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Unknowns

As expressions accepted during constraint generation can at most be quadratic only, certain checks and constraints are imposed on the use of unknown values at compile.

In circom, constant values and template parameters are always considered known, while signals are always considered unknown.

Expressions depending only on knowns are considered knowns, while those depending on unknowns are considered unknowns.

pragma circom 2.0.0;

template A(n1, n2){ // known
   signal input in1; // unknown
   signal input in2; // unknown
   var x = 0; // known
   var y = n1; // known
   var z = in1; // unknown
}

component main = A(1, 2);

In the code above, the template parameters n1, n2 and the constant value 0 are considered known. Consequently, the variables x and y are also considered known.

Meanwhile, the signals in1, in2 are considered unknown. Consequently, the variable z is also considered unknown.

Array

A constraint with an array access must have a known accessing position.

pragma circom 2.0.0;

template A(n){
   signal input in;
   signal output out;
   var array[n];

   out <== array[in];
   // Error: Non-quadratic constraint was detected statically, using unknown index will cause the constraint to be non-quadratic
}

component main = A(10);

In the code above, an array is defined with a known size of value n (as template parameters are always considered known), while a constraint is set to be dependent on the array element at an unknown position in (as signals are always considered unknown).

An array must also be defined with a known size.

pragma circom 2.0.0;

template A(){
   signal input in;
   var array[in];
   // Error: The length of every array must known during the constraint generation phase
}

component main = A();

In the code above, an array is defined with an unknown size of value in (as signals are always considered unknown).

Control Flow

A constraint generated in a control flow must have a known condition.

Take an if-then statement as an example:

pragma circom 2.0.0;

template A(){
   signal input in;
   signal output out;

   if (in < 0){
   // Error: There are constraints depending on the value of the condition and it can be unknown during the constraint generation phase
       out <== 0;
   }
}

component main = A();

In the code above, a constraint is defined in an if-then statement with a comparitive condition involving an unknown value in (as signals are always considered unknown).

Similarly, using a for-loop as an example:

pragma circom 2.0.0;

template A(){
   signal input in;
   signal output out;

   for (var i = 0; i < in; i++){
   // Error: There are constraints depending on the value of the condition and it can be unknown during the constraint generation phase
       out <== i;
   }
}

component main = A();

In the code above, a constraint is defined in a for-loop with a counting condition to an unknown value in (as signals are always considered unknown).

For additional details, see Control Flow.