How does Scala transform case classes to be accepted as functions? - scala

I am trying to understand how a case class can be passed as an argument to a function which accepts functions as arguments. Below is an example:
Consider the below function
def !![B](h: Out[B] => A): In[B] = { ... }
If I understood correctly, this is a polymorphic method which has a type parameter B and accepts a function h as a parameter. Out and In are other two classes defined previously.
This function is then being used as shown below:
case class Q(p: boolean)(val cont: Out[R])
case class R(p: Int)
def g(c: Out[Q]) = {
val rin = c !! Q(true)_
...
}
I am aware that currying is being used to avoid writing the type annotation and instead just writing _. However, I cannot grasp why and how the case class Q is transformed to a function (h) of type Out[B] => A.
EDIT 1 Updated !! above and the In and Out definitions:
abstract class In[+A] {
def future: Future[A]
def receive(implicit d: Duration): A = {
Await.result[A](future, d)
}
def ?[B](f: A => B)(implicit d: Duration): B = {
f(receive)
}
}
abstract class Out[-A]{
def promise[B <: A]: Promise[B]
def send(msg: A): Unit = promise.success(msg)
def !(msg: A) = send(msg)
def create[B](): (In[B], Out[B])
}
These code samples are taken from the following paper: http://drops.dagstuhl.de/opus/volltexte/2016/6115/

TLDR;
Using a case class with multiple parameter lists and partially applying it will yield a partially applied apply call + eta expansion will transform the method into a function value:
val res: Out[Q] => Q = Q.apply(true) _
Longer explanation
To understand the way this works in Scala, we have to understand some fundamentals behind case classes and the difference between methods and functions.
Case classes in Scala are a compact way of representing data. When you define a case class, you get a bunch of convenience methods which are created for you by the compiler, such as hashCode and equals.
In addition, the compiler also generates a method called apply, which allows you to create a case class instance without using the new keyword:
case class X(a: Int)
val x = X(1)
The compiler will expand this call to
val x = X.apply(1)
The same thing will happen with your case class, only that your case class has multiple argument lists:
case class Q(p: boolean)(val cont: Out[R])
val q: Q = Q(true)(new Out[Int] { })
Will get translated to
val q: Q = Q.apply(true)(new Out[Int] { })
On top of that, Scala has a way to transform methods, which are a non value type, into a function type which has the type of FunctionX, X being the arity of the function. In order to transform a method into a function value, we use a trick called eta expansion where we call a method with an underscore.
def foo(i: Int): Int = i
val f: Int => Int = foo _
This will transform the method foo into a function value of type Function1[Int, Int].
Now that we posses this knowledge, let's go back to your example:
val rin = c !! Q(true) _
If we just isolate Q here, this call gets translated into:
val rin = Q.apply(true) _
Since the apply method is curried with multiple argument lists, we'll get back a function that given a Out[Q], will create a Q:
val rin: Out[R] => Q = Q.apply(true) _

I cannot grasp why and how the case class Q is transformed to a function (h) of type Out[B] => A.
It isn't. In fact, the case class Q has absolutely nothing to do with this! This is all about the object Q, which is the companion module to the case class Q.
Every case class has an automatically generated companion module, which contains (among others) an apply method whose signature matches the primary constructor of the companion class, and which constructs an instance of the companion class.
I.e. when you write
case class Foo(bar: Baz)(quux: Corge)
You not only get the automatically defined case class convenience methods such as accessors for all the elements, toString, hashCode, copy, and equals, but you also get an automatically defined companion module that serves both as an extractor for pattern matching and as a factory for object construction:
object Foo {
def apply(bar: Baz)(quux: Corge) = new Foo(bar)(quux)
def unapply(that: Foo): Option[Baz] = ???
}
In Scala, apply is a method that allows you to create "function-like" objects: if foo is an object (and not a method), then foo(bar, baz) is translated to foo.apply(bar, baz).
The last piece of the puzzle is η-expansion, which lifts a method (which is not an object) into a function (which is an object and can thus be passed as an argument, stored in a variable, etc.) There are two forms of η-expansion: explicit η-expansion using the _ operator:
val printFunction = println _
And implicit η-expansion: in cases where Scala knows 100% that you mean a function but you give it the name of a method, Scala will perform η-expansion for you:
Seq(1, 2, 3) foreach println
And you already know about currying.
So, if we put it all together:
Q(true)_
First, we know that Q here cannot possibly be the class Q. How do we know that? Because Q here is used as a value, but classes are types, and like most programming languages, Scala has a strict separation between types and values. Therefore, Q must be a value. In particular, since we know class Q is a case class, object Q is the companion module for class Q.
Secondly, we know that for a value Q
Q(true)
is syntactic sugar for
Q.apply(true)
Thirdly, we know that for case classes, the companion module has an automatically generated apply method that matches the primary constructor, so we know that Q.apply has two parameter lists.
So, lastly, we have
Q.apply(true) _
which passes the first argument list to Q.apply and then lifts Q.apply into a function which accepts the second argument list.
Note that case classes with multiple parameter lists are unusual, since only the parameters in the first parameter list are considered elements of the case class, and only elements benefit from the "case class magic", i.e. only elements get accessors implemented automatically, only elements are used in the signature of the copy method, only elements are used in the automatically generated equals, hashCode, and toString() methods, and so on.

Related

Difference between function and methods in scala [duplicate]

I read Scala Functions (part of Another tour of Scala). In that post he stated:
Methods and functions are not the same thing
But he didn't explain anything about it. What was he trying to say?
Jim has got this pretty much covered in his blog post, but I'm posting a briefing here for reference.
First, let's see what the Scala Specification tell us. Chapter 3 (types) tell us about Function Types (3.2.9) and Method Types (3.3.1). Chapter 4 (basic declarations) speaks of Value Declaration and Definitions (4.1), Variable Declaration and Definitions (4.2) and Functions Declarations and Definitions (4.6). Chapter 6 (expressions) speaks of Anonymous Functions (6.23) and Method Values (6.7). Curiously, function values is spoken of one time on 3.2.9, and no where else.
A Function Type is (roughly) a type of the form (T1, ..., Tn) => U, which is a shorthand for the trait FunctionN in the standard library. Anonymous Functions and Method Values have function types, and function types can be used as part of value, variable and function declarations and definitions. In fact, it can be part of a method type.
A Method Type is a non-value type. That means there is no value - no object, no instance - with a method type. As mentioned above, a Method Value actually has a Function Type. A method type is a def declaration - everything about a def except its body.
Value Declarations and Definitions and Variable Declarations and Definitions are val and var declarations, including both type and value - which can be, respectively, Function Type and Anonymous Functions or Method Values. Note that, on the JVM, these (method values) are implemented with what Java calls "methods".
A Function Declaration is a def declaration, including type and body. The type part is the Method Type, and the body is an expression or a block. This is also implemented on the JVM with what Java calls "methods".
Finally, an Anonymous Function is an instance of a Function Type (ie, an instance of the trait FunctionN), and a Method Value is the same thing! The distinction is that a Method Value is created from methods, either by postfixing an underscore (m _ is a method value corresponding to the "function declaration" (def) m), or by a process called eta-expansion, which is like an automatic cast from method to function.
That is what the specs say, so let me put this up-front: we do not use that terminology! It leads to too much confusion between so-called "function declaration", which is a part of the program (chapter 4 -- basic declarations) and "anonymous function", which is an expression, and "function type", which is, well a type -- a trait.
The terminology below, and used by experienced Scala programmers, makes one change from the terminology of the specification: instead of saying function declaration, we say method. Or even method declaration. Furthermore, we note that value declarations and variable declarations are also methods for practical purposes.
So, given the above change in terminology, here's a practical explanation of the distinction.
A function is an object that includes one of the FunctionX traits, such as Function0, Function1, Function2, etc. It might be including PartialFunction as well, which actually extends Function1.
Let's see the type signature for one of these traits:
trait Function2[-T1, -T2, +R] extends AnyRef
This trait has one abstract method (it has a few concrete methods as well):
def apply(v1: T1, v2: T2): R
And that tell us all that there is to know about it. A function has an apply method which receives N parameters of types T1, T2, ..., TN, and returns something of type R. It is contra-variant on the parameters it receives, and co-variant on the result.
That variance means that a Function1[Seq[T], String] is a subtype of Function1[List[T], AnyRef]. Being a subtype means it can be used in place of it. One can easily see that if I'm going to call f(List(1, 2, 3)) and expect an AnyRef back, either of the two types above would work.
Now, what is the similarity of a method and a function? Well, if f is a function and m is a method local to the scope, then both can be called like this:
val o1 = f(List(1, 2, 3))
val o2 = m(List(1, 2, 3))
These calls are actually different, because the first one is just a syntactic sugar. Scala expands it to:
val o1 = f.apply(List(1, 2, 3))
Which, of course, is a method call on object f. Functions also have other syntactic sugars to its advantage: function literals (two of them, actually) and (T1, T2) => R type signatures. For example:
val f = (l: List[Int]) => l mkString ""
val g: (AnyVal) => String = {
case i: Int => "Int"
case d: Double => "Double"
case o => "Other"
}
Another similarity between a method and a function is that the former can be easily converted into the latter:
val f = m _
Scala will expand that, assuming m type is (List[Int])AnyRef into (Scala 2.7):
val f = new AnyRef with Function1[List[Int], AnyRef] {
def apply(x$1: List[Int]) = this.m(x$1)
}
On Scala 2.8, it actually uses an AbstractFunction1 class to reduce class sizes.
Notice that one can't convert the other way around -- from a function to a method.
Methods, however, have one big advantage (well, two -- they can be slightly faster): they can receive type parameters. For instance, while f above can necessarily specify the type of List it receives (List[Int] in the example), m can parameterize it:
def m[T](l: List[T]): String = l mkString ""
I think this pretty much covers everything, but I'll be happy to complement this with answers to any questions that may remain.
One big practical difference between a method and a function is what return means. return only ever returns from a method. For example:
scala> val f = () => { return "test" }
<console>:4: error: return outside method definition
val f = () => { return "test" }
^
Returning from a function defined in a method does a non-local return:
scala> def f: String = {
| val g = () => { return "test" }
| g()
| "not this"
| }
f: String
scala> f
res4: String = test
Whereas returning from a local method only returns from that method.
scala> def f2: String = {
| def g(): String = { return "test" }
| g()
| "is this"
| }
f2: String
scala> f2
res5: String = is this
function A function can be invoked with a list of arguments to produce a
result. A function has a parameter list, a body, and a result type.
Functions that are members of a class, trait, or singleton object are
called methods. Functions defined inside other functions are called
local functions. Functions with the result type of Unit are called procedures.
Anonymous functions in source code are called function literals.
At run time, function literals are instantiated into objects called
function values.
Programming in Scala Second Edition.
Martin Odersky - Lex Spoon - Bill Venners
Let Say you have a List
scala> val x =List.range(10,20)
x: List[Int] = List(10, 11, 12, 13, 14, 15, 16, 17, 18, 19)
Define a Method
scala> def m1(i:Int)=i+2
m1: (i: Int)Int
Define a Function
scala> (i:Int)=>i+2
res0: Int => Int = <function1>
scala> x.map((x)=>x+2)
res2: List[Int] = List(12, 13, 14, 15, 16, 17, 18, 19, 20, 21)
Method Accepting Argument
scala> m1(2)
res3: Int = 4
Defining Function with val
scala> val p =(i:Int)=>i+2
p: Int => Int = <function1>
Argument to function is Optional
scala> p(2)
res4: Int = 4
scala> p
res5: Int => Int = <function1>
Argument to Method is Mandatory
scala> m1
<console>:9: error: missing arguments for method m1;
follow this method with `_' if you want to treat it as a partially applied function
Check the following Tutorial that explains passing other differences with examples like other example of diff with Method Vs Function, Using function as Variables, creating function that returned function
Functions don't support parameter defaults. Methods do. Converting from a method to a function loses parameter defaults. (Scala 2.8.1)
There is a nice article here from which most of my descriptions are taken.
Just a short comparison of Functions and Methods regarding my understanding. Hope it helps:
Functions:
They are basically an object. More precisely, functions are objects with an apply method; Therefore, they are a little bit slower than methods because of their overhead. It is similar to static methods in the sense that they are independent of an object to be invoked.
A simple example of a function is just like bellow:
val f1 = (x: Int) => x + x
f1(2) // 4
The line above is nothing except assigning one object to another like object1 = object2. Actually the object2 in our example is an anonymous function and the left side gets the type of an object because of that. Therefore, now f1 is an object(Function). The anonymous function is actually an instance of Function1[Int, Int] that means a function with 1 parameter of type Int and return value of type Int.
Calling f1 without the arguments will give us the signature of the anonymous function (Int => Int = )
Methods:
They are not objects but assigned to an instance of a class,i.e., an object. Exactly the same as method in java or member functions in c++ (as Raffi Khatchadourian pointed out in a comment to this question) and etc.
A simple example of a method is just like bellow:
def m1(x: Int) = x + x
m1(2) // 4
The line above is not a simple value assignment but a definition of a method. When you invoke this method with the value 2 like the second line, the x is substituted with 2 and the result will be calculated and you get 4 as an output. Here you will get an error if just simply write m1 because it is method and need the input value. By using _ you can assign a method to a function like bellow:
val f2 = m1 _ // Int => Int = <function1>
Here is a great post by Rob Norris which explains the difference, here is a TL;DR
Methods in Scala are not values, but functions are. You can construct a function that delegates to a method via η-expansion (triggered by the trailing underscore thingy).
with the following definition:
a method is something defined with def and a value is something you can assign to a val
In a nutshell (extract from the blog):
When we define a method we see that we cannot assign it to a val.
scala> def add1(n: Int): Int = n + 1
add1: (n: Int)Int
scala> val f = add1
<console>:8: error: missing arguments for method add1;
follow this method with `_' if you want to treat it as a partially applied function
val f = add1
Note also the type of add1, which doesn’t look normal; you can’t declare a variable of type (n: Int)Int. Methods are not values.
However, by adding the η-expansion postfix operator (η is pronounced “eta”), we can turn the method into a function value. Note the type of f.
scala> val f = add1 _
f: Int => Int = <function1>
scala> f(3)
res0: Int = 4
The effect of _ is to perform the equivalent of the following: we construct a Function1 instance that delegates to our method.
scala> val g = new Function1[Int, Int] { def apply(n: Int): Int = add1(n) }
g: Int => Int = <function1>
scala> g(3)
res18: Int = 4
Practically, a Scala programmer only needs to know the following three rules to use functions and methods properly:
Methods defined by def and function literals defined by => are functions. It is defined in page 143, Chapter 8 in the book of Programming in Scala, 4th edition.
Function values are objects that can be passed around as any values. Function literals and partially applied functions are function values.
You can leave off the underscore of a partially applied function if a function value is required at a point in the code. For example: someNumber.foreach(println)
After four editions of Programming in Scala, it is still an issue for people to differentiate the two important concepts: function and function value because all editions don't give a clear explanation. The language specification is too complicated. I found the above rules are simple and accurate.
In Scala 2.13, unlike functions, methods can take/return
type parameters (polymorphic methods)
implicit parameters
dependent types
However, these restrictions are lifted in dotty (Scala 3) by Polymorphic function types #4672, for example, dotty version 0.23.0-RC1 enables the following syntax
Type parameters
def fmet[T](x: List[T]) = x.map(e => (e, e))
val ffun = [T] => (x: List[T]) => x.map(e => (e, e))
Implicit parameters (context parameters)
def gmet[T](implicit num: Numeric[T]): T = num.zero
val gfun: [T] => Numeric[T] ?=> T = [T] => (using num: Numeric[T]) => num.zero
Dependent types
class A { class B }
def hmet(a: A): a.B = new a.B
val hfun: (a: A) => a.B = hmet
For more examples, see tests/run/polymorphic-functions.scala
The difference is subtle but substantial and it is related to the type system in use (besides the nomenclature coming from Object Oriented or Functional paradigm).
When we talk about a function, we talk about the type Function: it being a type, an instance of it can be passed around as input or output to other functions (at least in the case of Scala).
When we talk about a method (of a class), we are actually talking about the type represented by the class it is part of: that is, the method is just a component of a larger type, and cannot be passed around by itself. It must be passed around with the instance of the type it is part of (i.e. the instance of the class).
A method belongs to an object (usually the class, trait or object in which you define it), whereas a function is by itself a value, and because in Scala every value is an object, therefore, a function is an object.
For example, given a method and a function below:
def timesTwoMethod(x :Int): Int = x * 2
def timesTwoFunction = (x: Int) => x * 2
The second def is an object of type Int => Int (the syntactic sugar for Function1[Int, Int]).
Scala made functions objects so they could be used as first-class entities. This way you can pass functions to other functions as arguments.
However, Scala can also treat methods as functions via a mechanism called Eta Expansion.
For example, the higher-order function map defined on List, receives another function f: A => B as its only parameter. The next two lines are equivalent:
List(1, 2, 3).map(timesTwoMethod)
List(1, 2, 3).map(timesTwoFunction)
When the compiler sees a def given in a place where a function is needed, it automatically converts the method into an equivalent function.
A method operates on an object but a function doesn't.
Scala and C++ has Fuction but in JAVA, you have to imitate them with static methods.

Function and method in Scala [duplicate]

I read Scala Functions (part of Another tour of Scala). In that post he stated:
Methods and functions are not the same thing
But he didn't explain anything about it. What was he trying to say?
Jim has got this pretty much covered in his blog post, but I'm posting a briefing here for reference.
First, let's see what the Scala Specification tell us. Chapter 3 (types) tell us about Function Types (3.2.9) and Method Types (3.3.1). Chapter 4 (basic declarations) speaks of Value Declaration and Definitions (4.1), Variable Declaration and Definitions (4.2) and Functions Declarations and Definitions (4.6). Chapter 6 (expressions) speaks of Anonymous Functions (6.23) and Method Values (6.7). Curiously, function values is spoken of one time on 3.2.9, and no where else.
A Function Type is (roughly) a type of the form (T1, ..., Tn) => U, which is a shorthand for the trait FunctionN in the standard library. Anonymous Functions and Method Values have function types, and function types can be used as part of value, variable and function declarations and definitions. In fact, it can be part of a method type.
A Method Type is a non-value type. That means there is no value - no object, no instance - with a method type. As mentioned above, a Method Value actually has a Function Type. A method type is a def declaration - everything about a def except its body.
Value Declarations and Definitions and Variable Declarations and Definitions are val and var declarations, including both type and value - which can be, respectively, Function Type and Anonymous Functions or Method Values. Note that, on the JVM, these (method values) are implemented with what Java calls "methods".
A Function Declaration is a def declaration, including type and body. The type part is the Method Type, and the body is an expression or a block. This is also implemented on the JVM with what Java calls "methods".
Finally, an Anonymous Function is an instance of a Function Type (ie, an instance of the trait FunctionN), and a Method Value is the same thing! The distinction is that a Method Value is created from methods, either by postfixing an underscore (m _ is a method value corresponding to the "function declaration" (def) m), or by a process called eta-expansion, which is like an automatic cast from method to function.
That is what the specs say, so let me put this up-front: we do not use that terminology! It leads to too much confusion between so-called "function declaration", which is a part of the program (chapter 4 -- basic declarations) and "anonymous function", which is an expression, and "function type", which is, well a type -- a trait.
The terminology below, and used by experienced Scala programmers, makes one change from the terminology of the specification: instead of saying function declaration, we say method. Or even method declaration. Furthermore, we note that value declarations and variable declarations are also methods for practical purposes.
So, given the above change in terminology, here's a practical explanation of the distinction.
A function is an object that includes one of the FunctionX traits, such as Function0, Function1, Function2, etc. It might be including PartialFunction as well, which actually extends Function1.
Let's see the type signature for one of these traits:
trait Function2[-T1, -T2, +R] extends AnyRef
This trait has one abstract method (it has a few concrete methods as well):
def apply(v1: T1, v2: T2): R
And that tell us all that there is to know about it. A function has an apply method which receives N parameters of types T1, T2, ..., TN, and returns something of type R. It is contra-variant on the parameters it receives, and co-variant on the result.
That variance means that a Function1[Seq[T], String] is a subtype of Function1[List[T], AnyRef]. Being a subtype means it can be used in place of it. One can easily see that if I'm going to call f(List(1, 2, 3)) and expect an AnyRef back, either of the two types above would work.
Now, what is the similarity of a method and a function? Well, if f is a function and m is a method local to the scope, then both can be called like this:
val o1 = f(List(1, 2, 3))
val o2 = m(List(1, 2, 3))
These calls are actually different, because the first one is just a syntactic sugar. Scala expands it to:
val o1 = f.apply(List(1, 2, 3))
Which, of course, is a method call on object f. Functions also have other syntactic sugars to its advantage: function literals (two of them, actually) and (T1, T2) => R type signatures. For example:
val f = (l: List[Int]) => l mkString ""
val g: (AnyVal) => String = {
case i: Int => "Int"
case d: Double => "Double"
case o => "Other"
}
Another similarity between a method and a function is that the former can be easily converted into the latter:
val f = m _
Scala will expand that, assuming m type is (List[Int])AnyRef into (Scala 2.7):
val f = new AnyRef with Function1[List[Int], AnyRef] {
def apply(x$1: List[Int]) = this.m(x$1)
}
On Scala 2.8, it actually uses an AbstractFunction1 class to reduce class sizes.
Notice that one can't convert the other way around -- from a function to a method.
Methods, however, have one big advantage (well, two -- they can be slightly faster): they can receive type parameters. For instance, while f above can necessarily specify the type of List it receives (List[Int] in the example), m can parameterize it:
def m[T](l: List[T]): String = l mkString ""
I think this pretty much covers everything, but I'll be happy to complement this with answers to any questions that may remain.
One big practical difference between a method and a function is what return means. return only ever returns from a method. For example:
scala> val f = () => { return "test" }
<console>:4: error: return outside method definition
val f = () => { return "test" }
^
Returning from a function defined in a method does a non-local return:
scala> def f: String = {
| val g = () => { return "test" }
| g()
| "not this"
| }
f: String
scala> f
res4: String = test
Whereas returning from a local method only returns from that method.
scala> def f2: String = {
| def g(): String = { return "test" }
| g()
| "is this"
| }
f2: String
scala> f2
res5: String = is this
function A function can be invoked with a list of arguments to produce a
result. A function has a parameter list, a body, and a result type.
Functions that are members of a class, trait, or singleton object are
called methods. Functions defined inside other functions are called
local functions. Functions with the result type of Unit are called procedures.
Anonymous functions in source code are called function literals.
At run time, function literals are instantiated into objects called
function values.
Programming in Scala Second Edition.
Martin Odersky - Lex Spoon - Bill Venners
Let Say you have a List
scala> val x =List.range(10,20)
x: List[Int] = List(10, 11, 12, 13, 14, 15, 16, 17, 18, 19)
Define a Method
scala> def m1(i:Int)=i+2
m1: (i: Int)Int
Define a Function
scala> (i:Int)=>i+2
res0: Int => Int = <function1>
scala> x.map((x)=>x+2)
res2: List[Int] = List(12, 13, 14, 15, 16, 17, 18, 19, 20, 21)
Method Accepting Argument
scala> m1(2)
res3: Int = 4
Defining Function with val
scala> val p =(i:Int)=>i+2
p: Int => Int = <function1>
Argument to function is Optional
scala> p(2)
res4: Int = 4
scala> p
res5: Int => Int = <function1>
Argument to Method is Mandatory
scala> m1
<console>:9: error: missing arguments for method m1;
follow this method with `_' if you want to treat it as a partially applied function
Check the following Tutorial that explains passing other differences with examples like other example of diff with Method Vs Function, Using function as Variables, creating function that returned function
Functions don't support parameter defaults. Methods do. Converting from a method to a function loses parameter defaults. (Scala 2.8.1)
There is a nice article here from which most of my descriptions are taken.
Just a short comparison of Functions and Methods regarding my understanding. Hope it helps:
Functions:
They are basically an object. More precisely, functions are objects with an apply method; Therefore, they are a little bit slower than methods because of their overhead. It is similar to static methods in the sense that they are independent of an object to be invoked.
A simple example of a function is just like bellow:
val f1 = (x: Int) => x + x
f1(2) // 4
The line above is nothing except assigning one object to another like object1 = object2. Actually the object2 in our example is an anonymous function and the left side gets the type of an object because of that. Therefore, now f1 is an object(Function). The anonymous function is actually an instance of Function1[Int, Int] that means a function with 1 parameter of type Int and return value of type Int.
Calling f1 without the arguments will give us the signature of the anonymous function (Int => Int = )
Methods:
They are not objects but assigned to an instance of a class,i.e., an object. Exactly the same as method in java or member functions in c++ (as Raffi Khatchadourian pointed out in a comment to this question) and etc.
A simple example of a method is just like bellow:
def m1(x: Int) = x + x
m1(2) // 4
The line above is not a simple value assignment but a definition of a method. When you invoke this method with the value 2 like the second line, the x is substituted with 2 and the result will be calculated and you get 4 as an output. Here you will get an error if just simply write m1 because it is method and need the input value. By using _ you can assign a method to a function like bellow:
val f2 = m1 _ // Int => Int = <function1>
Here is a great post by Rob Norris which explains the difference, here is a TL;DR
Methods in Scala are not values, but functions are. You can construct a function that delegates to a method via η-expansion (triggered by the trailing underscore thingy).
with the following definition:
a method is something defined with def and a value is something you can assign to a val
In a nutshell (extract from the blog):
When we define a method we see that we cannot assign it to a val.
scala> def add1(n: Int): Int = n + 1
add1: (n: Int)Int
scala> val f = add1
<console>:8: error: missing arguments for method add1;
follow this method with `_' if you want to treat it as a partially applied function
val f = add1
Note also the type of add1, which doesn’t look normal; you can’t declare a variable of type (n: Int)Int. Methods are not values.
However, by adding the η-expansion postfix operator (η is pronounced “eta”), we can turn the method into a function value. Note the type of f.
scala> val f = add1 _
f: Int => Int = <function1>
scala> f(3)
res0: Int = 4
The effect of _ is to perform the equivalent of the following: we construct a Function1 instance that delegates to our method.
scala> val g = new Function1[Int, Int] { def apply(n: Int): Int = add1(n) }
g: Int => Int = <function1>
scala> g(3)
res18: Int = 4
Practically, a Scala programmer only needs to know the following three rules to use functions and methods properly:
Methods defined by def and function literals defined by => are functions. It is defined in page 143, Chapter 8 in the book of Programming in Scala, 4th edition.
Function values are objects that can be passed around as any values. Function literals and partially applied functions are function values.
You can leave off the underscore of a partially applied function if a function value is required at a point in the code. For example: someNumber.foreach(println)
After four editions of Programming in Scala, it is still an issue for people to differentiate the two important concepts: function and function value because all editions don't give a clear explanation. The language specification is too complicated. I found the above rules are simple and accurate.
In Scala 2.13, unlike functions, methods can take/return
type parameters (polymorphic methods)
implicit parameters
dependent types
However, these restrictions are lifted in dotty (Scala 3) by Polymorphic function types #4672, for example, dotty version 0.23.0-RC1 enables the following syntax
Type parameters
def fmet[T](x: List[T]) = x.map(e => (e, e))
val ffun = [T] => (x: List[T]) => x.map(e => (e, e))
Implicit parameters (context parameters)
def gmet[T](implicit num: Numeric[T]): T = num.zero
val gfun: [T] => Numeric[T] ?=> T = [T] => (using num: Numeric[T]) => num.zero
Dependent types
class A { class B }
def hmet(a: A): a.B = new a.B
val hfun: (a: A) => a.B = hmet
For more examples, see tests/run/polymorphic-functions.scala
The difference is subtle but substantial and it is related to the type system in use (besides the nomenclature coming from Object Oriented or Functional paradigm).
When we talk about a function, we talk about the type Function: it being a type, an instance of it can be passed around as input or output to other functions (at least in the case of Scala).
When we talk about a method (of a class), we are actually talking about the type represented by the class it is part of: that is, the method is just a component of a larger type, and cannot be passed around by itself. It must be passed around with the instance of the type it is part of (i.e. the instance of the class).
A method belongs to an object (usually the class, trait or object in which you define it), whereas a function is by itself a value, and because in Scala every value is an object, therefore, a function is an object.
For example, given a method and a function below:
def timesTwoMethod(x :Int): Int = x * 2
def timesTwoFunction = (x: Int) => x * 2
The second def is an object of type Int => Int (the syntactic sugar for Function1[Int, Int]).
Scala made functions objects so they could be used as first-class entities. This way you can pass functions to other functions as arguments.
However, Scala can also treat methods as functions via a mechanism called Eta Expansion.
For example, the higher-order function map defined on List, receives another function f: A => B as its only parameter. The next two lines are equivalent:
List(1, 2, 3).map(timesTwoMethod)
List(1, 2, 3).map(timesTwoFunction)
When the compiler sees a def given in a place where a function is needed, it automatically converts the method into an equivalent function.
A method operates on an object but a function doesn't.
Scala and C++ has Fuction but in JAVA, you have to imitate them with static methods.

Why can't I apply pattern-matching against non-case classes?

Is there a better explanation than "this is how it works". I mean I tried this one:
class TestShortMatch[T <: AnyRef] {
def foo(t: T): Unit = {
val f = (_: Any) match {
case Val(t) => println(t)
case Sup(l) => println(l)
}
}
class Val(t: T)
class Sup(l: Number)
}
and compiler complaints:
Cannot resolve symbol 'Val'
Cannot resolve symbol 'Sup'
Of course if I add case before each of the classes it will work fine. But what is the reason? Does compiler make some optimization and generate a specific byte-code?
The reason is twofold. Pattern matching is just syntactic sugar for using extractors and case classes happen to give you a couple methods for free, one of which is an extractor method that corresponds to the main constructor.
If you want your example above to work, you need to define an unapply method inside objects Val and Sup. To do that you'd need extractor methods (which are only defined on val fields, so you'll have to make your fields vals):
class Val[T](val t: T)
class Sup(val l: Number)
object Val {
def unapply[T](v: Val[T]): Option[T] = Some(v.t)
}
object Sup {
def unapply(s: Sup): Option[Number] = Some(s.l)
}
And which point you can do something like val Val(v) = new Val("hi"). More often than not, though, it is better to make your class a case class. Then, the only times you should be defining extra extractors.
The usual example (to which I can't seem to find a reference) is coordinates:
case class Coordinate(x: Double, val: Double)
And then you can define a custom extractors like
object Polar {
def unapply(c: Coordinate): Option[(Double,Double)] = {...}
}
object Cartesian {
def unapply(c: Coordinate): Option[(Double,Double)] = Some((c.x,c.y))
}
to convert to the two different representations, all when you pattern match.
You can use pattern matching on arbitrary classes, but you need to implement an unapply method, used to "de-construct" the object.
With a case class, the unapply method is automatically generated by the compiler, so you don't need to implement it yourself.
When you write match exp { case Val(pattern) => ... case ... }, that is equivalent to something like this:
match Val.unapply(exp) {
case Some(pattern) =>
...
case _ =>
// code to match the other cases goes here
}
That is, it uses the result of the companion object's unapply method to see whether the match succeeded.
If you define a case class, it automatically defines a companion object with a suitable unapply method. For a normal class it doesn't. The motivation for that is the same as for the other things that gets automatically defined for case classes (like equals and hashCode for example): By declaring a class as a case class, you're making a statement about how you want the class to behave. Given that, there's a good chance that the auto generated will do what you want. For a general class, it's up to you to define these methods like you want them to behave.
Note that parameters for case classes are vals by default, which isn't true for normal classes. So your class class Val(t: T) doesn't even have any way to access t from the outside. So it isn't even possible to define an unapply method that gets at the value of t. That's another reason why you don't get an automatically generated unapply for normal classes: It isn't even possible to generate one unless all parameters are vals.

Scala Function Definitions and Performance [duplicate]

I read Scala Functions (part of Another tour of Scala). In that post he stated:
Methods and functions are not the same thing
But he didn't explain anything about it. What was he trying to say?
Jim has got this pretty much covered in his blog post, but I'm posting a briefing here for reference.
First, let's see what the Scala Specification tell us. Chapter 3 (types) tell us about Function Types (3.2.9) and Method Types (3.3.1). Chapter 4 (basic declarations) speaks of Value Declaration and Definitions (4.1), Variable Declaration and Definitions (4.2) and Functions Declarations and Definitions (4.6). Chapter 6 (expressions) speaks of Anonymous Functions (6.23) and Method Values (6.7). Curiously, function values is spoken of one time on 3.2.9, and no where else.
A Function Type is (roughly) a type of the form (T1, ..., Tn) => U, which is a shorthand for the trait FunctionN in the standard library. Anonymous Functions and Method Values have function types, and function types can be used as part of value, variable and function declarations and definitions. In fact, it can be part of a method type.
A Method Type is a non-value type. That means there is no value - no object, no instance - with a method type. As mentioned above, a Method Value actually has a Function Type. A method type is a def declaration - everything about a def except its body.
Value Declarations and Definitions and Variable Declarations and Definitions are val and var declarations, including both type and value - which can be, respectively, Function Type and Anonymous Functions or Method Values. Note that, on the JVM, these (method values) are implemented with what Java calls "methods".
A Function Declaration is a def declaration, including type and body. The type part is the Method Type, and the body is an expression or a block. This is also implemented on the JVM with what Java calls "methods".
Finally, an Anonymous Function is an instance of a Function Type (ie, an instance of the trait FunctionN), and a Method Value is the same thing! The distinction is that a Method Value is created from methods, either by postfixing an underscore (m _ is a method value corresponding to the "function declaration" (def) m), or by a process called eta-expansion, which is like an automatic cast from method to function.
That is what the specs say, so let me put this up-front: we do not use that terminology! It leads to too much confusion between so-called "function declaration", which is a part of the program (chapter 4 -- basic declarations) and "anonymous function", which is an expression, and "function type", which is, well a type -- a trait.
The terminology below, and used by experienced Scala programmers, makes one change from the terminology of the specification: instead of saying function declaration, we say method. Or even method declaration. Furthermore, we note that value declarations and variable declarations are also methods for practical purposes.
So, given the above change in terminology, here's a practical explanation of the distinction.
A function is an object that includes one of the FunctionX traits, such as Function0, Function1, Function2, etc. It might be including PartialFunction as well, which actually extends Function1.
Let's see the type signature for one of these traits:
trait Function2[-T1, -T2, +R] extends AnyRef
This trait has one abstract method (it has a few concrete methods as well):
def apply(v1: T1, v2: T2): R
And that tell us all that there is to know about it. A function has an apply method which receives N parameters of types T1, T2, ..., TN, and returns something of type R. It is contra-variant on the parameters it receives, and co-variant on the result.
That variance means that a Function1[Seq[T], String] is a subtype of Function1[List[T], AnyRef]. Being a subtype means it can be used in place of it. One can easily see that if I'm going to call f(List(1, 2, 3)) and expect an AnyRef back, either of the two types above would work.
Now, what is the similarity of a method and a function? Well, if f is a function and m is a method local to the scope, then both can be called like this:
val o1 = f(List(1, 2, 3))
val o2 = m(List(1, 2, 3))
These calls are actually different, because the first one is just a syntactic sugar. Scala expands it to:
val o1 = f.apply(List(1, 2, 3))
Which, of course, is a method call on object f. Functions also have other syntactic sugars to its advantage: function literals (two of them, actually) and (T1, T2) => R type signatures. For example:
val f = (l: List[Int]) => l mkString ""
val g: (AnyVal) => String = {
case i: Int => "Int"
case d: Double => "Double"
case o => "Other"
}
Another similarity between a method and a function is that the former can be easily converted into the latter:
val f = m _
Scala will expand that, assuming m type is (List[Int])AnyRef into (Scala 2.7):
val f = new AnyRef with Function1[List[Int], AnyRef] {
def apply(x$1: List[Int]) = this.m(x$1)
}
On Scala 2.8, it actually uses an AbstractFunction1 class to reduce class sizes.
Notice that one can't convert the other way around -- from a function to a method.
Methods, however, have one big advantage (well, two -- they can be slightly faster): they can receive type parameters. For instance, while f above can necessarily specify the type of List it receives (List[Int] in the example), m can parameterize it:
def m[T](l: List[T]): String = l mkString ""
I think this pretty much covers everything, but I'll be happy to complement this with answers to any questions that may remain.
One big practical difference between a method and a function is what return means. return only ever returns from a method. For example:
scala> val f = () => { return "test" }
<console>:4: error: return outside method definition
val f = () => { return "test" }
^
Returning from a function defined in a method does a non-local return:
scala> def f: String = {
| val g = () => { return "test" }
| g()
| "not this"
| }
f: String
scala> f
res4: String = test
Whereas returning from a local method only returns from that method.
scala> def f2: String = {
| def g(): String = { return "test" }
| g()
| "is this"
| }
f2: String
scala> f2
res5: String = is this
function A function can be invoked with a list of arguments to produce a
result. A function has a parameter list, a body, and a result type.
Functions that are members of a class, trait, or singleton object are
called methods. Functions defined inside other functions are called
local functions. Functions with the result type of Unit are called procedures.
Anonymous functions in source code are called function literals.
At run time, function literals are instantiated into objects called
function values.
Programming in Scala Second Edition.
Martin Odersky - Lex Spoon - Bill Venners
Let Say you have a List
scala> val x =List.range(10,20)
x: List[Int] = List(10, 11, 12, 13, 14, 15, 16, 17, 18, 19)
Define a Method
scala> def m1(i:Int)=i+2
m1: (i: Int)Int
Define a Function
scala> (i:Int)=>i+2
res0: Int => Int = <function1>
scala> x.map((x)=>x+2)
res2: List[Int] = List(12, 13, 14, 15, 16, 17, 18, 19, 20, 21)
Method Accepting Argument
scala> m1(2)
res3: Int = 4
Defining Function with val
scala> val p =(i:Int)=>i+2
p: Int => Int = <function1>
Argument to function is Optional
scala> p(2)
res4: Int = 4
scala> p
res5: Int => Int = <function1>
Argument to Method is Mandatory
scala> m1
<console>:9: error: missing arguments for method m1;
follow this method with `_' if you want to treat it as a partially applied function
Check the following Tutorial that explains passing other differences with examples like other example of diff with Method Vs Function, Using function as Variables, creating function that returned function
Functions don't support parameter defaults. Methods do. Converting from a method to a function loses parameter defaults. (Scala 2.8.1)
There is a nice article here from which most of my descriptions are taken.
Just a short comparison of Functions and Methods regarding my understanding. Hope it helps:
Functions:
They are basically an object. More precisely, functions are objects with an apply method; Therefore, they are a little bit slower than methods because of their overhead. It is similar to static methods in the sense that they are independent of an object to be invoked.
A simple example of a function is just like bellow:
val f1 = (x: Int) => x + x
f1(2) // 4
The line above is nothing except assigning one object to another like object1 = object2. Actually the object2 in our example is an anonymous function and the left side gets the type of an object because of that. Therefore, now f1 is an object(Function). The anonymous function is actually an instance of Function1[Int, Int] that means a function with 1 parameter of type Int and return value of type Int.
Calling f1 without the arguments will give us the signature of the anonymous function (Int => Int = )
Methods:
They are not objects but assigned to an instance of a class,i.e., an object. Exactly the same as method in java or member functions in c++ (as Raffi Khatchadourian pointed out in a comment to this question) and etc.
A simple example of a method is just like bellow:
def m1(x: Int) = x + x
m1(2) // 4
The line above is not a simple value assignment but a definition of a method. When you invoke this method with the value 2 like the second line, the x is substituted with 2 and the result will be calculated and you get 4 as an output. Here you will get an error if just simply write m1 because it is method and need the input value. By using _ you can assign a method to a function like bellow:
val f2 = m1 _ // Int => Int = <function1>
Here is a great post by Rob Norris which explains the difference, here is a TL;DR
Methods in Scala are not values, but functions are. You can construct a function that delegates to a method via η-expansion (triggered by the trailing underscore thingy).
with the following definition:
a method is something defined with def and a value is something you can assign to a val
In a nutshell (extract from the blog):
When we define a method we see that we cannot assign it to a val.
scala> def add1(n: Int): Int = n + 1
add1: (n: Int)Int
scala> val f = add1
<console>:8: error: missing arguments for method add1;
follow this method with `_' if you want to treat it as a partially applied function
val f = add1
Note also the type of add1, which doesn’t look normal; you can’t declare a variable of type (n: Int)Int. Methods are not values.
However, by adding the η-expansion postfix operator (η is pronounced “eta”), we can turn the method into a function value. Note the type of f.
scala> val f = add1 _
f: Int => Int = <function1>
scala> f(3)
res0: Int = 4
The effect of _ is to perform the equivalent of the following: we construct a Function1 instance that delegates to our method.
scala> val g = new Function1[Int, Int] { def apply(n: Int): Int = add1(n) }
g: Int => Int = <function1>
scala> g(3)
res18: Int = 4
Practically, a Scala programmer only needs to know the following three rules to use functions and methods properly:
Methods defined by def and function literals defined by => are functions. It is defined in page 143, Chapter 8 in the book of Programming in Scala, 4th edition.
Function values are objects that can be passed around as any values. Function literals and partially applied functions are function values.
You can leave off the underscore of a partially applied function if a function value is required at a point in the code. For example: someNumber.foreach(println)
After four editions of Programming in Scala, it is still an issue for people to differentiate the two important concepts: function and function value because all editions don't give a clear explanation. The language specification is too complicated. I found the above rules are simple and accurate.
In Scala 2.13, unlike functions, methods can take/return
type parameters (polymorphic methods)
implicit parameters
dependent types
However, these restrictions are lifted in dotty (Scala 3) by Polymorphic function types #4672, for example, dotty version 0.23.0-RC1 enables the following syntax
Type parameters
def fmet[T](x: List[T]) = x.map(e => (e, e))
val ffun = [T] => (x: List[T]) => x.map(e => (e, e))
Implicit parameters (context parameters)
def gmet[T](implicit num: Numeric[T]): T = num.zero
val gfun: [T] => Numeric[T] ?=> T = [T] => (using num: Numeric[T]) => num.zero
Dependent types
class A { class B }
def hmet(a: A): a.B = new a.B
val hfun: (a: A) => a.B = hmet
For more examples, see tests/run/polymorphic-functions.scala
The difference is subtle but substantial and it is related to the type system in use (besides the nomenclature coming from Object Oriented or Functional paradigm).
When we talk about a function, we talk about the type Function: it being a type, an instance of it can be passed around as input or output to other functions (at least in the case of Scala).
When we talk about a method (of a class), we are actually talking about the type represented by the class it is part of: that is, the method is just a component of a larger type, and cannot be passed around by itself. It must be passed around with the instance of the type it is part of (i.e. the instance of the class).
A method belongs to an object (usually the class, trait or object in which you define it), whereas a function is by itself a value, and because in Scala every value is an object, therefore, a function is an object.
For example, given a method and a function below:
def timesTwoMethod(x :Int): Int = x * 2
def timesTwoFunction = (x: Int) => x * 2
The second def is an object of type Int => Int (the syntactic sugar for Function1[Int, Int]).
Scala made functions objects so they could be used as first-class entities. This way you can pass functions to other functions as arguments.
However, Scala can also treat methods as functions via a mechanism called Eta Expansion.
For example, the higher-order function map defined on List, receives another function f: A => B as its only parameter. The next two lines are equivalent:
List(1, 2, 3).map(timesTwoMethod)
List(1, 2, 3).map(timesTwoFunction)
When the compiler sees a def given in a place where a function is needed, it automatically converts the method into an equivalent function.
A method operates on an object but a function doesn't.
Scala and C++ has Fuction but in JAVA, you have to imitate them with static methods.

scala loan pattern, optional function param

I have a loan pattern that applies a function n times where 'i' is the incrementing variable. "Occasionally", I want the function passed in to have access to 'i'....but I don't want to require all functions passed in to require defining a param to accept 'i'. Example below...
def withLoaner = (n:Int) => (op:(Int) => String) => {
val result = for(i <- 1 to n) yield op(i)
result.mkString("\n")
}
def bob = (x:Int) => "bob" // don't need access to i. is there a way use () => "bob" instead?
def nums = (x:Int) => x.toString // needs access to i, define i as an input param
println(withLoaner(3)(bob))
println(withLoaner(3)(nums))
def withLoaner(n: Int) = new {
def apply(op: Int => String) : String = (1 to n).map(op).mkString("\n")
def apply(op: () => String) : String = apply{i: Int => op()}
}
(not sure how it is related to the loan pattern)
Edit Little explanation as requested in comment.
Not sure what you know and don't know of scala and what you don't undestand in that code. so sorry if what I just belabor the obvious.
First, a scala program consist of traits/classes (also singleton object) and methods. Everything that is done is done by methods (leaving constructor aside). Functions (as opposed to methods) are instances of (subtypes of) the various FunctionN traits (N the number of arguments). Each of them has as apply method that is the actual implemention.
If you write
val inc = {i: Int => i + 1}
it is desugared to
val inc = new Function1[Int, Int] {def apply(i: Int) = i + 1}
(defines an anonymous class extending Function1, with given apply method and creating an instance)
So writing a function has rather more weight than a simple method. Also you cannot have overloading (several methods with the same name, differing by the signature, just what I did above), nor use named arguments, or default value for arguments.
On the other hand, functions are first classes values (they can be passed as arguments, returned as result) while methods are not. They are automatically converted to functions when needed, however there may be some edges cases when doing that. If a method is intended solely to be used as a function value, rather than called as a method, it might be better to write a function.
A function f, with its apply method, is called with f(x) rather than f.apply(x) (which works too), because scala desugars function call notation on a value (value followed by parentheses and 0 or more args) to a call to method apply. f(x) is syntactic sugar for f.apply(x). This works whatever the type of f, it does not need to be one of the FunctionN.
What is done in withLoaner is returning an object (of an anonymous type, but one could have defined a class separately and returned an instance of it). The object has two apply methods, one accepting an Int => String, the other one an () => String. When you do withLoaner(n)(f) it means withLoaner(n).apply(f). The appropriate apply method is selected, if f has the proper type for one of them, otherwise, compile error.
Just in case you wonder withLoaner(n) does not mean withLoaner.apply(n) (or it would never stop, that could just as well mean withLoaner.apply.apply(n)), as withLoaner is a method, not a value.