Monoid (core 5.0 API)

java.lang.Object
- fj.Monoid<A>

```
public final class Monoid<A>
extends java.lang.Object
```
A monoid abstraction to be defined across types of the given type argument. Implementations must follow the monoidal laws:
- Left Identity; forall x. sum(zero(), x) == x
- Right Identity; forall x. sum(x, zero()) == x
- Associativity; forall x y z. sum(sum(x, y), z) == sum(x, sum(y, z))

Nested Class Summary

Nested Classes
Modifier and Type	Class and Description
`static interface`	`Monoid.AltDefinition<A>` Primitives functions of Monoid: alternative minimal definition and overridable methods.
`static interface`	`Monoid.Definition<A>` Primitives functions of Monoid: minimal definition and overridable methods.

Field Summary

Fields
Modifier and Type	Field and Description
`static Monoid<java.math.BigDecimal>`	`bigdecimalAdditionMonoid` A monoid that adds big decimals.
`static Monoid<java.math.BigDecimal>`	`bigdecimalMultiplicationMonoid` A monoid that multiplies big decimals.
`static Monoid<java.math.BigInteger>`	`bigintAdditionMonoid` A monoid that adds big integers.
`static Monoid<java.math.BigInteger>`	`bigintMultiplicationMonoid` A monoid that multiplies big integers.
`static Monoid<java.lang.Boolean>`	`conjunctionMonoid` A monoid that ANDs booleans.
`static Monoid<java.lang.Boolean>`	`disjunctionMonoid` A monoid that ORs booleans.
`static Monoid<java.lang.Boolean>`	`exclusiveDisjunctionMonoid` A monoid that XORs booleans.
`static Monoid<java.lang.Integer>`	`intAdditionMonoid` A monoid that adds integers.
`static Monoid<java.lang.Integer>`	`intMaxMonoid` A monoid for the maximum of two integers.
`static Monoid<java.lang.Integer>`	`intMinMonoid` A monoid for the minimum of two integers.
`static Monoid<java.lang.Integer>`	`intMultiplicationMonoid` A monoid that multiplies integers.
`static Monoid<java.lang.Long>`	`longAdditionMonoid` A monoid that adds longs.
`static Monoid<java.lang.Long>`	`longMultiplicationMonoid` A monoid that multiplies longs.
`static Monoid<Natural>`	`naturalAdditionMonoid` A monoid that adds natural numbers.
`static Monoid<Natural>`	`naturalMultiplicationMonoid` A monoid that multiplies natural numbers.
`static Monoid<java.lang.StringBuffer>`	`stringBufferMonoid` A monoid that appends string buffers.
`static Monoid<java.lang.StringBuilder>`	`stringBuilderMonoid` A monoid that appends string builders.
`static Monoid<java.lang.String>`	`stringMonoid` A monoid that appends strings.
`static Monoid<Unit>`	`unitMonoid` A monoid for the Unit value.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`static <A> Monoid<Array<A>>`	`arrayMonoid()` A monoid for arrays.
`<B> Monoid<P2<A,B>>`	`compose(Monoid<B> m)` Composes this monoid with another.
`<B,C> Monoid<C>`	`compose(Monoid<B> mb, F<C,A> a, F<C,B> b, F2<A,B,C> c)`
`Monoid<A>`	`dual()` Swaps the arguments when summing.
`static <A> Monoid<Option<A>>`	`firstOptionMonoid()` A monoid for options that take the first available value.
`static <A,B> Monoid<F<A,B>>`	`functionMonoid(Monoid<B> mb)` A monoid for functions.
`static <A> Monoid<IO<A>>`	`ioMonoid(Monoid<A> ma)` A monoid for IO values.
`A`	`join(java.lang.Iterable<A> as, A a)` Intersperses the given value between each two elements of the iterable, and sums the result.
`static <A> Monoid<Option<A>>`	`lastOptionMonoid()` A monoid for options that take the last available value.
`static <A> Monoid<List<A>>`	`listMonoid()` A monoid for lists.
`static <A> Monoid<A>`	`monoid(F<A,F<A,A>> sum, A zero)` Constructs a monoid from the given sum function and zero value, which must follow the monoidal laws.
`static <A> Monoid<A>`	`monoid(F2<A,A,A> sum, A zero)` Constructs a monoid from the given sum function and zero value, which must follow the monoidal laws.
`static <A> Monoid<A>`	`monoidDef(Monoid.AltDefinition<A> def)` Constructs a monoid from the given definition, which must follow the monoidal laws.
`static <A> Monoid<A>`	`monoidDef(Monoid.Definition<A> def)` Constructs a monoid from the given definition, which must follow the monoidal laws.
`static <A> Monoid<A>`	`monoidDef(Semigroup.AltDefinition<A> s, A zero)` Constructs a monoid from the given semigroup definition and zero value, which must follow the monoidal laws.
`static <A> Monoid<A>`	`monoidDef(Semigroup.Definition<A> s, A zero)` Constructs a monoid from the given semigroup definition and zero value, which must follow the monoidal laws.
`A`	`multiply(int n, A a)` Returns a value summed `n` times (`a + a + ...`
`static <A> Monoid<Option<A>>`	`optionMonoid(Semigroup<A> aSemigroup)` Lift a `Semigroup<A>` for A to a `Monoid<Option<A>>`, using Option.none() as zero.
`Semigroup<A>`	`semigroup()` Returns a semigroup projection of this monoid.
`static <A> Monoid<Set<A>>`	`setIntersectionMonoid(Bounded<A> bounded, Enumerator<A> enumerator)` A intersection monoid for sets.
`static <A> Monoid<Set<A>>`	`setMonoid(Ord<A> o)` A union monoid for sets.
`static <A> Monoid<Stream<A>>`	`streamMonoid()` A monoid for streams.
`F<A,F<A,A>>`	`sum()` Returns a function that sums according to this monoid.
`F<A,A>`	`sum(A a1)` Returns a function that sums the given value according to this monoid.
`A`	`sum(A a1, A a2)` Sums the two given arguments.
`F<List<A>,A>`	`sumLeft()` Returns a function that sums the given values with left-fold.
`A`	`sumLeft(List<A> as)` Sums the given values with left-fold.
`A`	`sumLeft(Stream<A> as)` Sums the given values with left-fold.
`F<Stream<A>,A>`	`sumLeftS()` Returns a function that sums the given values with left-fold.
`F<List<A>,A>`	`sumRight()` Returns a function that sums the given values with right-fold.
`A`	`sumRight(List<A> as)` Sums the given values with right-fold.
`A`	`sumRight(Stream<A> as)` Sums the given values with right-fold.
`<B> Monoid<B>`	`xmap(F<A,B> f, F<B,A> g)` Maps the given functions across this monoid as an invariant functor.
`A`	`zero()` The zero value for this monoid.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
 - intAdditionMonoid
```
public static final Monoid<java.lang.Integer> intAdditionMonoid
```
 A monoid that adds integers.
 - intMultiplicationMonoid
```
public static final Monoid<java.lang.Integer> intMultiplicationMonoid
```
 A monoid that multiplies integers.
 - bigintAdditionMonoid
```
public static final Monoid<java.math.BigInteger> bigintAdditionMonoid
```
 A monoid that adds big integers.
 - bigintMultiplicationMonoid
```
public static final Monoid<java.math.BigInteger> bigintMultiplicationMonoid
```
 A monoid that multiplies big integers.
 - bigdecimalAdditionMonoid
```
public static final Monoid<java.math.BigDecimal> bigdecimalAdditionMonoid
```
 A monoid that adds big decimals.
 - bigdecimalMultiplicationMonoid
```
public static final Monoid<java.math.BigDecimal> bigdecimalMultiplicationMonoid
```
 A monoid that multiplies big decimals.
 - naturalAdditionMonoid
```
public static final Monoid<Natural> naturalAdditionMonoid
```
 A monoid that adds natural numbers.
 - naturalMultiplicationMonoid
```
public static final Monoid<Natural> naturalMultiplicationMonoid
```
 A monoid that multiplies natural numbers.
 - longAdditionMonoid
```
public static final Monoid<java.lang.Long> longAdditionMonoid
```
 A monoid that adds longs.
 - longMultiplicationMonoid
```
public static final Monoid<java.lang.Long> longMultiplicationMonoid
```
 A monoid that multiplies longs.
 - disjunctionMonoid
```
public static final Monoid<java.lang.Boolean> disjunctionMonoid
```
 A monoid that ORs booleans.
 - exclusiveDisjunctionMonoid
```
public static final Monoid<java.lang.Boolean> exclusiveDisjunctionMonoid
```
 A monoid that XORs booleans.
 - conjunctionMonoid
```
public static final Monoid<java.lang.Boolean> conjunctionMonoid
```
 A monoid that ANDs booleans.
 - stringMonoid
```
public static final Monoid<java.lang.String> stringMonoid
```
 A monoid that appends strings.
 - stringBufferMonoid
```
public static final Monoid<java.lang.StringBuffer> stringBufferMonoid
```
 A monoid that appends string buffers.
 - stringBuilderMonoid
```
public static final Monoid<java.lang.StringBuilder> stringBuilderMonoid
```
 A monoid that appends string builders.
 - intMaxMonoid
```
public static final Monoid<java.lang.Integer> intMaxMonoid
```
 A monoid for the maximum of two integers.
 - intMinMonoid
```
public static final Monoid<java.lang.Integer> intMinMonoid
```
 A monoid for the minimum of two integers.
 - unitMonoid
```
public static final Monoid<Unit> unitMonoid
```
 A monoid for the Unit value.
- Method Detail
 - compose
```
public  Monoid<P2<A,B>> compose(Monoid m)
```
 Composes this monoid with another.
 - semigroup
```
public Semigroup<A> semigroup()
```
 Returns a semigroup projection of this monoid.
 
 Returns:
 
 A semigroup projection of this monoid.
 - xmap
```
public  Monoid xmap(F<A,B> f,
 F<B,A> g)
```
 Maps the given functions across this monoid as an invariant functor.
 
 Parameters:
 
 f - The covariant map.
 
 g - The contra-variant map.
 
 Returns:
 
 A new monoid.
 - compose
```
public <B,C> Monoid<C> compose(Monoid mb,
 F<C,A> a,
 F<C,B> b,
 F2<A,B,C> c)
```
 - sum
```
public A sum(A a1,
 A a2)
```
 Sums the two given arguments.
 
 Parameters:
 
 a1 - A value to sum with another.
 
 a2 - A value to sum with another.
 
 Returns:
 
 The of the two given arguments.
 - sum
```
public F<A,A> sum(A a1)
```
 Returns a function that sums the given value according to this monoid.
 
 Parameters:
 
 a1 - The value to sum.
 
 Returns:
 
 A function that sums the given value according to this monoid.
 - sum
```
public F<A,F<A,A>> sum()
```
 Returns a function that sums according to this monoid.
 
 Returns:
 
 A function that sums according to this monoid.
 - zero
```
public A zero()
```
 The zero value for this monoid.
 
 Returns:
 
 The zero value for this monoid.
 - multiply
```
public A multiply(int n,
 A a)
```
 Returns a value summed n times (a + a + ... + a). The default definition uses peasant multiplication, exploiting associativity to only require O(log n) uses of sum(Object, Object).
 
 Parameters:
 
 n - multiplier
 
 a - the value to be reapeatly summed
 
 Returns:
 
 a summed n times. If n <= 0, returns zero()
 - sumRight
```
public A sumRight(List<A> as)
```
 Sums the given values with right-fold.
 
 Parameters:
 
 as - The values to sum.
 
 Returns:
 
 The sum of the given values.
 - sumRight
```
public A sumRight(Stream<A> as)
```
 Sums the given values with right-fold.
 
 Parameters:
 
 as - The values to sum.
 
 Returns:
 
 The sum of the given values.
 - sumLeft
```
public A sumLeft(List<A> as)
```
 Sums the given values with left-fold.
 
 Parameters:
 
 as - The values to sum.
 
 Returns:
 
 The sum of the given values.
 - sumLeft
```
public A sumLeft(Stream<A> as)
```
 Sums the given values with left-fold.
 
 Parameters:
 
 as - The values to sum.
 
 Returns:
 
 The sum of the given values.
 - sumLeft
```
public F<List<A>,A> sumLeft()
```
 Returns a function that sums the given values with left-fold.
 
 Returns:
 
 a function that sums the given values with left-fold.
 - sumRight
```
public F<List<A>,A> sumRight()
```
 Returns a function that sums the given values with right-fold.
 
 Returns:
 
 a function that sums the given values with right-fold.
 - sumLeftS
```
public F<Stream<A>,A> sumLeftS()
```
 Returns a function that sums the given values with left-fold.
 
 Returns:
 
 a function that sums the given values with left-fold.
 - join
```
public A join(java.lang.Iterable<A> as,
 A a)
```
 Intersperses the given value between each two elements of the iterable, and sums the result.
 
 Parameters:
 
 as - An iterable of values to sum.
 
 a - The value to intersperse between values of the given iterable.
 
 Returns:
 
 The sum of the given values and the interspersed value.
 - dual
```
public Monoid<A> dual()
```
 Swaps the arguments when summing.
 - monoidDef
```
public static <A> Monoid<A> monoidDef(Monoid.Definition<A> def)
```
 Constructs a monoid from the given definition, which must follow the monoidal laws.
 
 Parameters:
 
 def - The definition for the monoid.
 
 Returns:
 
 A monoid instance that uses the given sun function and zero value.
 - monoidDef
```
public static <A> Monoid<A> monoidDef(Monoid.AltDefinition<A> def)
```
 Constructs a monoid from the given definition, which must follow the monoidal laws.
 
 Parameters:
 
 def - The definition for the monoid.
 
 Returns:
 
 A monoid instance that uses the given sun function and zero value.
 - monoidDef
```
public static <A> Monoid<A> monoidDef(Semigroup.Definition<A> s,
 A zero)
```
 Constructs a monoid from the given semigroup definition and zero value, which must follow the monoidal laws.
 
 Parameters:
 
 s - The semigroup definition for the monoid.
 
 zero - The zero for the monoid.
 
 Returns:
 
 A monoid instance that uses the given sun function and zero value.
 - monoidDef
```
public static <A> Monoid<A> monoidDef(Semigroup.AltDefinition<A> s,
 A zero)
```
 Constructs a monoid from the given semigroup definition and zero value, which must follow the monoidal laws.
 
 Parameters:
 
 s - The semigroup definition for the monoid.
 
 zero - The zero for the monoid.
 
 Returns:
 
 A monoid instance that uses the given sun function and zero value.
 - monoid
```
public static <A> Monoid<A> monoid(F<A,F<A,A>> sum,
 A zero)
```
 Constructs a monoid from the given sum function and zero value, which must follow the monoidal laws. Java 8+ users: use monoidDef(Semigroup.Definition, Object) instead.
 
 Parameters:
 
 sum - The sum function for the monoid.
 
 zero - The zero for the monoid.
 
 Returns:
 
 A monoid instance that uses the given sun function and zero value.
 - monoid
```
public static <A> Monoid<A> monoid(F2<A,A,A> sum,
 A zero)
```
 Constructs a monoid from the given sum function and zero value, which must follow the monoidal laws. Java 8+ users: use monoidDef(Semigroup.Definition, Object) instead.
 
 Parameters:
 
 sum - The sum function for the monoid.
 
 zero - The zero for the monoid.
 
 Returns:
 
 A monoid instance that uses the given sun function and zero value.
 - functionMonoid
```
public static <A,B> Monoid<F<A,B>> functionMonoid(Monoid mb)
```
 A monoid for functions.
 
 Parameters:
 
 mb - The monoid for the function codomain.
 
 Returns:
 
 A monoid for functions.
 - listMonoid
```
public static <A> Monoid<List<A>> listMonoid()
```
 A monoid for lists.
 
 Returns:
 
 A monoid for lists.
 - optionMonoid
```
public static <A> Monoid<Option<A>> optionMonoid(Semigroup<A> aSemigroup)
```
 Lift a Semigroup<A> for A to a Monoid<Option<A>>, using Option.none() as zero.
 
 Returns:
 
 A monoid for option.
 - firstOptionMonoid
```
public static <A> Monoid<Option<A>> firstOptionMonoid()
```
 A monoid for options that take the first available value.
 
 Returns:
 
 A monoid for options that take the first available value.
 - lastOptionMonoid
```
public static <A> Monoid<Option<A>> lastOptionMonoid()
```
 A monoid for options that take the last available value.
 
 Returns:
 
 A monoid for options that take the last available value.
 - streamMonoid
```
public static <A> Monoid<Stream<A>> streamMonoid()
```
 A monoid for streams.
 
 Returns:
 
 A monoid for streams.
 - arrayMonoid
```
public static <A> Monoid<Array<A>> arrayMonoid()
```
 A monoid for arrays.
 
 Returns:
 
 A monoid for arrays.
 - ioMonoid
```
public static <A> Monoid<IO<A>> ioMonoid(Monoid<A> ma)
```
 A monoid for IO values.
 - setMonoid
```
public static <A> Monoid<Set<A>> setMonoid(Ord<A> o)
```
 A union monoid for sets.
 
 Parameters:
 
 o - An order for set elements.
 
 Returns:
 
 A monoid for sets whose elements have the given order.
 - setIntersectionMonoid
```
public static <A> Monoid<Set<A>> setIntersectionMonoid(Bounded<A> bounded,
 Enumerator<A> enumerator)
```
 A intersection monoid for sets.
 
 Parameters:
 
 bounded - A bound for all possible elements
 
 enumerator - An enumerator for all possible elements
 
 Returns:
 
 A monoid for sets whose elements have the given order.

Class Monoid<A>

Nested Class Summary

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

intAdditionMonoid

intMultiplicationMonoid

bigintAdditionMonoid

bigintMultiplicationMonoid

bigdecimalAdditionMonoid

bigdecimalMultiplicationMonoid

naturalAdditionMonoid

naturalMultiplicationMonoid

longAdditionMonoid

longMultiplicationMonoid

disjunctionMonoid

exclusiveDisjunctionMonoid

conjunctionMonoid

stringMonoid

stringBufferMonoid

stringBuilderMonoid

intMaxMonoid

intMinMonoid

unitMonoid

Method Detail

compose

semigroup

xmap

compose

sum

sum

sum

zero

multiply

sumRight

sumRight

sumLeft

sumLeft

sumLeft

sumRight

sumLeftS

join

dual

monoidDef

monoidDef

monoidDef

monoidDef

monoid

monoid

functionMonoid

listMonoid

optionMonoid

firstOptionMonoid

lastOptionMonoid

streamMonoid

arrayMonoid

ioMonoid

setMonoid

setIntersectionMonoid