Related
Is there any way to initialize a Sequential value not in one fellow swoop?
Like, can I declare it, then use a for loop to populate it, step by step?
As this could all happen inside a class body, the true immutability of the Sequential value could then kick in once the class instance construction phase has been completed.
Example:
Sequential<String> strSeq;
for (i in span(0,10)) {
strSeq[i] = "hello";
}
This code doesn't work, as I get this error:
Error:(12, 9) ceylon: illegal receiving type for index expression:
'Sequential' is not a subtype of 'KeyedCorrespondenceMutator' or
'IndexedCorrespondenceMutator'
So what I can conclude is that sequences must be assigned in one statement, right?
Yes, several language guarantees hinge on the immutability of sequential objects, so that immutability must be guaranteed by the language – it can’t just trust you that you won’t mutate it after the initialization is done :)
Typically, what you do in this situation is construct some sort of collection (e. g. an ArrayList from ceylon.collection), mutate it however you want, and then take its .sequence() when you’re done.
Your specific case can also be written as a comprehension in a sequential literal:
String[] strSeq = [for (i in 0..10) "hello"];
The square brackets used to create a sequence literal accept not only a comma-separated list of values, but also a for-comprehension:
String[] strSeq = [for (i in 0..10) "hello"];
You can also do both at the same time, as long as the for-comprehension comes last:
String[] strSeq = ["hello", "hello", for (i in 0..8) "hello"];
In this specific case, you could also do this:
String[] strSeq = ["hello"].repeat(11);
You can also get a sequence of sequences via nesting:
String[][] strSeqSeq = [for (i in 0..2) [for (j in 0..2) "hello"]];
And you can do the cartesian product (notice that the nested for-comprehension here isn't in square brackets):
[Integer, Character][] pairs = [for (i in 0..2) for (j in "abc") [i, j]];
Foo[] is an abbreviation for Sequential<Foo>, and x..y translates to span(x, y).
If you know upfront the size of the sequence you want to create, then a very efficient way is to use an Array:
value array = Array.ofSize(11, "");
for (i in 0:11) {
array[i] = "hello";
}
String[] strSeq = array.sequence();
On the other hand, if you don't know the size upfront, then, as described by Lucas, you need to use either:
a comprehension, or
some sort of growable array, like ArrayList.
At the beginning of a method I want to check if the method is called with these exact parameters before, and if so, return the result that was returned back then.
At first, with one parameter, I used a Dictionary, but now I need to check 3 parameters (a String, an Object and a boolean).
I tried making a custom Object like so:
var cacheKey:Object = { identifier:identifier, type:type, someBoolean:someBoolean };
//if key already exists, return it (not working)
if (resultCache[cacheKey]) return resultCache[cacheKey];
//else: create result ...
//and save it in the cache
resultCache[cacheKey] = result;
But this doesn't work, because the seccond time the function is called, the new cacheKey is not the same object as the first, even though it's properties are the same.
So my question is: is there a datatype that will check the properties of the object used as key for a matching key?
And what else is my best option? Create a cache for the keys as well? :/
Note there are two aspects to the technical solution: equality comparison and indexing.
The Cliff Notes version:
It's easy to do custom equality comparison
In order to perform indexing, you need to know more than whether one object is equal to another -- you need to know which is object is "bigger" than the other.
If all of your properties are primitives you should squash them into a single string and use an Object to keep track of them (NOT a Dictionary).
If you need to compare some of the individual properties for reference equality you're going to have a write a function to determine which set of properties is bigger than the other, and then make your own collection class that uses the output of the comparison function to implement its own a binary search tree based indexing.
If the number of unique sets of arguments is in the several hundreds or less AND you do need reference comparison for your Object argument, just use an Array and the some method to do a naive comparison to all cached keys. Only you know how expensive your actual method is, so it's up to you to decide what lookup cost (which depends on the number of unique arguments provided to the function) is acceptable.
Equality comparison
To address equality comparison it is easy enough to write some code to compare objects for the values of their properties, rather than for reference equality. The following function enforces strict set comparison, so that both objects must contain exactly the same properties (no additional properties on either object allowed) with the same values:
public static propsEqual(obj1:Object, obj2:Object):Boolean {
for(key1:* in obj1) {
if(obj2[key1] === undefined)
return false;
if(obj2[key1] != obj2[key1])
return false;
}
for(key2:* in obj2)
if(obj1[key2] === undefined)
return false;
return true;
}
You could speed it up by eliminating the second for loop with the tradeoff that {A:1, B:2} will be deemed equal to {A:1, B:2, C:'An extra property'}.
Indexing
The problem with this in your case is that you lose the indexing that a Dictionary provides for reference equality or that an Object provides for string keys. You would have to compare each new set of function arguments to the entire list of previously seen arguments, such as using Array.some. I use the field currentArgs and the method to avoid generating a new closure every time.
private var cachedArgs:Array = [];
private var currentArgs:Object;
function yourMethod(stringArg:String, objArg:Object, boolArg:Boolean):* {
currentArgs = { stringArg:stringArg, objArg:objArg, boolArg:boolArg };
var iveSeenThisBefore:Boolean = cachedArgs.some(compareToCurrent);
if(!iveSeenThisBefore)
cachedArgs.push(currentArgs);
}
function compareToCurrent(obj:Object):Boolean {
return someUtil.propsEqual(obj, currentArgs);
}
This means comparison will be O(n) time, where n is the ever increasing number of unique sets of function arguments.
If all the arguments to your function are primitive, see the very similar question In AS3, where do you draw the line between Dictionary and ArrayCollection?. The title doesn't sound very similar but the solution in the accepted answer (yes I wrote it) addresses the exact same techinical issue -- using multiple primitive values as a single compound key. The basic gist in your case would be:
private var cachedArgs:Object = {};
function yourMethod(stringArg:String, objArg:Object, boolArg:Boolean):* {
var argKey:String = stringArg + objArg.toString() + (boolArg ? 'T' : 'F');
if(cachedArgs[argKey] === undefined)
cachedArgs[argKey] = _yourMethod(stringArg, objArg, boolArg);
return cachedArgs[argKey];
}
private function _yourMethod(stringArg:String, objArg:Object, boolArg:Boolean):* {
// Do stuff
return something;
}
If you really need to determine which reference is "bigger" than another (as the Dictionary does internally) you're going to have to wade into some ugly stuff, since Adobe has not yet provided any API to retrieve the "value" / "address" of a reference. The best thing I've found so far is this interesting hack: How can I get an instance's "memory location" in ActionScript?. Without doing a bunch of performance tests I don't know if using this hack to compare references will kill the advantages gained by binary search tree indexnig. Naturally it would depend on the number of keys.
I'm trying to define a new type and have not had much luck finding any information about using lists within them. Basically my new type will contain two lists, lets say x and y of type SqlSingle (the user defined type is written in C#) is this even possible?
If not how are you supposed to go about simulating a two lists of an arbitary length in an SQL Server 2008 column?
I'm possibly going about this the wrong way but it is the best approach I can think of at the moment. Any help is very much appreciated.
You can use a List<T> in a CLR UDT - although CLR types are structs, which should be immutable, so a ReadOnlyCollection<T> would be a better choice if you don't have a very compelling reason for the mutability. What you need to know in either case is that SQL won't know how to use the list itself; you can't simply expose the list type as a public IList<T> or IEnumerable<T> and be on your merry way, like you would be able to do in pure .NET.
Typically the way to get around this would be to expose a Count property and some methods to get at the individual list items.
Also, in this case, instead of maintaining two separate lists of SqlSingle instances, I would create an additional type to represent a single point, so you can manage it independently and pass it around in SQL if you need to:
[Serializable]
[SqlUserDefinedType(Format.Native)]
public struct MyPoint
{
private SqlSingle x;
private SqlSingle y;
public MyPoint()
{
}
public MyPoint(SqlSingle x, SqlSingle y) : this()
{
this.x = x;
this.y = y;
}
// You need this method because SQL can't use the ctors
[SqlFunction(Name = "CreateMyPoint")]
public static MyPoint Create(SqlSingle x, SqlSingle y)
{
return new MyPoint(x, y);
}
// Snip Parse method, Null property, etc.
}
The main type would look something like this:
[Serializable]
[SqlUserDefinedType(Format.UserDefined, IsByteOrdered = true, MaxByteSize = ...)]
public struct MyUdt
{
// Make sure to initialize this in any constructors/builders
private IList<MyPoint> points;
[SqlMethod(OnNullCall = false, IsDeterministic = true, IsPrecise = true)]
public MyPoint GetPoint(int index)
{
if ((index >= 0) && (index < points.Count))
{
return points[index];
}
return MyPoint.Null;
}
public int Count
{
get { return points.Count; }
}
}
If you need SQL to be able to get a sequence of all the points, then you can add an enumerable method to the sequence type as well:
[SqlFunction(FillRowMethodName = "FillPointRow",
TableDefinition = "[X] real, [Y] real")]
public static IEnumerable GetPoints(MyUdt obj)
{
return obj.Points;
}
public static void FillPointRow(object obj, out SqlSingle x, out SqlSingle y)
{
MyPoint point = (MyPoint)obj;
x = point.X;
y = point.Y;
}
You might think that it's possible to use an IEnumerable<T> and/or use an instance method instead of a static one, but don't even bother trying, it doesn't work.
So the way you can use the resulting type in SQL Server is:
DECLARE #UDT MyUdt
SET #UDT = <whatever>
-- Will show the number of points
SELECT #UDT.Count
-- Will show the binary representation of the second point
SELECT #UDT.GetPoint(1) AS [Point]
-- Will show the X and Y values for the second point
SELECT #UDT.GetPoint(1).X AS [X], #UDT.GetPoint(1).Y AS [Y]
-- Will show all the points
SELECT * FROM dbo.GetPoints(#UDT)
Hope this helps get you on the right track. UDTs can get pretty complicated to manage when they're dealing with list/sequence data.
Also note that you'll obviously need to add serialization methods, builder methods, aggregate methods, and so on. It can be quite an ordeal; make sure that this is actually the direction you want to go in, because once you start adding UDT columns it can be very difficult to make changes if you realize that you made the wrong choice.
Lists as you describe are usually normalized - that is, stored in separate tables with one row per item - rather than trying to cram them into a single column. If you can share more info on what you are trying to accomplish, maybe we can offer more assistance.
Edit - suggested table structure:
-- route table--
route_id int (PK)
route_length int (or whatever)
route_info <other fields as needed>
-- waypoint table --
route_id int (PK)
sequence tinyint (PK)
lat decimal(9,6)
lon decimal(9,6)
waypoint_info <other fields as needed>
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)
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When learning a new programming language, one of the possible roadblocks you might encounter is the question whether the language is, by default, pass-by-value or pass-by-reference.
So here is my question to all of you, in your favorite language, how is it actually done? And what are the possible pitfalls?
Your favorite language can, of course, be anything you have ever played with: popular, obscure, esoteric, new, old...
Here is my own contribution for the Java programming language.
first some code:
public void swap(int x, int y)
{
int tmp = x;
x = y;
y = tmp;
}
calling this method will result in this:
int pi = 3;
int everything = 42;
swap(pi, everything);
System.out.println("pi: " + pi);
System.out.println("everything: " + everything);
"Output:
pi: 3
everything: 42"
even using 'real' objects will show a similar result:
public class MyObj {
private String msg;
private int number;
//getters and setters
public String getMsg() {
return this.msg;
}
public void setMsg(String msg) {
this.msg = msg;
}
public int getNumber() {
return this.number;
}
public void setNumber(int number) {
this.number = number;
}
//constructor
public MyObj(String msg, int number) {
setMsg(msg);
setNumber(number);
}
}
public static void swap(MyObj x, MyObj y)
{
MyObj tmp = x;
x = y;
y = tmp;
}
public static void main(String args[]) {
MyObj x = new MyObj("Hello world", 1);
MyObj y = new MyObj("Goodbye Cruel World", -1);
swap(x, y);
System.out.println(x.getMsg() + " -- "+ x.getNumber());
System.out.println(y.getMsg() + " -- "+ y.getNumber());
}
"Output:
Hello world -- 1
Goodbye Cruel World -- -1"
thus it is clear that Java passes its parameters by value, as the value for pi and everything and the MyObj objects aren't swapped.
be aware that "by value" is the only way in java to pass parameters to a method. (for example a language like c++ allows the developer to pass a parameter by reference using '&' after the parameter's type)
now the tricky part, or at least the part that will confuse most of the new java developers: (borrowed from javaworld)
Original author: Tony Sintes
public void tricky(Point arg1, Point arg2)
{
arg1.x = 100;
arg1.y = 100;
Point temp = arg1;
arg1 = arg2;
arg2 = temp;
}
public static void main(String [] args)
{
Point pnt1 = new Point(0,0);
Point pnt2 = new Point(0,0);
System.out.println("X: " + pnt1.x + " Y: " +pnt1.y);
System.out.println("X: " + pnt2.x + " Y: " +pnt2.y);
System.out.println(" ");
tricky(pnt1,pnt2);
System.out.println("X: " + pnt1.x + " Y:" + pnt1.y);
System.out.println("X: " + pnt2.x + " Y: " +pnt2.y);
}
"Output
X: 0 Y: 0
X: 0 Y: 0
X: 100 Y: 100
X: 0 Y: 0"
tricky successfully changes the value of pnt1!
This would imply that Objects are passed by reference, this is not the case!
A correct statement would be: the Object references are passed by value.
more from Tony Sintes:
The method successfully alters the
value of pnt1, even though it is
passed by value; however, a swap of
pnt1 and pnt2 fails! This is the major
source of confusion. In the main()
method, pnt1 and pnt2 are nothing more
than object references. When you pass
pnt1 and pnt2 to the tricky() method,
Java passes the references by value
just like any other parameter. This
means the references passed to the
method are actually copies of the
original references. Figure 1 below
shows two references pointing to the
same object after Java passes an
object to a method.
(source: javaworld.com)
Conclusion or a long story short:
Java passes it parameters by value
"by value" is the only way in java to pass a parameter to a method
using methods from the object given as parameter will alter the object as the references point to the original objects. (if that method itself alters some values)
useful links:
http://www.javaworld.com/javaworld/javaqa/2000-05/03-qa-0526-pass.html
http://www.ibm.com/developerworks/java/library/j-passbyval/
http://www.ibm.com/developerworks/library/j-praxis/pr1.html
http://javadude.com/articles/passbyvalue.htm
Here is another article for the c# programming language
c# passes its arguments by value (by default)
private void swap(string a, string b) {
string tmp = a;
a = b;
b = tmp;
}
calling this version of swap will thus have no result:
string x = "foo";
string y = "bar";
swap(x, y);
"output:
x: foo
y: bar"
however, unlike java c# does give the developer the opportunity to pass parameters by reference, this is done by using the 'ref' keyword before the type of the parameter:
private void swap(ref string a, ref string b) {
string tmp = a;
a = b;
b = tmp;
}
this swap will change the value of the referenced parameter:
string x = "foo";
string y = "bar";
swap(x, y);
"output:
x: bar
y: foo"
c# also has a out keyword, and the difference between ref and out is a subtle one.
from msdn:
The caller of a method which takes an
out parameter is not required to
assign to the variable passed as the
out parameter prior to the call;
however, the callee is required to
assign to the out parameter before
returning.
and
In contrast ref parameters are
considered initially assigned by the
callee. As such, the callee is not
required to assign to the ref
parameter before use. Ref parameters
are passed both into and out of a
method.
a small pitfall is, like in java, that objects passed by value can still be changed using their inner methods
conclusion:
c# passes its parameters, by default, by value
but when needed parameters can also be passed by reference using the ref keyword
inner methods from a parameter passed by value will alter the object (if that method itself alters some values)
useful links:
http://msdn.microsoft.com/en-us/vcsharp/aa336814.aspx
http://www.c-sharpcorner.com/UploadFile/saragana/Willswapwork11162005012542AM/Willswapwork.aspx
http://en.csharp-online.net/Value_vs_Reference
Python uses pass-by-value, but since all such values are object references, the net effect is something akin to pass-by-reference. However, Python programmers think more about whether an object type is mutable or immutable. Mutable objects can be changed in-place (e.g., dictionaries, lists, user-defined objects), whereas immutable objects can't (e.g., integers, strings, tuples).
The following example shows a function that is passed two arguments, an immutable string, and a mutable list.
>>> def do_something(a, b):
... a = "Red"
... b.append("Blue")
...
>>> a = "Yellow"
>>> b = ["Black", "Burgundy"]
>>> do_something(a, b)
>>> print a, b
Yellow ['Black', 'Burgundy', 'Blue']
The line a = "Red" merely creates a local name, a, for the string value "Red" and has no effect on the passed-in argument (which is now hidden, as a must refer to the local name from then on). Assignment is not an in-place operation, regardless of whether the argument is mutable or immutable.
The b parameter is a reference to a mutable list object, and the .append() method performs an in-place extension of the list, tacking on the new "Blue" string value.
(Because string objects are immutable, they don't have any methods that support in-place modifications.)
Once the function returns, the re-assignment of a has had no effect, while the extension of b clearly shows pass-by-reference style call semantics.
As mentioned before, even if the argument for a is a mutable type, the re-assignment within the function is not an in-place operation, and so there would be no change to the passed argument's value:
>>> a = ["Purple", "Violet"]
>>> do_something(a, b)
>>> print a, b
['Purple', 'Violet'] ['Black', 'Burgundy', 'Blue', 'Blue']
If you didn't want your list modified by the called function, you would instead use the immutable tuple type (identified by the parentheses in the literal form, rather than square brackets), which does not support the in-place .append() method:
>>> a = "Yellow"
>>> b = ("Black", "Burgundy")
>>> do_something(a, b)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "<stdin>", line 3, in do_something
AttributeError: 'tuple' object has no attribute 'append'
Since I haven't seen a Perl answer yet, I thought I'd write one.
Under the hood, Perl works effectively as pass-by-reference. Variables as function call arguments are passed referentially, constants are passed as read-only values, and results of expressions are passed as temporaries. The usual idioms to construct argument lists by list assignment from #_, or by shift tend to hide this from the user, giving the appearance of pass-by-value:
sub incr {
my ( $x ) = #_;
$x++;
}
my $value = 1;
incr($value);
say "Value is now $value";
This will print Value is now 1 because the $x++ has incremented the lexical variable declared within the incr() function, rather than the variable passed in. This pass-by-value style is usually what is wanted most of the time, as functions that modify their arguments are rare in Perl, and the style should be avoided.
However, if for some reason this behaviour is specifically desired, it can be achieved by operating directly on elements of the #_ array, because they will be aliases for variables passed into the function.
sub incr {
$_[0]++;
}
my $value = 1;
incr($value);
say "Value is now $value";
This time it will print Value is now 2, because the $_[0]++ expression incremented the actual $value variable. The way this works is that under the hood #_ is not a real array like most other arrays (such as would be obtained by my #array), but instead its elements are built directly out of the arguments passed to a function call. This allows you to construct pass-by-reference semantics if that would be required. Function call arguments that are plain variables are inserted as-is into this array, and constants or results of more complex expressions are inserted as read-only temporaries.
It is however exceedingly rare to do this in practice, because Perl supports reference values; that is, values that refer to other variables. Normally it is far clearer to construct a function that has an obvious side-effect on a variable, by passing in a reference to that variable. This is a clear indication to the reader at the callsite, that pass-by-reference semantics are in effect.
sub incr_ref {
my ( $ref ) = #_;
$$ref++;
}
my $value = 1;
incr(\$value);
say "Value is now $value";
Here the \ operator yields a reference in much the same way as the & address-of operator in C.
There's a good explanation here for .NET.
A lot of people are surprise that reference objects are actually passed by value (in both C# and Java). It's a copy of a stack address. This prevents a method from changing where the object actually points to, but still allows a method to change the values of the object. In C# its possible to pass a reference by reference, which means you can change where an actual object points to.
Don't forget there is also pass by name, and pass by value-result.
Pass by value-result is similar to pass by value, with the added aspect that the value is set in the original variable that was passed as the parameter. It can, to some extent, avoid interference with global variables. It is apparently better in partitioned memory, where a pass by reference could cause a page fault (Reference).
Pass by name means that the values are only calculated when they are actually used, rather than at the start of the procedure. Algol used pass-by-name, but an interesting side effect is that is it very difficult to write a swap procedure (Reference). Also, the expression passed by name is re-evaluated each time it is accessed, which can also have side effects.
Whatever you say as pass-by-value or pass-by-reference must be consistent across languages. The most common and consistent definition used across languages is that with pass-by-reference, you can pass a variable to a function "normally" (i.e. without explicitly taking address or anything like that), and the function can assign to (not mutate the contents of) the parameter inside the function and it will have the same effect as assigning to the variable in the calling scope.
From this view, the languages are grouped as follows; each group having the same passing semantics. If you think that two languages should not be put in the same group, I challenge you to come up with an example that distinguishes them.
The vast majority of languages including C, Java, Python, Ruby, JavaScript, Scheme, OCaml, Standard ML, Go, Objective-C, Smalltalk, etc. are all pass-by-value only. Passing a pointer value (some languages call it a "reference") does not count as pass by reference; we are only concerned about the thing passed, the pointer, not the thing pointed to.
Languages such as C++, C#, PHP are by default pass-by-value like the languages above, but functions can explicitly declare parameters to be pass-by-reference, using & or ref.
Perl is always pass-by-reference; however, in practice people almost always copy the values after getting it, thus using it in a pass-by-value way.
by value
is slower than by reference since the system has to copy the parameter
used for input only
by reference
faster since only a pointer is passed
used for input and output
can be very dangerous if used in conjunction with global variables
Concerning J, while there is only, AFAIK, passing by value, there is a form of passing by reference which enables moving a lot of data. You simply pass something known as a locale to a verb (or function). It can be an instance of a class or just a generic container.
spaceused=: [: 7!:5 <
exectime =: 6!:2
big_chunk_of_data =. i. 1000 1000 100
passbyvalue =: 3 : 0
$ y
''
)
locale =. cocreate''
big_chunk_of_data__locale =. big_chunk_of_data
passbyreference =: 3 : 0
l =. y
$ big_chunk_of_data__l
''
)
exectime 'passbyvalue big_chunk_of_data'
0.00205586720663967
exectime 'passbyreference locale'
8.57957102144893e_6
The obvious disadvantage is that you need to know the name of your variable in some way in the called function. But this technique can move a lot of data painlessly. That's why, while technically not pass by reference, I call it "pretty much that".
PHP is also pass by value.
<?php
class Holder {
private $value;
public function __construct($value) {
$this->value = $value;
}
public function getValue() {
return $this->value;
}
}
function swap($x, $y) {
$tmp = $x;
$x = $y;
$y = $tmp;
}
$a = new Holder('a');
$b = new Holder('b');
swap($a, $b);
echo $a->getValue() . ", " . $b->getValue() . "\n";
Outputs:
a b
However in PHP4 objects were treated like primitives. Which means:
<?php
$myData = new Holder('this should be replaced');
function replaceWithGreeting($holder) {
$myData->setValue('hello');
}
replaceWithGreeting($myData);
echo $myData->getValue(); // Prints out "this should be replaced"
By default, ANSI/ISO C uses either--it depends on how you declare your function and its parameters.
If you declare your function parameters as pointers then the function will be pass-by-reference, and if you declare your function parameters as not-pointer variables then the function will be pass-by-value.
void swap(int *x, int *y); //< Declared as pass-by-reference.
void swap(int x, int y); //< Declared as pass-by-value (and probably doesn't do anything useful.)
You can run into problems if you create a function that returns a pointer to a non-static variable that was created within that function. The returned value of the following code would be undefined--there is no way to know if the memory space allocated to the temporary variable created in the function was overwritten or not.
float *FtoC(float temp)
{
float c;
c = (temp-32)*9/5;
return &c;
}
You could, however, return a reference to a static variable or a pointer that was passed in the parameter list.
float *FtoC(float *temp)
{
*temp = (*temp-32)*9/5;
return temp;
}