.gitlab-ci.yml

@@ -26,7 +26,7 @@ grade:
   tags:
     - cs210
   image:
-    name: registry.gitlab.com/fnux/cs210-grading-images/progfun2-codecs:20191027-dfbea8aed96096ed3af1cf1958549b97328d4c25
+    name: registry.gitlab.com/fnux/cs210-grading-images/progfun2-quickcheck:20191030-a3e376e6385659be92ad7972a94c2f289fdfafb7
     entrypoint: [""]
   allow_failure: true
   before_script:

README.md

@@ -1,6 +1,7 @@
-# CS-210: Codecs
+# CS-210: Quickcheck
+
 
 Please follow the [instructions from the main course
-respository](https://gitlab.epfl.ch/lamp/cs-210-functional-programming-2019/blob/master/week11/00-homework8.md).
+respository](https://gitlab.epfl.ch/lamp/cs-210-functional-programming-2019/blob/master/week7/00-homework6.md).
 
 Grading and submission details can be found [here](https://gitlab.epfl.ch/lamp/cs-210-functional-programming-2019/blob/master/week1/02-grading-and-submission.md).

build.sbt

@@ -1,16 +1,11 @@
 course := "progfun2"
-assignment := "codecs"
+assignment := "quickcheck"
 name := course.value + "-" + assignment.value
-testSuite := "codecs.CodecsSuite"
+testSuite := "quickcheck.QuickCheckSuite"
 
 scalaVersion := "0.19.0-RC1"
-scalacOptions ++= Seq("-deprecation")
+scalacOptions ++= Seq("-language:implicitConversions", "-deprecation")
-libraryDependencies ++= Seq(
+libraryDependencies += "com.novocode" % "junit-interface" % "0.11" % Test
-  ("org.scalacheck" %% "scalacheck" % "1.14.2" % Test).withDottyCompat(scalaVersion.value),
+libraryDependencies += ("org.scalacheck" %% "scalacheck" % "1.14.2").withDottyCompat(scalaVersion.value)
-  ("org.typelevel" %% "jawn-parser" % "0.14.2").withDottyCompat(scalaVersion.value),
-  "com.novocode" % "junit-interface" % "0.11" % Test
-)
 
 testOptions in Test += Tests.Argument(TestFrameworks.JUnit, "-a", "-v", "-s")
-
-initialCommands in console := """import codecs.{_, given}"""

src/main/scala/codecs/codecs.scala

@@ -1,283 +0,0 @@
-package codecs
-
-/**
-  * A data type modeling JSON values.
-  *
-  * For example, the `42` integer JSON value can be modeled as `Json.Num(42)`
-  */
-sealed trait Json {
-  /**
-   * Try to decode this JSON value into a value of type `A` by using
-   * the given decoder.
-   *
-   * Note that you have to explicitly fix `A` type parameter when you call the method:
-   *
-   * {{{
-   *   someJsonValue.decodeAs[User] // OK
-   *   someJsonValue.decodeAs       // Wrong!
-   * }}}
-   */
-  def decodeAs[A](given decoder: Decoder[A]): Option[A] = decoder.decode(this)
-}
-
-object Json {
-  /** The JSON `null` value */
-  case object Null extends Json
-  /** JSON boolean values */
-  case class Bool(value: Boolean) extends Json
-  /** JSON numeric values */
-  case class Num(value: BigDecimal) extends Json
-  /** JSON string values */
-  case class Str(value: String) extends Json
-  /** JSON objects */
-  case class Obj(fields: Map[String, Json]) extends Json
-  /** JSON arrays */
-  case class Arr(items: List[Json]) extends Json
-}
-
-/**
-  * A type class that turns a value of type `A` into its JSON representation.
-  */
-trait Encoder[-A] {
-
-  def encode(value: A): Json
-
-    /**
-    * Transforms this `Encoder[A]` into an `Encoder[B]`, given a transformation function
-    * from `B` to `A`.
-    *
-    * For instance, given a `Encoder[String]`, we can get an `Encoder[UUID]`:
-    *
-    * {{{
-    *   def uuidEncoder(given stringEncoder: Encoder[String]): Encoder[UUID] =
-    *     stringEncoder.transform[UUID](uuid => uuid.toString)
-    * }}}
-    *
-    * This operation is also known as ?contramap?.
-    */
-  def transform[B](f: B => A): Encoder[B] =
-    Encoder.fromFunction[B](value => this.encode(f(value)))  
-}
-
-object Encoder extends GivenEncoders {
-
-  /**
-   * Convenient method for creating an instance of encoder from a function `f`
-   */
-  def fromFunction[A](f: A => Json) = new Encoder[A] {
-    def encode(value: A): Json = f(value)
-  }
-
-}
-
-trait GivenEncoders {
-
-  /** An encoder for the `Unit` value */
-  given Encoder[Unit] = Encoder.fromFunction(_ => Json.Null)
-
-  /** An encoder for `Int` values */
-  given Encoder[Int] = Encoder.fromFunction(n => Json.Num(BigDecimal(n)))
-
-  /** An encoder for `String` values */
-  given Encoder[String] =
-    Encoder.fromFunction(str => Json.Str(str))
-
-  /** An encoder for `Boolean` values */
-  given Encoder[Boolean] =
-    Encoder.fromFunction(v => Json.Bool(v))
-
-  /**
-    * Encodes a list of values of type `A` into a JSON array containing
-    * the list elements encoded with the given `encoder`
-    */
-  given [A](given encoder: Encoder[A]): Encoder[List[A]] =
-    Encoder.fromFunction(as => Json.Arr(as.map(encoder.encode)))
-
-}
-
-/**
-  * A specialization of `Encoder` that returns JSON objects only
-  */
-trait ObjectEncoder[-A] extends Encoder[A] {
-  // Refines the encoding result to `Json.Obj`
-  def encode(value: A): Json.Obj
-
-  /**
-    * Combines `this` encoder with `that` encoder.
-    * Returns an encoder producing a JSON object containing both
-    * fields of `this` encoder and fields of `that` encoder.
-    */
-  def zip[B](that: ObjectEncoder[B]): ObjectEncoder[(A, B)] =
-    ObjectEncoder.fromFunction { (a, b) =>
-      Json.Obj(this.encode(a).fields ++ that.encode(b).fields)
-    }
-}
-
-object ObjectEncoder {
-
-  /**
-    * Convenient method for creating an instance of object encoder from a function `f`
-    */
-  def fromFunction[A](f: A => Json.Obj): ObjectEncoder[A] = new ObjectEncoder[A] {
-    def encode(value: A): Json.Obj = f(value)
-  }
-
-  /**
-    * An encoder for values of type `A` that produces a JSON object with one field
-    * named according to the supplied `name` and containing the encoded value.
-    */
-  def field[A](name: String)(given encoder: Encoder[A]): ObjectEncoder[A] =
-    ObjectEncoder.fromFunction(a => Json.Obj(Map(name -> encoder.encode(a))))
-
-}
-
-/**
-  * The dual of an encoder. Decodes a serialized value into its initial type `A`.
-  */
-trait Decoder[+A] {
-  /**
-    * @param data The data to de-serialize
-    * @return The decoded value wrapped in `Some`, or `None` if decoding failed
-    */
-  def decode(data: Json): Option[A]
-
-  /**
-    * Combines `this` decoder with `that` decoder.
-    * Returns a decoder that invokes both `this` decoder and `that`
-    * decoder and returns a pair of decoded value in case both succeed,
-    * or `None` if at least one failed.
-    */
-  def zip[B](that: Decoder[B]): Decoder[(A, B)] =
-    Decoder.fromFunction { json =>
-      this.decode(json).zip(that.decode(json))
-    }
-
-  /**
-    * Transforms this `Decoder[A]` into a `Decoder[B]`, given a transformation function
-    * from `A` to `B`.
-    *
-    * This operation is also known as ?map?.
-    */
-  def transform[B](f: A => B): Decoder[B] =
-    Decoder.fromFunction(json => this.decode(json).map(f))
-}
-
-object Decoder extends GivenDecoders {
-
-  /**
-    * Convenient method to build a decoder instance from a function `f`
-    */
-  def fromFunction[A](f: Json => Option[A]): Decoder[A] = new Decoder[A] {
-    def decode(data: Json): Option[A] = f(data)
-  }
-
-  /**
-    * Alternative method for creating decoder instances
-    */
-  def fromPartialFunction[A](pf: PartialFunction[Json, A]): Decoder[A] =
-    fromFunction(pf.lift)
-
-}
-
-trait GivenDecoders {
-
-  /** A decoder for the `Unit` value */
-  given Decoder[Unit] =
-    Decoder.fromPartialFunction { case Json.Null => () }
-
-  /** A decoder for `Int` values. Hint: use the `isValidInt` method of `BigDecimal`. */
-  // TODO Define a given `Decoder[Int]` instance
-  given Decoder[Int] = 
-    Decoder.fromFunction{ case Json.Num(v) => if v.isValidInt then Some(v.intValue) else None
-                          case _ => None}
-
-  /** A decoder for `String` values */
-  // TODO Define a given `Decoder[String]` instance
-  given Decoder[String] = 
-    Decoder.fromPartialFunction{ case Json.Str(str) => str}
-
-  /** A decoder for `Boolean` values */
-  // TODO Define a given `Decoder[Boolean]` instance
-  given Decoder[Boolean] = 
-    Decoder.fromPartialFunction{ case Json.Bool(v) => v}
-  /**
-    * A decoder for JSON arrays. It decodes each item of the array
-    * using the given `decoder`. The resulting decoder succeeds only
-    * if all the JSON array items are successfully decoded.
-    */
-  given [A](given decoder: Decoder[A]): Decoder[List[A]] =
-    Decoder.fromFunction {
-      case Json.Arr(items: List[Json]) => Some(items.map(v => decoder.decode(v).get))
-      case _ => None
-    }
-
-  /**
-    * A decoder for JSON objects. It decodes the value of a field of
-    * the supplied `name` using the given `decoder`.
-    */
-  def field[A](name: String)(given decoder: Decoder[A]): Decoder[A] =
-    Decoder.fromFunction{
-      case Json.Obj(field: Map[String, Json]) => decoder.decode(field.get(name).get)
-      case _ => None
-    }
-
-}
-
-case class Person(name: String, age: Int)
-
-object Person extends PersonCodecs
-
-trait PersonCodecs {
-
-  /** The encoder for `Person` */
-  given Encoder[Person] =
-    ObjectEncoder.field[String]("name")
-      .zip(ObjectEncoder.field[Int]("age"))
-      .transform[Person](user => (user.name, user.age))
-
-  /** The corresponding decoder for `Person` */
-  given Decoder[Person] ={
-    Decoder.field[String]("name").zip(Decoder.field[Int]("age")).transform[Person](user => Person(user._1, user._2))
-    }
-
-}
-
-case class Contacts(people: List[Person])
-
-object Contacts extends ContactsCodecs
-
-trait ContactsCodecs {
-
-  // TODO Define the encoder and the decoder for `Contacts`
-  // The JSON representation of a value of type `Contacts` should be
-  // a JSON object with a single field named ?people? containing an
-  // array of values of type `Person` (reuse the `Person` codecs)
-  given Encoder[Contacts] = 
-    ObjectEncoder.field[List[Person]]("people").transform[Contacts](c => c.people)
-
-  given Decoder[Contacts] = 
-    Decoder.field[List[Person]]("people").transform[Contacts](p => Contacts(p))
-
-}
-
-// In case you want to try your code, here is a simple `Main`
-// that can be used as a starting point. Otherwise, you can use
-// the REPL (use the `console` sbt task).
-object Main {
-
-  def main(args: Array[String]): Unit = {
-    println(renderJson(42))
-    println(renderJson("foo"))
-
-    val maybeJsonString = parseJson(""" "foo" """)
-    val maybeJsonObj    = parseJson(""" { "name": "Alice", "age": 42 } """)
-    val maybeJsonObj2   = parseJson(""" { "name": "Alice", "age": "42" } """)
-    // Uncomment the following lines as you progress in the assignment
-    println(maybeJsonString.flatMap(_.decodeAs[Int]))
-    println(maybeJsonString.flatMap(_.decodeAs[String]))
-    println(maybeJsonObj.flatMap(_.decodeAs[Person]))
-    println(maybeJsonObj2.flatMap(_.decodeAs[Person]))
-    println(renderJson(Person("Bob", 66)))
-  }
-
-}

src/main/scala/codecs/json.scala

@@ -1,74 +0,0 @@
-package codecs
-
-import org.typelevel.jawn.{ Parser, SimpleFacade }
-import scala.collection.mutable
-import scala.util.Try
-
-// Utility methods that decode values from `String` JSON blobs, and
-// render values to `String` JSON blobs
-
-/**
- * Parse a JSON document contained in a `String` value into a `Json` value, returns
- * `None` in case the supplied `s` value is not a valid JSON document.
- */
-def parseJson(s: String): Option[Json] = Parser.parseFromString[Json](s).toOption
-
-/**
-  * Parse the JSON value from the supplied `s` parameter, and then try to decode
-  * it as a value of type `A` using the given `decoder`.
-  *
-  * Returns `None` if JSON parsing failed, or if decoding failed.
-  */
-def parseAndDecode[A](s: String)(given decoder: Decoder[A]): Option[A] =
-  for {
-    json <- parseJson(s)
-    a    <- decoder.decode(json)
-  } yield a
-
-/**
-  * Render the supplied `value` into JSON using the given `encoder`.
-  */
-def renderJson[A](value: A)(given encoder: Encoder[A]): String =
-  render(encoder.encode(value))
-
-private def render(json: Json): String = json match {
-  case Json.Null    => "null"
-  case Json.Bool(b) => b.toString
-  case Json.Num(n)  => n.toString
-  case Json.Str(s)  => renderString(s)
-  case Json.Arr(vs) => vs.map(render).mkString("[", ",", "]")
-  case Json.Obj(vs) => vs.map { case (k, v) => s"${renderString(k)}:${render(v)}" }.mkString("{", ",", "}")
-}
-
-private def renderString(s: String): String = {
-  val sb = new StringBuilder
-  sb.append('"')
-  var i = 0
-  val len = s.length
-  while (i < len) {
-    s.charAt(i) match {
-      case '"' => sb.append("\\\"")
-      case '\\' => sb.append("\\\\")
-      case '\b' => sb.append("\\b")
-      case '\f' => sb.append("\\f")
-      case '\n' => sb.append("\\n")
-      case '\r' => sb.append("\\r")
-      case '\t' => sb.append("\\t")
-      case c =>
-        if (c < ' ') sb.append("\\u%04x" format c.toInt)
-        else sb.append(c)
-    }
-    i += 1
-  }
-  sb.append('"').toString
-}
-
-given SimpleFacade[Json] {
-  def jnull() = Json.Null
-  def jtrue() = Json.Bool(true)
-  def jfalse() = Json.Bool(false)
-  def jnum(s: CharSequence, decIndex: Int, expIndex: Int) = Json.Num(BigDecimal(s.toString))
-  def jstring(s: CharSequence) = Json.Str(s.toString)
-  def jarray(vs: List[Json]) = Json.Arr(vs)
-  def jobject(vs: Map[String, Json]) = Json.Obj(vs)
-}

src/main/scala/quickcheck/Heap.scala

@@ -0,0 +1,119 @@
+package quickcheck
+
+trait IntHeap extends Heap {
+  override type A = Int
+  override def ord = scala.math.Ordering.Int
+}
+
+// http://www.brics.dk/RS/96/37/BRICS-RS-96-37.pdf
+
+// Figure 1, page 3
+trait Heap {
+  type H // type of a heap
+  type A // type of an element
+  def ord: Ordering[A] // ordering on elements
+
+  def empty: H // the empty heap
+  def isEmpty(h: H): Boolean // whether the given heap h is empty
+
+  def insert(x: A, h: H): H // the heap resulting from inserting x into h
+  def meld(h1: H, h2: H): H // the heap resulting from merging h1 and h2
+
+  def findMin(h: H): A // a minimum of the heap h
+  def deleteMin(h: H): H // a heap resulting from deleting a minimum of h
+}
+
+// Figure 3, page 7
+trait BinomialHeap extends Heap {
+
+  type Rank = Int
+  case class Node(x: A, r: Rank, c: List[Node])
+  override type H = List[Node]
+
+  protected def root(t: Node) = t.x
+  protected def rank(t: Node) = t.r
+  protected def link(t1: Node, t2: Node): Node = // t1.r == t2.r
+    if ord.lteq(t1.x, t2.x) then
+      Node(t1.x, t1.r + 1, t2 :: t1.c)
+    else
+      Node(t2.x, t2.r + 1, t1 :: t2.c)
+  protected def ins(t: Node, ts: H): H = ts match
+    case Nil => List(t)
+    case tp :: ts => // t.r <= tp.r
+      if t.r < tp.r then
+        t :: tp :: ts
+      else
+        ins(link(t, tp), ts)
+
+  override def empty = Nil
+  override def isEmpty(ts: H) = ts.isEmpty
+
+  override def insert(x: A, ts: H) = ins(Node(x, 0, Nil), ts)
+  override def meld(ts1: H, ts2: H) = (ts1, ts2) match
+    case (Nil, ts) => ts
+    case (ts, Nil) => ts
+    case (t1 :: ts1, t2 :: ts2) =>
+      if t1.r < t2.r then
+        t1 :: meld(ts1, t2 :: ts2)
+      else if t2.r < t1.r then
+        t2 :: meld(t1 :: ts1, ts2)
+      else
+        ins(link(t1, t2), meld(ts1, ts2))
+
+  override def findMin(ts: H) = ts match
+    case Nil => throw new NoSuchElementException("min of empty heap")
+    case t :: Nil => root(t)
+    case t :: ts =>
+      val x = findMin(ts)
+      if ord.lteq(root(t), x) then
+        root(t)
+      else
+        x
+  override def deleteMin(ts: H) = ts match
+    case Nil => throw new NoSuchElementException("delete min of empty heap")
+    case t :: ts =>
+      def getMin(t: Node, ts: H): (Node, H) = ts match
+        case Nil => (t, Nil)
+        case tp :: tsp =>
+          val (tq, tsq) = getMin(tp, tsp)
+          if ord.lteq(root(t), root(tq)) then
+            (t, ts)
+          else
+            (tq, t :: tsq)
+      val (Node(_, _, c), tsq) = getMin(t, ts)
+      meld(c.reverse, tsq)
+}
+
+trait Bogus1BinomialHeap extends BinomialHeap {
+  override def findMin(ts: H) = ts match
+    case Nil => throw new NoSuchElementException("min of empty heap")
+    case t :: ts => root(t)
+}
+
+trait Bogus2BinomialHeap extends BinomialHeap {
+  override protected def link(t1: Node, t2: Node): Node = // t1.r == t2.r
+    if !ord.lteq(t1.x, t2.x) then
+      Node(t1.x, t1.r + 1, t2 :: t1.c)
+    else
+      Node(t2.x, t2.r + 1, t1 :: t2.c)
+}
+
+trait Bogus3BinomialHeap extends BinomialHeap {
+  override protected def link(t1: Node, t2: Node): Node = // t1.r == t2.r
+    if ord.lteq(t1.x, t2.x) then
+      Node(t1.x, t1.r + 1, t1 :: t1.c)
+    else
+      Node(t2.x, t2.r + 1, t2 :: t2.c)
+}
+
+trait Bogus4BinomialHeap extends BinomialHeap {
+  override def deleteMin(ts: H) = ts match
+    case Nil => throw new NoSuchElementException("delete min of empty heap")
+    case t :: ts => meld(t.c.reverse, ts)
+}
+
+trait Bogus5BinomialHeap extends BinomialHeap {
+  override def meld(ts1: H, ts2: H) = ts1 match
+    case Nil => ts2
+    case t1 :: ts1 => List(Node(t1.x, t1.r, ts1 ++ ts2))
+}

src/main/scala/quickcheck/QuickCheck.scala

@@ -0,0 +1,66 @@
+package quickcheck
+
+import org.scalacheck._
+import Arbitrary._
+import Gen._
+import Prop.{BooleanOperators => _, _}
+
+abstract class QuickCheckHeap extends Properties("Heap") with IntHeap {
+
+  lazy val genHeap: Gen[H] = for {
+    a <- arbitrary[Int]
+    h <- oneOf(const(empty), genHeap)
+  } yield insert(a, h)
+
+  implicit lazy val arbHeap: Arbitrary[H] = Arbitrary(genHeap)
+
+  property("min1") = forAll { (a: Int) =>
+    val h = insert(a, empty)
+    findMin(h) == a
+  }
+
+  property("gen1") = forAll { (h: H) =>
+    val m = if isEmpty(h) then 0 else findMin(h)
+    findMin(insert(m, h)) == m
+  }
+
+  property("smallest") = forAll { (a: Int, b: Int) =>
+    val h = insert(b, insert(a, empty))
+    val min = if (a<b) then a else b
+    if (a==b) true else
+      findMin(h) == min
+  }
+
+  property("deleteSingle") = forAll { (a: Int) =>
+    val h = insert(a, empty)
+    val h1 = deleteMin(h)
+    isEmpty(h1)
+  }
+
+  def multiMins(h: H, l: List[Int]): List[Int] = {
+    if (isEmpty(h)) then l
+    else findMin(h) :: multiMins(deleteMin(h), l)
+  }
+
+  property("multiMins") = forAll { (h1: H) =>
+    val xs = multiMins(h1, Nil)
+    xs == xs.sorted
+  }
+
+  property("meldMin") = forAll { (h1: H, h2: H) =>
+    val min1 = findMin(h1)
+    val min2 = findMin(h2)
+    val m = meld(h1, h2)
+    val minMeld = findMin(m)
+    minMeld == min1 || minMeld == min2
+  }
+
+  property("meldMinMove") = forAll { (h1: H, h2: H) =>
+    val meld1 = meld(h1, h2)
+    val min1 = findMin(h1)
+    val meld2 = meld(deleteMin(h1), insert(min1, h2))
+    val xs1 = multiMins(meld1, Nil)
+    val xs2 = multiMins(meld2, Nil)
+    xs1 == xs2
+  }
+}

src/test/scala/codecs/CodecsSuite.scala

@@ -1,115 +0,0 @@
-package codecs
-
-import org.scalacheck
-import org.scalacheck.{ Gen, Prop }
-import org.scalacheck.Prop.propBoolean
-import org.junit.{ Assert, Test }
-import scala.reflect.ClassTag
-
-class CodecsSuite extends GivenEncoders, GivenDecoders, PersonCodecs, ContactsCodecs, TestEncoders, TestDecoders {
-
-  def checkProperty(prop: Prop): Unit = {
-    val result = scalacheck.Test.check(scalacheck.Test.Parameters.default, prop)
-    def fail(labels: Set[String], fallback: String): Nothing =
-      if labels.isEmpty then throw new AssertionError(fallback)
-      else throw new AssertionError(labels.mkString(". "))
-    result.status match {
-      case scalacheck.Test.Passed | _: scalacheck.Test.Proved => ()
-      case scalacheck.Test.Failed(_, labels)                  => fail(labels, "A property failed.")
-      case scalacheck.Test.PropException(_, e, labels)        => fail(labels, s"An exception was thrown during property evaluation: $e.")
-      case scalacheck.Test.Exhausted                          => fail(Set.empty, "Unable to generate data.")
-    }
-  }
-
-  /**
-    * Check that a value of an arbitrary type `A` can be encoded and then successfully
-    * decoded with the given pair of encoder and decoder.
-    */
-  def encodeAndThenDecodeProp[A](a: A)(given encA: Encoder[A], decA: Decoder[A]): Prop = {
-    val maybeDecoded = decA.decode(encA.encode(a))
-    maybeDecoded.contains(a) :| s"Encoded value '$a' was not successfully decoded. Got '$maybeDecoded'."
-  }
-
-  @Test def `it is possible to encode and decode the 'Unit' value (0pts)`(): Unit = {
-    checkProperty(Prop.forAll((unit: Unit) => encodeAndThenDecodeProp(unit)))
-  }
-
-  @Test def `it is possible to encode and decode 'Int' values (1pt)`(): Unit = {
-    checkProperty(Prop.forAll((x: Int) => encodeAndThenDecodeProp(x)))
-  }
-
-  @Test def `the 'Int' decoder should reject invalid 'Int' values (2pts)`(): Unit = {
-    val decoded = summon[Decoder[Int]].decode(Json.Num(4.2))
-    assert(decoded.isEmpty, "decoding 4.2 as an integer value should fail")
-  }
-
-  @Test def `a 'String' value should be encoded as a JSON string (1pt)`(): Unit = {
-    assert(summon[Encoder[String]].encode("foo") == Json.Str("foo"))
-  }
-
-  @Test def `it is possible to encode and decode 'String' values (1pt)`(): Unit = {
-    checkProperty(Prop.forAll((s: String) => encodeAndThenDecodeProp(s)))
-  }
-
-  @Test def `a 'Boolean' value should be encoded as a JSON boolean (1pt)`(): Unit = {
-    val encoder = summon[Encoder[Boolean]]
-    assert(encoder.encode(true) == Json.Bool(true))
-    assert(encoder.encode(false) == Json.Bool(false))
-  }
-
-  @Test def `it is possible to encode and decode 'Boolean' values (1pt)`(): Unit = {
-    checkProperty(Prop.forAll((b: Boolean) => encodeAndThenDecodeProp(b)))
-  }
-
-  @Test def `a 'List[A]' value should be encoded as a JSON array (0pts)`(): Unit = {
-    val xs = 1 :: 2 :: Nil
-    val encoder = summon[Encoder[List[Int]]]
-    assert(encoder.encode(xs) == Json.Arr(List(Json.Num(1), Json.Num(2))))
-  }
-
-  @Test def `it is possible to encode and decode lists (5pts)`(): Unit = {
-    checkProperty(Prop.forAll((xs: List[Int]) => encodeAndThenDecodeProp(xs)))
-  }
-
-  @Test def `a 'Person' value should be encoded as a JSON object (1pt)`(): Unit = {
-    val person = Person("Alice", 42)
-    val json = Json.Obj(Map("name" -> Json.Str("Alice"), "age" -> Json.Num(42)))
-    val encoder = summon[Encoder[Person]]
-    assert(encoder.encode(person) == json)
-  }
-
-  @Test def `it is possible to encode and decode people (4pts)`(): Unit = {
-    checkProperty(Prop.forAll((s: String, x: Int) => encodeAndThenDecodeProp(Person(s, x))))
-  }
-  
-  @Test def `a 'Contacts' value should be encoded as a JSON object (1pt)`(): Unit = {
-    val contacts = Contacts(List(Person("Alice", 42)))
-    val json = Json.Obj(Map("people" ->
-      Json.Arr(List(Json.Obj(Map("name" -> Json.Str("Alice"), "age" -> Json.Num(42)))))
-    ))
-    val encoder = summon[Encoder[Contacts]]
-    assert(encoder.encode(contacts) == json)
-  }
-
-  @Test def `it is possible to encode and decode contacts (4pts)`(): Unit = {
-    val peopleGenerator = Gen.listOf(Gen.resultOf((s: String, x: Int) => Person(s, x)))
-    checkProperty(Prop.forAll(peopleGenerator)(people => encodeAndThenDecodeProp(Contacts(people))))
-  }
-
-}
-
-trait TestEncoders extends EncoderFallbackInstance
-
-trait EncoderFallbackInstance {
-
-  given [A](given ct: ClassTag[A]): Encoder[A] = throw new AssertionError(s"No given instance of `Encoder[${ct.runtimeClass.getSimpleName}]`")
-
-}
-
-trait TestDecoders extends DecoderFallbackInstance
-
-trait DecoderFallbackInstance {
-
-  given [A](given ct: ClassTag[A]): Decoder[A] = throw new AssertionError(s"No given instance of `Decoder[${ct.runtimeClass.getSimpleName}]")
-
-}

src/test/scala/quickcheck/QuickCheckSuite.scala

@@ -0,0 +1,55 @@
+package quickcheck
+
+import org.scalacheck.Properties
+import org.junit._
+
+import org.scalacheck.Arbitrary._
+import org.scalacheck.Prop
+import org.scalacheck.Prop.{BooleanOperators => _, _}
+import org.scalacheck.Test.{check, Result, Failed, PropException}
+
+object QuickCheckBinomialHeap extends QuickCheckHeap with BinomialHeap
+
+class QuickCheckSuite {
+  def checkBogus(p: Properties): Unit =
+    def fail = throw new AssertionError(
+      s"A bogus heap should NOT satisfy all properties. Try to find the bug!")
+
+    check(asProp(p))(identity) match
+      case r: Result => r.status match
+        case _: Failed =>
+          () // OK: scalacheck found a counter example!
+        case p: PropException =>
+          p.e match
+            case e: NoSuchElementException =>
+              () // OK: the implementation throws NSEE
+            case _ =>
+              fail
+        case _ =>
+          fail
+
+  /** Turns a `Properties` instance into a single `Prop` by combining all the properties */
+  def asProp(properties: Properties): Prop = Prop.all(properties.properties.map(_._2).toSeq:_*)
+
+  @Test def `Binomial heap satisfies properties. (5pts)`: Unit =
+    Assert.assertTrue(
+      check(asProp(new QuickCheckHeap with quickcheck.test.BinomialHeap))(identity).passed
+    )
+
+  @Test def `Bogus (1) binomial heap does not satisfy properties. (10pts)`: Unit =
+    checkBogus(new QuickCheckHeap with quickcheck.test.Bogus1BinomialHeap)
+
+  @Test def `Bogus (2) binomial heap does not satisfy properties. (10pts)`: Unit =
+    checkBogus(new QuickCheckHeap with quickcheck.test.Bogus2BinomialHeap)
+
+  @Test def `Bogus (3) binomial heap does not satisfy properties. (10pts)`: Unit =
+    checkBogus(new QuickCheckHeap with quickcheck.test.Bogus3BinomialHeap)
+
+  @Test def `Bogus (4) binomial heap does not satisfy properties. (10pts)`: Unit =
+    checkBogus(new QuickCheckHeap with quickcheck.test.Bogus4BinomialHeap)
+
+  @Test def `Bogus (5) binomial heap does not satisfy properties. (10pts)`: Unit =
+    checkBogus(new QuickCheckHeap with quickcheck.test.Bogus5BinomialHeap)
+
+  @Rule def individualTestTimeout = new org.junit.rules.Timeout(10 * 1000)
+}

src/test/scala/quickcheck/test/Heap.scala

@@ -0,0 +1,96 @@
+package quickcheck.test
+
+// Figure 3, page 7
+trait BinomialHeap extends quickcheck.Heap {
+
+  type Rank = Int
+  case class Node(x: A, r: Rank, c: List[Node])
+  override type H = List[Node]
+
+  protected def root(t: Node) = t.x
+  protected def rank(t: Node) = t.r
+  protected def link(t1: Node, t2: Node): Node = // t1.r == t2.r
+    if ord.lteq(t1.x, t2.x) then
+      Node(t1.x, t1.r + 1, t2 :: t1.c)
+    else
+      Node(t2.x, t2.r + 1, t1 :: t2.c)
+  protected def ins(t: Node, ts: H): H = ts match
+    case Nil => List(t)
+    case tp :: ts => // t.r<=tp.r
+      if t.r < tp.r then
+        t :: tp :: ts
+      else
+        ins(link(t, tp), ts)
+
+  override def empty = Nil
+  override def isEmpty(ts: H) = ts.isEmpty
+
+  override def insert(x: A, ts: H) = ins(Node(x, 0, Nil), ts)
+  override def meld(ts1: H, ts2: H) = (ts1, ts2) match
+    case (Nil, ts) => ts
+    case (ts, Nil) => ts
+    case (t1 :: ts1, t2 :: ts2) =>
+      if t1.r < t2.r then
+        t1 :: meld(ts1, t2 :: ts2)
+      else if t2.r < t1.r then
+        t2 :: meld(t1 :: ts1, ts2)
+      else
+        ins(link(t1, t2), meld(ts1, ts2))
+
+  override def findMin(ts: H) = ts match
+    case Nil => throw new NoSuchElementException("min of empty heap")
+    case t :: Nil => root(t)
+    case t :: ts =>
+      val x = findMin(ts)
+      if ord.lteq(root(t), x) then
+        root(t)
+      else
+        x
+  override def deleteMin(ts: H) = ts match
+    case Nil => throw new NoSuchElementException("delete min of empty heap")
+    case t :: ts =>
+      def getMin(t: Node, ts: H): (Node, H) = ts match
+        case Nil => (t, Nil)
+        case tp :: tsp =>
+          val (tq, tsq) = getMin(tp, tsp)
+          if ord.lteq(root(t), root(tq)) then
+            (t, ts)
+          else
+            (tq, t :: tsq)
+      val (Node(_, _, c), tsq) = getMin(t, ts)
+      meld(c.reverse, tsq)
+}
+
+trait Bogus1BinomialHeap extends BinomialHeap {
+  override def findMin(ts: H) = ts match
+    case Nil => throw new NoSuchElementException("min of empty heap")
+    case t :: ts => root(t)
+}
+
+trait Bogus2BinomialHeap extends BinomialHeap {
+  override protected def link(t1: Node, t2: Node): Node = // t1.r == t2.r
+    if !ord.lteq(t1.x, t2.x) then
+      Node(t1.x, t1.r + 1, t2 :: t1.c)
+    else
+      Node(t2.x, t2.r + 1, t1 :: t2.c)
+}
+
+trait Bogus3BinomialHeap extends BinomialHeap {
+  override protected def link(t1: Node, t2: Node): Node = // t1.r == t2.r
+    if ord.lteq(t1.x, t2.x) then
+      Node(t1.x, t1.r + 1, t1 :: t1.c)
+    else
+      Node(t2.x, t2.r + 1, t2 :: t2.c)
+}
+
+trait Bogus4BinomialHeap extends BinomialHeap {
+  override def deleteMin(ts: H) = ts match
+    case Nil => throw new NoSuchElementException("delete min of empty heap")
+    case t :: ts => meld(t.c.reverse, ts)
+}
+
+trait Bogus5BinomialHeap extends BinomialHeap {
+  override def meld(ts1: H, ts2: H) = ts1 match
+    case Nil => ts2
+    case t1 :: ts1 => List(Node(t1.x, t1.r, ts1++ts2))
+}