Does anyone know the reasons why Julia chose a design of functions where the parameters given as inputs cannot be modified? This requires, if we want to use it anyway, to go through a very artificial process, by representing these data in the form of a ridiculous single element table.
Ada, which had the same kind of limitation, abandoned it in its 2012 redesign to the great satisfaction of its users. A small keyword (like out in Ada) could very well indicate that the possibility of keeping the modifications of a parameter at the output is required.
From my experience in Julia it is useful to understand the difference between a value and a binding.
Values
Each value in Julia has a concrete type and location in memory. Value can be mutable or immutable. In particular when you define your own composite type you can decide if objects of this type should be mutable (mutable struct) or immutable (struct).
Of course Julia has in-built types and some of them are mutable (e.g. arrays) and other are immutable (e.g. numbers, strings). Of course there are design trade-offs between them. From my perspective two major benefits of immutable values are:
if a compiler works with immutable values it can perform many optimizations to speed up code;
a user is can be sure that passing an immutable to a function will not change it and such encapsulation can simplify code analysis.
However, in particular, if you want to wrap an immutable value in a mutable wrapper a standard way to do it is to use Ref like this:
julia> x = Ref(1)
Base.RefValue{Int64}(1)
julia> x[]
1
julia> x[] = 10
10
julia> x
Base.RefValue{Int64}(10)
julia> x[]
10
You can pass such values to a function and modify them inside. Of course Ref introduces a different type so method implementation has to be a bit different.
Variables
A variable is a name bound to a value. In general, except for some special cases like:
rebinding a variable from module A in module B;
redefining some constants, e.g. trying to reassign a function name with a non-function value;
rebinding a variable that has a specified type of allowed values with a value that cannot be converted to this type;
you can rebind a variable to point to any value you wish. Rebinding is performed most of the time using = or some special constructs (like in for, let or catch statements).
Now - getting to the point - function is passed a value not a binding. You can modify a binding of a function parameter (in other words: you can rebind a value that a parameter is pointing to), but this parameter is a fresh variable whose scope lies inside a function.
If, for instance, we wanted a call like:
x = 10
f(x)
change a binding of variable x it is impossible because f does not even know of existence of x. It only gets passed its value. In particular - as I have noted above - adding such a functionality would break the rule that module A cannot rebind variables form module B, as f might be defined in a module different than where x is defined.
What to do
Actually it is easy enough to work without this feature from my experience:
What I typically do is simply return a value from a function that I assign to a variable. In Julia it is very easy because of tuple unpacking syntax like e.g. x,y,z = f(x,y,z), where f can be defined e.g. as f(x,y,z) = 2x,3y,4z;
You can use macros which get expanded before code execution and thus can have an effect modifying a binding of a variable, e.g. macro plusone(x) return esc(:($x = $x+1)) end and now writing y=100; #plusone(y) will change the binding of y;
Finally you can use Ref as discussed above (or any other mutable wrapper - as you have noted in your question).
"Does anyone know the reasons why Julia chose a design of functions where the parameters given as inputs cannot be modified?" asked by Schemer
Your question is wrong because you assume the wrong things.
Parameters are variables
When you pass things to a function, often those things are values and not variables.
for example:
function double(x::Int64)
2 * x
end
Now what happens when you call it using
double(4)
What is the point of the function modifying it's parameter x , it's pointless. Furthermore the function has no idea how it is called.
Furthermore, Julia is built for speed.
A function that modifies its parameter will be hard to optimise because it causes side effects. A side effect is when a procedure/function changes objects/things outside of it's scope.
If a function does not modifies a variable that is part of its calling parameter then you can be safe knowing.
the variable will not have its value changed
the result of the function can be optimised to a constant
not calling the function will not break the program's behaviour
Those above three factors are what makes FUNCTIONAL language fast and NON FUNCTIONAL language slow.
Furthermore when you move into Parallel programming or Multi Threaded programming, you absolutely DO NOT WANT a variable having it's value changed without you (The programmer) knowing about it.
"How would you implement with your proposed macro, the function F(x) which returns a boolean value and modifies c by c:= c + 1. F can be used in the following piece of Ada code : c:= 0; While F(c) Loop ... End Loop;" asked by Schemer
I would write
function F(x)
boolean_result = perform_some_logic()
return (boolean_result,x+1)
end
flag = true
c = 0
(flag,c) = F(c)
while flag
do_stuff()
(flag,c) = F(c)
end
"Unfortunately no, because, and I should have said that, c has to take again the value 0 when F return the value False (c increases as long the Loop lives and return to 0 when it dies). " said Schemer
Then I would write
function F(x)
boolean_result = perform_some_logic()
if boolean_result == true
return (true,x+1)
else
return (false,0)
end
end
flag = true
c = 0
(flag,c) = F(c)
while flag
do_stuff()
(flag,c) = F(c)
end
Related
In Pascal, I understand that one could create a function returning a pointer which can be dereferenced and then assign a value to that, such as in the following (obnoxiously useless) example:
type ptr = ^integer;
var d: integer;
function f(x: integer): ptr;
begin
f := #x;
end;
begin
f(d)^ := 4;
end.
And now d is 4.
(The actual usage is to access part of a quite complicated array of records data structure. I know that a class would be better than an array of nested records, but it isn't my code (it's TeX: The Program) and was written before Pascal implementations supported object-orientation. The code was written using essentially a language built on top of Pascal that added macros which expand before the compiler sees them. Thus you could define some macro m that takes an argument x and expands into thearray[x + 1].f1.f2 instead of writing that every time; the usage would be m(x) := somevalue. I want to replicate this functionality with a function instead of a macro.)
However, is it possible to achieve this functionality without the ^ operator? Can a function f be written such that f(x) := y (no caret) assigns the value y to x? I know that this is stupid and the answer is probably no, but I just (a) don't really like the look of it and (b) am trying to mimic exactly the form of the macro I mentioned above.
References are not first class objects in Pascal, unlike languages such as C++ or D. So the simple answer is that you cannot directly achieve what you want.
Using a pointer as you illustrated is one way to achieve the same effect although in real code you'd need to return the address of an object whose lifetime extends beyond that of the function. In your code that is not the case because the argument x is only valid until the function returns.
You could use an enhanced record with operator overloading to encapsulate the pointer, and so encapsulate the pointer dereferencing code. That may be a good option, but it very much depends on your overall problem, of which we do not have sight.
I am puzzled by the following results of typeof in the Julia 1.0.0 REPL:
# This makes sense.
julia> typeof(10)
Int64
# This surprised me.
julia> typeof(function)
ERROR: syntax: unexpected ")"
# No answer at all for return example and no error either.
julia> typeof(return)
# In the next two examples the REPL returns the input code.
julia> typeof(in)
typeof(in)
julia> typeof(typeof)
typeof(typeof)
# The "for" word returns an error like the "function" word.
julia> typeof(for)
ERROR: syntax: unexpected ")"
The Julia 1.0.0 documentation says for typeof
"Get the concrete type of x."
The typeof(function) example is the one that really surprised me. I expected a function to be a first-class object in Julia and have a type. I guess I need to understand types in Julia.
Any suggestions?
Edit
Per some comment questions below, here is an example based on a small function:
julia> function test() return "test"; end
test (generic function with 1 method)
julia> test()
"test"
julia> typeof(test)
typeof(test)
Based on this example, I would have expected typeof(test) to return generic function, not typeof(test).
To be clear, I am not a hardcore user of the Julia internals. What follows is an answer designed to be (hopefully) an intuitive explanation of what functions are in Julia for the non-hardcore user. I do think this (very good) question could also benefit from a more technical answer provided by one of the more core developers of the language. Also, this answer is longer than I'd like, but I've used multiple examples to try and make things as intuitive as possible.
As has been pointed out in the comments, function itself is a reserved keyword, and is not an actual function istself per se, and so is orthogonal to the actual question. This answer is intended to address your edit to the question.
Since Julia v0.6+, Function is an abstract supertype, much in the same way that Number is an abstract supertype. All functions, e.g. mean, user-defined functions, and anonymous functions, are subtypes of Function, in the same way that Float64 and Int are subtypes of Number.
This structure is deliberate and has several advantages.
Firstly, for reasons I don't fully understand, structuring functions in this way was the key to allowing anonymous functions in Julia to run just as fast as in-built functions from Base. See here and here as starting points if you want to learn more about this.
Secondly, because each function is its own subtype, you can now dispatch on specific functions. For example:
f1(f::T, x) where {T<:typeof(mean)} = f(x)
and:
f1(f::T, x) where {T<:typeof(sum)} = f(x) + 1
are different dispatch methods for the function f1
So, given all this, why does, e.g. typeof(sum) return typeof(sum), especially given that typeof(Float64) returns DataType? The issue here is that, roughly speaking, from a syntactical perspective, sum needs to serves two purposes simultaneously. It needs to be both a value, like e.g. 1.0, albeit one that is used to call the sum function on some input. But, it is also needs to be a type name, like Float64.
Obviously, it can't do both at the same time. So sum on its own behaves like a value. You can write f = sum ; f(randn(5)) to see how it behaves like a value. But we also need some way of representing the type of sum that will work not just for sum, but for any user-defined function, and any anonymous function. The developers decided to go with the (arguably) simplest option and have the type of sum print literally as typeof(sum), hence the behaviour you observe. Similarly if I write f1(x) = x ; typeof(f1), that will also return typeof(f1).
Anonymous functions are a bit more tricky, since they are not named as such. What should we do for typeof(x -> x^2)? What actually happens is that when you build an anonymous function, it is stored as a temporary global variable in the module Main, and given a number that serves as its type for lookup purposes. So if you write f = (x -> x^2), you'll get something back like #3 (generic function with 1 method), and typeof(f) will return something like getfield(Main, Symbol("##3#4")), where you can see that Symbol("##3#4") is the temporary type of this anonymous function stored in Main. (a side effect of this is that if you write code that keeps arbitrarily generating the same anonymous function over and over you will eventually overflow memory, since they are all actually being stored as separate global variables of their own type - however, this does not prevent you from doing something like this for n = 1:largenumber ; findall(y -> y > 1.0, x) ; end inside a function, since in this case the anonymous function is only compiled once at compile-time).
Relating all of this back to the Function supertype, you'll note that typeof(sum) <: Function returns true, showing that the type of sum, aka typeof(sum) is indeed a subtype of Function. And note also that typeof(typeof(sum)) returns DataType, in much the same way that typeof(typeof(1.0)) returns DataType, which shows how sum actually behaves like a value.
Now, given everything I've said, all the examples in your question now make sense. typeof(function) and typeof(for) return errors as they should, since function and for are reserved syntax. typeof(typeof) and typeof(in) correctly return (respectively) typeof(typeof), and typeof(in), since typeof and in are both functions. Note of course that typeof(typeof(typeof)) returns DataType.
When I create some array A and assign it to B
A = [1:10]
B = A
I can modify A and the change reflects in B
A[1] = 42
# B[1] is now 42
But if I do that with scalar variables, the change doesn't propagate:
a = 1
b = a
a = 2
# b remains being 1
I can even mix the things up and transform the vector to a scalar, and the change doesn't propagate:
A = [1:10]
B = A
A = 0
# B remains being 1,2,...,10
What exactly does the = operator does? When I want to copy variables and modify the old ones preserving the integrity of the new variables, when should I use b = copy(a) over just b=a?
The confusion stems from this: assignment and mutation are not the same thing.
Assignment. Assignment looks like x = ... – what's left of the = is an identifier, i.e. a variable name. Assignment changes which object the variable x refers to (this is called a variable binding). It does not mutate any objects at all.
Mutation. There are two typical ways to mutate something in Julia:
x.f = ... – what's left of the = is a field access expression;
x[i] = ... – what's left of the = is an indexing expression. Currently, field mutation is fundamental – that syntax can only mean that you are mutating a structure by changing its field. This may change. Array mutation syntax is not fundamental – x[i] = y means setindex!(x, y, i) and you can either add methods to setindex! or locally change which generic function setindex!. Actual array assignment is a builtin – a function implemented in C (and for which we know how to generate corresponding LLVM code).
Mutation changes the values of objects; it doesn't change any variable bindings. After doing either of the above, the variable x still refers to the same object it did before; that object may have different contents, however. In particular, if that object is accessible from some other scope – say the function that called one doing the mutation – then the changed value will be visible there. But no bindings have changed – all bindings in all scopes still refer to the same objects.
You'll note that in this explanation I never once talked about mutability or immutability. That's because it has nothing to do with any of this – mutable and immutable objects have exactly the same semantics when it comes to assignment, argument passing, etc. The only difference is that if you try to do x.f = ... when x is immutable, you will get an error.
This behavior is similar to Java. A and B are variables that can hold either a "plain" data type, such as an integer, float etc, or a references (aka pointers) to a more complex data structure. In contrast to Java, Julia handles many non-abstract types as "plain" data.
You can test with isbits(A) whether your variable A holds a bit value, or contains a reference to another data object. In the first case B=A will copy every bit from A to a new memory allocation for B, otherwise, only the reference to the object will be copied.
Also play around with pointer_from_objref(A).
My program has the following global variable:
let a = (0.0,0.0);;
And the following, where eval e1 returns a string_of_float and somefunc e2 returns a tuple.
let rec output_expr = function
Binop(e1, op, e2) ->
let onDist = float_of_string(eval e1) and onDir = somefunc e2 in
let newA = onDir in (
fprintf oc "\n\t%s" ("blah");
fprintf oc "\n\t%s" ("blah");
fprintf oc "\n\t%s" ("blah");
let a = newA
)
Now, the code above gives me the following error:
Error: This expression has type bool
but an expression was expected of type unit
Command exited with code 2.
I want let a = newA to change the value of the global variable a. How can I do that?
To do it you need to make the value a reference,
let a = ref (0.0, 0.0)
then later that state can change by,
a := (1.0, 2.0);
In a functional world you would not want to have this global state. Sometimes it is very helpful, but in this particular case that is doubtful. You should pass the value a into your function and return a new value (a') that can be used subsequently; note that the value never changes, but new values take the place and are used in further computation.
In your particular case, I think you need to ask yourself why a function named output_expr modifies some global state, or returns anything but unit. But maybe this is a toy example for our consumption, so I will leave it at that.
You cannot assign to a variable (local or global is the same) in OCaml. There's simply no syntax in the language for it. In other words, variables in OCaml are what other languages call "constants" -- they get a value once in initialization, and that's it.
However, you can use a mutable data structure, which offers ways to modify its contents. Data structures are reference types, you can hold a reference to the data structure in a variable, and modify the contents, without needing to assign to the variable.
nlucaroni mentioned such a data structure, ref, which is a simple mutable cell holding a value of the desired type. There are other mutable data structures, like arrays, strings, and any record with mutable fields. Each has its own way of modifying the contents.
However, mutable state can mostly be avoided in functional programming, and if you are relying on mutable state, it may be an indication that you are not doing it the functional way.
In OCaml, values are immutable. You can't change the content of a value and should reorganize your code so that you don't need to.
Here your function output_expr should return the newA and this value should be used instead of a after that.
Actually you can have mutable variables using references but you should only use them if you know what you do and think they are better suited for a particular use case, never because you don't understand immutability.
I've been watching this MSDN video with Brian Beckman and I'd like to better understand something he says:
Every imperitive programmer goes through this phase of learning that
functions can be replaced with table lookups
Now, I'm a C# programmer who never went to university, so perhaps somewhere along the line I missed out on something everyone else learned to understand.
What does Brian mean by:
functions can be replaced with table lookups
Are there practical examples of this being done and does it apply to all functions? He gives the example of the sin function, which I can make sense of, but how do I make sense of this in more general terms?
Brian just showed that the functions are data too. Functions in general are just a mapping of one set to another: y = f(x) is mapping of set {x} to set {y}: f:X->Y. The tables are mappings as well: [x1, x2, ..., xn] -> [y1, y2, ..., yn].
If function operates on finite set (this is the case in programming) then it's can be replaced with a table which represents that mapping. As Brian mentioned, every imperative programmer goes through this phase of understanding that the functions can be replaced with the table lookups just for performance reason.
But it doesn't mean that all functions easily can or should be replaced with the tables. It only means that you theoretically can do that for every function. So the conclusion would be that the functions are data because tables are (in the context of programming of course).
There is a lovely trick in Mathematica that creates a table as a side-effect of evaluating function-calls-as-rewrite-rules. Consider the classic slow-fibonacci
fib[1] = 1
fib[2] = 1
fib[n_] := fib[n-1] + fib[n-2]
The first two lines create table entries for the inputs 1 and 2. This is exactly the same as saying
fibTable = {};
fibTable[1] = 1;
fibTable[2] = 1;
in JavaScript. The third line of Mathematica says "please install a rewrite rule that will replace any occurrence of fib[n_], after substituting the pattern variable n_ with the actual argument of the occurrence, with fib[n-1] + fib[n-2]." The rewriter will iterate this procedure, and eventually produce the value of fib[n] after an exponential number of rewrites. This is just like the recursive function-call form that we get in JavaScript with
function fib(n) {
var result = fibTable[n] || ( fib(n-1) + fib(n-2) );
return result;
}
Notice it checks the table first for the two values we have explicitly stored before making the recursive calls. The Mathematica evaluator does this check automatically, because the order of presentation of the rules is important -- Mathematica checks the more specific rules first and the more general rules later. That's why Mathematica has two assignment forms, = and :=: the former is for specific rules whose right-hand sides can be evaluated at the time the rule is defined; the latter is for general rules whose right-hand sides must be evaluated when the rule is applied.
Now, in Mathematica, if we say
fib[4]
it gets rewritten to
fib[3] + fib[2]
then to
fib[2] + fib[1] + 1
then to
1 + 1 + 1
and finally to 3, which does not change on the next rewrite. You can imagine that if we say fib[35], we will generate enormous expressions, fill up memory, and melt the CPU. But the trick is to replace the final rewrite rule with the following:
fib[n_] := fib[n] = fib[n-1] + fib[n-2]
This says "please replace every occurrence of fib[n_] with an expression that will install a new specific rule for the value of fib[n] and also produce the value." This one runs much faster because it expands the rule-base -- the table of values! -- at run time.
We can do likewise in JavaScript
function fib(n) {
var result = fibTable[n] || ( fib(n-1) + fib(n-2) );
fibTable[n] = result;
return result;
}
This runs MUCH faster than the prior definition of fib.
This is called "automemoization" [sic -- not "memorization" but "memoization" as in creating a memo for yourself].
Of course, in the real world, you must manage the sizes of the tables that get created. To inspect the tables in Mathematica, do
DownValues[fib]
To inspect them in JavaScript, do just
fibTable
in a REPL such as that supported by Node.JS.
In the context of functional programming, there is the concept of referential transparency. A function that is referentially transparent can be replaced with its value for any given argument (or set of arguments), without changing the behaviour of the program.
Referential Transparency
For example, consider a function F that takes 1 argument, n. F is referentially transparent, so F(n) can be replaced with the value of F evaluated at n. It makes no difference to the program.
In C#, this would look like:
public class Square
{
public static int apply(int n)
{
return n * n;
}
public static void Main()
{
//Should print 4
Console.WriteLine(Square.apply(2));
}
}
(I'm not very familiar with C#, coming from a Java background, so you'll have to forgive me if this example isn't quite syntactically correct).
It's obvious here that the function apply cannot have any other value than 4 when called with an argument of 2, since it's just returning the square of its argument. The value of the function only depends on its argument, n; in other words, referential transparency.
I ask you, then, what the difference is between Console.WriteLine(Square.apply(2)) and Console.WriteLine(4). The answer is, there's no difference at all, for all intents are purposes. We could go through the entire program, replacing all instances of Square.apply(n) with the value returned by Square.apply(n), and the results would be the exact same.
So what did Brian Beckman mean with his statement about replacing function calls with a table lookup? He was referring to this property of referentially transparent functions. If Square.apply(2) can be replaced with 4 with no impact on program behaviour, then why not just cache the values when the first call is made, and put it in a table indexed by the arguments to the function. A lookup table for values of Square.apply(n) would look somewhat like this:
n: 0 1 2 3 4 5 ...
Square.apply(n): 0 1 4 9 16 25 ...
And for any call to Square.apply(n), instead of calling the function, we can simply find the cached value for n in the table, and replace the function call with this value. It's fairly obvious that this will most likely bring about a large speed increase in the program.