Shorter syntax for context bounds? - scala

Is there a way to use shorter syntax when using context-bound type parameters? At the moment I have something like this
case class Vector2D[a : Numeric](x: a, y: a) {
val numA = implicitly[Numeric[a]]
def length2 = numA.plus(numA.times(x, x), numA.times(y, y))
}
and it makes more complex formulae unreadable.

Try this REPL session:
scala> case class Vector2D[T : Numeric](x: T, y: T) {
val numeric = implicitly[Numeric[T]]
import numeric._
def length2 = (x*x)+(y*y)
}
defined class Vector2D
scala> Vector2D(3,4).length2
res0: Int = 25
This is because Numeric contains an implicit conversion called mkNumericOps which you can import as shown above. If it didn't come out of the box, the way you could roll this yourself would be something like:
scala> implicit class NumericOps[T](val x: T) extends AnyVal { def +(y: T)(implicit n: Numeric[T]): T = n.plus(x, y)
| def *(y: T)(implicit n: Numeric[T]): T = n.times(x, y)
| }
defined class NumericOps
scala> case class Vector2D[a : Numeric](x: a, y: a) { def length2 = (x*x)+(y*y) }
defined class Vector2D
scala> Vector2D(3,4).length2
res0: Int = 25
If you make NumericOps not a value class (don't extend AnyVal) then the implicit Numeric can go on the constructor instead of each method, which might be better, or not really matter.
Anyway there's no need to write your own since Numeric already has mkNumericOps.
These "ops" classes are called the "enrich my library" pattern.
Numeric.Ops is here
and the implicit being imported to auto-create it is mkNumericOps on Numeric, here.

Just
import Numeric.Implicits._
then for every type that for which an implicit Numeric can be found
(importing just the NumericOps conversion of one Numeric instance as suggested by #Havoc P gives you finer control as to for which types operations are available, but most of the time, Numeric.Implicits should be fine)
On the more general question is there a shorter syntax when using context bounds type parameters: in general, there is not. It is up to the typeclass to provide some sugar to make it easy to use, as Numeric does here.
For instance, it is more or less customary to have an apply method in the companion object which makes getting the instance a little easier than with implicitly
object Ordering {
def apply[T](implicit ord: Ordering[T]): Ordering[T] = implicitly[Ordering[T]]
}
so that you can get the implicit just with e.g Ordering[Int], rather than implicitly[Ordering[Int]].

Related

unclear why my in-scope implicit conversions are not accepted as 'implicit evidence'

I've been experimenting with implicit conversions, and I have a decent understanding of the 'enrich-my-libray' pattern that uses these. I tried to combine my understanding of basic implicits with the use of implicit evidence... But I'm misunderstanding something crucial, as shown by the method below:
import scala.language.implicitConversions
object Moo extends App {
case class FooInt(i: Int)
implicit def cvtInt(i: Int) : FooInt = FooInt(i)
implicit def cvtFoo(f: FooInt) : Int = f.i
class Pair[T, S](var first: T, var second: S) {
def swap(implicit ev: T =:= S, ev2: S =:= T) {
val temp = first
first = second
second = temp
}
def dump() = {
println("first is " + first)
println("second is " + second)
}
}
val x = new Pair(FooInt(200), 100)
x.dump
x.swap
x.dump
}
When I run the above method I get this error:
Error:(31, 5) Cannot prove that nodescala.Moo.FooInt =:= Int.
x.swap
^
I am puzzled because I would have thought that my in-scope implict conversion would be sufficient 'evidence' that Int's can be converted to FooInt's and vice versa. Thanks in advance for setting me straight on this !
UPDATE:
After being unconfused by Peter's excellent answer, below, the light bulb went on for me one good reason you would want to use implicit evidence in your API. I detail that in my own answer to this question (also below).
=:= checks if the two types are equal and FooInt and Int are definitely not equal, although there exist implicit conversion for values of these two types.
I would create a CanConvert type class which can convert an A into a B :
trait CanConvert[A, B] {
def convert(a: A): B
}
We can create type class instances to transform Int into FooInt and vise versa :
implicit val Int2FooInt = new CanConvert[Int, FooInt] {
def convert(i: Int) = FooInt(i)
}
implicit val FooInt2Int = new CanConvert[FooInt, Int] {
def convert(f: FooInt) = f.i
}
Now we can use CanConvert in our Pair.swap function :
class Pair[A, B](var a: A, var b: B) {
def swap(implicit a2b: CanConvert[A, B], b2a: CanConvert[B, A]) {
val temp = a
a = b2a.convert(b)
b = a2b.convert(temp)
}
override def toString = s"($a, $b)"
def dump(): Unit = println(this)
}
Which we can use as :
scala> val x = new Pair(FooInt(200), 100)
x: Pair[FooInt,Int] = (FooInt(200), 100)
scala> x.swap
scala> x.dump
(FooInt(100), 200)
A =:= B is not evidence that A can be converted to B. It is evidence that A can be cast to B. And you have no implicit evidence anywhere that Int can be cast to FooInt vice versa (for good reason ;).
What you are looking for is:
def swap(implicit ev: T => S, ev2: S => T) {
After working through this excercise I think I have a better understanding of WHY you'd want to use implicit evidence serves in your API.
Implicit evidence can be very useful when:
you have a type parameterized class that provides various methods
that act on the types given by the parameters, and
when one or more of those methods only make sense when additional
constraints are placed on parameterized types.
So, in the case of the simple API given in my original question:
class Pair[T, S](var first: T, var second: S) {
def swap(implicit ev: T =:= S, ev2: S =:= T) = ???
def dump() = ???
}
We have a type Pair, which keeps two things together, and we can always call dump() to examine the two things. We can also, under certain conditions, swap the positions of the first and second items in the pair. And those conditions are given by the implicit evidence constraints.
The Programming in Scala book gives a nice example of how this technique
is used in Scala collections, specifically on the toMap method of Traversables.
The book points out that Map's constructor
wants key-value pairs, i.e., two-tuples, as arguments. If we have a
sequence [Traversable] of pairs, wouldn’t it be nice to create a Map
out of them in one step? That’s what toMap does, but we have a
dilemma. We can’t allow the user to call toMap if the sequence is not
a sequence of pairs.
So there's an example of a type [Traversable] that has a method [toMap] that can't be used in all situations... It can only be used when the compiler can 'prove' (via implicit evidence) that the items in the Traversable are pairs.

Typeclass instances for unnamed types in Scala

How would one encode the following constraint in Scala (pseudocode)?
def foo(x: T forSome { type T has a Numeric[T] instance in scope }) = {
val n= implicitly[...] // obtain the Numeric instance for x
n.negate(x) // and use it with x
}
In words: I need a type class instance for my input argument, but I don't care about the argument's type, I just need to obtain the instance and use it on my argument.
It doesn't have to be an existential type, but I need to avoid type parameters in the def's signature.
Edit: just to clarify, the standard approach in these cases, i.e.:
def foo[T: Numeric](x: T) = ...
doesn't work for me, as it requires the addition of a type parameter on the method.
Thanks.
I managed to make it work like this:
implicit class InstanceWithNumeric[T](val inst: T)(implicit val n: Numeric[T])
def foo(iwn: InstanceWithNumeric[_]) {
def genFoo[T](iwn: InstanceWithNumeric[T]) {
println(iwn.n.negate(iwn.inst))
}
genFoo(iwn)
}
And now:
scala> foo(1)
-1
scala> foo(1.2)
-1.2
Not the prettiest, but seems to work.
EDIT: You can avoid defining inner function like this:
implicit class InstanceWithNumeric[T](val inst: T)(implicit val n: Numeric[T]) {
def negate = n.negate(inst)
}
Also, if you want to make implicit conversion to InstanceWithNumeric globally visible, you can do something like this:
class InstanceWithNumeric[T](val inst: T)(implicit val n: Numeric[T])
object InstanceWithNumeric {
implicit def apply[T: Numeric](inst: T) =
new InstanceWithNumeric(inst)
}
If you want to understand how this works, read about so called implicit scope (this question seems to contain good explanation).
Not quite sure what you are attempting, because it seems you need a type once you make the call to implicitly. Would the following work for you?
def foo(implicit x: Numeric[_]) {
//code goes here.
}

Why is there no Tuple1 Literal for single element tuples in Scala?

Python has (1,) for a single element tuple. In Scala, (1,2) works for Tuple2(1,2) but we must use Tuple1(1) to get a single element tuple. This may seem like a small issue but designing APIs that expect a Product is a pain to deal for users that are passing single elements since they have to write Tuple1(1).
Maybe this is a small issue, but a major selling point of Scala is more typing with less typing. But in this case it seems it's more typing with more typing.
Please tell me:
1) I've missed this and it exists in another form, or
2) It will be added to a future version of the language (and they'll accept patches).
You can define an implicit conversion:
implicit def value2tuple[T](x: T): Tuple1[T] = Tuple1(x)
The implicit conversion will only apply if the argument's static type does not already conform to the method parameter's type. Assuming your method takes a Product argument
def m(v: Product) = // ...
the conversion will apply to a non-product value but will not apply to a Tuple2, for example. Warning: all case classes extend the Product trait, so the conversion will not apply to them either. Instead, the product elements will be the constructor parameters of the case class.
Product is the least upper bound of the TupleX classes, but you can use a type class if you want to apply the implicit Tuple1 conversion to all non-tuples:
// given a Tupleable[T], you can call apply to convert T to a Product
sealed abstract class Tupleable[T] extends (T => Product)
sealed class ValueTupler[T] extends Tupleable[T] {
def apply(x: T) = Tuple1(x)
}
sealed class TupleTupler[T <: Product] extends Tupleable[T] {
def apply(x: T) = x
}
// implicit conversions
trait LowPriorityTuple {
// this provides a Tupleable[T] for any type T, but is the
// lowest priority conversion
implicit def anyIsTupleable[T]: Tupleable[T] = new ValueTupler
}
object Tupleable extends LowPriorityTuple {
implicit def tuple2isTuple[T1, T2]: Tupleable[Tuple2[T1,T2]] = new TupleTupler
implicit def tuple3isTuple[T1, T2, T3]: Tupleable[Tuple3[T1,T2,T3]] = new TupleTupler
// ... etc ...
}
You can use this type class in your API as follows:
def m[T: Tupleable](v: T) = {
val p = implicitly[Tupleable[T]](v)
// ... do something with p
}
If you have your method return the product, you can see how the conversions are being applied:
scala> def m[T: Tupleable](v: T) = implicitly[Tupleable[T]](v)
m: [T](v: T)(implicit evidence$1: Tupleable[T])Product
scala> m("asdf") // as Tuple1
res12: Product = (asdf,)
scala> m(Person("a", "n")) // also as Tuple1, *not* as (String, String)
res13: Product = (Person(a,n),)
scala> m((1,2)) // as Tuple2
res14: Product = (1,2)
You could, of course, add an implicit conversion to your API:
implicit def value2tuple[A](x: A) = Tuple1(x)
I do find it odd that Tuple1.toString includes the trailing comma:
scala> Tuple1(1)
res0: (Int,) = (1,)
Python is not statically typed, so tuples there act more like fixed-size collections. That is not true of Scala, where each element of a tuple has a distinct type. Tuples, in Scala, doesn't have the same uses as in Python.

how to define a structural type that refers to itself?

I want to create a method sum that I can call on different types, specifically sum(1,2).
def sum[A](a1: A, a2: A) = a1 + a2
This fails because the compiler can't tell if A has a method '+'
I tried to define a structural type:
type Addable = {def +(a: Addable)}
This fails because of an illegal cyclic reference
How can I achieve this in a type safe way without requiring A to extend a specific trait?
Scala does not support recursive type aliases without additional compiler arguments (specifically, -Yrecursion). This is partially to keep the type checker at least somewhat in the realm of decidability (though, as we have discovered, the type system is Turing Complete even without recursive type aliases, so it doesn't much matter).
The correct way to do this sort of thing is with a typeclass. Scala encodes these as implicit view bounds. For example:
trait Addable[A] {
def zero: A
def add(x: A, y: A): A
}
implicit object IntAddable extends Addable[Int] {
def zero = 0
def add(x: Int, y: Int) = x + y
}
implicit object DoubleAddable extends Addable[Double] {
def zero = 0
def add(x: Double, y: Double) = x + y
}
// ...
def sum[A](x: A, y: A)(implicit tc: Addable[A]) = tc.add(x, y)
And of course, this also allows you to do fancy things like sum the contents of a Seq in a type-safe manner:
implicit def summableSeqSyntax[A](seq: Seq[A])(implicit tc: Addable[A]) = new {
def sum = seq.foldLeft(tc.zero)(tc.add)
}
List(1, 2, 3, 4).sum // => 10
List(true, false).sum // does not compile
It is worth noting that Scala 2.8 has something very close to this with the Numeric typeclass.

Scala: How to define "generic" function parameters?

I am trying to learn Scala now, with a little bit of experience in Haskell. One thing that stood out as odd to me is that all function parameters in Scala must be annotated with a type - something that Haskell does not require. Why is this? To try to put it as a more concrete example: an add function is written like this:
def add(x:Double, y:Double) = x + y
But, this only works for doubles(well, ints work too because of the implicit type conversion). But what if you want to define your own type that defines its own + operator. How would you write an add function which works for any type that defines a + operator?
Haskell uses Hindley-Milner type inference algorithm whereas Scala, in order to support Object Oriented side of things, had to forgo using it for now.
In order to write an add function for all applicable types easily, you will need to use Scala 2.8.0:
Welcome to Scala version 2.8.0.r18189-b20090702020221 (Java HotSpot(TM) 64-Bit Server VM, Java 1.6.0_15).
Type in expressions to have them evaluated.
Type :help for more information.
scala> import Numeric._
import Numeric._
scala> def add[A](x: A, y: A)(implicit numeric: Numeric[A]): A =
| numeric.plus(x, y)
add: [A](x: A,y: A)(implicit numeric: Numeric[A])A
scala> add(1, 2)
res0: Int = 3
scala> add(1.1, 2.2)
res1: Double = 3.3000000000000003
In order to solidify the concept of using implicit for myself, I wrote an example that does not require scala 2.8, but uses the same concept. I thought it might be helpful for some.
First, you define an generic-abstract class Addable:
scala> abstract class Addable[T]{
| def +(x: T, y: T): T
| }
defined class Addable
Now you can write the add function like this:
scala> def add[T](x: T, y: T)(implicit addy: Addable[T]): T =
| addy.+(x, y)
add: [T](T,T)(implicit Addable[T])T
This is used like a type class in Haskell. Then to realize this generic class for a specific type, you would write(examples here for Int, Double and String):
scala> implicit object IntAddable extends Addable[Int]{
| def +(x: Int, y: Int): Int = x + y
| }
defined module IntAddable
scala> implicit object DoubleAddable extends Addable[Double]{
| def +(x: Double, y: Double): Double = x + y
| }
defined module DoubleAddable
scala> implicit object StringAddable extends Addable[String]{
| def +(x: String, y: String): String = x concat y
| }
defined module StringAddable
At this point you can call the add function with all three types:
scala> add(1,2)
res0: Int = 3
scala> add(1.0, 2.0)
res1: Double = 3.0
scala> add("abc", "def")
res2: java.lang.String = abcdef
Certainly not as nice as Haskell which will essentially do all of this for you. But, that's where the trade-off lies.
Haskell uses the Hindley-Milner type inference. This kind of type-inference is powerful, but limits the type system of the language. Supposedly, for instance, subclassing doesn't work well with H-M.
At any rate, Scala type system is too powerful for H-M, so a more limited kind of type inference must be used.
I think the reason Scala requires the type annotation on the parameters of a newly defined function comes from the fact that Scala uses a more local type inference analysis than that used in Haskell.
If all your classes mixed in a trait, say Addable[T], that declared the + operator, you could write your generic add function as:
def add[T <: Addable[T]](x : T, y : T) = x + y
This restricts the add function to types T that implement the Addable trait.
Unfortunately, there is not such trait in the current Scala libraries. But you can see how it would be done by looking at a similar case, the Ordered[T] trait. This trait declares comparison operators and is mixed in by the RichInt, RichFloat, etc. classes. Then you can write a sort function that can take, for example, a List[T] where [T <: Ordered[T]] to sort a list of elements that mix in the ordered trait. Because of implicit type conversions like Float to RichFloat, you can even use your sort function on lists of Int, or Float or Double.
As I said, unfortunately, there is no corresponding trait for the + operator. So, you would have to write out everything yourself. You would do the Addable[T] trait, create AddableInt, AddableFloat, etc., classes that extend Int, Float, etc. and mix in the Addable trait, and finally add implicit conversion functions to turn, for example, and Int into an AddableInt, so that the compiler can instantiate and use your add function with it.
The function itself will be pretty straightforward:
def add(x: T, y: T): T = ...
Better yet, you can just overload the + method:
def +(x: T, y: T): T = ...
There's a missing piece, though, which is the type parameter itself. As written, the method is missing its class. The most likely case is that you're calling the + method on an instance of T, passing it another instance of T. I did this recently, defining a trait that said, "an additive group consists of an add operation plus the means to invert an element"
trait GroupAdditive[G] extends Structure[G] {
def +(that: G): G
def unary_- : G
}
Then, later, I define a Real class that knows how to add instances of itself (Field extends GroupAdditive):
class Real private (s: LargeInteger, err: LargeInteger, exp: Int) extends Number[Real] with Field[Real] with Ordered[Real] {
...
def +(that: Real): Real = { ... }
...
}
That may be more than you really wanted to know right now, but it does show both how to define generic arguments and how to realize them.
Ultimately, the specific types aren't required, but the compiler does need to know at least the type bounds.