|
Scala example source code file (Semigroup.scala)
The Semigroup.scala Scala example source codepackage scalaz //// /** * An associative binary operation, circumscribed by type and the * semigroup laws. Unlike [[scalaz.Monoid]], there is not necessarily * a zero. * * @see [[scalaz.Semigroup.SemigroupLaw]] * @see [[scalaz.syntax.SemigroupOps]] * @see [[http://mathworld.wolfram.com/Semigroup.html]] */ //// trait Semigroup[F] { self => //// /** * The binary operation to combine `f1` and `f2`. * * Implementations should not evaluate the by-name parameter `f2` if result * can be determined by `f1`. */ def append(f1: F, f2: => F): F // derived functions /** * For `n = 0`, `value` * For `n = 1`, `append(value, value)` * For `n = 2`, `append(append(value, value), value)` * * The default definition uses peasant multiplication, exploiting associativity to only * require `O(log n)` uses of [[append]] */ def multiply1(value: F, n: Int): F = { @scala.annotation.tailrec def go(x: F, y: Int, z: F): F = y match { case y if (y & 1) == 0 => go(append(x, x), y >>> 1, z) case y if (y == 1) => append(x, z) case _ => go(append(x, x), (y - 1) >>> 1, append(x, z)) } if (n <= 0) value else go(value, n, value) } protected[this] trait SemigroupCompose extends Compose[λ[(α, β) => F]] { def compose[A, B, C](f: F, g: F) = append(f, g) } /** Every `Semigroup` gives rise to a [[scalaz.Compose]], for which * the type parameters are phantoms. * * @note `compose.semigroup` = `this` */ final def compose: Compose[λ[(α, β) => F]] = new SemigroupCompose {} protected[this] trait SemigroupApply extends Apply[λ[α => F]] { override def map[A, B](fa: F)(f: A => B) = fa def ap[A, B](fa: => F)(f: => F) = append(f, fa) } /** * An [[scalaz.Apply]], that implements `ap` with `append`. Note * that the type parameter `α` in `Apply[λ[α => F]]` is * discarded; it is a phantom type. As such, the functor cannot * support [[scalaz.Bind]]. */ final def apply: Apply[λ[α => F]] = new SemigroupApply {} /** * A semigroup in type F must satisfy two laws: * * - '''closure''': `∀ a, b in F, append(a, b)` is also in `F`. This is enforced by the type system. * - '''associativity''': `∀ a, b, c` in `F`, the equation `append(append(a, b), c) = append(a, append(b , c))` holds. */ trait SemigroupLaw { def associative(f1: F, f2: F, f3: F)(implicit F: Equal[F]): Boolean = F.equal(append(f1, append(f2, f3)), append(append(f1, f2), f3)) } def semigroupLaw = new SemigroupLaw {} //// val semigroupSyntax = new scalaz.syntax.SemigroupSyntax[F] { def F = Semigroup.this } } object Semigroup { @inline def apply[F](implicit F: Semigroup[F]): Semigroup[F] = F //// /** Make an associative binary function into an instance. */ def instance[A](f: (A, => A) => A): Semigroup[A] = new Semigroup[A] { def append(f1: A, f2: => A): A = f(f1,f2) } /** A purely left-biased semigroup. */ def firstSemigroup[A] = new Semigroup[A] { def append(f1: A, f2: => A): A = f1 } @inline implicit def firstTaggedSemigroup[A] = firstSemigroup[A @@ Tags.FirstVal] /** A purely right-biased semigroup. */ def lastSemigroup[A] = new Semigroup[A] { def append(f1: A, f2: => A): A = f2 } @inline implicit def lastTaggedSemigroup[A] = lastSemigroup[A @@ Tags.LastVal] def minSemigroup[A](implicit o: Order[A]): Semigroup[A @@ Tags.MinVal] = new Semigroup[A @@ Tags.MinVal] { def append(f1: A @@ Tags.MinVal, f2: => A @@ Tags.MinVal) = Tags.MinVal(o.min(Tag.unwrap(f1), Tag.unwrap(f2))) } @inline implicit def minTaggedSemigroup[A : Order] = minSemigroup[A] def maxSemigroup[A](implicit o: Order[A]): Semigroup[A @@ Tags.MaxVal] = new Semigroup[A @@ Tags.MaxVal] { def append(f1: A @@ Tags.MaxVal, f2: => A @@ Tags.MaxVal) = Tags.MaxVal(o.max(Tag.unwrap(f1), Tag.unwrap(f2))) } @inline implicit def maxTaggedSemigroup[A : Order] = maxSemigroup[A] private[scalaz] trait ApplySemigroup[F[_], M] extends Semigroup[F[M]] { implicit def F: Apply[F] implicit def M: Semigroup[M] def append(x: F[M], y: => F[M]): F[M] = F.lift2[M, M, M]((m1, m2) => M.append(m1, m2))(x, y) } /**A semigroup for sequencing Apply effects. */ def liftSemigroup[F[_], M](implicit F0: Apply[F], M0: Semigroup[M]): Semigroup[F[M]] = new ApplySemigroup[F, M] { implicit def F: Apply[F] = F0 implicit def M: Semigroup[M] = M0 } /** `point(a) append (point(a) append (point(a)...` */ def repeat[F[_], A](a: A)(implicit F: Applicative[F], m: Semigroup[F[A]]): F[A] = m.append(F.point(a), repeat[F, A](a)) /** `point(a) append (point(f(a)) append (point(f(f(a)))...` */ def iterate[F[_], A](a: A)(f: A => A)(implicit F: Applicative[F], m: Semigroup[F[A]]): F[A] = m.append(F.point(a), iterate[F, A](f(a))(f)) /** Semigroup is an invariant functor. */ implicit val semigroupInvariantFunctor: InvariantFunctor[Semigroup] = new InvariantFunctor[Semigroup] { def xmap[A, B](ma: Semigroup[A], f: A => B, g: B => A): Semigroup[B] = new Semigroup[B] { def append(x: B, y: => B): B = f(ma.append(g(x), g(y))) } } //// } Other Scala examples (source code examples)Here is a short list of links related to this Scala Semigroup.scala source code file: |
... this post is sponsored by my books ... | |
#1 New Release! |
FP Best Seller |
Copyright 1998-2021 Alvin Alexander, alvinalexander.com
All Rights Reserved.
A percentage of advertising revenue from
pages under the /java/jwarehouse
URI on this website is
paid back to open source projects.