Circuit Programming Overview

Achronyme is a dual-mode language. The same source code can run as a general-purpose program or compile into an arithmetic circuit for zero-knowledge proofs.

What Is a Circuit?

A ZK circuit is a system of polynomial constraints over a finite field. Given public inputs (known to the verifier) and witness inputs (known only to the prover), the circuit enforces that certain relationships hold — without revealing the witness.

In Achronyme, you write circuits using the same syntax as regular programs, with a few restrictions.

Two Ways to Build Circuits

1. Standalone circuit file

public output
witness secret

assert_eq(poseidon(secret, 0), output)

Compile with the CLI:

ach circuit hash.ach --inputs "output=17159...,secret=42"

2. Inline prove {} block

let secret = field(42)
let hash = field("17159...")

let p = prove {
    witness secret
    public hash
    assert_eq(poseidon(secret, 0), hash)
}

The prove {} block runs inside the VM, captures variables from scope, compiles the body as a circuit, and generates a proof.

What Works in Circuits

Feature	Behavior
Arithmetic (+, -, *, /, ^)	Compiles to field operations and constraints
let bindings	Aliases (zero cost)
if/else	Compiles to mux — both branches evaluated
for loops (range or array)	Statically unrolled
fn calls	Inlined at each call site
assert_eq(a, b)	Enforces a == b (1 constraint)
poseidon(a, b)	Poseidon 2-to-1 hash (361 constraints)
range_check(x, bits)	Value fits in N bits
Comparisons (==, !=, <, <=, >, >=)	Field-safe gadgets
Boolean logic (&&, ||, !)	With boolean enforcement

What Doesn’t Work in Circuits

Feature	Reason
while loops	Unknown iteration count — can’t unroll
break / continue	Requires dynamic control flow
print()	Side effect, no circuit equivalent
Strings, maps	Not representable as field elements
Recursion	Functions are inlined, no stack

These are rejected at compile time with clear error messages.

Compilation Pipeline

Source → Parser → AST → IR Lowering → SSA IR → Optimize → Backend → Constraints

1. Parse — PEG grammar produces an AST
2. Lower — AST becomes flat SSA instructions (Add, Mul, Mux, PoseidonHash, …)
3. Optimize — Constant folding, dead code elimination, boolean propagation
4. Compile — R1CS or Plonkish backend generates constraints
5. Witness — Concrete values fill the constraint system
6. Export — Binary .r1cs + .wtns files (R1CS) or in-memory verification (Plonkish)

Backends

Achronyme supports two constraint system backends:

R1CS (default) — Rank-1 Constraint System. Each constraint is A * B = C where A, B, C are linear combinations of wires. Compatible with Groth16 via snarkjs.

Plonkish — Gate-based system with custom gates, lookups, and copy constraints. Uses KZG polynomial commitments. Some operations (like range_check) are more efficient with lookups.

Select the backend with --backend:

ach circuit file.ach --backend plonkish --inputs "x=42"