Package fj

Class 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))

    • 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 <B> Monoid<P2<A,​B>> compose​(Monoid<B> 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 <B> Monoid<B> 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<B> 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<B> 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.