish - first > 3) + { + mid = Math.floor((finish + first) / 2); + + var i = checkitem(mid); + if (i == 0) i = dir; + if (i == -1) + finish = mid; + else + first = mid; + } + var a = (dir == 1 ? first : finish); + var b = (dir == 1 ? finish : first); + for (var i = b; i != a - dir; i -= dir) + { + if (checkitem(i) == 0) return i; + } + return -1; + } + + + // from an index, decide what the result is + // 0 = match, -1 is lower, 1 is higher + function checkitem(i) + { + var s = getitem(i).toLowerCase().substr(0, text.length); + if (s == text) return 0; + else return (s > text ? -1 : 1); + } + + + // from an index, get its string + // this abstracts over alternates + function getitem(i) + { + for ( ; i >= 0; i--) + { + var s = children[i].firstChild.firstChild.data; + if (s.indexOf(' ') == -1) + return s; + } + return ""; // should never be reached + } +} addfile ./doc/html/monoids/haddock.css hunk ./doc/html/monoids/haddock.css 1 +/* -------- Global things --------- */ + +BODY { + background-color: #ffffff; + color: #000000; + font-family: sans-serif; + } + +A:link { color: #0000e0; text-decoration: none } +A:visited { color: #0000a0; text-decoration: none } +A:hover { background-color: #e0e0ff; text-decoration: none } + +TABLE.vanilla { + width: 100%; + border-width: 0px; + /* I can't seem to specify cellspacing or cellpadding properly using CSS... */ +} + +TABLE.vanilla2 { + border-width: 0px; +} + +/* font is a little too small in MSIE */ +TT { font-size: 100%; } +PRE { font-size: 100%; } + +LI P { margin: 0pt } + +TD { + border-width: 0px; +} + +TABLE.narrow { + border-width: 0px; +} + +TD.s8 { height: 8px; } +TD.s15 { height: 15px; } + +SPAN.keyword { text-decoration: underline; } + +/* Resize the buttom image to match the text size */ +IMG.coll { width : 0.75em; height: 0.75em; margin-bottom: 0; margin-right: 0.5em } + +/* --------- Contents page ---------- */ + +DIV.node { + padding-left: 3em; +} + +DIV.cnode { + padding-left: 1.75em; +} + +SPAN.pkg { + position: absolute; + left: 50em; +} + +/* --------- Documentation elements ---------- */ + +TD.children { + padding-left: 25px; + } + +TD.synopsis { + padding: 2px; + background-color: #f0f0f0; + font-family: monospace + } + +TD.decl { + padding: 2px; + background-color: #f0f0f0; + font-family: monospace; + vertical-align: top; + } + +TD.topdecl { + padding: 2px; + background-color: #f0f0f0; + font-family: monospace; + vertical-align: top; +} + +TABLE.declbar { + border-spacing: 0px; + } + +TD.declname { + width: 100%; + } + +TD.declbut { + padding-left: 5px; + padding-right: 5px; + border-left-width: 1px; + border-left-color: #000099; + border-left-style: solid; + white-space: nowrap; + font-size: small; + } + +/* + arg is just like decl, except that wrapping is not allowed. It is + used for function and constructor arguments which have a text box + to the right, where if wrapping is allowed the text box squashes up + the declaration by wrapping it. +*/ +TD.arg { + padding: 2px; + background-color: #f0f0f0; + font-family: monospace; + vertical-align: top; + white-space: nowrap; + } + +TD.recfield { padding-left: 20px } + +TD.doc { + padding-top: 2px; + padding-left: 10px; + } + +TD.ndoc { + padding: 2px; + } + +TD.rdoc { + padding: 2px; + padding-left: 10px; + width: 100%; + } + +TD.body { + padding-left: 10px + } + +TD.pkg { + width: 100%; + padding-left: 10px +} + +TABLE.indexsearch TR.indexrow { + display: none; +} +TABLE.indexsearch TR.indexshow { + display: table-row; +} + +TD.indexentry { + vertical-align: top; + padding-right: 10px + } + +TD.indexannot { + vertical-align: top; + padding-left: 20px; + white-space: nowrap + } + +TD.indexlinks { + width: 100% + } + +/* ------- Section Headings ------- */ + +TD.section1 { + padding-top: 15px; + font-weight: bold; + font-size: 150% + } + +TD.section2 { + padding-top: 10px; + font-weight: bold; + font-size: 130% + } + +TD.section3 { + padding-top: 5px; + font-weight: bold; + font-size: 110% + } + +TD.section4 { + font-weight: bold; + font-size: 100% + } + +/* -------------- The title bar at the top of the page */ + +TD.infohead { + color: #ffffff; + font-weight: bold; + padding-right: 10px; + text-align: left; +} + +TD.infoval { + color: #ffffff; + padding-right: 10px; + text-align: left; +} + +TD.topbar { + background-color: #000099; + padding: 5px; +} + +TD.title { + color: #ffffff; + padding-left: 10px; + width: 100% + } + +TD.topbut { + padding-left: 5px; + padding-right: 5px; + border-left-width: 1px; + border-left-color: #ffffff; + border-left-style: solid; + white-space: nowrap; + } + +TD.topbut A:link { + color: #ffffff + } + +TD.topbut A:visited { + color: #ffff00 + } + +TD.topbut A:hover { + background-color: #6060ff; + } + +TD.topbut:hover { + background-color: #6060ff + } + +TD.modulebar { + background-color: #0077dd; + padding: 5px; + border-top-width: 1px; + border-top-color: #ffffff; + border-top-style: solid; + } + +/* --------- The page footer --------- */ + +TD.botbar { + background-color: #000099; + color: #ffffff; + padding: 5px + } +TD.botbar A:link { + color: #ffffff; + text-decoration: underline + } +TD.botbar A:visited { + color: #ffff00 + } +TD.botbar A:hover { + background-color: #6060ff + } + addfile ./doc/html/monoids/haskell_icon.gif binary ./doc/html/monoids/haskell_icon.gif oldhex * newhex *47494638376110001000f70f00000000800000008000808000000080800080008080c0c0c08080 *80ff000000ff00ffff000000ffff00ff00ffffffffff0000000000000000000000000000000000 *000000000000000000000000000000000000000000000000000000000000000000000000000000 *000000000000000000000000000000000000000000000000000000000000000000000000000000 *000000000000000000000000000000000000000000000000000000000000000000000000000000 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+----------------------------------------------------------------------------- +-- | +-- Module : Data.Group.Combinators +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : portable +-- +-- Utilities for working with Groups that conflict with names from the "Prelude". +-- +-- Intended to be imported qualified. +-- +-- > import Data.Group.Combinators as Group (replicate) +-- +----------------------------------------------------------------------------- + +module Data.Group.Combinators + ( module Data.Group + , replicate + ) where + +import Prelude hiding (replicate) +import Data.Group + +-- shamelessly stolen from Lennart Augustsson's post: +-- http://augustss.blogspot.com/2008/07/lost-and-found-if-i-write-108-in.html +-- adapted to groups, which can permit negative exponents +replicate :: (Group m, Integral n) => m -> n -> m +replicate x0 y0 + | y0 < 0 = f (gnegate x0) (negate y0) + | y0 == 0 = mempty + | otherwise = f x0 y0 + where + f x y + | even y = f (x `mappend` x) (y `quot` 2) + | y == 1 = x + | otherwise = g (x `mappend` x) ((y - 1) `quot` 2) x + g x y z + | even y = g (x `mappend` x) (y `quot` 2) z + | y == 1 = x `mappend` z + | otherwise = g (x `mappend` x) ((y - 1) `quot` 2) (x `mappend` z) + + + addfile ./doc/html/monoids/src/Data-Group-Sugar.html hunk ./doc/html/monoids/src/Data-Group-Sugar.html 1 + + + + +Data/Group/Sugar.hs + + + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Group.Sugar +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : portable +-- +-- Syntactic sugar for working with groups that conflicts with names from the "Prelude". +-- +-- > import Prelude hiding ((-), (+), negate, subtract) +-- > import Data.Group.Sugar +-- +----------------------------------------------------------------------------- + +module Data.Group.Sugar + ( module Data.Monoid.Additive.Sugar + , module Data.Group + , (-) + , negate + , subtract + ) where + +import Data.Monoid.Additive.Sugar +import Data.Group +import Prelude hiding ((-), negate, subtract) + +infixl 7 - + +(-) :: Group g => g -> g -> g +(-) = minus + +negate :: Group g => g -> g +negate = gnegate + +subtract :: Group g => g -> g -> g +subtract = gsubtract + + addfile ./doc/html/monoids/src/Data-Group.html hunk ./doc/html/monoids/src/Data-Group.html 1 + + + + +Data/Group.hs + + + +---------------------------------------------------------------------------- +-- | +-- Module : Data.Group +-- Copyright : 2007-2009 Edward Kmett +-- License : BSD +-- +-- Maintainer : Edward Kmett <ekmett@gmail.com> +-- Stability : experimental +-- Portability : portable +-- +-- Extends 'Monoid' to support 'Group' operations +----------------------------------------------------------------------------- + +module Data.Group + ( module Data.Monoid.Additive + , Group + , gnegate + , gsubtract + , minus + ) where + +import Data.Monoid.Additive +import Data.Monoid.Self +import Data.Monoid.FromString + +infixl 6 `minus` + +-- | Minimal complete definition: 'gnegate' or 'minus' +class Monoid a => Group a where + -- additive inverse + gnegate :: a -> a + minus :: a -> a -> a + gsubtract :: a -> a -> a + + gnegate = minus zero + a `minus` b = a `plus` gnegate b + a `gsubtract` b = gnegate a `plus` b + +instance Num a => Group (Sum a) where + gnegate = Sum . negate . getSum + Sum a `minus` Sum b = Sum (a - b) + +instance Fractional a => Group (Product a) where + gnegate = Product . negate . getProduct + Product a `minus` Product b = Product (a / b) + +instance Group a => Group (Dual a) where + gnegate = Dual . gnegate . getDual + +instance Group a => Group (Self a) where + gnegate = Self . gnegate . getSelf + Self a `minus` Self b = Self (a `minus` b) + +instance Group a => Group (FromString a) where + gnegate = FromString . gnegate . getFromString + FromString a `minus` FromString b = FromString (a `minus` b) + + addfile ./doc/html/monoids/src/Data-Monoid-Additive-Sugar.html hunk ./doc/html/monoids/src/Data-Monoid-Additive-Sugar.html 1 + + + + +Data/Monoid/Additive/Sugar.hs + + + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Additive.Sugar +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : portable +-- +-- Syntactic sugar for working with a 'Monoid' that conflicts with names from the "Prelude". +-- +-- > import Prelude hiding ((+)) +-- > import Data.Monoid.Additive.Sugar +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Additive.Sugar + ( module Data.Monoid.Additive + , (+) + ) where + +import Data.Monoid.Additive +import Prelude hiding ((+)) + +infixl 6 + + +(+) :: Monoid m => m -> m -> m +(+) = mappend + + addfile ./doc/html/monoids/src/Data-Monoid-Additive.html hunk ./doc/html/monoids/src/Data-Monoid-Additive.html 1 + + + + +Data/Monoid/Additive.hs + + + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Additive +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : portable +-- +-- More easily understood aliases for "mappend" and "mempty" +-- +-- > import Data.Monoid.Additive +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Additive + ( module Data.Monoid + , plus + , zero + ) where + +import Data.Monoid + +infixl 6 `plus` + +plus :: Monoid m => m -> m -> m +plus = mappend + +zero :: Monoid m => m +zero = mempty + + addfile ./doc/html/monoids/src/Data-Monoid-Applicative.html hunk ./doc/html/monoids/src/Data-Monoid-Applicative.html 1 + + + + +Data/Monoid/Applicative.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, GeneralizedNewtypeDeriving, FlexibleContexts, TypeOperators #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Applicative +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs) +-- +-- Monoids for working with an 'Applicative' 'Functor'. +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Applicative + ( module Data.Monoid.Reducer + , module Data.Ring.Semi.Near + , module Data.Ring.Module + , Traversal(Traversal,getTraversal) + , WrappedApplicative(WrappedApplicative,getWrappedApplicative) + , TraversalWith(TraversalWith,getTraversalWith) + , snocTraversal + ) where + +import Control.Applicative +import Data.Monoid.Reducer +import Data.Ring.Semi.Near +import Data.Ring.Module +import Control.Functor.Pointed + +-- | A 'Traversal' uses an glues together 'Applicative' actions with (*>) +-- in the manner of 'traverse_' from "Data.Foldable". Any values returned by +-- reduced actions are discarded. +newtype Traversal f = Traversal { getTraversal :: f () } + +instance Applicative f => Monoid (Traversal f) where + mempty = Traversal (pure ()) + Traversal a `mappend` Traversal b = Traversal (a *> b) + +instance Applicative f => Reducer (f a) (Traversal f) where + unit a = Traversal (a *> pure ()) + a `cons` Traversal b = Traversal (a *> b) + Traversal a `snoc` b = Traversal (a *> b *> pure ()) + +{-# RULES "unitTraversal" unit = Traversal #-} +{-# RULES "snocTraversal" snoc = snocTraversal #-} + +-- | Efficiently avoid needlessly rebinding when using 'snoc' on an action that already returns () +-- A rewrite rule automatically applies this when possible +snocTraversal :: Reducer (f ()) (Traversal f) => Traversal f -> f () -> Traversal f +snocTraversal a = mappend a . Traversal + + +-- | A 'WrappedApplicative' turns any 'Alternative' instance into a 'Monoid'. +-- It also provides a 'Multiplicative' instance for an 'Applicative' functor wrapped around a 'Monoid' +-- and asserts that any 'Alternative' applied to a 'Monoid' forms a 'LeftSemiNearRing' +-- under these operations. + +newtype WrappedApplicative f a = WrappedApplicative { getWrappedApplicative :: f a } + deriving (Eq,Ord,Show,Read,Functor,Pointed,Applicative,Alternative,Copointed) + +instance Alternative f => Monoid (WrappedApplicative f a) where + mempty = empty + WrappedApplicative a `mappend` WrappedApplicative b = WrappedApplicative (a <|> b) + +instance (Alternative f, Monoid a) => Multiplicative (WrappedApplicative f a) where + one = pure mempty + times = liftA2 mappend + +instance (Alternative f, c `Reducer` a) => Reducer c (WrappedApplicative f a) where + unit = WrappedApplicative . pure . unit + +instance (Alternative f, Monoid a) => LeftSemiNearRing (WrappedApplicative f a) + +-- | if @m@ is a 'Module' and @f@ is a 'Applicative' then @f `TraversalWith` m@ is a 'Module' as well + +newtype TraversalWith f m = TraversalWith { getTraversalWith :: f m } + deriving (Eq,Ord,Show,Read,Functor,Pointed,Applicative,Alternative,Copointed) + +instance (Monoid m, Applicative f) => Monoid (f `TraversalWith` m) where + mempty = pure mempty + mappend = liftA2 mappend + +instance (Group m, Applicative f) => Group (f `TraversalWith` m) where + gnegate = fmap gnegate + minus = liftA2 minus + gsubtract = liftA2 gsubtract + +instance (c `Reducer` m, Applicative f) => Reducer c (f `TraversalWith` m) where + unit = pure . unit + +instance (LeftModule r m, Applicative f) => LeftModule r (f `TraversalWith` m) where + x *. m = (x *.) <$> m + +instance (RightModule r m, Applicative f) => RightModule r (f `TraversalWith` m) where + m .* y = (.* y) <$> m + +instance (Module r m, Applicative f) => Module r (f `TraversalWith` m) + + addfile ./doc/html/monoids/src/Data-Monoid-Categorical.html hunk ./doc/html/monoids/src/Data-Monoid-Categorical.html 1 + + + + +Data/Monoid/Categorical.hs + + + +{-# LANGUAGE GADTs, FlexibleInstances, MultiParamTypeClasses #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Categorical +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : portable +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Categorical + ( module Data.Monoid.Reducer + , module Control.Category + -- * Generalized Endo + , GEndo(GEndo, getGEndo) + -- * Monoids as Categories + , Mon(Mon) + , getMon + ) where + +import Prelude hiding ((.),id) +import Data.Monoid.Reducer +import Control.Category + +-- | The 'Monoid' of the endomorphisms over some object in an arbitrary 'Category'. +data GEndo k a = GEndo { getGEndo :: k a a } + +instance Category k => Monoid (GEndo k a) where + mempty = GEndo id + GEndo f `mappend` GEndo g = GEndo (f . g) + +-- | A 'Monoid' is just a 'Category' with one object. +data Mon m n o where + Mon :: Monoid m => m -> Mon m a a + +-- | Extract the 'Monoid' from its representation as a 'Category' +getMon :: Mon m m m -> m +getMon (Mon m) = m + +instance Monoid m => Category (Mon m) where + id = Mon mempty + Mon a . Mon b = Mon (a `mappend` b) + +instance Monoid m => Monoid (Mon m m m) where + mempty = id + mappend = (.) + +instance (c `Reducer` m) => Reducer c (Mon m m m) where + unit = Mon . unit + + addfile ./doc/html/monoids/src/Data-Monoid-Combinators.html hunk ./doc/html/monoids/src/Data-Monoid-Combinators.html 1 + + + + +Data/Monoid/Combinators.hs + + + +{-# LANGUAGE UndecidableInstances, TypeOperators, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances, TypeFamilies #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Combinators +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (type families, MPTCs) +-- +-- Utilities for working with Monoids that conflict with names from the "Prelude", +-- "Data.Foldable", "Control.Monad" or elsewhere. Intended to be imported qualified. +-- +-- > import Data.Group.Combinators as Monoid +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Combinators + ( module Data.Monoid.Generator + -- * Monadic Reduction + , mapM_ + , forM_ + -- * Applicative Reduction + , traverse_ + , for_ + -- * Logical Reduction + , and + , or + , any + , all + -- * Monoidal Reduction + , foldMap + , fold + -- * List-Like Reduction + , concatMap + , elem + , filter + , find + , sum + , product + , notElem + -- * List-Like Monoid Generation + , repeat + , replicate + , cycle + ) where + +import Prelude hiding (mapM_, any, elem, filter, concatMap, and, or, all, sum, product, notElem, replicate, cycle, repeat) +import Control.Applicative +import Data.Monoid.Generator +import Data.Monoid.Applicative +import Data.Monoid.Self +import Data.Monoid.Monad + +-- | Efficiently 'mapReduce' a 'Generator' using the 'Traversal' monoid. A specialized version of its namesake in "Data.Foldable" +traverse_ :: (Generator c, Applicative f) => (Elem c -> f b) -> c -> f () +traverse_ f = getTraversal . mapReduce f + +-- | flipped 'traverse_' as in "Data.Foldable" +for_ :: (Generator c, Applicative f) => c -> (Elem c -> f b) -> f () +for_ = flip traverse_ + +-- | Efficiently 'mapReduce' a 'Generator' using the 'Action' monoid. A specialized version of its namesake from "Data.Foldable" and "Control.Monad" +mapM_ :: (Generator c, Monad m) => (Elem c -> m b) -> c -> m () +mapM_ f = getAction . mapReduce f + +-- | flipped 'mapM_' as in "Data.Foldable" and "Control.Monad" +forM_ :: (Generator c, Monad m) => c -> (Elem c -> m b) -> m () +forM_ = flip mapM_ + +-- | Efficiently 'mapReduce' a 'Generator' using the 'Self' monoid. A specialized version of its namesake from "Data.Foldable" +foldMap :: (Monoid m, Generator c) => (Elem c -> m) -> c -> m +foldMap f = getSelf . mapReduce f + +-- | Efficiently 'reduce' a 'Generator' using the 'Self' monoid. A specialized version of its namesake from "Data.Foldable" +fold :: (Monoid m, Generator c, Elem c ~ m) => c -> m +fold = getSelf . reduce + +-- | A further specialization of "foldMap" +concatMap :: Generator c => (Elem c -> [b]) -> c -> [b] +concatMap = foldMap + +-- | Efficiently 'reduce' a 'Generator' that contains values of type 'Bool' +and :: (Generator c, Elem c ~ Bool) => c -> Bool +and = getAll . reduce + +-- | Efficiently 'reduce' a 'Generator' that contains values of type 'Bool' +or :: (Generator c, Elem c ~ Bool) => c -> Bool +or = getAny . reduce + +-- | Efficiently 'mapReduce' any 'Generator' checking to see if any of its values match the supplied predicate +any :: Generator c => (Elem c -> Bool) -> c -> Bool +any f = getAny . mapReduce f + +-- | Efficiently 'mapReduce' any 'Generator' checking to see if all of its values match the supplied predicate +all :: Generator c => (Elem c -> Bool) -> c -> Bool +all f = getAll . mapReduce f + +-- | Efficiently 'mapReduce' any 'Generator' using the 'Sum' 'Monoid' +sum :: (Generator c, Num (Elem c)) => c -> Elem c +sum = getSum . reduce + +-- | Efficiently 'mapReduce' any 'Generator' using the 'Product' 'Monoid' +product :: (Generator c, Num (Elem c)) => c -> Elem c +product = getProduct . reduce + +-- | Check to see if 'any' member of the 'Generator' matches the supplied value +elem :: (Generator c, Eq (Elem c)) => Elem c -> c -> Bool +elem = any . (==) + +-- | Check to make sure that the supplied value is not a member of the 'Generator' +notElem :: (Generator c, Eq (Elem c)) => Elem c -> c -> Bool +notElem x = not . elem x + +-- | Efficiently 'mapReduce' a subset of the elements in a 'Generator' +filter :: (Generator c, Elem c `Reducer` m) => (Elem c -> Bool) -> c -> m +filter p = foldMap f where + f x | p x = unit x + | otherwise = mempty + +-- | A specialization of 'filter' using the 'First' 'Monoid', analogous to 'Data.List.find' +find :: Generator c => (Elem c -> Bool) -> c -> Maybe (Elem c) +find p = getFirst . filter p + +-- | A generalization of 'Data.List.replicate' to an arbitrary 'Monoid'. Adapted from +-- <http://augustss.blogspot.com/2008/07/lost-and-found-if-i-write-108-in.html> +replicate :: (Monoid m, Integral n) => m -> n -> m +replicate x0 y0 + | y0 < 0 = mempty -- error "negative length" + | y0 == 0 = mempty + | otherwise = f x0 y0 + where + f x y + | even y = f (x `mappend` x) (y `quot` 2) + | y == 1 = x + | otherwise = g (x `mappend` x) ((y - 1) `quot` 2) x + g x y z + | even y = g (x `mappend` x) (y `quot` 2) z + | y == 1 = x `mappend` z + | otherwise = g (x `mappend` x) ((y - 1) `quot` 2) (x `mappend` z) + +-- | A generalization of 'Data.List.cycle' to an arbitrary 'Monoid'. May fail to terminate for some values in some monoids. +cycle :: Monoid m => m -> m +cycle xs = xs' where xs' = xs `mappend` xs' + +-- | A generalization of 'Data.List.repeat' to an arbitrary 'Monoid'. May fail to terminate for some values in some monoids. +repeat :: (e `Reducer` m) => e -> m +repeat x = xs where xs = cons x xs + + addfile ./doc/html/monoids/src/Data-Monoid-FromString.html hunk ./doc/html/monoids/src/Data-Monoid-FromString.html 1 + + + + +Data/Monoid/FromString.hs + + + +{-# LANGUAGE FlexibleContexts, FlexibleInstances, MultiParamTypeClasses, UndecidableInstances #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Additive +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (overloaded strings, MPTCs) +-- +-- Transform any 'Char' 'Reducer' into an 'IsString' instance so it can be +-- used directly with overloaded string literals. +-- +----------------------------------------------------------------------------- + +module Data.Monoid.FromString + ( module Data.Monoid.Reducer + , FromString(FromString,getFromString) + ) where + +import Control.Functor.Pointed +import Data.Monoid.Generator +import Data.Monoid.Reducer +import Data.Monoid.Instances () +import GHC.Exts + +data FromString m = FromString { getFromString :: m } + +instance Monoid m => Monoid (FromString m) where + mempty = FromString mempty + FromString a `mappend` FromString b = FromString (a `mappend` b) + +instance (Char `Reducer` m) => Reducer Char (FromString m) where + unit = FromString . unit + +instance (Char `Reducer` m) => IsString (FromString m) where + fromString = FromString . reduce + +instance Pointed FromString where + point = FromString + +instance Copointed FromString where + extract = getFromString + +instance Functor FromString where + fmap f (FromString x) = FromString (f x) + + addfile ./doc/html/monoids/src/Data-Monoid-Generator-LZ78.html hunk ./doc/html/monoids/src/Data-Monoid-Generator-LZ78.html 1 + + + + +Data/Monoid/Generator/LZ78.hs + + + +{-# LANGUAGE TypeFamilies, MultiParamTypeClasses #-} +module Data.Monoid.Generator.LZ78 + ( module Data.Monoid.Generator + , LZ78(LZ78, getLZ78) + , decode + , encode + ) where + +import qualified Data.Sequence as Seq +import Data.Sequence (Seq,(|>)) +import qualified Data.Map as Map +import Data.Map (Map) +import Data.Monoid.Generator +import Data.Monoid.Self + +newtype LZ78 a = LZ78 { getLZ78 :: [(Int,a)] } + +emptyDict :: Monoid m => Seq m +emptyDict = Seq.singleton mempty + +instance Generator (LZ78 a) where + type Elem (LZ78 a) = a + mapTo f m (LZ78 xs) = mapTo' f m emptyDict xs + +mapTo' :: (e `Reducer` m) => (a -> e) -> m -> Seq m -> [(Int,a)] -> m +mapTo' _ m _ [] = m +mapTo' f m s ((w,c):ws) = mapTo' f (m `mappend` v) (s |> v) ws + where + v = Seq.index s w `mappend` unit (f c) + +decode :: LZ78 a -> [a] +decode = reduce + +encode :: Ord a => [a] -> LZ78 a +encode = LZ78 . encode' Map.empty 1 0 + +encode' :: Ord a => Map (Int,a) Int -> Int -> Int -> [a] -> [(Int,a)] +encode' _ _ p [c] = [(p,c)] +encode' d f p (c:cs) = case Map.lookup (p,c) d of + Just p' -> encode' d f p' cs + Nothing -> (p,c):encode' (Map.insert (p,c) f d) (succ f) 0 cs +encode' _ _ _ [] = [] + + +-- QuickCheck properties, this holds as long as Eq is structural +prop_DecodeEncode :: Ord a => [a] -> Bool +prop_DecodeEncode xs = decode (encode xs) == xs + + addfile ./doc/html/monoids/src/Data-Monoid-Generator.html hunk ./doc/html/monoids/src/Data-Monoid-Generator.html 1 + + + + +Data/Monoid/Generator.hs + + + +{-# LANGUAGE UndecidableInstances, TypeOperators, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances, TypeFamilies #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Generator +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : portable +-- +-- A 'Generator' @c@ is a possibly-specialized container, which contains values of +-- type 'Elem' @c@, and which knows how to efficiently apply a 'Reducer' to extract +-- an answer. +-- +-- Since a 'Generator' is not polymorphic in its contents, it is more specialized +-- than "Data.Foldable.Foldable", and a 'Reducer' may supply efficient left-to-right +-- and right-to-left reduction strategies that a 'Generator' may avail itself of. +----------------------------------------------------------------------------- + +module Data.Monoid.Generator + ( module Data.Monoid.Reducer + , Generator + , Elem + , mapReduce + , mapTo + , mapFrom + , reduce + , Keys(Keys, getKeys) + , Values(Values, getValues) + , Char8(Char8, getChar8) + ) where + +import Data.Array +import Data.Word (Word8) +import Data.Text (Text) +import Data.Foldable (fold,foldMap) +import qualified Data.Text as Text +import qualified Data.ByteString as Strict (ByteString, foldl') +import qualified Data.ByteString.Char8 as Strict8 (foldl') +import qualified Data.ByteString.Lazy as Lazy (ByteString, toChunks) +import qualified Data.ByteString.Lazy.Char8 as Lazy8 (toChunks) +import qualified Data.Sequence as Seq +import Data.FingerTree (Measured, FingerTree) +import Data.Sequence (Seq) +import qualified Data.Set as Set +import Data.Set (Set) +import qualified Data.IntSet as IntSet +import Data.IntSet (IntSet) +import qualified Data.IntMap as IntMap +import Data.IntMap (IntMap) +import qualified Data.Map as Map +import Data.Map (Map) + +import Control.Parallel.Strategies +import Data.Monoid.Reducer + +-- | minimal definition 'mapReduce' or 'mapTo' +class Generator c where + type Elem c :: * + mapReduce :: (e `Reducer` m) => (Elem c -> e) -> c -> m + mapTo :: (e `Reducer` m) => (Elem c -> e) -> m -> c -> m + mapFrom :: (e `Reducer` m) => (Elem c -> e) -> c -> m -> m + + mapReduce f = mapTo f mempty + mapTo f m = mappend m . mapReduce f + mapFrom f = mappend . mapReduce f + +instance Generator Strict.ByteString where + type Elem Strict.ByteString = Word8 + mapTo f = Strict.foldl' (\a -> snoc a . f) + +instance Generator Lazy.ByteString where + type Elem Lazy.ByteString = Word8 + mapReduce f = fold . parMap rwhnf (mapReduce f) . Lazy.toChunks + +instance Generator Text where + type Elem Text = Char + mapTo f = Text.foldl' (\a -> snoc a . f) + +instance Generator [c] where + type Elem [c] = c + mapReduce f = foldMap (unit . f) + +instance Measured v e => Generator (FingerTree v e) where + type Elem (FingerTree v e) = e + mapReduce f = foldMap (unit . f) + +instance Generator (Seq c) where + type Elem (Seq c) = c + mapReduce f = foldMap (unit . f) + +instance Generator IntSet where + type Elem IntSet = Int + mapReduce f = mapReduce f . IntSet.toList + +instance Generator (Set a) where + type Elem (Set a) = a + mapReduce f = mapReduce f . Set.toList + +instance Generator (IntMap v) where + type Elem (IntMap v) = (Int,v) + mapReduce f = mapReduce f . IntMap.toList + +instance Generator (Map k v) where + type Elem (Map k v) = (k,v) + mapReduce f = mapReduce f . Map.toList + +instance Ix i => Generator (Array i e) where + type Elem (Array i e) = (i,e) + mapReduce f = mapReduce f . assocs + +-- | a 'Generator' transformer that asks only for the keys of an indexed container +newtype Keys c = Keys { getKeys :: c } + +instance Generator (Keys (IntMap v)) where + type Elem (Keys (IntMap v)) = Int + mapReduce f = mapReduce f . IntMap.keys . getKeys + +instance Generator (Keys (Map k v)) where + type Elem (Keys (Map k v)) = k + mapReduce f = mapReduce f . Map.keys . getKeys + +instance Ix i => Generator (Keys (Array i e)) where + type Elem (Keys (Array i e)) = i + mapReduce f = mapReduce f . range . bounds . getKeys + +-- | a 'Generator' transformer that asks only for the values contained in an indexed container +newtype Values c = Values { getValues :: c } + +instance Generator (Values (IntMap v)) where + type Elem (Values (IntMap v)) = v + mapReduce f = mapReduce f . IntMap.elems . getValues + +instance Generator (Values (Map k v)) where + type Elem (Values (Map k v)) = v + mapReduce f = mapReduce f . Map.elems . getValues + +instance Ix i => Generator (Values (Array i e)) where + type Elem (Values (Array i e)) = e + mapReduce f = mapReduce f . elems . getValues + +-- | a 'Generator' transformer that treats 'Word8' as 'Char' +-- This lets you use a 'ByteString' as a 'Char' source without going through a 'Monoid' transformer like 'UTF8' +newtype Char8 c = Char8 { getChar8 :: c } + +instance Generator (Char8 Strict.ByteString) where + type Elem (Char8 Strict.ByteString) = Char + mapTo f m = Strict8.foldl' (\a -> snoc a . f) m . getChar8 + +instance Generator (Char8 Lazy.ByteString) where + type Elem (Char8 Lazy.ByteString) = Char + mapReduce f = fold . parMap rwhnf (mapReduce f . Char8) . Lazy8.toChunks . getChar8 + +{-# SPECIALIZE reduce :: (Word8 `Reducer` m) => Strict.ByteString -> m #-} +{-# SPECIALIZE reduce :: (Word8 `Reducer` m) => Lazy.ByteString -> m #-} +{-# SPECIALIZE reduce :: (Char `Reducer` m) => Char8 Strict.ByteString -> m #-} +{-# SPECIALIZE reduce :: (Char `Reducer` m) => Char8 Lazy.ByteString -> m #-} +{-# SPECIALIZE reduce :: (c `Reducer` m) => [c] -> m #-} +{-# SPECIALIZE reduce :: (Generator (FingerTree v e), e `Reducer` m) => FingerTree v e -> m #-} +{-# SPECIALIZE reduce :: (Char `Reducer` m) => Text -> m #-} +{-# SPECIALIZE reduce :: (e `Reducer` m) => Seq e -> m #-} +{-# SPECIALIZE reduce :: (Int `Reducer` m) => IntSet -> m #-} +{-# SPECIALIZE reduce :: (a `Reducer` m) => Set a -> m #-} +{-# SPECIALIZE reduce :: ((Int,v) `Reducer` m) => IntMap v -> m #-} +{-# SPECIALIZE reduce :: ((k,v) `Reducer` m) => Map k v -> m #-} +{-# SPECIALIZE reduce :: (Int `Reducer` m) => Keys (IntMap v) -> m #-} +{-# SPECIALIZE reduce :: (k `Reducer` m) => Keys (Map k v) -> m #-} +{-# SPECIALIZE reduce :: (v `Reducer` m) => Values (IntMap v) -> m #-} +{-# SPECIALIZE reduce :: (v `Reducer` m) => Values (Map k v) -> m #-} +-- | Apply a 'Reducer' directly to the elements of a 'Generator' +reduce :: (Generator c, Elem c `Reducer` m) => c -> m +reduce = mapReduce id + + addfile ./doc/html/monoids/src/Data-Monoid-Lexical-RunLengthEncoding.html hunk ./doc/html/monoids/src/Data-Monoid-Lexical-RunLengthEncoding.html 1 + + + + +Data/Monoid/Lexical/RunLengthEncoding.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Lexical.RunLengthEncoding +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs) +-- +-- A simple 'Monoid' transformer that turns any monoidal 'Reducer' into a +-- a reducer that expects to be supplied both a run length @n@ with each item +-- and which efficiently exponentiates the result of 'unit' @n@ times through +-- 'replicate'. +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Lexical.RunLengthEncoding + ( module Data.Monoid.Reducer + , RLE(RLE,getRLE) + ) where + +import Prelude hiding (replicate) +import Data.Monoid.Reducer +import Data.Monoid.Combinators (replicate) + +newtype RLE n m = RLE { getRLE :: m } + +instance (Integral n, Monoid m) => Monoid (RLE n m) where + mempty = RLE mempty + RLE a `mappend` RLE b = RLE (a `mappend` b) + +instance (Integral n, Reducer c m) => Reducer (n,c) (RLE n m) where + unit ~(n,c) = RLE $ replicate (unit c) n + + addfile ./doc/html/monoids/src/Data-Monoid-Lexical-SourcePosition.html hunk ./doc/html/monoids/src/Data-Monoid-Lexical-SourcePosition.html 1 + + + + +Data/Monoid/Lexical/SourcePosition.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, OverloadedStrings #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Lexical.SourcePosition +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs, OverloadedStrings) +-- +-- Incrementally determine locations in a source file through local information +-- This allows for efficient recomputation of line #s and token locations +-- while the file is being interactively updated by storing this as a supplemental +-- measure on a 'FingerTree'. +-- +-- The general idea is to use this as part of a measure in a 'FingerTree' so you can +-- use `mappend` to prepend a 'startOfFile' with the file information. +----------------------------------------------------------------------------- + +module Data.Monoid.Lexical.SourcePosition + ( module Data.Monoid.Reducer.Char + , nextTab + , SourcePosition + , SourceLine + , SourceColumn + , sourceLine + , sourceColumn + , startOfFile + , showSourcePosition + ) where + +import Prelude hiding (lex) +import Control.Functor.Extras +import Control.Functor.Pointed +import Data.Monoid.Reducer.Char +import Data.Monoid.Generator +import Data.String + +type SourceLine = Int +type SourceColumn = Int + +-- | A 'Monoid' of partial information about locations in a source file. +-- This is polymorphic in the kind of information you want to maintain about each source file. +data SourcePosition file + = Pos file {-# UNPACK #-} !SourceLine !SourceColumn -- ^ An absolute position in a file is known, or an overriding #line directive has been seen + | Lines {-# UNPACK #-} !SourceLine !SourceColumn -- ^ We've seen some carriage returns. + | Columns {-# UNPACK #-} !SourceColumn -- ^ We've only seen part of a line. + | Tab {-# UNPACK #-} !SourceColumn !SourceColumn -- ^ We have an unhandled tab to deal with. + deriving (Read,Show,Eq) + +-- | Compute the location of the next standard 8-column aligned tab +nextTab :: Int -> Int +nextTab x = x + (8 - (x-1) `mod` 8) + +instance Functor SourcePosition where + fmap g (Pos f l c) = Pos (g f) l c + fmap _ (Lines l c) = Lines l c + fmap _ (Columns c) = Columns c + fmap _ (Tab x y) = Tab x y + +instance Pointed SourcePosition where + point f = Pos f 1 1 + +instance FunctorZero SourcePosition where + fzero = mempty + +instance FunctorPlus SourcePosition where + fplus = mappend + +instance IsString (SourcePosition file) where + fromString = reduce + +-- accumulate partial information +instance Monoid (SourcePosition file) where + mempty = Columns 0 + + Pos f l _ `mappend` Lines m d = Pos f (l + m) d + Pos f l c `mappend` Columns d = Pos f l (c + d) + Pos f l c `mappend` Tab x y = Pos f l (nextTab (c + x) + y) + Lines l _ `mappend` Lines m d = Lines (l + m) d + Lines l c `mappend` Columns d = Lines l (c + d) + Lines l c `mappend` Tab x y = Lines l (nextTab (c + x) + y) + Columns c `mappend` Columns d = Columns (c + d) + Columns c `mappend` Tab x y = Tab (c + x) y + Tab _ _ `mappend` Lines m d = Lines m d + Tab x y `mappend` Columns d = Tab x (y + d) + Tab x y `mappend` Tab x' y' = Tab x (nextTab (y + x') + y') + _ `mappend` pos = pos + +instance Reducer Char (SourcePosition file) where + unit '\n' = Lines 1 1 + unit '\t' = Tab 0 0 + unit _ = Columns 1 + +-- Indicate that we ignore invalid characters to the UTF8 parser +instance CharReducer (SourcePosition file) + +-- | lift information about a source file into a starting 'SourcePosition' for that file +startOfFile :: f -> SourcePosition f +startOfFile = point + +-- | extract partial information about the current column, even in the absence of knowledge of the source file +sourceColumn :: SourcePosition f -> Maybe SourceColumn +sourceColumn (Pos _ _ c) = Just c +sourceColumn (Lines _ c) = Just c +sourceColumn _ = Nothing + +-- | extract partial information about the current line number if possible +sourceLine :: SourcePosition f -> Maybe SourceLine +sourceLine (Pos _ l _) = Just l +sourceLine _ = Nothing + +-- | extract the standard format for an absolute source position +showSourcePosition :: SourcePosition String -> String +showSourcePosition pos = showSourcePosition' (point "-" `mappend` pos) where + showSourcePosition' (Pos f l c) = f ++ ":" ++ show l ++ ":" ++ show c + showSourcePosition' _ = undefined + + addfile ./doc/html/monoids/src/Data-Monoid-Lexical-UTF8-Decoder.html hunk ./doc/html/monoids/src/Data-Monoid-Lexical-UTF8-Decoder.html 1 + + + + +Data/Monoid/Lexical/UTF8/Decoder.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Lexical.UTF8.Decoder +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs) +-- +-- UTF8 encoded unicode characters can be parsed both forwards and backwards, +-- since the start of each 'Char' is clearly marked. This 'Monoid' accumulates +-- information about the characters represented and reduces that information +-- using a 'CharReducer', which is just a 'Reducer' 'Monoid' that knows what +-- it wants to do about an 'invalidChar' -- a string of 'Word8' values that +-- don't form a valid UTF8 character. +-- +-- As this monoid parses chars it just feeds them upstream to the underlying +-- CharReducer. Efficient left-to-right and right-to-left traversals are +-- supplied so that a lazy 'ByteString' can be parsed efficiently by +-- chunking it into strict chunks, and batching the traversals over each +-- before stitching the edges together. +-- +-- Because this needs to be a 'Monoid' and should return the exact same result +-- regardless of forward or backwards parsing, it chooses to parse only +-- canonical UTF8 unlike most Haskell UTF8 parsers, which will blissfully +-- accept illegal alternative long encodings of a character. +-- +-- This actually fixes a potential class of security issues in some scenarios: +-- +-- <http://prowebdevelopmentblog.com/content/big-overhaul-java-utf-8-charset> +-- +-- NB: Due to naive use of a list to track the tail of an unfinished character +-- this may exhibit @O(n^2)@ behavior parsing backwards along an invalid sequence +-- of a large number of bytes that all claim to be in the tail of a character. +-- +----------------------------------------------------------------------------- + + +module Data.Monoid.Lexical.UTF8.Decoder + ( module Data.Monoid.Reducer.Char + , UTF8 + , runUTF8 + ) where + +import Data.Bits (shiftL,(.&.),(.|.)) +import Data.Word (Word8) + + +import Control.Functor.Pointed + +import Data.Monoid.Reducer.Char + +-- Incrementally reduce canonical RFC3629 UTF-8 Characters + +-- utf8 characters are at most 4 characters long, so we need only retain state for 3 of them +-- moreover their length is able to be determined a priori, so lets store that intrinsically in the constructor +data H = H0 + | H2_1 {-# UNPACK #-} !Word8 + | H3_1 {-# UNPACK #-} !Word8 + | H3_2 {-# UNPACK #-} !Word8 !Word8 + | H4_1 {-# UNPACK #-} !Word8 + | H4_2 {-# UNPACK #-} !Word8 !Word8 + | H4_3 {-# UNPACK #-} !Word8 !Word8 !Word8 + +-- words expressing the tail of a character, each between 0x80 and 0xbf +-- this is arbitrary length to simplify making the parser truly monoidal +-- this probably means we have O(n^2) worst case performance in the face of very long runs of chars that look like 10xxxxxx +type T = [Word8] + +-- S is a segment that contains a possible tail of a character, the result of reducing some full characters, and the start of another character +-- T contains a list of bytes each between 0x80 and 0xbf +data UTF8 m = S T m !H + | T T + +-- flush any extra characters in a head, when the next character isn't between 0x80 and 0xbf +flushH :: CharReducer m => H -> m +flushH (H0) = mempty +flushH (H2_1 x) = invalidChar [x] +flushH (H3_1 x) = invalidChar [x] +flushH (H3_2 x y) = invalidChar [x,y] +flushH (H4_1 x) = invalidChar [x] +flushH (H4_2 x y) = invalidChar [x,y] +flushH (H4_3 x y z) = invalidChar [x,y,z] + +-- flush a character tail +flushT :: CharReducer m => [Word8] -> m +flushT = invalidChar + +snocH :: CharReducer m => H -> Word8 -> (m -> H -> UTF8 m) -> m -> UTF8 m +snocH H0 c k m + | c < 0x80 = k (m `mappend` b1 c) H0 + | c < 0xc0 = k (m `mappend` invalidChar [c]) H0 + | c < 0xe0 = k m (H2_1 c) + | c < 0xf0 = k m (H3_1 c) + | c < 0xf5 = k m (H4_1 c) + | otherwise = k (m `mappend` invalidChar [c]) H0 +snocH (H2_1 c) d k m + | d >= 0x80 && d < 0xc0 = k (m `mappend` b2 c d) H0 + | otherwise = k (m `mappend` invalidChar [c]) H0 +snocH (H3_1 c) d k m + | d >= 0x80 && d < 0xc0 = k m (H3_2 c d) + | otherwise = k (m `mappend` invalidChar [c]) H0 +snocH (H3_2 c d) e k m + | d >= 0x80 && d < 0xc0 = k (m `mappend` b3 c d e) H0 + | otherwise = k (m `mappend` invalidChar [c,d]) H0 +snocH (H4_1 c) d k m + | d >= 0x80 && d < 0xc0 = k m (H4_2 c d) + | otherwise = k (m `mappend` invalidChar [c,d]) H0 +snocH (H4_2 c d) e k m + | d >= 0x80 && d < 0xc0 = k m (H4_3 c d e) + | otherwise = k (m `mappend` invalidChar [c,d,e]) H0 +snocH (H4_3 c d e) f k m + | d >= 0x80 && d < 0xc0 = k (m `mappend` b4 c d e f) H0 + | otherwise = k (m `mappend` invalidChar [c,d,e,f]) H0 + +mask :: Word8 -> Word8 -> Int +mask c m = fromEnum (c .&. m) + +combine :: Int -> Word8 -> Int +combine a r = shiftL a 6 .|. fromEnum (r .&. 0x3f) + +b1 :: CharReducer m => Word8 -> m +b1 c | c < 0x80 = fromChar . toEnum $ fromEnum c + | otherwise = invalidChar [c] + +b2 :: CharReducer m => Word8 -> Word8 -> m +b2 c d | valid_b2 c d = fromChar (toEnum (combine (mask c 0x1f) d)) + | otherwise = invalidChar [c,d] + +b3 :: CharReducer m => Word8 -> Word8 -> Word8 -> m +b3 c d e | valid_b3 c d e = fromChar (toEnum (combine (combine (mask c 0x0f) d) e)) + | otherwise = invalidChar [c,d,e] + + +b4 :: CharReducer m => Word8 -> Word8 -> Word8 -> Word8 -> m +b4 c d e f | valid_b4 c d e f = fromChar (toEnum (combine (combine (combine (mask c 0x07) d) e) f)) + | otherwise = invalidChar [c,d,e,f] + +valid_b2 :: Word8 -> Word8 -> Bool +valid_b2 c d = (c >= 0xc2 && c <= 0xdf && d >= 0x80 && d <= 0xbf) + +valid_b3 :: Word8 -> Word8 -> Word8 -> Bool +valid_b3 c d e = (c == 0xe0 && d >= 0xa0 && d <= 0xbf && e >= 0x80 && e <= 0xbf) || + (c >= 0xe1 && c <= 0xef && d >= 0x80 && d <= 0xbf && e >= 0x80 && e <= 0xbf) + +valid_b4 :: Word8 -> Word8 -> Word8 -> Word8 -> Bool +valid_b4 c d e f = (c == 0xf0 && d >= 0x90 && d <= 0xbf && e >= 0x80 && e <= 0xbf && f >= 0x80 && f <= 0xbf) || + (c >= 0xf1 && c <= 0xf3 && d >= 0x80 && d <= 0xbf && e >= 0x80 && e <= 0xbf && f >= 0x80 && f <= 0xbf) || + (c == 0xf4 && d >= 0x80 && d <= 0x8f && e >= 0x80 && e <= 0xbf && f >= 0x80 && f <= 0xbf) + +consT :: CharReducer m => Word8 -> T -> (H -> UTF8 m) -> (m -> UTF8 m) -> (T -> UTF8 m) -> UTF8 m +consT c cs h m t + | c < 0x80 = m $ b1 c `mappend` invalidChars cs + | c < 0xc0 = t (c:cs) + | c < 0xe0 = case cs of + [] -> h $ H2_1 c + (d:ds) -> m $ b2 c d `mappend` invalidChars ds + | c < 0xf0 = case cs of + [] -> h $ H3_1 c + [d] -> h $ H3_2 c d + (d:e:es) -> m $ b3 c d e `mappend` invalidChars es + | c < 0xf5 = case cs of + [] -> h $ H4_1 c + [d] -> h $ H4_2 c d + [d,e] -> h $ H4_3 c d e + (d:e:f:fs) -> m $ b4 c d e f `mappend` invalidChars fs + | otherwise = mempty + +invalidChars :: CharReducer m => [Word8] -> m +invalidChars = foldr (mappend . invalidChar . return) mempty + +merge :: CharReducer m => H -> T -> (m -> a) -> (H -> a) -> a +merge H0 cs k _ = k $ invalidChars cs +merge (H2_1 c) [] _ p = p $ H2_1 c +merge (H2_1 c) (d:ds) k _ = k $ b2 c d `mappend` invalidChars ds +merge (H3_1 c) [] _ p = p $ H3_1 c +merge (H3_1 c) [d] _ p = p $ H3_2 c d +merge (H3_1 c) (d:e:es) k _ = k $ b3 c d e `mappend` invalidChars es +merge (H3_2 c d) [] _ p = p $ H3_2 c d +merge (H3_2 c d) (e:es) k _ = k $ b3 c d e `mappend` invalidChars es +merge (H4_1 c) [] _ p = p $ H4_1 c +merge (H4_1 c) [d] _ p = p $ H4_2 c d +merge (H4_1 c) [d,e] _ p = p $ H4_3 c d e +merge (H4_1 c) (d:e:f:fs) k _ = k $ b4 c d e f `mappend` invalidChars fs +merge (H4_2 c d) [] _ p = p $ H4_2 c d +merge (H4_2 c d) [e] _ p = p $ H4_3 c d e +merge (H4_2 c d) (e:f:fs) k _ = k $ b4 c d e f `mappend` invalidChars fs +merge (H4_3 c d e) [] _ p = p $ H4_3 c d e +merge (H4_3 c d e) (f:fs) k _ = k $ b4 c d e f `mappend` invalidChars fs + +instance CharReducer m => Monoid (UTF8 m) where + mempty = T [] + T c `mappend` T d = T (c ++ d) + T c `mappend` S l m r = S (c ++ l) m r + S l m c `mappend` S c' m' r = S l (m `mappend` merge c c' id flushH `mappend` m') r + s@(S _ _ _) `mappend` T [] = s + S l m c `mappend` T c' = merge c c' k (S l m) where + k m' = S l (m `mappend` m') H0 + +instance CharReducer m => Reducer Word8 (UTF8 m) where + unit c | c >= 0x80 && c < 0xc0 = T [c] + | otherwise = snocH H0 c (S []) mempty + S t m h `snoc` c = snocH h c (S t) m + T t `snoc` c | c >= 0x80 && c < 0xc0 = T (t ++ [c]) + | otherwise = snocH H0 c (S t) mempty + + c `cons` T cs = consT c cs (S [] mempty) (flip (S []) H0) T + c `cons` S cs m h = consT c cs k1 k2 k3 where + k1 h' = S [] (flushH h' `mappend` m) h + k2 m' = S [] (m' `mappend` m) h + k3 t' = S t' m h + +instance Functor UTF8 where + fmap f (S t x h) = S t (f x) h + fmap _ (T t) = T t + +instance Pointed UTF8 where + point f = S [] f H0 + +runUTF8 :: CharReducer m => UTF8 m -> m +runUTF8 (T t) = flushT t +runUTF8 (S t m h) = flushT t `mappend` m `mappend` flushH h + + addfile ./doc/html/monoids/src/Data-Monoid-Lexical-Words.html hunk ./doc/html/monoids/src/Data-Monoid-Lexical-Words.html 1 + + + + +Data/Monoid/Lexical/Words.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, FlexibleContexts, GeneralizedNewtypeDeriving, ParallelListComp, TypeFamilies, OverloadedStrings, UndecidableInstances #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Lexical.Words +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs, OverloadedStrings) +-- +-- A simple demonstration of tokenizing a 'Generator' into distinct words +-- and/or lines using a word-parsing 'Monoid' that accumulates partial +-- information about words and then builds up a token stream. +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Lexical.Words + ( module Data.Monoid.Reducer.Char + -- * Words + , Words + , runWords + , Unspaced(runUnspaced) + , wordsFrom + -- * Lines + , Lines + , runLines + , Unlined(runUnlined) + , linesFrom + ) where + +import Data.String +import Data.Char (isSpace) +import Data.Maybe (maybeToList) +import Data.Monoid.Reducer.Char +import Data.Monoid.Generator +import Control.Functor.Pointed + +-- | A 'CharReducer' transformer that breaks a 'Char' 'Generator' into distinct words, feeding a 'Char' 'Reducer' each line in turn +data Words m = Chunk (Maybe m) + | Segment (Maybe m) [m] (Maybe m) + deriving (Show,Read) + +-- | Extract the matched words from the 'Words' 'Monoid' +runWords :: Words m -> [m] +runWords (Chunk m) = maybeToList m +runWords (Segment l m r) = maybeToList l ++ m ++ maybeToList r + +instance Monoid m => Monoid (Words m) where + mempty = Chunk mempty + Chunk l `mappend` Chunk r = Chunk (l `mappend` r) + Chunk l `mappend` Segment l' m r = Segment (l `mappend` l') m r + Segment l m r `mappend` Chunk r' = Segment l m (r `mappend` r') + Segment l m r `mappend` Segment l' m' r' = Segment l (m ++ maybeToList (r `mappend` l') ++ m') r' + +instance Reducer Char m => Reducer Char (Words m) where + unit c | isSpace c = Segment (Just (unit c)) [] mempty + | otherwise = Chunk (Just (unit c)) + +instance Functor Words where + fmap f (Chunk m) = Chunk (fmap f m) + fmap f (Segment m ms m') = Segment (fmap f m) (fmap f ms) (fmap f m') + +instance (CharReducer m) => CharReducer (Words m) where + invalidChar xs = Segment (Just (invalidChar xs)) [] mempty + +instance Reducer Char m => IsString (Words m) where + fromString = reduce + +-- | A 'CharReducer' transformer that breaks a 'Char' 'Generator' into distinct lines, feeding a 'Char' 'Reducer' each line in turn. +newtype Lines m = Lines (Words m) deriving (Show,Read,Monoid,Functor) + +instance Reducer Char m => Reducer Char (Lines m) where + unit '\n' = Lines $ Segment (Just (unit '\n')) [] mempty + unit c = Lines $ Chunk (Just (unit c)) + +instance (CharReducer m) => CharReducer (Lines m) where + invalidChar xs = Lines $ Segment (Just (invalidChar xs)) [] mempty + +instance Reducer Char m => IsString (Lines m) where + fromString = reduce + +-- | Extract the matched lines from the 'Lines' 'Monoid' +runLines :: Lines m -> [m] +runLines (Lines x) = runWords x + +-- | A 'CharReducer' transformer that strips out any character matched by `isSpace` +newtype Unspaced m = Unspaced { runUnspaced :: m } deriving (Eq,Ord,Show,Read,Monoid) + +instance Reducer Char m => Reducer Char (Unspaced m) where + unit c | isSpace c = mempty + | otherwise = Unspaced (unit c) + +instance CharReducer m => CharReducer (Unspaced m) where + invalidChar = Unspaced . invalidChar + +instance Functor Unspaced where + fmap f (Unspaced x) = Unspaced (f x) + +instance Pointed Unspaced where + point = Unspaced + +instance Copointed Unspaced where + extract = runUnspaced + +instance Reducer Char m => IsString (Unspaced m) where + fromString = reduce + +-- | A 'CharReducer' transformer that strips out newlines +newtype Unlined m = Unlined { runUnlined :: m } deriving (Eq,Ord,Show,Read,Monoid) + +instance Reducer Char m => Reducer Char (Unlined m) where + unit '\n' = mempty + unit c = Unlined (unit c) + +instance CharReducer m => CharReducer (Unlined m) where + invalidChar = Unlined . invalidChar + +instance Functor Unlined where + fmap f (Unlined x) = Unlined (f x) + +instance Pointed Unlined where + point = Unlined + +instance Copointed Unlined where + extract = runUnlined + +instance Reducer Char m => IsString (Unlined m) where + fromString = reduce + +-- | Utility function to extract words using accumulator, inside-word, and until-next-word monoids +wordsFrom :: (Generator c, Elem c ~ Char, Char `Reducer` m, Char `Reducer` n, Char `Reducer` o) => m -> c -> [(m,n,o)] +wordsFrom s c = [(x,runUnlined y,z) | x <- scanl mappend s ls | (y,z) <- rs ] where + (ls,rs) = unzip (runWords (mapReduce id c)) + +-- | Utility function to extract lines using accumulator, inside-line, and until-next-line monoids +linesFrom :: (Generator c, Elem c ~ Char, Char `Reducer` m, Char `Reducer` n, Char `Reducer` o) => m -> c -> [(m,n,o)] +linesFrom s c = [(x,runUnlined y,z) | x <- scanl mappend s ls | (y,z) <- rs ] where + (ls,rs) = unzip (runLines (mapReduce id c)) + + addfile ./doc/html/monoids/src/Data-Monoid-Monad.html hunk ./doc/html/monoids/src/Data-Monoid-Monad.html 1 + + + + +Data/Monoid/Monad.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, GeneralizedNewtypeDeriving, FlexibleContexts, TypeOperators #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Applicative +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs) +-- +-- 'Monoid' instances for working with a 'Monad' +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Monad + ( module Data.Monoid.Reducer + , module Data.Ring.Semi.Near + -- * Actions + , Action(Action,getAction) + , snocAction + -- * Lifting Modules + , ActionWith(ActionWith,getActionWith) + -- * Wrapped Monads + , WrappedMonad(WrappedMonad, getWrappedMonad) + ) where + +import Control.Functor.Pointed +import Data.Monoid.Reducer +import Data.Ring.Semi.Near +import Data.Ring.Module +import Control.Monad + +-- | An 'Action' uses glues together 'Monad' actions with (>>) +-- in the manner of 'mapM_' from "Data.Foldable". Any values returned by +-- reduced actions are discarded. +newtype Action m = Action { getAction :: m () } + +instance Monad m => Monoid (Action m) where + mempty = Action (return ()) + Action a `mappend` Action b = Action (a >> b) + +instance Monad m => Reducer (m a) (Action m) where + unit a = Action (a >> return ()) + a `cons` Action b = Action (a >> b) + Action a `snoc` b = Action (a >> b >> return ()) + +{-# RULES "unitAction" unit = Action #-} +{-# RULES "snocAction" snoc = snocAction #-} + +-- | Efficiently avoid needlessly rebinding when using 'snoc' on an action that already returns () +-- A rewrite rule automatically applies this when possible +snocAction :: Reducer (m ()) (Action m) => Action m -> m () -> Action m +snocAction a = mappend a . Action + +-- | A 'WrappedMonad' turns any 'MonadPlus' instance into a 'Monoid'. +-- It also provides a 'Multiplicative' instance for a 'Monad' wrapped around a 'Monoid' +-- and asserts that any 'MonadPlus' applied to a 'Monoid' forms a 'LeftSemiNearRing' +-- under these operations. + +newtype WrappedMonad m a = WrappedMonad { getWrappedMonad :: m a } + deriving (Eq,Ord,Show,Read,Functor,Pointed, Monad,MonadPlus) + +instance (Monad m, Monoid a) => Multiplicative (WrappedMonad m a) where + one = WrappedMonad (return mempty) + WrappedMonad m `times` WrappedMonad n = WrappedMonad (liftM2 mappend m n) + +instance (MonadPlus m) => Monoid (WrappedMonad m a) where + mempty = mzero + mappend = mplus + +instance (MonadPlus m, c `Reducer` a) => Reducer c (WrappedMonad m a) where + unit = WrappedMonad . return . unit + +instance (MonadPlus m, Monoid a) => LeftSemiNearRing (WrappedMonad m a) + +-- | if @m@ is a 'Module' over @r@ and @f@ is a 'Monad' then @f `ActionWith` m@ is a 'Module' as well + +newtype ActionWith f m = ActionWith { getActionWith :: f m } + deriving (Eq,Ord,Show,Read,Functor,Pointed, Monad,MonadPlus) + +instance (Monoid m, Monad f) => Monoid (f `ActionWith` m) where + mempty = return mempty + mappend = liftM2 mappend + +instance (Group m, Monad f) => Group (f `ActionWith` m) where + gnegate = liftM gnegate + minus = liftM2 minus + gsubtract = liftM2 gsubtract + +instance (c `Reducer` m, Monad f) => Reducer c (f `ActionWith` m) where + unit = return . unit + +instance (LeftModule r m, Monad f) => LeftModule r (f `ActionWith` m) where + x *. m = liftM (x *.) m + +instance (RightModule r m, Monad f) => RightModule r (f `ActionWith` m) where + m .* y = liftM (.* y) m + +instance (Module r m, Monad f) => Module r (f `ActionWith` m) + + addfile ./doc/html/monoids/src/Data-Monoid-Multiplicative-Sugar.html hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative-Sugar.html 1 + + + + +Data/Monoid/Multiplicative/Sugar.hs + + + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Multiplicative.Sugar +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : portable +-- +-- Syntactic sugar for working with a 'Multiplicative' monoids that conflicts with names from the "Prelude". +-- +-- > import Prelude hiding ((+),(*)) +-- > import Data.Monoid.Multiplicative.Sugar +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Multiplicative.Sugar + ( module Data.Monoid.Additive.Sugar + , module Data.Monoid.Multiplicative + , (*) + ) where + +import Data.Monoid.Additive.Sugar +import Data.Monoid.Multiplicative +import Prelude hiding ((*)) + +infixl 7 * + +(*) :: Multiplicative r => r -> r -> r +(*) = times + + addfile ./doc/html/monoids/src/Data-Monoid-Multiplicative.html hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 1 + + + + +Data/Monoid/Multiplicative.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Multiplicative +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : portable (but instances use MPTCs) +-- +-- When dealing with a 'Ring' or other structure, you often need a pair of +-- 'Monoid' instances that are closely related. Making a @newtype@ for one +-- is unsatisfying and yields an unnatural programming style. +-- +-- A 'Multiplicative' is a 'Monoid' that is intended for use in a scenario +-- that can be extended to have another 'Monoid' slot in for addition. This +-- enables one to use common notation. +-- +-- Any 'Multiplicative' can be turned into a 'Monoid' using the 'Log' wrapper. +-- +-- Any 'Monoid' can be turned into a 'Multiplicative' using the 'Exp' wrapper. +-- +-- Instances are supplied for common Monads of Monoids, in a fashion +-- which can be extended if the 'Monad' is a 'MonadPlus' to yield a 'LeftSemiNearRing' +-- +-- Instances are also supplied for common Applicatives of Monoids, in a +-- fashion which can be extended if the 'Applicative' is 'Alternative' to +-- yield a 'LeftSemiNearRing' +----------------------------------------------------------------------------- + +module Data.Monoid.Multiplicative + ( module Data.Monoid.Additive + -- * Multiplicative Monoids + , Multiplicative + , one, times + -- * Multiplicative to Monoid + , Log(Log, getLog) + -- * Monoid to Multiplicative + , Exp(Exp, getExp) + ) where + +import Control.Applicative + +import Control.Concurrent.STM + +import Control.Monad.Cont +import Control.Monad.Identity + +import Control.Monad.Reader + +import qualified Control.Monad.RWS.Lazy as LRWS +import qualified Control.Monad.RWS.Strict as SRWS + +import qualified Control.Monad.State.Lazy as LState +import qualified Control.Monad.State.Strict as SState + +import qualified Control.Monad.Writer.Lazy as LWriter +import qualified Control.Monad.Writer.Strict as SWriter + +import qualified Control.Monad.ST.Lazy as LST +import qualified Control.Monad.ST.Strict as SST + +import Data.FingerTree + +import Data.Monoid.Additive +import Data.Monoid.FromString +import Data.Monoid.Generator +import Data.Monoid.Instances () +import Data.Monoid.Self + +import Data.Ratio + +import qualified Data.Sequence as Seq +import Data.Sequence (Seq) + +import Text.Parsec.Prim + +class Multiplicative m where + one :: m + times :: m -> m -> m + +-- | Convert a 'Multiplicative' into a 'Monoid'. Mnemonic: @Log a + Log b = Log (a * b)@ +data Log m = Log { getLog :: m } + +instance Multiplicative m => Monoid (Log m) where + mempty = Log one + Log a `mappend` Log b = Log (a `times` b) + +-- | Convert a 'Monoid' into a 'Multiplicative'. Mnemonic: @Exp a * Exp b = Exp (a + b)@ +data Exp m = Exp { getExp :: m } + +instance Monoid m => Multiplicative (Exp m) where + one = Exp mempty + Exp a `times` Exp b = Exp (a `mappend` b) + +-- simple monoid transformer instances +instance Multiplicative m => Multiplicative (Self m) where + one = Self one + Self a `times` Self b = Self (a `times` b) + +instance Multiplicative m => Multiplicative (FromString m) where + one = FromString one + FromString a `times` FromString b = FromString (a `times` b) + +-- the goal of this is that I can make left seminearrings out of any 'Alternative' wrapped around a monoid +-- in particular its useful for containers + +instance Monoid m => Multiplicative [m] where + one = return mempty + times = liftM2 mappend + +instance Monoid m => Multiplicative (Seq m) where + one = return mempty + times = liftM2 mappend + +-- and things that can't quite be a Monad in Haskell +instance (Measured v m, Monoid m) => Multiplicative (FingerTree v m) where + one = singleton mempty + xss `times` yss = getSelf $ mapReduce (flip fmap' yss . mappend) xss + +-- but it can at least serve as a canonical multiplication for any monad. +instance Monoid m => Multiplicative (Maybe m) where + one = return mempty + times = liftM2 mappend + +instance Monoid m => Multiplicative (Identity m) where + one = return mempty + times = liftM2 mappend + +instance (Monoid m) => Multiplicative (Cont r m) where + one = return mempty + times = liftM2 mappend + +instance (Monoid w, Monoid m) => Multiplicative (SRWS.RWS r w s m) where + one = return mempty + times = liftM2 mappend + +instance (Monoid w, Monoid m) => Multiplicative (LRWS.RWS r w s m) where + one = return mempty + times = liftM2 mappend + +instance Monoid m => Multiplicative (SState.State s m) where + one = return mempty + times = liftM2 mappend + +instance Monoid m => Multiplicative (LState.State s m) where + one = return mempty + times = liftM2 mappend + +instance Monoid m => Multiplicative (Reader e m) where + one = return mempty + times = liftM2 mappend + +instance (Monoid w, Monoid m) => Multiplicative (SWriter.Writer w m) where + one = return mempty + times = liftM2 mappend + +instance (Monoid w, Monoid m) => Multiplicative (LWriter.Writer w m) where + one = return mempty + times = liftM2 mappend + +instance (Monad m, Monoid n) => Multiplicative (ContT r m n) where + one = return mempty + times = liftM2 mappend + +instance (Monad m, Monoid w, Monoid n) => Multiplicative (SRWS.RWST r w s m n) where + one = return mempty + times = liftM2 mappend + +instance (Monad m, Monoid w, Monoid n) => Multiplicative (LRWS.RWST r w s m n) where + one = return mempty + times = liftM2 mappend + +instance (Monad m, Monoid n) => Multiplicative (SState.StateT s m n) where + one = return mempty + times = liftM2 mappend + +instance (Monad m, Monoid n) => Multiplicative (LState.StateT s m n) where + one = return mempty + times = liftM2 mappend + +instance (Monad m, Monoid n) => Multiplicative (ReaderT e m n) where + one = return mempty + times = liftM2 mappend + +instance (Monad m, Monoid w, Monoid n) => Multiplicative (SWriter.WriterT w m n) where + one = return mempty + times = liftM2 mappend + +instance (Monad m, Monoid w, Monoid n) => Multiplicative (LWriter.WriterT w m n) where + one = return mempty + times = liftM2 mappend + +instance Monoid n => Multiplicative (IO n) where + one = return mempty + times = liftM2 mappend + +instance Monoid n => Multiplicative (SST.ST s n) where + one = return mempty + times = liftM2 mappend + +instance Monoid n => Multiplicative (LST.ST s n) where + one = return mempty + times = liftM2 mappend + +instance Monoid n => Multiplicative (STM n) where + one = return mempty + times = liftM2 mappend + +instance (Stream s m t, Monoid n) => Multiplicative (ParsecT s u m n) where + one = return mempty + times = liftM2 mappend + +-- Applicative instances + +instance Monoid n => Multiplicative (ZipList n) where + one = pure mempty + times = liftA2 mappend + +instance Monoid m => Multiplicative (Const m a) where + one = pure undefined + times = liftA2 undefined + + +-- Numeric instances + +instance Multiplicative Int where + one = 1 + times = (*) + + +instance Multiplicative Integer where + one = 1 + times = (*) + +instance Integral m => Multiplicative (Ratio m) where + one = 1 + times = (*) + + + addfile ./doc/html/monoids/src/Data-Monoid-Ord.html hunk ./doc/html/monoids/src/Data-Monoid-Ord.html 1 + + + + +Data/Monoid/Ord.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-} +----------------------------------------------------------------------------- +---- | +---- Module : Data.Monoid.Ord +---- Copyright : (c) Edward Kmett 2009 +---- License : BSD-style +---- Maintainer : libraries@haskell.org +---- Stability : experimental +---- Portability : portable +---- +---- Some 'Monoid' instances that should probably be in "Data.Monoid". +---- +----------------------------------------------------------------------------- + +module Data.Monoid.Ord + ( module Data.Monoid.Reducer + -- * Max + , Max(Max,getMax) + -- * Min + , Min(Min,getMin) + -- * MaxPriority: Max semigroup w/ added bottom + , MaxPriority(MaxPriority,getMaxPriority) + , minfinity + -- * MinPriority: Min semigroup w/ added top + , MinPriority(MinPriority,getMinPriority) + , infinity + ) where + +import Control.Functor.Pointed +import Data.Monoid.Reducer (Reducer, unit, Monoid, mappend, mempty) +import Data.Ring.Semi + +-- | The 'Monoid' @('max','minBound')@ +newtype Max a = Max { getMax :: a } deriving (Eq,Ord,Show,Read,Bounded) + +instance (Ord a, Bounded a) => Monoid (Max a) where + mempty = Max minBound + mappend = max + +instance (Ord a, Bounded a) => Reducer a (Max a) where + unit = Max + +instance Functor Max where + fmap f (Max a) = Max (f a) + +instance Pointed Max where + point = Max + +instance Copointed Max where + extract = getMax + +-- | The 'Monoid' given by @('min','maxBound')@ +newtype Min a = Min { getMin :: a } deriving (Eq,Ord,Show,Read,Bounded) + +instance (Ord a, Bounded a) => Monoid (Min a) where + mempty = Min maxBound + mappend = min + +instance (Ord a, Bounded a) => Reducer a (Min a) where + unit = Min + +instance Functor Min where + fmap f (Min a) = Min (f a) + +instance Pointed Min where + point = Min + +instance Copointed Min where + extract = getMin + +minfinity :: MaxPriority a +minfinity = MaxPriority Nothing + +-- | The 'Monoid' @('max','Nothing')@ over @'Maybe' a@ where 'Nothing' is the bottom element +newtype MaxPriority a = MaxPriority { getMaxPriority :: Maybe a } deriving (Eq,Ord,Show,Read) + +instance Ord a => Monoid (MaxPriority a) where + mempty = MaxPriority Nothing + mappend = max + +instance Ord a => Reducer (Maybe a) (MaxPriority a) where + unit = MaxPriority + +instance Functor MaxPriority where + fmap f (MaxPriority a) = MaxPriority (fmap f a) + +instance Pointed MaxPriority where + point = MaxPriority . Just + +infinity :: MinPriority a +infinity = MinPriority Nothing + +-- | The 'Monoid' @('min','Nothing')@ over @'Maybe' a@ where 'Nothing' is the top element +newtype MinPriority a = MinPriority { getMinPriority :: Maybe a } deriving (Eq,Show,Read) + +instance Ord a => Ord (MinPriority a) where + MinPriority Nothing `compare` MinPriority Nothing = EQ + MinPriority Nothing `compare` _ = GT + _ `compare` MinPriority Nothing = LT + MinPriority (Just a) `compare` MinPriority (Just b) = a `compare` b + +instance Ord a => Monoid (MinPriority a) where + mempty = MinPriority Nothing + mappend = min + +instance Ord a => Reducer (Maybe a) (MinPriority a) where + unit = MinPriority + +instance Functor MinPriority where + fmap f (MinPriority a) = MinPriority (fmap f a) + +instance Pointed MinPriority where + point = MinPriority . Just + + addfile ./doc/html/monoids/src/Data-Monoid-Reducer-Char.html hunk ./doc/html/monoids/src/Data-Monoid-Reducer-Char.html 1 + + + + +Data/Monoid/Reducer/Char.hs + + + +{-# LANGUAGE UndecidableInstances, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Reducer.Char +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs) +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Reducer.Char + ( module Data.Monoid.Reducer + , CharReducer + , invalidChar + , fromChar + ) where + +import Data.Monoid.Reducer +import Data.Word (Word8) + +-- | Provides a mechanism for the UTF8 'Monoid' to report invalid characters to one or more monoids. + +class Reducer Char m => CharReducer m where + fromChar :: Char -> m + fromChar = unit + + invalidChar :: [Word8] -> m + invalidChar = const mempty + +instance (CharReducer m, CharReducer m') => CharReducer (m,m') where + invalidChar bs = (invalidChar bs, invalidChar bs) + +instance (CharReducer m, CharReducer m', CharReducer m'') => CharReducer (m,m',m'') where + invalidChar bs = (invalidChar bs, invalidChar bs, invalidChar bs) + +instance (CharReducer m, CharReducer m', CharReducer m'', CharReducer m''') => CharReducer (m,m',m'',m''') where + invalidChar bs = (invalidChar bs, invalidChar bs, invalidChar bs, invalidChar bs) + +instance CharReducer [Char] + + addfile ./doc/html/monoids/src/Data-Monoid-Reducer-With.html hunk ./doc/html/monoids/src/Data-Monoid-Reducer-With.html 1 + + + + +Data/Monoid/Reducer/With.hs + + + +{-# LANGUAGE UndecidableInstances, TypeOperators, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Reducer.With +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs) +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Reducer.With + ( module Data.Monoid.Reducer + , WithReducer(WithReducer,withoutReducer) + ) where + +import Data.Monoid.Reducer +import Data.FingerTree + +-- | If @m@ is a @c@-"Reducer", then m is @(c `WithReducer` m)@-"Reducer" +-- This can be used to quickly select a "Reducer" for use as a 'FingerTree' +-- 'measure'. + +newtype WithReducer c m = WithReducer { withoutReducer :: c } + +instance (c `Reducer` m) => Reducer (c `WithReducer` m) m where + unit = unit . withoutReducer + +instance (c `Reducer` m) => Measured m (c `WithReducer` m) where + measure = unit . withoutReducer + + addfile ./doc/html/monoids/src/Data-Monoid-Reducer.html hunk ./doc/html/monoids/src/Data-Monoid-Reducer.html 1 + + + + +Data/Monoid/Reducer.hs + + + +{-# LANGUAGE UndecidableInstances , FlexibleContexts , MultiParamTypeClasses , FlexibleInstances , GeneralizedNewtypeDeriving #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Monoid.Reducer +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs) +-- +-- A @c@-'Reducer' is a 'Monoid' with a canonical mapping from @c@ to the Monoid. +-- This 'unit' acts in many ways like 'return' for a 'Monad' but is limited +-- to a single type. +-- +----------------------------------------------------------------------------- + +module Data.Monoid.Reducer + ( module Data.Monoid + , Reducer + , unit, snoc, cons + , foldMapReduce + , foldReduce + , pureUnit + , returnUnit + ) where + +import Control.Applicative +import Control.Monad + +import Data.Monoid +import Data.Monoid.Instances () + +import Data.Foldable +import Data.FingerTree + +import qualified Data.Sequence as Seq +import Data.Sequence (Seq) + +import qualified Data.Set as Set +import Data.Set (Set) + +import qualified Data.IntSet as IntSet +import Data.IntSet (IntSet) + +import qualified Data.IntMap as IntMap +import Data.IntMap (IntMap) + +import qualified Data.Map as Map + +import Data.Map (Map) + +import Text.Parsec.Prim + +--import qualified Data.BitSet as BitSet +--import Data.BitSet (BitSet) + +-- | This type may be best read infix. A @c `Reducer` m@ is a 'Monoid' @m@ that maps +-- values of type @c@ through @unit@ to values of type @m@. A @c@-'Reducer' may also +-- supply operations which tack-on another @c@ to an existing 'Monoid' @m@ on the left +-- or right. These specialized reductions may be more efficient in some scenarios +-- and are used when appropriate by a 'Generator'. The names 'cons' and 'snoc' work +-- by analogy to the synonymous operations in the list monoid. +-- +-- This class deliberately avoids functional-dependencies, so that () can be a @c@-Reducer +-- for all @c@, and so many common reducers can work over multiple types, for instance, +-- First and Last may reduce both @a@ and 'Maybe' @a@. Since a 'Generator' has a fixed element +-- type, the input to the reducer is generally known and extracting from the monoid usually +-- is sufficient to fix the result type. Combinators are available for most scenarios where +-- this is not the case, and the few remaining cases can be handled by using an explicit +-- type annotation. +-- +-- Minimal definition: 'unit' or 'snoc' +class Monoid m => Reducer c m where + -- | Convert a value into a 'Monoid' + unit :: c -> m + -- | Append a value to a 'Monoid' for use in left-to-right reduction + snoc :: m -> c -> m + -- | Prepend a value onto a 'Monoid' for use during right-to-left reduction + cons :: c -> m -> m + + unit = snoc mempty + snoc m = mappend m . unit + cons = mappend . unit + +-- | Apply a 'Reducer' to a 'Foldable' container, after mapping the contents into a suitable form for reduction. +foldMapReduce :: (Foldable f, e `Reducer` m) => (a -> e) -> f a -> m +foldMapReduce f = foldMap (unit . f) + +-- | Apply a 'Reducer' to a 'Foldable' mapping each element through 'unit' +foldReduce :: (Foldable f, e `Reducer` m) => f e -> m +foldReduce = foldMap unit + +returnUnit :: (Monad m, c `Reducer` n) => c -> m n +returnUnit = return . unit + +pureUnit :: (Applicative f, c `Reducer` n) => c -> f n +pureUnit = pure . unit + +instance (Reducer c m, Reducer c n) => Reducer c (m,n) where + unit x = (unit x,unit x) + (m,n) `snoc` x = (m `snoc` x, n `snoc` x) + x `cons` (m,n) = (x `cons` m, x `cons` n) + +instance (Reducer c m, Reducer c n, Reducer c o) => Reducer c (m,n,o) where + unit x = (unit x,unit x, unit x) + (m,n,o) `snoc` x = (m `snoc` x, n `snoc` x, o `snoc` x) + x `cons` (m,n,o) = (x `cons` m, x `cons` n, x `cons` o) + +instance (Reducer c m, Reducer c n, Reducer c o, Reducer c p) => Reducer c (m,n,o,p) where + unit x = (unit x,unit x, unit x, unit x) + (m,n,o,p) `snoc` x = (m `snoc` x, n `snoc` x, o `snoc` x, p `snoc` x) + x `cons` (m,n,o,p) = (x `cons` m, x `cons` n, x `cons` o, x `cons` p) + +instance Reducer c [c] where + unit = return + cons = (:) + xs `snoc` x = xs ++ [x] + +instance Reducer c () where + unit _ = () + _ `snoc` _ = () + _ `cons` _ = () + +instance Reducer Bool Any where + unit = Any + +instance Reducer Bool All where + unit = All + +instance Reducer (a -> a) (Endo a) where + unit = Endo + +instance Monoid a => Reducer a (Dual a) where + unit = Dual + +instance Num a => Reducer a (Sum a) where + unit = Sum + +instance Num a => Reducer a (Product a) where + unit = Product + +instance Reducer (Maybe a) (First a) where + unit = First + +instance Reducer a (First a) where + unit = First . Just + +instance Reducer (Maybe a) (Last a) where + unit = Last + +instance Reducer a (Last a) where + unit = Last . Just + +instance Measured v a => Reducer a (FingerTree v a) where + unit = singleton + cons = (<|) + snoc = (|>) + +instance (Stream s m t, c `Reducer` a) => Reducer c (ParsecT s u m a) where + unit = return . unit + +instance Reducer a (Seq a) where + unit = Seq.singleton + cons = (Seq.<|) + snoc = (Seq.|>) + +instance Reducer Int IntSet where + unit = IntSet.singleton + cons = IntSet.insert + snoc = flip IntSet.insert -- left bias irrelevant + +instance Ord a => Reducer a (Set a) where + unit = Set.singleton + cons = Set.insert + -- pedantic about order in case 'Eq' doesn't implement structural equality + snoc s m | Set.member m s = s + | otherwise = Set.insert m s + +instance Reducer (Int,v) (IntMap v) where + unit = uncurry IntMap.singleton + cons = uncurry IntMap.insert + snoc = flip . uncurry . IntMap.insertWith $ const id + +instance Ord k => Reducer (k,v) (Map k v) where + unit = uncurry Map.singleton + cons = uncurry Map.insert + snoc = flip . uncurry . Map.insertWith $ const id + +{- +instance Enum a => Reducer a (BitSet a) where + unit m = BitSet.insert m BitSet.empty +-} + + addfile ./doc/html/monoids/src/Data-Monoid-Union.html hunk ./doc/html/monoids/src/Data-Monoid-Union.html 1 + + + + +Data/Monoid/Union.hs + + + +{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, GeneralizedNewtypeDeriving #-} +module Data.Monoid.Union + ( module Data.Monoid.Reducer + -- * Unions of Containers + , HasUnion + , empty + , union + , Union(Union,getUnion) + -- * Unions of Containers of Monoids + , HasUnionWith + , emptyWith + , unionWith + , UnionWith(UnionWith,getUnionWith) + ) where + +import qualified Data.IntMap as IntMap +import Data.IntMap (IntMap) + +import qualified Data.IntSet as IntSet +import Data.IntSet (IntSet) + +import qualified Data.Map as Map +import Data.Map (Map) + +import qualified Data.Set as Set +import Data.Set (Set) + +import qualified Data.List as List + +import Control.Functor.Pointed + +import Data.Monoid.Reducer (Reducer, unit, cons, snoc, Monoid, mappend, mempty) + +-- | A Container suitable for the 'Union' 'Monoid' +class HasUnion f where + empty :: f + {-# SPECIALIZE union :: IntMap a -> IntMap a -> IntMap a #-} + {-# SPECIALIZE union :: Ord k => Map k a -> Map k a -> Map k a #-} + {-# SPECIALIZE union :: Eq a => [a] -> [a] -> [a] #-} + {-# SPECIALIZE union :: Ord a => Set a -> Set a -> Set a #-} + {-# SPECIALIZE union :: IntSet -> IntSet -> IntSet #-} + union :: f -> f -> f + +instance HasUnion (IntMap a) where + empty = IntMap.empty + union = IntMap.union + +instance Ord k => HasUnion (Map k a) where + empty = Map.empty + union = Map.union + +instance Eq a => HasUnion [a] where + empty = [] + union = List.union + +instance Ord a => HasUnion (Set a) where + empty = Set.empty + union = Set.union + +instance HasUnion IntSet where + empty = IntSet.empty + union = IntSet.union + +-- | The 'Monoid' @('union','empty')@ +newtype Union f = Union { getUnion :: f } + deriving (Eq,Ord,Show,Read) + +instance (HasUnion f) => Monoid (Union f) where + mempty = Union empty + Union a `mappend` Union b = Union (a `union` b) + +instance (HasUnion f) => Reducer f (Union f) where + unit = Union + +instance Functor Union where + fmap f (Union a) = Union (f a) + +instance Pointed Union where + point = Union + +instance Copointed Union where + extract = getUnion + +-- | Polymorphic containers that we can supply an operation to handle unions with +class HasUnionWith f where + {-# SPECIALIZE unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a #-} + {-# SPECIALIZE unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a #-} + unionWith :: (a -> a -> a) -> f a -> f a -> f a + emptyWith :: f a + +instance HasUnionWith IntMap where + emptyWith = IntMap.empty + unionWith = IntMap.unionWith + +instance Ord k => HasUnionWith (Map k) where + emptyWith = Map.empty + unionWith = Map.unionWith + + +-- | The 'Monoid' @('unionWith mappend','empty')@ for containers full of monoids. +newtype UnionWith f m = UnionWith { getUnionWith :: f m } + deriving (Eq,Ord,Show,Read,Functor,Pointed,Monad) + +instance (HasUnionWith f, Monoid m) => Monoid (UnionWith f m) where + mempty = UnionWith emptyWith + UnionWith a `mappend` UnionWith b = UnionWith (unionWith mappend a b) + +instance (HasUnionWith f, Monoid m) => Reducer (f m) (UnionWith f m) where + unit = UnionWith + + + addfile ./doc/html/monoids/src/Data-Ring-Boolean.html hunk ./doc/html/monoids/src/Data-Ring-Boolean.html 1 + + + + +Data/Ring/Boolean.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Ring.Boolean +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs) +-- +-- A Boolean 'Ring' over 'Bool'. Note well that the 'mappend' of this ring is +-- symmetric difference and not disjunction like you might expect. To get that +-- you should use use 'Ord' from "Data.Ring.Semi.Ord.Order" on 'Bool' to get the '&&'/'||'-based +-- distributive-lattice 'SemiRing' +----------------------------------------------------------------------------- + +module Data.Ring.Boolean + ( module Data.Ring + , BoolRing(BoolRing, getBoolRing) + ) where + +import Data.Ring +import Data.Monoid.Reducer + +newtype BoolRing = BoolRing { getBoolRing :: Bool } deriving (Eq,Ord,Show,Read) + +instance Monoid BoolRing where + mempty = BoolRing False + BoolRing a `mappend` BoolRing b = BoolRing ((a || b) && not (a && b)) + +instance Group BoolRing where + gnegate = BoolRing . not . getBoolRing + +instance Multiplicative BoolRing where + one = BoolRing True + BoolRing a `times` BoolRing b = BoolRing (a && b) + +instance LeftSemiNearRing BoolRing +instance RightSemiNearRing BoolRing +instance SemiRing BoolRing +instance Ring BoolRing + +instance Reducer Bool BoolRing where + unit = BoolRing + + addfile ./doc/html/monoids/src/Data-Ring-FromNum.html hunk ./doc/html/monoids/src/Data-Ring-FromNum.html 1 + + + + +Data/Ring/FromNum.hs + + + +{-# LANGUAGE FlexibleInstances, FlexibleContexts, MultiParamTypeClasses, GeneralizedNewtypeDeriving #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Ring.FromNum +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs) +-- +-- A wrapper that lies for you and claims any instance of 'Num' is a 'Ring'. +-- Who knows, for your type it might even be telling the truth! +-- +----------------------------------------------------------------------------- + +module Data.Ring.FromNum + ( module Data.Ring + , FromNum(FromNum, getFromNum) + ) where + +import Data.Ring +import Data.Monoid.Reducer + +newtype FromNum a = FromNum { getFromNum :: a } deriving (Eq,Show,Num) + +instance Num a => Monoid (FromNum a) where + mempty = fromInteger 0 + mappend = (+) + +instance Num a => Group (FromNum a) where + minus = (-) + gnegate = negate + +instance Num a => Multiplicative (FromNum a) where + one = fromInteger 1 + times = (*) + +-- you can assume these, but you're probably lying to yourself +instance Num a => LeftSemiNearRing (FromNum a) +instance Num a => RightSemiNearRing (FromNum a) +instance Num a => SemiRing (FromNum a) +instance Num a => Ring (FromNum a) + +instance Num a => Reducer Integer (FromNum a) where + unit = fromInteger + + + addfile ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 1 + + + + +Data/Ring/Module/AutomaticDifferentiation.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-} +module Data.Ring.Module.AutomaticDifferentiation + ( module Data.Ring.Module + , D + ) where + +import Prelude hiding ((*),(+),(-),subtract,negate) +import Data.Ring.Sugar +import Data.Ring.Module +import Data.Monoid.Reducer + +data D r m = D r m + +instance (Monoid r, Monoid m) => Monoid (D r m) where + mempty = D mempty mempty + D x m `mappend` D y n = D (x + y) (m + n) + +instance (Module r m) => Multiplicative (D r m) where + one = D one zero + D x m `times` D y n = D (x * y) (x *. n + m .* y) + +instance (Group r, Module r m, Group m) => Group (D r m) where + gnegate (D x m) = D (gnegate x) (gnegate m) + D x m `minus` D y n = D (x `minus` y) (m `minus` n) + D x m `gsubtract` D y n = D (x `gsubtract` y) (m `gsubtract` n) + +instance (LeftSemiNearRing r, Module r m) => LeftSemiNearRing (D r m) +instance (RightSemiNearRing r, Module r m) => RightSemiNearRing (D r m) +instance (SemiRing r, Module r m) => SemiRing (D r m) +instance (Ring r, Module r m, Group m) => Ring (D r m) + +instance (c `Reducer` r, c `Reducer` m) => Reducer c (D r m) where + unit c = D (unit c) (unit c) + c `cons` D x m = D (c `cons` x) (c `cons` m) + D x m `snoc` c = D (x `snoc` c) (m `snoc` c) + +{-- +infix 0 >< + +(><) :: Multiplicatve a => (a -> a) -> (AD a -> AD a) -> AD a -> AD a +(f >< f') a@(AD a0 a') = D (f a0) (a' * f' a) + +data AD r = AD r (Maybe (AD r)) + +instance (Monoid r) => Monoid (AD r) where + mempty = K mempty + AD x m + AD y n = D (x + y) (m + n) + +instance (c `Reducer` r) => Reducer c (AD r) where + unit c = c' where c' = AD (unit c) c' +--} + + addfile ./doc/html/monoids/src/Data-Ring-Module.html hunk ./doc/html/monoids/src/Data-Ring-Module.html 1 + + + + +Data/Ring/Module.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-} +----------------------------------------------------------------------------- +-- | +-- Module : Data.Ring.Module +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs) +-- +-- Left- and right- modules over rings, semirings, and Seminearrings. +-- To avoid a proliferation of classes. These only require that there +-- be an addition and multiplication operation for the 'Ring' +-- +----------------------------------------------------------------------------- + +module Data.Ring.Module + ( module Data.Ring + , LeftModule + , (*.) + , RightModule + , (.*) + , Module + ) where + +import Data.Ring +-- import qualified Data.Monoid.Combinators as Monoid + +-- | @ (x * y) *. m = x * (y *. m) @ +class (Monoid r, Multiplicative r, Monoid m) => LeftModule r m where + (*.) :: r -> m -> m + +-- | @ (m .* x) * y = m .* (x * y) @ +class (Monoid r, Multiplicative r, Monoid m) => RightModule r m where + (.*) :: m -> r -> m + +-- | @ (x *. m) .* y = x *. (m .* y) @ +class (LeftModule r m, RightModule r m) => Module r m + +-- instance Monoid m => LeftModule Int m where i *. m = Monoid.replicate m i +-- instance Monoid m => RightModule Int m where m .* i = Monoid.replicate m i +-- instance Monoid m => Module Int m + +-- instance Monoid m => LeftModule Integer m where i *. m = Monoid.replicate m i +-- instance Monoid m => RightModule Integer m where m .* i = Monoid.replicate m i +-- instance Monoid m => Module Integer m + + addfile ./doc/html/monoids/src/Data-Ring-Semi-Near.html hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 1 + + + + +Data/Ring/Semi/Near.hs + + + +{-# OPTIONS_GHC -fno-warn-orphans #-} +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Ring.Semi.Near +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : portable (instances use MPTCs) +-- +-- Defines left- and right- seminearrings. Every 'MonadPlus' wrapped around +-- a 'Monoid' qualifies due to the distributivity of (>>=) over 'mplus'. +-- +-- See <http://conway.rutgers.edu/~ccshan/wiki/blog/posts/WordNumbers1/> +-- +----------------------------------------------------------------------------- + +module Data.Ring.Semi.Near + ( module Data.Monoid.Multiplicative + , LeftSemiNearRing + , RightSemiNearRing + ) where + +import Control.Monad.Reader + +import qualified Control.Monad.RWS.Lazy as LRWS +import qualified Control.Monad.RWS.Strict as SRWS + +import qualified Control.Monad.State.Lazy as LState +import qualified Control.Monad.State.Strict as SState + +import qualified Control.Monad.Writer.Lazy as LWriter +import qualified Control.Monad.Writer.Strict as SWriter + +import Data.Monoid.Multiplicative +import Data.FingerTree +import Data.Monoid.FromString +import Data.Monoid.Self +import Data.Monoid.Generator + +import qualified Data.Sequence as Seq +import Data.Sequence (Seq) + +import Text.Parsec.Prim + +-- | @(a + b) * c = (a * c) + (b * c)@ +class (Multiplicative m, Monoid m) => RightSemiNearRing m + +-- 'Monoid' transformers +instance RightSemiNearRing m => RightSemiNearRing (Self m) +instance RightSemiNearRing m => RightSemiNearRing (FromString m) + +-- | @a * (b + c) = (a * b) + (a * c)@ +class (Multiplicative m, Monoid m) => LeftSemiNearRing m + +-- 'Monoid' transformers +instance LeftSemiNearRing m => LeftSemiNearRing (Self m) +instance LeftSemiNearRing m => LeftSemiNearRing (FromString m) + +-- non-'Monad' instances +instance (Measured v m, Monoid m) => LeftSemiNearRing (FingerTree v m) + +-- 'Monad' instances +-- Every 'MonadPlus' over a 'Monoid' with an appropriate 'Multiplicative' instance +-- for 'liftM2 mappend' is a 'LeftSemiNearRing' by 'MonadPlus' left-distributivity + +instance Monoid m => LeftSemiNearRing [m] + +instance Monoid m => LeftSemiNearRing (Maybe m) + +instance Monoid m => LeftSemiNearRing (Seq m) + +instance (Stream s m t, Monoid a) => LeftSemiNearRing (ParsecT s u m a) + +instance (MonadPlus m, Monoid n) => LeftSemiNearRing (SState.StateT s m n) + +instance (MonadPlus m, Monoid n) => LeftSemiNearRing (LState.StateT s m n) + +instance (MonadPlus m, Monoid n) => LeftSemiNearRing (ReaderT e m n) + +instance (MonadPlus m, Monoid w, Monoid n) => LeftSemiNearRing (SRWS.RWST r w s m n) + +instance (MonadPlus m, Monoid w, Monoid n) => LeftSemiNearRing (LRWS.RWST r w s m n) + +instance (MonadPlus m, Monoid w, Monoid n) => LeftSemiNearRing (SWriter.WriterT w m n) + +instance (MonadPlus m, Monoid w, Monoid n) => LeftSemiNearRing (LWriter.WriterT w m n) + + + addfile ./doc/html/monoids/src/Data-Ring-Semi-Ord.html hunk ./doc/html/monoids/src/Data-Ring-Semi-Ord.html 1 + + + + +Data/Ring/Semi/Ord.hs + + + +{-# LANGUAGE FlexibleInstances, FlexibleContexts, MultiParamTypeClasses, GeneralizedNewtypeDeriving #-} +---------------------------------------------------------------------- +-- | +-- Module : Data.Ring.Semi.Ord +-- Copyright : (c) Edward Kmett 2009, Conal Elliott 2008 +-- License : BSD3 +-- +-- Maintainer : ekmett@gmail.com +-- Stability : experimental +-- +-- Turn an instance of 'Ord' into a 'SemiRing' over 'max' and 'min' +------------------------------------------------------------------------ + +module Data.Ring.Semi.Ord + ( module Data.Ring.Semi + , Order(Order,getOrder) + , Priority(MinBound,Priority,MaxBound) + ) where + +import Test.QuickCheck +-- import Control.Applicative +import Control.Functor.Pointed +import Data.Ring.Semi +import Data.Monoid.Ord +import Data.Monoid.Reducer + +-- | A 'SemiRing' using a type's built-in Bounded instance. +newtype Order a = Order { getOrder :: a } deriving (Eq,Ord,Read,Show,Bounded,Arbitrary) + +instance (Bounded a, Ord a) => Monoid (Order a) where + mappend = max + mempty = minBound + +instance (Bounded a, Ord a) => Multiplicative (Order a) where + times = min + one = maxBound + +instance (Bounded a, Ord a) => RightSemiNearRing (Order a) +instance (Bounded a, Ord a) => LeftSemiNearRing (Order a) +instance (Bounded a, Ord a) => SemiRing (Order a) +instance (Bounded a, Ord a) => Reducer a (Order a) where + unit = Order + +instance Functor Order where + fmap f (Order a) = Order (f a) + +instance Pointed Order where + point = Order + +instance Copointed Order where + extract = getOrder + +-- | A 'SemiRing' which adds 'minBound' and 'maxBound' to a pre-existing type. +data Priority a = MinBound | Priority a | MaxBound deriving (Eq,Read,Show) + +instance Bounded (Priority a) where + minBound = MinBound + maxBound = MaxBound + +instance Ord a => Ord (Priority a) where + MinBound <= _ = True + Priority _ <= MinBound = False + Priority a <= Priority b = a <= b + Priority _ <= MaxBound = True + MaxBound <= MaxBound = True + MaxBound <= _ = False + + MinBound `min` _ = MinBound + _ `min` MinBound = MinBound + Priority a `min` Priority b = Priority (a `min` b) + u `min` MaxBound = u + MaxBound `min` v = v + + MinBound `max` v = v + u `max` MinBound = u + Priority a `max` Priority b = Priority (a `max` b) + _ `max` MaxBound = MaxBound + MaxBound `max` _ = MaxBound + +instance Arbitrary a => Arbitrary (Priority a) where + arbitrary = frequency [ (1 ,return MinBound) + , (10, fmap Priority arbitrary) + , (1 ,return MaxBound) ] + coarbitrary MinBound = variant 0 + coarbitrary (Priority a) = variant 1 . coarbitrary a + coarbitrary MaxBound = variant 2 + +instance Ord a => Monoid (Priority a) where + mappend = max + mempty = minBound + +instance Ord a => Multiplicative (Priority a) where + times = min + one = maxBound + +instance Ord a => LeftSemiNearRing (Priority a) +instance Ord a => RightSemiNearRing (Priority a) +instance Ord a => SemiRing (Priority a) + +instance Ord a => Reducer a (Priority a) where + unit = Priority + +instance Ord a => Reducer (MinPriority a) (Priority a) where + unit (MinPriority Nothing) = MaxBound + unit (MinPriority (Just x)) = Priority x + +instance Ord a => Reducer (MaxPriority a) (Priority a) where + unit (MaxPriority Nothing) = MinBound + unit (MaxPriority (Just x)) = Priority x + +instance Functor Priority where + fmap _ MaxBound = MaxBound + fmap f (Priority a) = Priority (f a) + fmap _ MinBound = MinBound + +instance Pointed Priority where + point = Priority + + addfile ./doc/html/monoids/src/Data-Ring-Semi-Tropical.html hunk ./doc/html/monoids/src/Data-Ring-Semi-Tropical.html 1 + + + + +Data/Ring/Semi/Tropical.hs + + + +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-} +----------------------------------------------------------------------------- +---- | +---- Module : Data.Ring.Semi.Tropical +---- Copyright : (c) Edward Kmett 2009 +---- License : BSD-style +---- Maintainer : libraries@haskell.org +---- Stability : experimental +---- Portability : portable +---- +----------------------------------------------------------------------------- + +module Data.Ring.Semi.Tropical + ( module Data.Monoid.Reducer + , module Data.Ring.Semi + -- * Tropical Semirings + , infinity + , Tropical(Tropical,getTropical) + ) where + +import Control.Functor.Pointed +import Data.Monoid.Reducer (Reducer, unit, Monoid, mappend, mempty) +import Data.Ring.Semi +import Data.Monoid.Ord hiding (infinity) + +infinity :: Tropical a +infinity = Tropical Nothing + +-- | The 'SemiRing' @('min','+')@ over @'a' extended with 'infinity'@. +-- When @a@ has a Num instance with an addition that respects order, then this is +-- transformed into a tropical semiring. It is assumed that 0 is the least element +-- of a. +-- +-- <http://hal.archives-ouvertes.fr/docs/00/11/37/79/PDF/Tropical.pdf> + +newtype Tropical a = Tropical { getTropical :: Maybe a } deriving (Eq,Show,Read) + +instance Ord a => Ord (Tropical a) where + Tropical Nothing `compare` Tropical Nothing = EQ + Tropical Nothing `compare` _ = GT + _ `compare` Tropical Nothing = LT + Tropical (Just a) `compare` Tropical (Just b) = a `compare` b + +instance Ord a => Monoid (Tropical a) where + mempty = infinity + mappend = min + +instance Ord a => Reducer a (Tropical a) where + unit = Tropical . Just + +instance Ord a => Reducer (Maybe a) (Tropical a) where + unit = Tropical + +instance Ord a => Reducer (MinPriority a) (Tropical a) where + unit = Tropical . getMinPriority + +instance Functor Tropical where + fmap f (Tropical a) = Tropical (fmap f a) + +instance Pointed Tropical where + point = Tropical . Just + +instance Num a => Multiplicative (Tropical a) where + one = point $ fromInteger 0 + Tropical Nothing `times` _ = infinity + Tropical (Just a) `times` Tropical (Just b) = point (a + b) + _ `times` Tropical Nothing = infinity + +instance (Ord a, Num a) => LeftSemiNearRing (Tropical a) +instance (Ord a, Num a) => RightSemiNearRing (Tropical a) +instance (Ord a, Num a) => SemiRing (Tropical a) + + addfile ./doc/html/monoids/src/Data-Ring-Semi.html hunk ./doc/html/monoids/src/Data-Ring-Semi.html 1 + + + + +Data/Ring/Semi.hs + + + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Ring.Semi +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : non-portable (MPTCs) +-- +-- +----------------------------------------------------------------------------- + +module Data.Ring.Semi + ( module Data.Ring.Semi.Near + , SemiRing + ) where + +import Data.Ring.Semi.Near + +-- | A 'SemiRing' is an instance of both 'Multiplicative' and 'Monoid' where +-- 'times' distributes over 'plus'. +class (RightSemiNearRing a, LeftSemiNearRing a) => SemiRing a + + addfile ./doc/html/monoids/src/Data-Ring-Sugar.html hunk ./doc/html/monoids/src/Data-Ring-Sugar.html 1 + + + + +Data/Ring/Sugar.hs + + + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Ring.Sugar +-- Copyright : (c) Edward Kmett 2009 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : portable +-- +-- Syntactic sugar for working with rings that conflicts with names from the "Prelude". +-- +-- > import Prelude hiding ((-), (+), (*), negate, subtract) +-- > import Data.Ring.Sugar +-- +----------------------------------------------------------------------------- + +module Data.Ring.Sugar + ( module Data.Monoid.Multiplicative.Sugar + , module Data.Ring.Semi.Near + ) where + +import Data.Monoid.Multiplicative.Sugar +import Data.Ring.Semi.Near + + addfile ./doc/html/monoids/src/Data-Ring.html hunk ./doc/html/monoids/src/Data-Ring.html 1 + + + + +Data/Ring.hs + + + +{-# OPTIONS_GHC -fno-warn-orphans #-} +module Data.Ring + ( module Data.Group + , module Data.Ring.Semi + , Ring + ) where + +import Data.Group +import Data.Ring.Semi + +class (Group a, SemiRing a) => Ring a + + addfile ./doc/html/monoids/src/hscolour.css hunk ./doc/html/monoids/src/hscolour.css 1 +.hs-keyglyph, .hs-layout {color: red;} +.hs-keyword {color: blue;} +.hs-comment, .hs-comment a {color: green;} +.hs-str, .hs-chr {color: teal;} +.hs-keyword, .hs-conid, .hs-varid, .hs-conop, .hs-varop, .hs-num, .hs-cpp, .hs-sel, .hs-definition {} }