I am new to scala , I have written same code in 2 ways . But i am bit confused between 2 ways. In Second way argument type of f are derived automatically but in type1 scala compiler is not able to do the same . I just want to understand what is the thought behind this .
Type1: Gives compilation error
def rightFold[A,B](xs:List[A],z:B,f:(A,B) => B ): B = xs match {
case Nil => z
case Cons(x,xs) => f(x,rightFold(xs,z,f))
}
def sum1(l:List[Int]) = rightFold(l,0.0,_ + _)
Type2 : Works fine
def rightFold[A,B](xs:List[A],z:B)(f:(A,B) => B ): B = xs match {
case Nil => z
case Cons(x,xs) => f(x,rightFold(xs,z)(f))
}
def sum1(l:List[Int]) = rightFold(l,0.0)(_ + _)
Type inference flows from left-to-right through argument lists. In other words, type information from left argument lists is available in right argument lists, but argument types within the same list are inferred independently.
This is not about function types need to be passed in a separate group of arguments (currying).The problem is with your usage of + on types that the Scala doesn't know about yet.
When you curry a function, the compiler is able to infer the type of the first two arguments as being List[Int] and Double already. This allows the + to be resolved as it knows that the types are Int and Dobule on the two sides.
Now why can't the compiler do the same with the single arguments list - that's just how it is, type information is not available within an argument list.
Type 1 would work if instead of passing in _ + _ you pass in (a: Int, b: Double) => (a + b)). Currying the function lets you use the underline syntax, because the scala compiler has inferred what types A and B are by the time you try and pass in the addition function.
With single list an inferred type of A depends on the types of xs and f. But with the two lists of arguments it depends just on the xs type.
Related
I am new to Scala, and I hope this question is not too basic. I couldn't find the answer to this question on the web (which might be because I don't know the relevant keywords).
I am trying to understand the following definition:
def functionName[T <: AnyRef](name: Symbol)(range: String*)(f: T => String)(implicit tag: ClassTag[T]): DiscreteAttribute[T] = {
val r = ....
new anotherFunctionName[T](name.toString, f, Some(r))
}
First , why is it defined as def functionName[...](...)(...)(...)(...)? Can't we define it as def functionName[...](..., ..., ..., ...)?
Second, how does range: String* from range: String?
Third, would it be a problem if implicit tag: ClassTag[T] did not exist?
First , why is it defined as def functionName...(...)(...)(...)? Can't we define it as def functionName[...](..., ..., ..., ...)?
One good reason to use currying is to support type inference. Consider these two functions:
def pred1[A](x: A, f: A => Boolean): Boolean = f(x)
def pred2[A](x: A)(f: A => Boolean): Boolean = f(x)
Since type information flows from left to right if you try to call pred1 like this:
pred1(1, x => x > 0)
type of the x => x > 0 cannot be determined yet and you'll get an error:
<console>:22: error: missing parameter type
pred1(1, x => x > 0)
^
To make it work you have to specify argument type of the anonymous function:
pred1(1, (x: Int) => x > 0)
pred2 from the other hand can be used without specifying argument type:
pred2(1)(x => x > 0)
or simply:
pred2(1)(_ > 0)
Second, how does range: String* from range: String?
It is a syntax for defining Repeated Parameters a.k.a varargs. Ignoring other differences it can be used only on the last position and is available as a scala.Seq (here scala.Seq[String]). Typical usage is apply method of the collections types which allows for syntax like SomeDummyCollection(1, 2, 3). For more see:
What does `:_*` (colon underscore star) do in Scala?
Scala variadic functions and Seq
Is there a difference in Scala between Seq[T] and T*?
Third, would it be a problem if implicit tag: ClassTag[T] did not exist?
As already stated by Aivean it shouldn't be the case here. ClassTags are automatically generated by the compiler and should be accessible as long as the class exists. In general case if implicit argument cannot be accessed you'll get an error:
scala> import scala.concurrent._
import scala.concurrent._
scala> val answer: Future[Int] = Future(42)
<console>:13: error: Cannot find an implicit ExecutionContext. You might pass
an (implicit ec: ExecutionContext) parameter to your method
or import scala.concurrent.ExecutionContext.Implicits.global.
val answer: Future[Int] = Future(42)
Multiple argument lists: this is called "currying", and enables you to call a function with only some of the arguments, yielding a function that takes the rest of the arguments and produces the result type (partial function application). Here is a link to Scala documentation that gives an example of using this. Further, any implicit arguments to a function must be specified together in one argument list, coming after any other argument lists. While defining functions this way is not necessary (apart from any implicit arguments), this style of function definition can sometimes make it clearer how the function is expected to be used, and/or make the syntax for partial application look more natural (f(x) rather than f(x, _)).
Arguments with an asterisk: "varargs". This syntax denotes that rather than a single argument being expected, a variable number of arguments can be passed in, which will be handled as (in this case) a Seq[String]. It is the equivalent of specifying (String... range) in Java.
the implicit ClassTag: this is often needed to ensure proper typing of the function result, where the type (T here) cannot be determined at compile time. Since Scala runs on the JVM, which does not retain type information beyond compile time, this is a work-around used in Scala to ensure information about the type(s) involved is still available at runtime.
Check currying:Methods may define multiple parameter lists. When a method is called with a fewer number of parameter lists, then this will yield a function taking the missing parameter lists as its arguments.
range:String* is the syntax for varargs
implicit TypeTag parameter in Scala is the alternative for Class<T> clazzparameter in Java. It will be always available if your class is defined in scope. Read more about type tags.
I am trying to define a higher order function f which accepts a variable number of parameters args of type Wrapper[T]* and a function parameter g in Scala.
The function f should decapsulate each object passed in args and then call g with the decapsulated parameters. Therefore, g has to accept exactly the same number of parameters of type T as args contains.
The closest thing I could achieve was to pass a Seq[T] to g and to use pattern matching inside of g. Like the following:
f("This", "Is", "An", "Example")(x => x match {
case Seq(a:String, b:String, c:String): //Do something.
})
With f defined like:
def f[V](args: Wrapper[T]*)
(g: (Seq[T]) => (V)) : V = {
val params = args.map(x => x.unwrap())
g(params)
}
How is it possible to accomplish a thing like this without pattern
matching?
It is possible to omit the types in the signature of g
by using type inference, but only if the number of parameters is
fixed. How could this be done in this case?
It is possible to pass
different types of parameters into varargs, if a type wildcard is
used args: Wrapper[_]*. Additionally, casting the result of
x.unwrap to AnyRef and using pattern matching in g is
necessary. This, however, completely breaks type inference and type
safety. Is there a better way to make mixing types in the varargs
possible in this special case?
I am also considering the use of scala makros to accomplish these tasks.
Did I get you right? I replaced your Wrapper with some known type, but that doesn't seem to be essential.
def f[T, V](args: T*)(g: PartialFunction[Seq[T], V]): V = g(args)
So later you can do this:
f(1,2,3) { case Seq(a,b,c) => c } // Int = 3
Okay, I've made my own Wrapper to be totally clear:
case class Wrapper[T](val x:T) {
def unwrap = x
}
def f[V](args: Wrapper[_]*)(g: PartialFunction[Seq[_], V]): V =
g(args.map(_.unwrap))
f(Wrapper("1"), Wrapper(1), Wrapper(BigInt(1))) {
case Seq(s: String, i: Int, b: BigInt) => (s, i, b)
} // res3: (String, Int, BigInt) = (1,1,1)
Regarding your concerns about type safety and conversions: as you can see, there aren't any explicit conversions in the code above, and since you are going to pattern-match with explicitly defined types, you may not to worry about these things - if some items of an undefined origin are going to show in your input, scala.MatchError will be thrown.
From working on the first problem of the 99 Scala Puzzles I defined my own version of last like so:
def last[A](xs: List[A]): A = xs match {
case x :: Nil => x
case x :: xs => last(xs)
}
My question is: Why is it necessary for last to be directly followed by the type variable, as in last[A]? Why couldn't the compiler just do the right thing if I wrote the function like so:
def last(xs: List[A]): A
.....
(leaving the [A] off the end of last[A]?)
And if the compiler is capable of figuring it out, then what is the rationale for designing the language this way?
A appears 3 times:
last[A]
List[A]
: A(after the argument list)
The 2nd one is needed to specify that the List contains objects of type A. The 3rd one is needed to specify that the function returns an object of type A.
The 1st one is where you actually declare A, so it could be used in the other two places.
You need to write last[A] because A does not exist. Since it does not exist, by declaring it after the name of the function you actually get a chance to define some expectations or constraints for this type.
For example: last[A <: Int] to enforce the fact that A has to be a subtype of Int
Once it's declared, you can use it to define the type of your parameters and your return type.
I got an insight from #Lee's comment:
How would the compiler know that the A in List[A] doesn't refer to an
actual type called A?
To demonstrate to myself that this made sense, I tried substituting the type variable A, with the name of an actual type String, and then passed the function a List[Int], seeing that when last is declared like def last[String](xs: List[String]): String, I was able to pass last a List[Int]:
scala> def last[String](xs: List[String]): String = xs match {
| case x :: Nil => x
| case x :: xs => last(xs)
| }
last: [String](xs: List[String])String
scala> last(List(1,2,3,4))
res7: Int = 4
Therefore proving the identifier String does behave like a type variable, and does not reference the concrete type String.
It would also make debugging more difficult if the compiler just assumed that any identifier not in scope was a type variable. It therefore, makes sense to have to declare it at the beginning of the function definition.
A friend of mine posed a seemingly innocuous Scala language question last week that I didn't have a good answer to: whether there's an easy way to declare a collection of things belonging to some common typeclass. Of course there's no first-class notion of "typeclass" in Scala, so we have to think of this in terms of traits and context bounds (i.e. implicits).
Concretely, given some trait T[_] representing a typeclass, and types A, B and C, with corresponding implicits in scope T[A], T[B] and T[C], we want to declare something like a List[T[a] forAll { type a }], into which we can throw instances of A, B and C with impunity. This of course doesn't exist in Scala; a question last year discusses this in more depth.
The natural follow-up question is "how does Haskell do it?" Well, GHC in particular has a type system extension called impredicative polymorphism, described in the "Boxy Types" paper. In brief, given a typeclass T one can legally construct a list [forall a. T a => a]. Given a declaration of this form, the compiler does some dictionary-passing magic that lets us retain the typeclass instances corresponding to the types of each value in the list at runtime.
Thing is, "dictionary-passing magic" sounds a lot like "vtables." In an object-oriented language like Scala, subtyping is a much more simple, natural mechanism than the "Boxy Types" approach. If our A, B and C all extend trait T, then we can simply declare List[T] and be happy. Likewise, as Miles notes in a comment below, if they all extend traits T1, T2 and T3 then I can use List[T1 with T2 with T3] as an equivalent to the impredicative Haskell [forall a. (T1 a, T2 a, T3 a) => a].
However, the main, well-known disadvantage with subtyping compared to typeclasses is tight coupling: my A, B and C types have to have their T behavior baked in. Let's assume this is a major dealbreaker, and I can't use subtyping. So the middle ground in Scala is pimps^H^H^H^H^Himplicit conversions: given some A => T, B => T and C => T in implicit scope, I can again quite happily populate a List[T] with my A, B and C values...
... Until we want List[T1 with T2 with T3]. At that point, even if we have implicit conversions A => T1, A => T2 and A => T3, we can't put an A into the list. We could restructure our implicit conversions to literally provide A => T1 with T2 with T3, but I've never seen anybody do that before, and it seems like yet another form of tight coupling.
Okay, so my question finally is, I suppose, a combination of a couple questions that were previously asked here: "why avoid subtyping?" and "advantages of subtyping over typeclasses" ... is there some unifying theory that says impredicative polymorphism and subtype polymorphism are one and the same? Are implicit conversions somehow the secret love-child of the two? And can somebody articulate a good, clean pattern for expressing multiple bounds (as in the last example above) in Scala?
You're confusing impredicative types with existential types. Impredicative types allow you to put polymorphic values in a data structure, not arbitrary concrete ones. In other words [forall a. Num a => a] means that you have a list where each element works as any numeric type, so you can't put e.g. Int and Double in a list of type [forall a. Num a => a], but you can put something like 0 :: Num a => a in it. Impredicative types is not what you want here.
What you want is existential types, i.e. [exists a. Num a => a] (not real Haskell syntax), which says that each element is some unknown numeric type. To write this in Haskell, however, we need to introduce a wrapper data type:
data SomeNumber = forall a. Num a => SomeNumber a
Note the change from exists to forall. That's because we're describing the constructor. We can put any numeric type in, but then the type system "forgets" which type it was. Once we take it back out (by pattern matching), all we know is that it's some numeric type. What's happening under the hood, is that the SomeNumber type contains a hidden field which stores the type class dictionary (aka. vtable/implicit), which is why we need the wrapper type.
Now we can use the type [SomeNumber] for a list of arbitrary numbers, but we need to wrap each number on the way in, e.g. [SomeNumber (3.14 :: Double), SomeNumber (42 :: Int)]. The correct dictionary for each type is looked up and stored in the hidden field automatically at the point where we wrap each number.
The combination of existential types and type classes is in some ways similar to subtyping, since the main difference between type classes and interfaces is that with type classes the vtable travels separately from the objects, and existential types packages objects and vtables back together again.
However, unlike with traditional subtyping, you're not forced to pair them one to one, so we can write things like this which packages one vtable with two values of the same type.
data TwoNumbers = forall a. Num a => TwoNumbers a a
f :: TwoNumbers -> TwoNumbers
f (TwoNumbers x y) = TwoNumbers (x+y) (x*y)
list1 = map f [TwoNumbers (42 :: Int) 7, TwoNumbers (3.14 :: Double) 9]
-- ==> [TwoNumbers (49 :: Int) 294, TwoNumbers (12.14 :: Double) 28.26]
or even fancier things. Once we pattern match on the wrapper, we're back in the land of type classes. Although we don't know which type x and y are, we know that they're the same, and we have the correct dictionary available to perform numeric operations on them.
Everything above works similarly with multiple type classes. The compiler will simply generate hidden fields in the wrapper type for each vtable and bring them all into scope when we pattern match.
data SomeBoundedNumber = forall a. (Bounded a, Num a) => SBN a
g :: SomeBoundedNumber -> SomeBoundedNumber
g (SBN n) = SBN (maxBound - n)
list2 = map g [SBN (42 :: Int32), SBN (42 :: Int64)]
-- ==> [SBN (2147483605 :: Int32), SBN (9223372036854775765 :: Int64)]
As I'm very much a beginner when it comes to Scala, I'm not sure I can help with the final part of your question, but I hope this has at least cleared up some of the confusion and given you some ideas on how to proceed.
#hammar's answer is perfectly right. Here is the scala way of doint it. For the example i'll take Show as the type class and the values i and d to pack in a list :
// The type class
trait Show[A] {
def show(a : A) : String
}
// Syntactic sugar for Show
implicit final class ShowOps[A](val self : A)(implicit A : Show[A]) {
def show = A.show(self)
}
implicit val intShow = new Show[Int] {
def show(i : Int) = "Show of int " + i.toString
}
implicit val stringShow = new Show[String] {
def show(s : String) = "Show of String " + s
}
val i : Int = 5
val s : String = "abc"
What we want is to be able run the following code
val list = List(i, s)
for (e <- list) yield e.show
Building the list is easy but the list won't "remember" the exact type of each of its elements. Instead it will upcast each element to a common super type T. The more precise super super type between String and Int being Any, the type of the list is List[Any].
The problem is: what to forget and what to remember? We want to forget the exact type of the elements BUT we want to remember that they are all instances of Show. The following class does exactly that
abstract class Ex[TC[_]] {
type t
val value : t
implicit val instance : TC[t]
}
implicit def ex[TC[_], A](a : A)(implicit A : TC[A]) = new Ex[TC] {
type t = A
val value = a
val instance = A
}
This is an encoding of the existential :
val ex_i : Ex[Show] = ex[Show, Int](i)
val ex_s : Ex[Show] = ex[Show, String](s)
It pack a value with the corresponding type class instance.
Finally we can add an instance for Ex[Show]
implicit val exShow = new Show[Ex[Show]] {
def show(e : Ex[Show]) : String = {
import e._
e.value.show
}
}
The import e._ is required to bring the instance into scope. Thanks to the magic of implicits:
val list = List[Ex[Show]](i , s)
for (e <- list) yield e.show
which is very close to the expected code.
I'm trying to understand the point of this language feature of multiple parameter clauses and why you would use it.
Eg, what's the difference between these two functions really?
class WTF {
def TwoParamClauses(x : Int)(y: Int) = x + y
def OneParamClause(x: Int, y : Int) = x + y
}
>> val underTest = new WTF
>> underTest.TwoParamClauses(1)(1) // result is '2'
>> underTest.OneParamClause(1,1) // result is '2'
There's something on this in the Scala specification at point 4.6. See if that makes any sense to you.
NB: the spec calls these 'parameter clauses', but I think some people may also call them 'parameter lists'.
Here are three practical uses of multiple parameter lists,
To aid type inference. This is especially useful when using higher order methods. Below, the type parameter A of g2 is inferred from the first parameter x, so the function arguments in the second parameter f can be elided,
def g1[A](x: A, f: A => A) = f(x)
g1(2, x => x) // error: missing parameter type for argument x
def g2[A](x: A)(f: A => A) = f(x)
g2(2) {x => x} // type is inferred; also, a nice syntax
For implicit parameters. Only the last parameter list can be marked implicit, and a single parameter list cannot mix implicit and non-implicit parameters. The definition of g3 below requires two parameter lists,
// analogous to a context bound: g3[A : Ordering](x: A)
def g3[A](x: A)(implicit ev: Ordering[A]) {}
To set default values based on previous parameters,
def g4(x: Int, y: Int = 2*x) {} // error: not found value x
def g5(x: Int)(y: Int = 2*x) {} // OK
TwoParamClause involves two method invocations while the OneParamClause invokes the function method only once. I think the term you are looking for is currying. Among the many use cases, it helps you to breakdown the computation into small steps. This answer may convince you of usefulness of currying.
There is a difference between both versions concerning type inference. Consider
def f[A](a:A, aa:A) = null
f("x",1)
//Null = null
Here, the type A is bound to Any, which is a super type of String and Int. But:
def g[A](a:A)(aa:A) = null
g("x")(1)
error: type mismatch;
found : Int(1)
required: java.lang.String
g("x")(1)
^
As you see, the type checker only considers the first argument list, so A gets bound to String, so the Int value for aa in the second argument list is a type error.
Multiple parameter lists can help scala type inference for more details see: Making the most of Scala's (extremely limited) type inference
Type information does not flow from left to right within an argument list, only from left to right across argument lists. So, even though Scala knows the types of the first two arguments ... that information does not flow to our anonymous function.
...
Now that our binary function is in a separate argument list, any type information from the previous argument lists is used to fill in the types for our function ... therefore we don't need to annotate our lambda's parameters.
There are some cases where this distinction matters:
Multiple parameter lists allow you to have things like TwoParamClauses(2); which is automatically-generated function of type Int => Int which adds 2 to its argument. Of course you can define the same thing yourself using OneParamClause as well, but it will take more keystrokes
If you have a function with implicit parameters which also has explicit parameters, implicit parameters must be all in their own parameter clause (this may seem as an arbitrary restriction but is actually quite sensible)
Other than that, I think, the difference is stylistic.