I'm a new in Visual Prolog, and as I understand, this language seems as functional. And so on, I have a question: can we do smth like this (and if 'can' then 'how'):
func1(X, Y, Func2) :-
R = somefunc(X,Y),
if R = "yes", ! then
Func2 %here I want to call function with name, which is in variable 'Func2'
else
stdIO::write("End of work"),
stdIO::nl,
fail
end if.
The cause of this question - I need to call different functions in same way, with checking answer from console. and if it wasn't 'yes' - stop running program.
First of all, Prolog doesn't have functions, those things are predicates. The difference matter a lot, since there can be multiple ways to satisfy (prove) a predicate is true, but there is typically only one way to interpret a function.
I've never used Visual Prolog, but what you are asking can be accomplished in most flavors of Prolog I've seen using =../2 and call/1 as follows:
Func2WithArgs =.. [Func2, Arg1, Arg2],
call(Func2WithArgs).
for instance:
X = writeln, Call =.. [X, 'Hellow World'], call(Call).
The code seems correct except that you need parentheses when invoking the function. i.e. you must write Func2() rather than Func2.
func1(X, Y, Func2) :-
R = somefunc(X,Y),
if R = "yes", ! then
Func2() % parentheses here
else
stdio::write("End of work\n"),
fail
end if.
However if func1 and Func2 are indeed functions you need to deal with the return value:
func1(X, Y, Func2) = Result :-
R = somefunc(X,Y),
if R = "yes", ! then
Result = Func2()
else
stdio::write("End of work\n"),
fail % No result when failing
end if.
Also notice that there is a dedicated Visual Prolog forum: http://discuss.visual-prolog.com
I'm struggling a bit with this: I need a function that takes any function
of type fun(Any*) : Boolean as parameter, evaluates the function and returns true or
false, depending on the success of the function evaluation.
Essentially, what I need is a function type that allows any number and any type of parameter but the function must return Boolean.
Which would allow me to write functions like:
def checkLenght(str : String, length : Int) : Boolean ={
if (str.lenght == length)}
or
def ceckAB(a : Int, b : Int) : Boolean = {
if(a < b && a >= 23 && b < 42) }
so that, for example
eval(checkLenght(abc, 3)) //returns true
eval(ceckAB(4,1)) // returns false
I thought, a function type of:
type CheckFunction = (Any*) => Boolean
may does the trick but I struggle with writing the generic eval function.
Any advise?
Thank you
Solution:
The function requires
1) Another function of return type Boolean: "(func : => Boolean)"
2) Return type Boolean ": Boolean"
3) Returns the value of the passed function-parameter: " = func"
Altogether the function is:
def eval(func : => Boolean) : Boolean = func
It amazes me over again how simple simple things are in Scala.
As pointed out by the comments, this is a rather unusual function with no obvious
sense. Just a word about the underlying reasons.
Motivation:
There were a lot of question about the underlying motivation, so here a short
summary why such a function is needed.
Essentially, there are two reasons.
First one is about moving the failure handling away from the function itself
into a handler function. This preserves the purity of the check function and even allows
re-usage of generic checks.
Second, it's all about "pluggable failure handling". This means, the eval function only
tells if a failure happened (or not). In case of a failure, a handler is called through an interface. The implementation of the handler can be swapped using profiles as required.
Why?
Swapping profiles means, I code my checks and functions as usual but by switching the
profile, I switch the handler which means I can chose between full-stop, console print out, email alert, SNMP notification, push message... you name it. To do so, I need to decouple the check function from its evaluation and from its handling. That's the motivation for such a rather strange looking eval function.
And for the sake of completeness, I've already implemented all that stuff but was I facing the limitation of only handling trivial checks i.e. check(Boolean*) which is neat but often I would prefer to write a function to do more sophisticated checks.
Solved
The function is defined by returning the value of the passed function:
def eval(func : => Boolean) : Boolean = {func}
I can't say that I really understand your motivations for wanting to do what you want to do, but I guess that's beside the point. Maybe the eval function will check something before invoking the supplied function and not invoke that other function (like a fast fail) given some certain condition. Maybe you do some post checking after invoking the function and change the result based on something else. Either way, I suppose you could accomplish something similar to what you want with code looking like this:
def main(args: Array[String]) {
val str = "hello world"
println(eval(checkLength(str, 3)))
println(eval(intsEqual(1,1)))
}
def eval(func: => Boolean):Boolean = {
//Do whetever you want before invoking func, maybe
//not even invoke it if some other condition is present
val fres = func
//Maybe change something here before returning based on post conditions
fres
}
def checkLength(s:String, len:Int) = s.length() == len
def intsEqual(a:Int, b:Int) = a == b
If you really want the eval function to be able to support any function that takes any types of args and returns a Boolean, then using a by-name function like this, and then leveraging closure inside the by-name function to pass any params along to whatever actual function you want to invoke. A better way to demonstrate this is as follows:
def checkMyString(str:String, len:Int) = {
eval(str.length == len)
}
It's probably hard to see that the check str.length == len is not invoked unless eval decides to invoke it until you expand it to it's true form:
def checkMyString(str:String, len:Int) = {
def check = {
str.length == len
}
eval(check)
}
Here, the nested function check has access to str and len due to closure, and this will allow you to get around the requirement that eval must be able to invoke a function with any params that returns a Boolean.
This is just one way to solve your problem, and it might not even be suitable given your needs, but I just wanted to throw it out there.
If your input functions only have 2 arguments, like your two examples, you can write a semi generic function take takes all functions with two arguments of any type:
def eval[A,B](func: (A,B) => Boolean, arg1: A, arg2: B) = {
func(arg1, arg2)
}
def checkLength(str: String, length: Int) : Boolean = {
str.length == length
}
eval(checkLength, "ham", 4)
res0: Boolean = false
But if you want to support functions with more arguments, you would have to write one eval function for three arguments, four arguments, etc
Maybe there is a better way that can handle all cases?
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)