I'm new to the language and trying to figure out how to read some of the code in it. Here is the example code that I'm trying to figure out:
lazy val genHeap: Gen[H] = for{
n <- arbitrary[A]
h <- frequency((1,value(empty)),(9,genHeap))
} yield insert(n,h)
I don't quite understand what is going on:
The return type is Gen?
Does the <- act as an = operator?
Is the yield statement building a heap with each iteration by inserting a new element?
Hello fellow Coursera student! The Principles of Reactive Programming Course is not exactly the easiest place to start to learn Scala! It is an advanced Scala course.
The type return is a Gen?
Yes, that's what the : means. (The Gen itself is an object, a random generator to be precise, which can produce a sequence of values, each having the same type as its type parameter - in this case, H.)
Does the <- act as an '=' operator?
Not exactly.
and the yield statement.. as I understand, it is building a heap with each iteration by inserting a new element?
Actually it's a recursion, not an iteration... but essentially, yes.
A for..yield expression is a fancy way to write a series of map, flatMap and withFilter invocations. Let's desugar it down into ordinary Scala code:
lazy val genHeap: Gen[H] = arbitrary[A].flatMap(n => frequency((1,value(empty)),(9,genHeap)).map(h => insert(n,h)))
So a H generator (genHeap) is one that starts by generating an arbitrary A, then generating an arbitrary H (an empty H with probability 0.1, or the result of invoking genHeap itself again with probability 0.9), and then inserting the A into the H to get a new H.
These As and Hs are both abstract types, by the way.
Yes, I'd say this is pretty advanced stuff. If you don't even know what : means, you're definitely starting in the wrong place.
Related
Based on the first comment in this discussion, it seems that Martin Odersky
sees no need for a 'times' method in scala.
suggests that for (_ <- 1 to 3) println is acceptable
Has anything changed on this since 2009 or is this still state-of-the-art in scala?
As an extension, does that mean that for (_ <- 1 to 3) yield math.random and/or (1 to 3).map(_ => math.random) are idiomatic ways of creating List-like objects?
Using Range is still the way to do it, though I would use foreach explicitly:
(1 to 3).foreach{println}
To fill a collection use tabulate or fill
val even = List.tabulate(10)(_*2)
val random = List.fill(10)(math.random)
fill takes a by-name parameter so it is evaluated for each new element in the collection.
I’ve been using Scala at work and to understand Functional Programming more deeply I picked Graham Hutton’s Programming in Haskell (love it :)
In the chapter on Monads I got my first look into the concept of Applicative Functors (AFs)
In my (limited) professional-Scala capacity I’ve never had to use AFs and have always written code that uses Monads. I’m trying to distill the understanding of “when to use AFs” and hence the question. Is this insight correct:
If all your computations are independent and parallelizable (i.e., the result of one doesn’t determine the output of another) your needs would be better served by an AF if the output needs to be piped to a pure function without effects. If however, you have even a single dependency AFs won’t help and you’ll be forced to use Monads. If the output needs to be piped to a function with effects (e.g., returning Maybe) you’ll need Monads.
For example, if you have “monadic” code like so:
val result = for {
x <- callServiceX(...)
y <- callServiceY(...) //not dependent on X
} yield f(x,y)
It’s better to do something like (pseudo-AF syntax for scala where |#| is like a separator between parallel/asynch calls).
val result = (callServiceX(...) |#| callServiceY(...)).f(_,_)
If f == pure and callService* are independent AFs will serve you better
If f has effects i.e., f(x,y): Option[Response] you’ll need Monads
If callServiceX(...), y <- callServiceY(...), callServiceZ(y) i.e., there is even a single dependency in the chain, use Monads.
Is my understanding correct? I know there’s a lot more to AFs/Monads and I believe I understand the advantages of one over the other (for the most part). What I want to know is the decision making process of deciding which one to use in a particular context.
There is not really a decision to be made here: always use the Applicative interface, unless it is too weak.1
It's the essential tension of abstraction strength: more computations can be expressed with Monad; computations expressed with Applicative can be used in more ways.
You seem to be mostly correct about the conditions where you need to use Monad. I'm not sure about this one:
If f has effects i.e. f(x,y) : Option[Response] you'll need Monads.
Not necessarily. What is the functor in question here? There is nothing stopping you from creating a F[Option[X]] if F is the applicative. But just as before you won't be able to make further decisions in F depending on whether the Option succeeded or not -- the whole "call tree" of F actions must be knowable without computing any values.
1 Readability concerns aside, that is. Monadic code will probably be more approachable to people from traditional backgrounds because of its imperative look.
I think you'll need to be a little cautious about terms like "independent" or "parallelizable" or "dependency". For example, in the IO monad, consider the computation:
foo :: IO (String, String)
foo = do
line1 <- getLine
line2 <- getLine
return (line1, line2)
The first and second lines are not independent or parallelizable in the usual sense. The second getLine's result is affected by the action of the first getLine through their shared external state (i.e., the first getLine reads a line, implying the second getLine will not read that same line but will rather read the next line). Nonetheless, this action is applicative:
foo = (,) <$> getLine <*> getLine
As a more realistic example, a monadic parser for the expression 3 + 4 might look like:
expr :: Parser Expr
expr = do
x <- factor
op <- operator
y <- factor
return $ x `op` y
The three actions here are interdependent. The success of the first factor parser determines whether or not the others will be run, and its behavior (e.g., how much of the input stream it absorbs) clearly affects the results of the other parsers. It would not be reasonable to consider these actions as operating "in parallel" or being "independent". Still, it's an applicative action:
expr = factor <**> operator <*> factor
Or, consider this State Int action:
bar :: Int -> Int -> State Int Int
bar x y = do
put (x + y)
z <- gets (2*)
return z
Clearly, the result of the gets (*2) action depends on the computation performed in the put (x + y) action. But, again, this is an applicative action:
bar x y = put (x + y) *> gets (2*)
I'm not sure that there's a really straightforward way of thinking about this intuitively. Roughly, if you think of a monadic action/computation m a as having "monadic structure" m as well as a "value structure" a, then applicatives keep the monadic and value structures separate. For example, the applicative computation:
λ> [(1+),(10+)] <*> [3,4,5]
[4,5,6,13,14,15]
has a monadic (list) structure whereby we always have:
[f,g] <*> [a,b,c] = [f a, f b, f c, g a, g b, g c]
regardless of the actual values involves. Therefore, the resulting list length is the product of the length of both "input" lists, the first element of the result involves the first elements of the "input" lists, etc. It also has a value structure whereby the value 4 in the result clearly depends on the value (1+) and the value 3 in the inputs.
A monadic computation, on the other hand, permits a dependency of the monadic structure on the value structure, so for example in:
quux :: [Int]
quux = do
n <- [1,2,3]
drop n [10..15]
we can't write down the structural list computation independent of the values. The list structure (e.g., the length of the final list) is dependent on the value level data (the actual values in the list [1,2,3]). This is the kind of dependency that requires a monad instead of an applicative.
Consider the following composition
for {
v1 <- transform1(v)
v2 <- transform2(v1)
v3 <- transformThatErrors(v2)
v4 <- transfrom4(v3)
} yield { v4 }
Is there a monad M that would allow for the above to evaluate to M(v2)?
I am trying to model a situation where the program should apply the full chain of transformations until the first transformation that fails, in which case the chain evaluates to the last successful transformation. In the worst case, the whole chain represents identity(v).
Monads like Either and Option do not fit this requirement because on an error they evaluate the whole chain to an error, while it is required for the chain to always evaluate to success. In other words, I would like the program to try to do as much as it can, but if it cannot do anything, that is fine too.
The Either monad does exactly what you want. Nothing in the interface of Either forces you to use different types for Left and Right case. In particular, the Left type parameter can be the same as the Right type parameter, they both can equal to something like Result (or "PartialSuccess"?), where you define what constitutes a Result.
Thus, you simply declare all your transformN functions to have return type
def transformN(previousStep: Result): Either[Result, Result] = ???
and in the very end, you fold it into a single result:
val res: Result = (for {
v1 <- transform1(v)
v2 <- transform2(v1)
v3 <- transformThatErrors(v2)
v4 <- transfrom4(v3)
} yield v4).fold(
partialRes => partialRes,
completeRes => completeRes
)
or even just
.fold(identity, identity)
As soon as the first transformation fails, the Either will package the partial result as a Left, and return it, without applying any further transformations. If every single transformation step succeeds, the very final result will be returned as Right. No matter at which point the transformation stops, the final fold will extract the (partial) result out of it.
If I understand it correctly, every other monad M you could possibly come up with, would be essentially the same as Either[Result, Result] with some special getResult method that is equivalent to .fold(identity, identity), so there is no need to multiply entities unnecessarily.
So in reading this question it was pointed out that instead of the procedural code:
def expand(exp: String, replacements: Traversable[(String, String)]): String = {
var result = exp
for ((oldS, newS) <- replacements)
result = result.replace(oldS, newS)
result
}
You could write the following functional code:
def expand(exp: String, replacements: Traversable[(String, String)]): String = {
replacements.foldLeft(exp){
case (result, (oldS, newS)) => result.replace(oldS, newS)
}
}
I would almost certainly write the first version because coders familiar with either procedural or functional styles can easily read and understand it, while only coders familiar with functional style can easily read and understand the second version.
But setting readability aside for the moment, is there something that makes foldLeft a better choice than the procedural version? I might have thought it would be more efficient, but it turns out that the implementation of foldLeft is actually just the procedural code above. So is it just a style choice, or is there a good reason to use one version or the other?
Edit: Just to be clear, I'm not asking about other functions, just foldLeft. I'm perfectly happy with the use of foreach, map, filter, etc. which all map nicely onto for-comprehensions.
Answer: There are really two good answers here (provided by delnan and Dave Griffith) even though I could only accept one:
Use foldLeft because there are additional optimizations, e.g. using a while loop which will be faster than a for loop.
Use fold if it ever gets added to regular collections, because that will make the transition to parallel collections trivial.
It's shorter and clearer - yes, you need to know what a fold is to understand it, but when you're programming in a language that's 50% functional, you should know these basic building blocks anyway. A fold is exactly what the procedural code does (repeatedly applying an operation), but it's given a name and generalized. And while it's only a small wheel you're reinventing, but it's still a wheel reinvention.
And in case the implementation of foldLeft should ever get some special perk - say, extra optimizations - you get that for free, without updating countless methods.
Other than a distaste for mutable variable (even mutable locals), the basic reason to use fold in this case is clarity, with occasional brevity. Most of the wordiness of the fold version is because you have to use an explicit function definition with a destructuring bind. If each element in the list is used precisely once in the fold operation (a common case), this can be simplified to use the short form. Thus the classic definition of the sum of a collection of numbers
collection.foldLeft(0)(_+_)
is much simpler and shorter than any equivalent imperative construct.
One additional meta-reason to use functional collection operations, although not directly applicable in this case, is to enable a move to using parallel collection operations if needed for performance. Fold can't be parallelized, but often fold operations can be turned into commutative-associative reduce operations, and those can be parallelized. With Scala 2.9, changing something from non-parallel functional to parallel functional utilizing multiple processing cores can sometimes be as easy as dropping a .par onto the collection you want to execute parallel operations on.
One word I haven't seen mentioned here yet is declarative:
Declarative programming is often defined as any style of programming that is not imperative. A number of other common definitions exist that attempt to give the term a definition other than simply contrasting it with imperative programming. For example:
A program that describes what computation should be performed and not how to compute it
Any programming language that lacks side effects (or more specifically, is referentially transparent)
A language with a clear correspondence to mathematical logic.
These definitions overlap substantially.
Higher-order functions (HOFs) are a key enabler of declarativity, since we only specify the what (e.g. "using this collection of values, multiply each value by 2, sum the result") and not the how (e.g. initialize an accumulator, iterate with a for loop, extract values from the collection, add to the accumulator...).
Compare the following:
// Sugar-free Scala (Still better than Java<5)
def sumDoubled1(xs: List[Int]) = {
var sum = 0 // Initialized correctly?
for (i <- 0 until xs.size) { // Fenceposts?
sum = sum + (xs(i) * 2) // Correct value being extracted?
// Value extraction and +/* smashed together
}
sum // Correct value returned?
}
// Iteration sugar (similar to Java 5)
def sumDoubled2(xs: List[Int]) = {
var sum = 0
for (x <- xs) // We don't need to worry about fenceposts or
sum = sum + (x * 2) // value extraction anymore; that's progress
sum
}
// Verbose Scala
def sumDoubled3(xs: List[Int]) = xs.map((x: Int) => x*2). // the doubling
reduceLeft((x: Int, y: Int) => x+y) // the addition
// Idiomatic Scala
def sumDoubled4(xs: List[Int]) = xs.map(_*2).reduceLeft(_+_)
// ^ the doubling ^
// \ the addition
Note that our first example, sumDoubled1, is already more declarative than (most would say superior to) C/C++/Java<5 for loops, because we haven't had to micromanage the iteration state and termination logic, but we're still vulnerable to off-by-one errors.
Next, in sumDoubled2, we're basically at the level of Java>=5. There are still a couple things that can go wrong, but we're getting pretty good at reading this code-shape, so errors are quite unlikely. However, don't forget that a pattern that's trivial in a toy example isn't always so readable when scaled up to production code!
With sumDoubled3, desugared for didactic purposes, and sumDoubled4, the idiomatic Scala version, the iteration, initialization, value extraction and choice of return value are all gone.
Sure, it takes time to learn to read the functional versions, but we've drastically foreclosed our options for making mistakes. The "business logic" is clearly marked, and the plumbing is chosen from the same menu that everyone else is reading from.
It is worth pointing out that there is another way of calling foldLeft which takes advantages of:
The ability to use (almost) any Unicode symbol in an identifier
The feature that if a method name ends with a colon :, and is called infix, then the target and parameter are switched
For me this version is much clearer, because I can see that I am folding the expr value into the replacements collection
def expand(expr: String, replacements: Traversable[(String, String)]): String = {
(expr /: replacements) { case (r, (o, n)) => r.replace(o, n) }
}
I'm pretty new to Scala and most of the time before I've used Java. Right now I have warnings all over my code saying that i should "Avoid mutable local variables" and I have a simple question - why?
Suppose I have small problem - determine max int out of four. My first approach was:
def max4(a: Int, b: Int,c: Int, d: Int): Int = {
var subMax1 = a
if (b > a) subMax1 = b
var subMax2 = c
if (d > c) subMax2 = d
if (subMax1 > subMax2) subMax1
else subMax2
}
After taking into account this warning message I found another solution:
def max4(a: Int, b: Int,c: Int, d: Int): Int = {
max(max(a, b), max(c, d))
}
def max(a: Int, b: Int): Int = {
if (a > b) a
else b
}
It looks more pretty, but what is ideology behind this?
Whenever I approach a problem I'm thinking about it like: "Ok, we start from this and then we incrementally change things and get the answer". I understand that the problem is that I try to change some initial state to get an answer and do not understand why changing things at least locally is bad? How to iterate over collection then in functional languages like Scala?
Like an example: Suppose we have a list of ints, how to write a function that returns sublist of ints which are divisible by 6? Can't think of solution without local mutable variable.
In your particular case there is another solution:
def max4(a: Int, b: Int,c: Int, d: Int): Int = {
val submax1 = if (a > b) a else b
val submax2 = if (c > d) c else d
if (submax1 > submax2) submax1 else submax2
}
Isn't it easier to follow? Of course I am a bit biased but I tend to think it is, BUT don't follow that rule blindly. If you see that some code might be written more readably and concisely in mutable style, do it this way -- the great strength of scala is that you don't need to commit to neither immutable nor mutable approaches, you can swing between them (btw same applies to return keyword usage).
Like an example: Suppose we have a list of ints, how to write a
function that returns the sublist of ints which are divisible by 6?
Can't think of solution without local mutable variable.
It is certainly possible to write such function using recursion, but, again, if mutable solution looks and works good, why not?
It's not so related with Scala as with the functional programming methodology in general. The idea is the following: if you have constant variables (final in Java), you can use them without any fear that they are going to change. In the same way, you can parallelize your code without worrying about race conditions or thread-unsafe code.
In your example is not so important, however imagine the following example:
val variable = ...
new Future { function1(variable) }
new Future { function2(variable) }
Using final variables you can be sure that there will not be any problem. Otherwise, you would have to check the main thread and both function1 and function2.
Of course, it's possible to obtain the same result with mutable variables if you do not ever change them. But using inmutable ones you can be sure that this will be the case.
Edit to answer your edit:
Local mutables are not bad, that's the reason you can use them. However, if you try to think approaches without them, you can arrive to solutions as the one you posted, which is cleaner and can be parallelized very easily.
How to iterate over collection then in functional languages like Scala?
You can always iterate over a inmutable collection, while you do not change anything. For example:
val list = Seq(1,2,3)
for (n <- list)
println n
With respect to the second thing that you said: you have to stop thinking in a traditional way. In functional programming the usage of Map, Filter, Reduce, etc. is normal; as well as pattern matching and other concepts that are not typical in OOP. For the example you give:
Like an example: Suppose we have a list of ints, how to write a function that returns sublist of ints which are divisible by 6?
val list = Seq(1,6,10,12,18,20)
val result = list.filter(_ % 6 == 0)
Firstly you could rewrite your example like this:
def max(first: Int, others: Int*): Int = {
val curMax = Math.max(first, others(0))
if (others.size == 1) curMax else max(curMax, others.tail : _*)
}
This uses varargs and tail recursion to find the largest number. Of course there are many other ways of doing the same thing.
To answer your queston - It's a good question and one that I thought about myself when I first started to use scala. Personally I think the whole immutable/functional programming approach is somewhat over hyped. But for what it's worth here are the main arguments in favour of it:
Immutable code is easier to read (subjective)
Immutable code is more robust - it's certainly true that changing mutable state can lead to bugs. Take this for example:
for (int i=0; i<100; i++) {
for (int j=0; j<100; i++) {
System.out.println("i is " + i = " and j is " + j);
}
}
This is an over simplified example but it's still easy to miss the bug and the compiler won't help you
Mutable code is generally not thread safe. Even trivial and seemingly atomic operations are not safe. Take for example i++ this looks like an atomic operation but it's actually equivalent to:
int i = 0;
int tempI = i + 0;
i = tempI;
Immutable data structures won't allow you to do something like this so you would need to explicitly think about how to handle it. Of course as you point out local variables are generally threadsafe, but there is no guarantee. It's possible to pass a ListBuffer instance variable as a parameter to a method for example
However there are downsides to immutable and functional programming styles:
Performance. It is generally slower in both compilation and runtime. The compiler must enforce the immutability and the JVM must allocate more objects than would be required with mutable data structures. This is especially true of collections.
Most scala examples show something like val numbers = List(1,2,3) but in the real world hard coded values are rare. We generally build collections dynamically (from a database query etc). Whilst scala can reassign the values in a colection it must still create a new collection object every time you modify it. If you want to add 1000 elements to a scala List (immutable) the JVM will need to allocate (and then GC) 1000 objects
Hard to maintain. Functional code can be very hard to read, it's not uncommon to see code like this:
val data = numbers.foreach(_.map(a => doStuff(a).flatMap(somethingElse)).foldleft("", (a : Int,b: Int) => a + b))
I don't know about you but I find this sort of code really hard to follow!
Hard to debug. Functional code can also be hard to debug. Try putting a breakpoint halfway into my (terrible) example above
My advice would be to use a functional/immutable style where it genuinely makes sense and you and your colleagues feel comfortable doing it. Don't use immutable structures because they're cool or it's "clever". Complex and challenging solutions will get you bonus points at Uni but in the commercial world we want simple solutions to complex problems! :)
Your two main questions:
Why warn against local state changes?
How can you iterate over collections without mutable state?
I'll answer both.
Warnings
The compiler warns against the use of mutable local variables because they are often a cause of error. That doesn't mean this is always the case. However, your sample code is pretty much a classic example of where mutable local state is used entirely unnecessarily, in a way that not only makes it more error prone and less clear but also less efficient.
Your first code example is more inefficient than your second, functional solution. Why potentially make two assignments to submax1 when you only ever need to assign one? You ask which of the two inputs is larger anyway, so why not ask that first and then make one assignment? Why was your first approach to temporarily store partial state only halfway through the process of asking such a simple question?
Your first code example is also inefficient because of unnecessary code duplication. You're repeatedly asking "which is the biggest of two values?" Why write out the code for that 3 times independently? Needlessly repeating code is a known bad habit in OOP every bit as much as FP and for precisely the same reasons. Each time you needlessly repeat code, you open a potential source of error. Adding mutable local state (especially when so unnecessary) only adds to the fragility and to the potential for hard to spot errors, even in short code. You just have to type submax1 instead of submax2 in one place and you may not notice the error for a while.
Your second, FP solution removes the code duplication, dramatically reducing the chance of error, and shows that there was simply no need for mutable local state. It's also, as you yourself say, cleaner and clearer - and better than the alternative solution in om-nom-nom's answer.
(By the way, the idiomatic Scala way to write such a simple function is
def max(a: Int, b: Int) = if (a > b) a else b
which terser style emphasises its simplicity and makes the code less verbose)
Your first solution was inefficient and fragile, but it was your first instinct. The warning caused you to find a better solution. The warning proved its value. Scala was designed to be accessible to Java developers and is taken up by many with a long experience of imperative style and little or no knowledge of FP. Their first instinct is almost always the same as yours. You have demonstrated how that warning can help improve code.
There are cases where using mutable local state can be faster but the advice of Scala experts in general (not just the pure FP true believers) is to prefer immutability and to reach for mutability only where there is a clear case for its use. This is so against the instincts of many developers that the warning is useful even if annoying to experienced Scala devs.
It's funny how often some kind of max function comes up in "new to FP/Scala" questions. The questioner is very often tripping up on errors caused by their use of local state... which link both demonstrates the often obtuse addiction to mutable state among some devs while also leading me on to your other question.
Functional Iteration over Collections
There are three functional ways to iterate over collections in Scala
For Comprehensions
Explicit Recursion
Folds and other Higher Order Functions
For Comprehensions
Your question:
Suppose we have a list of ints, how to write a function that returns sublist of ints which are divisible by 6? Can't think of solution without local mutable variable
Answer: assuming xs is a list (or some other sequence) of integers, then
for (x <- xs; if x % 6 == 0) yield x
will give you a sequence (of the same type as xs) containing only those items which are divisible by 6, if any. No mutable state required. Scala just iterates over the sequence for you and returns anything matching your criteria.
If you haven't yet learned the power of for comprehensions (also known as sequence comprehensions) you really should. Its a very expressive and powerful part of Scala syntax. You can even use them with side effects and mutable state if you want (look at the final example on the tutorial I just linked to). That said, there can be unexpected performance penalties and they are overused by some developers.
Explicit Recursion
In the question I linked to at the end of the first section, I give in my answer a very simple, explicitly recursive solution to returning the largest Int from a list.
def max(xs: List[Int]): Option[Int] = xs match {
case Nil => None
case List(x: Int) => Some(x)
case x :: y :: rest => max( (if (x > y) x else y) :: rest )
}
I'm not going to explain how the pattern matching and explicit recursion work (read my other answer or this one). I'm just showing you the technique. Most Scala collections can be iterated over recursively, without any need for mutable state. If you need to keep track of what you've been up to along the way, you pass along an accumulator. (In my example code, I stick the accumulator at the front of the list to keep the code smaller but look at the other answers to those questions for more conventional use of accumulators).
But here is a (naive) explicitly recursive way of finding those integers divisible by 6
def divisibleByN(n: Int, xs: List[Int]): List[Int] = xs match {
case Nil => Nil
case x :: rest if x % n == 0 => x :: divisibleByN(n, rest)
case _ :: rest => divisibleByN(n, rest)
}
I call it naive because it isn't tail recursive and so could blow your stack. A safer version can be written using an accumulator list and an inner helper function but I leave that exercise to you. The result will be less pretty code than the naive version, no matter how you try, but the effort is educational.
Recursion is a very important technique to learn. That said, once you have learned to do it, the next important thing to learn is that you can usually avoid using it explicitly yourself...
Folds and other Higher Order Functions
Did you notice how similar my two explicit recursion examples are? That's because most recursions over a list have the same basic structure. If you write a lot of such functions, you'll repeat that structure many times. Which makes it boilerplate; a waste of your time and a potential source of error.
Now, there are any number of sophisticated ways to explain folds but one simple concept is that they take the boilerplate out of recursion. They take care of the recursion and the management of accumulator values for you. All they ask is that you provide a seed value for the accumulator and the function to apply at each iteration.
For example, here is one way to use fold to extract the highest Int from the list xs
xs.tail.foldRight(xs.head) {(a, b) => if (a > b) a else b}
I know you aren't familiar with folds, so this may seem gibberish to you but surely you recognise the lambda (anonymous function) I'm passing in on the right. What I'm doing there is taking the first item in the list (xs.head) and using it as the seed value for the accumulator. Then I'm telling the rest of the list (xs.tail) to iterate over itself, comparing each item in turn to the accumulator value.
This kind of thing is a common case, so the Collections api designers have provided a shorthand version:
xs.reduce {(a, b) => if (a > b) a else b}
(If you look at the source code, you'll see they have implemented it using a fold).
Anything you might want to do iteratively to a Scala collection can be done using a fold. Often, the api designers will have provided a simpler higher-order function which is implemented, under the hood, using a fold. Want to find those divisible-by-six Ints again?
xs.foldRight(Nil: List[Int]) {(x, acc) => if (x % 6 == 0) x :: acc else acc}
That starts with an empty list as the accumulator, iterates over every item, only adding those divisible by 6 to the accumulator. Again, a simpler fold-based HoF has been provided for you:
xs filter { _ % 6 == 0 }
Folds and related higher-order functions are harder to understand than for comprehensions or explicit recursion, but very powerful and expressive (to anybody else who understands them). They eliminate boilerplate, removing a potential source of error. Because they are implemented by the core language developers, they can be more efficient (and that implementation can change, as the language progresses, without breaking your code). Experienced Scala developers use them in preference to for comprehensions or explicit recursion.
tl;dr
Learn For comprehensions
Learn explicit recursion
Don't use them if a higher-order function will do the job.
It is always nicer to use immutable variables since they make your code easier to read. Writing a recursive code can help solve your problem.
def max(x: List[Int]): Int = {
if (x.isEmpty == true) {
0
}
else {
Math.max(x.head, max(x.tail))
}
}
val a_list = List(a,b,c,d)
max_value = max(a_list)