# Scala Functional Design & Programming - Chapter 5 (5)

I bought "Scala Functional Design & Programming - A Comprehensive Guide to Functional Programming by Scalaz Contributors".

I'll read it bit by bit and summarize each chapter.

This time, I'll cover Chapter 5. It's about lazy evaluation.

## Chapter 5

This chapter deals with non-strictness, which is essentially lazy evaluation. This is a very functional programming-like concept and has a significant impact on execution efficiency. I want to delve deeper into it.

### Scala's Non-Strict Functions

This is often represented in the form of `↓`

in JS.

```
def hoge(f: () => Int) = ... f()
hoge( () => 21 )
```

This form is called a thunk and is commonly used. Even in JS libraries, the name "redux-thunk" is used.

However, writing it every time is cumbersome, so in Scala, the initial empty parentheses are omitted, and the parentheses are not needed when calling it either. Convenient!

```
def hoge(f: => Int) = ... f
```

When retrieving a value from a sink, the result is not cached, so it's necessary to put it in a lazy constant.

```
lazy val x = f
```

This way, `x`

is evaluated when it's first used, and the result is cached.

### Stream

After introducing the smart constructor for caching, it's time for the usual practice problems.

Create a

`toList`

for Stream.

```
def toList: List[A] = {
this match {
case Cons(h, t) => h() :: t().toList
case _ => Nil
}
}
```

This works, but it's not tail-recursive, so it's slow. The answer also included a solution using `reverse`

and `tailrec`

with `mutable.ListBuffer`

.

Create

`take`

,`drop`

, and`takeWhile`

for Stream.

```
def take(n: Int): Stream[A] =
this match {
case Cons(h, t) if n > 0 => cons(h(), t().take(n - 1))
case _ => Empty
}
def drop(n: Int): Stream[A] =
this match {
case Cons(h, t) if n > 0 => t().drop(n - 1)
case _ => this
}
def takeWhile(p: A => Boolean): Stream[A] =
this match {
case Cons(h, t) if p(h()) => cons(h(), t().takeWhile(p))
case _ => Empty
}
```

In the answer for `take`

, it's pointed out that when `n == 1`

, an unnecessary `t()`

is called, so it's better to branch for `n == 1`

. It's a small but important detail.

Next, the implementation of `exists`

is explained, which utilizes Stream to stop evaluating as soon as it finds a match. `foldRight`

is also implemented in a way that stops evaluating as soon as it finds a match.

Here's another practice problem.

Implement

`forAll`

to check if all elements satisfy a condition.

```
def forAll(p: A => Boolean): Boolean =
foldRight(true)((a, b) => p(a) && b)
```

I was able to write it without thinking about Stream at all. It's truly generalized.

Implement

`takeWhile`

using`foldRight`

.

```
def takeWhile2(p: A => Boolean): Stream[A] =
foldRight(Empty: Stream[A])((a, b) => if (p(a)) cons(a, b) else Empty)
```

Implement

`headOption`

using`foldRight`

.

```
def headOption: Option[A] = foldRight(None: Option[A])((a, _) => Some(a))
```

If the list is empty, it returns `None`

, so this implementation is straightforward. The second argument `b`

is not evaluated, so the loop doesn't occur, and Stream is utilized properly.

Implement

`map`

,`filter`

,`append`

, and`flatMap`

using`foldRight`

.

I realized that the type specification for `Empty`

can be done in this way, which is convenient.

```
def map[B](f: A => B): Stream[B] =
foldRight(Empty: Stream[B])((a,b) => cons(f(a), b))
def filter(f: A => Boolean): Stream[A] =
foldRight(Empty: Stream[A])((a,b) => if(f(a)) cons(a, b) else b)
```

When I wrote it enthusiastically, I encountered a compile error for `append`

. It's a problem related to covariance and contravariance, which I didn't fully understand, so I had to rely on another site.

It's very easy to understand. I'm not sure if I can use it fluently, but I was able to avoid the variance check for now.

```
def append[B>:A](a: => Stream[B]): Stream[B] =
foldRight(a)((c,d) => cons(c, d))
def flatMap[B>:A](s: A => Stream[B]): Stream[B] =
foldRight(Empty: Stream[B])((a,b) => s(a).append(b))
```

By using these functions to process Stream, only the necessary parts are evaluated, and unnecessary instances are not generated. Even when processing heavy lists, it's very efficient.

```
st.map(---).filter(---)
st.filter(---).headOption
```

The order of loop application itself seems to change, so Stream is also called "first-class loop". It's also memory-friendly because the filtered-out elements and newly generated elements are immediately garbage-collected.

Next, I'll cover the basics of Stream and then move on to infinite streams, which are often cited as examples.

Create a function

`constant`

that generates an infinite stream of a specified value.

```
def constant[A](a: A): Stream[A] = cons(a, constant(a))
```

It's simple, but it's a bit wasteful to create a new `cons`

every time. A better approach is to create a lazy object and reuse it.

```
def constant2[A](a: A): Stream[A] = {
lazy val v: Stream[A] = Cons(() => a, () => v)
v
}
```

Create a function

`from`

that generates an infinite stream of`n`

,`n+1`

,`n+2`

, ...

```
def from(n: Int): Stream[Int] = cons(n, from(n+1))
```

Create a function

`fibs`

that generates a Fibonacci sequence stream.

```
def fibs(): Stream[Int] = {
def loop(i1: Int, i2: Int): Stream[Int] = cons(i2, loop(i1 + i2, i1))
loop(1, 0)
}
```

It's a common example.

Create a more general stream generation function

`unfold`

and use it to implement`fibs`

,`from`

,`constant`

, and`ones`

.

```
def u_fibs(): Stream[Int] =
unfold((0, 1))(a => Some(a._1, (a._2, a._1 + a._2)))
def u_fibs2(): Stream[Int] =
unfold((0, 1))(a => {
a match {
case (i1, i2) => Some(i1, (i2, i1 + i2))
}
})
def u_fibs3(): Stream[Int] =
unfold((0, 1)) { case (i1, i2) => Some(i1, (i2, i1 + i2)) }
def u_from(n: Int): Stream[Int] =
unfold(n)(s => Some(s, s + 1))
def u_constant(n: Int): Stream[Int] =
unfold(n)(s => Some(s, s))
def u_ones: Stream[Int] =
unfold(1)(s => Some(s, s))
```

There are three implementations of `fibs`

, but they're all the same. When separating variables, I can omit `match`

and write it more concisely.

Implement

`map`

,`take`

,`takeWhile`

,`zipWith`

, and`zipAll`

using`unfold`

.

```
def u_take(n: Int): Stream[A] =
unfold((this, n)) {
case (Cons(h, t), i) if i > 0 => Some(h(), (t(), i-1))
case _ => None
}
def u_takeWhile(f: A => Boolean): Stream[A] =
unfold(this) {
case Cons(h, t) if f(h()) => Some(h(), t())
case _ => None
}
def zipWith[B, C](l2: Stream[B])(f: (A, B) => C): Stream[C] = {
unfold((this, l2)) {
case (Cons(h1, t1), Cons(h2, t2)) => Some(f(h1(), h2()), (t1(), t2()))
case _ => None
}
}
def zipAll[B](l2: Stream[B]): Stream[(Option[A], Option[B])] = {
unfold((this, l2)) {
case (Empty, Cons(h2, t2)) => Some((None, Some(h2())), (Empty, t2()))
case (Cons(h1, t1), Empty) => Some((Some(h1()), None), (t1(), Empty))
case (Cons(h1, t1), Cons(h2, t2)) => Some((Some(h1()), Some(h2())), (t1(), t2()))
case _ => None
}
}
```

According to the answer, `zipAll`

returns `(Option[A], Option[B])`

, so I followed that.

Implement

`startsWith`

.

```
def startsWith[B](s: Stream[B]): Boolean =
zipAll(s).takeWhile(_._2.isDefined).forAll({
case (Some(a), Some(b)) => a == b
case _ => false
})
```

I paired the two streams and took the prefix part, then checked if all elements matched.

Implement

`tails`

using`unfold`

.

It seems like I can implement it by gradually reducing the stream. I need to explicitly append an empty stream.

```
def tails: Stream[Stream[A]] =
unfold(this) {
case Empty => None
case s => Some(s, s.drop(1))
}.append(Stream(empty))
```

Implement

`scanRight`

by generalizing`tails`

.

I didn't understand, so I checked the answer. It seems like it's generating a memoized variable and using `foldRight`

. It's strange that `unfold`

is not used here, even though it was used in `tails`

.

## Thoughts

I finally finished it. It looks light, but it's actually heavy. I still need to practice to master it, but it seems like the range of applications will expand greatly depending on whether I know it or not. It's essential for efficient processing, and it's said to improve modularity by separating description and evaluation.

There are many examples in the next chapter, and it seems like there's still a lot to learn.

Next: