Add spec test for the mountain car example

src/main/scala/symsim/examples/concrete/mountaincar/MountainCar.scala

@@ -66,9 +66,9 @@ object MountainCar
 
   // TODO: this is now deterministic but eventually needs to be randomized
   def step (s: CarState) (a: CarAction): Randomized[(CarState, CarReward)] =
-    val v = s.v + (gravity * mass * cos (3.0 * s.p) + a / mass - friction * s.v) * dt
+    val v = s.v + (-gravity * mass * cos (3.0 * s.p) + a / mass - friction * s.v) * dt
     val p = s.p + (v * dt)
-    val (v1, p1) = if p < -1.2 then (-1.2, 0.0) else (v, p) 
+    val (v1, p1) = if p < -1.2 then (0.0, -1.2) else (v, p)
     val s1 = CarState (v = v1.max (-1.5).min (1.5), 
                        p = p1.min (0.5))
     Randomized.const (s1 -> carReward (s1) (a))

src/test/scala/symsim/examples/concrete/mountaincar/MountainCarSpec.scala

@@ -0,0 +1,59 @@
+package symsim
+package examples.concrete.mountaincar
+
+import symsim.concrete.Randomized.given
+import CanTestIn.given
+import org.scalatest.*
+import prop.*
+import org.scalacheck.Gen
+import org.scalacheck.Prop.{exists, forAll, forAllNoShrink, propBoolean}
+import examples.concrete.mountaincar.CarState
+import examples.concrete.mountaincar.MountainCar
+import Math.cos
+
+// To eliminate the warning on MountainCarSpec, until scalacheck makes it open
+import scala.language.adhocExtensions
+
+/** Sanity tests for Randomized as a Scheduler */
+class MountainCarSpec
+  extends org.scalacheck.Properties ("mountaincar.Car"):
+
+  // Generators of test data
+  val positions = Gen.choose[Double] (-1.2, 0.5)
+  val velocities = Gen.choose[Double] (-1.5,1.5)
+  val negPos = Gen.choose[Double] (-1.2, -1.1)
+  val actions = Gen.oneOf (MountainCar.instances.enumAction.membersAscending)
+
+
+  // Tests
+
+  property ("Achieving the goal state from state (0.0, 0.0) with a single action is impossible") =
+    forAll (actions) { a =>
+      for (s1, r) <- MountainCar.step (CarState (0.0, 0.0)) (a)
+      yield s1.p < 0.5
+    }
+
+  property ("The car cannot move beyond -1.2 on the left") =
+    val dt: Double = 0.1
+    val mass: Double = 0.2
+    val friction: Double = 0.3
+    val gravity: Double = 9.8
+    forAll (velocities, negPos, actions) { (v, p, a) =>
+      val v1 = v + (-gravity * mass * cos(3.0 * p) + a / mass - friction * v) * dt
+      val p1 = p + (v1 * dt)
+      for (s1, r) <- MountainCar.step (CarState (v, p)) (a)
+        yield (p1 < -1.2) ==> (s1.p == -1.2)
+    }
+
+  property ("The car can move to the position -1.2") =
+    val (s1, r) = MountainCar.step (
+      CarState (-1.1601645563843357, -1.1533417842134712)) (-0.2).head
+    s1.p == -1.2
+
+  property ("gravity and friction are both decreasing the velocity") =
+    forAllNoShrink (velocities, negPos) { (v, p1) =>
+      for
+        (s1, r1) <- MountainCar.step(CarState(v, p1))(0)
+        (s2, r2) <- MountainCar.step(CarState(v, s1.p))(0)
+      yield ((p1 < s1.p) ==> (s1.v < s2.v)) || ((p1 > s1.p) ==> (s1.v > s2.v))
+    }