Package com.jnape.palatable.lambda.monoid

Interface Monoid<A>

Type Parameters:

A - the element type this Monoid is formed over

All Superinterfaces:

Applicative<Fn1<A,A>,Fn1<A,?>>, Cartesian<A,Fn1<A,A>,Fn1<?,?>>, Cocartesian<A,Fn1<A,A>,Fn1<?,?>>, Contravariant<A,Profunctor<?,Fn1<A,A>,Fn1<?,?>>>, Fn1<A,Fn1<A,A>>, Fn2<A,A,A>, Functor<Fn1<A,A>,Fn1<A,?>>, Monad<Fn1<A,A>,Fn1<A,?>>, MonadReader<A,Fn1<A,A>,Fn1<A,?>>, MonadRec<Fn1<A,A>,Fn1<A,?>>, MonadWriter<A,Fn1<A,A>,Fn1<A,?>>, Profunctor<A,Fn1<A,A>,Fn1<?,?>>, Semigroup<A>

All Known Implementing Classes:

And, Concat, Endo, First, Join, Last, MergeHMaps, Or, PutAll, Trivial, Union, Xor

public interface Monoid<A>
extends Semigroup<A>

A Monoid is the pairing of a Semigroup with an identity element.

Method Summary

Modifier and Type	Method	Description
default Monoid<A>	flip()	Flip the order of the arguments.
default A	foldLeft(A a, java.lang.Iterable<A> as)	Catamorphism under this semigroup using FoldLeft, where the binary operator is this semigroup, and the starting accumulator is provided.
default <B> A	foldMap(Fn1<? super B,? extends A> fn, java.lang.Iterable<B> bs)	Homomorphism combined with catamorphism.
default Lazy<A>	foldRight(A a, java.lang.Iterable<A> as)	Catamorphism under this semigroup using FoldRight, where the binary operator is this semigroup, and the starting accumulator is provided.
A	identity()	The identity element of this monoid.
static <A> Monoid<A>	monoid(Semigroup<A> semigroup, A identity)	Promote a Semigroup to a Monoid by supplying an identity element.
static <A> Monoid<A>	monoid(Semigroup<A> semigroup, Fn0<A> identityFn0)
default A	reduceLeft(java.lang.Iterable<A> as)	Catamorphism under this monoid using ReduceLeft, where the result is the reduction, or, if empty, the identity of this monoid.
default A	reduceRight(java.lang.Iterable<A> as)	Catamorphism under this monoid using ReduceRight, where the result is the reduction, or, if empty, the identity of this monoid.

Methods inherited from interface com.jnape.palatable.lambda.functions.Fn1

andThen, carry, cartesian, censor, choose, cocartesian, diMap, diMapR, discardL, flatMap, fmap, lazyZip, listens, local, pure, self, thunk, toFunction, trampolineM, zip, zip

Methods inherited from interface com.jnape.palatable.lambda.functions.Fn2

apply, apply, checkedApply, checkedApply, compose, contraMap, diMapL, discardR, toBiFunction, uncurry, widen

Methods inherited from interface com.jnape.palatable.lambda.functor.Functor

coerce

Method Detail

identity

A identity()

The identity element of this monoid.

Returns:

the identity

reduceLeft

default A reduceLeft(java.lang.Iterable<A> as)

Catamorphism under this monoid using ReduceLeft, where the result is the reduction, or, if empty, the identity of this monoid.

Parameters:

as - the elements to reduce

Returns:

the reduction, or identity() if empty

See Also:

ReduceLeft

reduceRight

default A reduceRight(java.lang.Iterable<A> as)

Catamorphism under this monoid using ReduceRight, where the result is the reduction, or, if empty, the identity of this monoid.

Parameters:

as - an Iterable of elements in this monoid

Returns:

the reduction, or identity() if empty

See Also:

ReduceRight

foldMap

default <B> A foldMap(Fn1<? super B,? extends A> fn,
                      java.lang.Iterable<B> bs)

Homomorphism combined with catamorphism. Convert an Iterable<B> to an Iterable<A> (that is, an Iterable of elements this monoid is formed over), then reduce the result from left to right. Under algebraic data types, this is isomorphic to a flatMap.

Type Parameters:

B - the input Iterable element type

Parameters:

fn - the mapping function from A to B

bs - the Iterable of Bs

Returns:

the folded result under this Monoid

See Also:

Map, reduceLeft(Iterable)

foldLeft

default A foldLeft(A a,
                   java.lang.Iterable<A> as)

Catamorphism under this semigroup using FoldLeft, where the binary operator is this semigroup, and the starting accumulator is provided.

Specified by:

foldLeft in interface Semigroup<A>

Parameters:

a - the starting accumulator

as - the elements to fold over

Returns:

the folded result

See Also:

FoldLeft

foldRight

default Lazy<A> foldRight(A a,
                          java.lang.Iterable<A> as)

Catamorphism under this semigroup using FoldRight, where the binary operator is this semigroup, and the starting accumulator is provided.

Specified by:

foldRight in interface Semigroup<A>

Parameters:

a - the starting accumulator

as - the elements to fold over

Returns:

the folded result

See Also:

FoldRight

flip

default Monoid<A> flip()

Flip the order of the arguments.

Specified by:

flip in interface Fn2<A,A,A>

Specified by:

flip in interface Semigroup<A>

Returns:

an Fn2<B, A, C>

monoid

static <A> Monoid<A> monoid(Semigroup<A> semigroup,
                            A identity)

Promote a Semigroup to a Monoid by supplying an identity element.

Type Parameters:

A - the element type of this monoid

Parameters:

semigroup - the semigroup

identity - the identity element

Returns:

the monoid

monoid

static <A> Monoid<A> monoid(Semigroup<A> semigroup,
                            Fn0<A> identityFn0)