I am a beginner and using pascal and i am trying this problem that i attach. What should i do next? I am trying to make this program work by showing the "ayam" Function. But i don't know how to code the rest.
function ayam(a, b:integer) :
integer;
var
m: integer;
begin
readln(a) ;
readln(b) ;
readln(m) ;
begin
if (b=0) then
ayam:= 1 else
ayam:= a * ayam(a, b-1) mod m;
end;
writeln(ayam);
end;
The first thing I should say is that when a question is to do with coursework, as is obviously the case here, there is an unwritten convention that we do not write an answer which simply does your programming task for you. So in the following, I have not commented on whether the code inside your ayam function actually correctly implements what is required - that is for you to do.
Secondly, you did not say which Pascal implementation you are using. I have written the code of this answer in Lazarus, the IDE for FreePascal (aka FPC), which is the best of the freeware Pascal implementations currently available.
The first thing to do with your code is to re-format it the way it should be formatted,
using indentation of statements to reflect the structure of the steps you are
trying to code. Basically, your eye should be able to follow the code structure
as easily as possible. This gives something like this:
function ayam(a, b:integer) : integer;
var
m: integer;
begin
readln(a) ;
readln(b) ;
readln(m) ;
begin
if (b=0) then
ayam:= 1
else
ayam:= a * ayam(a, b-1) mod m;
end;
writeln(ayam);
end;
With that change made, it is pretty obvious that there is something wrong with
the logic of your code, because a and b are declared as input variables to
the ayam function but your code actually reads in their values via the
readln statements inside the function. This is what made me think that you think
you have done all that's necessary to write your program. In fact, you have not. What you are missing
is some code which sets up the input parameters a and b (and m, see below) in some way and then
invokes your ayam function to calculate its value and then does something with
the result. At the moment, your code simply defines ayam but takes no steps
to use it. So, to get your ayam function to do anything, you need to write a complete
Pascal program that uses it. Something like this:
program ayamprogram;
{ the following declares some variables for the program to use }
var
varA,
varB,
varM,
varResult : Integer;
{ next, we define the ayam function }
function ayam(a, b, m:integer) : integer;
begin
begin
if (b=0) then
ayam:= 1
else
ayam:= a * ayam(a, b-1, m) mod m;
end;
end;
{ now we write the code of the program, which reads in the values to be
used by ayam, then invokes ("calls") ayam to calculate its value and
assign its value to the varResult variable and then outputs the calculated
result using the writeln statement
}
begin
{ this is the code of the program }
readln(varA);
readln(varB);
readln(varM);
varResult := ayam(varA, varB, varM);
writeln('function ayam evaluates to ', varResult);
readln; { this causes the program to pause so you can see the result of the writeln statement }
end. { end of program }
Note that I have used different variable names for the variables which are supplied to ayam, varA, varB, varM, from the variable names used inside ayam to avoid confusion between them.
Note also that as it is bad practice to read user input inside an executing function, the value to be used for M is read in before ayam is called and is supplied to ayam as a third parameter.
A point you need to consider regarding the expression
ayam:= a * ayam(a, b-1, m) mod m
is whether the mod m should operate on the value of ayam(a, b-1, m) or on the entire expression including the a * as well; if so, parentheses can enforce the evaluation order you need, by writing
ayam:= (a * ayam(a, b-1, m)) mod m
I've just started learning Ada and I cannot figure out how to keep the program running when the user input is beyond the declared range of a variable. I'd like to print info about bad range of input and then ask user for input again.
This is my simple code:
with Ada.Text_IO;
use Ada.Text_IO;
procedure Main is
type Score is range 0..100;
a : Score;
begin
Put_Line ("Enter value range 0-100: ");
a := Score'Value(Get_Line);
if a'Valid then
Put_Line ("You entered" & Score'Image (a));
else
Put_Line ("Bad range of input");
end if;
end Main;
Shouldn't I use the "range" in order to check the input, but rather some if's with >, < restrictions?
My other approach was to try this with exceptions, but it also doesn't work as I want it to:
with Ada.Text_IO;
with Ada.IO_Exceptions;
use Ada.Text_IO;
procedure Main is
type Score is range 0..100;
a : Score;
begin
loop
begin
Put_Line ("Enter value range 0-100: ");
a := Score'Value(Get_Line);
Put_Line ("You entered" & Score'Image (a));
exit;
exception
when Ada.IO_Exceptions.Data_Error =>
Put_Line("Bad range of input");
end;
end loop;
end Main;
I believe the problem is in my lack of understanding this language, but I hope there is some kind of easy solution for this, thanks for any help.
Now you know a magical incantation that works, but I doubt you understand why it works, or why your other incantations didn't work. I will go into painful pedagogical detail about that, in hopes that some of it might be useful or of interest.
In Ada, when you declare a type, the type is anonymous, and the name (Score) you give is the name of the first-named subtype. The first-named subtype may have constraints that don't apply to the anonymous base type. For some types, including integer types, it's possible to refer to the anonymous base type with 'Base.
Since you declared Score using range, it is a signed integer type and its base type is (roughly) symmetrical around zero. So your declaration is equivalent to something like
type Score'Base is range -128 .. 127;
subtype Score is Score'Base range 0 .. 100;
(this is not Ada and will not compile).
Score'Value returns a value of Score'Base (ARM 3.5 (53)), so if you input "101" or "-3", Score'Value will succeed and return the appropriate value. When you assign that value to your variable of subtype Score, a check is performed that the value is in the range of Score; when that fails, Constraint_Error is raised. If you input an invalid image, such as "200" or "xyz", Score'Value fails and raises Constraint_Error. So you have two kinds of incorrect input resulting in two different failures, both of which happen to raise the same exception.
Your first version failed because you never got to the if statement. Your second version failed because Ada.Text_IO.Get_Line never raises Data_Error.
When dealing with numeric input, I advise that a complete line be read into a String and you then parse out the value(s) from that String, as you have done. However, 'Value will reject some input that you might want to consider valid. For example, you might want to accept "23 skidoo" and get the value 23 from it. For that, you might want to instantiate Ada.Text_IO.Integer_IO for your numeric (sub)type and use the Get function that takes a String parameter:
package Score_IO is new Ada.Text_IO.Integer_IO (Num => Score);
...
Score_IO.Get (From => "23 skidoo", Item => A, Last => Last);
will set A to 23 and Last to the index of '3' in From (2).
HTH
I've been learning lua and can't seem to make a simple implementation of this binary tree work...
function createTree(tree, max)
if max > 0 then
tree = {data = max, left = {}, right = {}}
createTree(tree.left, max - 1)
createTree(tree.right, max - 1)
end
end
function printTree(tree)
if tree then
print(tree.data)
printTree(tree.left)
printTree(tree.right)
end
end
tree = {}
createTree(tree, 3)
printTree(tree)
the program just returns nil after execution. I've searched around the web to understand how argument passing works in lua (if it is by reference or by value) and found out that some types are passed by reference (like tables and functions) while others by value. Still, I made the global variable "tree" a table before passing it to the "createTree" function, and I even initialized "left" and "right" to be empty tables inside of "createTree" for the same purpose. What am I doing wrong?
It is probably necessary to initialize not by a new table, but only to set its values.
function createTree(tree, max)
if max > 0 then
tree.data = max
tree.left = {}
tree.right = {}
createTree(tree.left, max - 1)
createTree(tree.right, max - 1)
end
end
in Lua, arguments are passed by value. Assigning to an argument does not change the original variable.
Try this:
function createTree(max)
if max == 0 then
return nil
else
return {data = max, left = createTree(max-1), right = createTree(max-1)}
end
end
It is safe to think that for the most of the cases lua passes arguments by value. But for any object other than a number (numbers aren't objects actually), the "value" is actually a pointer to the said object.
When you do something like a={1,2,3} or b="asda" the values on the right are allocated somewhere dynamically, and a and b only get addresses of those. Thus, when you pass a to the function fun(a), the pointer is copied to a new variable inside function, but the a itself is unaffected:
function fun(p)
--p stores address of the same object, but `p` is not `a`
p[1]=3--by using the address you can
p[4]=1--alter the contents of the object
p[2]=nil--this will be seen outside
q={}
p={}--here you assign address of another object to the pointer
p=q--(here too)
end
Functions are also represented by pointers to them, you can use debug library to tinker with function object (change upvalues for example), this may affect how function executes, but, once again, you can not change where external references are pointing.
Strings are immutable objects, you can pass them around, there is a library that does stuff to them, but all the functions in that library return new string. So once, again external variable b from b="asda" would not be affected if you tried to do something with "asda" string inside the function.
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)