First batch of exercises regarding Streams

Author: Javier de Silóniz Sandino

src/main/scala/fpinscalalib/FPinScalaLibrary.scala

@@ -15,6 +15,7 @@ object FPinScalaLibrary extends Library {
   override def sections = scala.collection.immutable.List(
     GettingStartedWithFPSection,
     FunctionalDataStructuresSection,
-    ErrorHandlingSection
+    ErrorHandlingSection,
+    StrictnessAndLazinessSection
   )
 }

src/main/scala/fpinscalalib/StrictnessAndLazinessSection.scala

@@ -0,0 +1,331 @@
+package fpinscalalib
+
+import fpinscalalib.customlib.laziness._
+import fpinscalalib.customlib.laziness.Stream
+import fpinscalalib.customlib.laziness.Stream._
+import org.scalatest.{FlatSpec, Matchers}
+import fpinscalalib.customlib.laziness.ExampleHelper._
+
+/** @param name sctriness_and_laziness
+  */
+object StrictnessAndLazinessSection extends FlatSpec with Matchers with org.scalaexercises.definitions.Section {
+
+  /**
+    * = Strict and non-strict functions =
+    *
+    * Non-strictness is a property of a function. To say a function is `non-strict` just means that the function may
+    * choose not to evaluate one or more of its arguments. In contrast, a `strict` function always evaluates its
+    * arguments.  Unless we tell it otherwise, any function definition in Scala will be strict. As an example, consider
+    * the following function:
+    *
+    * {{{
+    *   def square(x: Double): Double = x * x
+    * }}}
+    *
+    * When you invoke `square(41.0 + 1.0)`, the function `square` will receive the evaluated value of `42.0` because
+    * it's strict. If you invoke `square(sys.error("failure"))`, you’ll get an exception before square has a chance to do
+    * anything, since the `sys.error("failure")` expression will be evaluated before entering the body of square.
+    *
+    * For example, the short-circuiting Boolean functions `&&` and `||`, found in many programming languages including
+    * Scala, are non-strict. You can think of them as functions that may choose not to evaluate their arguments. The
+    * function `&&` takes two `Boolean` arguments, but only evaluates the second argument if the first is `true`:
+    *
+    * {{{
+    *   false && { println("!!"); true } // does not print anything
+    * }}}
+    *
+    * And `||` only evaluates its second argument if the first is `false`:
+    *
+    * {{{
+    *   true || { println("!!"); false } // doesn't print anything either
+    * }}}
+    *
+    * Another example of non-strictness is the `if` control construct in Scala. It can be thought of as a function
+    * accepting three parameters: a condition of type `Boolean`, an expression of some type `A` to return in the case that
+    * the condition is `true`, and another expression of the same type `A` to return if the condition is `false`. We'd
+    * say that the if function is strict in its condition parameter, since it’ll always evaluate the condition to
+    * determine which branch to take, and non-strict in the two branches for the `true` and `false` cases,
+    * since it’ll only evaluate one or the other based on the condition. We can re-implement it the following way:
+    *
+    * {{{
+    *   def if2[A](cond: Boolean, onTrue: () => A, onFalse: () => A): A =
+    *     if (cond) onTrue() else onFalse()
+    * }}}
+    *
+    *
+    *
+    * Play a little bit with it, note what happens when you force a `true` or a `false` condition on the `if2` call:
+    */
+
+  def if2Assert(res0: Boolean): Unit = {
+    if2(res0, () => true, () => { sys.error("Exception occurred: if2 call went through the false branch") })
+  }
+
+  /**
+    * The arguments we’d like to pass unevaluated have a `() =>` immediately before their type. A value of type
+    * `() => A` is a function that accepts zero arguments and returns an `A`. In general, the unevaluated form of an
+    * expression is called a `thunk`, and we can force the thunk to evaluate the expression and get a result. We do
+    * so by invoking the function, passing an empty argument list, as in `onTrue()` or `onFalse()`. Likewise, callers
+    * of `if2` have to explicitly create thunks, and the syntax follows the same conventions as the function literal
+    * syntax we’ve already seen. But this is such a common case that Scala provides some nicer syntax:
+    *
+    * {{{
+    *   def if2[A](cond: Boolean, onTrue: => A, onFalse: => A): A =
+    *     if (cond) onTrue else onFalse
+    *
+    *   if2(false, sys.error("fail"), 3)
+    * }}}
+    *
+    * With either syntax, an argument that’s passed unevaluated to a function will be evalu- ated once for each place
+    * it’s referenced in the body of the function. That is, Scala won’t (by default) cache the result of evaluating an
+    * argument:
+    *
+    * {{{
+    *   def maybeTwice(b: Boolean, i: => Int) = if (b) i+i else 0
+    *
+    *   scala> val x = maybeTwice(true, { println("hi"); 1 + 41 })
+    *   hi
+    *   hi
+    *   x: Int = 84
+    * }}}
+    *
+    * Here, i is referenced twice in the body of maybeTwice, and we’ve made it particularly obvious that it’s evaluated
+    * each time by passing the block `{ println("hi"); 1+41 }`, which prints hi as a side effect before returning a
+    * result of `42`. The expression `1 + 41` will be computed twice as well. We can cache the value explicitly if we
+    * wish to only evaluate the result once, by using the `lazy` keyword:
+    *
+    * {{{
+    *   def maybeTwice2(b: Boolean, i: => Int) = {
+    *     lazy val j = i
+    *     if (b) j + j else 0
+    *   }
+    *
+    *   scala> val x = maybeTwice2(true, { println("hi"); 1 + 41 })
+    *   hi
+    *   x: Int = 84
+    * }}}
+    *
+    * Adding the `lazy` keyword to a `val` declaration will cause Scala to delay evaluation of the right-hand side of that
+    * `lazy val` declaration until it’s first referenced. It will also cache the result so that subsequent references to
+    * it don’t trigger repeated evaluation.
+    *
+    * = Lazy lists =
+    *
+    * We’ll explore how laziness can be used to improve the efficiency and modularity of functional programs using lazy
+    * lists, or streams, as an example.
+    *
+    * {{{
+    *   sealed trait Stream[+A]
+    *   case object Empty extends Stream[Nothing]
+    *   case class Cons[+A](h: () => A, t: () => Stream[A]) extends Stream[A]
+    *
+    *   object Stream {
+    *     def cons[A](hd: => A, tl: => Stream[A]): Stream[A] = {
+    *       lazy val head = hd
+    *       lazy val tail = tl
+    *       Cons(() => head, () => tail)
+    *     }
+    *     def empty[A]: Stream[A] = Empty
+    *
+    *     def apply[A](as: A*): Stream[A] =
+    *       if (as.isEmpty) empty else cons(as.head, apply(as.tail: _*))
+    *   }
+    * }}}
+    *
+    * This type looks identical to our List type, except that the Cons data constructor takes `explicit` thunks
+    * `(() => A and () => Stream[A])` instead of regular strict values. If we wish to examine or traverse the Stream,
+    * we need to force these thunks as we did earlier in our definition of `if2`. For example:
+    *
+    * {{{
+    *   def headOption: Option[A] = this match {
+    *     case Empty => None
+    *     case Cons(h, t) => Some(h())  // explicit forcing of h using h()
+    *   }
+    * }}}
+    *
+    *
+    * Now let's write a few helper functions to make inspecting streams easier, starting with a function to convert a
+    * `Stream` to a `List` (which will force its evaluation):
+    */
+
+  def streamToListAssert(res0: List[Int]): Unit = {
+    def toList[A](s: Stream[A]): List[A] = s match {
+      case Cons(h,t) => h() :: t().toListRecursive
+      case _ => List()
+    }
+
+    val s = Stream(1, 2, 3)
+    toList(s) shouldBe res0
+  }
+
+  /**
+    * Let's continue by writing the function `take` for returning the fist `n` elements of a `Stream`. Note that in the
+    * following implementation we're using `Stream`'s smart constructors `cons` and `empty`, defined as follows:
+    *
+    * {{{
+    *   def cons[A](hd: => A, tl: => Stream[A]): Stream[A] = {
+    *     lazy val head = hd
+    *     lazy val tail = tl
+    *     Cons(() => head, () => tail)
+    *   }
+    *
+    *   def empty[A]: Stream[A] = Empty
+    * }}}
+    */
+
+  def streamTakeAssert(res0: Int): Unit = {
+    def take[A](s: Stream[A], n: Int): Stream[A] = s match {
+      case Cons(h, t) if n > 0 => cons[A](h(), t().take(n - res0))
+      case Cons(h, _) if n == 0 => cons[A](h(), Stream.empty)
+      case _ => Stream.empty
+    }
+
+    take(Stream(1, 2, 3), 2).toList shouldBe List(1, 2)
+  }
+
+  /**
+    * `drop` is similar to `take`, but instead skips the first `n` elements of a `Stream`:
+    */
+
+  def streamDropAssert(res0: Int): Unit = {
+    def drop[A](s: Stream[A], n: Int): Stream[A] = s match {
+      case Cons(_, t) if n > 0 => t().drop(n - res0)
+      case _ => s
+    }
+
+    drop(Stream(1, 2, 3, 4, 5), 2).toList shouldBe List(3, 4, 5)
+  }
+
+  /**
+    * We can also implement `takeWhile` for returning all starting elements of a `Stream` that match the given predicate:
+    */
+
+  def streamTakeWhileAssert(res0: List[Int], res1: List[Int]): Unit = {
+    def takeWhile[A](s: Stream[A], f: A => Boolean): Stream[A] = s match {
+      case Cons(h,t) if f(h()) => cons(h(), t() takeWhile f)
+      case _ => Stream.empty
+    }
+
+    takeWhile(Stream(1, 2, 3, 4, 5), (x: Int) => x < 3).toList shouldBe res0
+    takeWhile(Stream(1, 2, 3, 4, 5), (x: Int) => x < 0).toList shouldBe res1
+  }
+
+  /**
+    * = Separating program description from evaluation =
+    *
+    * Laziness lets us separate the description of an expression from the evaluation of that expression. This gives us
+    * a powerful ability — we may choose to describe a “larger” expression than we need, and then evaluate only a portion
+    * of it. As an example, let’s look at the function exists that checks whether an element matching a `Boolean`
+    * function exists in this Stream:
+    *
+    * {{{
+    *   def exists(p: A => Boolean): Boolean = this match {
+    *     case Cons(h, t) => p(h()) || t().exists(p)
+    *     case _ => false
+    *   }
+    * }}}
+    *
+    * Note that `||` is non-strict in its second argument. If `p(h())` returns `true`, then exists terminates the
+    * traversal early and returns true as well. Remember also that the tail of the stream is a `lazy val`. So not only
+    * does the traversal terminate early, the tail of the stream is never evaluated at all!
+    *
+    * We can implement a `foldRight` similar to that of `List`, but expressed in a lazy way:
+    *
+    * {{{
+    *   def foldRight[B](z: => B)(f: (A, => B) => B): B = this match {
+    *     case Cons(h,t) => f(h(), t().foldRight(z)(f))
+    *     case _ => z
+    *   }
+    * }}}
+    *
+    * This looks very similar to the `foldRight` we wrote for `List`, but note how our combining function `f` is
+    * non-strict in its second parameter. If `f` chooses not to evaluate its second parameter, this terminates the
+    * traversal early. We can see this by using `foldRight` to implement `exists`:
+    *
+    * {{{
+    *   def exists(p: A => Boolean): Boolean = foldRight(false)((a, b) => p(a) || b)
+    * }}}
+    *
+    * Let's use this to implement `forAll`, which checks that all elements in the `Stream` match a given predicate. Note
+    * that the implementation will terminate the traversal as soon as it encounters a nonmatching value.
+    */
+
+  def streamForAllAssert(res0: Boolean): Unit = {
+    def forAll[A](s: Stream[A], f: A => Boolean): Boolean =
+      s.foldRight(res0)((a, b) => f(a) && b)
+
+    forAll(Stream(1, 2, 3), (x: Int) => x % 2 == 0) shouldBe false
+    forAll(Stream("a", "b", "c"), (x: String) => x.size > 0) shouldBe true
+  }
+
+  /**
+    * Let's put `foldRight` to good use, by implementing `takeWhile` based on it:
+    *
+    * {{{
+    *   def takeWhile_1(f: A => Boolean): Stream[A] =
+    *     foldRight(empty[A])((h,t) =>
+    *       if (f(h)) cons(h,t)
+    *       else      empty)
+    * }}}
+    *
+    * We can also do the same with `headOption`:
+    *
+    * {{{
+    *   def headOption: Option[A] = foldRight(None: Option[A])((h,_) => Some(h))
+    * }}}
+    *
+    * Implementations for `map`, `filter`, `append` and `flatMap` using `foldRight` should sound familiar already:
+    *
+    * {{{
+    *   def map[B](f: A => B): Stream[B] = foldRight(empty[B])((h,t) => cons(f(h), t))
+    *
+    *   def filter(f: A => Boolean): Stream[A] = foldRight(empty[A])((h,t) =>
+    *     if (f(h)) cons(h, t)
+    *     else t)
+    *
+    *   def append[B>:A](s: => Stream[B]): Stream[B] = foldRight(s)((h,t) => cons(h,t))
+    *
+    *   def flatMap[B](f: A => Stream[B]): Stream[B] = foldRight(empty[B])((h,t) => f(h) append t)
+    * }}}
+    *
+    * Note that these implementations are incremental — they don’t fully generate their answers. It’s not until some
+    * other computation looks at the elements of the resulting `Stream` that the computation to generate that `Stream`
+    * actually takes place. Let's look at a simplified program trace for the next piece of code.
+    *
+    * {{{
+    *   Stream(1, 2, 3, 4).map(_ + 10).filter(_ % 2 == 0)
+    * }}}
+    *
+    * We'll convert that expression to a `List` to force evaluation. Try to follow what's happening in each step:
+    */
+
+  def streamTraceAssert(res0: Int, res1: Stream[Int], res2: Stream[Int], res3: Int, res4: Stream[Int], res5: Int): Unit = {
+    val startingPoint = Stream(1, 2, 3, 4).map(_ + 10).filter(_ % 2 == 0).toList
+
+    // Apply map to the first element:
+    val step1 = cons(res0, Stream(2,3,4).map(_ + 10)).filter(_ % 2 == 0).toList
+    // Apply filter to the first element:
+    val step2 = res1.map(_ + 10).filter(_ % 2 == 0).toList
+    // Apply map to the second element:
+    val step3 = cons(12, res2.map(_ + 10)).filter(_ % 2 == 0).toList
+    // Apply filter to the second element. Produce the first element of the result:
+    val step4 = 12 :: Stream(3,4).map(_ + 10).filter(_ % 2 == 0).toList
+    val step5 = 12 :: cons(res3, res4.map(_ + 10)).filter(_ % 2 == 0).toList
+    val step6 = 12 :: Stream(4).map(_ + 10).filter(_ % 2 == 0).toList
+    val step7 = 12 :: cons(res5, Stream[Int]().map(_ + 10)).filter(_ % 2 == 0).toList
+    // Apply filter to the fourth element and produce the final element of the result.
+    val step8 = 12 :: 14 :: Stream[Int]().map(_ + 10).filter(_ % 2 == 0).toList
+    // map and filter have no more work to do, and the empty stream becomes the empty list.
+    val finalStep = 12 :: 14 :: List()
+
+    startingPoint shouldBe step1
+    step1 shouldBe step2
+    step2 shouldBe step3
+    step3 shouldBe step4
+    step4 shouldBe step5
+    step5 shouldBe step6
+    step6 shouldBe step7
+    step7 shouldBe step8
+    step8 shouldBe finalStep
+  }
+}

src/main/scala/fpinscalalib/customlib/laziness/ExampleHelper.scala

@@ -0,0 +1,5 @@
+package fpinscalalib.customlib.laziness
+
+object ExampleHelper {
+  def if2[A](cond: Boolean, onTrue: () => A, onFalse: () => A): A = if (cond) onTrue() else onFalse()
+}