Complete ch08

Author: Abhijit Sarkar

.scalafmt.conf

@@ -7,5 +7,6 @@ assumeStandardLibraryStripMargin = true
 project.excludePaths = [
     "glob:**/ch04/src/**.scala",
     "glob:**/ch06/src/Cat.scala",
-    "glob:**/ch07/src/*.scala"
+    "glob:**/ch07/src/*.scala",
+    "glob:**/ch08/src/*.scala"
   ]

README.md

@@ -15,6 +15,7 @@ The older code is available in branches.
 5. [Reified Interpreters](ch05)
 6. [Using Cats](ch06)
 7. [Monoids and Semigroups](ch07)
+8. [Functors](ch08)
 
 ## Running tests
 ```

ch08/src/Codec.scala

@@ -0,0 +1,41 @@
+package ch08
+
+/*
+8.6.2.1 Transformative Thinking with imap
+Implement the imap method for Codec.
+ */
+trait Codec[A]:
+  def encode(value: A): String
+  def decode(value: String): A
+  def imap[B](dec: A => B, enc: B => A): Codec[B] =
+    val self = this
+    new Codec[B]:
+      override def encode(value: B): String =
+        self.encode(enc(value))
+
+      override def decode(value: String): B =
+        dec(self.decode(value))
+
+def encode[A : Codec as c](value: A): String =
+  c.encode(value)
+
+def decode[A : Codec as c](value: String): A =
+  c.decode(value)
+
+object Codec:
+  final case class Box[A](value: A)
+
+  given stringCodec: Codec[String]:
+    def encode(value: String): String = value
+    def decode(value: String): String = value
+
+  given Codec[Int] =
+    stringCodec.imap(_.toInt, _.toString)
+
+  // Demonstrate your imap method works by creating a Codec for Double.
+  given Codec[Double] =
+    stringCodec.imap(_.toDouble, _.toString)
+
+  // Implement a Codec for the Box type.
+  given boxCodec: [A : Codec as c] => Codec[Box[A]] =
+    c.imap[Box[A]](Box(_), _.value)

ch08/src/Display.scala

@@ -0,0 +1,42 @@
+package ch08
+
+/*
+8.6.1.1 Exercise: Showing off with Contramap
+Implement the contramap method for Display above.
+ */
+trait Display[A]:
+  def display(value: A): String
+
+  def contramap[B](f: B => A): Display[B] =
+    val self = this
+    new Display[B]:
+      def display(value: B): String =
+        self.display(f(value))
+
+def display[A: Display as d](value: A): String =
+  d.display(value)
+
+object Display:
+  final case class Box[A](value: A)
+
+  given Display[String]:
+    def display(value: String): String =
+      s"'${value}'"
+
+  given Display[Boolean]:
+    def display(value: Boolean): String =
+      if (value) "yes" else "no"
+
+  /*
+  Define an instance of Display for the following Box case class.
+  Rather than writing out the complete definition from scratch
+  (new Display[Box] etc...), create your instance from an existing
+  instance using contramap.
+   */
+  // Given a Display[A], and a Box[A], we can create
+  // Display[Box[A]] by the reverse mapping Box[A] => A.
+  // The forward mapping would be A => Box[A].
+  
+  // Parameterized typeclass with named context bound.
+  given [A : Display as d] => Display[Box[A]] =
+    d.contramap[Box[A]](_.value)

ch08/src/Tree.scala

@@ -0,0 +1,28 @@
+package ch08
+
+import cats.Functor
+
+sealed trait Tree[+A]
+
+final case class Branch[A](left: Tree[A], right: Tree[A]) extends Tree[A]
+
+final case class Leaf[A](value: A) extends Tree[A]
+
+object Tree:
+  /* 8.5.4 Exercise: Branching out with Functors
+  Write a Functor for the following binary tree data type. 
+  Verify that the code works as expected on instances of Branch and Leaf.
+ */
+  given Functor[Tree]:
+    override def map[A, B](fa: Tree[A])(f: A => B): Tree[B] =
+      fa match
+        case Branch(l, r) => Branch(map(l)(f), map(r)(f))
+        case Leaf(value)  => Leaf(f(value))
+
+  // The compiler can find a Functor instance for Tree but not for Branch or Leaf (Functor is invariant in F).
+  // Let's add some smart constructors to compensate.
+  def branch[A](left: Tree[A], right: Tree[A]): Tree[A] =
+    Branch(left, right)
+
+  def leaf[A](value: A): Tree[A] =
+    Leaf(value)

ch08/src/ch08.worksheet.sc

@@ -0,0 +1,89 @@
+import ch08.{display, Display, encode, decode, Codec}
+
+display("hello")
+display(true)
+display(Display.Box("hello"))
+// If we don’t have a Display for the type inside the Box,
+// calls to display should fail to compile:
+
+// display(Box(123))
+
+val ca = encode(123.4)
+val cb = decode[Double]("123.4")
+
+val cc = encode(Codec.Box(123.4))
+val cd = decode[Codec.Box[Double]]("123.4")
+
+// 3.5.2 Functor Syntax
+val func1 = (a: Int) => a + 1
+val func2 = (a: Int) => a * 2
+val func3 = (a: Int) => s"${a}!"
+val func4 = func1.map(func2).map(func3)
+
+func4(123)
+
+def doMath[F[_]](start: F[Int])(using functor: Functor[F]): F[Int] =
+  start.map(n => n + 1 * 2)
+
+doMath(Option(20))
+doMath(List(1, 2, 3))
+
+// 8.7.1 Contravariant in Cats
+import cats.Contravariant
+import cats.Show
+import cats.instances.string.catsStdShowForString
+
+val showString = Show[String]
+
+// trait Contravariant[F[_]]:
+//   def contramap[A, B](fa: F[A])(f: B => A): F[B]
+
+val showSymbol: Show[Symbol] = Contravariant[Show].contramap(showString)((sym: Symbol) => s"'${sym.name}")
+
+showSymbol.show(Symbol("dave"))
+
+import cats.syntax.contravariant.toContravariantOps
+
+showString
+  .contramap[Symbol](sym => s"'${sym.name}")
+  .show(Symbol("dave"))
+
+// 8.7.2 Invariant in Cats
+import cats.Monoid
+import cats.instances.string.catsKernelStdMonoidForString
+import cats.syntax.invariant.toInvariantOps
+import cats.syntax.semigroup.catsSyntaxSemigroup
+
+given Monoid[Symbol] =
+  Monoid[String].imap(Symbol.apply)(_.name)
+
+Monoid[Symbol].empty
+
+Symbol("a") |+| Symbol("few") |+| Symbol("words")
+
+// 8.8 Aside: Partial Unification
+val f1 = (x: Int) => x.toDouble
+val f2 = (y: Double) => y * 2
+
+val f3 = func1.map(func2)
+
+val either: Either[String, Int] = Right(123)
+
+either.map(_ + 1)
+
+val f3a: Int => Double =
+  a => f2(f1(a))
+
+val f3b: Int => Double =
+  f2.compose(f1)
+
+// error: value contramap is not a member of Double => Double
+// val f3c = f2.contramap(f1)
+
+type <=[B, A] = A => B
+
+type F[A] = Double <= A
+
+val f2b: Double <= Double = f2
+
+val f3c = f2b.contramap(f1)

ch08/test/src/TreeSpec.scala

@@ -0,0 +1,14 @@
+package ch08
+import org.scalatest.funspec.AnyFunSpec
+import org.scalatest.matchers.should.Matchers.shouldBe
+import cats.syntax.functor.toFunctorOps
+
+class TreeSpec extends AnyFunSpec:
+  describe("Tree Functor"):
+    it("should map on leaf"):
+      val actual = Tree.leaf(100).map(_ * 2)
+      actual `shouldBe` Leaf(200)
+
+    it("should map on branch"):
+      val actual = Tree.branch(Tree.leaf(10), Tree.leaf(20)).map(_ * 2)
+      actual `shouldBe` Branch(Leaf(20), Leaf(40))