Complete ch05

Author: Abhijit Sarkar

.scalafmt.conf

@@ -3,6 +3,7 @@ align.preset = more
 maxColumn = 120
 runner.dialect = scala3
 assumeStandardLibraryStripMargin = true
+# https://github.com/scalameta/scalameta/issues/4090
 project.excludePaths = [
     "glob:**/ch04/src/**.scala"
   ]

README.md

@@ -11,6 +11,8 @@ The older code is available in branches.
 
 2. [Algebraic Data Types](ch02)
 3. [Objects as Codata](ch03)
+4. [Contextual Abstraction](ch04)
+5. [Reified Interpreters](ch05)
 
 ## Running tests
 ```

ch05/src/Expression.scala

@@ -0,0 +1,48 @@
+package ch05
+
+/*
+The core of the interpreter strategy is a separation between description and action.
+The description is the program, and the interpreter is the action that carries out the program.
+
+This separation is allows for composition of programs, and managing effects by delaying
+them till the time the program is run. We sometimes call this structure an algebra, with
+constructs and combinators defining programs and destructors defining interpreters.
+The interpreter is then a structural recursion over this ADT.
+
+We saw that the straightforward implementation is not stack-safe, and which caused us to
+to introduction the idea of tail recursion and continuations. We reified continuations
+functions, and saw that we can convert any program into continuation-passing style which
+has every method call in tail position. Due to Scala runtime limitations not all calls
+in tail position can be converted to tail calls, so we reified calls and returns into
+data structures used by a recursive loop called a trampoline.
+ */
+enum Expression:
+  case Literal(value: Double)
+  case Addition(left: Expression, right: Expression)
+  case Subtraction(left: Expression, right: Expression)
+  case Multiplication(left: Expression, right: Expression)
+  case Division(left: Expression, right: Expression)
+
+  def +(that: Expression): Expression =
+    Addition(this, that)
+
+  def -(that: Expression): Expression =
+    Subtraction(this, that)
+
+  def *(that: Expression): Expression =
+    Multiplication(this, that)
+
+  def /(that: Expression): Expression =
+    Division(this, that)
+
+  def eval: Double =
+    this match
+      case Literal(value)              => value
+      case Addition(left, right)       => left.eval + right.eval
+      case Subtraction(left, right)    => left.eval - right.eval
+      case Multiplication(left, right) => left.eval * right.eval
+      case Division(left, right)       => left.eval / right.eval
+
+object Expression:
+  def apply(value: Double): Expression =
+    Literal(value)

ch05/src/ExpressionC.scala

@@ -0,0 +1,42 @@
+package ch05
+
+// Continuation-Passing style.
+enum ExpressionC:
+  case Literal(value: Double)
+  case Addition(left: ExpressionC, right: ExpressionC)
+  case Subtraction(left: ExpressionC, right: ExpressionC)
+  case Multiplication(left: ExpressionC, right: ExpressionC)
+  case Division(left: ExpressionC, right: ExpressionC)
+
+  def +(that: ExpressionC): ExpressionC =
+    Addition(this, that)
+
+  def -(that: ExpressionC): ExpressionC =
+    Subtraction(this, that)
+
+  def *(that: ExpressionC): ExpressionC =
+    Multiplication(this, that)
+
+  def /(that: ExpressionC): ExpressionC =
+    Division(this, that)
+
+  def eval: Double =
+    type Continuation = Double => Double
+
+    def loop(expr: ExpressionC, cont: Continuation): Double =
+      expr match
+        case Literal(value) => cont(value)
+        case Addition(left, right) =>
+          loop(left, l => loop(right, r => cont(l + r)))
+        case Subtraction(left, right) =>
+          loop(left, l => loop(right, r => cont(l - r)))
+        case Multiplication(left, right) =>
+          loop(left, l => loop(right, r => cont(l * r)))
+        case Division(left, right) =>
+          loop(left, l => loop(right, r => cont(l / r)))
+
+    loop(this, identity)
+
+object ExpressionC:
+  def apply(value: Double): ExpressionC =
+    Literal(value)

ch05/src/ExpressionT.scala

@@ -0,0 +1,55 @@
+package ch05
+
+enum ExpressionT:
+  case Literal(value: Double)
+  case Addition(left: ExpressionT, right: ExpressionT)
+  case Subtraction(left: ExpressionT, right: ExpressionT)
+  case Multiplication(left: ExpressionT, right: ExpressionT)
+  case Division(left: ExpressionT, right: ExpressionT)
+
+  def eval: Double =
+    // Trampoline style.
+    type Continuation = Double => Call
+
+    enum Call:
+      case Continue(value: Double, k: Continuation)
+      case Loop(expr: ExpressionT, k: Continuation)
+      case Done(result: Double)
+
+    def loop2(left: ExpressionT, right: ExpressionT, cont: Continuation, op: (Double, Double) => Double): Call =
+      Call.Loop(
+        left,
+        l => Call.Loop(right, r => Call.Continue(op(l, r), cont))
+      )
+
+    def loop(expr: ExpressionT, cont: Continuation): Call =
+      expr match
+        case Literal(value)              => Call.Continue(value, cont)
+        case Addition(left, right)       => loop2(left, right, cont, _ + _)
+        case Subtraction(left, right)    => loop2(left, right, cont, _ - _)
+        case Multiplication(left, right) => loop2(left, right, cont, _ * _)
+        case Division(left, right)       => loop2(left, right, cont, _ / _)
+
+    def trampoline(call: Call): Double =
+      call match
+        case Call.Continue(value, k) => trampoline(k(value))
+        case Call.Loop(expr, k)      => trampoline(loop(expr, k))
+        case Call.Done(result)       => result
+
+    trampoline(loop(this, x => Call.Done(x)))
+
+  def +(that: ExpressionT): ExpressionT =
+    Addition(this, that)
+
+  def -(that: ExpressionT): ExpressionT =
+    Subtraction(this, that)
+
+  def *(that: ExpressionT): ExpressionT =
+    Multiplication(this, that)
+
+  def /(that: ExpressionT): ExpressionT =
+    Division(this, that)
+
+object ExpressionT:
+  def apply(value: Double): ExpressionT =
+    Literal(value)

ch05/src/Regexp.scala

@@ -0,0 +1,43 @@
+package ch05
+
+enum Regexp:
+  case Append(left: Regexp, right: Regexp)
+  case OrElse(first: Regexp, second: Regexp)
+  case Repeat(source: Regexp)
+  case Apply(string: String)
+  case Empty
+
+  def ++(that: Regexp): Regexp =
+    Append(this, that)
+
+  def orElse(that: Regexp): Regexp =
+    OrElse(this, that)
+
+  def repeat: Regexp =
+    Repeat(this)
+
+  def `*`: Regexp = this.repeat
+
+  def matches(input: String): Boolean =
+    def loop(regexp: Regexp, idx: Int): Option[Int] =
+      regexp match
+        case Append(left, right) =>
+          loop(left, idx).flatMap(loop(right, _))
+        case OrElse(first, second) =>
+          loop(first, idx).orElse(loop(second, idx))
+        case Repeat(source) =>
+          loop(source, idx)
+            .flatMap(loop(regexp, _))
+            .orElse(Some(idx))
+        case Apply(string) =>
+          Option.when(input.startsWith(string, idx))(idx + string.size)
+        case Empty => None
+
+    // Check we matched the entire input
+    loop(this, 0).map(_ == input.size).getOrElse(false)
+
+object Regexp:
+  val empty: Regexp = Empty
+
+  def apply(string: String): Regexp =
+    Apply(string)

ch05/src/RegexpC.scala

@@ -0,0 +1,64 @@
+package ch05
+
+// Continuation-Passing style.
+enum RegexpC:
+  case Append(left: RegexpC, right: RegexpC)
+  case OrElse(first: RegexpC, second: RegexpC)
+  case Repeat(source: RegexpC)
+  case Apply(string: String)
+  case Empty
+
+  def ++(that: RegexpC): RegexpC =
+    Append(this, that)
+
+  def orElse(that: RegexpC): RegexpC =
+    OrElse(this, that)
+
+  def repeat: RegexpC =
+    Repeat(this)
+
+  def `*`: RegexpC = this.repeat
+
+  def matches(input: String): Boolean =
+    // Define a type alias so we can easily write continuations.
+    type Continuation = Option[Int] => Option[Int]
+
+    def loop(
+        regexp: RegexpC,
+        idx: Int,
+        cont: Continuation
+    ): Option[Int] =
+      regexp match
+        case Append(left, right) =>
+          val k: Continuation = _ match
+            case None    => cont(None)
+            case Some(i) => loop(right, i, cont)
+          loop(left, idx, k)
+
+        case OrElse(first, second) =>
+          val k: Continuation = _ match
+            case None => loop(second, idx, cont)
+            case some => cont(some)
+          loop(first, idx, k)
+
+        case Repeat(source) =>
+          val k: Continuation =
+            _ match
+              case None    => cont(Some(idx))
+              case Some(i) => loop(regexp, i, cont)
+          loop(source, idx, k)
+
+        case Apply(string) =>
+          cont(Option.when(input.startsWith(string, idx))(idx + string.size))
+
+        case Empty =>
+          cont(None)
+
+    // Check we matched the entire input
+    loop(this, 0, identity).map(_ == input.size).getOrElse(false)
+
+object RegexpC:
+  val empty: RegexpC = Empty
+
+  def apply(string: String): RegexpC =
+    Apply(string)

ch05/src/RegexpT.scala

@@ -0,0 +1,85 @@
+package ch05
+
+enum RegexpT:
+  def ++(that: RegexpT): RegexpT =
+    Append(this, that)
+
+  def orElse(that: RegexpT): RegexpT =
+    OrElse(this, that)
+
+  def repeat: RegexpT =
+    Repeat(this)
+
+  def `*`: RegexpT = this.repeat
+
+  def matches(input: String): Boolean =
+    /*
+    Scala's runtimes don't support full tail calls, so calls from a continuation
+    to loop or from loop to a continuation will use a stack frame.
+    So, instead of making a call, we return a value that reifies the call we want to make.
+    This idea is the core of trampolining.
+     */
+    // Define a type alias so we can easily write continuations.
+    type Continuation = Option[Int] => Call
+
+    enum Call:
+      case Loop(regexp: RegexpT, index: Int, continuation: Continuation)
+      case Continue(index: Option[Int], continuation: Continuation)
+      case Done(index: Option[Int])
+
+    def loop(regexp: RegexpT, idx: Int, cont: Continuation): Call =
+      regexp match
+        case Append(left, right) =>
+          val k: Continuation = _ match
+            case None    => Call.Continue(None, cont)
+            case Some(i) => Call.Loop(right, i, cont)
+          Call.Loop(left, idx, k)
+
+        case OrElse(first, second) =>
+          val k: Continuation = _ match
+            case None => Call.Loop(second, idx, cont)
+            case some => Call.Continue(some, cont)
+          Call.Loop(first, idx, k)
+
+        case Repeat(source) =>
+          val k: Continuation =
+            _ match
+              case None    => Call.Continue(Some(idx), cont)
+              case Some(i) => Call.Loop(regexp, i, cont)
+          Call.Loop(source, idx, k)
+
+        // The following could directly call 'cont' with the Option
+        // if Scala had support for full tail calls.
+        case Apply(string) =>
+          Call.Continue(
+            Option.when(input.startsWith(string, idx))(idx + string.size),
+            cont
+          )
+
+        case Empty =>
+          Call.Continue(None, cont)
+
+    def trampoline(next: Call): Option[Int] =
+      next match
+        case Call.Loop(regexp, index, continuation) =>
+          trampoline(loop(regexp, index, continuation))
+        case Call.Continue(index, continuation) =>
+          trampoline(continuation(index))
+        case Call.Done(index) => index
+
+    // Check we matched the entire input
+    trampoline(loop(this, 0, Call.Done(_)))
+      .map(_ == input.size)
+      .getOrElse(false)
+
+  case Append(left: RegexpT, right: RegexpT)
+  case OrElse(first: RegexpT, second: RegexpT)
+  case Repeat(source: RegexpT)
+  case Apply(string: String)
+  case Empty
+
+object RegexpT:
+  val empty: RegexpT = Empty
+
+  def apply(string: String): RegexpT =
+    Apply(string)

ch05/test/src/ExpressionCSpec.scala

@@ -0,0 +1,11 @@
+package ch05
+
+import org.scalatest.funspec.AnyFunSpec
+import org.scalatest.matchers.should.Matchers.shouldBe
+
+class ExpressionCSpec extends AnyFunSpec:
+  describe("ExpressionC"):
+    it("eval"):
+      val fortyTwo = ((ExpressionC(15.0) + ExpressionC(5.0)) * ExpressionC(2.0) + ExpressionC(2.0)) / ExpressionC(1.0)
+      fortyTwo.eval shouldBe 42.0d
+

ch05/test/src/ExpressionSpec.scala

@@ -0,0 +1,11 @@
+package ch05
+
+import org.scalatest.funspec.AnyFunSpec
+import org.scalatest.matchers.should.Matchers.shouldBe
+
+class ExpressionSpec extends AnyFunSpec:
+  describe("Expression"):
+    it("eval"):
+      val fortyTwo = ((Expression(15.0) + Expression(5.0)) * Expression(2.0) + Expression(2.0)) / Expression(1.0)
+      fortyTwo.eval shouldBe 42.0d
+

ch05/test/src/ExpressionTSpec.scala

@@ -0,0 +1,11 @@
+package ch05
+
+import org.scalatest.funspec.AnyFunSpec
+import org.scalatest.matchers.should.Matchers.shouldBe
+
+class ExpressionTSpec extends AnyFunSpec:
+  describe("ExpressionT"):
+    it("eval"):
+      val fortyTwo = ((ExpressionT(15.0) + ExpressionT(5.0)) * ExpressionT(2.0) + ExpressionT(2.0)) / ExpressionT(1.0)
+      fortyTwo.eval shouldBe 42.0d
+