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Absorbing Semigroup
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| trait Semigroup[A] { | |
| def op(a1: A, a2: A): A // op is associative | |
| } | |
| trait Monoid[A] extends Semigroup[A] { | |
| def id: A // id is the identity of op: op(a, id) == op(id, a) == a | |
| } | |
| trait SemigroupZero[A] extends Semigroup[A] { | |
| def zero: A // zero is the absorbing element of op: op(a, zero) == op(zero, a) == zero | |
| // https://en.wikipedia.org/wiki/Absorbing_element | |
| } | |
| new Monoid[Boolean] { def id = true; def op(a1: Boolean, a2: Boolean) = a1 && a2 } // true, && | |
| new SemigroupZero[Boolean] { def zero = false; def op(a1: Boolean, a2: Boolean) = a1 && a2 } // false, && | |
| new Monoid[Boolean] { def id = false; def op(a1: Boolean, a2: Boolean) = a1 || a2 } // false, || | |
| new SemigroupZero[Boolean] { def zero = true; def op(a1: Boolean, a2: Boolean) = a1 || a2 } // true, || |
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