I'm coming from a JS background. In JS I could write something as follows:
let x = [[1, 0], [2, 1], [3, 2], [4, 3]]
x.forEach(([n, i]) => console.log())
So I was trying to convert to Scala, and I found a bunch of ways to do it. But I don't understand how the match and case statement are disappearing.
val x = Array(1, 2, 3, 4).zipWithIndex
// does what I expect
x.foreach((a) => {
println(a)
})
// uses match
x.foreach((a) => {
a match {
case (n, i) => println(s"$n $i")
}
})
// gets rid of redundant variable name
x.foreach({
_ match {
case (n, i) => println(s"$n $i")
}
})
// gets rid of unnecesary scope
x.foreach(_ match {
case (n, i) => println(s"$n $i")
})
Up to here, it makes sense. The below code I found online when looking how to loop with index.
// where did `match` go?
x.foreach({
case (n, i) => println(s"$n $i")
})
// and now `case` is gone too?
x.foreach((n, i) => println(s"$n $i"))
What is going on here? I would call it destructuring coming from JS, but this seems like a hidden/implicit match/case statement. Are there rules around that? How do I know if there should be an implicit match/case statement?
// where did `match` go?
x.foreach({
case (n, i) => println(s"$n $i")
})
This is a Pattern Matching Anonymous Function, also sometimes called a Partial Function Literal. See Scala Language Specification 8.5 Pattern Matching Anonymous Functions for all the gory details. Simply put, the expression
{
case p1 => e1
case p2 => e2
// …
case pn => en
}
is equivalent to
(x1: S1, x2: S2, /* … */, xn: Sn) => (x1, x2, /* … */, xn) match {
case p1 => e1
case p2 => e2
// …
case pn => en
}
provided that the result type is SAM-convertible to FunctionN[S1, S2, /* … */, Sn, R], or as a special case PartialFunction1[S1, R] (which is where the name Partial Function Literal comes from.)
// and now `case` is gone too?
x.foreach((n, i) => println(s"$n $i"))
This is a new feature of Scala 3. For a very long time, the Scala Designers wanted to unify Tuples and Argument Lists. In other words, they wanted to make it so that methods in Scala only ever take one argument, and that argument is a tuple. Unfortunately, it turned out that a) this massively breaks backwards-compatibility and b) massively breaks platform interoperability.
Now, Scala 3 was an opportunity to ignore problem a), but you cannot ignore problem b) since one of the major design goals of Scala is to have seamless, tight, good, performant integration with the underlying host platform (e.g. .NET in the case of the now-abandoned Scala.NET, the ECMASCript / HTML5 / DOM / WebAPI platform in the case of Scala.js, the native Operating System in the case of Scala-native, or the Java platform (JRE, JDK, JVM, J2SE, J2EE, Java, Kotlin, Clojure, etc.) in the case of Scala-JVM).
However, the Scala designers managed to find a compromise, where arguments and tuples are not the same thing, but parameters can be easily converted to tuples and tuples can be easily converted to arguments.
This is called Parameter Untupling, and it basically means that a function of type FunctionN[S1, S2, /* … */, Sn, R] can be automatically converted to a function of type Function1[(S1, S2, /* … */, Sn), R] which is syntactic sugar for Function1[TupleN[S1, S2, /* … */, Sn], R].
Simply put,
(p1: S1, p2: S2, /* … */, pn: Sn) => e: R
can automatically be converted to
(x: (S1, S2, /* … */, Sn)) => {
val p1: S1 = x._1
val p2: S2 = x._2
// …
val pn: Sn = x._n
e
}
Note: unfortunately, there is no comprehensive specification of Scala 3 yet. There is a partial Language Reference, which however only describes differences to Scala 2. So, you typically have to bounce back and forth between the SLS and the Scala 3 docs.
About match keyword:
// where did `match` go?
x.foreach({
case (n, i) => println(s"$n $i")
})
This is the language specification, you can ignore match keyword in anonymous functions: https://scala-lang.org/files/archive/spec/2.13/08-pattern-matching.html#pattern-matching-anonymous-functions
Related
I am composing function literals, though unlike most examples I've seen I'm starting with a multi-argument function that is then curried.
I have:
//types
case class Thing1(v: Double)
case class Thing2(v: Double)
case class Thing3(v: Double)
type Multiplier = Double
//functions
val f1 = (t: Thing1, m: Multiplier) => Thing2(m * t.v)
val f2 = (t: Thing2) => Thing3(t.v)
I want to compose f1 and f2 to get a combined function
Thing1 => (Multiplier => Thing3)
As expected, the following doesn't compile:
val fcomposed1 = f1.curried.andThen(f2) // does not compile
By experimentation, I was able to work out that the following does compile and has the right signature for fcomposed:
val fcomposed2 = f1.curried(_:Thing1).andThen(f2)
I've read various sources like What are all the uses of an underscore in Scala? and possibly relevant Why does Scala apply thunks automatically, sometimes? but unfortunately I still cannot work out exactly step-by-step what is happening here and why it works.
Furthermore, I would expect the above separated into two expressions to work identically to fcomposed2, however instead the second does not compile:
val f1partial = f1.curried(_:Thing1)
val fcomposed3 = f1partial.andThen(f2) // does not compile - same error as fcomposed1
Looks like f1partial returns the same signature as f1.curried, which makes me wonder further how the earlier fcomposed2 works.
Could someone please explain both behaviours step by step?
Here, the _ is acting as syntactical sugar for a lambda expression, but at a level you might not expect.
f1.curried has type Thing1 => Multiplier => Thing2
f1.curried(_:Thing1) is the same as { x: Thing1 => f1.curried(x) }. Since the result of f1.curried(x) has type Multiplier => Thing2, the final type of the whole expression is still Thing1 => Multiplier => Thing2. So it is not valid to call andThen(f2) on the result (f1partial) because the input type of function f2 (Thing2) is not the same as the output of the previous function (Multiplier => Thing2).
By contrast, f1.curried(_:Thing1).andThen(f2) expands to { x: Thing1 => f1.curried(x).andThen(f2) }. f1.curried(x) evaluates to type Multiplier => Thing2, like stated earlier, so you can call andThen(f2) on that, resulting in a Multiplier => Thing3. So then the entire expression evaluates to a Thing1 => Multiplier => Thing3
Perhaps it's more clear if you think about the differences between these two expressions:
val fcomposed1 = { x: Thing1 => f1.curried(x).andThen(f2) } // valid
val fcomposed2 = { x: Thing1 => f1.curried(x) }.andThen(f2) // error
I have superficially read a couple of blog articles/Wikipedia about continuation-passing style. My high-level goal is to find a systematic technique to make any recursive function (or, if there are restrictions, being aware of them) tail-recursive. However, I have trouble articulating my thoughts and I'm not sure if what my attempts of it make any sense.
For the purpose of the example, I'll propose a simple problem. The goal is, given a sorted list of unique characters, to output all possible words made out of these characters in alphabetical order. For example, sol("op".toList, 3) should return ooo,oop,opo,opp,poo,pop,ppo,ppp.
My recursive solution is the following:
def sol(chars: List[Char], n: Int) = {
def recSol(n: Int): List[List[Char]] = (chars, n) match {
case (_ , 0) => List(Nil)
case (Nil, _) => Nil
case (_ , _) =>
val tail = recSol(n - 1)
chars.map(ch => tail.map(ch :: _)).fold(Nil)(_ ::: _)
}
recSol(n).map(_.mkString).mkString(",")
}
I did try to rewrite this by adding a function as a parameter but I did not manage to make something I was convinced to be tail-recursive. I prefer not including my attempt(s) in the question as I'm ashamed of their naiveness, so please excuse me for this.
Therefore the question is basically: how would the function above be written in CPS ?
Try that:
import scala.annotation.tailrec
def sol(chars: List[Char], n: Int) = {
#tailrec
def recSol(n: Int)(cont: (List[List[Char]]) => List[List[Char]]): List[List[Char]] = (chars, n) match {
case (_ , 0) => cont(List(Nil))
case (Nil, _) => cont(Nil)
case (_ , _) =>
recSol(n-1){ tail =>
cont(chars.map(ch => tail.map(ch :: _)).fold(Nil)(_ ::: _))
}
}
recSol(n)(identity).map(_.mkString).mkString(",")
}
The first order of business in performing the CPS transform is deciding on a representation for continuations. We can think of continuations as a suspended computation with a "hole". When the hole is filled in with a value, the remainder of the computation can be computed. So functions are a natural choice for representing continuations, at least for toy examples:
type Cont[Hole,Result] = Hole => Result
Here Hole represents the type of the hole that needs to be filled in, and Result represents the type of value the computation ultimately computes.
Now that we have a way to represent continuations, we can worry about the CPS transform itself. Basically, this involves the following steps:
The transformation is applied recursively to an expression, stopping at "trivial" expressions / function calls. In this context, "trivial" includes functions defined by Scala (since they are not CPS-transformed, and thus do not have a continuation parameter).
We need to add a parameter of type Cont[Return,Result] to each function, where Return is the return type of the untransformed function and Result is the type of the ultimate result of the computation as a whole. This new parameter represents the current continuation. The return type for the transformed function is also changed to Result.
Every function call needs to be transformed to accommodate the new continuation parameter. Everything after the call needs to be put into a continuation function, which is then added to the parameter list.
For example, a function:
def f(x : Int) : Int = x + 1
becomes:
def fCps[Result](x : Int)(k : Cont[Int,Result]) : Result = k(x + 1)
and
def g(x : Int) : Int = 2 * f(x)
becomes:
def gCps[Result](x : Int)(k : Cont[Int,Result]) : Result = {
fCps(x)(y => k(2 * y))
}
Now gCps(5) returns (via currying) a function that represents a partial computation. We can extract the value from this partial computation and use it by supplying a continuation function. For example, we can use the identity function to extract the value unchanged:
gCps(5)(x => x)
// 12
Or, we can print it by using println instead:
gCps(5)(println)
// prints 12
Applying this to your code, we obtain:
def solCps[Result](chars : List[Char], n : Int)(k : Cont[String, Result]) : Result = {
#scala.annotation.tailrec
def recSol[Result](n : Int)(k : Cont[List[List[Char]], Result]) : Result = (chars, n) match {
case (_ , 0) => k(List(Nil))
case (Nil, _) => k(Nil)
case (_ , _) =>
recSol(n - 1)(tail =>
k(chars.map(ch => tail.map(ch :: _)).fold(Nil)(_ ::: _)))
}
recSol(n)(result =>
k(result.map(_.mkString).mkString(",")))
}
As you can see, although recSol is now tail-recursive, it comes with the cost of building a more complex continuation at each iteration. So all we've really done is trade space on the JVM's control stack for space on the heap -- the CPS transform does not magically reduce the space complexity of an algorithm.
Also, recSol is only tail-recursive because the recursive call to recSol happens to be the first (non-trivial) expression recSol performs. In general, though, recursive calls would be take place inside a continuation. In the case where there is one recursive call, we can work around that by transforming only calls to the recursive function to CPS. Even so, in general, we would still just be trading stack space for heap space.
I find myself constantly doing things like the following:
val adjustedActions = actions.scanLeft((1.0, null: CorpAction)){
case ((runningSplitAdj, _), action) => action match {
case Dividend(date, amount) =>
(runningSplitAdj, Dividend(date, amount * runningSplitAdj))
case s # Split(date, sharesForOne) =>
((runningSplitAdj * sharesForOne), s)
}
}
.drop(1).map(_._2)
Where I need to accumulate the runningSplitAdj, in this case, in order to correct the dividends in the actions list. Here, I use scan to maintain the state that I need in order to correct the actions, but in the end, I only need the actions. Hence, I need to use null for the initial action in the state, but in the end, drop that item and map away all the states.
Is there a more elegant way of structuring these? In the context of RxScala Observables, I actually made a new operator to do this (after some help from the RxJava mailing list):
implicit class ScanMappingObs[X](val obs: Observable[X]) extends AnyVal {
def scanMap[S,Y](f: (X,S) => (Y,S), s0: S): Observable[Y] = {
val y0: Y = null.asInstanceOf[Y]
// drop(1) because scan also emits initial state
obs.scan((y0, s0)){case ((y, s), x) => f(x, s)}.drop(1).map(_._1)
}
}
However, now I find myself doing it to Lists and Vectors too, so I wonder if there is something more general I can do?
The combinator you're describing (or at least something very similar) is often called mapAccum. Take the following simplified use of scanLeft:
val xs = (1 to 10).toList
val result1 = xs.scanLeft((1, 0.0)) {
case ((acc, _), i) => (acc + i, i.toDouble / acc)
}.tail.map(_._2)
This is equivalent to the following (which uses Scalaz's implementation of mapAccumLeft):
xs.mapAccumLeft[Double, Int](1, {
case (acc, i) => (acc + i, i.toDouble / acc)
})._2
mapAccumLeft returns a pair of the final state and a sequence of the results at each step, but it doesn't require you to specify a spurious initial result (that will just be ignored and then dropped), and you don't have to map over the entire collection to get rid of the state—you just take the second member of the pair.
Unfortunately mapAccumLeft isn't available in the standard library, but if you're looking for a name or for ideas about implementation, this is a place to start.
I found myself writing something like this quite often:
a match {
case `b` => // do stuff
case _ => // do nothing
}
Is there a shorter way to check if some value matches a pattern? I mean, in this case I could just write if (a == b) // do stuff, but what if the pattern is more complex? Like when matching against a list or any pattern of arbitrary complexity. I'd like to be able to write something like this:
if (a matches b) // do stuff
I'm relatively new to Scala, so please pardon, if I'm missing something big :)
This is exactly why I wrote these functions, which are apparently impressively obscure since nobody has mentioned them.
scala> import PartialFunction._
import PartialFunction._
scala> cond("abc") { case "def" => true }
res0: Boolean = false
scala> condOpt("abc") { case x if x.length == 3 => x + x }
res1: Option[java.lang.String] = Some(abcabc)
scala> condOpt("abc") { case x if x.length == 4 => x + x }
res2: Option[java.lang.String] = None
The match operator in Scala is most powerful when used in functional style. This means, rather than "doing something" in the case statements, you would return a useful value. Here is an example for an imperative style:
var value:Int = 23
val command:String = ... // we get this from somewhere
command match {
case "duplicate" => value = value * 2
case "negate" => value = -value
case "increment" => value = value + 1
// etc.
case _ => // do nothing
}
println("Result: " + value)
It is very understandable that the "do nothing" above hurts a little, because it seems superflous. However, this is due to the fact that the above is written in imperative style. While constructs like these may sometimes be necessary, in many cases you can refactor your code to functional style:
val value:Int = 23
val command:String = ... // we get this from somewhere
val result:Int = command match {
case "duplicate" => value * 2
case "negate" => -value
case "increment" => value + 1
// etc.
case _ => value
}
println("Result: " + result)
In this case, you use the whole match statement as a value that you can, for example, assign to a variable. And it is also much more obvious that the match statement must return a value in any case; if the last case would be missing, the compiler could not just make something up.
It is a question of taste, but some developers consider this style to be more transparent and easier to handle in more real-world examples. I would bet that the inventors of the Scala programming language had a more functional use in mind for match, and indeed the if statement makes more sense if you only need to decide whether or not a certain action needs to be taken. (On the other hand, you can also use if in the functional way, because it also has a return value...)
This might help:
class Matches(m: Any) {
def matches[R](f: PartialFunction[Any, R]) { if (f.isDefinedAt(m)) f(m) }
}
implicit def any2matches(m: Any) = new Matches(m)
scala> 'c' matches { case x: Int => println("Int") }
scala> 2 matches { case x: Int => println("Int") }
Int
Now, some explanation on the general nature of the problem.
Where may a match happen?
There are three places where pattern matching might happen: val, case and for. The rules for them are:
// throws an exception if it fails
val pattern = value
// filters for pattern, but pattern cannot be "identifier: Type",
// though that can be replaced by "id1 # (id2: Type)" for the same effect
for (pattern <- object providing map/flatMap/filter/withFilter/foreach) ...
// throws an exception if none of the cases match
value match { case ... => ... }
There is, however, another situation where case might appear, which is function and partial function literals. For example:
val f: Any => Unit = { case i: Int => println(i) }
val pf: PartialFunction[Any, Unit] = { case i: Int => println(i) }
Both functions and partial functions will throw an exception if called with an argument that doesn't match any of the case statements. However, partial functions also provide a method called isDefinedAt which can test whether a match can be made or not, as well as a method called lift, which will turn a PartialFunction[T, R] into a Function[T, Option[R]], which means non-matching values will result in None instead of throwing an exception.
What is a match?
A match is a combination of many different tests:
// assign anything to x
case x
// only accepts values of type X
case x: X
// only accepts values matches by pattern
case x # pattern
// only accepts a value equal to the value X (upper case here makes a difference)
case X
// only accepts a value equal to the value of x
case `x`
// only accept a tuple of the same arity
case (x, y, ..., z)
// only accepts if extractor(value) returns true of Some(Seq()) (some empty sequence)
case extractor()
// only accepts if extractor(value) returns Some something
case extractor(x)
// only accepts if extractor(value) returns Some Seq or Tuple of the same arity
case extractor(x, y, ..., z)
// only accepts if extractor(value) returns Some Tuple2 or Some Seq with arity 2
case x extractor y
// accepts if any of the patterns is accepted (patterns may not contain assignable identifiers)
case x | y | ... | z
Now, extractors are the methods unapply or unapplySeq, the first returning Boolean or Option[T], and the second returning Option[Seq[T]], where None means no match is made, and Some(result) will try to match result as described above.
So there are all kinds of syntactic alternatives here, which just aren't possible without the use of one of the three constructions where pattern matches may happen. You may able to emulate some of the features, like value equality and extractors, but not all of them.
Patterns can also be used in for expressions. Your code sample
a match {
case b => // do stuff
case _ => // do nothing
}
can then be expressed as
for(b <- Some(a)) //do stuff
The trick is to wrap a to make it a valid enumerator. E.g. List(a) would also work, but I think Some(a) is closest to your intended meaning.
The best I can come up with is this:
def matches[A](a:A)(f:PartialFunction[A, Unit]) = f.isDefinedAt(a)
if (matches(a){case ... =>}) {
//do stuff
}
This won't win you any style points though.
Kim's answer can be “improved” to better match your requirement:
class AnyWrapper[A](wrapped: A) {
def matches(f: PartialFunction[A, Unit]) = f.isDefinedAt(wrapped)
}
implicit def any2wrapper[A](wrapped: A) = new AnyWrapper(wrapped)
then:
val a = "a" :: Nil
if (a matches { case "a" :: Nil => }) {
println("match")
}
I wouldn't do it, however. The => }) { sequence is really ugly here, and the whole code looks much less clear than a normal match. Plus, you get the compile-time overhead of looking up the implicit conversion, and the run-time overhead of wrapping the match in a PartialFunction (not counting the conflicts you could get with other, already defined matches methods, like the one in String).
To look a little bit better (and be less verbose), you could add this def to AnyWrapper:
def ifMatch(f: PartialFunction[A, Unit]): Unit = if (f.isDefinedAt(wrapped)) f(wrapped)
and use it like this:
a ifMatch { case "a" :: Nil => println("match") }
which saves you your case _ => line, but requires double braces if you want a block instead of a single statement... Not so nice.
Note that this construct is not really in the spirit of functional programming, as it can only be used to execute something that has side effects. We can't easily use it to return a value (therefore the Unit return value), as the function is partial — we'd need a default value, or we could return an Option instance. But here again, we would probably unwrap it with a match, so we'd gain nothing.
Frankly, you're better off getting used to seeing and using those match frequently, and moving away from this kind of imperative-style constructs (following Madoc's nice explanation).
I have a recursive function that takes a Map as single parameter. It then adds new entries to that Map and calls itself with this larger Map. Please ignore the return values for now. The function isn't finished yet. Here's the code:
def breadthFirstHelper( found: Map[AIS_State,(Option[AIS_State], Int)] ): List[AIS_State] = {
val extension =
for(
(s, v) <- found;
next <- this.expand(s) if (! (found contains next) )
) yield (next -> (Some(s), 0))
if ( extension.exists( (s -> (p,c)) => this.isGoal( s ) ) )
List(this.getStart)
else
breadthFirstHelper( found ++ extension )
}
In extension are the new entries that shall get added to the map. Note that the for-statement generates an iterable, not a map. But those entries shall later get added to the original map for the recursive call. In the break condition, I need to test whether a certain value has been generated inside extension. I try to do this by using the exists method on extension. But the syntax for extracting values from the map entries (the stuff following the yield) doesn't work.
Questions:
How do I get my break condition (the boolean statement to the if) to work?
Is it a good idea to do recursive work on a immutable Map like this? Is this good functional style?
When using a pattern-match (e.g. against a Tuple2) in a function, you need to use braces {} and the case statement.
if (extension.exists { case (s,_) => isGoal(s) } )
The above also uses the fact that it is more clear when matching to use the wildcard _ for any allowable value (which you subsequently do not care about). The case xyz gets compiled into a PartialFunction which in turn extends from Function1 and hence can be used as an argument to the exists method.
As for the style, I am not functional programming expert but this seems like it will be compiled into a iterative form (i.e. it's tail-recursive) by scalac. There's nothing which says "recursion with Maps is bad" so why not?
Note that -> is a method on Any (via implicit conversion) which creates a Tuple2 - it is not a case class like :: or ! and hence cannot be used in a case pattern match statement. This is because:
val l: List[String] = Nil
l match {
case x :: xs =>
}
Is really shorthand/sugar for
case ::(x, xs) =>
Similarly a ! b is equivalent to !(a, b). Of course, you may have written your own case class ->...
Note2: as Daniel says below, you cannot in any case use a pattern-match in a function definition; so while the above partial function is valid, the following function is not:
(x :: xs) =>
This is a bit convoluted for me to follow, whatever Oxbow Lakes might think.
I'd like first to clarify one point: there is no break condition in for-comprehensions. They are not loops like C's (or Java's) for.
What an if in a for-comprehension means is a guard. For instance, let's say I do this:
for {i <- 1 to 10
j <- 1 to 10
if i != j
} yield (i, j)
The loop isn't "stopped" when the condition is false. It simply skips the iterations for which that condition is false, and proceed with the true ones. Here is another example:
for {i <- 1 to 10
j <- 1 to 10
if i % 2 != 0
} yield (i, j)
You said you don't have side-effects, so I can skip a whole chapter about side effects and guards on for-comprehensions. On the other hand, reading a blog post I made recently on Strict Ranges is not a bad idea.
So... give up on break conditions. They can be made to work, but they are not functional. Try to rephrase the problem in a more functional way, and the need for a break condition will be replaced by something else.
Next, Oxbow is correct in that (s -> (p,c) => isn't allowed because there is no extractor defined on an object called ->, but, alas, even (a :: b) => would not be allowed, because there is no pattern matching going on in functional literal parameter declaration. You must simply state the parameters on the left side of =>, without doing any kind of decomposition. You may, however, do this:
if ( extension.exists( t => val (s, (p,c)) = t; this.isGoal( s ) ) )
Note that I replaced -> with ,. This works because a -> b is a syntactic sugar for (a, b), which is, itself, a syntactic sugar for Tuple2(a, b). As you don't use neither p nor c, this works too:
if ( extension.exists( t => val (s, _) = t; this.isGoal( s ) ) )
Finally, your recursive code is perfectly fine, though probably not optimized for tail-recursion. For that, you either make your method final, or you make the recursive function private to the method. Like this:
final def breadthFirstHelper
or
def breadthFirstHelper(...) {
def myRecursiveBreadthFirstHelper(...) { ... }
myRecursiveBreadthFirstHelper(...)
}
On Scala 2.8 there is an annotation called #TailRec which will tell you if the function can be made tail recursive or not. And, in fact, it seems there will be a flag to display warnings about functions that could be made tail-recursive if slightly changed, such as above.
EDIT
Regarding Oxbow's solution using case, that's a function or partial function literal. It's type will depend on what the inference requires. In that case, because that's that exists takes, a function. However, one must be careful to ensure that there will always be a match, otherwise you get an exception. For example:
scala> List(1, 'c') exists { case _: Int => true }
res0: Boolean = true
scala> List(1, 'c') exists { case _: String => true }
scala.MatchError: 1
at $anonfun$1.apply(<console>:5)
... (stack trace elided)
scala> List(1, 'c') exists { case _: String => true; case _ => false }
res3: Boolean = false
scala> ({ case _: Int => true } : PartialFunction[AnyRef,Boolean])
res5: PartialFunction[AnyRef,Boolean] = <function1>
scala> ({ case _: Int => true } : Function1[Int, Boolean])
res6: (Int) => Boolean = <function1>
EDIT 2
The solution Oxbow proposes does use pattern matching, because it is based on function literals using case statements, which do use pattern matching. When I said it was not possible, I was speaking of the syntax x => s.