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Semigroup.java
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package fj;
import fj.data.Array;
import fj.data.List;
import fj.data.IO;
import fj.data.IOFunctions;
import fj.data.Natural;
import fj.data.NonEmptyList;
import fj.data.Option;
import fj.data.Set;
import fj.data.Stream;
import java.math.BigDecimal;
import java.math.BigInteger;
import static fj.Function.curry;
import static fj.Function.flip;
/**
* Implementations must satisfy the law of associativity:
* <ul>
* <li><em>Associativity</em>; forall x. forall y. forall z. sum(sum(x, y), z) == sum(x, sum(y, z))</li>
* </ul>
*
* @version %build.number%
*/
public final class Semigroup<A> {
private final F<A, F<A, A>> sum;
private Semigroup(final F<A, F<A, A>> sum) {
this.sum = sum;
}
/**
* Sums the two given arguments.
*
* @param a1 A value to sum with another.
* @param a2 A value to sum with another.
* @return The of the two given arguments.
*/
public A sum(final A a1, final A a2) {
return sum.f(a1).f(a2);
}
/**
* Returns a function that sums the given value according to this semigroup.
*
* @param a1 The value to sum.
* @return A function that sums the given value according to this semigroup.
*/
public F<A, A> sum(final A a1) {
return sum.f(a1);
}
/**
* Returns a function that sums according to this semigroup.
*
* @return A function that sums according to this semigroup.
*/
public F<A, F<A, A>> sum() {
return sum;
}
/**
* Returns a value summed <code>n + 1</code> times (
* <code>a + a + ... + a</code>) The default definition uses peasant
* multiplication, exploiting associativity to only require `O(log n)` uses of
* {@link #sum(Object, Object)}.
*
* @param n multiplier
* @param a the value to be reapeatly summed n + 1 times
* @return {@code a} summed {@code n} times. If {@code n <= 0}, returns
* {@code zero()}
*/
public A multiply1p(int n, A a) {
return multiply1p(sum, n, a);
}
// shared implementation between Semigroup and Monoid
static <A> A multiply1p(F<A, F<A, A>> sum, int n, A a) {
if (n <= 0) {
return a;
}
A xTmp = a;
int yTmp = n;
A zTmp = a;
while (true) {
if ((yTmp & 1) == 1) {
zTmp = sum.f(xTmp).f(zTmp);
if (yTmp == 1) {
return zTmp;
}
}
xTmp = sum.f(xTmp).f(xTmp);
yTmp = yTmp >>> 1;
}
}
/**
* Sums the given values with left-fold.
*/
public A sumNel(final NonEmptyList<A> as) {
return as.foldLeft1(sum);
}
/**
* Swaps the arguments when summing.
*/
public Semigroup<A> dual() {
return semigroup(flip(sum));
}
/**
* Lifts the semigroup to obtain a trivial monoid.
*/
public Monoid<Option<A>> lift() {
return Monoid.monoid(a -> b -> Option.liftM2(sum).f(a).f(b).orElse(a).orElse(b), Option.none());
}
/**
* Constructs a semigroup from the given function.
*
* @param sum The function to construct this semigroup with.
* @return A semigroup from the given function.
*/
public static <A> Semigroup<A> semigroup(final F<A, F<A, A>> sum) {
return new Semigroup<>(sum);
}
/**
* Constructs a semigroup from the given function.
*
* @param sum The function to construct this semigroup with.
* @return A semigroup from the given function.
*/
public static <A> Semigroup<A> semigroup(final F2<A, A, A> sum) {
return new Semigroup<>(curry(sum));
}
/**
* A semigroup that adds integers.
*/
public static final Semigroup<Integer> intAdditionSemigroup = semigroup((i1, i2) -> i1 + i2);
/**
* A semigroup that adds doubles.
*/
public static final Semigroup<Double> doubleAdditionSemigroup = semigroup((d1, d2) -> d1 + d2);
/**
* A semigroup that multiplies integers.
*/
public static final Semigroup<Integer> intMultiplicationSemigroup = semigroup((i1, i2) -> i1 * i2);
/**
* A semigroup that multiplies doubles.
*/
public static final Semigroup<Double> doubleMultiplicationSemigroup = semigroup((d1, d2) -> d1 * d2);
/**
* A semigroup that yields the maximum of integers.
*/
public static final Semigroup<Integer> intMaximumSemigroup = Ord.intOrd.maxSemigroup();
/**
* A semigroup that yields the minimum of integers.
*/
public static final Semigroup<Integer> intMinimumSemigroup = Ord.intOrd.minSemigroup();
/**
* A semigroup that adds big integers.
*/
public static final Semigroup<BigInteger> bigintAdditionSemigroup =
semigroup(BigInteger::add);
/**
* A semigroup that multiplies big integers.
*/
public static final Semigroup<BigInteger> bigintMultiplicationSemigroup =
semigroup(BigInteger::multiply);
/**
* A semigroup that yields the maximum of big integers.
*/
public static final Semigroup<BigInteger> bigintMaximumSemigroup = Ord.bigintOrd.maxSemigroup();
/**
* A semigroup that yields the minimum of big integers.
*/
public static final Semigroup<BigInteger> bigintMinimumSemigroup = Ord.bigintOrd.minSemigroup();
/**
* A semigroup that adds big decimals.
*/
public static final Semigroup<BigDecimal> bigdecimalAdditionSemigroup =
semigroup(BigDecimal::add);
/**
* A semigroup that multiplies big decimals.
*/
public static final Semigroup<BigDecimal> bigdecimalMultiplicationSemigroup =
semigroup(BigDecimal::multiply);
/**
* A semigroup that yields the maximum of big decimals.
*/
public static final Semigroup<BigDecimal> bigDecimalMaximumSemigroup = Ord.bigdecimalOrd.maxSemigroup();
/**
* A semigroup that yields the minimum of big decimals.
*/
public static final Semigroup<BigDecimal> bigDecimalMinimumSemigroup = Ord.bigdecimalOrd.minSemigroup();
/**
* A semigroup that multiplies natural numbers.
*/
public static final Semigroup<Natural> naturalMultiplicationSemigroup =
semigroup(Natural::multiply);
/**
* A semigroup that multiplies natural numbers.
*/
public static final Semigroup<Natural> naturalAdditionSemigroup =
semigroup(Natural::add);
/**
* A semigroup that yields the maximum of natural numbers.
*/
public static final Semigroup<Natural> naturalMaximumSemigroup = Ord.naturalOrd.maxSemigroup();
/**
* A semigroup that yields the minimum of natural numbers.
*/
public static final Semigroup<Natural> naturalMinimumSemigroup = Ord.naturalOrd.minSemigroup();
/**
* A semigroup that adds longs.
*/
public static final Semigroup<Long> longAdditionSemigroup = semigroup((x, y) -> x + y);
/**
* A semigroup that multiplies longs.
*/
public static final Semigroup<Long> longMultiplicationSemigroup = semigroup((x, y) -> x * y);
/**
* A semigroup that yields the maximum of longs.
*/
public static final Semigroup<Long> longMaximumSemigroup = Ord.longOrd.maxSemigroup();
/**
* A semigroup that yields the minimum of longs.
*/
public static final Semigroup<Long> longMinimumSemigroup = Ord.longOrd.minSemigroup();
/**
* A semigroup that ORs booleans.
*/
public static final Semigroup<Boolean> disjunctionSemigroup = semigroup((b1, b2) -> b1 || b2);
/**
* A semigroup that XORs booleans.
*/
public static final Semigroup<Boolean> exclusiveDisjunctionSemiGroup = semigroup((p, q) -> p ? !q : q);
/**
* A semigroup that ANDs booleans.
*/
public static final Semigroup<Boolean> conjunctionSemigroup = semigroup((b1, b2) -> b1 && b2);
/**
* A semigroup that appends strings.
*/
public static final Semigroup<String> stringSemigroup = semigroup((s1, s2) -> s1 + s2);
/**
* A semigroup that appends string buffers.
*/
public static final Semigroup<StringBuffer> stringBufferSemigroup =
semigroup((s1, s2) -> new StringBuffer(s1).append(s2));
/**
* A semigroup that appends string builders.
*/
public static final Semigroup<StringBuilder> stringBuilderSemigroup =
semigroup((s1, s2) -> new StringBuilder(s1).append(s2));
/**
* A semigroup which always uses the "first" (left-hand side) value.
*/
public static <A> Semigroup<A> firstSemigroup() {
return semigroup((a1, a2) -> a1);
}
/**
* A semigroup which always uses the "last" (right-hand side) value.
*/
public static <A> Semigroup<A> lastSemigroup() {
return semigroup((a1, a2) -> a2);
}
/**
* A semigroup for functions.
*
* @param sb The smeigroup for the codomain.
* @return A semigroup for functions.
*/
public static <A, B> Semigroup<F<A, B>> functionSemigroup(final Semigroup<B> sb) {
return semigroup((a1, a2) -> a -> sb.sum(a1.f(a), a2.f(a)));
}
/**
* A semigroup for lists.
*
* @return A semigroup for lists.
*/
public static <A> Semigroup<List<A>> listSemigroup() {
return semigroup(List::append);
}
/**
* A semigroup for non-empty lists.
*
* @return A semigroup for non-empty lists.
*/
public static <A> Semigroup<NonEmptyList<A>> nonEmptyListSemigroup() {
return semigroup(NonEmptyList::append);
}
/**
* A semigroup for optional values.
** @return A semigroup for optional values.
*/
public static <A> Semigroup<Option<A>> optionSemigroup() {
return semigroup((a1, a2) -> a1.isSome() ? a1 : a2);
}
/**
* A semigroup for optional values that take the first available value.
*
* @return A semigroup for optional values that take the first available value.
*/
public static <A> Semigroup<Option<A>> firstOptionSemigroup() {
return semigroup((a1, a2) -> a1.orElse(a2));
}
/**
* A semigroup for optional values that take the last available value.
*
* @return A semigroup for optional values that take the last available value.
*/
public static <A> Semigroup<Option<A>> lastOptionSemigroup() {
return semigroup((a1, a2) -> a2.orElse(a1));
}
/**
* A semigroup for streams.
*
* @return A semigroup for streams.
*/
public static <A> Semigroup<Stream<A>> streamSemigroup() {
return semigroup((a1, a2) -> a1.append(a2));
}
/**
* A semigroup for arrays.
*
* @return A semigroup for arrays.
*/
public static <A> Semigroup<Array<A>> arraySemigroup() {
return semigroup(Array::append);
}
/**
* A semigroup for unary products.
*
* @param sa A semigroup for the product's type.
* @return A semigroup for unary products.
*/
public static <A> Semigroup<P1<A>> p1Semigroup(final Semigroup<A> sa) {
return semigroup((a1, a2) -> P.lazy(() -> sa.sum(a1._1(), a2._1())));
}
/**
* A semigroup for binary products.
*
* @param sa A semigroup for the product's first type.
* @param sb A semigroup for the product's second type.
* @return A semigroup for binary products.
*/
public static <A, B> Semigroup<P2<A, B>> p2Semigroup(final Semigroup<A> sa, final Semigroup<B> sb) {
return semigroup((a1, a2) -> P.lazy(() -> sa.sum(a1._1(), a2._1()), () -> sb.sum(a1._2(), a2._2())));
}
/**
* A semigroup for IO values.
*/
public static <A> Semigroup<IO<A>> ioSemigroup(final Semigroup <A> sa) {
return semigroup((a1, a2) -> IOFunctions.liftM2(a1, a2, sa::sum));
}
/**
* A semigroup for the Unit value.
*/
public static final Semigroup<Unit> unitSemigroup = semigroup((u1, u2) -> Unit.unit());
/**
* A semigroup for sets.
*
* @return a semigroup for sets.
*/
public static <A> Semigroup<Set<A>> setSemigroup() {
return semigroup(Set::union);
}
}