I've seen references to curried functions in several articles and blogs but I can't find a good explanation (or at least one that makes sense!)
Currying is when you break down a function that takes multiple arguments into a series of functions that each take only one argument. Here's an example in JavaScript:
function add (a, b) {
return a + b;
}
add(3, 4); // returns 7
This is a function that takes two arguments, a and b, and returns their sum. We will now curry this function:
function add (a) {
return function (b) {
return a + b;
}
}
This is a function that takes one argument, a, and returns a function that takes another argument, b, and that function returns their sum.
add(3)(4); // returns 7
var add3 = add(3); // returns a function
add3(4); // returns 7
The first statement returns 7, like the add(3, 4) statement.
The second statement defines a new function called add3 that will
add 3 to its argument. (This is what some may call a closure.)
The third statement uses the add3 operation to add 3 to 4, again
producing 7 as a result.
In an algebra of functions, dealing with functions that take multiple arguments (or equivalent one argument that's an N-tuple) is somewhat inelegant -- but, as Moses Schönfinkel (and, independently, Haskell Curry) proved, it's not needed: all you need are functions that take one argument.
So how do you deal with something you'd naturally express as, say, f(x,y)? Well, you take that as equivalent to f(x)(y) -- f(x), call it g, is a function, and you apply that function to y. In other words, you only have functions that take one argument -- but some of those functions return other functions (which ALSO take one argument;-).
As usual, wikipedia has a nice summary entry about this, with many useful pointers (probably including ones regarding your favorite languages;-) as well as slightly more rigorous mathematical treatment.
Here's a concrete example:
Suppose you have a function that calculates the gravitational force acting on an object. If you don't know the formula, you can find it here. This function takes in the three necessary parameters as arguments.
Now, being on the earth, you only want to calculate forces for objects on this planet. In a functional language, you could pass in the mass of the earth to the function and then partially evaluate it. What you'd get back is another function that takes only two arguments and calculates the gravitational force of objects on earth. This is called currying.
It can be a way to use functions to make other functions.
In javascript:
let add = function(x){
return function(y){
return x + y
};
};
Would allow us to call it like so:
let addTen = add(10);
When this runs the 10 is passed in as x;
let add = function(10){
return function(y){
return 10 + y
};
};
which means we are returned this function:
function(y) { return 10 + y };
So when you call
addTen();
you are really calling:
function(y) { return 10 + y };
So if you do this:
addTen(4)
it's the same as:
function(4) { return 10 + 4} // 14
So our addTen() always adds ten to whatever we pass in. We can make similar functions in the same way:
let addTwo = add(2) // addTwo(); will add two to whatever you pass in
let addSeventy = add(70) // ... and so on...
Now the obvious follow up question is why on earth would you ever want to do that? It turns what was an eager operation x + y into one that can be stepped through lazily, meaning we can do at least two things
1. cache expensive operations
2. achieve abstractions in the functional paradigm.
Imagine our curried function looked like this:
let doTheHardStuff = function(x) {
let z = doSomethingComputationallyExpensive(x)
return function (y){
z + y
}
}
We could call this function once, then pass around the result to be used in lots of places, meaning we only do the computationally expensive stuff once:
let finishTheJob = doTheHardStuff(10)
finishTheJob(20)
finishTheJob(30)
We can get abstractions in a similar way.
Currying is a transformation that can be applied to functions to allow them to take one less argument than previously.
For example, in F# you can define a function thus:-
let f x y z = x + y + z
Here function f takes parameters x, y and z and sums them together so:-
f 1 2 3
Returns 6.
From our definition we can can therefore define the curry function for f:-
let curry f = fun x -> f x
Where 'fun x -> f x' is a lambda function equivilent to x => f(x) in C#. This function inputs the function you wish to curry and returns a function which takes a single argument and returns the specified function with the first argument set to the input argument.
Using our previous example we can obtain a curry of f thus:-
let curryf = curry f
We can then do the following:-
let f1 = curryf 1
Which provides us with a function f1 which is equivilent to f1 y z = 1 + y + z. This means we can do the following:-
f1 2 3
Which returns 6.
This process is often confused with 'partial function application' which can be defined thus:-
let papply f x = f x
Though we can extend it to more than one parameter, i.e.:-
let papply2 f x y = f x y
let papply3 f x y z = f x y z
etc.
A partial application will take the function and parameter(s) and return a function that requires one or more less parameters, and as the previous two examples show is implemented directly in the standard F# function definition so we could achieve the previous result thus:-
let f1 = f 1
f1 2 3
Which will return a result of 6.
In conclusion:-
The difference between currying and partial function application is that:-
Currying takes a function and provides a new function accepting a single argument, and returning the specified function with its first argument set to that argument. This allows us to represent functions with multiple parameters as a series of single argument functions. Example:-
let f x y z = x + y + z
let curryf = curry f
let f1 = curryf 1
let f2 = curryf 2
f1 2 3
6
f2 1 3
6
Partial function application is more direct - it takes a function and one or more arguments and returns a function with the first n arguments set to the n arguments specified. Example:-
let f x y z = x + y + z
let f1 = f 1
let f2 = f 2
f1 2 3
6
f2 1 3
6
A curried function is a function of several arguments rewritten such that it accepts the first argument and returns a function that accepts the second argument and so on. This allows functions of several arguments to have some of their initial arguments partially applied.
Currying means to convert a function of N arity into N functions of arity 1. The arity of the function is the number of arguments it requires.
Here is the formal definition:
curry(f) :: (a,b,c) -> f(a) -> f(b)-> f(c)
Here is a real world example that makes sense:
You go to ATM to get some money. You swipe your card, enter pin number and make your selection and then press enter to submit the "amount" alongside the request.
here is the normal function for withdrawing money.
const withdraw=(cardInfo,pinNumber,request){
// process it
return request.amount
}
In this implementation function expects us entering all arguments at once. We were going to swipe the card, enter the pin and make the request, then function would run. If any of those steps had issue, you would find out after you enter all the arguments. With curried function, we would create higher arity, pure and simple functions. Pure functions will help us easily debug our code.
this is Atm with curried function:
const withdraw=(cardInfo)=>(pinNumber)=>(request)=>request.amount
ATM, takes the card as input and returns a function that expects pinNumber and this function returns a function that accepts the request object and after the successful process, you get the amount that you requested. Each step, if you had an error, you will easily predict what went wrong. Let's say you enter the card and got error, you know that it is either related to the card or machine but not the pin number. Or if you entered the pin and if it does not get accepted you know that you entered the pin number wrong. You will easily debug the error.
Also, each function here is reusable, so you can use the same functions in different parts of your project.
Currying is translating a function from callable as f(a, b, c) into callable as f(a)(b)(c).
Otherwise currying is when you break down a function that takes multiple arguments into a series of functions that take part of the arguments.
Literally, currying is a transformation of functions: from one way of calling into another. In JavaScript, we usually make a wrapper to keep the original function.
Currying doesn’t call a function. It just transforms it.
Let’s make curry function that performs currying for two-argument functions. In other words, curry(f) for two-argument f(a, b) translates it into f(a)(b)
function curry(f) { // curry(f) does the currying transform
return function(a) {
return function(b) {
return f(a, b);
};
};
}
// usage
function sum(a, b) {
return a + b;
}
let carriedSum = curry(sum);
alert( carriedSum(1)(2) ); // 3
As you can see, the implementation is a series of wrappers.
The result of curry(func) is a wrapper function(a).
When it is called like sum(1), the argument is saved in the Lexical Environment, and a new wrapper is returned function(b).
Then sum(1)(2) finally calls function(b) providing 2, and it passes the call to the original multi-argument sum.
Here's a toy example in Python:
>>> from functools import partial as curry
>>> # Original function taking three parameters:
>>> def display_quote(who, subject, quote):
print who, 'said regarding', subject + ':'
print '"' + quote + '"'
>>> display_quote("hoohoo", "functional languages",
"I like Erlang, not sure yet about Haskell.")
hoohoo said regarding functional languages:
"I like Erlang, not sure yet about Haskell."
>>> # Let's curry the function to get another that always quotes Alex...
>>> am_quote = curry(display_quote, "Alex Martelli")
>>> am_quote("currying", "As usual, wikipedia has a nice summary...")
Alex Martelli said regarding currying:
"As usual, wikipedia has a nice summary..."
(Just using concatenation via + to avoid distraction for non-Python programmers.)
Editing to add:
See http://docs.python.org/library/functools.html?highlight=partial#functools.partial,
which also shows the partial object vs. function distinction in the way Python implements this.
Here is the example of generic and the shortest version for function currying with n no. of params.
const add = a => b => b ? add(a + b) : a;
const add = a => b => b ? add(a + b) : a;
console.log(add(1)(2)(3)(4)());
Currying is one of the higher-order functions of Java Script.
Currying is a function of many arguments which is rewritten such that it takes the first argument and return a function which in turns uses the remaining arguments and returns the value.
Confused?
Let see an example,
function add(a,b)
{
return a+b;
}
add(5,6);
This is similar to the following currying function,
function add(a)
{
return function(b){
return a+b;
}
}
var curryAdd = add(5);
curryAdd(6);
So what does this code means?
Now read the definition again,
Currying is a function of many arguments which is rewritten such that it takes first argument and return a function which in turns uses the remaining arguments and returns the value.
Still, Confused?
Let me explain in deep!
When you call this function,
var curryAdd = add(5);
It will return you a function like this,
curryAdd=function(y){return 5+y;}
So, this is called higher-order functions. Meaning, Invoking one function in turns returns another function is an exact definition for higher-order function. This is the greatest advantage for the legend, Java Script.
So come back to the currying,
This line will pass the second argument to the curryAdd function.
curryAdd(6);
which in turns results,
curryAdd=function(6){return 5+6;}
// Which results in 11
Hope you understand the usage of currying here.
So, Coming to the advantages,
Why Currying?
It makes use of code reusability.
Less code, Less Error.
You may ask how it is less code?
I can prove it with ECMA script 6 new feature arrow functions.
Yes! ECMA 6, provide us with the wonderful feature called arrow functions,
function add(a)
{
return function(b){
return a+b;
}
}
With the help of the arrow function, we can write the above function as follows,
x=>y=>x+y
Cool right?
So, Less Code and Fewer bugs!!
With the help of these higher-order function one can easily develop a bug-free code.
I challenge you!
Hope, you understood what is currying. Please feel free to comment over here if you need any clarifications.
Thanks, Have a nice day!
If you understand partial you're halfway there. The idea of partial is to preapply arguments to a function and give back a new function that wants only the remaining arguments. When this new function is called it includes the preloaded arguments along with whatever arguments were supplied to it.
In Clojure + is a function but to make things starkly clear:
(defn add [a b] (+ a b))
You may be aware that the inc function simply adds 1 to whatever number it's passed.
(inc 7) # => 8
Let's build it ourselves using partial:
(def inc (partial add 1))
Here we return another function that has 1 loaded into the first argument of add. As add takes two arguments the new inc function wants only the b argument -- not 2 arguments as before since 1 has already been partially applied. Thus partial is a tool from which to create new functions with default values presupplied. That is why in a functional language functions often order arguments from general to specific. This makes it easier to reuse such functions from which to construct other functions.
Now imagine if the language were smart enough to understand introspectively that add wanted two arguments. When we passed it one argument, rather than balking, what if the function partially applied the argument we passed it on our behalf understanding that we probably meant to provide the other argument later? We could then define inc without explicitly using partial.
(def inc (add 1)) #partial is implied
This is the way some languages behave. It is exceptionally useful when one wishes to compose functions into larger transformations. This would lead one to transducers.
Curry can simplify your code. This is one of the main reasons to use this. Currying is a process of converting a function that accepts n arguments into n functions that accept only one argument.
The principle is to pass the arguments of the passed function, using the closure (closure) property, to store them in another function and treat it as a return value, and these functions form a chain, and the final arguments are passed in to complete the operation.
The benefit of this is that it can simplify the processing of parameters by dealing with one parameter at a time, which can also improve the flexibility and readability of the program. This also makes the program more manageable. Also dividing the code into smaller pieces would make it reuse-friendly.
For example:
function curryMinus(x)
{
return function(y)
{
return x - y;
}
}
var minus5 = curryMinus(1);
minus5(3);
minus5(5);
I can also do...
var minus7 = curryMinus(7);
minus7(3);
minus7(5);
This is very great for making complex code neat and handling of unsynchronized methods etc.
I found this article, and the article it references, useful, to better understand currying:
http://blogs.msdn.com/wesdyer/archive/2007/01/29/currying-and-partial-function-application.aspx
As the others mentioned, it is just a way to have a one parameter function.
This is useful in that you don't have to assume how many parameters will be passed in, so you don't need a 2 parameter, 3 parameter and 4 parameter functions.
As all other answers currying helps to create partially applied functions. Javascript does not provide native support for automatic currying. So the examples provided above may not help in practical coding. There is some excellent example in livescript (Which essentially compiles to js)
http://livescript.net/
times = (x, y) --> x * y
times 2, 3 #=> 6 (normal use works as expected)
double = times 2
double 5 #=> 10
In above example when you have given less no of arguments livescript generates new curried function for you (double)
A curried function is applied to multiple argument lists, instead of just
one.
Here is a regular, non-curried function, which adds two Int
parameters, x and y:
scala> def plainOldSum(x: Int, y: Int) = x + y
plainOldSum: (x: Int,y: Int)Int
scala> plainOldSum(1, 2)
res4: Int = 3
Here is similar function that’s curried. Instead
of one list of two Int parameters, you apply this function to two lists of one
Int parameter each:
scala> def curriedSum(x: Int)(y: Int) = x + y
curriedSum: (x: Int)(y: Int)Intscala> second(2)
res6: Int = 3
scala> curriedSum(1)(2)
res5: Int = 3
What’s happening here is that when you invoke curriedSum, you actually get two traditional function invocations back to back. The first function
invocation takes a single Int parameter named x , and returns a function
value for the second function. This second function takes the Int parameter
y.
Here’s a function named first that does in spirit what the first traditional
function invocation of curriedSum would do:
scala> def first(x: Int) = (y: Int) => x + y
first: (x: Int)(Int) => Int
Applying 1 to the first function—in other words, invoking the first function
and passing in 1 —yields the second function:
scala> val second = first(1)
second: (Int) => Int = <function1>
Applying 2 to the second function yields the result:
scala> second(2)
res6: Int = 3
An example of currying would be when having functions you only know one of the parameters at the moment:
For example:
func aFunction(str: String) {
let callback = callback(str) // signature now is `NSData -> ()`
performAsyncRequest(callback)
}
func callback(str: String, data: NSData) {
// Callback code
}
func performAsyncRequest(callback: NSData -> ()) {
// Async code that will call callback with NSData as parameter
}
Here, since you don't know the second parameter for callback when sending it to performAsyncRequest(_:) you would have to create another lambda / closure to send that one to the function.
Most of the examples in this thread are contrived (adding numbers). These are useful for illustrating the concept, but don't motivate when you might actually use currying in an app.
Here's a practical example from React, the JavaScript user interface library. Currying here illustrates the closure property.
As is typical in most user interface libraries, when the user clicks a button, a function is called to handle the event. The handler typically modifies the application's state and triggers the interface to re-render.
Lists of items are common user interface components. Each item might have an identifier associated with it (usually related to a database record). When the user clicks a button to, for example, "like" an item in the list, the handler needs to know which button was clicked.
Currying is one approach for achieving the binding between id and handler. In the code below, makeClickHandler is a function that accepts an id and returns a handler function that has the id in its scope.
The inner function's workings aren't important for this discussion. But if you're curious, it searches through the array of items to find an item by id and increments its "likes", triggering another render by setting the state. State is immutable in React so it takes a bit more work to modify the one value than you might expect.
You can think of invoking the curried function as "stripping" off the outer function to expose an inner function ready to be called. That new inner function is the actual handler passed to React's onClick. The outer function is a closure for the loop body to specify the id that will be in scope of a particular inner handler function.
const List = () => {
const [items, setItems] = React.useState([
{name: "foo", likes: 0},
{name: "bar", likes: 0},
{name: "baz", likes: 0},
].map(e => ({...e, id: crypto.randomUUID()})));
// .----------. outer func inner func
// | currying | | |
// `----------` V V
const makeClickHandler = (id) => (event) => {
setItems(prev => {
const i = prev.findIndex(e => e.id === id);
const cpy = {...prev[i]};
cpy.likes++;
return [
...prev.slice(0, i),
cpy,
...prev.slice(i + 1)
];
});
};
return (
<ul>
{items.map(({name, likes, id}) =>
<li key={id}>
<button
onClick={
/* strip off first function layer to get a click
handler bound to `id` and pass it to onClick */
makeClickHandler(id)
}
>
{name} ({likes} likes)
</button>
</li>
)}
</ul>
);
};
ReactDOM.createRoot(document.querySelector("#app"))
.render(<List />);
button {
font-family: monospace;
font-size: 2em;
}
<script crossorigin src="https://unpkg.com/react#18/umd/react.development.js"></script>
<script crossorigin src="https://unpkg.com/react-dom#18/umd/react-dom.development.js"></script>
<div id="app"></div>
Here you can find a simple explanation of currying implementation in C#. In the comments, I have tried to show how currying can be useful:
public static class FuncExtensions {
public static Func<T1, Func<T2, TResult>> Curry<T1, T2, TResult>(this Func<T1, T2, TResult> func)
{
return x1 => x2 => func(x1, x2);
}
}
//Usage
var add = new Func<int, int, int>((x, y) => x + y).Curry();
var func = add(1);
//Obtaining the next parameter here, calling later the func with next parameter.
//Or you can prepare some base calculations at the previous step and then
//use the result of those calculations when calling the func multiple times
//with different input parameters.
int result = func(1);
"Currying" is the process of taking the function of multiple arguments and converting it into a series of functions that each take a single argument and return a function of a single argument, or in the case of the final function, return the actual result.
The other answers have said what currying is: passing fewer arguments to a curried function than it expects is not an error, but instead returns a function that expects the rest of the arguments and returns the same result as if you had passed them all in at once.
I’ll try to motivate why it’s useful. It’s one of those tools that you never realized you needed until you do. Currying is above all a way to make your programs more expressive - you can combine operations together with less code.
For example, if you have a curried function add, you can write the equivalent of JS x => k + x (or Python lambda x: k + x or Ruby { |x| k + x } or Lisp (lambda (x) (+ k x)) or …) as just add(k). In Haskelll you can even use the operator: (k +) or (+ k) (The two forms let you curry either way for non-commutative operators: (/ 9) is a function that divides a number by 9, which is probably the more common use case, but you also have (9 /) for a function that divides 9 by its argument.) Besides being shorter, the curried version contains no made-up parameter name like the x found in all the other versions. It’s not needed. You’re defining a function that adds some constant k to a number, and you don’t need to give that number a name just to talk about the function. Or even to define it. This is an example of what’s called “point-free style”. You can combine operations together given nothing but the operations themselves. You don’t have to declare anonymous functions that do nothing but apply some operation to their argument, because *that’s what the operations already are.
This becomes very handy with higher-order functions when they’re defined in a currying-friendly way. For instance, a curried map(fn, list) let’s you define a mapper with just map(fn) that can be applied it to any list later. But currying a map defined instead as map(list, fn) just lets you define a function that will apply some other function to a constant list, which is probably less generally useful.
Currying reduces the need for things like pipes and threading. In Clojure, you might define a temperature conversion function using the threading macro ->: (defn f2c (deg) (-> deg (- 32) (* 5) (/ 9)). That’s cool, it reads nicely left to right (“subtract 32, multiply by 5 and divide by 9.”) and you only have to mention the parameter twice instead of once for every suboperation… but it only works because -> is a macro that transforms the whole form syntactically before anything is evaluated. It turns into a regular nested expression behind the scenes: (/ (* (- deg 32) 5) 9). If the math ops were curried, you wouldn’t need a macro to combine them so nicely, as in Haskell let f2c = (subtract 32) & (* 5) & (/ 9). (Although it would admittedly be more idiomatic to use function composition, which reads right to left: (/ 9) . (* 5) . (subtract 32).)
Again, it’s hard to find good demo examples; currying is most useful in complex cases where it really helps the readability of the solution, but those take so much explanation just to get you to understand the problem that the overall lesson about currying can get lost in the noise.
There is an example of "Currying in ReasonML".
let run = () => {
Js.log("Curryed function: ");
let sum = (x, y) => x + y;
Printf.printf("sum(2, 3) : %d\n", sum(2, 3));
let per2 = sum(2);
Printf.printf("per2(3) : %d\n", per2(3));
};
Below is one of currying example in JavaScript, here the multiply return the function which is used to multiply x by two.
const multiply = (presetConstant) => {
return (x) => {
return presetConstant * x;
};
};
const multiplyByTwo = multiply(2);
// now multiplyByTwo is like below function & due to closure property in JavaScript it will always be able to access 'presetConstant' value
// const multiplyByTwo = (x) => {
// return presetConstant * x;
// };
console.log(`multiplyByTwo(8) : ${multiplyByTwo(8)}`);
Output
multiplyByTwo(8) : 16
Related
I've seen many OCaml programs that have all their functions at the top and then a unit definition at the end, like:
let rec factorial num =
if num = 0 then 1
else num * factorial (num-1)
let () =
let num2 = read_int () in
print_int (factorial num2)
Why is this? Does it act like a main function? If so, you shouldn't be able to use several of them right?
What is the best way to handle several input for example? Writing several unit definitions?
Yes, a unit expression at the top level of a module acts like the main function of the module. I.e., it gets executed at the time the program is started.
You can have many unit expressions anywhere you can have one unit expression. The ; operator is specifically intended for such cases:
let () =
Printf.printf "hello\n";
Printf.printf "world\n"
As a side comment, I often write a main function in my main module:
let main () =
(* main calculation of program *)
let () = main ()
This is possibly a holdover from all the years I wrote C code.
I have also seen this in other people's code (possibly there are a lot of us who used to write C code).
I really like Jeffrey's answer, but in case if you want extra details and what to know what let () = foo means here is some extracurricular reading.
Abstractly speaking the operation of OCaml programs could be defined as a machine that reduces expressions until they become irreducible. And an irreducible expression is called a value. For example, 5 + 3 is reduced to 8 and there is no other way to reduce 8 so 8 is a value. A more complex example of a value is (fun x -> x + 1). And a more complex example of expression would be
(fun x -> x + 1) 5
Which is reduced to 6.
The whole semantics of the language is defined as a set of such reduction rules. And a program in OCaml is an ordered list of definitions of the form,
let <pattern> = <expression>
So that when an OCaml program is evaluated (executed) it reduces the part of each definition and assigns it to the pattern on the left-hand side, e.g.,
let 5 = 2 + 3
is a valid definition in OCaml. It will reduce the 2 + 3 expression to 5 and then try to match the resulting value with the left-hand side. If it matches, then the next definition is evaluated, and so on. If it doesn't the program is terminated.
Here 5 is a very simple value that matches only with 5 and, in general, your values will be more complex. However, there is a value that is even more primitive than 5. It is a value of type unit that has only one inhabitant, denoted as (). And this is also the value, to which colloquially expressions with side effects are reduced. Since in OCaml every expression must reduce to a value, we need a value that represents no value, and that is unit. For example print_endline "foo" reduces to () with a side effect of emitting string foo to the standard output.
Therefore, when we write
let foo () = print_endline "foo"
let () = foo ()
We evaluate (reduce) the function foo until it reaches the () value that indicates that we fully reduced foo ().
We could also use a wildcard matcher and write
let _ = foo ()
or bind the result to a variable, e.g.,
let bar = foo ()
But it is considered a good style to use () on the left-hand side of an expression that evaluates to () to indicate that the right-hand side doesn't produce any interesting value. It also prevents common errors, e.g.,
let () = foo
will yield an error saying that unit -> unit and can't be matched with unit and even provide a hint: Did you forget to provide ()' as argument?`
I'm learning basic Haskell so I can configure Xmonad, and I ran into this code snippet:
newKeys x = myKeys x `M.union` keys def x
Now I understand what the M.union in backticks is and means. Here's how I'm interpreting it:
newKeys(x) = M.union(myKeys(x),???)
I don't know what to make of the keys def x. Is it like keys(def(x))? Or keys(def,x)? Or is def some sort of other keyword?
It's keys(def,x).
This is basic Haskell syntax for function application: first the function itself, then its arguments separated by spaces. For example:
f x y = x + y
z = f 5 6
-- z = 11
However, it is not clear what def is without larger context.
In response to your comment: no, def couldn't be a function that takes x as argument, and then the result of that is passed to keys. This is because function application is left-associative, which basically means that in any bunch of things separated by spaces, only the first one is the function being applied, and the rest are its arguments. In order to express keys(def(x)), one would have to write keys (def x).
If you want to be super technical, then the right way to think about it is that all functions have exactly one parameter. When we declare a function of two parameters, e.g. f x y = x + y, what we really mean is that it's a function of one parameter, which returns another function, to which we can then pass the remaining parameter. In other words, f 5 6 means (f 5) 6.
This idea is kind of one of the core things in Haskell (and any ML offshoot) syntax. It's so important that it has its own name - "currying" (after Haskell Curry, the mathematician).
I have a recursive function working within the scope of strictly defined interface, so I can't change the function signatures.
The code compiles fine, and even runs fines without error. My problem is that it's a large result set, so it's very hard to test if there is a semantic error.
My primary question is: In a sequence of function calls A to B to A to B to breaking condition, considering the same original Map is passed to all functions until breaking condition, and that some functions only return an Integer, would an insert on a Map in a function that only returns an Integer still be reflected once control is returned to the first function?
primaryFunc :: SuperType -> MyMap -> (Integer, MyMap)
primaryFunc (SubType1 a) mapInstance = do
let returnInt = func1 a mapInstance
(returnInt, mapInstance)
primaryFunc (SubType2 c) mapInstance = do
let returnInt = primaryFunc_nonprefix_SuperType c mapInstance
let returnSuperType = (Const returnInt)
let returnTable = H.insert c returnSuperType mapInstance
(returnInt, returnTable)
primaryFunc (ConstSubType d) mapInstance = do
let returnInt = d
(returnInt, mapInstance)
func1 :: SubType1 -> MyMap -> Integer
func1 oe vt = do
--do stuff with input and map data to get return int
returnInt = primaryFunc
returnInt
func2 :: SubType2 -> MyMap -> Integer
func2 pe vt = do
--do stuff with input and map data to get return int
returnInt = primaryFunc
returnInt
Your question is almost impossibly dense and ambiguous, but it should be possible to answer what you term your "primary" question from the simplest first principles of Haskell:
No Haskell function updates a value (e.g. a map). At most it can return a modified copy of its input.
Outside of the IO monad, no function can have side effects. No function can affect the value of any variable assigned before it was called; all it can do is return a value.
So if you pass a map as a parameter to a function, nothing the function does can alter your existing reference to that value. If you want an updated value, you can only get that from the output of a function to which you have passed the original value as input. New value, new reference.
Because of this, you should have absolute clarity at any depth within your web of functions about which value you are working with. Knowing this, you should be able to answer your own question. Frankly, this is such a fundamental characteristic of Haskell that I am perplexed that you even need to ask.
If a function only returns an integer, then any operations you perform on any values made available to the function can only affect the output - that is, the integer value returned. Nothing done within the function can affect anything else (short of causing the whole program to crash).
So if function A has a reference to a map and it passes this value to function B which returns an int, nothing function B does can affect A's copy of the map. If function B were allowed to secretly alter A's copy of the map, that would be a side effect. Side effects are not allowed.
You need to understand that Haskell does not have variables as you understand them. It has immutable values, references to immutable values and functions (which take inputs and return new outputs). Functions do not have variables which are in scope for other functions which might alter those variables on the fly. That cannot happen.
As an aside, not only does the code you posted show that you do not understand the basics of Haskell syntax, the question you asked shows that you haven't understood the primary characteristics of Haskell as a language. Not only are these fundamentals things which can be understood before having learned any syntax, they are things you need to know to make sense of the syntax.
If you have a deadline, meet it using a tool you do understand. Then go learn Haskell properly.
In addition, you will find that
an insert on a Map in a function that only returns an Integer
is nearly impossible to express. Yes, you can technically do it like in
insert k v map `seq` 42 -- force an insert and throw away the result
but if you think that, for example:
let done = insert k v map in 42
does anything with the map, you're probably wrong.
In no case, however, is the original map altered.
I have read quite a few articles on closures, and, embarassingly enough, I still don't understand this concept! Articles explain how to create a closure with a few examples, but I don't see any point in paying much attention to them, as they largely look contrived examples. I am not saying all of them are contrived, just that the ones I found looked contrived, and I dint see how even after understanding them, I will be able to use them. So in order to understand closures, I am looking at a few real problems, that can be solved very naturally using closures.
For instance, a natural way to explain recursion to a person could be to explain the computation of n!. It is very natural to understand a problem like computing the factorial of a number using recursion. Similarly, it is almost a no-brainer to find an element in an unsorted array by reading each element, and comparing with the number in question. Also, at a different level, doing Object-oriented programming also makes sense.
So I am trying to find a number of problems that could be solved with or without closures, but using closures makes thinking about them and solving them easier. Also, there are two types to closures, where each call to a closure can create a copy of the environment variables, or reference the same variables. So what sort of problems can be solved more naturally in which of the closure implementations?
Callbacks are a great example. Let's take JavaScript.
Imagine you have a news site, with headlines and short blurbs and "Read More..." buttons next to each one. When the user clicks the button, you want to asynchronously load the content corresponding to the clicked button, and present the user with an indicator next to the requested headline so that the user can "see the page working at it".
function handleClickOnReadMore(element) {
// the user clicked on one of our 17 "request more info" buttons.
// we'll put a whirly gif next to the clicked one so the user knows
// what he's waiting for...
spinner = makeSpinnerNextTo(element);
// now get the data from the server
performAJAXRequest('http://example.com/',
function(response) {
handleResponse(response);
// this is where the closure comes in
// the identity of the spinner did not
// go through the response, but the handler
// still knows it, even seconds later,
// because the closure remembers it.
stopSpinner(spinner);
}
);
}
Alright, say you're generating a menu in, say, javascript.
var menuItems = [
{ id: 1, text: 'Home' },
{ id: 2, text: 'About' },
{ id: 3, text: 'Contact' }
];
And your creating them in a loop, like this:
for(var i = 0; i < menuItems.length; i++) {
var menuItem = menuItems[i];
var a = document.createElement('a');
a.href = '#';
a.innerHTML = menuItem.text;
// assign onclick listener
myMenu.appendChild(a);
}
Now, for the onclick listener, you might attempt something like this:
a.addEventListener('click', function() {
alert( menuItem.id );
}, false);
But you'll find that this will have every link alert '3'. Because at the time of the click, your onclick code is executed, and the value of menuItem is evaluated to the last item, since that was the value it was last assigned, upon the last iteration of the for loop.
Instead, what you can do is to create a new closure for each link, using the value of menuItem as it is at that point in execution
a.addEventListener('click', (function(item) {
return function() {
alert( item.id );
}
})( menuItem ), false);
So what's going on here? We're actually creating a function that accepts item and then immediately call that function, passing menuItem. So that 'wrapper' function is not what will be executed when you click the link. We're executing it immediately, and assigning the returned function as the click handler.
What happens here is that, for each iteration, the function is called with a new value of menuItem, and a function is returned which has access to that value, which is effectively creating a new closure.
Hope that cleared things up =)
Personally I hated to write sort routines when I had a list of objects.
Usually you had the sort function and a separate function to compare the two objects.
Now you can do it in one statement
List<Person> fList = new List<Person>();
fList.Sort((a, b) => a.Age.CompareTo(b.Age));
Well, after some time, spent with Scala, I can not imagine a code, operating on some list without closures. Example:
val multiplier = (i:Int) => i * 2
val list1 = List(1, 2, 3, 4, 5) map multiplier
val divider = (i:Int) => i / 2
val list2 = List(1, 2, 3, 4, 5) map divider
val map = list1 zip list2
println(map)
The output would be
List((2,0), (4,1), (6,1), (8,2), (10,2))
I'm not sure, if it is the example, you are looking for, but I personally think, that best examples of closures's real power can be seen on lists-examples: all kinds of sortings, searchings, iterating, etc.
I personally find massively helpful presentation by Stuart Langridge on Closures in JavaScript (slides in pdf). It's full of good examples and a bit of sense of humour as well.
In C#, a function can implement the concept of filtering by proximity to a point:
IEnumerable<Point> WithinRadius(this IEnumerable<Point> points, Point c, double r)
{
return points.Where(p => (p - c).Length <= r);
}
The lambda (closure) captures the supplied parameters and binds them up into a computation that will performed at some later time.
Well, I use Closures on a daily basis in the form of a function composition operator and a curry operator, both are implemented in Scheme by closures:
Quicksort in Scheme for instance:
(define (qsort lst cmp)
(if (null? lst) lst
(let* ((pivot (car lst))
(stacks (split-by (cdr lst) (curry cmp pivot))))
(append (qsort (cadr stacks) cmp)
(cons pivot
(qsort (car stacks) cmp))))))
Where I cmp is a binary function usually applied as (cmp one two), I curried it in this case to split my stack in two by creating a unitary predicate if you like, my curry operators:
(define (curry f . args)
(lambda lst (apply f (append args lst))))
(define (curryl f . args)
(lambda lst (apply f (append lst args))))
Which respectively curry righthanded and lefthanded.
So currying is a good example of closures, another example is functional composition. Or for instance a function which takes list and makes from that a predicate that tests if its argument is a member of that list or not, that's a closure too.
Closure is one of the power strengths of JavaScript, because JavaScript is a lambda language. For more on this subject go here:
Trying to simplify some Javascript with closures
For example, I would write:
x = 2
y = x + 4
print(y)
x = 5
print(y)
And it would output:
6 (=2+4)
9 (=5+4)
Also, are there any cases where this could actually be useful?
Clarification: Yes, lambdas etc. solve this problem (they were how I arrived at this idea); I was wondering if there were specific languages where this was the default: no function or lambda keywords required or needed.
Haskell will meet you halfway, because essentially everything is a function, but variables are only bound once (meaning you cannot reassign x in the same scope).
It's easy to consider y = x + 4 a variable assignment, but when you look at y = map (+4) [1..] (which means add 4 to every number in the infinite list from 1 upwards), what is y now? Is it an infinite list, or is it a function that returns an infinite list? (Hint: it's the second one.) In this case, treating variables as functions can be extremely beneficial, if not an absolute necessity, when taking advantage of laziness.
Really, in Haskell, your definition of y is a function accepting no arguments and returning x+4, where x is also a function that takes no arguments, but returns the value 2.
In any language with first order functions, it's trivial to assign anonymous functions to variables, but for most languages you'll have to add the parentheses to indicate a function call.
Example Lua code:
x = function() return 2 end
y = function() return x() + 4 end
print(y())
x = function() return 5 end
print(y())
$ lua x.lua
6
9
Or the same thing in Python (sticking with first-order functions, but we could have just used plain integers for x):
x = lambda: 2
y = lambda: x() + 4
print(y())
x = lambda: 5
print(y())
$ python x.py
6
9
you can use func expressions in C#
Func<int, int> y = (x) => x + 5;
Console.WriteLine(y(5)); // 10
Console.WriteLine(y(3)); // 8
... or ...
int x = 0;
Func<int> y = () => x + 5;
x = 5;
Console.WriteLine(y()); // 10
x = 3;
Console.WriteLine(y()); // 8
... if you are really wanting to program in a functional style the first option would probably be best.
it looks more like the stuff you saw in math class.
you don't have to worry about external state.
Check out various functional languages like F#, Haskell, and Scala. Scala treats functions as objects that have an apply() method, and you can store them in variables and pass them around like you can any other kind of object. I don't know that you can print out the definition of a Scala function as code though.
Update: I seem to recall that at least some Lisps allow you to pretty-print a function as code (eg, Scheme's pretty-print function).
This is the way spreadsheets work.
It is also related to call by name semantics for evaluating function arguments. Algol 60 had that, but it didn't catch on, too complicated to implement.
The programming language Lucid does this, although it calls x and y "streams" rather than functions.
The program would be written:
y
where
y = x + 4
end
And then you'd input:
x(0): 2
y = 6
x(1): 5
y = 7
Of course, Lucid (like most interesting programming languages) is fairly obscure, so I'm not surprised that nobody else found it. (or looked for it)
Try checking out F# here and on Wikipedia about Functional programming languages.
I myself have not yet worked on these types of languages since I've been concentrated on OOP, but will be delving soon once F# is out.
Hope this helps!
The closest I've seen of these have been part of Technical Analysis systems in charting components. (Tradestation, metastock, etc), but mainly they focus on returning multiple sets of metadata (eg buy/sell signals) which can be then fed into other functions that accept either meta data, or financial data, or plotted directly.
My 2c:
I'd say a language as you suggest would be highly confusing to say the least. Functions are generally r-values for good reason. This code (javascript) shows how enforcing functions as r-values increases readability (and therefore maintenance) n-fold:
var x = 2;
var y = function() { return x+2; }
alert(y());
x= 5;
alert(y());
Self makes no distinction between fields and methods, both are slots and can be accessed in exactly the same way. A slot can contain a value or a function (so those two are still separate entities), but the distinction doesn't matter to the user of the slot.
In Scala, you have lazy values and call-by-name arguments in functions.
def foo(x : => Int) {
println(x)
println(x) // x is evaluated again!
}
In some way, this can have the effect you looked for.
I believe the mathematically oriented languages like Octave, R and Maxima do that. I could be wrong, but no one else has mentioned them, so I thought I would.