typequux.DenseSet.scala Maven / Gradle / Ivy
/**
* Copyright 2019 Harshad Deo
*
* 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 typequux
import Bool._
import Dense._
import language.higherKinds
/** Typelevel set of [[Dense]] numbers, implemented as a binary tree
*
* @author Harshad Deo
* @since 0.1
*/
sealed trait DenseSet {
/** Checks if the key is present in the set
*
* @author Harshad Deo
* @since 0.1
*/
type Contains[X <: Dense] <: Bool
/** Adds a key to the set
*
* @author Harshad Deo
* @since 0.1
*/
type Include[X <: Dense] <: DenseSet
/** Removes a key from the set
*
* @author Harshad Deo
* @since 0.1
*/
type Remove[X <: Dense] <: DenseSet
/** Union with the other set
*
* @author Harshad Deo
* @since 0.1
*/
type Union[X <: DenseSet] <: DenseSet
/** Set difference
*
* @author Harshad Deo
* @since 0.6.1
*/
type Diff[X <: DenseSet] <: DenseSet
/** Size of the set (count of the elements present in it)
*
* @author Harshad Deo
* @since 0.1
*/
type Size <: Dense
/** Fold over the set
*
* @author Harshad Deo
* @since 0.6
*/
type FoldL[Init <: Type, Type, F <: Fold[Dense, Type]] <: Type
}
/** Contains implementation traits for [[DenseSet]] and typeconstructor aliases that make usage more pleasant.
*
* @author Harshad Deo
* @since 0.1
*/
object DenseSet {
/** Empty set, base case for constructing all dense sets
*
* @group Implementation
* @author Harshad Deo
* @since 0.1
*/
trait EmptyDenseSet extends DenseSet {
override type Contains[X <: Dense] = False
override type Include[X <: Dense] = NonEmptyDenseSet[X, EmptyDenseSet, EmptyDenseSet]
override type Remove[X <: Dense] = EmptyDenseSet
override type Union[X <: DenseSet] = X
override type Diff[X <: DenseSet] = EmptyDenseSet
override type Size = Dense._0
override type FoldL[Init <: Type, Type, F <: Fold[Dense, Type]] = Init
}
/** Non empty set of dense numbers, implemented as a binary tree
*
* @tparam V Type at the node
* @tparam L DenseSet in which all values are less than V
* @tparam R DenseSet in which all values are greater than V
*
* @group Implementation
* @author Harshad Deo
* @since 0.1
*/
trait NonEmptyDenseSet[V <: Dense, L <: DenseSet, R <: DenseSet] extends DenseSet {
override type Contains[X <: Dense] = X#Compare[V]#Match[L#Contains[X], True, R#Contains[X], Bool]
override type Include[X <: Dense] = X#Compare[V]#Match[NonEmptyDenseSet[V, L#Include[X], R],
NonEmptyDenseSet[V, L, R],
NonEmptyDenseSet[V, L, R#Include[X]],
DenseSet]
override type Remove[X <: Dense] =
X#Compare[V]#Match[NonEmptyDenseSet[V, L#Remove[X], R], L#Union[R], NonEmptyDenseSet[V, L, R#Remove[X]], DenseSet]
override type Union[X <: DenseSet] = FoldL[X, DenseSet, UnionFold]
override type Diff[X <: DenseSet] = FoldL[EmptyDenseSet, DenseSet, DifferenceFold[X]]
override type Size = _1 + L#Size + R#Size
override type FoldL[Init <: Type, Type, F <: Fold[Dense, Type]] =
R#FoldL[F#Apply[V, L#FoldL[Init, Type, F]], Type, F]
}
trait UnionFold extends Fold[Dense, DenseSet] {
override type Apply[E <: Dense, Acc <: DenseSet] = Acc#Include[E]
}
trait DifferenceFold[Arg <: DenseSet] extends Fold[Dense, DenseSet] {
override type Apply[E <: Dense, Acc <: DenseSet] = Arg#Contains[E]#If[Acc, Acc#Include[E], DenseSet]
}
trait AllContainedFold[Arg <: DenseSet] extends Fold[Dense, Bool] {
override type Apply[E <: Dense, Acc <: Bool] = Acc#If[Arg#Contains[E], False, Bool]
}
/** Alias to check if a key is present in the set
*
* @group Operations
* @author Harshad Deo
* @since 0.1
*/
type Contains[A <: DenseSet, X <: Dense] = A#Contains[X]
/** Alias to add a key to the set
*
* @group Operations
* @author Harshad Deo
* @since 0.1
*/
type Include[A <: DenseSet, X <: Dense] = A#Include[X]
/** Alias to remove a key from the set
*
* @group Operations
* @author Harshad Deo
* @since 0.1
*/
type Remove[A <: DenseSet, X <: Dense] = A#Remove[X]
/** Alias to build the union of two sets
*
* @group Operations
* @author Harshad Deo
* @since 0.1
*/
type Union[A <: DenseSet, B <: DenseSet] = A#Union[B]
/** Typeconstructor to check whether two sets have the same elements
*
* @group Operations
* @author Harshad Deo
* @since 0.1
*/
type Eq[A <: DenseSet, B <: DenseSet] =
&&[A#FoldL[True, Bool, AllContainedFold[B]], B#FoldL[True, Bool, AllContainedFold[A]]]
/** Builds a value level [[scala.collection.immutable.Set]] representation of a dense set type
*
* @tparam DS Type of the dense set for which the representation is being constructed
*
* @group Implementation
* @author Harshad Deo
* @since 0.3.3
*/
class DenseSetRep[DS] private (val rep: Set[Long])(implicit ev: DS <:< DenseSet)
/** Contains implicit definitions to build a [[DenseSetRep]]
*
* @group Implementation
* @author Harshad Deo
* @since 0.3.3
*/
object DenseSetRep {
/** Representation for [[EmptyDenseSet]]. Is the base case to build a [[DenseSetRep]]
*
* @author Harshad Deo
* @since 0.3.3
*/
implicit object EmptyToRep extends DenseSetRep[EmptyDenseSet](Set.empty)
/** Builds a representation for [[NonEmptyDenseSet]]. Is the induction case to build a [[DenseSetRep]]
*
* @author Harshad Deo
* @since 0.3.3
*/
implicit def nomEmptyToRep[V <: Dense, L <: DenseSet, R <: DenseSet](
implicit ev0: Dense.DenseRep[V],
ev1: DenseSetRep[L],
ev2: DenseSetRep[R]): DenseSetRep[NonEmptyDenseSet[V, L, R]] =
new DenseSetRep[NonEmptyDenseSet[V, L, R]](ev1.rep ++ ev2.rep + ev0.v)
}
/** Method to convert a [[DenseSet]] type to a value-level set
*
* @group Operations
* @author Harshad Deo
* @since 0.3.3
*/
def toSet[DS <: DenseSet](implicit ev: DenseSetRep[DS]): Set[Long] = ev.rep
}
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