Types & Values

Achronyme's type system and value representations.

Achronyme is dynamically typed. All values are represented as tagged 64-bit words with a 4-bit tag and 60-bit payload.

Types

Integers

Integers are 60-bit signed values stored inline (no heap allocation). Range: -576460752303423488 to 576460752303423487.

let x = 42
let y = -7
let big = 100000000000

If an arithmetic operation overflows the i60 range, a runtime error is raised. Use 0p field literals when you need modular field arithmetic (e.g., 0p42).

Booleans

let yes = true
let no = false

In circuits, true maps to field element 1 and false maps to 0.

Strings

let greeting = "hello, world"
let empty = ""

Lists

let nums = [1, 2, 3]
let mixed = [1, "two", true]
let nested = [[1, 2], [3, 4]]

Maps

let person = {"name": "Alice", "age": 30}

Field Elements

BN254 scalar field elements for cryptographic operations. Montgomery form internally. Created using the 0p prefix, which works like 0x for hex:

let a = 0p42         // decimal field literal
let b = 0pxFF        // hex field literal
let c = 0pb1010      // binary field literal
let d = 0p21888242871839275222246405745257275088548364400416034343698204186575808495617  // large decimal

let sum = a + b
let prod = a * b
let inv = 0p1 / a    // modular inverse

Int and Field cannot be mixed in arithmetic. 0p3 + 5 is a runtime error — use 0p3 + 0p5 instead.

Field elements are essential for circuit programming — all circuit values are field elements under the hood.

BigInt (VM only)

Fixed-width unsigned integers for cryptographic operations. Two widths: 256-bit (4 limbs) and 512-bit (8 limbs). Non-modular arithmetic with overflow/underflow errors.

Literals

BigInt literals use the 0i prefix, followed by width and radix:

let a = 0i256xFF           // 256-bit hex
let b = 0i256d255          // 256-bit decimal
let c = 0i256b11111111     // 256-bit binary
let d = 0i512x1234         // 512-bit hex

Constructor functions

let a = bigint256(42)       // from integer
let b = bigint256("0xFF")   // from hex string
let c = bigint512(100)      // 512-bit from integer

Arithmetic

Standard operators work between BigInts of the same width:

let x = 0i256d10
let y = 0i256d20
let sum = x + y              // 30
let diff = y - x             // 10
let prod = x * y             // 200
let q = y / x                // 2
let r = 0i256d25 % 0i256d7   // 4
let p = 0i256d2 ^ 10         // 1024

Type safety

BigInt cannot be mixed with Int, Field, or a different BigInt width:

// All of these are runtime errors:
// bigint256(1) + 1           -- BigInt + Int
// bigint256(1) + 0p1         -- BigInt + Field
// bigint256(1) + bigint512(1) -- width mismatch

Bitwise operations

bit_and(a, b)     // bitwise AND
bit_or(a, b)      // bitwise OR
bit_xor(a, b)     // bitwise XOR
bit_not(a)        // bitwise NOT
bit_shl(a, n)     // shift left (errors if bits overflow)
bit_shr(a, n)     // shift right

let bits = to_bits(a)          // list of 0/1 (LSB-first)
let val = from_bits(bits, 256) // reconstruct from bits

typeof

typeof() returns "BigInt256" or "BigInt512" for BigInt values.

Nil

let nothing = nil

nil represents the absence of a value. Functions without a return statement return nil.

Static Namespaces

Use Type::MEMBER syntax to access type-level constants:

// Integer bounds
print(Int::MAX)      // 576460752303423487 (2^59 - 1)
print(Int::MIN)      // -576460752303423488 (-2^59)

// Field constants
let zero = Field::ZERO
let one = Field::ONE
let order = Field::ORDER   // BN254 Fr modulus as string

// BigInt constructor
let val = BigInt::from_bits(bits, 256)

See Methods & Static Namespaces for the full reference.

Variable Bindings

let x = 42          // immutable binding
mut y = 0           // mutable binding
y = y + 1           // reassignment (only for mut)

let creates an immutable binding. mut creates a mutable binding that can be reassigned.

Type Annotations

Achronyme supports optional type annotations on variable bindings and function signatures. In circuit mode, annotations enable compile-time type checking and constraint optimization. In VM mode, annotations are parsed and accepted but execution remains dynamic.

let x: Field = 0p42
let flag: Bool = true
mut counter: Field = 0p0

See Type Annotations for the full reference in circuit context.