What is the use of minizinc fix function?

Question

i see that fix documentation says:

http://www.minizinc.org/doc-lib/doc-builtins-reflect.html#Ifunction-dd-T-cl-fix-po-var-opt-dd-T-cl-x-pc

function array [$U] of $T: fix(array [$U] of var opt $T: x)
Check if the value of every element of the array x is fixedat this point in evaluation. If all are fixed, return an array of their values, otherwise abort.

I am thinking it can be used to coerce a var to a par. Here is the code.

array [1..num]   of var int: value  ;
%% generate random numbers from 0..num-1, this should fix the value of the var "value"  or so i think
constraint forall(i in index_set(value))(let {int:temp_value=discrete_distribution([1|i in index_set(value)]); } in value[i]=trace(show(temp_value)++"\n", temp_value));

%%% this i was expecting to work, as "value" elements are fixed above
array [1..num]   of int:value__  =[ trace(show(fix(value[i])), fix(value[i])) | i in index_set(value)] ;

But i get:

MiniZinc: evaluation error:
    with i = 1
  in call 'trace'
  in call 'fix'
  expression is not fixed

My questions are:

1) I think i should expect this error as minizinc is not sequential execution language?

2) Examples of fix in user guide is only where output statement is used. Is it the only place to use fix ?

3) How would i coerce a var to a par ?

By the way I am trying this var to par conversion because i am having problem with array generator expression. Here is the code

int:num__=200;
int:seed=134;
int: two_m=2097184;
%% prepare weights for generating numbers form 1..(two_m div 64), basically same weight
array [1..(two_m div 64)] of int: value_6_wt= [seed+1 | i in 1..(two_m div 64)] ;
%% generate numbers. this dose not work gives out 
%% in variable declaration for 'value6'
%% parameter value out of range
array [1..num__] of int : value6 = [ discrete_distribution(value_6_wt) | j in 1..num__];

Answer 1

In the MiniZinc language the difference between a parameter and a variable is only the fact that a parameter must have a value at compile time. Within the compiler we turn as many variables into parameters as we can. This saves the solver from having to do some work. When we know that a variable has been turned into a parameter, then we can use the fix function to convince the type system that we really can use this variable as a parameter and see its value.

The problem here however is that fix is defined to abort when the variable is not fixed to one value. If no testing is done, this requires some (magic/)knowledge about the compilation process. In your case it seems that the second array is evaluated before the optimisation stage, in which all aliasing is resolved. This is the reason why it does not work. (This is indeed one of the things that is a consequence of a declarative language)

Although fix might only be used in the output statements in the examples (where it's guaranteed to work), it is used in many locations in the MiniZinc libraries. If we for example look at the library that is used for MIP solvers, there are many constraints that can be encoded more efficiently if one of the arguments is a parameter. Therefore, you will often see that the a constraint in this library first tests its arguments with is_fixed , and then use a better encoding if this returns true.

The output statement and when is_fixed returns true will both give the guarantee that a variable is fixed and ensure that the compilation doesn't abort. There is no other way to coerce a variable to a parameter, but unless you are dealing with dependant predicate definitions, you can just trust the MiniZinc compiler to ensure that the resulting FlatZinc will contain a parameter instead of a variable.