Scala: Passing Vs applying function - function

Let's say we have the following code snippet:
List(1, 2, 3)
.map(doubleIt) // passing function
.map(x => doubleIt(x)) // applying function
def doubleIt(i: Int): Int = 2 * i
As you can see we can either pass doubleIt as a function literal or apply it inside another anonymous Lambda. I have always wondered which approach is better. I personally prefer passing a function literal as it seems like second approach would end up creating an extra wrapper Lambda for no good reason, but I am not 100% positive my reasoning is correct.
I am curious to know what the pro/cons of each style are and whether one is definitely better than the other.

This might change in Scala 2.12+, but at the moment both approaches are identical. As a test, I created the following:
class Test {
def testPassingFunction: List[Int] = List(1, 2, 3).map(doubleIt)
def testApplyingFunction: List[Int] = List(1, 2, 3).map(x => doubleIt(x))
def doubleIt(i: Int): Int = 2 * i
}
I then compiled it and used javap to disassemble the bytecode. Both functions are identical (except for different Strings. In all cases a new class that extends from Function1 is created that calls the appropriate method. As #Mike says in the comments, the Scala compiler converts everything to the second form.

It turns out that it depends somewhat on what your "function" is. If it is actually a function (that is, a function value, defined as val doubleIt = (x: Int) => 2 * x), then your hunch is correct. The version in which you pass a function literal that simply applies doubleIt (i.e., l map { x => doubleIt(x) } is compiled just as written, resulting in an anonymous function that delegates to doubleIt. Passing doubleIt as a function value takes out the middle man. If doubleIt is a method, on the other hand, then both forms are compiled identically.
You can easily verify this yourself at the REPL. Define the following class:
class A {
val l = List(1,2,3)
val f = (x: Int) => 2 * x
def g(x: Int) = 2 * x
def m1 = l map f
def m2 = l map { x => f(x) }
def m3 = l map g
def m4 = l map { x => g(x) }
}
Then run :power and :javap -v A.
That said, the distinction is unlikely to make a practical difference in any but the most performance-critical code. In ordinary circumstances, code clarity is the more important consideration and depends somewhat on who will be reading your code in the future. Personally, I tend to prefer the concise lst map doubleIt form; this form eliminates a bunch of syntactic noise that adds nothing semantically. I suppose the longer form may be considered more explicit, especially for developers that aren't very familiar with the map method. The literal reading matches the intent quite well: "(Given) list, map (each) x to doubleIt(x)". Your team will have to decide what's best for you and your organization.

Related

Chisel variable Declaration Syntax Meaning rvs: Bool*

Looking at object DecoupledHelper and class DecoupledHelper code, I see the following.
object DecoupledHelper {
def apply(rvs: Bool*) = new DecoupledHelper(rvs)
}
class DecoupledHelper(val rvs: Seq[Bool]) {
def fire(exclude: Bool, includes: Bool*) = {
(rvs.filter(_ ne exclude) ++ includes).reduce(_ && _)
}
}
I don't understand the parameters declaration syntax in apply method. (rvs: Bool*). What is the meaning of * at end of Type Bool.
Looking at constructor parameters of class DecoupledHelper, it expects (rvs: Seq[Bool])
Does this mean that type Bool* is automatically converted to type Seq[Bool]?
While at this, can anyone also explain what rvs.filter method is doing?
As Kamyar said, Type* is the Scala syntax for variable number of arguments (also known as "varags"). It let's you call the DecoupledHelper apply method like so:
val helper = DecoupledHelper(a, b, c) // calling apply on the companion object
// instead of
val helper2 = new DecoupledHelper(Seq(a, b, c)) // calling constructor of the class
For those new to Chisel and Scala, note that apply is a special function Scala that is called when you "apply" parentheses to an object or instance. Thus DecoupledHelper(a, b, c) is equivalent to DecoupledHelper.apply(a, b, c).
While at this, can anyone also explain what rvs.filter method is doing?
It is taking advantage of the implementation of Chisel which I would not recommend doing. ne is the Scala function for not referentially equal. It lets you check if two object are not the same object in memory.
In this case, it let's you do things like the following:
val helper = DecoupledHelper(a, b, c)
helper.fire() // a && b && c
helper.fire(b) // a && c
Now because this is dangerously using referential equality instead of actual hardware equality (and there are limitations of the implementation that motivated this), something that should work does not:
val helper = DecoupledHelper(a, b, c)
val d = b // Same reference
val e = WireInit(b) // Equivalent Wire but different reference
helper.fire(d) // a && c
helper.fire(e) // a && b && c
d points to the same object on the heap as b, but e does not despite the fact that it is equivalent from the hardware perspective.
For more information, see the related bug report and discussion: https://github.com/chipsalliance/rocket-chip/issues/1616

Error while passing values using peekpoketester

I am trying to pass some random integers (which I have stored in an array) to my hardware as an Input through the poke method in peekpoketester. But I am getting this error:
chisel3.internal.ChiselException: Error: Not in a UserModule. Likely cause: Missed Module() wrap, bare chisel API call, or attempting to construct hardware inside a BlackBox.
What could be the reason? I don't think I need a module wrap here as this is not hardware.
class TesterSimple (dut: DeviceUnderTest)(parameter1 : Int)(parameter2 : Int) extends
PeekPokeTester (dut) {
var x = Array[Int](parameter1)
var y = Array[Int](parameter2)
var z = 1
poke(dut.io.IP1, z.asUInt)
for(i <- 0 until parameter1){poke(dut.io.IP2(i), x(i).asUInt)}
for(j <- 0 until parameter2){poke(dut.io.IP3(j), y(j).asUInt)}
}
object TesterSimple extends App {
implicit val parameter1 = 2
implicit val parameter2 = 2
chisel3.iotesters.Driver (() => DeviceUnderTest(parameter1 :Int, parameter2 :Int)) { c =>
new TesterSimple (c)(parameter1, parameter2)}
}
I'd suggest a couple of things.
Main problem, I think you are not initializing your arrays properly
Try using Array.fill or Array.tabulate to create and initialize arrays
val rand = scala.util.Random
var x = Array.fill(parameter1)(rand.nextInt(100))
var y = Array.fill(parameter2)(rand.nextInt(100))
You don't need the .asUInt in the poke, it accepts Ints or BigInts
When defining hardware constants, use .U instead of .asUInt, the latter is a way of casting other chisel types, it does work but it a backward compatibility thing.
It's better to not start variables or methods with capital letters
I suggest us class DutName(val parameter1: Int, val parameter2: Int) or class DutName(val parameter1: Int)(val parameter2: Int) if you prefer.
This will allow to use the dut's paremeters when you are writing your test.
E.g. for(i <- 0 until dut.parameter1){poke(dut.io.IP2(i), x(i))}
This will save you have to duplicate parameter objects on your DUT and your Tester
Good luck!
Could you also share your DUT?
I believe the most likely case is your DUT does not extend Module

def or val for defining Function in Scala

I'm learning Programming Paradigms in my University and reading this course material provided by the lecturer that defined a function this way:
val double = (x: Int) => 2 * x
double: Int => Int = <function1>
But from my own studies I found and got used to defining the same function like this:
def d (x: Int) = 2 * x
d: (x: Int)Int
I'm new to Scala. And both definitions give a result of:
res21: Int = 8
Upon passing 4 as the parameter.
Now my main question is why would the lecturer prefer to use val to define a function? I see it as longer and not really necessary unless using val gives some added advantages that I don't know of. Besides I understand using val makes some name a placeholder so later in the program, I could mistakenly write val double = 5 and the function would be gone!
At this stage I'm quite convinced I learned a better way of defining a function unless someone would tell me otherwise.
Strictly speaking def d (x: Int) = 2 * x is a method, not a Function, however scala can transparently convert (lift) methods into Functions for us. So that means you can use the d method anywhere that requires a Int => Int Function.
There is a small overhead of performing this conversion, as a new Function instance is created every time. We can see this happening here:
val double = (x: Int) => 2 * x
def d (x: Int) = 2 * x
def printFunc(f: Int => Int) = println(f.hashCode())
printFunc(double)
printFunc(double)
printFunc(d)
printFunc(d)
Which results in output like so:
1477986427
1477986427
574533740
1102091268
You can see when explicitly defining a Function using a val, our program only creates a single Function and reuses it when we pass as an argument to printFunc (we see the same hash code). When we use a def, the conversion to a Function happens every time we pass it to printFunc and we create several instances of the Function with different hash codes. Try it
That said, the performance overhead is small and often doesn't make any real difference to our program, so defs are often used to define Functions as many people find them more concise and easier to read.
In Scala, function values are monomorphic (i.e. they can not have type parameters, aka "generics"). If you want a polymorphic function, you have to work around this, for example by defining it using a method:
def headOption[A]: List[A] => Option[A] = {
case Nil => None
case x::xs => Some(x)
}
It would not be valid syntax to write val headOption[A]. Note that this didn't make a polymorphic function value, it is just a polymorphic method, returning a monomorphic function value of the appropriate type.
Because you might have something like the following:
abstract class BaseClass {
val intToIntFunc: Int => Int
}
class A extends BaseClass {
override val intToIntFunc = (i: Int) => i * 2
}
So its purpose might not be obvious with a very simple example. But that Function value could itself be passed to higher order functions: functions that take functions as parameters. If you look in the Scala collections documentation you will see numerous methods that take functions as parameters. Its a very powerful and versatile tool, but you need to get to a certain complexity and familiarity with algorithms before the cost /benefit becomes obvious.
I would also suggest not using "double" as an identifier name. Although legal Scala, it is easy to confuse it with the type Double.

Passing functions and operating on their results within Scala's Actors

I'm implementing an actor-based app in scala and I'm trying to be able to pass functions between the actors for them to be processed only when some message is received by the actor.
import actors.Actor
import java.util.Random
import scala.Numeric._
import Implicits._
class Constant(val n:Number) extends Actor{
def act(){
loop{
receive{
case "value" => reply( {n} )
}
}
}
}
class Arithmetic[T: Numeric](A: ()=>T, B: ()=>T) extends Actor{
def act(){
receive{
case "sum" => reply ( A() + B() )
/* case "mul" => reply ( A * B )
*/
}
}
}
object Main extends App{
val c5 = new Constant(5)
c5.start
val a = new Arithmetic({c5 !! "value"}, {c5!!"value"} )
a.start
println(a!?"sum")
println(a!?"mul")
}
In the example code above I would expect the output to be both 5+5 and 5*5. The issue is that reply is not a typed function and as such I'm unable to have the operator (+,*) to operate over the result from A and B.
Can you provide any help on how to better design/implement such system?
Edit: Code updated to better reflect the problem. Error in:
error: could not find implicit value for evidence parameter of type Numeric[Any]
val a = new Arithmetic({c5 !! "value"}, {c5!!"value"} )
I need to be able to pass the function to be evaluated in the actor whenever I call it. This example uses static values but I'll bu using dynamic values in the future, so, passing the value won't solve the problem. Also, I would like to receive different var types (Int/Long/Double) and still be able to use the same code.
The error: Error in: error: could not find implicit value for evidence parameter of type Numeric[Any]. The definition of !!:
def !! (msg: Any): Future[Any]
So the T that Arithmetic is getting is Any. There truly isn't a Numeric[Any].
I'm pretty sure that is not your problem. First, A and B are functions, and functions don't have + or *. If you called A() and B(), then you might stand a chance... except for the fact that they are java.lang.Number, which also does not have + or * (or any other method you'd expect it to have).
Basically, there's no "Number" type that is a superclass or interface of all numbers for the simple reason that Java doesn't have it. There's a lot of questions touching this subject on Stack Overflow, including some of my own very first questions about Scala -- investigate scala.math.Numeric, which is the best approximation for the moment.
Method vs Function and lack of parenthesis
Methods and functions are different things -- see tons of related questions here, and the rule regarding dropping parenthesis is different as well. I'll let REPL speak for me:
scala> def f: () => Int = () => 5
f: () => Int
scala> def g(): Int = 5
g: ()Int
scala> f
res2: () => Int = <function0>
scala> f()
res3: Int = 5
scala> g
res4: Int = 5
scala> g()
res5: Int = 5

What is the difference between currying and partial application?

I quite often see on the Internet various complaints that other peoples examples of currying are not currying, but are actually just partial application.
I've not found a decent explanation of what partial application is, or how it differs from currying. There seems to be a general confusion, with equivalent examples being described as currying in some places, and partial application in others.
Could someone provide me with a definition of both terms, and details of how they differ?
Currying is converting a single function of n arguments into n functions with a single argument each. Given the following function:
function f(x,y,z) { z(x(y));}
When curried, becomes:
function f(x) { lambda(y) { lambda(z) { z(x(y)); } } }
In order to get the full application of f(x,y,z), you need to do this:
f(x)(y)(z);
Many functional languages let you write f x y z. If you only call f x y or f(x)(y) then you get a partially-applied function—the return value is a closure of lambda(z){z(x(y))} with passed-in the values of x and y to f(x,y).
One way to use partial application is to define functions as partial applications of generalized functions, like fold:
function fold(combineFunction, accumulator, list) {/* ... */}
function sum = curry(fold)(lambda(accum,e){e+accum}))(0);
function length = curry(fold)(lambda(accum,_){1+accum})(empty-list);
function reverse = curry(fold)(lambda(accum,e){concat(e,accum)})(empty-list);
/* ... */
#list = [1, 2, 3, 4]
sum(list) //returns 10
#f = fold(lambda(accum,e){e+accum}) //f = lambda(accumulator,list) {/*...*/}
f(0,list) //returns 10
#g = f(0) //same as sum
g(list) //returns 10
The easiest way to see how they differ is to consider a real example. Let's assume that we have a function Add which takes 2 numbers as input and returns a number as output, e.g. Add(7, 5) returns 12. In this case:
Partial applying the function Add with a value 7 will give us a new function as output. That function itself takes 1 number as input and outputs a number. As such:
Partial(Add, 7); // returns a function f2 as output
// f2 takes 1 number as input and returns a number as output
So we can do this:
f2 = Partial(Add, 7);
f2(5); // returns 12;
// f2(7)(5) is just a syntactic shortcut
Currying the function Add will give us a new function as output. That function itself takes 1 number as input and outputs yet another new function. That third function then takes 1 number as input and returns a number as output. As such:
Curry(Add); // returns a function f2 as output
// f2 takes 1 number as input and returns a function f3 as output
// i.e. f2(number) = f3
// f3 takes 1 number as input and returns a number as output
// i.e. f3(number) = number
So we can do this:
f2 = Curry(Add);
f3 = f2(7);
f3(5); // returns 12
In other words, "currying" and "partial application" are two totally different functions. Currying takes exactly 1 input, whereas partial application takes 2 (or more) inputs.
Even though they both return a function as output, the returned functions are of totally different forms as demonstrated above.
Note: this was taken from F# Basics an excellent introductory article for .NET developers getting into functional programming.
Currying means breaking a function with many arguments into a series
of functions that each take one argument and ultimately produce the
same result as the original function. Currying is probably the most
challenging topic for developers new to functional programming, particularly because it
is often confused with partial application. You can see both at work
in this example:
let multiply x y = x * y
let double = multiply 2
let ten = double 5
Right away, you should see behavior that is different from most
imperative languages. The second statement creates a new function
called double by passing one argument to a function that takes two.
The result is a function that accepts one int argument and yields the
same output as if you had called multiply with x equal to 2 and y
equal to that argument. In terms of behavior, it’s the same as this
code:
let double2 z = multiply 2 z
Often, people mistakenly say that multiply is curried to form double.
But this is only somewhat true. The multiply function is curried, but
that happens when it is defined because functions in F# are curried by
default. When the double function is created, it’s more accurate to
say that the multiply function is partially applied.
The multiply function is really a series of two functions. The first
function takes one int argument and returns another function,
effectively binding x to a specific value. This function also accepts
an int argument that you can think of as the value to bind to y. After
calling this second function, x and y are both bound, so the result is
the product of x and y as defined in the body of double.
To create double, the first function in the chain of multiply
functions is evaluated to partially apply multiply. The resulting
function is given the name double. When double is evaluated, it uses
its argument along with the partially applied value to create the
result.
Interesting question. After a bit of searching, "Partial Function Application is not currying" gave the best explanation I found. I can't say that the practical difference is particularly obvious to me, but then I'm not an FP expert...
Another useful-looking page (which I confess I haven't fully read yet) is "Currying and Partial Application with Java Closures".
It does look like this is widely-confused pair of terms, mind you.
I have answered this in another thread https://stackoverflow.com/a/12846865/1685865 . In short, partial function application is about fixing some arguments of a given multivariable function to yield another function with fewer arguments, while Currying is about turning a function of N arguments into a unary function which returns a unary function...[An example of Currying is shown at the end of this post.]
Currying is mostly of theoretical interest: one can express computations using only unary functions (i.e. every function is unary). In practice and as a byproduct, it is a technique which can make many useful (but not all) partial functional applications trivial, if the language has curried functions. Again, it is not the only means to implement partial applications. So you could encounter scenarios where partial application is done in other way, but people are mistaking it as Currying.
(Example of Currying)
In practice one would not just write
lambda x: lambda y: lambda z: x + y + z
or the equivalent javascript
function (x) { return function (y){ return function (z){ return x + y + z }}}
instead of
lambda x, y, z: x + y + z
for the sake of Currying.
Currying is a function of one argument which takes a function f and returns a new function h. Note that h takes an argument from X and returns a function that maps Y to Z:
curry(f) = h
f: (X x Y) -> Z
h: X -> (Y -> Z)
Partial application is a function of two(or more) arguments which takes a function f and one or more additional arguments to f and returns a new function g:
part(f, 2) = g
f: (X x Y) -> Z
g: Y -> Z
The confusion arises because with a two-argument function the following equality holds:
partial(f, a) = curry(f)(a)
Both sides will yield the same one-argument function.
The equality is not true for higher arity functions because in this case currying will return a one-argument function, whereas partial application will return a multiple-argument function.
The difference is also in the behavior, whereas currying transforms the whole original function recursively(once for each argument), partial application is just a one step replacement.
Source: Wikipedia Currying.
Simple answer
Curry: lets you call a function, splitting it in multiple calls, providing one argument per-call.
Partial: lets you call a function, splitting it in multiple calls, providing multiple arguments per-call.
Simple hints
Both allow you to call a function providing less arguments (or, better, providing them cumulatively). Actually both of them bind (at each call) a specific value to specific arguments of the function.
The real difference can be seen when the function has more than 2 arguments.
Simple e(c)(sample)
(in Javascript)
We want to run the following process function on different subjects (e.g. let's say our subjects are "subject1" and "foobar" strings):
function process(context, successCallback, errorCallback, subject) {...}
why always passing the arguments, like context and the callbacks, if they will be always the same?
Just bind some values for the the function:
processSubject = _.partial(process, my_context, my_success, my_error)
// assign fixed values to the first 3 arguments of the `process` function
and call it on subject1 and foobar, omitting the repetition of the first 3 arguments, with:
processSubject('subject1');
processSubject('foobar');
Comfy, isn't it? 😉
With currying you'd instead need to pass one argument per time
curriedProcess = _.curry(process); // make the function curry-able
processWithBoundedContext = curriedProcess(my_context);
processWithCallbacks = processWithBoundedContext(my_success)(my_error); // note: these are two sequential calls
result1 = processWithCallbacks('subject1');
// same as: process(my_context, my_success, my_error, 'subject1');
result2 = processWithCallbacks('foobar');
// same as: process(my_context, my_success, my_error, 'foobar');
Disclaimer
I skipped all the academic/mathematical explanation. Cause I don't know it. Maybe it helped 🙃
EDIT:
As added by #basickarl, a further slight difference in use of the two functions (see Lodash for examples) is that:
partial returns a pre-cooked function that can be called once with the missing argument(s) and return the final result;
while curry is being called multiple times (one for each argument), returning a pre-cooked function each time; except in the case of calling with the last argument, that will return the actual result from the processing of all the arguments.
With ES6:
here's a quick example of how immediate Currying and Partial-application are in ECMAScript 6.
const partialSum = math => (eng, geo) => math + eng + geo;
const curriedSum = math => eng => geo => math + eng + geo;
The difference between curry and partial application can be best illustrated through this following JavaScript example:
function f(x, y, z) {
return x + y + z;
}
var partial = f.bind(null, 1);
6 === partial(2, 3);
Partial application results in a function of smaller arity; in the example above, f has an arity of 3 while partial only has an arity of 2. More importantly, a partially applied function would return the result right away upon being invoke, not another function down the currying chain. So if you are seeing something like partial(2)(3), it's not partial application in actuality.
Further reading:
Functional Programming in 5 minutes
Currying: Contrast with Partial Function Application
I had this question a lot while learning and have since been asked it many times. The simplest way I can describe the difference is that both are the same :) Let me explain...there are obviously differences.
Both partial application and currying involve supplying arguments to a function, perhaps not all at once. A fairly canonical example is adding two numbers. In pseudocode (actually JS without keywords), the base function may be the following:
add = (x, y) => x + y
If I wanted an "addOne" function, I could partially apply it or curry it:
addOneC = curry(add, 1)
addOneP = partial(add, 1)
Now using them is clear:
addOneC(2) #=> 3
addOneP(2) #=> 3
So what's the difference? Well, it's subtle, but partial application involves supplying some arguments and the returned function will then execute the main function upon next invocation whereas currying will keep waiting till it has all the arguments necessary:
curriedAdd = curry(add) # notice, no args are provided
addOne = curriedAdd(1) # returns a function that can be used to provide the last argument
addOne(2) #=> returns 3, as we want
partialAdd = partial(add) # no args provided, but this still returns a function
addOne = partialAdd(1) # oops! can only use a partially applied function once, so now we're trying to add one to an undefined value (no second argument), and we get an error
In short, use partial application to prefill some values, knowing that the next time you call the method, it will execute, leaving undefined all unprovided arguments; use currying when you want to continually return a partially-applied function as many times as necessary to fulfill the function signature. One final contrived example:
curriedAdd = curry(add)
curriedAdd()()()()()(1)(2) # ugly and dumb, but it works
partialAdd = partial(add)
partialAdd()()()()()(1)(2) # second invocation of those 7 calls fires it off with undefined parameters
Hope this helps!
UPDATE: Some languages or lib implementations will allow you to pass an arity (total number of arguments in final evaluation) to the partial application implementation which may conflate my two descriptions into a confusing mess...but at that point, the two techniques are largely interchangeable.
For me partial application must create a new function where the used arguments are completely integrated into the resulting function.
Most functional languages implement currying by returning a closure: do not evaluate under lambda when partially applied. So, for partial application to be interesting, we need to make a difference between currying and partial application and consider partial application as currying plus evaluation under lambda.
I could be very wrong here, as I don't have a strong background in theoretical mathematics or functional programming, but from my brief foray into FP, it seems that currying tends to turn a function of N arguments into N functions of one argument, whereas partial application [in practice] works better with variadic functions with an indeterminate number of arguments. I know some of the examples in previous answers defy this explanation, but it has helped me the most to separate the concepts. Consider this example (written in CoffeeScript for succinctness, my apologies if it confuses further, but please ask for clarification, if needed):
# partial application
partial_apply = (func) ->
args = [].slice.call arguments, 1
-> func.apply null, args.concat [].slice.call arguments
sum_variadic = -> [].reduce.call arguments, (acc, num) -> acc + num
add_to_7_and_5 = partial_apply sum_variadic, 7, 5
add_to_7_and_5 10 # returns 22
add_to_7_and_5 10, 11, 12 # returns 45
# currying
curry = (func) ->
num_args = func.length
helper = (prev) ->
->
args = prev.concat [].slice.call arguments
return if args.length < num_args then helper args else func.apply null, args
helper []
sum_of_three = (x, y, z) -> x + y + z
curried_sum_of_three = curry sum_of_three
curried_sum_of_three 4 # returns a function expecting more arguments
curried_sum_of_three(4)(5) # still returns a function expecting more arguments
curried_sum_of_three(4)(5)(6) # returns 15
curried_sum_of_three 4, 5, 6 # returns 15
This is obviously a contrived example, but notice that partially applying a function that accepts any number of arguments allows us to execute a function but with some preliminary data. Currying a function is similar but allows us to execute an N-parameter function in pieces until, but only until, all N parameters are accounted for.
Again, this is my take from things I've read. If anyone disagrees, I would appreciate a comment as to why rather than an immediate downvote. Also, if the CoffeeScript is difficult to read, please visit coffeescript.org, click "try coffeescript" and paste in my code to see the compiled version, which may (hopefully) make more sense. Thanks!
I'm going to assume most people who ask this question are already familiar with the basic concepts so their is no need to talk about that. It's the overlap that is the confusing part.
You might be able to fully use the concepts, but you understand them together as this pseudo-atomic amorphous conceptual blur. What is missing is knowing where the boundary between them is.
Instead of defining what each one is, it's easier to highlight just their differences—the boundary.
Currying is when you define the function.
Partial Application is when you call the function.
Application is math-speak for calling a function.
Partial application requires calling a curried function and getting a function as the return type.
A lot of people here do not address this properly, and no one has talked about overlaps.
Simple answer
Currying: Lets you call a function, splitting it in multiple calls, providing one argument per-call.
Partial Application: Lets you call a function, splitting it in multiple calls, providing multiple arguments per-call.
One of the significant differences between the two is that a call to a
partially applied function returns the result right away, not another
function down the currying chain; this distinction can be illustrated
clearly for functions whose arity is greater than two.
What does that mean? That means that there are max two calls for a partial function. Currying has as many as the amount of arguments. If the currying function only has two arguments, then it is essentially the same as a partial function.
Examples
Partial Application and Currying
function bothPartialAndCurry(firstArgument) {
return function(secondArgument) {
return firstArgument + secondArgument;
}
}
const partialAndCurry = bothPartialAndCurry(1);
const result = partialAndCurry(2);
Partial Application
function partialOnly(firstArgument, secondArgument) {
return function(thirdArgument, fourthArgument, fifthArgument) {
return firstArgument + secondArgument + thirdArgument + fourthArgument + fifthArgument;
}
}
const partial = partialOnly(1, 2);
const result = partial(3, 4, 5);
Currying
function curryOnly(firstArgument) {
return function(secondArgument) {
return function(thirdArgument) {
return function(fourthArgument ) {
return function(fifthArgument) {
return firstArgument + secondArgument + thirdArgument + fourthArgument + fifthArgument;
}
}
}
}
}
const curryFirst = curryOnly(1);
const currySecond = curryFirst(2);
const curryThird = currySecond(3);
const curryFourth = curryThird(4);
const result = curryFourth(5);
// or...
const result = curryOnly(1)(2)(3)(4)(5);
Naming conventions
I'll write this when I have time, which is soon.
There are other great answers here but I believe this example (as per my understanding) in Java might be of benefit to some people:
public static <A,B,X> Function< B, X > partiallyApply( BiFunction< A, B, X > aBiFunction, A aValue ){
return b -> aBiFunction.apply( aValue, b );
}
public static <A,X> Supplier< X > partiallyApply( Function< A, X > aFunction, A aValue ){
return () -> aFunction.apply( aValue );
}
public static <A,B,X> Function< A, Function< B, X > > curry( BiFunction< A, B, X > bif ){
return a -> partiallyApply( bif, a );
}
So currying gives you a one-argument function to create functions, where partial-application creates a wrapper function that hard codes one or more arguments.
If you want to copy&paste, the following is noisier but friendlier to work with since the types are more lenient:
public static <A,B,X> Function< ? super B, ? extends X > partiallyApply( final BiFunction< ? super A, ? super B, X > aBiFunction, final A aValue ){
return b -> aBiFunction.apply( aValue, b );
}
public static <A,X> Supplier< ? extends X > partiallyApply( final Function< ? super A, X > aFunction, final A aValue ){
return () -> aFunction.apply( aValue );
}
public static <A,B,X> Function< ? super A, Function< ? super B, ? extends X > > curry( final BiFunction< ? super A, ? super B, ? extends X > bif ){
return a -> partiallyApply( bif, a );
}
In writing this, I confused currying and uncurrying. They are inverse transformations on functions. It really doesn't matter what you call which, as long as you get what the transformation and its inverse represent.
Uncurrying isn't defined very clearly (or rather, there are "conflicting" definitions that all capture the spirit of the idea). Basically, it means turning a function that takes multiple arguments into a function that takes a single argument. For example,
(+) :: Int -> Int -> Int
Now, how do you turn this into a function that takes a single argument? You cheat, of course!
plus :: (Int, Int) -> Int
Notice that plus now takes a single argument (that is composed of two things). Super!
What's the point of this? Well, if you have a function that takes two arguments, and you have a pair of arguments, it is nice to know that you can apply the function to the arguments, and still get what you expect. And, in fact, the plumbing to do it already exists, so that you don't have to do things like explicit pattern matching. All you have to do is:
(uncurry (+)) (1,2)
So what is partial function application? It is a different way to turn a function in two arguments into a function with one argument. It works differently though. Again, let's take (+) as an example. How might we turn it into a function that takes a single Int as an argument? We cheat!
((+) 0) :: Int -> Int
That's the function that adds zero to any Int.
((+) 1) :: Int -> Int
adds 1 to any Int. Etc. In each of these cases, (+) is "partially applied".
Currying
Wikipedia says
Currying is the technique of converting a function that takes multiple arguments into a sequence of functions that each takes a single argument.
Example
const add = (a, b) => a + b
const addC = (a) => (b) => a + b // curried function. Where C means curried
Partial application
Article Just Enough FP: Partial Application
Partial application is the act of applying some, but not all, of the arguments to a function and returning a new function awaiting the rest of the arguments. These applied arguments are stored in closure and remain available to any of the partially applied returned functions in the future.
Example
const add = (a) => (b) => a + b
const add3 = add(3) // add3 is a partially applied function
add3(5) // 8
The difference is
currying is a technique (pattern)
partial application is a function with some predefined arguments (like add3 from the previous example)