@Override
public Natural abs() {
if (this.value < 0) {
return Natural.valueOfNative(-this.value);
} else {
return Natural.valueOfNative(this.value);
}
}
/**
* Abstracts over a type that may have a successor and/or predecessor value. This implies ordering
* for that type. A user may construct an enumerator with an optimised version for <code>plus</code>
* , otherwise a default is implemented using the given successor/predecessor implementations.
*
* <p>For any enumerator e, the following laws must satisfy:
*
* <ul>
* <li>forall a. e.successor(a).forall(\t -> e.predecessor(t).forall(\z -> z == a))
* <li>forall a. e.predecessor(a).forall(\t -> e.successor(t).forall(\z -> z == a))
* <li>e.max().forall(\t -> e.successor(t).isNone)
* <li>e.min().forall(\t -> e.predecessor(t).isNone)
* <li>forall a n. e.plus(a, 0) == Some(a)
* <li>forall a n | n > 0. e.plus(a, n) == e.plus(a, n - 1)
* <li>forall a n | n < 0. e.plus(a, n) == e.plus(a, n + 1)
* </ul>
*
* @version %build.number%
*/
public final class Enumerator<A> {
private final F<A, Option<A>> successor;
private final F<A, Option<A>> predecessor;
private final Option<A> max;
private final Option<A> min;
private final Ord<A> order;
private final F<A, F<Long, Option<A>>> plus;
private Enumerator(
final F<A, Option<A>> successor,
final F<A, Option<A>> predecessor,
final Option<A> max,
final Option<A> min,
final Ord<A> order,
final F<A, F<Long, Option<A>>> plus) {
this.successor = successor;
this.predecessor = predecessor;
this.max = max;
this.min = min;
this.order = order;
this.plus = plus;
}
/**
* Returns the potential successor of a value for this enumerator in curried form.
*
* @return The potential successor of a value for this enumerator in curried form.
*/
public F<A, Option<A>> successor() {
return successor;
}
/**
* Returns the potential successor of a value for this enumerator.
*
* @param a The value to return the successor of.
* @return The potential successor of a value for this enumerator.
*/
public Option<A> successor(final A a) {
return successor.f(a);
}
/**
* Returns the potential predecessor of a value for this enumerator in curried form.
*
* @return The potential predecessor of a value for this enumerator in curried form.
*/
public F<A, Option<A>> predecessor() {
return predecessor;
}
/**
* Returns the potential predecessor of a value for this enumerator.
*
* @param a The value to return the predecessor of.
* @return The potential predecessor of a value for this enumerator.
*/
public Option<A> predecessor(final A a) {
return predecessor.f(a);
}
/**
* Returns the maximum value for this enumerator if there is one.
*
* @return The maximum value for this enumerator if there is one.
*/
public Option<A> max() {
return max;
}
/**
* Returns the minimum value for this enumerator if there is one.
*
* @return The minimum value for this enumerator if there is one.
*/
public Option<A> min() {
return min;
}
/**
* Returns a function that moves a value along the enumerator a given number of times.
*
* @return A function that moves a value along the enumerator a given number of times.
*/
public F<A, F<Long, Option<A>>> plus() {
return plus;
}
/**
* Returns a function that moves a value along the enumerator a given number of times.
*
* @param a The value to begin moving along from.
* @return A function that moves a value along the enumerator a given number of times.
*/
public F<Long, Option<A>> plus(final A a) {
return plus.f(a);
}
/**
* Returns a function that moves a value along the enumerator a given number of times.
*
* @param l The number of times to move along the enumerator.
* @return A function that moves a value along the enumerator a given number of times.
*/
public F<A, Option<A>> plus(final long l) {
return flip(plus).f(l);
}
/**
* Moves a value along the enumerator a given number of times.
*
* @param a The value to begin moving along from.
* @param l The number of times to move along the enumerator.
* @return A potential value after having moved the given number of times.
*/
public Option<A> plus(final A a, final long l) {
return plus.f(a).f(l);
}
/**
* Returns the ordering for the enumerator.
*
* @return The ordering for the enumerator.
*/
public Ord<A> order() {
return order;
}
/**
* Invariant functor map over this enumerator.
*
* @param f The covariant map.
* @param g The contra-variant map.
* @return An enumerator after the given functions are applied.
*/
public <B> Enumerator<B> xmap(final F<A, B> f, final F<B, A> g) {
final F<Option<A>, Option<B>> of = o -> o.map(f);
return enumerator(
compose(compose(of, successor), g),
compose(compose(of, predecessor), g),
max.map(f),
min.map(f),
order.contramap(g),
compose(compose(Function.<Long, Option<A>, Option<B>>compose().f(of), plus), g));
}
/**
* Returns a stream of the values from this enumerator, starting at the given value, counting up.
*
* @param a A value at which to begin the stream.
* @return a stream of the values from this enumerator, starting at the given value, counting up.
*/
public Stream<A> toStream(final A a) {
final F<A, A> id = identity();
return Stream.fromFunction(this, id, a);
}
/**
* Create a new enumerator with the given minimum value.
*
* @param min A minimum value.
* @return A new enumerator identical to this one, but with the given minimum value.
*/
public Enumerator<A> setMin(final Option<A> min) {
return enumerator(successor, predecessor, max, min, order, plus);
}
/**
* Create a new enumerator with the given maximum value.
*
* @param max A maximum value.
* @return A new enumerator identical to this one, but with the given maximum value.
*/
public Enumerator<A> setMax(final Option<A> max) {
return enumerator(successor, predecessor, max, min, order, plus);
}
/**
* Construct an enumerator. `
*
* @param successor The successor function.
* @param predecessor The predecessor function.
* @param max The potential maximum value.
* @param min The potential minimum value.
* @param order The ordering for the type.
* @param plus The function to move the enumeration a given number of times. This may be supplied
* for a performance enhancement for certain types.
* @return An enumerator with the given values.
*/
public static <A> Enumerator<A> enumerator(
final F<A, Option<A>> successor,
final F<A, Option<A>> predecessor,
final Option<A> max,
final Option<A> min,
final Ord<A> order,
final F<A, F<Long, Option<A>>> plus) {
return new Enumerator<A>(successor, predecessor, max, min, order, plus);
}
/**
* Construct an enumerator. The <code>plus</code> function is derived from the <code>successor
* </code> and <code>predecessor</code>.
*
* @param successor The successor function.
* @param predecessor The predecessor function.
* @param max The potential maximum value.
* @param min The potential minimum value.
* @param order The ordering for the type.
* @return An enumerator with the given values.
*/
public static <A> Enumerator<A> enumerator(
final F<A, Option<A>> successor,
final F<A, Option<A>> predecessor,
final Option<A> max,
final Option<A> min,
final Ord<A> order) {
return new Enumerator<A>(
successor,
predecessor,
max,
min,
order,
curry(
(a, l) -> {
if (l == 0L) return some(a);
else if (l < 0L) {
A aa = a;
for (long x = l; x < 0; x++) {
final Option<A> s = predecessor.f(aa);
if (s.isNone()) return none();
else aa = s.some();
}
return some(aa);
} else {
A aa = a;
for (long x = l; x > 0; x--) {
final Option<A> s = successor.f(aa);
if (s.isNone()) return none();
else aa = s.some();
}
return some(aa);
}
}));
}
/** An enumerator for <code>boolean</code>. */
public static final Enumerator<Boolean> booleanEnumerator =
enumerator(
b -> b ? Option.<Boolean>none() : some(true),
b -> b ? some(false) : Option.<Boolean>none(),
some(true),
some(false),
booleanOrd);
/** An enumerator for <code>byte</code>. */
public static final Enumerator<Byte> byteEnumerator =
enumerator(
b -> b == Byte.MAX_VALUE ? Option.<Byte>none() : some((byte) (b + 1)),
b -> b == Byte.MIN_VALUE ? Option.<Byte>none() : some((byte) (b - 1)),
some(Byte.MAX_VALUE),
some(Byte.MIN_VALUE),
byteOrd);
/** An enumerator for <code>char</code>. */
public static final Enumerator<Character> charEnumerator =
enumerator(
c -> c == Character.MAX_VALUE ? Option.<Character>none() : some((char) (c + 1)),
c -> c == Character.MIN_VALUE ? Option.<Character>none() : some((char) (c - 1)),
some(Character.MAX_VALUE),
some(Character.MIN_VALUE),
charOrd);
/** An enumerator for <code>double</code>. */
public static final Enumerator<Double> doubleEnumerator =
enumerator(
d -> d == Double.MAX_VALUE ? Option.<Double>none() : some(d + 1D),
d -> d == Double.MIN_VALUE ? Option.<Double>none() : some(d - 1D),
some(Double.MAX_VALUE),
some(Double.MIN_VALUE),
doubleOrd);
/** An enumerator for <code>float</code>. */
public static final Enumerator<Float> floatEnumerator =
enumerator(
f -> f == Float.MAX_VALUE ? Option.<Float>none() : some(f + 1F),
f -> f == Float.MIN_VALUE ? Option.<Float>none() : some(f - 1F),
some(Float.MAX_VALUE),
some(Float.MIN_VALUE),
floatOrd);
/** An enumerator for <code>int</code>. */
public static final Enumerator<Integer> intEnumerator =
enumerator(
i -> i == Integer.MAX_VALUE ? Option.<Integer>none() : some(i + 1),
i -> i == Integer.MIN_VALUE ? Option.<Integer>none() : some(i - 1),
some(Integer.MAX_VALUE),
some(Integer.MIN_VALUE),
intOrd);
/** An enumerator for <code>BigInteger</code>. */
public static final Enumerator<BigInteger> bigintEnumerator =
enumerator(
i -> some(i.add(BigInteger.ONE)),
i -> some(i.subtract(BigInteger.ONE)),
Option.<BigInteger>none(),
Option.<BigInteger>none(),
bigintOrd,
curry((i, l) -> some(i.add(BigInteger.valueOf(l)))));
/** An enumerator for <code>BigDecimal</code>. */
public static final Enumerator<BigDecimal> bigdecimalEnumerator =
enumerator(
i -> some(i.add(BigDecimal.ONE)),
i -> some(i.subtract(BigDecimal.ONE)),
Option.<BigDecimal>none(),
Option.<BigDecimal>none(),
bigdecimalOrd,
curry((d, l) -> some(d.add(BigDecimal.valueOf(l)))));
/** An enumerator for <code>long</code>. */
public static final Enumerator<Long> longEnumerator =
enumerator(
i -> i == Long.MAX_VALUE ? Option.<Long>none() : some(i + 1L),
i -> i == Long.MIN_VALUE ? Option.<Long>none() : some(i - 1L),
some(Long.MAX_VALUE),
some(Long.MIN_VALUE),
longOrd);
/** An enumerator for <code>short</code>. */
public static final Enumerator<Short> shortEnumerator =
enumerator(
i -> i == Short.MAX_VALUE ? Option.<Short>none() : some((short) (i + 1)),
i -> i == Short.MIN_VALUE ? Option.<Short>none() : some((short) (i - 1)),
some(Short.MAX_VALUE),
some(Short.MIN_VALUE),
shortOrd);
/** An enumerator for <code>Ordering</code>. */
public static final Enumerator<Ordering> orderingEnumerator =
enumerator(
o -> o == LT ? some(EQ) : o == EQ ? some(GT) : Option.<Ordering>none(),
o -> o == GT ? some(EQ) : o == EQ ? some(LT) : Option.<Ordering>none(),
some(GT),
some(LT),
orderingOrd);
/** An enumerator for <code>Natural</code> */
public static final Enumerator<Natural> naturalEnumerator =
enumerator(
n -> Option.some(n.succ()),
n -> n.pred(),
Option.<Natural>none(),
some(Natural.ZERO),
naturalOrd,
curry(
(n, l) ->
some(n).apply(Natural.natural(l).map(Function.curry((n1, n2) -> n1.add(n2))))));
}
public Natural f(final Natural n1, final Natural n2) {
return n1.add(n2);
}
public Natural f(final Natural n1, final Natural n2) {
return n1.multiply(n2);
}
/**
* Multiplies the given Integer amount to this Natural
*
* @param amount The amount to multiply
* @throws IllegalArgumentException If multiplying the given amount makes the Natural less than 0
*/
public void multiply(Integer amount) {
Integer val = this.value * amount;
Natural.ensureValidity(val);
this.value = val;
}
/**
* Subtracts the given Integer amount from this Natural
*
* @param amount The amount to subtract
* @throws IllegalArgumentException If subtracting the given amount makes the Natural less than 0
*/
public void subtract(Integer amount) {
Integer val = this.value - amount;
Natural.ensureValidity(val);
this.value = val;
}
/**
* Adds the given Integer amount to this Natural
*
* @param amount The amount to add
* @throws IllegalArgumentException If adding the given amount makes the Natural less than 0
*/
public void add(Integer amount) {
Integer val = this.value + amount;
Natural.ensureValidity(val);
this.value = val;
}
/**
* Constructor for creating a Natural
*
* @param value The value to be created, which is a positive integer
* @throws IllegalArgumentException If the value is less than zero.
*/
public Natural(Integer value) {
Natural.ensureValidity(value);
this.value = value;
}
/**
* Divides this Natural by the given Integer amount
*
* @param amount The amount to divide by
* @throws IllegalArgumentException If dividing the given amount makes the Natural less than 0
*/
public void divide(Integer amount) {
Integer val = this.value / amount;
Natural.ensureValidity(val);
this.value = val;
}
