Given a function with signature: A => F[G[B]]. There are monads instances for F and G types.
Is it possible to transform it into something with the signature: F[G[A=>B]? Is there any general name for such transformation?
In other words what would be the implementation of prettify2?
def pretiffy(x: String): Future[Option[String]] = Future{if(x == "") None else Some(s">>>$x<<<")}
val pretiffy2: Future[Option[String => String]] = ???
Update: I'd appreciate answers using cats or scalaz.
Suppose we have a String=>List[Option[Integer]]. We need to produce a List[Option[String=>Integer]]. How should we approach this? For example, how long the resulting list should be? How many Nones should it contain?
Obviously these questions have no answers, which means the requested transformation cannot exist for an arbitrary monad (or indeed most monads, as one can ask similar questions about most monads).
Related
I had spent weeks on trying to understand the idea behind "lifting" in scala.
Originally, it was from the example related to Chapter 4 of book "Functional Programming in Scala"
Then I found below topic "How map work on Options in Scala?"
The selected answer specify that:
def map[B](f: A => B): Option[B] = this match (Let's considered this as (*) )
So, from above code, I assume that function "map" is derived from function match. Hence, the mechanism behind "map"
is a kind of pattern matching to provide a case selection between Some, and None
Then, I created below examples by using function map for Seq, Option, and Map (Let's considered below examples as (**) )
Example 1: map for Seq
val xs = Seq(1, 2, 3)
xs.map(println)
Example 2: map for Option
val a:Option[Int] = Some(5)
a.map(println)
val b:Option[Int] = None
b.map(println)
Example 3: map for Map
val capitals = Map("France" -> "Paris", "Japan" -> "Tokyo")
capitals.map(println)
From (*) and (**), I could not know whether "map" is a pattern matching or an iteration, or both.
Thank you for helping me to understand this.
#Jwvh provided a more programming based answer but I want to dig a little bit deeper.
I certainly appreciate you trying to understand how things work in Scala, however if you really want to dig that deep, I am afraid you will need to obtain some basic knowledge of Category Theory since there is no "idea behind lifting in scala" but just the "idea behind lifting"
This is also why functions like "map" can be very confusing. Inherently, programmers are taught map etc. as operations on collections, where as they are actually operations that come with Functors and Natural Transformations (this is normally referred to as fmap in Category Theory and also Haskell).
Before I move on, the short answer is it is a pattern matching in the examples you gave and in some of them it is both. Map is defined specifically to the case, the only condition is that it maintains functoriality
Attention: I will not be defining every single term below, since I would need to write a book to build up to some of the following definitions, interested readers are welcome to research them on their own. You should be able to get some basic understanding by following the types
Let's consider these as Functors, the definition will be something along the lines of this:
In (very very) short, we consider types as objects in the category of our language. The functions between these types (type constructors) are morphisms between types in this category. The set of these transformations are called Endo-Functors (take us from the category of Scala and drop us back in the category of Scala). Functors have to have a polymorphic (which actually has a whole different (extra) definition in category theory) map function, that will take some object A, through some type constructor turn it into object B.
implicit val option: Functor[Option] = new Functor[Option] {
override def map[A,B](optA: Option[A])(f: (A) => B): Option[B] = optA match{
case Some(a) => Some(f(a))
case _ => None
}
}
implicit val seq: Functor[Seq[_]] = new Functor[Seq[_]] {
override def map[A,B](sA: Seq[A])(f: (A) => B): Seq[B] = sA match{
case a :: tail => Seq(f(a), map(tail)(f))
case Nil => Nil
}
}
As you can see in the second case, there is a little bit of both (more of a recursion than iteration but still).
Now before the internet blows up on me, I will say you cant pattern match on Seq in Scala. It works here because the default Seq is also a List. I just provided this example because it is simpler to understand. The underlying definition something along the lines of that.
Now hold on a second. If you look at these types, you see that they also have flatMap defined on them. This means they are something more special than plain Functors. They are Monads. So beyond satisfying functoriality, they obey the monadic laws.
Turns out Monad has a different kind of meaning in the core scala, more on that here: What exactly makes Option a monad in Scala?
But again very very short, this means that we are now in a category where the endofunctors from our previous category are the objects and the mappings between them are morphisms (natural transformations), this is slightly more accurate because if you think about it when you take a type and transform it, you take (carry over) all of it's internal type constructors (2-cell or internal morphisms) with it, you do not only take this sole idea of a type without it's functions.
implicit val optionMonad: Monad[Option] = new Monad[Option] {
override def flatMap[A, B](optA: Option[A])(f: (A) => Option[B]): Option[B] = optA match{
case Some(a) => f(a)
case _ => None
}
def pure[A](a: A): Option[A] = Some(a)
//You can define map using pure and flatmap
}
implicit val seqMonad: Monad[Seq[_]] = new Monad[Seq[_]] {
override def flatMap[A, B](sA: Seq[A])(f: (A) => Seq[B]): Seq[B] = sA match{
case x :: xs => f(a).append(flatMap(tail)(f))
case Nil => Nil
}
override def pure[A](a: A): Seq[A] = Seq(a)
//Same warning as above, also you can implement map with the above 2 funcs
}
One thing you can always count on is map being having pattern match (or some if statement). Why?
In order to satisfy the identity laws, we need to have some sort of a "base case", a unit object and in many cases (such as Lists) those types are gonna be what we call either a product or coproduct.
Hopefully, this did not confuse you further. I wish I could get into every detail of this but it would simply take pages, I highly recommend getting into categories to fully understand where these come from.
From the ScalaDocs page we can see that the type profile for the Standard Library map() method is a little different.
def map[B](f: (A) => B): Seq[B]
So the Standard Library map() is the means to transition from a collection of elements of type A to the same collection but the elements are type B. (A and B might be the same type. They aren't required to be different.)
So, yes, it iterates through the collection applying function f() to each element A to create each new element B. And function f() might use pattern matching in its code, but it doesn't have to.
Now consider a.map(println). Every element of a is sent to println which returns Unit. So if a is List[Int] then the result of a.map(println) is List[Unit], which isn't terribly useful.
When all we want is the side effect of sending information to StdOut then we use foreach() which doesn't create a new collection: a.foreach(println)
Function map for Option isn't about pattern matching. The match/case used in your referred link is just one of the many ways to define the function. It could've been defined using if/else. In fact, that's how it's defined in Scala 2.13 source of class Option:
sealed abstract class Option[+A] extends IterableOnce[A] with Product with Serializable {
self =>
...
final def map[B](f: A => B): Option[B] =
if (isEmpty) None else Some(f(this.get))
...
}
If you view Option like a "collection" of either one element (Some(x)) or no elements (None), it might be easier to see the resemblance of how map transforms an Option versus, say, a List:
val f: Int => Int = _ + 1
List(42).map(f)
// res1: List[Int] = List(43)
List.empty[Int].map(f)
// res2: List[Int] = List()
Some(42).map(f)
// res3: Option[Int] = Some(43)
None.map(f)
// res4: Option[Int] = None
HMap seems to be the perfect data structure for my use case, however, I can't get it working:
case class Node[N](node: N)
class ImplVal[K, V]
implicit val iv1 = new ImplVal[Int, Node[Int]]
implicit val iv2 = new ImplVal[Int, Node[String]]
implicit val iv3 = new ImplVal[String, Node[Int]]
val hm = HMap[ImplVal](1 -> Node(1), 2 -> Node("two"), "three" -> Node(3))
My first question is whether it is possible to create those implicits vals automatically. For sure, for typical combinations I could create them manually, but I'm wondering if there is something more generic, less boilerplate way.
Next question is, how to get values out of the map:
val res1 = hm.get(1) // (1) ambiguous implicit values: both value iv2 [...] and value iv1 [...] match expected type ImplVal[Int,V]`
To me, Node[Int] (iv1) and Node[String] (iv2) look pretty different :) I thought, despite the JVM type erasure limitations, Scala could differentiate here. What am I missing? Do I have to use other implicit values to make the difference clear?
The explicit version works:
val res2 = hm.get[Int, Node[Int]](1) // (2) works
Of course, in this simple case, I could add the type information to the get call. But in the following case, where only the keys are known in advance, I don't know how to do it:
def get[T <: HList](keys: T): HList = // return associated values for keys
Is there any simple solution to this problem?
BTW, what documentation about Scala's type system (or Shapeless or in functional programming in general) could be recommended to understand the whole topic better as I have to admit, I'm lacking some background for this topic.
The type of the key determines the type of the value. You have Int keys corresponding to both Node[Int] and Node[String] values, hence the ambiguity. You might find this article helpful in explaining the general mechanism underlying this.
I've trying to sort a list by a future boolean.
I have a list of IDs and I need to query an external service to find out if there's contextual information behind them. The method I use to do this returns an optional future.
By using the partition method I hoped to create two lists of IDs, one with contextual information and one without.
The following answer on here provided a lot of help for this: Scala - sort based on Future result predicate
I now have an rough, untested method that looks like so,
val futureMatch = listOfIds.map( b => b.map{ j =>
getContext(j).map{ k =>
Map( j -> k)
}
}).map(Future.sequence(_)).flatMap(identity)
val partitionedList = futureMatch.map(_.partition{
case (k, Some(v)) => true
case _ => false
})
So as advised in the other question, I'm attempting to get all my answers at the same level, and then using Future.sequence and flatMap(identity) to flatten nested layers of futures.
The problem is this doesn't feel very efficient.
Ideally the successful list would have a signature of List[Map[String, String]] not List[Map[String, Option[String]] and the failed list would just be a list of Strings, so it'd only need to be one dimensional. As it currently stands I have two identical list signatures which have some redundancy. For example in the successful list, I know this is going exist so it doesn't need to be an option.
Any ideas how I could achieve this structure and produce two lists with different signatures or even if this is the most efficient way.
Thanks.
EDIT: Looking at the signature for partition it looks like I can only produce two lists of the same signature, so a different signature is probably too much to ask. I guess I can just flatten the list afterwards.
I found a suitable solution in the comments of the question I linked too.
val (matched, unmatched) =
finalMatch.foldLeft(List.empty[Map[String, String]], List.empty[String]) {
case ((matched, unmatched), p) => p match {
case m:Map[String, String] => (m :: matched, unmatched)
case s:String => (matched, s :: unmatched)
}
}
The only issue with this is it leads to type erasure. I've opened another question to discuss this issue.
Dealing with Type Erasure with foldLeft
Thanks all.
take this as a follow up to this SO question
I'm new to scala and working through the 99 problems. The given solution to p9 is:
object P09 {
def pack[A](ls: List[A]): List[List[A]] = {
if (ls.isEmpty) List(List())
else {
val (packed, next) = ls span { _ == ls.head }
if (next == Nil) List(packed)
else packed :: pack(next)
}
}
}
The span function is doing all the work here. As you can see from the API doc (it's the link) span returns a Tuple2 (actually the doc says it returns a pair - but that's been deprecated in favor or Tuple2). I was trying to figure out why you don't get something back like a list-of-lists or some such thing and stumbled across the SO link above. As I understand it, the reason for the Tuple2 has to do with increasing performance by not having to deal with Java's 'boxing/unboxing' of things like ints into objects like Integers. My question is
1) is that an accurate statement?
2) are there other reasons for something like span to return a Tuple2?
thx!
A TupleN object has at least two major differences when compared to a "standard" List+:
(less importantly) the size of the tuple is known beforehand, allowing to better reason about it (by the programmer and the compiler).
(more importantly) a tuple preserves the type information for each of its elements/"slots".
Note that, as alluded, the type Tuple2 is a part of the TupleN family, all utilizing the same concept. For example:
scala> ("1",2,3l)
res0: (String, Int, Long) = (1,2,3)
scala> res0.getClass
res1: Class[_ <: (String, Int, Long)] = class scala.Tuple3
As you can see here, each of the elements in the 3-tuple has a distinct type, allowing for better pattern matching, stricter type protection etc.
+heterogeneous lists are also possible in Scala, but, so far, they're not part of the standard library, and arguably harder to understand, especially for newcomers.
span returns exactly two values. A Tuple2 can hold exactly two values. A list can contain arbitrarily many values. Therefore Tuple2 is just a better fit than using a list.
In languages like SML, Erlang and in buch of others we may define functions like this:
fun reverse [] = []
| reverse x :: xs = reverse xs # [x];
I know we can write analog in Scala like this (and I know, there are many flaws in the code below):
def reverse[T](lst: List[T]): List[T] = lst match {
case Nil => Nil
case x :: xs => reverse(xs) ++ List(x)
}
But I wonder, if we could write former code in Scala, perhaps with desugaring to the latter.
Is there any fundamental limitations for such syntax being implemented in the future (I mean, really fundamental -- e.g. the way type inference works in scala, or something else, except parser obviously)?
UPD
Here is a snippet of how it could look like:
type T
def reverse(Nil: List[T]) = Nil
def reverse(x :: xs: List[T]): List[T] = reverse(xs) ++ List(x)
It really depends on what you mean by fundamental.
If you are really asking "if there is a technical showstopper that would prevent to implement this feature", then I would say the answer is no. You are talking about desugaring, and you are on the right track here. All there is to do is to basically stitch several separates cases into one single function, and this can be done as a mere preprocessing step (this only requires syntactic knowledge, no need for semantic knowledge). But for this to even make sense, I would define a few rules:
The function signature is mandatory (in Haskell by example, this would be optional, but it is always optional whether you are defining the function at once or in several parts). We could try to arrange to live without the signature and attempt to extract it from the different parts, but lack of type information would quickly come to byte us. A simpler argument is that if we are to try to infer an implicit signature, we might as well do it for all the methods. But the truth is that there are very good reasons to have explicit singatures in scala and I can't imagine to change that.
All the parts must be defined within the same scope. To start with, they must be declared in the same file because each source file is compiled separately, and thus a simple preprocessor would not be enough to implement the feature. Second, we still end up with a single method in the end, so it's only natural to have all the parts in the same scope.
Overloading is not possible for such methods (otherwise we would need to repeat the signature for each part just so the preprocessor knows which part belongs to which overload)
Parts are added (stitched) to the generated match in the order they are declared
So here is how it could look like:
def reverse[T](lst: List[T]): List[T] // Exactly like an abstract def (provides the signature)
// .... some unrelated code here...
def reverse(Nil) = Nil
// .... another bit of unrelated code here...
def reverse(x :: xs ) = reverse(xs) ++ List(x)
Which could be trivially transformed into:
def reverse[T](list: List[T]): List[T] = lst match {
case Nil => Nil
case x :: xs => reverse(xs) ++ List(x)
}
// .... some unrelated code here...
// .... another bit of unrelated code here...
It is easy to see that the above transformation is very mechanical and can be done by just manipulating a source AST (the AST produced by the slightly modified grammar that accepts this new constructs), and transforming it into the target AST (the AST produced by the standard scala grammar).
Then we can compile the result as usual.
So there you go, with a few simple rules we are able to implement a preprocessor that does all the work to implement this new feature.
If by fundamental you are asking "is there anything that would make this feature out of place" then it can be argued that this does not feel very scala. But more to the point, it does not bring that much to the table. Scala author(s) actually tend toward making the language simpler (as in less built-in features, trying to move some built-in features into libraries) and adding a new syntax that is not really more readable goes against the goal of simplification.
In SML, your code snippet is literally just syntactic sugar (a "derived form" in the terminology of the language spec) for
val rec reverse = fn x =>
case x of [] => []
| x::xs = reverse xs # [x]
which is very close to the Scala code you show. So, no there is no "fundamental" reason that Scala couldn't provide the same kind of syntax. The main problem is Scala's need for more type annotations, which makes this shorthand syntax far less attractive in general, and probably not worth the while.
Note also that the specific syntax you suggest would not fly well, because there is no way to distinguish one case-by-case function definition from two overloaded functions syntactically. You probably would need some alternative syntax, similar to SML using "|".
I don't know SML or Erlang, but I know Haskell. It is a language without method overloading. Method overloading combined with such pattern matching could lead to ambiguities. Imagine following code:
def f(x: String) = "String "+x
def f(x: List[_]) = "List "+x
What should it mean? It can mean method overloading, i.e. the method is determined in compile time. It can also mean pattern matching. There would be just a f(x: AnyRef) method that would do the matching.
Scala also has named parameters, which would be probably also broken.
I don't think that Scala is able to offer more simple syntax than you have shown in general. A simpler syntax may IMHO work in some special cases only.
There are at least two problems:
[ and ] are reserved characters because they are used for type arguments. The compiler allows spaces around them, so that would not be an option.
The other problem is that = returns Unit. So the expression after the | would not return any result
The closest I could come up with is this (note that is very specialized towards your example):
// Define a class to hold the values left and right of the | sign
class |[T, S](val left: T, val right: PartialFunction[T, T])
// Create a class that contains the | operator
class OrAssoc[T](left: T) {
def |(right: PartialFunction[T, T]): T | T = new |(left, right)
}
// Add the | to any potential target
implicit def anyToOrAssoc[S](left: S): OrAssoc[S] = new OrAssoc(left)
object fun {
// Use the magic of the update method
def update[T, S](choice: T | S): T => T = { arg =>
if (choice.right.isDefinedAt(arg)) choice.right(arg)
else choice.left
}
}
// Use the above construction to define a new method
val reverse: List[Int] => List[Int] =
fun() = List.empty[Int] | {
case x :: xs => reverse(xs) ++ List(x)
}
// Call the method
reverse(List(3, 2, 1))