07.Answer

def exists[I](f: I => Boolean): Pipe[I, Boolean] =
  src => src.map(f).toPull.tally(using Monoid.booleanOr).toStream

def takeThrough[I](f: I => Boolean): Pipe[I, I] =
  src => src.toPull.takeWhile(f)
           .flatMap(remainder => remainder.take(1)).void.toStream

def dropWhile[I](f: I => Boolean): Pipe[I, I] =
  src => src.toPull.dropWhile(f)
           .flatMap(remainder => remainder).void.toStream

def existsHalting[I](f: I => Boolean): Pipe[I, Boolean] =
  exists(f) andThen takeThrough(!_) andThen dropWhile(!_)

def last[I](init: I): Pipe[I, I] =
  def go(value: I, p: Pull[I, Unit]): Pull[I, Unit] =
    p.uncons.flatMap:
      case Left(_) => Pull.Output(value)
      case Right((hd, tl)) => go(hd, tl)
  src => go(init, src.toPull).toStream

def existsHalting[I](f: I => Boolean): Pipe[I, Boolean] =
  exists(f) andThen takeThrough(!_) andThen last(false)