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1. module Toml.Codec.Combinator.Monoid

   TOML-specific combinators for converting between TOML and Haskell Monoid wrapper data types. These codecs are especially handy when you are implementing the Partial Options Monoid pattern. TODO: table

2. module Numeric.Partial.Monoid

   No documentation available.

3. class Semigroup a => Monoid a

   classy-prelude-yesod	ClassyPrelude.Yesod

   The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

   • Right identity x <> mempty = x
   • Left identity mempty <> x = x
   • Associativity x <> (y <> z) = (x <> y) <> z (Semigroup law)
   • Concatenation mconcat = foldr (<>) mempty
   You can alternatively define mconcat instead of mempty, in which case the laws are:
   • Unit mconcat (pure x) = x
   • Multiplication mconcat (join xss) = mconcat (fmap mconcat xss)
   • Subclass mconcat (toList xs) = sconcat xs
   The method names refer to the monoid of lists under concatenation, but there are many other instances. Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product. NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

4. class Semigroup a => Monoid a

   constrained-categories	Control.Category.Constrained.Prelude

   The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

   • Right identity x <> mempty = x
   • Left identity mempty <> x = x
   • Associativity x <> (y <> z) = (x <> y) <> z (Semigroup law)
   • Concatenation mconcat = foldr (<>) mempty
   You can alternatively define mconcat instead of mempty, in which case the laws are:
   • Unit mconcat (pure x) = x
   • Multiplication mconcat (join xss) = mconcat (fmap mconcat xss)
   • Subclass mconcat (toList xs) = sconcat xs
   The method names refer to the monoid of lists under concatenation, but there are many other instances. Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product. NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

5. class Semigroup a => Monoid a

   constrained-categories	Control.Category.Hask

   The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

   • Right identity x <> mempty = x
   • Left identity mempty <> x = x
   • Associativity x <> (y <> z) = (x <> y) <> z (Semigroup law)
   • Concatenation mconcat = foldr (<>) mempty
   You can alternatively define mconcat instead of mempty, in which case the laws are:
   • Unit mconcat (pure x) = x
   • Multiplication mconcat (join xss) = mconcat (fmap mconcat xss)
   • Subclass mconcat (toList xs) = sconcat xs
   The method names refer to the monoid of lists under concatenation, but there are many other instances. Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product. NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

6. class Semigroup a => Monoid a

   copilot-language	Copilot.Language.Prelude

   The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

   • Right identity x <> mempty = x
   • Left identity mempty <> x = x
   • Associativity x <> (y <> z) = (x <> y) <> z (Semigroup law)
   • Concatenation mconcat = foldr (<>) mempty
   You can alternatively define mconcat instead of mempty, in which case the laws are:
   • Unit mconcat (pure x) = x
   • Multiplication mconcat (join xss) = mconcat (fmap mconcat xss)
   • Subclass mconcat (toList xs) = sconcat xs
   The method names refer to the monoid of lists under concatenation, but there are many other instances. Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product. NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

7. class Semigroup a => Monoid a

   quaalude	Essentials

   The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

   • Right identity x <> mempty = x
   • Left identity mempty <> x = x
   • Associativity x <> (y <> z) = (x <> y) <> z (Semigroup law)
   • Concatenation mconcat = foldr (<>) mempty
   You can alternatively define mconcat instead of mempty, in which case the laws are:
   • Unit mconcat (pure x) = x
   • Multiplication mconcat (join xss) = mconcat (fmap mconcat xss)
   • Subclass mconcat (toList xs) = sconcat xs
   The method names refer to the monoid of lists under concatenation, but there are many other instances. Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product. NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

8. class Semigroup a => Monoid a

   verset	Verset

   The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

   • Right identity x <> mempty = x
   • Left identity mempty <> x = x
   • Associativity x <> (y <> z) = (x <> y) <> z (Semigroup law)
   • Concatenation mconcat = foldr (<>) mempty
   You can alternatively define mconcat instead of mempty, in which case the laws are:
   • Unit mconcat (pure x) = x
   • Multiplication mconcat (join xss) = mconcat (fmap mconcat xss)
   • Subclass mconcat (toList xs) = sconcat xs
   The method names refer to the monoid of lists under concatenation, but there are many other instances. Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product. NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

9. class Semigroup a => Monoid a

   xmonad-contrib	XMonad.Config.Prime

   The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

   • Right identity x <> mempty = x
   • Left identity mempty <> x = x
   • Associativity x <> (y <> z) = (x <> y) <> z (Semigroup law)
   • Concatenation mconcat = foldr (<>) mempty
   You can alternatively define mconcat instead of mempty, in which case the laws are:
   • Unit mconcat (pure x) = x
   • Multiplication mconcat (join xss) = mconcat (fmap mconcat xss)
   • Subclass mconcat (toList xs) = sconcat xs
   The method names refer to the monoid of lists under concatenation, but there are many other instances. Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product. NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

10. monoid :: (Monoid a, Show a, Arbitrary a, EqProp a) => a -> TestBatch

    checkers	Test.QuickCheck.Classes

    Properties to check that the Monoid a satisfies the monoid properties. The argument value is ignored and is present only for its type.

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