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Functional Java is an open source library that supports closures for the Java programming language
package fj;
import static fj.Function.curry;
import fj.data.Array;
import fj.data.List;
import fj.data.Natural;
import fj.data.NonEmptyList;
import fj.data.Option;
import fj.data.Set;
import fj.data.Stream;
import java.math.BigInteger;
import java.math.BigDecimal;
/**
* Implementations must satisfy the law of associativity:
*
* - Associativity; forall x. forall y. forall z. sum(sum(x, y), z) == sum(x, sum(y, z))
*
*
* @version %build.number%
*/
public final class Semigroup {
private final F> sum;
private Semigroup(final F> 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 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> sum() {
return 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 Semigroup semigroup(final F> 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 Semigroup semigroup(final F2 sum) {
return new Semigroup(curry(sum));
}
/**
* A semigroup that adds integers.
*/
public static final Semigroup intAdditionSemigroup = semigroup((i1, i2) -> i1 + i2);
/**
* A semigroup that adds doubles.
*/
public static final Semigroup doubleAdditionSemigroup = semigroup((d1, d2) -> d1 + d2);
/**
* A semigroup that multiplies integers.
*/
public static final Semigroup intMultiplicationSemigroup = semigroup((i1, i2) -> i1 * i2);
/**
* A semigroup that multiplies doubles.
*/
public static final Semigroup doubleMultiplicationSemigroup = semigroup((d1, d2) -> d1 * d2);
/**
* A semigroup that yields the maximum of integers.
*/
public static final Semigroup intMaximumSemigroup = semigroup(Ord.intOrd.max);
/**
* A semigroup that yields the minimum of integers.
*/
public static final Semigroup intMinimumSemigroup = semigroup(Ord.intOrd.min);
/**
* A semigroup that adds big integers.
*/
public static final Semigroup bigintAdditionSemigroup =
semigroup((i1, i2) -> i1.add(i2));
/**
* A semigroup that multiplies big integers.
*/
public static final Semigroup bigintMultiplicationSemigroup =
semigroup((i1, i2) -> i1.multiply(i2));
/**
* A semigroup that yields the maximum of big integers.
*/
public static final Semigroup bigintMaximumSemigroup = semigroup(Ord.bigintOrd.max);
/**
* A semigroup that yields the minimum of big integers.
*/
public static final Semigroup bigintMinimumSemigroup = semigroup(Ord.bigintOrd.min);
/**
* A semigroup that adds big decimals.
*/
public static final Semigroup bigdecimalAdditionSemigroup =
semigroup((i1, i2) -> i1.add(i2));
/**
* A semigroup that multiplies big decimals.
*/
public static final Semigroup bigdecimalMultiplicationSemigroup =
semigroup((i1, i2) -> i1.multiply(i2));
/**
* A semigroup that yields the maximum of big decimals.
*/
public static final Semigroup bigDecimalMaximumSemigroup = semigroup(Ord.bigdecimalOrd.max);
/**
* A semigroup that yields the minimum of big decimals.
*/
public static final Semigroup bigDecimalMinimumSemigroup = semigroup(Ord.bigdecimalOrd.min);
/**
* A semigroup that multiplies natural numbers.
*/
public static final Semigroup naturalMultiplicationSemigroup =
semigroup((n1, n2) -> n1.multiply(n2));
/**
* A semigroup that multiplies natural numbers.
*/
public static final Semigroup naturalAdditionSemigroup =
semigroup((n1, n2) -> n1.add(n2));
/**
* A semigroup that yields the maximum of natural numbers.
*/
public static final Semigroup naturalMaximumSemigroup = semigroup(Ord.naturalOrd.max);
/**
* A semigroup that yields the minimum of natural numbers.
*/
public static final Semigroup naturalMinimumSemigroup = semigroup(Ord.naturalOrd.min);
/**
* A semigroup that adds longs.
*/
public static final Semigroup longAdditionSemigroup = semigroup((x, y) -> x + y);
/**
* A semigroup that multiplies longs.
*/
public static final Semigroup longMultiplicationSemigroup = semigroup((x, y) -> x * y);
/**
* A semigroup that yields the maximum of longs.
*/
public static final Semigroup longMaximumSemigroup = semigroup(Ord.longOrd.max);
/**
* A semigroup that yields the minimum of longs.
*/
public static final Semigroup longMinimumSemigroup = semigroup(Ord.longOrd.min);
/**
* A semigroup that ORs booleans.
*/
public static final Semigroup disjunctionSemigroup = semigroup((b1, b2) -> b1 || b2);
/**
* A semigroup that XORs booleans.
*/
public static final Semigroup exclusiveDisjunctionSemiGroup = semigroup((p, q) -> p && !q || !p && q);
/**
* A semigroup that ANDs booleans.
*/
public static final Semigroup conjunctionSemigroup = semigroup((b1, b2) -> b1 && b2);
/**
* A semigroup that appends strings.
*/
public static final Semigroup stringSemigroup = semigroup((s1, s2) -> s1 + s2);
/**
* A semigroup that appends string buffers.
*/
public static final Semigroup stringBufferSemigroup =
semigroup((s1, s2) -> new StringBuffer(s1).append(s2));
/**
* A semigroup that appends string builders.
*/
public static final Semigroup stringBuilderSemigroup =
semigroup((s1, s2) -> new StringBuilder(s1).append(s2));
/**
* A semigroup for functions.
*
* @param sb The smeigroup for the codomain.
* @return A semigroup for functions.
*/
public static Semigroup> functionSemigroup(final Semigroup 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 Semigroup> listSemigroup() {
return semigroup((a1, a2) -> a1.append(a2));
}
/**
* A semigroup for non-empty lists.
*
* @return A semigroup for non-empty lists.
*/
public static Semigroup> nonEmptyListSemigroup() {
return semigroup((a1, a2) -> a1.append(a2));
}
/**
* A semigroup for optional values.
** @return A semigroup for optional values.
*/
public static Semigroup> 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 Semigroup> 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 Semigroup> lastOptionSemigroup() {
return semigroup((a1, a2) -> a2.orElse(a1));
}
/**
* A semigroup for streams.
*
* @return A semigroup for streams.
*/
public static Semigroup> streamSemigroup() {
return semigroup((a1, a2) -> a1.append(a2));
}
/**
* A semigroup for arrays.
*
* @return A semigroup for arrays.
*/
public static Semigroup> arraySemigroup() {
return semigroup((a1, a2) -> a1.append(a2));
}
/**
* A semigroup for unary products.
*
* @param sa A semigroup for the product's type.
* @return A semigroup for unary products.
*/
public static Semigroup> p1Semigroup(final Semigroup sa) {
return semigroup((a1, a2) -> new P1() {
public A _1() {
return 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 Semigroup> p2Semigroup(final Semigroup sa, final Semigroup sb) {
return semigroup((a1, a2) -> new P2() {
public A _1() {
return sa.sum(a1._1(), a2._1());
}
public B _2() {
return sb.sum(a1._2(), a2._2());
}
});
}
/**
* A semigroup for the Unit value.
*/
public static final Semigroup unitSemigroup = semigroup((u1, u2) -> Unit.unit());
/**
* A semigroup for sets.
*
* @return a semigroup for sets.
*/
public static Semigroup> setSemigroup() {
return semigroup((a, b) -> a.union(b));
}
}