Why are there two kinds of functions in Elixir? - erlang

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.

Related

wxMaxima: subindexed variables in functions work when written as "x_1" but not when written as "x[1]"

I'm having trouble defining a function in terms of variables with subindices. Using the makelist command I can create an unspecified function that depends upon the subindexed variables x[1] and x[2]. However, when I try to give an expression to that function, wxMaxima does not allow it:
On the other hand, if I write the subindexed variables as x_1 and x_2 instead of x[1] and x_[2], things do work.
What is the reason for this behavior? Aren't the two subindexing methods equivalent in terms of functions?
Only symbols can be declared function arguments. In particular, subscripted expressions are not symbols and therefore can't be function arguments.
WxMaxima displays symbols which end in a number, e.g., x_1, the same as subscripted expressions, e.g., x[1]. This is intended as a convenience, although it is confusing because it makes it difficult to distinguish the two.
You can see the internal form of an expression via ?print (note the question mark is part of the name). E.g., ?print(x_1); versus ?print(x[1]);.

Julia create array of functions with matching arguments to execute in a loop

It's easy to create an array of functions and execute them in a loop.
It's easy to provide arguments in either a corresponding array of the same length or the array could be of tuples (fn, arg).
For 2, the loop is just
for fn_ar in arr # arr is [(myfunc, [1,2,3]), (func2, [10,11,12]), ...]
fn_ar[1](fn_ar[2])
end
Here is the problem: the arguments I am using are arrays of very large arrays. In #2, the argument that will be called with the function will be the current value of the array when the arg entry of the tuple is initially created. What I need is to provide the array names as the argument and defer evaluation of the arguments until the corresponding function is run in the loop body.
I could provide the arrays used as input as an expression and eval the expression in the loop to supply the needed arguments. But, eval can't eval in local scope.
What I did that worked (sort of) was to create a closure for each function that captured the arrays (which are really just a reference to storage). This works because the only argument to each function that varies in the loop body turns out to be the loop counter. The functions in question update the arrays in place. The array argument is really just a reference to the storage location, so each function executed in the loop body sees the latest values of the arrays. It worked. It wasn't hard to do. It is very, very slow. This is a known challenge in Julia.
I tried the recommended hints in the performance section of the manual. Make sure the captured variables are typed before they are captured so the JIT knows what they are. No effect on perf. The other hint is to put the definition of the curried function with the data for the closure in let block. Tried this. No effect on perf. It's possible I implemented the hints incorrectly--I can provide a code fragment if it helps.
But, I'd rather just ask the question about what I am trying to do and not muddy the waters with my past effort, which might not be going down the right path.
Here is a small fragment that is more realistic than the above:
Just a couple of functions and arguments:
(affine!, "(dat.z[hl], dat.a[hl-1], nnw.theta[hl], nnw.bias[hl])")
(relu!, "(dat.a[hl], dat.z[hl])")
Of course, the arguments could be wrapped as an expression with Meta.parse. dat.z and dat.a are matrices used in machine learning. hl indexes the layer of the model for the linear result and non-linear activation.
A simplified version of the loop where I want to run through the stack of functions across the model layers:
function feedfwd!(dat::Union{Batch_view,Model_data}, nnw, hp, ff_execstack)
for lr in 1:hp.n_layers
for f in ff_execstack[lr]
f(lr)
end
end
end
So, closures of the arrays is too slow. Eval I can't get to work.
Any suggestions...?
Thanks,
Lewis
I solved this with the beauty of function composition.
Here is the loop that runs through the feed forward functions for all layers:
for lr in 1:hp.n_layers
for f in ff_execstack[lr]
f(argfilt(dat, nnw, hp, bn, lr, f)...)
end
end
The inner function parameter to f called argfilt filters down from a generic list of all the inputs to return a tuple of arguments needed for the specific function. This also takes advantage of the beauty of method dispatch. Note that the function, f, is an input to argfilt. The types of functions are singletons: each function has a unique type as in typeof(relu!), for example. So, without any crazy if branching, method dispatch enables argfilt to return just the arguments needed. The performance cost compared to passing the arguments directly to a function is about 1.2 ns. This happens in a very hot loop that typically runs 24,000 times so that is 29 microseconds for the entire training pass.
The other great thing is that this runs in less than 1/10 of the time of the version using closures. I am getting slightly better performance than my original version that used some function variables and a bunch of if statements in the hot loop for feedfwd.
Here is what a couple of the methods for argfilt look like:
function argfilt(dat::Union{Model_data, Batch_view}, nnw::Wgts, hp::Hyper_parameters,
bn::Batch_norm_params, hl::Int, fn::typeof(affine!))
(dat.z[hl], dat.a[hl-1], nnw.theta[hl], nnw.bias[hl])
end
function argfilt(dat::Union{Model_data, Batch_view}, nnw::Wgts, hp::Hyper_parameters,
bn::Batch_norm_params, hl::Int, fn::typeof(relu!))
(dat.a[hl], dat.z[hl])
end
Background: I got here by reasoning that I could pass the same list of arguments to all of the functions: the union of all possible arguments--not that bad as there are only 9 args. Ignored arguments waste some space on the stack but it's teeny because for structs and arrays an argument is a pointer reference, not all of the data. The downside is that every one of these functions (around 20 or so) all need to have big argument lists. OK, but goofy: it doesn't make much sense when you look at the code of any of the functions. But, if I could filter down the arguments just to those needed, the function signatures don't need to change.
It's sort of a cool pattern. No introspection or eval needed; just functions.

What are the steps in doing incrementation in erlang?

increment([]) -> [];
increment([H|T]) -> [H+1|increment(T)].
decrement([]) -> [];
decrement([H|T]) -> [H-1|decrement(T)].
So I have this code but I don't know how they properly work like in java.
Java and Erlang are different beasts. I don't recommend trying to make comparisons to Java when learning Erlang, especially if Java is the only language you know so far. The code you've posted is a good example of the paradigm known as "functional programming". I'd suggest doing some reading on that subject to help you understand what's going on. To try to break this down as far as Erlang goes, you need to understand that an Erlang function is completely different from a Java method.
In Java, your method signature is composed of the method name and the types of its arguments. The return type can also be significant. A Java increment method like the function you wrote might be written like List<Integer> increment(List<Integer> input). The body of the Java method would probably iterate through the list an element at a time and set each element to itself plus one:
List<Integer> increment(List<Integer> input) {
for (int i = 0; i < input.size; i++) {
input.set(i, input.get(i) + 1);
}
}
Erlang has almost nothing in common with this. To begin with, an erlang function's "signature" is the name and arity of the function. Arity means how many arguments the function accepts. So your increment function is known as increment/1, and that's its unique signature. The way you write the argument list inside the parentheses after the function name has less to do with argument types than with the pattern of the data passed to it. A function like increment([]) -> ... can only successfully be called by passing it [], the empty list. Likewise, the function increment([Item]) -> ... can only be successfully called by passing it a list with one item in it, and increment([Item1, Item2]) -> ... must be passed a list with two items in it. This concept of matching data to patterns is quite aptly known as "pattern matching", and you'll find it in many functional languages. In Erlang functions, it's used to select which head of the function to execute. This bears a rough similarity to Java's method overloading, where you can have many methods with the same name but different argument types; however a pattern in an Erlang function head can bind variables to different pieces of the arguments that match the pattern.
In your code example, the function increment/1 has two heads. The first head is executed only if you pass an empty list to the function. The second head is executed only if you pass a non-empty list to the function. When that happens, two variables, H and T, are bound. H is bound to the first item of the list, and T is bound to the rest of the list, meaning all but the first item. That's because the pattern [H|T] matches a non-empty list, including a list with one element, in which case T would be bound to the empty list. The variables thus bound can be used in the body of the function.
The bodies of your functions are a very typical form of iterating a list in Erlang to produce a new list. It's typical because of another important difference from Java, which is that Erlang data is immutable. That means there's no such concept as "setting an element of a list" like I did in the Java code above. If you want to change a list, you have to build a new one, which is what your code does. It effectively says:
The result of incrementing the empty list is the empty list.
The result of incrementing a non-empty list is:
Take the first element of the list: H.
Increment the rest of the list: increment(T).
Prepend H+1 to the result of incrementing the rest of the list.
Note that you want to be careful about how you build lists in Erlang, or you can end up wasting a lot of resources. The List Handling User's Guide is a good place to learn about that. Also note that this code uses a concept known as "recursion", meaning that the function calls itself. In many popular languages, including Java, recursion is of limited usefulness because each new function call adds a stack frame, and your available memory space for stack frames is relatively limited. Erlang and many functional languages support a thing known as "tail call elimination", which is a feature that allows properly written code to recurse indefinitely without exhausting any resources.
Hopefully this helps explain things. If you can ask a more specific question, you might get a better answer.

Function closure versus continuation, in general and SML

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

When should we use FSharpFunc.Adapt?

Looking at the source in FSharp.Core and PowerPack, I see that a lot of higher-order functions that accept a function with two or more parameters use FSharpFunc.Adapt. For example:
let mapi f (arr: ResizeArray<_>) =
let f = FSharpFunc<_,_,_>.Adapt(f)
let len = length arr
let res = new ResizeArray<_>(len)
for i = 0 to len - 1 do
res.Add(f.Invoke(i, arr.[i]))
res
The documentation on FSharpFunc.Adapt is fairly thin. Is this a general best practice that we should be using any time we have a higher-order function with a similar signature? Only if the passed-in function is called multiple times? How much of an optimization is it? Should we be using Adapt everywhere we can, or only rarely?
Thanks for your time.
That's quite interesting! I don't have any official information (and I didn't see this documented anywhere), but here are some thoughts on how the Adapt function might work.
Functions like mapi take curried form of a function, which means that the type of the argument is compiled to something like FSharpFunc<int, FSharpFunc<T, R>>. However, many functions are actually compiled directly as functions of two arguments, so the actual value would typically be FSharpFunc<int, T, R> which inherits from FSharpFunc<int, FSharpFunc<T, R>>.
If you call this function (e.g. f 1 "a") the F# compiler generates something like this:
FSharpFunc<int, string>.InvokeFast<a>(f, 1, "a");
If you look at the InvokeFast function using Reflector, you'll see that it tests if the function is compiled as the optimized version (f :? FSharpFunc<int, T, R>). If yes, then it directly calls Invoke(1, "a") and if not then it needs to make two calls Invoke(1).Invoke("a").
This check is done each time you call a function passed as an argument (it is probably faster to do the check and then use the optimized call, because that's more common).
What the Adapt function does is that it converts any function to FSharpFunc<T1, T2, R> (if the function is not optimized, it creates a wrapper for it, but that's not the case most of the time). The calls to the adapted function will be faster, because they don't need to do the dynamic check every time (the check is done only once inside Adapt).
So, the summary is that Adapt could improve the performance if you're calling a function passed as an argument that takes more than 1 argument a large number of times. As with any optimizations, I wouldn't use this blindly, but it is an interesting thing to be aware of when tuning the performance!
(BTW: Thanks for a very interesting question, I didn't know the compiler does this :-))

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