Getting Started

arithmetic supplies small capability traits for analytic operations and a shared checked-error vocabulary. It does not define a universal number type.

Install and Import

moon add Luna-Flow/arithmetic@0.5.0
moon add Luna-Flow/luna-generic@0.3.1

import {
  "Luna-Flow/luna-generic" @lf_alg
  "Luna-Flow/arithmetic" @lf_arith
}

Request Only Needed Capabilities

using @lf_alg { trait Add, trait Mul }
using @lf_arith { trait Sqrt }

fn hypot2[T : Add + Mul + Sqrt](x : T, y : T) -> T {
  Sqrt::sqrt(x * x + y * y)
}

Choose an unchecked trait only when the concrete backend's direct behavior is acceptable. Use a checked trait when callers must handle a rejected operation.

Handle Checked and Certified Failures

let context = @lf_arith.ArithmeticContext::decimal64()
match @lf_arith.DivChecked::div_checked(1.0, 0.0, context) {
  Ok(value) => value.to_string()
  Err(error) if error.is_certification_failure() => {
    let detail = error.certification_failure_detail().unwrap()
    detail.operation() + " was not certified"
  }
  Err(error) => error.message
}

CertificationFailureDetail is present only for ArithmeticErrorKind::CertificationFailure. It identifies the operation, proof stage, reason, target precision, working precision, and refinement count. It lets a proof-backed backend report an inconclusive evaluation without misclassifying it as a domain or format failure.

Continue Reading

• Core tutorial for contexts and diagnostics.
• Core API for public names and semantic notes.
• Architecture for effect and error boundaries.
• Verification for the repository gate and release checks.