A function can be a highly nested structure:
function a(x) {
return b(c(x), d(e(f(x), g())))
}
First, wondering if a function has an instance. That is, the evaluation of the function being the instance of the function. In that sense, the type is the function, and the instance is the evaluation of it. If it can be, then how to model a function as a type (in some type-theory oriented language like Haskell or Coq).
It's almost like:
type a {
field: x
constructor b {
constructor c {
parameter: x
},
...
}
}
But I'm not sure if I'm not on the right track. I know you can say a function has a [return] type. But I'm wondering if a function can be considered a type, and if so, how to model it as a type in a type-theory-oriented language, where it models the actual implementation of the function.
I think the problem is that types based directly on the implementation (let's call them "i-types") don't seem very useful, and we already have good ways of modelling them (called "programs" -- ha ha).
In your specific example, the full i-type of your function, namely:
type a {
field: x
constructor b {
constructor c {
parameter: x
},
constructor d {
constructor e {
constructor f {
parameter: x
}
constructor g {
}
}
}
}
is just a verbose, alternative syntax for the implementation itself. That is, we could write this i-type (in a Haskell-like syntax) as:
itype a :: a x = b (c x) (d (e (f x) g))
On the other hand, we could convert your function implementation to Haskell term-level syntax directly to write it as:
a x = b (c x) (d (e (f x) g))
and the i-type and the implementation are exactly the same thing.
How would you use these i-types? The compiler might use them by deriving argument and return types to type-check the program. (Fortunately, there are well known algorithms, such as Algorithm W, for simultaneously deriving and type-checking argument and return types from i-types of this sort.) Programmers probably wouldn't use i-types directly -- they're too complicated to use for refactoring or reasoning about program behavior. They'd probably want to look at the types derived by the compiler for the arguments and return type.
In particular, "modelling" these i-types at the type level in Haskell doesn't seem productive. Haskell can already model them at the term level. Just write your i-types as a Haskell program:
a x = b (c x) (d (e (f x) g))
b s t = sqrt $ fromIntegral $ length (s ++ t)
c = show
d = reverse
e c ds = show (sum ds + fromIntegral (ord c))
f n = if even n then 'E' else 'O'
g = [1.5..5.5]
and don't run it. Congratulations, you've successfully modelled these i-types! You can even use GHCi to query derived argument and return types:
> :t a
a :: Floating a => Integer -> a -- "a" takes an Integer and returns a float
>
Now, you are perhaps imagining that there are situations where the implementation and i-type would diverge, maybe when you start introducing literal values. For example, maybe you feel like the function f above:
f n = if even n then 'E' else 'O'
should be assigned a type something like the following, that doesn't depend on the specific literal values:
type f {
field: n
if_then_else {
constructor even { -- predicate
parameter: n
}
literal Char -- then-branch
literal Char -- else-branch
}
Again, though, you'd be better off defining an arbitrary term-level Char, like:
someChar :: Char
someChar = undefined
and modeling this i-type at the term-level:
f n = if even n then someChar else someChar
Again, as long as you don't run the program, you've successfully modelled the i-type of f, can query its argument and return types, type-check it as part of a bigger program, etc.
I'm not clear exactly what you are aiming at, so I'll try to point at some related terms that you might want to read about.
A function has not only a return type, but a type that describes its arguments as well. So the (Haskell) type of f reads "f takes an Int and a Float, and returns a List of Floats."
f :: Int -> Float -> [Float]
f i x = replicate i x
Types can also describe much more of the specification of a function. Here, we might want the type to spell out that the length of the list will be the same as the first argument, or that every element of the list will be the same as the second argument. Length-indexed lists (often called Vectors) are a common first example of Dependent Types.
You might also be interested in functions that take types as arguments, and return types. These are sometimes called "type-level functions". In Coq or Idris, they can be defined the same way as more familiar functions. In Haskell, we usually implement them using Type Families, or using Type Classes with Functional Dependencies.
Returning to the first part of your question, Beta Reduction is the process of filling in concrete values for each of the function's arguments. I've heard people describe expressions as "after reduction" or "fully reduced" to emphasize some stage in this process. This is similar to a function Call Site, but emphasizes the expression & arguments, rather than the surrounding context.
Update 2: examples removed, because they were misleading. The ones below are more relevant.
My question:
Is there a programming language with such a construct?
Update:
Now when I think about it, Prolog has something similar.
I even allows defining operations at definition line.
(forget about backtracking and relations - think about syntax)
I asked this question because I believe, it's a nice thing to have symmetry in a language.
Symmetry between "in" parameters and "out" parameters.
If returning values like that would be easy, we could drop explicit returning in designed language.
retruning pairs ... I think this is a hack. we do not need a data structure to pass multiple parameters to a function.
Update 2:
To give an example of syntax I'm looking for:
f (s, d&) = // & indicates 'out' variable
d = s+s.
main =
f("say twice", &twice) // & indicates 'out' variable declaration
print(twice)
main2 =
print (f("say twice", _))
Or in functional + prolog style
f $s (s+s). // use $ to mark that s will get it's value in other part of the code
main =
f "say twice" $twice // on call site the second parameter will get it's value from
print twice
main2 =
print (f "Say twice" $_) // anonymous variable
In a proposed language, there are no expressions, because all returns are through parameters. This would be cumbersome in situations where deep hierarchical function calls are natural. Lisp'ish example:
(let x (* (+ 1 2) (+ 3 4))) // equivalent to C x = ((1 + 2) * (3 + 4))
would need in the language names for all temporary variables:
+ 1 2 res1
+ 3 4 res2
* res1 res2 x
So I propose anonymous variables that turn a whole function call into value of this variable:
* (+ 1 2 _) (+ 3 4 _)
This is not very natural, because all the cultural baggage we have, but I want to throw away all preconceptions about syntax we currently have.
<?php
function f($param, &$ret) {
$ret = $param . $param;
}
f("say twice", $twice);
echo $twice;
?>
$twice is seen after the call to f(), and it has the expected value. If you remove the ampersand, there are errors. So it looks like PHP will declare the variable at the point of calling. I'm not convinced that buys you much, though, especially in PHP.
"Is there a programming language with such a construct?"
Your question is in fact a little unclear.
In a sense, any language that supports assignment to [the variable state associated with] a function argument, supports "such a construct".
C supports it because "void f (type *address)" allows modification of anything address points to. Java supports it because "void f (Object x)" allows any (state-modifying) invocation of some method of x. COBOL supports it because "PROCEDURE DIVISION USING X" can involve an X that holds a pointer/memory address, ultimately allowing to go change the state of the thing pointed to by that address.
From that perspective, I'd say almost every language known to mankind supports "such a construct", with the exception perhaps of languages such as Tutorial D, which claim to be "absolutely pointer-free".
I'm having a hard time understanding what you want. You want to put the return type on call signature? I'm sure someone could hack that together but is it really useful?
// fakelang example - use a ; to separate ins and outs
function f(int in1, int in2; int out1, int out2, int out3) {...}
// C++0x-ish
auto f(int in1, int in2) -> int o1, int o2, int o3 {...}
int a, b, c;
a, b, c = f(1, 2);
I get the feeling this would be implemented internally this way:
LEA EAX, c // push output parameter pointers first, in reverse order
PUSH EAX
LEA EAX, b
PUSH EAX
LEA EAX, a
PUSH EAX
PUSH 1 // push input parameters
PUSH 2
CALL f // Caller treat the outputs as references
ADD ESP,20 // clean the stack
For your first code snippet, I'm not aware of any such languages, and frankly I'm glad it is the case. Declaring a variable in the middle of expression like that, and then using it outside said expression, looks very wrong to me. If anything, I'd expect the scope of such variable to be restricted to the function call, but then of course it's quite pointless in the first place.
For the second one - multiple return values - pretty much any language with first-class tuple support has something close to that. E.g. Python:
def foo(x, y):
return (x + 1), (y + 1)
x, y = foo(1, 2)
Lua doesn't have first-class tuples (i.e. you can't bind a tuple value to a single variable - you always have to expand it, possibly discarding part of it), but it does have multiple return values, with essentially the same syntax:
function foo(x, y)
return (x + 1), (y + 1)
end
local x, y = foo(x, y)
F# has first-class tuples, and so everything said earlier about Python applies to it as well. But it can also simulate tuple returns for methods that were declared in C# or VB with out or ref arguments, which is probably the closest to what you describe - though it is still implicit (i.e. you don't specify the out-argument at all, even as _). Example:
// C# definition
int Foo(int x, int y, out int z)
{
z = y + 1;
return x + 1;
}
// explicit F# call
let mutable y = 0
let x = Foo(1, 2, byref y);
// tupled F# call
let x, y = Foo(1, 2)
Here is how you would do it in Perl:
sub f { $_[1] = $_[0] . $_[0] } #in perl all variables are passed by reference
f("say twice", my $twice);
# or f("...", our $twice) or f("...", $twice)
# the last case is only possible if you are not running with "use strict;"
print $twice;
[edit] Also, since you seem interested in minimal syntax:
sub f { $_[1] = $_[0] x 2 } # x is the repetition operator
f "say twice" => $twice; # => is a quoting comma, used here just for clarity
print $twice;
is perfectly valid perl. Here's an example of normal quoting comma usage:
("abc", 1, "d e f", 2) # is the same as
(abc => 1, "d e f" => 2) # the => only quotes perl /\w+/ strings
Also, on return values, unless exited with a "return" early, all perl subroutines automatically return the last line they execute, be it a single value, or a list. Lastly, take a look at perl6's feed operators, which you might find interesting.
[/edit]
I am not sure exactly what you are trying to achieve with the second example, but the concept of implicit variables exists in a few languages, in Perl, it is $_.
an example would be some of perl's builtins which look at $_ when they dont have an argument.
$string = "my string\n";
for ($string) { # loads "my string" into $_
chomp; # strips the last newline from $_
s/my/our/; # substitutes my for our in $_
print; # prints $_
}
without using $_, the above code would be:
chomp $string;
$string =~ s/my/our/;
print $string;
$_ is used in many cases in perl to avoid repeatedly passing temporary variables to functions
Not programming languages, but various process calculi have syntax for binding names at the receiver call sites in the scope of process expressions dependent on them. While Pict has such syntax, it doesn't actually make sense in the derived functional syntax that you're asking about.
You might have a look at Oz. In Oz you only have procedures and you assign values to variables instead of returning them.
It looks like this:
proc {Max X Y Z}
if X >= Y then Z = X else Z = Y end
end
There are functions (that return values) but this is only syntactic sugar.
Also, Concepts, Techniques, and Models of Computer Programming is a great SICP-like book that teaches programming by using Oz and the Mozart Programming System.
I don't think so. Most languages that do something like that use Tuples so that there can be multiple return values. Come to think of it, the C-style reference and output parameters are mostly hacks around not being about to return Tuples...
Somewhat confusing, but C++ is quite happy with declaring variables and passing them as out parameters in the same statement:
void foo ( int &x, int &y, int &z ) ;
int a,b,c = (foo(a,b,c),c);
But don't do that outside of obfuscation contests.
You might also want to look at pass by name semantics in Algol, which your fuller description smells vaguely similar to.
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)