io.atlassian.fugue.law

Class MonoidLaws<A>

java.lang.Object

io.atlassian.fugue.law.MonoidLaws<A>

public final class MonoidLaws<A>
extends Object

Laws for a monoid

Constructor Summary

Constructors

Constructor and Description
MonoidLaws(Monoid<A> monoid) Build a law instance to check monoid properties

Method Summary

Modifier and Type	Method and Description
IsEq<A>	monoidLeftIdentity(A x) If the zero of your monoid is combine with an element of the type your monoid works with the result should be that element.
IsEq<A>	monoidRightIdentity(A x) If an element of the type your monoid works with is combined with the zero of your monoid result should be that element.
IsEq<A>	multiplyEqualRepeatedAppend(int n, A a) The multiply function of your monoid must be equal to the sum function called with an iterable containing n copies of the input type.
IsEq<A>	semigroupAssociative(A x, A y, A z) A monoid must not care about the order elements are combined.
IsEq<A>	sumEqualFold(Iterable<A> as) The sum function of your monoid must be equal to Functions.fold(BiFunction, Object, Iterable) using append as the folding function and zero() as the initial value

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

MonoidLaws

public MonoidLaws(Monoid<A> monoid)

Build a law instance to check monoid properties

Parameters:

monoid - a Monoid to check matches the desired behaviors of

Method Detail

semigroupAssociative

public IsEq<A> semigroupAssociative(A x,
                                    A y,
                                    A z)

A monoid must not care about the order elements are combined. If you combine x with y and then with z the result should be the same as combining y with z and then with x.

Parameters:

x - an A object

y - an A object

z - an A object

Returns:

a IsEq instance where append(append(x,y),z) is equal to append(x, append(y,z))

monoidLeftIdentity

public IsEq<A> monoidLeftIdentity(A x)

If the zero of your monoid is combine with an element of the type your monoid works with the result should be that element.

Parameters:

x - an element of your monoid type

Returns:

a IsEq where x is equal to append(zero(), x)

monoidRightIdentity

public IsEq<A> monoidRightIdentity(A x)

If an element of the type your monoid works with is combined with the zero of your monoid result should be that element.

Parameters:

x - an element of your monoid type

Returns:

a IsEq where x is equal to append(x, zero())

sumEqualFold

public IsEq<A> sumEqualFold(Iterable<A> as)

The sum function of your monoid must be equal to Functions.fold(BiFunction, Object, Iterable) using append as the folding function and zero() as the initial value

Parameters:

as - a Iterable

Returns:

a IsEq where sum(as) is equal to fold(append, zero, as)

multiplyEqualRepeatedAppend

public IsEq<A> multiplyEqualRepeatedAppend(int n,
                                           A a)

The multiply function of your monoid must be equal to the sum function called with an iterable containing n copies of the input type.

Parameters:

n - a int

a - an A

Returns:

a IsEq where multiply(n,a) is equal to sum(take(n, cycle(a))