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MA.scala
327 lines (216 loc) · 12 KB
/
MA.scala
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package scalaz
sealed trait MA[M[_], A] extends PimpedType[M[A]] {
import Scalaz._
def ∘[B](f: A => B)(implicit t: Functor[M]): M[B] = t.fmap(value, f)
def ∘∘[N[_], B, C](f: B => C)(implicit m: A <:< N[B], f1: Functor[M], f2: Functor[N]): M[N[C]] = ∘(k => (k: N[B]) ∘ f)
/**
* Returns a MA with the type parameter `M` equal to [A] M[N[A]], given that type `A` is contructed from type constructor `N`.
* This allows composition of type classes for `M` and `N`. For example:
* <code>(List(List(1)).comp.map {2 +}) assert_≟ List(List(3))</code>
*/
def comp[N[_], B](implicit n: A <:< N[B], f: Functor[M]): MA[Comp[M, N]#Apply, B] = ma[Comp[M, N]#Apply, B](value ∘ n)
def map[B](f: A => B)(implicit t: Functor[M]): M[B] = ∘(f)
def >|[B](f: => B)(implicit t: Functor[M]): M[B] = ∘(_ => f)
// I've resurrected `⊛` as part of an experiment to allow:
// a ⊛ b ⊛ c apply {_ + _ + _}
def ⊛[B](b: M[B]) = new ApplicativeBuilder[M, A, B](value, b)
import HList._
def ⊛:[B](mb: M[B]) = new ApplicativeBuilderHList[B :: A :: HNil, B :: HNil](mb :: HNil)
class ApplicativeBuilderHList[All <: HList, AllButOne <: HList](hl: AllButOne#Wrap[M]) {
// ap(ap(ap(t.fmap(a, f.curried), b), c), d)
def apply[B](f: All#Function[B])(implicit func: Functor[M], ap: Apply[M]) = {
def apply0[H <: HList](hl0: H) = hl0.fold[Rest, HNil]((h, t) => ap(apply0(t), h), func.fmap(a, f))
apply0(hl)
}
def ⊛:[B](b: M[B]) = new ApplicativeBuilderHList[B :: All, B :: AllButOne](HCons(b, hl))
}
def <*>[B](f: M[A => B])(implicit a: Apply[M]): M[B] = a(f, value)
def <**>[B, C](b: M[B])(z: (A, B) => C)(implicit t: Functor[M], a: Apply[M]): M[C] = a(t.fmap(value, z.curried), b)
def <***>[B, C, D](b: M[B], c: M[C])(z: (A, B, C) => D)(implicit t: Functor[M], a: Apply[M]): M[D] = a(a(t.fmap(value, z.curried), b), c)
def <****>[B, C, D, E](b: M[B], c: M[C], d: M[D])(z: (A, B, C, D) => E)(implicit t: Functor[M], a: Apply[M]): M[E] = a(a(a(t.fmap(value, z.curried), b), c), d)
def <*****>[B, C, D, E, F](b: M[B], c: M[C], d: M[D], e: M[E])(z: (A, B, C, D, E) => F)(implicit t: Functor[M], a: Apply[M]): M[F] = a(a(a(a(t.fmap(value, z.curried), b), c), d), e)
def *>[B](b: M[B])(implicit t: Functor[M], a: Apply[M]): M[B] = <**>(b)((a, b) => b)
def <*[B](b: M[B])(implicit t: Functor[M], a: Apply[M]): M[A] = <**>(b)((a, b) => a)
def <|*|>[B](b: M[B])(implicit t: Functor[M], a: Apply[M]): M[(A, B)] = <**>(b)((_, _))
def <|**|>[B, C](b: M[B], c: M[C])(implicit t: Functor[M], a: Apply[M]): M[(A, B, C)] = <***>(b, c)((_, _, _))
def <|***|>[B, C, D](b: M[B], c: M[C], d: M[D])(implicit t: Functor[M], a: Apply[M]): M[(A, B, C, D)] = <****>(b, c, d)( (_, _, _, _))
def <|****|>[B, C, D, E](b: M[B], c: M[C], d: M[D], e: M[E])(implicit t: Functor[M], a: Apply[M]): M[(A, B, C, D, E)] = <*****>(b, c, d, e)((_, _, _, _, _))
def xmap[B](f: A => B)(g: B => A)(implicit xf: InvariantFunctor[M]): M[B] = xf.xmap(value, f, g)
def ↦[F[_], B](f: A => F[B])(implicit a: Applicative[F], t: Traverse[M]): F[M[B]] =
traverse(f)
def traverse[F[_],B](f: A => F[B])(implicit a: Applicative[F], t: Traverse[M]): F[M[B]] =
t.traverse(f, value)
def >>=[B](f: A => M[B])(implicit b: Bind[M]): M[B] = b.bind(value, f)
def ∗[B](f: A => M[B])(implicit b: Bind[M]): M[B] = >>=(f)
def >>=|[B](f: => M[B])(implicit b: Bind[M]): M[B] = >>=(_ => f)
def ∗|[B](f: => M[B])(implicit b: Bind[M]): M[B] = >>=|(f)
def flatMap[B](f: A => M[B])(implicit b: Bind[M]): M[B] = >>=(f)
def join[B](implicit m: A <:< M[B], b: Bind[M]): M[B] = >>=(m)
def μ[B](implicit m: A <:< M[B], b: Bind[M]): M[B] = join
def ∞[B](implicit b: Bind[M]): M[B] = forever
def forever[B](implicit b: Bind[M]): M[B] = value ∗| value.forever
def <+>(z: => M[A])(implicit p: Plus[M]): M[A] = p.plus(value, z)
def +>:(a: A)(implicit s: Semigroup[M[A]], q: Pure[M]): M[A] = s append (q.pure(a), value)
def <+>:(a: A)(implicit p: Plus[M], q: Pure[M]): M[A] = p.plus(q.pure(a), value)
def foreach(f: A => Unit)(implicit e: Each[M]): Unit = e.each(value, f)
def |>|(f: A => Unit)(implicit e: Each[M]): Unit = foreach (f)
def foldl[B](b: B)(f: (B, A) => B)(implicit r: FoldLeft[M]): B = r.foldLeft[B, A](value, b, f)
def foldl1(f: (A, A) => A)(implicit r: FoldLeft[M]): Option[A] = foldl(none[A])((a1, a2) => Some(a1 match {
case None => a2
case Some(x) => f(a2, x)
}))
def listl(implicit r: FoldLeft[M]): List[A] = {
val b = new scala.collection.mutable.ListBuffer[A]
foldl(())((_, a) => b += a)
b.toList
}
def sum(implicit r: FoldLeft[M], m: Monoid[A]): A = foldl(m.zero)(m append (_, _))
def ∑(implicit r: FoldLeft[M], m: Monoid[A]): A = sum
def count(implicit r: FoldLeft[M]): Int = foldl(0)((b, _) => b + 1)
def ♯(implicit r: FoldLeft[M]): Int = count
def len(implicit l: Length[M]): Int = l len value
def max(implicit r: FoldLeft[M], ord: Order[A]): Option[A] =
foldl1((x: A, y: A) => if (x ≩ y) x else y)
def min(implicit r: FoldLeft[M], ord: Order[A]): Option[A] =
foldl1((x: A, y: A) => if (x ≨ y) x else y)
def longDigits(implicit d: A <:< Digit, t: FoldLeft[M]): Long =
foldl(0L)((n, a) => n * 10L + (a: Digit))
def digits(implicit c: A <:< Char, t: Functor[M]): M[Option[Digit]] =
∘((a: A) => (a: Char).digit)
def sequence[N[_], B](implicit a: A <:< N[B], t: Traverse[M], n: Applicative[N]): N[M[B]] =
traverse((z: A) => (z: N[B]))
def traverseDigits(implicit c: A <:< Char, t: Traverse[M]): Option[M[Digit]] = {
val k = ∘((f: A) => (f: Char)).digits.sequence
k
}
def foldr[B](b: B)(f: (A, => B) => B)(implicit r: FoldRight[M]): B = r.foldRight(value, b, f)
def foldr1(f: (A, => A) => A)(implicit r: FoldRight[M]): Option[A] = foldr(none[A])((a1, a2) => Some(a2 match {
case None => a1
case Some(x) => f(a1, x)
}))
def ∑∑(implicit r: FoldRight[M], m: Monoid[A]): A = foldr(m.zero)(m append (_, _))
def foldMap[B](f: A => B)(implicit r: FoldRight[M], m: Monoid[B]): B = foldr(m.zero)((a, b) => m.append(f(a), b))
def listr(implicit r: FoldRight[M]): List[A] = foldr(nil[A])(_ :: _)
def stream(implicit r: FoldRight[M]): Stream[A] = foldr(Stream.empty[A])(Stream.cons(_, _))
def !!(n: Int)(implicit r: FoldRight[M]): A = stream(r)(n)
def !(n: Int)(implicit i: Index[M]): Option[A] = i.index(value, n)
def -!-(n: Int)(implicit i: Index[M]): A = this.!(n) getOrElse (error("Index " + n + " out of bounds"))
def any(p: A => Boolean)(implicit r: FoldRight[M]): Boolean = foldr(false)(p(_) || _)
def ∃(p: A => Boolean)(implicit r: FoldRight[M]): Boolean = any(p)
def all(p: A => Boolean)(implicit r: FoldRight[M]): Boolean = foldr(true)(p(_) && _)
def ∀(p: A => Boolean)(implicit r: FoldRight[M]): Boolean = all(p)
def empty(implicit r: FoldRight[M]): Boolean = ∀(_ => false)
def ∈:(a: A)(implicit r: FoldRight[M], eq: Equal[A]): Boolean = element(a)
def ∋(a: A)(implicit r: FoldRight[M], eq: Equal[A]): Boolean = element(a)
def element(a: A)(implicit r: FoldRight[M], eq: Equal[A]): Boolean = ∃(a ≟ _)
/**
* Splits the elements into groups that alternatively satisfy and don't satisfy the predicate p.
*/
def splitWith(p: A => Boolean)(implicit r: FoldRight[M]): List[List[A]] =
foldr((nil[List[A]], none[Boolean]))((a, b) => {
val pa = p(a)
(b match {
case (_, None) => List(List(a))
case (x, Some(q)) => if (pa == q) (a :: x.head) :: x.tail else List(a) :: x
}, Some(pa))
})._1
/**
* Selects groups of elements that satisfy p and discards others.
*/
def selectSplit(p: A => Boolean)(implicit r: FoldRight[M]): List[List[A]] =
foldr((nil[List[A]], false))((a, xb) => xb match {
case (x, b) => {
val pa = p(a)
(if (pa)
if (b)
(a :: x.head) :: x.tail else
List(a) :: x
else x, pa)
}
})._1
def para[B](b: B, f: (=> A, => M[A], B) => B)(implicit p: Paramorphism[M]): B = p.para(value, b, f)
def ↣[B](f: A => B)(implicit t: Traverse[M], m: Monoid[B]): B = foldMapDefault(f)
def foldMapDefault[B](f: A => B)(implicit t: Traverse[M], m: Monoid[B]): B = {
t.traverse[PartialApply1Of2[Const, B]#Apply, A, B](a => Const[B, B](f(a)), value)
}
def collapse(implicit t: Traverse[M], m: Monoid[A]): A = ↣(identity[A])
def =>>[B](f: M[A] => B)(implicit w: Comonad[M]): M[B] = w.fmap(w.cojoin(value), f)
def copure(implicit p: Copure[M]): A = p copure value
def ε(implicit p: Copure[M]): A = copure
def cojoin(implicit j: Cojoin[M]): M[M[A]] = j cojoin value
def υ(implicit j: Cojoin[M]): M[M[A]] = cojoin
def <--->(w: M[A])(implicit l: Length[M], ind: Index[M], equ: Equal[A]): Int = {
def levenshteinMatrix(w: M[A])(implicit l: Length[M], ind: Index[M], equ: Equal[A]): (Int, Int) => Int = {
val m = mutableHashMapMemo[(Int, Int), Int]
def get(i: Int, j: Int): Int = if (i == 0) j else if (j == 0) i else {
lazy val t = this -!- (i - 1)
lazy val u = w -!- (j - 1)
lazy val e = t ≟ u
val g = m {case (a, b) => get(a, b)}
val a = g(i - 1, j) + 1
val b = g(i - 1, j - 1) + (if (e) 0 else 1)
def c = g(i, j - 1) + 1
if (a < b) a else if (b <= c) b else c
}
get
}
val k = levenshteinMatrix(w)
k(l.len(value), l.len(w))
}
def ifM[B](t: => M[B], f: => M[B])(implicit a: Monad[M], b: A <:< Boolean): M[B] = ∗ ((x: A) => if (x) t else f)
def foldLeftM[N[_], B](b: B)(f: (B, A) => N[B])(implicit fr: FoldLeft[M], m: Monad[N]): N[B] =
foldl[N[B]](b η)((b, a) => b ∗ ((z: B) => f(z, a)))
def foldRightM[N[_], B](b: B)(f: (B, A) => N[B])(implicit fr: FoldRight[M], m: Monad[N]): N[B] =
foldr[N[B]](b η)((a, b) => b ∗ ((z: B) => f(z, a)))
def replicateM[N[_]](n: Int)(implicit m: Monad[M], p: Pure[N], d: Monoid[N[A]]): M[N[A]] =
if (n <= 0) ∅ η
else value ∗ (a => replicateM[N](n - 1) ∘ (a +>: _) )
def zipWithA[F[_], B, C](b: M[B])(f: (A, B) => F[C])(implicit a: Applicative[M], t: Traverse[M], z: Applicative[F]): F[M[C]] =
(b <*> (a.fmap(value, f.curried))).sequence[F, C]
def bktree(implicit f: FoldLeft[M], m: MetricSpace[A]) =
foldl(emptyBKTree[A])(_ + _)
def fpair(implicit f: Functor[M]): M[(A, A)] = ∘(_.pair)
import FingerTree._
def &:(a: A) = OnL[M,A](a, value)
def :&(a: A) = OnR[M,A](value, a)
import concurrent._
def parMap[B](f: A => B)(implicit s: Strategy[Unit], t: Traverse[M]): Promise[M[B]] =
traverse(f.kleisli[Promise])
def parBind[B](f: A => M[B])(implicit m: Monad[M], s: Strategy[Unit], t: Traverse[M]): Promise[M[B]] =
parMap(f).map(((_: MA[M, M[B]]) μ) compose (ma(_)))
def parZipWith[B, C](bs: M[B])(f: (A, B) => C)(implicit z: Applicative[M], s: Strategy[Unit], t: Traverse[M]): Promise[M[C]] =
zipWithA(bs)((x, y) => promise(f(x, y)))
import concurrent.Strategy
def parM[B](implicit b: A <:< (() => B), m: Functor[M], s: Strategy[B]): () => M[B] =
() => value ∘ (z => s(z).apply)
}
// Previously there was an ambiguity because (A => B) could be considered as MA[(R => _), A] or MA[(_ => R), A].
// This is a hack to fix the pressing problem that this caused.
trait MACofunctor[M[_], A] extends PimpedType[M[A]] {
def ∙[B](f: B => A)(implicit t: Cofunctor[M]): M[B] = t.comap(value, f)
/**
* Alias for {@link scalaz.MACofunctor#∙}
*/
def comap[B](f: B => A)(implicit t: Cofunctor[M]): M[B] = ∙(f)
/**
* Comap the identity function
*/
def covary[B <: A](implicit t: Cofunctor[M]): M[B] = ∙[B](identity)
def |<[B](f: => A)(implicit t: Cofunctor[M]): M[B] = ∙((_: B) => f)
}
trait MAsLow {
implicit def maImplicit[MM[_], A](a: MM[A]): MA[MM, A] = new MA[MM, A] {
val value = a
}
implicit def maCofunctorImplicit[MM[_], A](a: MM[A]): MACofunctor[MM, A] = new MACofunctor[MM, A] {
val value = a
}
}
trait MAs {
def ma[M[_], A](a: M[A]): MA[M, A] = new MA[M, A] {
val value = a
}
def maCofunctor[M[_], A](a: M[A])(implicit cf: Cofunctor[M]): MACofunctor[M, A] = new MACofunctor[M, A] {
val value = a
}
}