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Streaming finite state machines

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/*
 * Copyright 2024 fs2-data Project
 *
 * 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.Foldable
import cats.syntax.foldable._

import Pred.syntax._

private[data] class PDFA[P, T](val init: Int,
                               val finals: Set[Int],
                               val trap: Option[Int],
                               val transitions: Array[List[(P, Int)]])(implicit P: Pred[P, T]) {

  def step(q: Int, t: T): Option[Int] =
    if (q >= transitions.length)
      None
    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)
      }

}