Semigroup (core 5.0 API)

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

```
public final class Semigroup<A>
extends java.lang.Object
```
Implementations must satisfy the law of associativity:
- Associativity; forall x. forall y. forall z. sum(sum(x, y), z) == sum(x, sum(y, z))

Nested Class Summary

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

Field Summary

Fields
Modifier and Type	Field and Description
`static Semigroup<java.math.BigDecimal>`	`bigdecimalAdditionSemigroup` A semigroup that adds big decimals.
`static Semigroup<java.math.BigDecimal>`	`bigDecimalMaximumSemigroup` A semigroup that yields the maximum of big decimals.
`static Semigroup<java.math.BigDecimal>`	`bigDecimalMinimumSemigroup` A semigroup that yields the minimum of big decimals.
`static Semigroup<java.math.BigDecimal>`	`bigdecimalMultiplicationSemigroup` A semigroup that multiplies big decimals.
`static Semigroup<java.math.BigInteger>`	`bigintAdditionSemigroup` A semigroup that adds big integers.
`static Semigroup<java.math.BigInteger>`	`bigintMaximumSemigroup` A semigroup that yields the maximum of big integers.
`static Semigroup<java.math.BigInteger>`	`bigintMinimumSemigroup` A semigroup that yields the minimum of big integers.
`static Semigroup<java.math.BigInteger>`	`bigintMultiplicationSemigroup` A semigroup that multiplies big integers.
`static Semigroup<java.lang.Boolean>`	`conjunctionSemigroup` A semigroup that ANDs booleans.
`static Semigroup<java.lang.Boolean>`	`disjunctionSemigroup` A semigroup that ORs booleans.
`static Semigroup<java.lang.Boolean>`	`exclusiveDisjunctionSemiGroup` A semigroup that XORs booleans.
`static Semigroup<java.lang.Integer>`	`intAdditionSemigroup` A semigroup that adds integers.
`static Semigroup<java.lang.Integer>`	`intMaximumSemigroup` A semigroup that yields the maximum of integers.
`static Semigroup<java.lang.Integer>`	`intMinimumSemigroup` A semigroup that yields the minimum of integers.
`static Semigroup<java.lang.Integer>`	`intMultiplicationSemigroup` A semigroup that multiplies integers.
`static Semigroup<java.lang.Long>`	`longAdditionSemigroup` A semigroup that adds longs.
`static Semigroup<java.lang.Long>`	`longMaximumSemigroup` A semigroup that yields the maximum of longs.
`static Semigroup<java.lang.Long>`	`longMinimumSemigroup` A semigroup that yields the minimum of longs.
`static Semigroup<java.lang.Long>`	`longMultiplicationSemigroup` A semigroup that multiplies longs.
`static Semigroup<Natural>`	`naturalAdditionSemigroup` A semigroup that adds natural numbers.
`static Semigroup<Natural>`	`naturalMaximumSemigroup` A semigroup that yields the maximum of natural numbers.
`static Semigroup<Natural>`	`naturalMinimumSemigroup` A semigroup that yields the minimum of natural numbers.
`static Semigroup<Natural>`	`naturalMultiplicationSemigroup` A semigroup that multiplies natural numbers.
`static Semigroup<java.lang.StringBuffer>`	`stringBufferSemigroup` A semigroup that appends string buffers.
`static Semigroup<java.lang.StringBuilder>`	`stringBuilderSemigroup` A semigroup that appends string builders.
`static Semigroup<java.lang.String>`	`stringSemigroup` A semigroup that appends strings.
`static Semigroup<Unit>`	`unitSemigroup` A semigroup for the Unit value.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`static <A> Semigroup<Array<A>>`	`arraySemigroup()` A semigroup for arrays.
`<B,C> Semigroup<C>`	`compose(Semigroup<B> sb, F<C,B> b, F<C,A> a, F2<A,B,C> c)`
`Semigroup<A>`	`dual()` Swaps the arguments when summing.
`static <A> Semigroup<Option<A>>`	`firstOptionSemigroup()` A semigroup for optional values that take the first available value.
`static <A> Semigroup<A>`	`firstSemigroup()` A semigroup which always uses the "first" (left-hand side) value.
`static <A,B> Semigroup<F<A,B>>`	`functionSemigroup(Semigroup<B> sb)` A semigroup for functions.
`static <A> Semigroup<IO<A>>`	`ioSemigroup(Semigroup<A> sa)` A semigroup for IO values.
`static <A> Semigroup<Option<A>>`	`lastOptionSemigroup()` A semigroup for optional values that take the last available value.
`static <A> Semigroup<A>`	`lastSemigroup()` A semigroup which always uses the "last" (right-hand side) value.
`Monoid<Option<A>>`	`lift()` Lifts the semigroup to obtain a trivial monoid.
`static <A> Semigroup<List<A>>`	`listSemigroup()` A semigroup for lists.
`Monoid<A>`	`monoid(A zero)` Constructs a monoid from this semigroup and a zero value, which must follow the monoidal laws.
`A`	`multiply1p(int n, A a)` Returns a value summed `n + 1` times ( `a + a + ...`
`static <A> Semigroup<NonEmptyList<A>>`	`nonEmptyListSemigroup()` A semigroup for non-empty lists.
`static <A> Semigroup<P1<A>>`	`p1Semigroup(Semigroup<A> sa)` A lazy semigroup for unary products.
`static <A,B> Semigroup<P2<A,B>>`	`p2Semigroup(Semigroup<A> sa, Semigroup<B> sb)` A lazy semigroup for binary products.
`static <A> Semigroup<A>`	`semigroup(F<A,F<A,A>> sum)` Constructs a semigroup from the given function.
`static <A> Semigroup<A>`	`semigroup(F2<A,A,A> sum)` Constructs a semigroup from the given function.
`static <A> Semigroup<A>`	`semigroupDef(Semigroup.AltDefinition<A> def)` Constructs a semigroup from the given definition.
`static <A> Semigroup<A>`	`semigroupDef(Semigroup.Definition<A> def)` Constructs a semigroup from the given definition.
`static <A> Semigroup<Set<A>>`	`setIntersectionSemigroup()` A intersection semigroup for sets.
`static <A> Semigroup<Set<A>>`	`setSemigroup()` A union semigroup for sets.
`static <A> Semigroup<Stream<A>>`	`streamSemigroup()` A semigroup for streams.
`F<A,F<A,A>>`	`sum()` Returns a function that sums according to this semigroup.
`F<A,A>`	`sum(A a1)` Returns a function that sums the given value according to this semigroup.
`A`	`sum(A a1, A a2)` Sums the two given arguments.
`A`	`sumNel(NonEmptyList<A> as)` Sums the given values with left-fold.
`A`	`sumStream(A a, F0<Stream<A>> as)` Sums the given values with left-fold, shortcutting the computation as early as possible.
`<B> Semigroup<B>`	`xmap(F<A,B> f, F<B,A> g)` Maps the given functions across this monoid as an invariant functor.

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

- Field Detail
 - intAdditionSemigroup
```
public static final Semigroup<java.lang.Integer> intAdditionSemigroup
```
 A semigroup that adds integers.
 - intMultiplicationSemigroup
```
public static final Semigroup<java.lang.Integer> intMultiplicationSemigroup
```
 A semigroup that multiplies integers.
 - intMaximumSemigroup
```
public static final Semigroup<java.lang.Integer> intMaximumSemigroup
```
 A semigroup that yields the maximum of integers.
 - intMinimumSemigroup
```
public static final Semigroup<java.lang.Integer> intMinimumSemigroup
```
 A semigroup that yields the minimum of integers.
 - bigintAdditionSemigroup
```
public static final Semigroup<java.math.BigInteger> bigintAdditionSemigroup
```
 A semigroup that adds big integers.
 - bigintMultiplicationSemigroup
```
public static final Semigroup<java.math.BigInteger> bigintMultiplicationSemigroup
```
 A semigroup that multiplies big integers.
 - bigintMaximumSemigroup
```
public static final Semigroup<java.math.BigInteger> bigintMaximumSemigroup
```
 A semigroup that yields the maximum of big integers.
 - bigintMinimumSemigroup
```
public static final Semigroup<java.math.BigInteger> bigintMinimumSemigroup
```
 A semigroup that yields the minimum of big integers.
 - bigdecimalAdditionSemigroup
```
public static final Semigroup<java.math.BigDecimal> bigdecimalAdditionSemigroup
```
 A semigroup that adds big decimals.
 - bigdecimalMultiplicationSemigroup
```
public static final Semigroup<java.math.BigDecimal> bigdecimalMultiplicationSemigroup
```
 A semigroup that multiplies big decimals.
 - bigDecimalMaximumSemigroup
```
public static final Semigroup<java.math.BigDecimal> bigDecimalMaximumSemigroup
```
 A semigroup that yields the maximum of big decimals.
 - bigDecimalMinimumSemigroup
```
public static final Semigroup<java.math.BigDecimal> bigDecimalMinimumSemigroup
```
 A semigroup that yields the minimum of big decimals.
 - naturalMultiplicationSemigroup
```
public static final Semigroup<Natural> naturalMultiplicationSemigroup
```
 A semigroup that multiplies natural numbers.
 - naturalAdditionSemigroup
```
public static final Semigroup<Natural> naturalAdditionSemigroup
```
 A semigroup that adds natural numbers.
 - naturalMaximumSemigroup
```
public static final Semigroup<Natural> naturalMaximumSemigroup
```
 A semigroup that yields the maximum of natural numbers.
 - naturalMinimumSemigroup
```
public static final Semigroup<Natural> naturalMinimumSemigroup
```
 A semigroup that yields the minimum of natural numbers.
 - longAdditionSemigroup
```
public static final Semigroup<java.lang.Long> longAdditionSemigroup
```
 A semigroup that adds longs.
 - longMultiplicationSemigroup
```
public static final Semigroup<java.lang.Long> longMultiplicationSemigroup
```
 A semigroup that multiplies longs.
 - longMaximumSemigroup
```
public static final Semigroup<java.lang.Long> longMaximumSemigroup
```
 A semigroup that yields the maximum of longs.
 - longMinimumSemigroup
```
public static final Semigroup<java.lang.Long> longMinimumSemigroup
```
 A semigroup that yields the minimum of longs.
 - disjunctionSemigroup
```
public static final Semigroup<java.lang.Boolean> disjunctionSemigroup
```
 A semigroup that ORs booleans.
 - exclusiveDisjunctionSemiGroup
```
public static final Semigroup<java.lang.Boolean> exclusiveDisjunctionSemiGroup
```
 A semigroup that XORs booleans.
 - conjunctionSemigroup
```
public static final Semigroup<java.lang.Boolean> conjunctionSemigroup
```
 A semigroup that ANDs booleans.
 - stringSemigroup
```
public static final Semigroup<java.lang.String> stringSemigroup
```
 A semigroup that appends strings.
 - stringBufferSemigroup
```
public static final Semigroup<java.lang.StringBuffer> stringBufferSemigroup
```
 A semigroup that appends string buffers.
 - stringBuilderSemigroup
```
public static final Semigroup<java.lang.StringBuilder> stringBuilderSemigroup
```
 A semigroup that appends string builders.
 - unitSemigroup
```
public static final Semigroup<Unit> unitSemigroup
```
 A semigroup for the Unit value.
- Method Detail
 - 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 semigroup.
 
 Parameters:
 
 a1 - The value to sum.
 
 Returns:
 
 A function that sums the given value according to this semigroup.
 - sum
```
public F<A,F<A,A>> sum()
```
 Returns a function that sums according to this semigroup.
 
 Returns:
 
 A function that sums according to this semigroup.
 - multiply1p
```
public A multiply1p(int n,
 A a)
```
 Returns a value summed n + 1 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 n + 1 times
 
 Returns:
 
 a summed n times. If n <= 0, returns zero()
 - sumNel
```
public A sumNel(NonEmptyList<A> as)
```
 Sums the given values with left-fold.
 - sumStream
```
public A sumStream(A a,
 F0<Stream<A>> as)
```
 Sums the given values with left-fold, shortcutting the computation as early as possible.
 - dual
```
public Semigroup<A> dual()
```
 Swaps the arguments when summing.
 - lift
```
public Monoid<Option<A>> lift()
```
 Lifts the semigroup to obtain a trivial monoid.
 - xmap
```
public  Semigroup 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> Semigroup<C> compose(Semigroup sb,
 F<C,B> b,
 F<C,A> a,
 F2<A,B,C> c)
```
 - monoid
```
public Monoid<A> monoid(A zero)
```
 Constructs a monoid from this semigroup and a zero value, which must follow the monoidal laws.
 
 Parameters:
 
 zero - The zero for the monoid.
 
 Returns:
 
 A monoid instance that uses the given sun function and zero value.
 - semigroupDef
```
public static <A> Semigroup<A> semigroupDef(Semigroup.Definition<A> def)
```
 Constructs a semigroup from the given definition.
 
 Parameters:
 
 def - The definition to construct this semigroup with.
 
 Returns:
 
 A semigroup from the given definition.
 - semigroupDef
```
public static <A> Semigroup<A> semigroupDef(Semigroup.AltDefinition<A> def)
```
 Constructs a semigroup from the given definition.
 
 Parameters:
 
 def - The definition to construct this semigroup with.
 
 Returns:
 
 A semigroup from the given definition.
 - semigroup
```
public static <A> Semigroup<A> semigroup(F<A,F<A,A>> sum)
```
 Constructs a semigroup from the given function. Java 8+ users: use semigroupDef(AltDefinition) instead.
 
 Parameters:
 
 sum - The function to construct this semigroup with.
 
 Returns:
 
 A semigroup from the given function.
 - semigroup
```
public static <A> Semigroup<A> semigroup(F2<A,A,A> sum)
```
 Constructs a semigroup from the given function. Java 8+ users: use semigroupDef(Definition) instead.
 
 Parameters:
 
 sum - The function to construct this semigroup with.
 
 Returns:
 
 A semigroup from the given function.
 - firstSemigroup
```
public static <A> Semigroup<A> firstSemigroup()
```
 A semigroup which always uses the "first" (left-hand side) value.
 - lastSemigroup
```
public static <A> Semigroup<A> lastSemigroup()
```
 A semigroup which always uses the "last" (right-hand side) value.
 - functionSemigroup
```
public static <A,B> Semigroup<F<A,B>> functionSemigroup(Semigroup sb)
```
 A semigroup for functions.
 
 Parameters:
 
 sb - The smeigroup for the codomain.
 
 Returns:
 
 A semigroup for functions.
 - listSemigroup
```
public static <A> Semigroup<List<A>> listSemigroup()
```
 A semigroup for lists.
 
 Returns:
 
 A semigroup for lists.
 - nonEmptyListSemigroup
```
public static <A> Semigroup<NonEmptyList<A>> nonEmptyListSemigroup()
```
 A semigroup for non-empty lists.
 
 Returns:
 
 A semigroup for non-empty lists.
 - firstOptionSemigroup
```
public static <A> Semigroup<Option<A>> firstOptionSemigroup()
```
 A semigroup for optional values that take the first available value.
 
 Returns:
 
 A semigroup for optional values that take the first available value.
 - lastOptionSemigroup
```
public static <A> Semigroup<Option<A>> lastOptionSemigroup()
```
 A semigroup for optional values that take the last available value.
 
 Returns:
 
 A semigroup for optional values that take the last available value.
 - streamSemigroup
```
public static <A> Semigroup<Stream<A>> streamSemigroup()
```
 A semigroup for streams.
 
 Returns:
 
 A semigroup for streams.
 - arraySemigroup
```
public static <A> Semigroup<Array<A>> arraySemigroup()
```
 A semigroup for arrays.
 
 Returns:
 
 A semigroup for arrays.
 - p1Semigroup
```
public static <A> Semigroup<P1<A>> p1Semigroup(Semigroup<A> sa)
```
 A lazy semigroup for unary products.
 
 Parameters:
 
 sa - A semigroup for the product's type.
 
 Returns:
 
 A semigroup for unary products.
 - p2Semigroup
```
public static <A,B> Semigroup<P2<A,B>> p2Semigroup(Semigroup<A> sa,
 Semigroup sb)
```
 A lazy semigroup for binary products.
 
 Parameters:
 
 sa - A semigroup for the product's first type.
 
 sb - A semigroup for the product's second type.
 
 Returns:
 
 A semigroup for binary products.
 - ioSemigroup
```
public static <A> Semigroup<IO<A>> ioSemigroup(Semigroup<A> sa)
```
 A semigroup for IO values.
 - setSemigroup
```
public static <A> Semigroup<Set<A>> setSemigroup()
```
 A union semigroup for sets.
 
 Returns:
 
 a semigroup for sets.
 - setIntersectionSemigroup
```
public static <A> Semigroup<Set<A>> setIntersectionSemigroup()
```
 A intersection semigroup for sets.
 
 Returns:
 
 a semigroup for sets.

Class Semigroup<A>

Nested Class Summary

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

intAdditionSemigroup

intMultiplicationSemigroup

intMaximumSemigroup

intMinimumSemigroup

bigintAdditionSemigroup

bigintMultiplicationSemigroup

bigintMaximumSemigroup

bigintMinimumSemigroup

bigdecimalAdditionSemigroup

bigdecimalMultiplicationSemigroup

bigDecimalMaximumSemigroup

bigDecimalMinimumSemigroup

naturalMultiplicationSemigroup

naturalAdditionSemigroup

naturalMaximumSemigroup

naturalMinimumSemigroup

longAdditionSemigroup

longMultiplicationSemigroup

longMaximumSemigroup

longMinimumSemigroup

disjunctionSemigroup

exclusiveDisjunctionSemiGroup

conjunctionSemigroup

stringSemigroup

stringBufferSemigroup

stringBuilderSemigroup

unitSemigroup

Method Detail

sum

sum

sum

multiply1p

sumNel

sumStream

dual

lift

xmap

compose

monoid

semigroupDef

semigroupDef

semigroup

semigroup

firstSemigroup

lastSemigroup

functionSemigroup

listSemigroup

nonEmptyListSemigroup

firstOptionSemigroup

lastOptionSemigroup

streamSemigroup

arraySemigroup

p1Semigroup

p2Semigroup

ioSemigroup

setSemigroup

setIntersectionSemigroup