Related
I don't know why pattern d is bad in this list below.
Why need expicit type declaration?
def adder1(m:Int,n:Int) = m + n
val a = adder1(2,_) //OK
val b = adder1(_,2) //OK
def adder2(m:Int)(n:Int) = m + n
val c = adder2(2)(_) //OK
val d = adder2(_)(2) //NG:missing parameter type
val e = adder2(_:Int)(2) //OK
I just want to know the reason pattern d needs parameter type.
Very welcome just showing citation language spec.
So I believe this comes from the concept of Partial Application.
Intuitively, partial function application says "if you fix the first arguments of the function, you get a function of the remaining arguments"
...
Scala implements optional partial application with placeholder, e.g. def add(x: Int, y: Int) = {x+y}; add(1, _: Int) returns an incrementing function. Scala also support multiple parameter lists as currying, e.g. def add(x: Int)(y: Int) = {x+y}; add(1) _.
Lets take a look at adder2
From the REPL:
scala> def adder2(m:Int)(n:Int) = m + n
def adder2(m: Int)(n: Int): Int
Lets get a value to represent this:
scala> val adder2Value = adder2
^
error: missing argument list for method adder2
Unapplied methods are only converted to functions when a function type is expected.
You can make this conversion explicit by writing `adder2 _` or `adder2(_)(_)` instead of `adder2`.
Ok, let's try:
val adder2Value = adder2 _
val adder2Value: Int => (Int => Int) = $Lambda$1382/0x0000000840703840#4b66a923
Ahha!
In English: "A function that takes an Int and returns a function that takes an Int and returns an Int"
How can we bind the second argument using this signature? How can we access the inner function unless we first have gone through the outer one?
As far as I know, this is not possible to do using this signature, unless you explicitly define the type of your first argument.
(But what about adder2(_)(_)?)
scala> adder2(_)(_)
^
error: missing parameter type for expanded function ((<x$1: error>, x$2) => adder2(x$1)(x$2))
^
error: missing parameter type for expanded function ((<x$1: error>, <x$2: error>) => adder2(x$1)(x$2))
(Maybe this hints at our solution?)
Notice what happens if we explicitly define both arguments:
val adder2Value2= adder2Value (_:Int) (_:Int)
val adder2Value2: (Int, Int) => Int = $Lambda$1394/0x000000084070d840#32f7d983
This is much more manageable, we can now fix either argument, and get a simplified partial function:
scala> val adder2FirstArg = adder2Value (_:Int) (10)
val adder2FirstArg: Int => Int = $Lambda$1395/0x000000084070d040#47f5ddf4
scala> val adder2SecondArg = adder2Value (5) (_:Int)
val adder2SecondArg: Int => Int = $Lambda$1396/0x000000084070c840#21ed7ce
So what's really going on here?
When you bind an argument to a value, you have explicitly expressed the type (maybe it's inferred, but it's definitely that type, in this case, Ints). It's sugar so we don't need to write it. But under the hood, these are composed functions, and how they are composed is very important. To be able to match and simplify the function signature, the compiler requires us to provide this information in an outside-in manner. Otherwise, we need to give it some help to get there.
EDIT:
I think that this question serves as more of a Scala language spec. puzzle exercise, however. I can't think of any good reason, from a design perspective, for which you would need to implement a curried function in such a way that you cannot order the parameters such that the last parameters are the ones being inferred.
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.
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.
I'm trying to understand the point of this language feature of multiple parameter clauses and why you would use it.
Eg, what's the difference between these two functions really?
class WTF {
def TwoParamClauses(x : Int)(y: Int) = x + y
def OneParamClause(x: Int, y : Int) = x + y
}
>> val underTest = new WTF
>> underTest.TwoParamClauses(1)(1) // result is '2'
>> underTest.OneParamClause(1,1) // result is '2'
There's something on this in the Scala specification at point 4.6. See if that makes any sense to you.
NB: the spec calls these 'parameter clauses', but I think some people may also call them 'parameter lists'.
Here are three practical uses of multiple parameter lists,
To aid type inference. This is especially useful when using higher order methods. Below, the type parameter A of g2 is inferred from the first parameter x, so the function arguments in the second parameter f can be elided,
def g1[A](x: A, f: A => A) = f(x)
g1(2, x => x) // error: missing parameter type for argument x
def g2[A](x: A)(f: A => A) = f(x)
g2(2) {x => x} // type is inferred; also, a nice syntax
For implicit parameters. Only the last parameter list can be marked implicit, and a single parameter list cannot mix implicit and non-implicit parameters. The definition of g3 below requires two parameter lists,
// analogous to a context bound: g3[A : Ordering](x: A)
def g3[A](x: A)(implicit ev: Ordering[A]) {}
To set default values based on previous parameters,
def g4(x: Int, y: Int = 2*x) {} // error: not found value x
def g5(x: Int)(y: Int = 2*x) {} // OK
TwoParamClause involves two method invocations while the OneParamClause invokes the function method only once. I think the term you are looking for is currying. Among the many use cases, it helps you to breakdown the computation into small steps. This answer may convince you of usefulness of currying.
There is a difference between both versions concerning type inference. Consider
def f[A](a:A, aa:A) = null
f("x",1)
//Null = null
Here, the type A is bound to Any, which is a super type of String and Int. But:
def g[A](a:A)(aa:A) = null
g("x")(1)
error: type mismatch;
found : Int(1)
required: java.lang.String
g("x")(1)
^
As you see, the type checker only considers the first argument list, so A gets bound to String, so the Int value for aa in the second argument list is a type error.
Multiple parameter lists can help scala type inference for more details see: Making the most of Scala's (extremely limited) type inference
Type information does not flow from left to right within an argument list, only from left to right across argument lists. So, even though Scala knows the types of the first two arguments ... that information does not flow to our anonymous function.
...
Now that our binary function is in a separate argument list, any type information from the previous argument lists is used to fill in the types for our function ... therefore we don't need to annotate our lambda's parameters.
There are some cases where this distinction matters:
Multiple parameter lists allow you to have things like TwoParamClauses(2); which is automatically-generated function of type Int => Int which adds 2 to its argument. Of course you can define the same thing yourself using OneParamClause as well, but it will take more keystrokes
If you have a function with implicit parameters which also has explicit parameters, implicit parameters must be all in their own parameter clause (this may seem as an arbitrary restriction but is actually quite sensible)
Other than that, I think, the difference is stylistic.
In Scala one can write (curried?) functions like this
def curriedFunc(arg1: Int) (arg2: String) = { ... }
What is the difference between the above curriedFunc function definition with two parameters lists and functions with multiple parameters in a single parameter list:
def curriedFunc(arg1: Int, arg2: String) = { ... }
From a mathematical point of view this is (curriedFunc(x))(y) and curriedFunc(x,y) but I can write def sum(x) (y) = x + y and the same will be def sum2(x, y) = x + y
I know only one difference - this is partially applied functions. But both ways are equivalent for me.
Are there any other differences?
Strictly speaking, this is not a curried function, but a method with multiple argument lists, although admittedly it looks like a function.
As you said, the multiple arguments lists allow the method to be used in the place of a partially applied function. (Sorry for the generally silly examples I use)
object NonCurr {
def tabulate[A](n: Int, fun: Int => A) = IndexedSeq.tabulate(n)(fun)
}
NonCurr.tabulate[Double](10, _) // not possible
val x = IndexedSeq.tabulate[Double](10) _ // possible. x is Function1 now
x(math.exp(_)) // complete the application
Another benefit is that you can use curly braces instead of parenthesis which looks nice if the second argument list consists of a single function, or thunk. E.g.
NonCurr.tabulate(10, { i => val j = util.Random.nextInt(i + 1); i - i % 2 })
versus
IndexedSeq.tabulate(10) { i =>
val j = util.Random.nextInt(i + 1)
i - i % 2
}
Or for the thunk:
IndexedSeq.fill(10) {
println("debug: operating the random number generator")
util.Random.nextInt(99)
}
Another advantage is, you can refer to arguments of a previous argument list for defining default argument values (although you could also say it's a disadvantage that you cannot do that in single list :)
// again I'm not very creative with the example, so forgive me
def doSomething(f: java.io.File)(modDate: Long = f.lastModified) = ???
Finally, there are three other application in an answer to related post Why does Scala provide both multiple parameters lists and multiple parameters per list? . I will just copy them here, but the credit goes to Knut Arne Vedaa, Kevin Wright, and extempore.
First: you can have multiple var args:
def foo(as: Int*)(bs: Int*)(cs: Int*) = as.sum * bs.sum * cs.sum
...which would not be possible in a single argument list.
Second, it aids the type inference:
def foo[T](a: T, b: T)(op: (T,T) => T) = op(a, b)
foo(1, 2){_ + _} // compiler can infer the type of the op function
def foo2[T](a: T, b: T, op: (T,T) => T) = op(a, b)
foo2(1, 2, _ + _) // compiler too stupid, unfortunately
And last, this is the only way you can have implicit and non implicit args, as implicit is a modifier for a whole argument list:
def gaga [A](x: A)(implicit mf: Manifest[A]) = ??? // ok
def gaga2[A](x: A, implicit mf: Manifest[A]) = ??? // not possible
There's another difference that was not covered by 0__'s excellent answer: default parameters. A parameter from one parameter list can be used when computing the default in another parameter list, but not in the same one.
For example:
def f(x: Int, y: Int = x * 2) = x + y // not valid
def g(x: Int)(y: Int = x * 2) = x + y // valid
That's the whole point, is that the curried and uncurried forms are equivalent! As others have pointed out, one or the other form can be syntactically more convenient to work with depending on the situation, and that is the only reason to prefer one over the other.
It's important to understand that even if Scala didn't have special syntax for declaring curried functions, you could still construct them; this is just a mathematical inevitability once you have the ability to create functions which return functions.
To demonstrate this, imagine that the def foo(a)(b)(c) = {...} syntax didn't exist. Then you could still achieve the exact same thing like so: def foo(a) = (b) => (c) => {...}.
Like many features in Scala, this is just a syntactic convenience for doing something that would be possible anyway, but with slightly more verbosity.
The two forms are isomorphic. The main difference is that curried functions are easier to apply partially, while non-curried functions have slightly nicer syntax, at least in Scala.