# Hoogle Search

1. 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.

2. base Prelude

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

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.

3. A type a is a Monoid if it provides an associative function (<>) that lets you combine any two values of type a into one, and a neutral element (mempty) such that

```a <> mempty == mempty <> a == a
```
A Monoid is a Semigroup with the added requirement of a neutral element. Thus any Monoid is a Semigroup, but not the other way around.

#### Examples

The Sum monoid is defined by the numerical addition operator and `0` as neutral element:
```>>> mempty :: Sum Int
Sum 0

>>> Sum 1 <> Sum 2 <> Sum 3 <> Sum 4 :: Sum Int
Sum {getSum = 10}
```
We can combine multiple values in a list into a single value using the mconcat function. Note that we have to specify the type here since Int is a monoid under several different operations:
```>>> mconcat [1,2,3,4] :: Sum Int
Sum {getSum = 10}

>>> mconcat [] :: Sum Int
Sum {getSum = 0}
```
Another valid monoid instance of Int is Product It is defined by multiplication and `1` as neutral element:
```>>> Product 1 <> Product 2 <> Product 3 <> Product 4 :: Product Int
Product {getProduct = 24}

>>> mconcat [1,2,3,4] :: Product Int
Product {getProduct = 24}

>>> mconcat [] :: Product Int
Product {getProduct = 1}
```

4. base Data.Monoid

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

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. base GHC.Base

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

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. hspec Test.Hspec.Discover

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

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. base-compat Data.Monoid.Compat

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

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. hedgehog Hedgehog.Internal.Prelude

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

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. validity Data.Validity

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

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. Cabal Distribution.Compat.Prelude.Internal

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

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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