Sofia/new lazy evaluation

Lazy Evaluation/Lazy Evaluation/task.md

@@ -1,7 +1,7 @@
 
 ## Lazy Evaluation
 
-The proposed `Stream` implementation suffers from a serious potential performance
+The proposed `LazyList` implementation suffers from a serious potential performance
 problem: If `tail` is called several times, the corresponding stream
 will be recomputed each time.
 
@@ -15,7 +15,7 @@ We call this scheme *lazy evaluation* (as opposed to *by-name evaluation* in
 the case where everything is recomputed, and *strict evaluation* for normal
 parameters and `val` definitions.)
 
-### Lazy Evaluation in Scala 
+### Lazy Evaluation in Scala
 
 Haskell is a functional programming language that uses lazy evaluation by default.
 
@@ -24,16 +24,6 @@ with the `lazy val` form:
 
       lazy val x = expr
 
-## Lazy Vals and Streams
-
-Using a lazy value for `tail`, `Stream.cons` can be implemented more efficiently:
-
-      def cons[T](hd: T, tl: => Stream[T]) = new Stream[T] {
-        def head = hd
-        lazy val tail = tl
-        …
-      }
-
 ## Exercise
 
 Complete the `y` variable declaration for it to be lazy.

Lazy Evaluation/Lazy Lists/build.sbt

@@ -0,0 +1,14 @@
+
+lazy val `Lazy-Lists` = (project in file("."))
+  .settings(
+    scalaSource in Compile := baseDirectory.value / "src",
+    scalaSource in Test := baseDirectory.value / "test",
+    libraryDependencies ++= Seq(
+      "org.scala-exercises"        %% "exercise-compiler"         % "0.6.7",
+      "org.scala-exercises"        %% "definitions"               % "0.6.7",
+      "com.chuusai"                %% "shapeless"                 % "2.3.7",
+      "org.scalatest"              %% "scalatest"                 % "3.2.9",
+      "org.scalacheck"             %% "scalacheck"                % "1.15.4",
+      "org.scalatestplus"          %% "scalacheck-1-14"           % "3.2.2.0",
+      "com.github.alexarchambault" %% "scalacheck-shapeless_1.14" % "1.2.5"
+    ))

Lazy Evaluation/Lazy Lists/src/LazyEvaluation.scala

@@ -0,0 +1,18 @@
+import scala.collection.compat.immutable.LazyList
+
+object LazyEvaluation {
+  var rec = 0
+  def llRange(lo: Int, hi: Int): LazyList[Int] = {
+    rec = rec + 1
+    if (lo >= hi) LazyList.empty
+    else LazyList.cons(lo, llRange(lo + 1, hi))
+  }
+  def main(args: Array[String]): Unit = {
+    llRange(1, 10).take(3).toList
+    println(rec)
+    llRange(1, 10).take(5).toList
+    println(rec)
+    llRange(1, 10).take(3).toList
+    println(rec)
+  }
+}

Lazy Evaluation/Stream Ranges/task-info.yaml → Lazy Evaluation/Lazy Lists/task-info.yaml

@@ -5,8 +5,8 @@ files:
 - name: src/LazyEvaluation.scala
   visible: true
   placeholders:
-  - offset: 208
-    length: 23
-    placeholder_text: /*call the streamRange for the rest of the list*/
+  - offset: 218
+    length: 19
+    placeholder_text: /*call the llRange for the rest of the list*/
 - name: test/Test.scala
   visible: false

Lazy Evaluation/Lazy Lists/task.md

@@ -0,0 +1,151 @@
+
+## Motivation
+
+Consider the following program that finds the second prime number between 1000 and 10000:
+
+      ((1000 to 10000) filter isPrime)(1)
+
+This is *much* shorter than the recursive alternative:
+
+
+      def nthPrime(from: Int, to: Int, n: Int): Int =
+        if (from >= to) throw new Error("no prime")
+        else if (isPrime(from))
+          if (n == 1) from else nthPrime(from + 1, to, n - 1)
+        else nthPrime(from + 1, to, n)
+
+      def secondPrime(from: Int, to: Int) = nthPrime(from, to, 2)
+
+But from a standpoint of performance, the first version is pretty bad; it constructs
+*all* prime numbers between `1000` and `10000` in a list, but only ever looks at
+the first two elements of that list.
+
+Reducing the upper bound would speed things up, but risks that we miss the
+second prime number altogether.
+
+## Delayed Evaluation
+
+However, we can make the short-code efficient by using a trick:
+
+- Avoid computing the tail of a sequence until it is needed for the evaluation
+  result (which might be never)
+
+This idea is implemented in a new class, the `LazyList`.
+
+LazyLists are similar to lists, but their elements are evaluated only ''on demand''.
+
+## Defining LazyLists
+
+LazyLists are defined from a constructor `LazyList.cons`.
+
+For instance,
+
+      val xs = LazyList.cons(1, LazyList.cons(2, LazyList.empty))
+
+## LazyList Ranges
+
+Let's try to write a function that returns a `LazyList` representing a range of numbers
+between `lo` and `hi`:
+
+      def llRange(lo: Int, hi: Int): LazyList[Int] =
+        if (lo >= hi) LazyList.empty
+        else LazyList.cons(lo, llRange(lo + 1, hi))
+
+Compare to the same function that produces a list:
+
+      def listRange(lo: Int, hi: Int): List[Int] =
+        if (lo >= hi) Nil
+        else lo :: listRange(lo + 1, hi)
+
+The functions have almost identical structure yet they evaluate quite differently.
+
+- `listRange(start, end)` will produce a list with `end - start` elements and return it.
+- `llRange(start, end)` returns a single object of type `LazyList` with `start` as head element.
+    - The other elements are only computed when they are needed, where “needed” means that someone calls `tail` on the stream.
+
+## Methods on LazyLists
+
+`LazyList` supports almost all methods of `List`.
+
+For instance, to find the second prime number between 1000 and 10000:
+
+      (llRange(1000, 10000) filter isPrime)(1)
+
+The one major exception is `::`.
+
+`x :: xs` always produces a list, never a lazy list.
+
+There is however an alternative operator `#::` which produces a lazy list.
+
+      x #:: xs  ==   LazyList.cons(x, xs)
+
+`#::` can be used in expressions as well as patterns.
+
+## Implementation of LazyLists
+
+The implementation of lazy lists is quite close to the one of lists.
+
+Here's the class `LazyList`:
+
+      final class LazyList[+A] ... extends ... {
+        override def isEmpty: Boolean = ...
+        override def head: A = ...
+        override def tail: LazyList[A] = ...
+        …
+      }
+
+As for lists, all other methods can be defined in terms of these three.
+
+Concrete implementations of streams are defined in the `LazyList.State` companion object.
+Here's a first draft:
+
+      private object State {
+        object Empty extends State[Nothing] {
+          def head: Nothing = throw new NoSuchElementException("head of empty lazy list")
+          def tail: LazyList[Nothing] = throw new UnsupportedOperationException("tail of empty lazy list")
+        }
+
+        final class Cons[A](val head: A, val tail: LazyList[A]) extends State[A]
+      }
+
+The only important difference between the implementations of `List` and `LazyList`
+concern `tail`, the second parameter of `LazyList.cons`.
+
+For lazy lists, this is a by-name parameter: the type of `tail` starts with `=>`. In such
+a case, this parameter is evaluated by following the rules of the call-by-name model.
+
+That's why the second argument to `LazyList.cons` is not evaluated at the point of call.
+
+Instead, it will be evaluated each time someone calls `tail` on a `LazyList` object.
+
+In Scala 2.13, LazyList (previously Stream) became fully lazy from head to tail. To make it possible,
+methods (`filter`, `flatMap`...) are implemented in a way where the head is not being evaluated if is
+not explicitly indicated.
+
+For instance, here's `filter`:
+
+      object LazyList extends SeqFactory[LazyList] {
+        …
+        private def filterImpl[A](ll: LazyList[A], p: A => Boolean, isFlipped: Boolean): LazyList[A] = {
+        // DO NOT REFERENCE `ll` ANYWHERE ELSE, OR IT WILL LEAK THE HEAD
+        var restRef = ll                         // val restRef = new ObjectRef(ll)
+        newLL {
+            var elem: A = null.asInstanceOf[A]
+            var found   = false
+            var rest    = restRef                  // var rest = restRef.elem
+            while (!found && !rest.isEmpty) {
+                elem    = rest.head
+                found   = p(elem) != isFlipped
+                rest    = rest.tail
+                restRef = rest                       // restRef.elem = rest
+            }
+            if (found) sCons(elem, filterImpl(rest, p, isFlipped)) else State.Empty
+        }
+      }
+
+## Exercise
+
+Consider the modification of `llRange` given in the code editor. When you write
+`llRange(1, 10).take(3).toList` what is the value of `rec`?
+
+Be careful, head is evaluating too!

Lazy Evaluation/Lazy Lists/test/Test.scala

@@ -0,0 +1,14 @@
+import LazyEvaluation.{llRange, rec}
+import org.scalatest.matchers.should.Matchers
+import org.scalatest.refspec.RefSpec
+
+class Test extends RefSpec with Matchers{
+  def `test encoding`(): Unit = {
+    llRange(1, 10).take(3).toList
+    rec shouldBe 4
+    llRange(1, 10).take(1).toList
+    rec shouldBe 6
+    llRange(1, 10).take(2).toList
+    rec shouldBe 9
+  }
+}