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Recursive.scala
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Recursive.scala
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/*
* Copyright 2014–2017 SlamData Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package matryoshka
import matryoshka.implicits._
import matryoshka.patterns.EnvT
import scala.{Boolean, Option, PartialFunction}
import scala.Predef.identity
import scala.collection.immutable.{List, Nil}
import scalaz._, Scalaz._
/** Folds for recursive data types. */
trait Recursive[T] extends Based[T] {
// TODO: This works around a bug in Simulacrum (#55). Delete once that is fixed.
type BaseT[A] = Base[A]
def project(t: T)(implicit BF: Functor[Base]): BaseT[T]
def cata[A](t: T)(f: Algebra[Base, A])(implicit BF: Functor[Base]): A =
f(project(t) ∘ (cata(_)(f)))
/** A Kleisli catamorphism. */
def cataM[M[_]: Monad, A](t: T)(f: AlgebraM[M, Base, A])(implicit BT: Traverse[Base]):
M[A] =
project(t).traverse(cataM(_)(f)).flatMap(f)
/** A catamorphism generalized with a comonad inside the functor. */
def gcata[W[_]: Comonad, A]
(t: T)
(k: DistributiveLaw[Base, W], g: GAlgebra[W, Base, A])
(implicit BF: Functor[Base])
: A = {
def loop(t: T): W[Base[W[A]]] = k(project(t) ∘ (loop(_).map(g).cojoin))
g(loop(t).copoint)
}
def gcataM[W[_]: Comonad: Traverse, M[_]: Monad, A](
t: T)(
k: DistributiveLaw[Base, W], g: GAlgebraM[W, M, Base, A])(
implicit BT: Traverse[Base]):
M[A] = {
def loop(t: T): M[W[Base[W[A]]]] =
project(t).traverse(loop(_) >>= (_.traverse(g) ∘ (_.cojoin))) ∘ (k(_))
loop(t) ∘ (_.copoint) >>= g
}
/** A catamorphism generalized with a comonad outside the functor. */
def elgotCata[W[_]: Comonad, A](
t: T)(
k: DistributiveLaw[Base, W], g: ElgotAlgebra[W, Base, A])
(implicit BF: Functor[Base]):
A = {
def loop(t: T): W[Base[A]] = k(project(t) ∘ (loop(_).cojoin.map(g)))
g(loop(t))
}
def para[A](t: T)(f: GAlgebra[(T, ?), Base, A])(implicit BF: Functor[Base])
: A =
// NB: This is not implemented with [[matryoshka.distPara]] because that
// would add a [[matryoshka.Corecursive]] constraint.
f(project(t) ∘ (t => (t, para(t)(f))))
def elgotPara[A]
(t: T)
(f: ElgotAlgebra[(T, ?), Base, A])
(implicit BF: Functor[Base])
: A =
// NB: This is not implemented with [[matryoshka.distPara]] because that
// would add a [[matryoshka.Corecursive]] constraint.
f((t, project(t) ∘ (elgotPara(_)(f))))
def paraM[M[_]: Monad, A](
t: T)(
f: GAlgebraM[(T, ?), M, Base, A])(
implicit BT: Traverse[Base]):
M[A] =
project(t).traverse(v => paraM(v)(f) ∘ ((v, _))).flatMap(f)
def zygo[A, B]
(t: T)
(f: Algebra[Base, B], g: GAlgebra[(B, ?), Base, A])
(implicit BF: Functor[Base])
: A =
gcata[(B, ?), A](t)(distZygo(f), g)
def elgotZygo[A, B]
(t: T)
(f: Algebra[Base, B], g: ElgotAlgebra[(B, ?), Base, A])
(implicit BF: Functor[Base])
: A =
elgotCata[(B, ?), A](t)(distZygo(f), g)
def gzygo[W[_]: Comonad, A, B](
t: T)(
f: Algebra[Base, B], w: DistributiveLaw[Base, W], g: GAlgebra[EnvT[B, W, ?], Base, A])
(implicit BF: Functor[Base]):
A =
gcata[EnvT[B, W, ?], A](t)(distZygoT(f, w), g)
def gElgotZygo[W[_]: Comonad, A, B](
t: T)(
f: Algebra[Base, B], w: DistributiveLaw[Base, W], g: ElgotAlgebra[EnvT[B, W, ?], Base, A])
(implicit BF: Functor[Base]):
A =
elgotCata[EnvT[B, W, ?], A](t)(distZygoT(f, w), g)
/** Mutually-recursive fold. */
def mutu[A, B]
(t: T)
(f: GAlgebra[(A, ?), Base, B], g: GAlgebra[(B, ?), Base, A])
(implicit BF: Functor[Base])
: A =
g(project(t) ∘ (x => (mutu(x)(g, f), mutu(x)(f, g))))
def histo[A]
(t: T)
(f: GAlgebra[Cofree[Base, ?], Base, A])
(implicit BF: Functor[Base])
: A =
gcata[Cofree[Base, ?], A](t)(distHisto, f)
def elgotHisto[A]
(t: T)
(f: ElgotAlgebra[Cofree[Base, ?], Base, A])
(implicit BF: Functor[Base])
: A =
elgotCata[Cofree[Base, ?], A](t)(distHisto, f)
def ghisto[H[_]: Functor, A](
t: T)(
g: DistributiveLaw[Base, H], f: GAlgebra[Cofree[H, ?], Base, A])
(implicit BF: Functor[Base]):
A =
gcata[Cofree[H, ?], A](t)(distGHisto(g), f)
def paraZygo[A, B](
t: T)(
f: GAlgebra[(T, ?), Base, B],
g: GAlgebra[(B, ?), Base, A])(
implicit BF: Functor[Base], BU: Unzip[Base]):
A = {
def h(t: T): (B, A) =
(project(t) ∘ { x =>
val (b, a) = h(x)
((x, b), (b, a))
}).unfzip.bimap(f, g)
h(t)._2
}
// TODO: figure out how to represent this as a elgotHylo with mergeTuple
/** Combines two functors that may fail to merge, also providing access to the
* inputs at each level. This is akin to an Elgot, not generalized, fold.
*/
def paraMerga[A]
(t: T, that: T)
(f: (T, T, Option[Base[A]]) => A)
(implicit BF: Functor[Base], BM: Merge[Base])
: A =
f(t, that, project(t).mergeWith(project(that))(paraMerga(_, _)(f)))
def isLeaf(t: T)(implicit BF: Functor[Base], B: Foldable[Base]): Boolean =
!Tag.unwrap(project(t).foldMap(_ => true.disjunction))
def children(t: T)(implicit BF: Functor[Base], B: Foldable[Base]): List[T] =
project(t).foldMap(_ :: Nil)
def universe(t: T)(implicit BF: Functor[Base], B: Foldable[Base]): List[T] =
t :: children(t).flatMap(universe)
/** Attribute a tree via an algebra starting from the root. */
def attributeTopDown[A]
(t: T, z: A)
(f: (A, Base[T]) => A)
(implicit BF: Functor[Base])
: Cofree[Base, A] = {
val ft = project(t)
val a = f(z, ft)
Cofree(a, ft ∘ (attributeTopDown(_, a)(f)))
}
/** Kleisli variant of attributeTopDown */
def attributeTopDownM[M[_]: Monad, A](
t: T, z: A)(
f: (A, Base[T]) => M[A])(
implicit BT: Traverse[Base]):
M[Cofree[Base, A]] = {
val ft = project(t)
f(z, ft) >>=
(a => ft.traverse(attributeTopDownM(_, a)(f)) ∘ (Cofree(a, _)))
}
// Foldable
def all(t: T)(p: T ⇒ Boolean)(implicit BF: Functor[Base], B: Foldable[Base]): Boolean =
Tag.unwrap(foldMap(t)(p(_).conjunction))
def any(t: T)(p: T ⇒ Boolean)(implicit BF: Functor[Base], B: Foldable[Base]): Boolean =
Tag.unwrap(foldMap(t)(p(_).disjunction))
def collect[B]
(t: T)
(pf: PartialFunction[T, B])
(implicit BF: Functor[Base], B: Foldable[Base])
: List[B] =
foldMap(t)(pf.lift(_).toList)
def contains
(t: T, c: T)
(implicit T: Equal[T], BF: Functor[Base], B: Foldable[Base])
: Boolean =
any(t)(_ ≟ c)
def foldMap[Z: Monoid]
(t: T)
(f: T => Z)
(implicit BF: Functor[Base], B: Foldable[Base])
: Z =
foldMapM[Free.Trampoline, Z](t)(f(_).pure[Free.Trampoline]).run
def foldMapM[M[_]: Monad, Z: Monoid]
(t: T)
(f: T => M[Z])
(implicit BF: Functor[Base], B: Foldable[Base])
: M[Z] = {
def loop(z0: Z, term: T): M[Z] = {
for {
z1 <- f(term)
z2 <- project(term).foldLeftM(z0 ⊹ z1)(loop(_, _))
} yield z2
}
loop(Monoid[Z].zero, t)
}
def convertTo[R]
(t: T)
(implicit R: Corecursive.Aux[R, Base], BF: Functor[Base])
: R =
cata[R](t)(R.embed(_))
def mapR[U, G[_]: Functor]
(t: T)
(f: Base[T] => G[U])
(implicit U: Corecursive.Aux[U, G], BF: Functor[Base])
: U =
f(project(t)).embed
def traverseR[M[_]: Functor, U, G[_]: Functor]
(t: T)
(f: Base[T] => M[G[U]])
(implicit U: Corecursive.Aux[U, G], BF: Functor[Base])
: M[U] =
f(project(t)) ∘ (_.embed)
def transCata[U, G[_]: Functor]
(t: T)
(f: Base[U] => G[U])
(implicit U: Corecursive.Aux[U, G], BF: Functor[Base])
: U =
mapR(t)(ft => f(ft.map(transCata(_)(f))))
def transAna[U, G[_]: Functor]
(t: T)
(f: Base[T] => G[T])
(implicit U: Corecursive.Aux[U, G], BF: Functor[Base])
: U =
mapR(t)(f(_).map(transAna(_)(f)))
def transPostpro[U, G[_]: Functor]
(t: T)
(e: G ~> G, f: Transform[T, Base, G])
(implicit UR: Recursive.Aux[U, G], UC: Corecursive.Aux[U, G], BF: Functor[Base])
: U =
mapR(t)(f(_) ∘ (x => UR.transAna(transPostpro(x)(e, f))(e)))
def transPara[U, G[_]: Functor]
(t: T)
(f: AlgebraicGTransform[(T, ?), U, Base, G])
(implicit U: Corecursive.Aux[U, G], BF: Functor[Base])
: U =
mapR(t)(ft => f(ft.map(tf => (tf, transPara(tf)(f)))))
def transApo[U, G[_]: Functor]
(t: T)
(f: CoalgebraicGTransform[(U \/ ?), T, Base, G])
(implicit U: Corecursive.Aux[U, G], BF: Functor[Base])
: U =
mapR(t)(f(_).map(_.fold(identity, transApo(_)(f))))
def transHylo[G[_]: Functor, U, H[_]: Functor]
(t: T)
(φ: G[U] => H[U], ψ: Base[T] => G[T])
(implicit U: Corecursive.Aux[U, H], BF: Functor[Base])
: U =
mapR(t)(ft => φ(ψ(ft) ∘ (transHylo(_)(φ, ψ))))
def transCataM[M[_]: Monad, U, G[_]: Functor]
(t: T)
(f: TransformM[M, U, Base, G])
(implicit U: Corecursive.Aux[U, G], BT: Traverse[Base])
: M[U] =
traverseR(t)(_.traverse(transCataM(_)(f)).flatMap(f))
def transAnaM[M[_]: Monad, U, G[_]: Traverse]
(t: T)
(f: TransformM[M, T, Base, G])
(implicit U: Corecursive.Aux[U, G], BF: Functor[Base])
: M[U] =
traverseR(t)(f(_).flatMap(_.traverse(transAnaM(_)(f))))
// TODO: Move these operations to `Birecursive` once #44 is fixed.
/** Roughly a default impl of `project`, given a [[matryoshka.Corecursive]]
* instance and an overridden `cata`.
*/
def lambek(tf: T)(implicit T: Corecursive.Aux[T, Base], BF: Functor[Base])
: Base[T] =
cata[Base[T]](tf)(_ ∘ (_.embed))
def gpara[W[_]: Comonad, A](
t: T)(
e: DistributiveLaw[Base, W], f: GAlgebra[EnvT[T, W, ?], Base, A])(
implicit T: Corecursive.Aux[T, Base], BF: Functor[Base]):
A =
gzygo[W, A, T](t)(T.embed(_), e, f)
def prepro[A]
(t: T)
(e: Base ~> Base, f: Algebra[Base, A])
(implicit T: Corecursive.Aux[T, Base], BF: Functor[Base])
: A =
f(project(t) ∘ (x => prepro(cata[T](x)(c => T.embed(e(c))))(e, f)))
def gprepro[W[_]: Comonad, A](
t: T)(
k: DistributiveLaw[Base, W], e: Base ~> Base, f: GAlgebra[W, Base, A])(
implicit T: Corecursive.Aux[T, Base], BF: Functor[Base]):
A = {
def loop(t: T): W[A] =
k(project(t) ∘ (x => loop(cata[T](x)(c => T.embed(e(c)))).cojoin)) ∘ f
loop(t).copoint
}
def topDownCata[A]
(t: T, a: A)
(f: (A, T) => (A, T))
(implicit T: Corecursive.Aux[T, Base], BF: Functor[Base])
: T = {
val (a0, tf) = f(a, t)
mapR(tf)(_.map(topDownCata(_, a0)(f)))
}
def topDownCataM[M[_]: Monad, A](
t: T, a: A)(
f: (A, T) => M[(A, T)])(
implicit T: Corecursive.Aux[T, Base], BT: Traverse[Base]):
M[T] =
f(a, t).flatMap { case (a, tf) =>
traverseR(tf)(_.traverse(topDownCataM(_, a)(f)))
}
def transPrepro[U, G[_]: Functor]
(t: T)
(e: Base ~> Base, f: Transform[U, Base, G])
(implicit T: Corecursive.Aux[T, Base], U: Corecursive.Aux[U, G], BF: Functor[Base])
: U =
mapR(t)(ft => f(ft ∘ (x => transPrepro(transCata[T, Base](x)(e(_)))(e, f))))
def transCataT
(t: T)
(f: T => T)
(implicit T: Corecursive.Aux[T, Base], BF: Functor[Base])
: T =
f(mapR(t)(_.map(transCataT(_)(f))))
/** This behaves like [[matryoshka.Recursive.elgotPara]]`, but it’s harder to
* see from the types that in the tuple, `_2` is the result so far and `_1`
* is the original structure.
*/
def transParaT
(t: T)
(f: ((T, T)) => T)
(implicit T: Corecursive.Aux[T, Base], BF: Functor[Base])
: T =
f((t, mapR(t)(_.map(transParaT(_)(f)))))
def transAnaT
(t: T)
(f: T => T)
(implicit T: Corecursive.Aux[T, Base], BF: Functor[Base])
: T =
mapR(f(t))(_.map(transAnaT(_)(f)))
/** This behaves like [[matryoshka.Corecursive.elgotApo]]`, but it’s harder to
* see from the types that in the disjunction, `-\/` is the final result for
* this node, while `\/-` means to keep processing the children.
*/
def transApoT
(t: T)
(f: T => T \/ T)
(implicit T: Corecursive.Aux[T, Base], BF: Functor[Base])
: T =
f(t).fold(identity, mapR(_)(_.map(transApoT(_)(f))))
def transCataTM[M[_]: Monad]
(t: T)
(f: T => M[T])
(implicit T: Corecursive.Aux[T, Base], BF: Traverse[Base])
: M[T] =
traverseR(t)(_.traverse(transCataTM(_)(f))).flatMap(f)
def transAnaTM[M[_]: Monad]
(t: T)
(f: T => M[T])
(implicit T: Corecursive.Aux[T, Base], BF: Traverse[Base])
: M[T] =
f(t).flatMap(traverseR(_)(_.traverse(transAnaTM(_)(f))))
}
object Recursive {
def equal[T, F[_]: Functor]
(implicit T: Recursive.Aux[T, F], F: Delay[Equal, F])
: Equal[T] =
Equal.equal((a, b) => F(equal[T, F]).equal(T.project(a), T.project(b)))
def show[T, F[_]: Functor](implicit T: Recursive.Aux[T, F], F: Delay[Show, F])
: Show[T] =
Show.show(T.cata(_)(F(Cord.CordShow).show))
// NB: The rest of this is what would be generated by simulacrum, except this
// type class is too complicated to take advantage of that.
type Aux[T, F[_]] = Recursive[T] { type Base[A] = F[A] }
def apply[T, F[_]](implicit instance: Aux[T, F]): Aux[T, F] = instance
trait Ops[T, F[_]] {
def typeClassInstance: Aux[T, F]
def self: T
def project(implicit BF: Functor[F]): F[T] = typeClassInstance.project(self)
def lambek(implicit T: Corecursive.Aux[T, F], BF: Functor[F]): F[T] =
typeClassInstance.lambek(self)
def cata[A](f: Algebra[F, A])(implicit BF: Functor[F]): A =
typeClassInstance.cata[A](self)(f)
def cataM[M[_]: Monad, A](f: AlgebraM[M, F, A])(implicit BT: Traverse[F])
: M[A] =
typeClassInstance.cataM[M, A](self)(f)
def gcata[W[_]: Comonad, A]
(k: DistributiveLaw[F, W], g: GAlgebra[W, F, A])
(implicit BF: Functor[F])
: A =
typeClassInstance.gcata[W, A](self)(k, g)
def gcataM[W[_]: Comonad: Traverse, M[_]: Monad, A]
(k: DistributiveLaw[F, W], g: GAlgebraM[W, M, F, A])
(implicit BT: Traverse[F])
: M[A] =
typeClassInstance.gcataM[W, M, A](self)(k, g)
def elgotCata[W[_]: Comonad, A]
(k: DistributiveLaw[F, W], g: ElgotAlgebra[W, F, A])
(implicit BF: Functor[F])
: A =
typeClassInstance.elgotCata[W, A](self)(k, g)
def para[A](f: GAlgebra[(T, ?), F, A])(implicit BF: Functor[F]): A =
typeClassInstance.para[A](self)(f)
def elgotPara[A]
(f: ElgotAlgebra[(T, ?), F, A])
(implicit BF: Functor[F])
: A =
typeClassInstance.elgotPara[A](self)(f)
def paraM[M[_]: Monad, A]
(f: GAlgebraM[(T, ?), M, F, A])
(implicit BT: Traverse[F])
: M[A] =
typeClassInstance.paraM[M, A](self)(f)
def gpara[W[_]: Comonad, A]
(e: DistributiveLaw[F, W], f: GAlgebra[EnvT[T, W, ?], F, A])
(implicit T: Corecursive.Aux[T, F], BF: Functor[F])
: A =
typeClassInstance.gpara[W, A](self)(e, f)
def zygo[A, B]
(f: Algebra[F, B], g: GAlgebra[(B, ?), F, A])
(implicit BF: Functor[F])
: A =
typeClassInstance.zygo[A, B](self)(f, g)
def elgotZygo[A, B]
(f: Algebra[F, B], g: ElgotAlgebra[(B, ?), F, A])
(implicit BF: Functor[F])
: A =
typeClassInstance.elgotZygo[A, B](self)(f, g)
def gzygo[W[_]: Comonad, A, B]
(f: Algebra[F, B],
w: DistributiveLaw[F, W],
g: GAlgebra[EnvT[B, W, ?], F, A])
(implicit BF: Functor[F])
: A =
typeClassInstance.gzygo[W, A, B](self)(f, w, g)
def gElgotZygo[W[_]: Comonad, A, B]
(f: Algebra[F, B],
w: DistributiveLaw[F, W],
g: ElgotAlgebra[EnvT[B, W, ?], F, A])
(implicit BF: Functor[F])
: A =
typeClassInstance.gElgotZygo [W, A, B](self)(f, w, g)
def mutu[A, B]
(f: GAlgebra[(A, ?), F, B], g: GAlgebra[(B, ?), F, A])
(implicit BF: Functor[F])
: A =
typeClassInstance.mutu[A, B](self)(f, g)
def prepro[A]
(e: F ~> F, f: Algebra[F, A])
(implicit T: Corecursive.Aux[T, F], BF: Functor[F])
: A =
typeClassInstance.prepro[A](self)(e, f)
def gprepro[W[_]: Comonad, A]
(k: DistributiveLaw[F, W], e: F ~> F, f: GAlgebra[W, F, A])
(implicit T: Corecursive.Aux[T, F], BF: Functor[F])
: A =
typeClassInstance.gprepro[W, A](self)(k, e, f)
def histo[A]
(f: GAlgebra[Cofree[F, ?], F, A])
(implicit BF: Functor[F])
: A =
typeClassInstance.histo(self)(f)
def elgotHisto[A]
(f: ElgotAlgebra[Cofree[F, ?], F, A])
(implicit BF: Functor[F])
: A =
typeClassInstance.elgotHisto(self)(f)
def ghisto[H[_]: Functor, A]
(g: DistributiveLaw[F, H], f: GAlgebra[Cofree[H, ?], F, A])
(implicit BF: Functor[F])
: A =
typeClassInstance.ghisto(self)(g, f)
def paraZygo[A, B]
(f: GAlgebra[(T, ?), F, B], g: GAlgebra[(B, ?), F, A])
(implicit BF: Functor[F], BU: Unzip[F])
: A =
typeClassInstance.paraZygo[A, B](self)(f, g)
def paraMerga[A]
(that: T)
(f: (T, T, Option[F[A]]) => A)
(implicit BF: Functor[F], BM: Merge[F])
: A =
typeClassInstance.paraMerga[A](self, that)(f)
def isLeaf(implicit BT: Traverse[F]): Boolean =
typeClassInstance.isLeaf(self)
def children(implicit BT: Traverse[F]): List[T] =
typeClassInstance.children(self)
def universe(implicit BT: Traverse[F]): List[T] =
typeClassInstance.universe(self)
def topDownCata[A]
(a: A)
(f: (A, T) => (A, T))
(implicit T: Corecursive.Aux[T, F], BF: Functor[F])
: T =
typeClassInstance.topDownCata[A](self, a)(f)
def topDownCataM[M[_]: Monad, A]
(a: A)
(f: (A, T) => M[(A, T)])
(implicit T: Corecursive.Aux[T, F], BT: Traverse[F])
: M[T] =
typeClassInstance.topDownCataM[M, A](self, a)(f)
def attributeTopDown[A]
(z: A)
(f: (A, F[T]) => A)
(implicit BF: Functor[F])
: Cofree[F, A] =
typeClassInstance.attributeTopDown[A](self, z)(f)
def attributeTopDownM[M[_]: Monad, A]
(z: A)
(f: (A, F[T]) => M[A])
(implicit BT: Traverse[F])
: M[Cofree[F, A]] =
typeClassInstance.attributeTopDownM[M, A](self, z)(f)
def all(p: T ⇒ Boolean)(implicit BF: Functor[F], B: Foldable[F])
: Boolean =
typeClassInstance.all(self)(p)
def any(p: T ⇒ Boolean)(implicit BF: Functor[F], B: Foldable[F])
: Boolean =
typeClassInstance.any(self)(p)
def collect[B]
(pf: PartialFunction[T, B])
(implicit BF: Functor[F], B: Foldable[F])
: List[B] =
typeClassInstance.collect[B](self)(pf)
def contains
(c: T)
(implicit T: Equal[T], BF: Functor[F], B: Foldable[F])
: Boolean =
typeClassInstance.contains(self, c)
def foldMap[Z: Monoid]
(f: T => Z)
(implicit BF: Functor[F], B: Foldable[F])
: Z =
typeClassInstance.foldMap[Z](self)(f)
def foldMapM[M[_]: Monad, Z: Monoid]
(f: T => M[Z])
(implicit BF: Functor[F], B: Foldable[F])
: M[Z] =
typeClassInstance.foldMapM[M, Z](self)(f)
def convertTo[R](implicit R: Corecursive.Aux[R, F], BF: Functor[F])
: R =
typeClassInstance.convertTo[R](self)
def mapR[U, G[_]: Functor]
(f: F[T] => G[U])
(implicit U: Corecursive.Aux[U, G], BF: Functor[F])
: U =
typeClassInstance.mapR(self)(f)
def traverseR[M[_]: Functor, U, G[_]: Functor]
(f: F[T] => M[G[U]])
(implicit U: Corecursive.Aux[U, G], BF: Functor[F])
: M[U] =
typeClassInstance.traverseR(self)(f)
object transCata {
def apply[U] = new PartiallyApplied[U]
final class PartiallyApplied[U] {
def apply[G[_]: Functor]
(f: F[U] => G[U])
(implicit U: Corecursive.Aux[U, G], BF: Functor[F])
: U =
typeClassInstance.transCata(self)(f)
}
}
object transAna {
def apply[U] = new PartiallyApplied[U]
final class PartiallyApplied[U] {
def apply[G[_]: Functor]
(f: F[T] => G[T])
(implicit U: Corecursive.Aux[U, G], BF: Functor[F])
: U =
typeClassInstance.transAna(self)(f)
}
}
object transPrepro {
def apply[U] = new PartiallyApplied[U]
final class PartiallyApplied[U] {
def apply[G[_]: Functor]
(e: F ~> F, f: Transform[U, F, G])
(implicit T: Corecursive.Aux[T, F], U: Corecursive.Aux[U, G], BF: Functor[F])
: U =
typeClassInstance.transPrepro(self)(e, f)
}
}
object transPostpro {
def apply[U] = new PartiallyApplied[U]
final class PartiallyApplied[U] {
def apply[G[_]: Functor]
(e: G ~> G, f: Transform[T, F, G])
(implicit UR: Recursive.Aux[U, G], UC: Corecursive.Aux[U, G], BF: Functor[F])
: U =
typeClassInstance.transPostpro(self)(e, f)
}
}
object transPara {
def apply[U] = new PartiallyApplied[U]
final class PartiallyApplied[U] {
def apply[G[_]: Functor]
(f: AlgebraicGTransform[(T, ?), U, F, G])
(implicit U: Corecursive.Aux[U, G], BF: Functor[F])
: U =
typeClassInstance.transPara(self)(f)
}
}
def transApo[U, G[_]: Functor]
(f: CoalgebraicGTransform[(U \/ ?), T, F, G])
(implicit U: Corecursive.Aux[U, G], BF: Functor[F])
: U =
typeClassInstance.transApo(self)(f)
def transHylo[G[_]: Functor, U, H[_]: Functor]
(φ: G[U] => H[U], ψ: F[T] => G[T])
(implicit U: Corecursive.Aux[U, H], BF: Functor[F])
: U =
typeClassInstance.transHylo(self)(φ, ψ)
def transCataM[M[_]: Monad, U, G[_]: Functor]
(f: TransformM[M, U, F, G])
(implicit U: Corecursive.Aux[U, G], BT: Traverse[F])
: M[U] =
typeClassInstance.transCataM(self)(f)
def transAnaM[M[_]: Monad, U, G[_]: Traverse]
(f: TransformM[M, T, F, G])
(implicit U: Corecursive.Aux[U, G], BF: Functor[F])
: M[U] =
typeClassInstance.transAnaM(self)(f)
def transCataT(f: T => T)(implicit T: Corecursive.Aux[T, F], BF: Functor[F]): T =
typeClassInstance.transCataT(self)(f)
def transParaT(f: ((T, T)) => T)(implicit T: Corecursive.Aux[T, F], BF: Functor[F]): T =
typeClassInstance.transParaT(self)(f)
def transAnaT(f: T => T)(implicit T: Corecursive.Aux[T, F], BF: Functor[F]): T =
typeClassInstance.transAnaT(self)(f)
def transApoT(f: T => T \/ T)(implicit T: Corecursive.Aux[T, F], BF: Functor[F]): T =
typeClassInstance.transApoT(self)(f)
def transCataTM[M[_]: Monad](f: T => M[T])(implicit T: Corecursive.Aux[T, F], BF: Traverse[F])
: M[T] =
typeClassInstance.transCataTM(self)(f)
def transAnaTM[M[_]: Monad](f: T => M[T])(implicit T: Corecursive.Aux[T, F], BF: Traverse[F])
: M[T] =
typeClassInstance.transAnaTM(self)(f)
}
trait ToRecursiveOps {
implicit def toRecursiveOps[T, F[_]](target: T)(implicit tc: Aux[T, F]): Ops[T, F] =
new Ops[T, F] {
val self = target
val typeClassInstance = tc
}
}
object nonInheritedOps extends ToRecursiveOps
trait AllOps[T, F[_]] extends Ops[T, F] {
def typeClassInstance: Aux[T, F]
}
object ops {
implicit def toAllRecursiveOps[T, F[_]](target: T)(implicit tc: Aux[T, F]): AllOps[T, F] =
new AllOps[T, F] {
val self = target
val typeClassInstance = tc
}
}
}