Merge pull request #427 from gnieh/finite-state/regular

Add regular language implementation

build.sbt

@@ -44,9 +44,7 @@ val commonSettings = List(
     "io.circe" %%% "circe-generic" % circeVersion % "test",
     "co.fs2" %%% "fs2-io" % fs2Version % "test",
     "com.disneystreaming" %%% "weaver-cats" % weaverVersion % "test",
-    "com.disneystreaming" %%% "weaver-cats-core" % weaverVersion % "test",
-    "com.disneystreaming" %%% "weaver-core" % weaverVersion % "test",
-    "com.disneystreaming" %%% "weaver-framework" % weaverVersion % "test",
+    "com.disneystreaming" %%% "weaver-scalacheck" % weaverVersion % Test,
     "com.eed3si9n.expecty" %%% "expecty" % "0.16.0" % "test",
     "org.portable-scala" %%% "portable-scala-reflect" % "1.1.2" cross CrossVersion.for3Use2_13
   ) ++ PartialFunction

finite-state/shared/src/main/scala/fs2/data/pfsa/Candidate.scala

@@ -0,0 +1,23 @@
+/*
+ * Copyright 2022 Lucas Satabin
+ *
+ * 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 fs2.data.pfsa
+
+trait Candidate[Set, C] {
+
+  def pick(set: Set): Option[C]
+
+}

finite-state/shared/src/main/scala/fs2/data/pfsa/PDFA.scala

@@ -16,6 +16,9 @@
 
 package fs2.data.pfsa
 
+import cats.Foldable
+import cats.syntax.foldable._
+
 import Pred.syntax._
 
 private[data] class PDFA[P, T](val init: Int, val finals: Set[Int], val transitions: Array[List[(P, Int)]])(implicit
@@ -27,4 +30,18 @@ private[data] class PDFA[P, T](val init: Int, val finals: Set[Int], val transiti
     else
       transitions(q).collectFirst { case (p, q) if p.satisfies(t) => q }
 
+  def recognizes[S[_]: Foldable](input: S[T]): Boolean =
+    input
+      .foldLeftM((init, 0)) { case ((q, idx), c) =>
+        transitions
+          .lift(q)
+          .flatMap(_.collectFirst {
+            case (p, q) if p.satisfies(c) =>
+              (q, idx + 1)
+          })
+      }
+      .exists { case (q, idx) =>
+        idx == input.size && finals.contains(q)
+      }
+
 }

finite-state/shared/src/main/scala/fs2/data/pfsa/Pred.scala

@@ -47,6 +47,13 @@ object Pred {
   def apply[P, T](implicit ev: Pred[P, T]): Pred[P, T] = ev
 
   object syntax {
+
+    def always[P](implicit P: Pred[P, _]): P =
+      P.always
+
+    def never[P](implicit P: Pred[P, _]): P =
+      P.never
+
     implicit class PredOps[P](val p1: P) extends AnyVal {
       def satisfies[Elt](e: Elt)(implicit P: Pred[P, Elt]): Boolean =
         P.satsifies(p1)(e)

finite-state/shared/src/main/scala/fs2/data/pfsa/Regular.scala

@@ -0,0 +1,267 @@
+/*
+ * Copyright 2022 Lucas Satabin
+ *
+ * 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 fs2.data.pfsa
+
+import cats.data.Chain
+import cats.syntax.all._
+import cats.{Eq, Show}
+
+import Pred.syntax._
+
+/** Simple regular language with character sets.
+  * This allows to model simple query languages (think XPath or JsonPath)
+  * and derive DFA out of it.
+  */
+sealed abstract class Regular[CharSet] {
+
+  def ~(that: Regular[CharSet])(implicit CharSet: Pred[CharSet, _], eq: Eq[CharSet]): Regular[CharSet] =
+    (this, that) match {
+      case (Regular.Epsilon(), _)               => that
+      case (_, Regular.Epsilon())               => this
+      case (Regular.Concatenation(re1, re2), _) => re1 ~ (re2 ~ that)
+      case (_, _) =>
+        if (this.isSatisfiable && that.isSatisfiable)
+          Regular.Concatenation(this, that)
+        else
+          Regular.empty
+    }
+
+  def &&(that: Regular[CharSet])(implicit CharSet: Pred[CharSet, _], eq: Eq[CharSet]): Regular[CharSet] =
+    (this, that) match {
+      case (Regular.And(re1, re2), _) => re1 && (re2 && that)
+      case (_, _) =>
+        if (this === that)
+          this
+        else if (this === Regular.any)
+          that
+        else if (that === Regular.any)
+          this
+        else if (this.isSatisfiable && that.isSatisfiable)
+          Regular.And(this, that)
+        else
+          Regular.empty
+    }
+
+  def ||(that: Regular[CharSet])(implicit CharSet: Pred[CharSet, _], eq: Eq[CharSet]): Regular[CharSet] =
+    (this, that) match {
+      case (Regular.Or(re1, re2), _)                => re1 || (re2 || that)
+      case (Regular.Chars(cs1), Regular.Chars(cs2)) => Regular.Chars(cs1 || cs2)
+      case (_, _) =>
+        if (this === that)
+          this
+        else if (this === Regular.any)
+          Regular.any
+        else if (that === Regular.any)
+          Regular.any
+        else if (!this.isSatisfiable)
+          that
+        else if (!that.isSatisfiable)
+          this
+        else
+          Regular.Or(this, that)
+    }
+
+  def unary_!(implicit CharSet: Pred[CharSet, _], eq: Eq[CharSet]): Regular[CharSet] =
+    this match {
+      case Regular.Not(re)   => re
+      case Regular.Chars(cs) => Regular.Chars(!cs)
+      case Regular.Epsilon() => Regular.any
+      case _ =>
+        if (this === Regular.any)
+          Regular.empty
+        else if (this === Regular.empty)
+          Regular.any
+        else
+          Regular.Not(this)
+    }
+
+  def rep(implicit CharSet: Pred[CharSet, _], eq: Eq[CharSet]): Regular[CharSet] =
+    this match {
+      case Regular.Star(_) => this
+      case _ =>
+        if (this === Regular.epsilon)
+          Regular.epsilon
+        else if (this === Regular.empty)
+          Regular.epsilon
+        else
+          Regular.Star(this)
+
+    }
+
+  def acceptEpsilon: Boolean =
+    this match {
+      case Regular.Epsilon()               => true
+      case Regular.Star(_)                 => true
+      case Regular.Or(re1, re2)            => re1.acceptEpsilon || re2.acceptEpsilon
+      case Regular.And(re1, re2)           => re1.acceptEpsilon && re2.acceptEpsilon
+      case Regular.Concatenation(re1, re2) => re1.acceptEpsilon && re2.acceptEpsilon
+      case Regular.Chars(_)                => false
+      case Regular.Not(re)                 => !re.acceptEpsilon
+    }
+
+  def derive[C](c: C)(implicit CharSet: Pred[CharSet, C], eq: Eq[CharSet]): Regular[CharSet] =
+    this match {
+      case Regular.Epsilon()                               => Regular.Chars(CharSet.never)
+      case Regular.Chars(set) if CharSet.satsifies(set)(c) => Regular.Epsilon()
+      case Regular.Chars(_)                                => Regular.Chars(CharSet.never)
+      case Regular.Concatenation(re1, re2) if re1.acceptEpsilon =>
+        (re1.derive(c) ~ re2) || re2.derive(c)
+      case Regular.Concatenation(re1, re2) =>
+        re1.derive(c) ~ re2
+      case Regular.Or(re1, re2) =>
+        re1.derive(c) || re2.derive(c)
+      case Regular.And(re1, re2) =>
+        re1.derive(c) && re2.derive(c)
+      case Regular.Star(re) =>
+        re.derive(c) ~ Regular.Star(re)
+      case Regular.Not(re) =>
+        !re.derive(c)
+    }
+
+  def classes[C](implicit CharSet: Pred[CharSet, C]): Set[CharSet] =
+    this match {
+      case Regular.Epsilon()                                    => Set(CharSet.always)
+      case Regular.Chars(chars)                                 => Set(chars, CharSet.not(chars))
+      case Regular.Concatenation(re1, re2) if re1.acceptEpsilon => combine(re1.classes, re2.classes)
+      case Regular.Concatenation(re1, _)                        => re1.classes
+      case Regular.Or(re1, re2)                                 => combine(re1.classes, re2.classes)
+      case Regular.And(re1, re2)                                => combine(re1.classes, re2.classes)
+      case Regular.Star(re)                                     => re.classes
+      case Regular.Not(re)                                      => re.classes
+    }
+
+  private def combine[C](c1: Set[CharSet], c2: Set[CharSet])(implicit CharSet: Pred[CharSet, C]): Set[CharSet] =
+    for {
+      cs1 <- c1
+      cs2 <- c2
+      both = CharSet.and(cs1, cs2)
+      if CharSet.isSatisfiable(both)
+    } yield both
+
+  def deriveDFA[C](implicit
+      CharSet: Pred[CharSet, C],
+      candidate: Candidate[CharSet, C],
+      eq: Eq[CharSet]): PDFA[CharSet, C] = {
+
+    def goto(re: Regular[CharSet],
+             q: Int,
+             cs: CharSet,
+             qs: Chain[Regular[CharSet]],
+             transitions: Map[Int, List[(CharSet, Int)]]): (Chain[Regular[CharSet]], Map[Int, List[(CharSet, Int)]]) =
+      candidate.pick(cs) match {
+        case Some(c) =>
+          val tgt = re.derive(c)
+          val equivalent = qs.zipWithIndex.collectFirst {
+            case (q, idx) if tgt === q => idx
+          }
+          equivalent match {
+            case Some(tgt) => (qs, transitions.combine(Map(q -> List(cs -> tgt))))
+            case None =>
+              val qs1 = qs.append(tgt)
+              val q1 = qs.size.toInt
+              val transitions1 = transitions.combine(Map(q -> List(cs -> q1)))
+              explore(qs1, transitions1, tgt)
+          }
+        case None =>
+          (qs, transitions)
+      }
+
+    def explore(qs: Chain[Regular[CharSet]],
+                transitions: Map[Int, List[(CharSet, Int)]],
+                re: Regular[CharSet]): (Chain[Regular[CharSet]], Map[Int, List[(CharSet, Int)]]) = {
+      val q = qs.size.toInt - 1
+      re.classes.foldLeft((qs, transitions)) { case ((qs, transitions), cs) =>
+        goto(re, q, cs, qs, transitions)
+      }
+    }
+
+    val (qs, transitions) = explore(Chain.one(this), Map.empty, this)
+    val finals = qs.zipWithIndex.collect { case (re, idx) if re.acceptEpsilon => idx }.toList.toSet
+    new PDFA[CharSet, C](0, finals, Array.tabulate(qs.size.toInt)(transitions.getOrElse(_, Nil)))
+  }
+
+}
+object Regular {
+  private case class Epsilon[CharSet]() extends Regular[CharSet]
+  private case class Chars[CharSet](set: CharSet) extends Regular[CharSet]
+  private case class Star[CharSet](re: Regular[CharSet]) extends Regular[CharSet]
+  private case class Concatenation[CharSet](re1: Regular[CharSet], re2: Regular[CharSet]) extends Regular[CharSet]
+  private case class Or[CharSet](re1: Regular[CharSet], re2: Regular[CharSet]) extends Regular[CharSet]
+  private case class And[CharSet](re1: Regular[CharSet], re2: Regular[CharSet]) extends Regular[CharSet]
+  private case class Not[CharSet](re: Regular[CharSet]) extends Regular[CharSet]
+
+  implicit def eq[CharSet: Eq]: Eq[Regular[CharSet]] = Eq.instance {
+    case (Epsilon(), Epsilon())                                 => true
+    case (Chars(cs1), Chars(cs2))                               => cs1 === cs2
+    case (Star(re1), Star(re2))                                 => re1 === re2
+    case (Concatenation(re11, re12), Concatenation(re21, re22)) => re11 === re21 && re12 === re22
+    case (Or(re11, re12), Or(re21, re22)) =>
+      (re11 === re21 && re12 === re22) || (re11 === re22 && re12 === re21)
+    case (And(re11, re12), And(re21, re22)) =>
+      (re11 === re21 && re12 === re22) || (re11 === re22 && re12 === re21)
+    case (Not(re1), Not(re2)) => re1 === re2
+    case _                    => false
+  }
+
+  def epsilon[CharSet]: Regular[CharSet] = Epsilon()
+
+  def chars[CharSet](cs: CharSet): Regular[CharSet] =
+    Regular.Chars(cs)
+
+  def any[CharSet](implicit CharSet: Pred[CharSet, _]): Regular[CharSet] = Chars(CharSet.always)
+
+  def empty[CharSet](implicit CharSet: Pred[CharSet, _]): Regular[CharSet] = Chars(CharSet.never)
+
+  implicit def pred[CharSet: Eq, C](implicit CharSet: Pred[CharSet, C]): Pred[Regular[CharSet], C] =
+    new Pred[Regular[CharSet], C] {
+
+      override def satsifies(p: Regular[CharSet])(e: C): Boolean =
+        p match {
+          case Epsilon()  => false
+          case Chars(set) => set.satisfies(e)
+          case Star(re)   => re.satisfies(e)
+          case Concatenation(re1, re2) =>
+            re1.satisfies(e) || (re1.acceptEpsilon && re2.satisfies(e))
+          case Or(re1, re2)  => re1.satisfies(e) || re2.satisfies(e)
+          case And(re1, re2) => re1.satisfies(e) && re2.satisfies(e)
+          case Not(re)       => !re.satisfies(e)
+        }
+
+      override def always: Regular[CharSet] = any
+
+      override def never: Regular[CharSet] = empty
+
+      override def and(p1: Regular[CharSet], p2: Regular[CharSet]): Regular[CharSet] = p1 && p2
+
+      override def or(p1: Regular[CharSet], p2: Regular[CharSet]): Regular[CharSet] = p1 || p2
+
+      override def not(p: Regular[CharSet]): Regular[CharSet] = !p
+
+      override def isSatisfiable(p: Regular[CharSet]): Boolean = p =!= empty
+
+    }
+
+  implicit def show[CS: Show]: Show[Regular[CS]] = Show.show {
+    case Epsilon()               => "ε"
+    case Chars(cs)               => cs.show
+    case Concatenation(re1, re2) => show"$re1$re2"
+    case Or(re1, re2)            => show"($re1) | ($re2)"
+    case And(re1, re2)           => show"($re1) & ($re2)"
+    case Star(re)                => show"($re)*"
+    case Not(re)                 => show"~($re)"
+  }
+}