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1. module Data.Monoid

   No documentation available.

2. module Test.Validity.Monoid

   Monoid properties You will need TypeApplications to use these.

3. module Generics.Deriving.Monoid

   No documentation available.

4. class Semigroup a => Monoid a

   rio	RIO.Prelude.Types

   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

   base-compat-batteries	Data.Monoid.Compat

   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. module Test.Syd.Validity.Monoid

   Monoid properties You will need TypeApplications to use these.

7. class Semigroup a => Monoid a

   basement	Basement.Compat.Base

   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

   basement	Basement.Imports

   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. module Relude.Monoid

   Reexports functions to work with monoids plus adds extra useful functions.

10. class Semigroup a => Monoid a

    relude	Relude.Monoid

    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.

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