# monoid-subclasses

Subclasses of Monoid https://github.com/blamario/monoid-subclasses/

 LTS Haskell 16.15: 1.0.1 Stackage Nightly 2020-09-26: 1.0.1 Latest on Hackage: 1.0.1

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#### Module documentation for 1.0.1

This version can be pinned in stack with:`monoid-subclasses-1.0.1@sha256:ed9e4c44c32990a492bab48e1ba1e3d6ba0e06cf3e34797f8add4465a5fdac71,2258`
• Data
• Data.Monoid
• Data.Semigroup

# monoid-subclasses

### Subclasses of Semigroup and Monoid with a solid theoretical foundation and practical purposes

The monoid-subclasses package has been released on Hackage. The package defines several classes that are richer than semigroups and monoids but less demanding than groups:

• Reductive provides the operator `</>` which acts as a partial inverse of the semigroup `<>` operator.

• Cancellative is a subclass of `Reductive` that provides additional guarantees about the `</>` operation result:

``````  (a <> b) </> a == Just b
(a <> b) </> b == Just a
``````

Every group (i.e., every `Monoid a` with the operation `inverse :: a -> a`) is a cancellative monoid where `a </> b = Just (a <> inverse b)` but not every `Cancellative` monoid is a group.

• GCDMonoid is a subclass of `Reductive` and `Monoid` that provides the `gcd` operation for getting the greatest common denominator for two given monoid values.

• Monus provides the `<\>` monus operation. The set difference is one familiar instance of this operation.

• MonoidNull class provides the Boolean `null` operation that checks if the argument monoid is `mempty`.

• Factorial and FactorialMonoid classes represent semigroups and monoids that can be split up into irreducible factors.

That’s the theoretical point of view. From the practical point of view, the main purpose of the monoid-subclasses package is similar to that of ListLike - to provide unifying abstractions for various monoidal data types in Haskell, primarily String, ByteString, and Text. All three types are already instances of the Monoid class. While that abstraction is useful for building sequences of data, it doesn’t help with deconstructing them.

That being said, there are two major differences in the goals of ListLike and monoid-subclasses:

• ListLike strives to reproduce the standard Data.List interface, whereas monoid-subclasses builds from deeper theoretical foundations; and
• The monoid-subclasses implementation uses standard Haskell 2010, with the exception of two minor extensions which can be worked around if necessary.

The incremental-parser package can serve as a compact example of a parser library that can be applied to different input types thanks to monoid-subclasses. There is also picoparsec, a fork of attoparsec, and the heavy-duty grammatical-parsers library.

A more thorough description of the library design can be found in the Haskell Symposium 2013 paper Adding Structure to Monoids

## Version 1.0.1

• Incremented the lower bound of the base dependency

## Version 1.0

• Fixed issue #24, unlawful LeftReductiveMonoid instance for Map
• Tightened the laws of GCD classes, dropped instances for Sum and Product
• Introduced the `Monus` class
• Introduced the `OverlappingGCDMonoid` class
• Added the instances of type `Sum Natural` and `Product Natural`
• Using the language extensions ‘FlexibleInstances’ and ‘OverlappingInstances’
• Removed the linear complexity requirement
• Added and documented less efficient instances
• Moved various GCD classes into the new module `Data.Monoid.GCD`
• Added module `Data.Semigroup.Cancellative` with `Semigroup` subclasses
• Added module `Data.Semigroup.Factorial` with `Semigroup` subclasses
• Deprecated several `Monoid` subclasses and made them constraint synonyms instead:
• `type CommutativeMonoid m = (Monoid m, Commutative m)`
• `type ReductiveMonoid m = (Monoid m, Reductive m)`
• `type LeftReductiveMonoid m = (Monoid m, LeftReductive m)`
• `type RightReductiveMonoid m = (Monoid m, RightReductive m)`
• `type CancellativeMonoid m = (Monoid m, Cancellative m)`
• `type LeftCancellativeMonoid m = (Monoid m, LeftCancellative m)`
• `type RightCancellativeMonoid m = (Monoid m, RightCancellative m)`

## Version 0.4.6.1

Bumped the containers dependency upper bounds

## Version 0.4.6

Added the Semigroup instances to fix the compilation errors with base-4.11

## Version 0.4.4

Fixed boundary condition bugs in ByteStringUTF8 uncovered by a new version of QuickCheck

## Version 0.4.3.2

Fixed compilation errors with GHC 7.8.4 and older

## Version 0.4.3.1

Bumped the vector dependency upper bounds

## Version 0.4.3

• Added instances for 3- and 4-tuples
• Re-implemented Concat as an own data type, dropping Seq

## Version 0.4.2.1

• Fixed compilation problems with GHC 8 and containers-0.5.7
• Fixed compilation problems with GHC 8 and containers-0.5.7
• Merge pull request #10 from mgiles: minor typo in FactorialMonoid laws

## Version 0.4.2

• Fixed a bug in splitAt implementation for ByteStringUTF8
• Merge pull request #9 from phadej: use newest quickcheck-instances
• Removed the overzealous assertions from ByteStringUTF8

## Version 0.4.1.2

Removing accidental reference to Instances.Markup module

## Version 0.4.1.1

• Bumped the vector dependency upper bounds
• Removed GHC-prof-options from the cabal file

## Version 0.4.1

• Changed the Prelude imports to enable compilation with GHC 7.4
• Added INLINE pragmas
• Added the toString method to TextualMonoid class
• Importing Text.Show.Functions to avoid overlapping instances
• Eliminated the redundant import warnings from GHC 7.10.1

## Version 0.4.0.4

• Added -Wall GHC option and eliminated almost all the warnings
• Fixed a bug in the Textual instance of ByteStringUTF8

## Version 0.4.0.3

• Excluding the imports of foldMap from Prelude

## Version 0.4.0.2

• Added more tests and fixed a bug in Stateful
• Fixed a bug in Positioned.span_
• Optimized the Stateful data type

## Version 0.3.6.2

• Added a bunch of pragmas

## Version 0.3.6

• Deprecated all the inject functions
• Registered the new Stateful module

## Version 0.3.4.1

Accommodating the text-1.0 release

• Introduced the function ByteStringUTF8.decode
• Removed the utf-string dependency
• Replaced the utf-string import by a more efficient UTF-8 encoding

## Version 0.3.1

• Added the Data.Monoid.Instances.Concat module and tests
• Added the PositiveMonoid class
• Added the StableFactorialMonoid subclass of FactorialMonoid
• Added more instances for ()

## Version 0.3

Added the CommutativeMonoid class at the root of the Cancellative classes

## Version 0.2

• Added TextualMonoid instances for Seq Char and Vector Char
• Renamed the FactorialMonoid method map to foldMap in keeping with Foldable

## Version 0.1.2

Optimizations of the default Factorial methods and of the ButeStringUTF8 instances

## Version 0.1

Initial release

Depends on 6 packages(full list with versions):
Used by 3 packages in lts-16.14(full list with versions):