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fthomas/absorbing.scala

Last active August 29, 2015 14:24
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Absorbing Semigroup
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absorbing.scala
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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