Declarations

Every circuit declares its inputs in the circuit signature. Each parameter specifies a visibility — Public (visible to the verifier) or Witness (known only to the prover).

Basic Syntax

A circuit declaration names the circuit and lists its parameters with their visibility:

circuit multiply(output: Public, a: Witness, b: Witness) {
    assert_eq(a * b, output)
}

Public inputs become part of the proof’s public statement — anyone verifying the proof can see their values. Witness inputs remain private to the prover.

Array Parameters

Declare a fixed-size array of inputs with bracket syntax after the type:

circuit merkle_verify(root: Public, path: Witness Field[3], indices: Witness Bool[3]) {
    // path and indices each have 3 elements
    // access with standard indexing: path[0], path[1], path[2]
}

Array parameters create indexed variables that you access with standard indexing. They work for both public and witness inputs:

circuit commitment_check(commitments: Public Field[4], secrets: Witness Field[4]) {
    for i in 0..4 {
        assert_eq(poseidon(secrets[i], 0), commitments[i])
    }
}

Type Annotations

Parameters can include optional type annotations (Field or Bool) between the visibility and the parameter name (or array brackets):

circuit typed_example(root: Public Field, flag: Witness Bool) {
    if flag {
        assert_eq(root, poseidon(root, 0))
    }
}

For array parameters, the type goes between the visibility and the brackets:

circuit merkle_path(root: Public Field, path: Witness Field[3], indices: Witness Bool[3]) {
    // indices are boolean-typed, saving 1 constraint each
}

Annotating a witness as Bool saves 1 constraint by skipping boolean enforcement. See Type Annotations for full details.

Using Declared Inputs

Inside the circuit body, parameters are ordinary variables. Use them in expressions, pass them to builtins, and index into arrays:

circuit product_check(output: Public, a: Witness, b: Witness) {
    let product = a * b
    assert_eq(product, output)

    let sum = a + b
    assert_eq(sum, a + b)
}

Array elements are accessed by index:

circuit sum_check(expected_sum: Public, vals: Witness Field[3]) {
    let acc = vals[0]
    let acc = acc + vals[1]
    let acc = acc + vals[2]
    assert_eq(acc, expected_sum)
}

CLI Usage

Pass concrete values for circuit inputs with the --inputs flag:

ach circuit program.ach --inputs "a=3,b=5,output=15"

Array inputs are passed with indexed names:

ach circuit merkle.ach --inputs "root=123,leaf=42,path_0=99,path_1=77,indices_0=0,indices_1=1"

Errors

Error	Cause
DuplicateInput	Same name declared twice in the parameter list
UndeclaredVariable	Using a variable inside the circuit body that is not a parameter
AnnotationMismatch	Declared type doesn’t match the inferred type