When are F# function calls evaluated; lazily or immediately? - f#

Curried functions in F#. I get the bit where passing in a subset of parameters yields a function with presets. I just wondered if passing all of the parameters is any different. For example:
let addTwo x y = x + y
let incr a = addTwo 1
let added = addTwo 2 2
incr is a function taking one argument.
Is added an int or a function? I can imagine an implementation where "added" is evaluated lazily only on use (like Schroedinger's Cat on opening the box). Is there any guarantee of when the addition is performed?

added is not a function; it is just a value that is calculated and bound to the name on the spot. A function always needs at least one parameter; if there is nothing useful to pass, that would be the unit value ():
let added () = addTwo 2 2

F# is an eagerly evaluated language, so an expression like addTwo 2 2 will immediately be evaluated to a value of the int type.
Haskell, by contrast, is lazily evaluated. An expression like addTwo 2 2 will not be evaluated until the value is needed. The type of the expression would still be a single integer, though. Even so, such an expression is, despite its laziness, not regarded as a function; in Haskell, such an unevaluated expression is called a thunk. That basically just means 'an arbitrarily complex expression that's not yet evaluated'.

incr is a function taking one argument. Is added an int or a function?
added, in this case, is a named binding that evaluates to an int. It is not a function.
I can imagine an implementation where "added" is evaluated lazily only on use (like Schroedinger's Cat on opening the box). Is there any guarantee of when the addition is performed?
The addition will be performed immediately when the binding is generated. There is no laziness involved.
As explained by TeaDrivenDev, you can change added to be a bound function instead of a bound value by adding a parameter, which can be unit:
let added () = addTwo 2 2
In this case, it will be a function, so the addition wouldn't happen until you call it:
let result = added () // Call the function, bind output to result

No. But kind of yes. But really, no.
You can construct a pure functional language that only has functions and nothing else. Lambda calculus is a complete algebra, so the theory is there. In this model, added can be considered a parameter-less function (in contrast to e.g. random(), where there's one parameter of type unit).
But F# is different. Since it's a rather pragmatic mix of imperative and functional programming, the result is not a function[1]. Instead, it's a value, just like a local in C#. This is no implementation detail - it's actually part of the F# specification. This does have disadvantages - it means its possible to have an ambiguous definition, where a definition could be either a value or a function definition (14.6.1).
[1] - Though in a pure functional program, you can't tell the difference - it's the same as just doing a substitution of the function with a cached value, which is perfectly legal.

Related

Why does reference equality for functions which are bound to the same variable return false?

let f x = System.Object.ReferenceEquals(x,x)
f id // false
I thought that at first it might because a function could be converted to a closure multiple times, but the above disproves that. Why does that last line return false?
You likely have optimizations turned on. This time it's the opposite problem.
What happens if inlining is turned on?
id will be rewritten to an instance of idFuncClass <: FSharpFunc.
The whole expression will be rewritten to:
Object.ReferenceEquals(new fsharpfun1(), new fsharpfun1())
You can turning off inlining with:
[<MethodImpl(MethodImplOptions.NoInlining)>]
let f x = System.Object.ReferenceEquals(x,x)
You'll find that the comparison works again.
But the bigger take-away is this - comparing two functions in F# is undefined behavior. In fact a function type doesn't even implement equality.
let illegal = id = id //this won't compile
Here's the relevant section in the F# Spec:
6.9.24 Values with Underspecified Object Identity and Type Identity
The CLI and F# support operations that detect object identity — that is, whether two object references refer to the same “physical” object.
For example, System.Object.ReferenceEquals(obj1, obj2) returns true if the two object references refer to the same object. Similarly, GetHashCode() returns a hash code that is partly based on physical object identity ...
The results of these operations are underspecified when used with values of the following F# types:
Function types
Tuple types
Immutable record types
Union types
Boxed immutable value types
For two values of such types, the results of System.Object.ReferenceEquals and
System.Runtime.CompilerServices.RuntimeHelpers.GetHashCode are underspecified; however, the operations terminate and do not raise exceptions.
An implementation of F# is not required to define the results of these
operations for values of these types.
What the spec advises is to treat the actual function-type and its CLR implementations as a black-box.

What's the advantage of having a type to represent a function?

What's the advantage of having a type represent a function?
For example, I have observed the following snippet:
type Soldier = Soldier of PieceProperties
type King = King of PieceProperties
type Crown = Soldier -> King
Is it just to support Partial Application when additional args have yet to be satisfied?
As Fyodor Soikin says in the comments
Same reason you give names to everything else - values, functions,
modules, etc.
In other words, think about programming in assembly which typically does not use types, (yes I am aware of typed assembly) and all of the problems that one can have and then how many of those problems are solved or reduced by adding types.
So before you programmed with a language that supported functions but that used static typing, you typed everything. Now that you are using F# which has static typing and functions, just extend what you have been using typing for but now add the ability to type the functions.
To quote Benjamin C. Pierce from "Types and Programming Languages"
A type system is a tractable syntactic method for proving the absence
of certain program behaviors by classifying phrases according to the
kinds of values they compute.
As noted in "Types and Programming Languages" Section 1.2
What Type Systems Are Good For
Detecting Errors
Abstraction
Documentation
Language Safety
Efficiency
TL;DR
One of the places that I find named type function definitions invaluable is when I am building parser combinators. During the construction of the functions I fully type the functions so that I know what the types are as opposed to what type inferencing will infer they are which might be different than what I want. Since the function types typically have several parameters it is easier to just give the function type a name, and then use that name everywhere it is needed. This also saves time because the function definition is consistent and avoid having to debug an improperly declared function definition; yes I have made mistakes by doing each function type by hand and learned my lesson. Once all of the functions work, I then remove the type definitions from the functions, but leave the type definition as comments so that it makes the code easier to understand.
A side benefit of using the named type definitions is that when creating test cases, the typing rules in the named function will ensure that the data used for the test is of the correct type. This also makes understanding the data for the test much easier to understand when you come back to it after many months.
Another advantage is that using function names makes the code easier to understand because when a person new to the code looks at if for the first time they can spot the consistency of the names. Also if the names are meaningful then it makes understanding the code much easier.
You have to remember that functions are also values in F#. And you can do pretty much the same stuff with them as other types. For example you can have a function that returns other functions. Or you can have a list that stores functions. In these cases it will help if you are explicit about the function signature. The function type definition will help you to constrain on the parameters and return types. Also, you might have a complicated type signature, a type definition will make it more readable. This maybe a bit contrived but you can do fun(ky) stuff like this:
type FuncX = int -> int
type FuncZ = float -> float -> float
let addxy (x:int) :FuncX = (+) x
let subxy :FuncX = (-) x
let addz (x:float) :FuncZ =
fun (x:float) -> (fun y -> x + y)
let listofFunc = [addxy 10;addxy 20; subxy 10]
If you check the type of listofFunc you will see it's FuncX list. Also the :FuncX refers to the return type of the function. But we could you use it as an input type as well:
let compFunc (x:FuncX) (z:FuncX) =
[(x 10);(z 10)]
compFunc (addxy 10) (addxy 20)

Why are there two kinds of functions in Elixir?

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.

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 :-))

F#: Why can't I use optional parameters in loose functions?

Why can't I use optional parameters in loose functions defined with "let"?
Why are they only allowed in member functions?
I suspect they are provided only for compatibility with .NET functions. They aren't something you encounter in functional languages. The problem with an optional parameter is you can't curry it. If a function f's second parameter is optional, what is
let g = f x
?
Is it a function taking one argument, or a value obtained by evaluating f on x plus the default second parameter?
It is allowed in OCaml. Therefore it should be possible to implement it in F#.
http://caml.inria.fr/pub/docs/manual-ocaml/lablexamples.html#sec43
I guess it has been omitted for simplicity in F#.

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