Variables
This section describes the syntax for declaring local variables and built-in variables.
Local variables¶
In AirScript, variables can be declared in boundary_constraints and integrity_constraints sections and can contain any expression that would be valid within that source section. Variables can be of type scalar, vector or matrix. In the example below, x is a variable of type scalar, y is a variable of type vector and z is a variable of type matrix.
def VariablesExample
const A = 1
const B = 2
trace_columns:
main: [a, b, c, d]
aux: [e, f]
public_inputs:
stack_inputs: [16]
random_values:
rand: [16]
boundary_constraints:
let x = stack_inputs[0] + stack_inputs[1]
let y = [$rand[0], $rand[1]]
enf e.first = x + y[0] + y[1]
integrity_constraints:
let z = [
[a + b, c + d],
[A * a, B * b]
]
enf a' = z[0][0] + z[0][1] + z[1][0] + z[1][1]
Syntax restrictions¶
Currently, it is not possible to:
-
Create matrices containing both arrays and references to arrays.
Example:
2. Create variables with list comprehension for which the source array is a inlined vector, a matrix row, or a range in matrix row.... boundary_constraints: let a = [[1,2], [3,4]] # <-- this is allowed let b = [1, 2] let c = [a[1], b] # <-- this is allowed let d = [b, [3, 4]] # <-- this is not allowed, because `d` consists of array `[3, 4]` and reference to array `b` enf ... ...Example:
... integrity_constraints: let a = [[1, 2], [3, 4]] let b = [5, 6] let c = 7 let d = [e for e in [8, 9, 10]] # <-- source array is an inlined vector let f = [g for g in a[1]] # <-- source is a matrix row let h = [i for i in a[0][0..2]] # <-- source is a range in matrix row enf ... ...
Built-in variables¶
Built-in variables are identified by the starting character $. There are two built-in variables:
$main¶
$main is used to access columns in the main execution trace.
These columns may be accessed by using the indexing operator on $main. For example, $main[i] provides the (i+1)th column in the main execution trace.
Columns using the $main built-in may only be accessed within source sections for integrity constraints, i.e. the integrity_constraints section.
$aux¶
$aux is used to access columns in the auxiliary execution trace.
These columns may be accessed by using the indexing operator on $aux. For example, $aux[i] provides the (i+1)th column in the auxiliary execution trace.
Columns using the $aux built-in may only be accessed within source sections for integrity constraints, i.e. the integrity_constraints section.