From 86c067f3fa608bf8fda149fdb385757dcd5b51f9 Mon Sep 17 00:00:00 2001
From: Pat Garrity <pfm@garrity.co>
Date: Wed, 17 Dec 2025 22:26:12 -0600
Subject: [PATCH] WIP, now with streaming DFS

---
 build.sbt                                     | 14 ++-
 .../gs/graph/v0/cats/syntax/extensions.scala  | 12 +--
 .../src/main/scala/gs/graph/v0/Edge.scala     |  7 ++
 .../src/main/scala/gs/graph/v0/Graph.scala    | 22 ++---
 .../scala/gs/graph/v0/GraphTraversal.scala    | 74 ++++++++++++---
 .../src/main/scala/gs/graph/v0/Size.scala     |  4 +
 .../scala/gs/graph/v0/UndirectedGraph.scala   |  6 ++
 .../gs/graph/v0/data/AnyGraphWithData.scala   | 21 +----
 .../scala/gs/graph/v0/directed/Digraph.scala  | 13 +++
 ...tedGraph.scala => SingleRootDigraph.scala} | 26 +++---
 .../scala/gs/graph/v0/syntax/extensions.scala | 92 +++++++++++++++++++
 .../scala/gs/graph/v0/directed/DagTests.scala | 59 ++++++++++++
 .../gs/graph/v0/fs2/GraphTraversalFs2.scala   | 61 ++++++++++++
 13 files changed, 338 insertions(+), 73 deletions(-)
 rename modules/core/src/main/scala/gs/graph/v0/directed/{SingleRootDirectedGraph.scala => SingleRootDigraph.scala} (76%)
 create mode 100644 modules/core/src/main/scala/gs/graph/v0/syntax/extensions.scala
 create mode 100644 modules/fs2/src/main/scala/gs/graph/v0/fs2/GraphTraversalFs2.scala

diff --git a/build.sbt b/build.sbt
index fe4cf38..d477c9f 100644
--- a/build.sbt
+++ b/build.sbt
@@ -30,6 +30,10 @@ val Deps = new {
     val Core: ModuleID = "org.typelevel" %% "cats-core" % "2.13.0"
   }
 
+  val Fs2 = new {
+    val Core: ModuleID = "co.fs2" %% "fs2-core" % "3.12.2"
+  }
+
   val Gs = new {
     val Datagen: ModuleID = "gs" %% "gs-datagen-core-v0" % "0.3.3"
   }
@@ -46,7 +50,7 @@ lazy val testSettings = Seq(
 
 lazy val `gs-graph` = project
   .in(file("."))
-  .aggregate(core, cats)
+  .aggregate(core, cats, fs2)
   .settings(sharedSettings)
   .settings(testSettings)
   .settings(name := s"${gsProjectName.value}-v${semVerMajor.value}")
@@ -64,3 +68,11 @@ lazy val cats = project
   .settings(testSettings)
   .settings(name := s"${gsProjectName.value}-cats-v${semVerMajor.value}")
   .settings(libraryDependencies ++= Seq(Deps.Cats.Core))
+
+lazy val fs2 = project
+  .in(file("modules/fs2"))
+  .dependsOn(core)
+  .settings(sharedSettings)
+  .settings(testSettings)
+  .settings(name := s"${gsProjectName.value}-fs2-v${semVerMajor.value}")
+  .settings(libraryDependencies ++= Seq(Deps.Fs2.Core))
diff --git a/modules/cats/src/main/scala/gs/graph/v0/cats/syntax/extensions.scala b/modules/cats/src/main/scala/gs/graph/v0/cats/syntax/extensions.scala
index 58eed06..226fe8d 100644
--- a/modules/cats/src/main/scala/gs/graph/v0/cats/syntax/extensions.scala
+++ b/modules/cats/src/main/scala/gs/graph/v0/cats/syntax/extensions.scala
@@ -1,10 +1,9 @@
-package graph.gs.v0.cats.syntax
+package gs.graph.v0.cats.syntax
 
 import cats.Monad
 import gs.graph.v0.Graph
 import gs.graph.v0.Vertex
 import gs.graph.v0.cats.GraphTraversalCats
-import gs.graph.v0.data.DataDigraph
 
 extension (graph: Graph)
 
@@ -13,12 +12,3 @@ extension (graph: Graph)
 
   def dfs[F[_]: Monad, Output](visit: Vertex => F[Output]): F[List[Output]] =
     GraphTraversalCats.dfs[F, Output](graph, visit)
-
-extension [A](graph: DataDigraph[A])
-
-  def dfsUnit[F[_]: Monad](visit: (Vertex, A) => F[Unit]): F[Unit] =
-    GraphTraversalCats.dfsUnit[F, A](graph, visit)
-
-  def dfs[F[_]: Monad, Output](visit: (Vertex, A) => F[Output])
-    : F[List[Output]] =
-    GraphTraversalCats.dfs[F, A, Output](graph, visit)
diff --git a/modules/core/src/main/scala/gs/graph/v0/Edge.scala b/modules/core/src/main/scala/gs/graph/v0/Edge.scala
index b77c316..bf47e76 100644
--- a/modules/core/src/main/scala/gs/graph/v0/Edge.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/Edge.scala
@@ -47,4 +47,11 @@ object Edge:
 
   given CanEqual[Edge, Edge] = CanEqual.derived
 
+  def apply(
+    v1: Vertex,
+    v2: Vertex
+  ): Edge = new Edge(v1, v2)
+
+  def apply(vs: (Vertex, Vertex)): Edge = new Edge(vs._1, vs._2)
+
 end Edge
diff --git a/modules/core/src/main/scala/gs/graph/v0/Graph.scala b/modules/core/src/main/scala/gs/graph/v0/Graph.scala
index 5522598..497f34d 100644
--- a/modules/core/src/main/scala/gs/graph/v0/Graph.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/Graph.scala
@@ -4,6 +4,7 @@ package gs.graph.v0
   *
   * See:
   *   - [[gs.graph.v0.directed.DirectedGraph]]
+  *   - [[gs.graph.v0.UndirectedGraph]]
   *
   * @param numberOfVertices
   *   The number of [[Vertex]] present in this Graph.
@@ -31,6 +32,11 @@ trait Graph:
     */
   def isEmpty: Boolean = numberOfVertices == Size.Zero
 
+  /** @return
+    *   The roots that should be used for traversal operations.
+    */
+  def selectRoots(): Vector[Vertex]
+
   /** Get the neighbors for any given vertex.
     *
     * @param vertex
@@ -52,19 +58,3 @@ trait Graph:
       case _ => false
 
 end Graph
-
-object Graph:
-
-  /** The empty graph. Contains no vertices and no edges.
-    */
-  object Empty extends Graph:
-
-    override def numberOfVertices: Size = Size.Zero
-
-    override def adjacency: Adjacency = Adjacency.Empty
-
-    override def disposition: GraphDisposition = GraphDisposition.Undirected
-
-  end Empty
-
-end Graph
diff --git a/modules/core/src/main/scala/gs/graph/v0/GraphTraversal.scala b/modules/core/src/main/scala/gs/graph/v0/GraphTraversal.scala
index 9a8c0d4..717be39 100644
--- a/modules/core/src/main/scala/gs/graph/v0/GraphTraversal.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/GraphTraversal.scala
@@ -1,6 +1,6 @@
 package gs.graph.v0
 
-import gs.graph.v0.data.DataDigraph
+import gs.graph.v0.data.AnyGraphWithData
 import scala.collection.mutable.ListBuffer
 import scala.collection.mutable.Stack
 
@@ -74,11 +74,35 @@ object GraphTraversal:
 
     output.toList
 
+  def dfsFold[Acc](
+    graph: Graph,
+    initial: Acc,
+    f: (Acc, Vertex) => Acc
+  ): Acc =
+    var acc        = initial
+    val s          = Stack.empty[Vertex]
+    val discovered = Array.fill(graph.numberOfVertices.value)(false)
+
+    graph.selectRoots().foreach { root =>
+      s.push(root)
+
+      while !s.isEmpty
+      do
+        val v = s.pop()
+        if !discovered(v.ordinal) then
+          acc = f(acc, v)
+          discovered(v.ordinal) = true
+          graph.neighbors(v).foreach(w => s.push(w))
+        else ()
+    }
+
+    acc
+
   /** Depth-first search that executes a side-effecting function on each
     * [[Vertex]], accepting the data stored for that [[Vertex]] as input.
     *
     * This implementation performs DFS for _each root_ in the input
-    * [[DataDigraph]].
+    * [[AnyGraphWithData]].
     *
     * @param graph
     *   The input [[Graph]] on which to run DFS.
@@ -86,22 +110,22 @@ object GraphTraversal:
     *   The visitor function.
     */
   def dfs[A](
-    digraph: DataDigraph[A],
+    graph: AnyGraphWithData[A],
     visit: (Vertex, A) => Unit
   ): Unit =
     val s          = Stack.empty[Vertex]
-    val discovered = Array.fill(digraph.numberOfVertices.value)(false)
+    val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
-    digraph.roots.foreach { root =>
+    graph.selectRoots().foreach { root =>
       s.push(root)
 
       while !s.isEmpty
       do
         val v = s.pop()
         if !discovered(v.ordinal) then
-          val _ = visit(v, digraph.data(v.ordinal))
+          val _ = visit(v, graph.data(v.ordinal))
           discovered(v.ordinal) = true
-          digraph.neighbors(v).foreach(w => s.push(w))
+          graph.neighbors(v).foreach(w => s.push(w))
         else ()
     }
 
@@ -111,7 +135,7 @@ object GraphTraversal:
     * some output, accepting the data stored for that [[Vertex]] as input.
     *
     * This implementation performs DFS for _each root_ in the input
-    * [[DataDigraph]].
+    * [[AnyGraphWithData]].
     *
     * @param graph
     *   The input [[Graph]] on which to run DFS.
@@ -121,26 +145,50 @@ object GraphTraversal:
     *   List of output, assembled in the order that vertices were visited.
     */
   def dfs[A, Out](
-    digraph: DataDigraph[A],
+    graph: AnyGraphWithData[A],
     visit: (Vertex, A) => Out
   ): List[Out] =
     val output     = ListBuffer.empty[Out]
     val s          = Stack.empty[Vertex]
-    val discovered = Array.fill(digraph.numberOfVertices.value)(false)
+    val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
-    digraph.roots.foreach { root =>
+    graph.selectRoots().foreach { root =>
       s.push(root)
 
       while !s.isEmpty
       do
         val v = s.pop()
         if !discovered(v.ordinal) then
-          val _ = output.addOne(visit(v, digraph.data(v.ordinal)))
+          val _ = output.addOne(visit(v, graph.data(v.ordinal)))
           discovered(v.ordinal) = true
-          digraph.neighbors(v).foreach(w => s.push(w))
+          graph.neighbors(v).foreach(w => s.push(w))
         else ()
     }
 
     output.toList
 
+  def dfsFold[A, Acc](
+    graph: AnyGraphWithData[A],
+    initial: Acc,
+    f: (Acc, A) => Acc
+  ): Acc =
+    var acc        = initial
+    val s          = Stack.empty[Vertex]
+    val discovered = Array.fill(graph.numberOfVertices.value)(false)
+
+    graph.selectRoots().foreach { root =>
+      s.push(root)
+
+      while !s.isEmpty
+      do
+        val v = s.pop()
+        if !discovered(v.ordinal) then
+          acc = f(acc, graph.data(v.ordinal))
+          discovered(v.ordinal) = true
+          graph.neighbors(v).foreach(w => s.push(w))
+        else ()
+    }
+
+    acc
+
 end GraphTraversal
diff --git a/modules/core/src/main/scala/gs/graph/v0/Size.scala b/modules/core/src/main/scala/gs/graph/v0/Size.scala
index fddb4c8..e98c192 100644
--- a/modules/core/src/main/scala/gs/graph/v0/Size.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/Size.scala
@@ -66,6 +66,10 @@ object Size:
     */
   final val Zero: Size = new Size(0)
 
+  /** The constant size: 1.
+    */
+  final val One: Size = new Size(1)
+
   /** Instantiate a new [[Size]].
     *
     * Throws an exception if a negative input is given.
diff --git a/modules/core/src/main/scala/gs/graph/v0/UndirectedGraph.scala b/modules/core/src/main/scala/gs/graph/v0/UndirectedGraph.scala
index f0cf3c7..cc96214 100644
--- a/modules/core/src/main/scala/gs/graph/v0/UndirectedGraph.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/UndirectedGraph.scala
@@ -14,6 +14,12 @@ class UndirectedGraph(
   /** @inheritDocs
     */
   final override val disposition: GraphDisposition = GraphDisposition.Undirected
+
+  /** @inheritDocs
+    */
+  override def selectRoots(): Vector[Vertex] =
+    if numberOfVertices == Size.Zero then Vector.empty else Vector(Vertex.Zero)
+
 end UndirectedGraph
 
 object UndirectedGraph:
diff --git a/modules/core/src/main/scala/gs/graph/v0/data/AnyGraphWithData.scala b/modules/core/src/main/scala/gs/graph/v0/data/AnyGraphWithData.scala
index bfb6839..30292b1 100644
--- a/modules/core/src/main/scala/gs/graph/v0/data/AnyGraphWithData.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/data/AnyGraphWithData.scala
@@ -1,35 +1,18 @@
 package gs.graph.v0.data
 
-import gs.graph.v0.Adjacency
-import gs.graph.v0.GraphDisposition
+import gs.graph.v0.Graph
 import gs.graph.v0.GraphException
-import gs.graph.v0.Size
 import gs.graph.v0.Vertex
 
 /** Trait that describes _any_ graph (undirected, directed, or other
   * specializations of those such as DAGs) that is correlated with data.
   */
-trait AnyGraphWithData[A]:
+trait AnyGraphWithData[A] extends Graph:
   /** @return
     *   The data stored by each [[gs.graph.v0.Vertex]] in this graph.
     */
   def data: Vector[A]
 
-  /** @return
-    *   The number of vertices present in this graph.
-    */
-  def numberOfVertices: Size
-
-  /** @return
-    *   The [[Adjacency]] that describes this graph.
-    */
-  def adjacency: Adjacency
-
-  /** @return
-    *   The underlying disposition of this graph.
-    */
-  def disposition: GraphDisposition
-
   /** Retrieve the data associated with some [[Vertex]].
     *
     * This implementation throws an exception if the input [[Vertex]] is out of
diff --git a/modules/core/src/main/scala/gs/graph/v0/directed/Digraph.scala b/modules/core/src/main/scala/gs/graph/v0/directed/Digraph.scala
index 9ef9cd2..980b20b 100644
--- a/modules/core/src/main/scala/gs/graph/v0/directed/Digraph.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/directed/Digraph.scala
@@ -25,6 +25,10 @@ class Digraph(
     */
   override val disposition: GraphDisposition = GraphDisposition.Directed
 
+  /** @inheritDocs
+    */
+  override def selectRoots(): Vector[Vertex] = roots
+
   override def equals(that: Any): Boolean =
     that match
       case other: Digraph =>
@@ -39,8 +43,17 @@ object Digraph:
 
   given CanEqual[Digraph, Digraph] = CanEqual.derived
 
+  /** @return
+    *   An empty [[Digraph]].
+    */
   def empty(): Digraph = new Digraph(Size.Zero, Adjacency.Empty, Vector.empty)
 
+  /** @return
+    *   A [[Digraph]] with a single [[Vertex]] and no edges.
+    */
+  def single(): Digraph =
+    new Digraph(Size.One, Adjacency(Vector(Vector.empty)), Vector(Vertex.Zero))
+
   def fromEdges(
     numberOfVertices: Size,
     edges: Iterable[Edge]
diff --git a/modules/core/src/main/scala/gs/graph/v0/directed/SingleRootDirectedGraph.scala b/modules/core/src/main/scala/gs/graph/v0/directed/SingleRootDigraph.scala
similarity index 76%
rename from modules/core/src/main/scala/gs/graph/v0/directed/SingleRootDirectedGraph.scala
rename to modules/core/src/main/scala/gs/graph/v0/directed/SingleRootDigraph.scala
index 12b73ef..48661ad 100644
--- a/modules/core/src/main/scala/gs/graph/v0/directed/SingleRootDirectedGraph.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/directed/SingleRootDigraph.scala
@@ -6,18 +6,18 @@ import gs.graph.v0.GraphException
 import gs.graph.v0.Size
 import gs.graph.v0.Vertex
 
-class SingleRootDirectedGraph(
+class SingleRootDigraph(
   n: Size,
   a: Adjacency,
   r: Vertex
 ) extends Digraph(n, a, Vector(r))
 
-object SingleRootDirectedGraph:
+object SingleRootDigraph:
 
-  def fromDirectedGraph(dg: Digraph): Option[SingleRootDirectedGraph] =
+  def fromDirectedGraph(dg: Digraph): Option[SingleRootDigraph] =
     if dg.roots.size == 1 then
       Some(
-        new SingleRootDirectedGraph(
+        new SingleRootDigraph(
           dg.numberOfVertices,
           dg.adjacency,
           dg.roots(0)
@@ -29,9 +29,9 @@ object SingleRootDirectedGraph:
     numberOfVertices: Size,
     edges: Iterable[Edge],
     root: Vertex
-  ): SingleRootDirectedGraph =
+  ): SingleRootDigraph =
     if root < numberOfVertices then
-      new SingleRootDirectedGraph(
+      new SingleRootDigraph(
         numberOfVertices,
         Adjacency.fromDirectedEdges(numberOfVertices, edges),
         root
@@ -41,11 +41,11 @@ object SingleRootDirectedGraph:
   def fromEdges(
     numberOfVertices: Size,
     edges: Iterable[Edge]
-  ): Option[SingleRootDirectedGraph] =
+  ): Option[SingleRootDigraph] =
     val roots = Digraph.findRootsForDirectedEdges(numberOfVertices, edges)
     if roots.size == 1 then
       Some(
-        new SingleRootDirectedGraph(
+        new SingleRootDigraph(
           numberOfVertices,
           Adjacency.fromDirectedEdges(numberOfVertices, edges),
           roots(0)
@@ -56,9 +56,9 @@ object SingleRootDirectedGraph:
   def fromAdjacencyUnsafe(
     adjacency: Adjacency,
     root: Vertex
-  ): SingleRootDirectedGraph =
+  ): SingleRootDigraph =
     if root < adjacency.numberOfVertices then
-      new SingleRootDirectedGraph(
+      new SingleRootDigraph(
         adjacency.numberOfVertices,
         adjacency,
         root
@@ -67,11 +67,11 @@ object SingleRootDirectedGraph:
 
   def fromAdjacency(
     adjacency: Adjacency
-  ): Option[SingleRootDirectedGraph] =
+  ): Option[SingleRootDigraph] =
     val roots = adjacency.findRoots()
     if roots.size == 1 then
       Some(
-        new SingleRootDirectedGraph(
+        new SingleRootDigraph(
           adjacency.numberOfVertices,
           adjacency,
           roots(0)
@@ -79,4 +79,4 @@ object SingleRootDirectedGraph:
       )
     else None
 
-end SingleRootDirectedGraph
+end SingleRootDigraph
diff --git a/modules/core/src/main/scala/gs/graph/v0/syntax/extensions.scala b/modules/core/src/main/scala/gs/graph/v0/syntax/extensions.scala
new file mode 100644
index 0000000..69c68e9
--- /dev/null
+++ b/modules/core/src/main/scala/gs/graph/v0/syntax/extensions.scala
@@ -0,0 +1,92 @@
+package gs.graph.v0.syntax
+
+import gs.graph.v0.Graph
+import gs.graph.v0.GraphTraversal
+import gs.graph.v0.Vertex
+import gs.graph.v0.data.AnyGraphWithData
+
+extension (graph: Graph)
+
+  /** Visit vertex node in this graph, using Depth-First Search (DFS) as the
+    * traversal method. For each vertex, execute the given visitor function
+    * against the vertex.
+    *
+    * In this variant, the visitor is a side-effecting function that does not
+    * return any value.
+    *
+    * @param visit
+    *   Side-effecting function to execute for each graph vertex.
+    */
+  def visitDfs(visit: Vertex => Unit): Unit =
+    GraphTraversal.dfs(graph, visit)
+
+  /** Visit vertex node in this graph, using Depth-First Search (DFS) as the
+    * traversal method. For each vertex, execute the given visitor function
+    * against the vertex.
+    *
+    * In this variant, the visitor produces some output, and the list of all
+    * such outputs is collected and returned.
+    *
+    * @param visit
+    *   Function to execute for each graph vertex.
+    * @return
+    *   The list of produced values.
+    */
+  def visitDfs[Out](visit: Vertex => Out): List[Out] =
+    GraphTraversal.dfs[Out](graph, visit)
+
+  /** Perform a fold on this graph, using Depth-First Search (DFS) as the
+    * traversal method.
+    *
+    * @param initial
+    *   The initial value for the accumulator.
+    * @param f
+    *   The function to execute on each vertex in the graph.
+    * @return
+    *   The final calculated value.
+    */
+  def foldDfs[Acc](initial: Acc)(f: (Acc, Vertex) => Acc): Acc =
+    GraphTraversal.dfsFold[Acc](graph, initial, f)
+
+extension [A](graph: AnyGraphWithData[A])
+
+  /** Visit vertex node in this graph, using Depth-First Search (DFS) as the
+    * traversal method. For each vertex, execute the given visitor function
+    * against the vertex and the data it stores.
+    *
+    * In this variant, the visitor is a side-effecting function that does not
+    * return any value.
+    *
+    * @param visit
+    *   Side-effecting function to execute for each graph vertex.
+    */
+  def visitDfs(visit: (Vertex, A) => Unit): Unit =
+    GraphTraversal.dfs[A](graph, visit)
+
+  /** Visit vertex node in this graph, using Depth-First Search (DFS) as the
+    * traversal method. For each vertex, execute the given visitor function
+    * against the vertex and the data it stores.
+    *
+    * In this variant, the visitor produces some output, and the list of all
+    * such outputs is collected and returned.
+    *
+    * @param visit
+    *   Function to execute for each graph vertex.
+    * @return
+    *   The list of produced values.
+    */
+  def visitDfs[Out](visit: (Vertex, A) => Out): List[Out] =
+    GraphTraversal.dfs[A, Out](graph, visit)
+
+  /** Perform a fold on this graph, using Depth-First Search (DFS) as the
+    * traversal method.
+    *
+    * @param initial
+    *   The initial value for the accumulator.
+    * @param f
+    *   The function to execute on each data point in the graph.
+    * @return
+    *   The final calculated value.
+    */
+  def foldDfs[Acc](initial: Acc)(f: (Acc, A) => Acc): Acc =
+    GraphTraversal.dfsFold[A, Acc](graph, initial, f)
diff --git a/modules/core/src/test/scala/gs/graph/v0/directed/DagTests.scala b/modules/core/src/test/scala/gs/graph/v0/directed/DagTests.scala
index 115e998..a1adc93 100644
--- a/modules/core/src/test/scala/gs/graph/v0/directed/DagTests.scala
+++ b/modules/core/src/test/scala/gs/graph/v0/directed/DagTests.scala
@@ -1,5 +1,9 @@
 package gs.graph.v0.directed
 
+import gs.graph.v0.Adjacency
+import gs.graph.v0.Edge
+import gs.graph.v0.Size
+import gs.graph.v0.Vertex
 import munit.*
 
 class DagTests extends FunSuite:
@@ -9,3 +13,58 @@ class DagTests extends FunSuite:
       case Right(dag) => assertEquals(dag, Digraph.empty())
       case _ => fail("Expected the empty graph to be validated as a DAG.")
   }
+
+  test("should validate a graph with one node") {
+    Dag.validate(Digraph.single()) match
+      case Right(dag) => assertEquals(dag, Digraph.single())
+      case _          =>
+        fail("Expected a graph with one vertex to be validated as a DAG.")
+  }
+
+  test("should validate a single-root graph") {
+    val size             = Size(8)
+    val vs               = (0 until size.value).map(Vertex(_))
+    val digraph: Digraph = Digraph.fromAdjacency(
+      Adjacency.fromDirectedEdges(
+        numberOfVertices = size,
+        edges = Seq(
+          Edge(vs(0) -> vs(1)),
+          Edge(vs(0) -> vs(2)),
+          Edge(vs(0) -> vs(3)),
+          Edge(vs(1) -> vs(4)),
+          Edge(vs(2) -> vs(4)),
+          Edge(vs(3) -> vs(5)),
+          Edge(vs(4) -> vs(6)),
+          Edge(vs(5) -> vs(6)),
+          Edge(vs(6) -> vs(7))
+        )
+      )
+    )
+
+    Dag.validate(digraph) match
+      case Right(dag) => assertEquals(dag, digraph)
+      case _ => fail("Expected a single-root graph to be validated as a DAG.")
+  }
+
+  test("should NOT validate a single-root digraph with a cycle") {
+    val size             = Size(4)
+    val vs               = (0 until size.value).map(Vertex(_))
+    val digraph: Digraph = Digraph.fromAdjacency(
+      Adjacency.fromDirectedEdges(
+        numberOfVertices = size,
+        edges = Seq(
+          Edge(vs(0) -> vs(1)),
+          Edge(vs(1) -> vs(2)),
+          Edge(vs(2) -> vs(3)),
+          Edge(vs(3) -> vs(1))
+        )
+      )
+    )
+
+    Dag.validate(digraph) match
+      case Right(_) =>
+        fail(
+          "Expected a single-root digraph with a cycle to fail DAG validation."
+        )
+      case _ => ()
+  }
diff --git a/modules/fs2/src/main/scala/gs/graph/v0/fs2/GraphTraversalFs2.scala b/modules/fs2/src/main/scala/gs/graph/v0/fs2/GraphTraversalFs2.scala
new file mode 100644
index 0000000..e0473bd
--- /dev/null
+++ b/modules/fs2/src/main/scala/gs/graph/v0/fs2/GraphTraversalFs2.scala
@@ -0,0 +1,61 @@
+package gs.graph.v0.fs2
+
+import cats.effect.Sync
+import fs2.Pull
+import fs2.Stream
+import gs.graph.v0.Graph
+import gs.graph.v0.Size
+import gs.graph.v0.Vertex
+import scala.collection.mutable.Stack
+
+object GraphTraversalFs2:
+
+  def dfs[F[_]: Sync, Out](
+    graph: Graph,
+    visit: Vertex => F[Out]
+  ): Stream[F, Out] =
+    val state = new DfsState(graph.numberOfVertices)
+    graph
+      .selectRoots()
+      .map(root => pull(graph, state, visit, root).stream.unNoneTerminate)
+      .reduce(_ ++ _)
+
+  private def pull[F[_]: Sync, Out](
+    graph: Graph,
+    state: DfsState,
+    visit: Vertex => F[Out],
+    current: Vertex
+  ): Pull[F, Option[Out], Unit] =
+    Pull.eval(Sync[F].delay(state.isDiscovered(current))).flatMap { discovered =>
+      if discovered then Pull.output1(None) >> Pull.done
+      else
+        Pull.eval(Sync[F].delay(state.discover(current)))
+          >> Pull.eval(visit(current)).flatMap(out => Pull.output1(Some(out)))
+          >> graph
+            .neighbors(current)
+            .foldLeft(Pull.done: Pull[F, Option[Out], Unit]) {
+              (
+                acc,
+                neighbor
+              ) => acc >> pull(graph, state, visit, neighbor)
+            }
+    }
+
+  final private class DfsState(n: Size):
+
+    val stack: Stack[Vertex]       = Stack.empty
+    val discovered: Array[Boolean] = Array.fill(n.value)(false)
+
+    def push(vertex: Vertex): Unit = stack.push(vertex)
+
+    def pop(): Vertex = stack.pop()
+
+    def isDiscovered(vertex: Vertex): Boolean =
+      discovered(vertex.ordinal)
+
+    def discover(vertex: Vertex): Unit =
+      discovered(vertex.ordinal) = true
+
+  end DfsState
+
+end GraphTraversalFs2