My understanding is that closures are basically functions (and by that I mean piece of code) using variables that are bound to some values.
The partial valuation of a function on the other and is nothing but a new function obtained by another one binding some of its variables/arguments.
It seems o me that two concepts are basically the same: indeed one could regard (i.e. implement) closures as partial valuations of functions, that use additional arguments for the variables to be bound in the closure, and on the other hand a partial valuation seems to be just the closure of a function in which some of its variables-arguments are bound to values.
Is this line of thought correct? Are these two concepts really the same? And if no, what are the differences between these concepts?
Thanks in advance for any answer.
I wouldn't say they are the same thing. They are two concepts that have the same power, but that does not mean they are the same thing.
There's a very narrow semantic difference between the two, and I find myself wondering why both options exist. Are they in any way different functionally, or is one likely just an alias of the other?
There is no difference at all. They are, in fact, the very same method.
To the compiler,
myQueue.async(execute: { foo() })
is exactly the same as
myQueue.async {
foo()
}
When the last argument of any function or method is a function, you can pass that argument as a trailing closure instead of passing it inside the argument list. This is done in order to make higher-order functions such as DispatchQueue.async feel more like part of the language, reduce syntactic overhead and ease the creation of domain-specific languages.
There's documentation on trailing closure syntax here.
And by the way, the idiomatic way to write my first example would be:
myQueue.async(execute: foo)
What you're referring to is called trailing closure syntax. It's a syntactic sugar for making closures easier to work with.
There are many other kinds of syntactic sugar features that pertain to closures, which I cover in my answer here.
As always, I highly recommend the Swift Language guide, which does a great job at explaining the basics like this.
I'm starting to doubt I really understand this topic.
Until now, I was understanding a continuation as calling a function with closure (typically returned by another function). But MLton seems to have a non‑standard special structure for this (a structure I'm not sure to understand), and also in some other documents, mention special optimizations (using jumps, as quickly mentioned on page 58, printed page 51) with continuations, namely, instead of naming call to functions with closure. Also, function closures seems to be sometime described as the basis for continuations, but not described as being continuations, while some other times people assert the opposite (that function closures are special case of continuations, not the other way).
As an example, how do continuations differs from this, and what would looks like the same, with continuations instead of function with closure:
datatype next = Next of (unit -> next)
fun f (i:int): next =
(print (Int.toString i);
Next (fn () => f (i + 1)))
val Next g = f 1
val Next g = g ()
val Next g = g ()
val Next g = g ()
…
I wonder about it, in the general computer‑science context, as much as specifically in the practical SML context.
Note: the question may looks the same as “difference between closures and continuations”, but reading this one did not answer my question and does not address a practical case as a basis. Except it drove me to add another question: why are continuations said to be more abstract than closures, if in the end continuations are made of closures as the incomplete (to my eyes) answer in the above link suggest?
Is the difference really important or just a matter of style / syntax / vocabulary?
I feel a similar question arise with monads versus continuations, but that would be too much for a single question post (but if on the opposite, that can be simply answered in the while, feel free…).
Update
Still from MLton's world, a wording which seems to suggest continuations and function closures are the same (unless I'm not understanding correctly).
CommonArg (mlton.org), near the bottom of the page, says:
What I think the common argument optimization shows is that the
dominator analysis does slightly better than the reviewer puts it:
we find more than just constant continuations, we find common
continuations. And I think this is further justified by the fact
that I have observed common argument eliminate some env_X arguments
which would appear to correspond to determining that while the
closure being executed isn’t constant it is at least the same as
the closure being passed elsewhere.
It's talking about the same using both words, isn't it?
Similarly and may be more explicitely, at the bottom on this page: ReturnStatement (mlton.org).
There too, it seems to be the same. Is it?
It seems there is a terminological confusion. 'Continuation' is an abstract concept, which is a meaning of a context of an expression. Closure is a very particular way to realize
values that represent functions (higher-order languages can be implemented without closures at all, for example, using substitution semantics).
Control operator can capture the current continuation and produce a particular representation of it (this is called reification). The particular representation of a captured continuation may indeed be a closure -- or may be not. For example, in OCaml, the continuations captured by the delimcc library are repersented as values of the abstract data type (whose realization is quite different from closures). You might find the introduction part of the following page useful.
Undelimited continuations are not functions
I'm learning Elixir and wonder why it has two types of function definitions:
functions defined in a module with def, called using myfunction(param1, param2)
anonymous functions defined with fn, called using myfn.(param1, param2)
Only the second kind of function seems to be a first-class object and can be passed as a parameter to other functions. A function defined in a module needs to be wrapped in a fn. There's some syntactic sugar which looks like otherfunction(&myfunction(&1, &2)) in order to make that easy, but why is it necessary in the first place? Why can't we just do otherfunction(myfunction))? Is it only to allow calling module functions without parenthesis like in Ruby? It seems to have inherited this characteristic from Erlang which also has module functions and funs, so does it actually comes from how the Erlang VM works internally?
It there any benefit having two types of functions and converting from one type to another in order to pass them to other functions? Is there a benefit having two different notations to call functions?
Just to clarify the naming, they are both functions. One is a named function and the other is an anonymous one. But you are right, they work somewhat differently and I am going to illustrate why they work like that.
Let's start with the second, fn. fn is a closure, similar to a lambda in Ruby. We can create it as follows:
x = 1
fun = fn y -> x + y end
fun.(2) #=> 3
A function can have multiple clauses too:
x = 1
fun = fn
y when y < 0 -> x - y
y -> x + y
end
fun.(2) #=> 3
fun.(-2) #=> 3
Now, let's try something different. Let's try to define different clauses expecting a different number of arguments:
fn
x, y -> x + y
x -> x
end
** (SyntaxError) cannot mix clauses with different arities in function definition
Oh no! We get an error! We cannot mix clauses that expect a different number of arguments. A function always has a fixed arity.
Now, let's talk about the named functions:
def hello(x, y) do
x + y
end
As expected, they have a name and they can also receive some arguments. However, they are not closures:
x = 1
def hello(y) do
x + y
end
This code will fail to compile because every time you see a def, you get an empty variable scope. That is an important difference between them. I particularly like the fact that each named function starts with a clean slate and you don't get the variables of different scopes all mixed up together. You have a clear boundary.
We could retrieve the named hello function above as an anonymous function. You mentioned it yourself:
other_function(&hello(&1))
And then you asked, why I cannot simply pass it as hello as in other languages? That's because functions in Elixir are identified by name and arity. So a function that expects two arguments is a different function than one that expects three, even if they had the same name. So if we simply passed hello, we would have no idea which hello you actually meant. The one with two, three or four arguments? This is exactly the same reason why we can't create an anonymous function with clauses with different arities.
Since Elixir v0.10.1, we have a syntax to capture named functions:
&hello/1
That will capture the local named function hello with arity 1. Throughout the language and its documentation, it is very common to identify functions in this hello/1 syntax.
This is also why Elixir uses a dot for calling anonymous functions. Since you can't simply pass hello around as a function, instead you need to explicitly capture it, there is a natural distinction between named and anonymous functions and a distinct syntax for calling each makes everything a bit more explicit (Lispers would be familiar with this due to the Lisp 1 vs. Lisp 2 discussion).
Overall, those are the reasons why we have two functions and why they behave differently.
I don't know how useful this will be to anyone else, but the way I finally wrapped my head around the concept was to realize that elixir functions aren't Functions.
Everything in elixir is an expression. So
MyModule.my_function(foo)
is not a function but the expression returned by executing the code in my_function. There is actually only one way to get a "Function" that you can pass around as an argument and that is to use the anonymous function notation.
It is tempting to refer to the fn or & notation as a function pointer, but it is actually much more. It's a closure of the surrounding environment.
If you ask yourself:
Do I need an execution environment or a data value in this spot?
And if you need execution use fn, then most of the difficulties become much
clearer.
I may be wrong since nobody mentioned it, but I was also under the impression that the reason for this is also the ruby heritage of being able to call functions without brackets.
Arity is obviously involved but lets put it aside for a while and use functions without arguments. In a language like javascript where brackets are mandatory, it is easy to make the difference between passing a function as an argument and calling the function. You call it only when you use the brackets.
my_function // argument
(function() {}) // argument
my_function() // function is called
(function() {})() // function is called
As you can see, naming it or not does not make a big difference. But elixir and ruby allow you to call functions without the brackets. This is a design choice which I personally like but it has this side effect you cannot use just the name without the brackets because it could mean you want to call the function. This is what the & is for. If you leave arity appart for a second, prepending your function name with & means that you explicitly want to use this function as an argument, not what this function returns.
Now the anonymous function is bit different in that it is mainly used as an argument. Again this is a design choice but the rational behind it is that it is mainly used by iterators kind of functions which take functions as arguments. So obviously you don't need to use & because they are already considered arguments by default. It is their purpose.
Now the last problem is that sometimes you have to call them in your code, because they are not always used with an iterator kind of function, or you might be coding an iterator yourself. For the little story, since ruby is object oriented, the main way to do it was to use the call method on the object. That way, you could keep the non-mandatory brackets behaviour consistent.
my_lambda.call
my_lambda.call()
my_lambda_with_arguments.call :h2g2, 42
my_lambda_with_arguments.call(:h2g2, 42)
Now somebody came up with a shortcut which basically looks like a method with no name.
my_lambda.()
my_lambda_with_arguments.(:h2g2, 42)
Again, this is a design choice. Now elixir is not object oriented and therefore call not use the first form for sure. I can't speak for José but it looks like the second form was used in elixir because it still looks like a function call with an extra character. It's close enough to a function call.
I did not think about all the pros and cons, but it looks like in both languages you could get away with just the brackets as long as you make brackets mandatory for anonymous functions. It seems like it is:
Mandatory brackets VS Slightly different notation
In both cases you make an exception because you make both behave differently. Since there is a difference, you might as well make it obvious and go for the different notation. The mandatory brackets would look natural in most cases but very confusing when things don't go as planned.
Here you go. Now this might not be the best explanation in the world because I simplified most of the details. Also most of it are design choices and I tried to give a reason for them without judging them. I love elixir, I love ruby, I like the function calls without brackets, but like you, I find the consequences quite misguiding once in a while.
And in elixir, it is just this extra dot, whereas in ruby you have blocks on top of this. Blocks are amazing and I am surprised how much you can do with just blocks, but they only work when you need just one anonymous function which is the last argument. Then since you should be able to deal with other scenarios, here comes the whole method/lambda/proc/block confusion.
Anyway... this is out of scope.
I've never understood why explanations of this are so complicated.
It's really just an exceptionally small distinction combined with the realities of Ruby-style "function execution without parens".
Compare:
def fun1(x, y) do
x + y
end
To:
fun2 = fn
x, y -> x + y
end
While both of these are just identifiers...
fun1 is an identifier that describes a named function defined with def.
fun2 is an identifier that describes a variable (that happens to contain a reference to function).
Consider what that means when you see fun1 or fun2 in some other expression? When evaluating that expression, do you call the referenced function or do you just reference a value out of memory?
There's no good way to know at compile time. Ruby has the luxury of introspecting the variable namespace to find out if a variable binding has shadowed a function at some point in time. Elixir, being compiled, can't really do this. That's what the dot-notation does, it tells Elixir that it should contain a function reference and that it should be called.
And this is really hard. Imagine that there wasn't a dot notation. Consider this code:
val = 5
if :rand.uniform < 0.5 do
val = fn -> 5 end
end
IO.puts val # Does this work?
IO.puts val.() # Or maybe this?
Given the above code, I think it's pretty clear why you have to give Elixir the hint. Imagine if every variable de-reference had to check for a function? Alternatively, imagine what heroics would be necessary to always infer that variable dereference was using a function?
There's an excellent blog post about this behavior: link
Two types of functions
If a module contains this:
fac(0) when N > 0 -> 1;
fac(N) -> N* fac(N-1).
You can’t just cut and paste this into the shell and get the same
result.
It’s because there is a bug in Erlang. Modules in Erlang are sequences
of FORMS. The Erlang shell evaluates a sequence of
EXPRESSIONS. In Erlang FORMS are not EXPRESSIONS.
double(X) -> 2*X. in an Erlang module is a FORM
Double = fun(X) -> 2*X end. in the shell is an EXPRESSION
The two are not the same. This bit of silliness has been Erlang
forever but we didn’t notice it and we learned to live with it.
Dot in calling fn
iex> f = fn(x) -> 2 * x end
#Function<erl_eval.6.17052888>
iex> f.(10)
20
In school I learned to call functions by writing f(10) not f.(10) -
this is “really” a function with a name like Shell.f(10) (it’s a
function defined in the shell) The shell part is implicit so it should
just be called f(10).
If you leave it like this expect to spend the next twenty years of
your life explaining why.
Elixir has optional braces for functions, including functions with 0 arity. Let's see an example of why it makes a separate calling syntax important:
defmodule Insanity do
def dive(), do: fn() -> 1 end
end
Insanity.dive
# #Function<0.16121902/0 in Insanity.dive/0>
Insanity.dive()
# #Function<0.16121902/0 in Insanity.dive/0>
Insanity.dive.()
# 1
Insanity.dive().()
# 1
Without making a difference between 2 types of functions, we can't say what Insanity.dive means: getting a function itself, calling it, or also calling the resulting anonymous function.
fn -> syntax is for using anonymous functions. Doing var.() is just telling elixir that I want you to take that var with a func in it and run it instead of referring to the var as something just holding that function.
Elixir has a this common pattern where instead of having logic inside of a function to see how something should execute, we pattern match different functions based on what kind of input we have. I assume this is why we refer to things by arity in the function_name/1 sense.
It's kind of weird to get used to doing shorthand function definitions (func(&1), etc), but handy when you're trying to pipe or keep your code concise.
In elixir we use def for simply define a function like we do in other languages.
fn creates an anonymous function refer to this for more clarification
Only the second kind of function seems to be a first-class object and can be passed as a parameter to other functions. A function defined in a module needs to be wrapped in a fn. There's some syntactic sugar which looks like otherfunction(myfunction(&1, &2)) in order to make that easy, but why is it necessary in the first place? Why can't we just do otherfunction(myfunction))?
You can do otherfunction(&myfunction/2)
Since elixir can execute functions without the brackets (like myfunction), using otherfunction(myfunction)) it will try to execute myfunction/0.
So, you need to use the capture operator and specify the function, including arity, since you can have different functions with the same name. Thus, &myfunction/2.
i am kinda confused reading the definition between the two. Can they actually intersect in terms of definition? or am i completely lost? Thanks.
Closures, as the word tends to be used, are just functions (or blocks of code, if you like) that you can treat like a piece of data and pass to other functions, etc. (the "closed" bit is that wherever you eventually call it, it behaves just as it would if you called it where it was originally defined). A monad is (roughly) more like a context in which functions can be chained together sequentially, and controls how data is passed from one function to the next.
They're quite different, although monads will often use closures to capture logic.
Personally I would try to get solid on the definition of closures (essentially a piece of logic which also captures its environment, i.e. local variables etc) before worrying about monads. They can come later :)
There are various questions about closures on Stack Overflow - the best one to help you will depend on what platform you're working on. For instance, there's:
What are closures in .NET?
Function pointers, closures and lambda
Personally I'm only just beginning to "grok" monads (thanks to the book I'm helping out on). One day I'll get round to writing an article about them, when I feel I understand them well enough :)
A "closure" is an object comprising 1) a function, and 2) the values of its free variables where it's constructed.
A "monad" is a class of functions that can be composed in a certain way, i.e. by using associated bind and return higher-order function operators, to produce other functions.
I think monads are a little more complicated than closures because closures are just blocks of code that remember something from the point of their definitions and monads are a construct for "twisting" the usual function composition operation.