Your first Nautilus program

Create the demo project with module prefix Demo using Reef and packages, then add Nautilus as described in Installation. Set reef.toml to pin Chelis 0.18.13 and list Nautilus 0.7.48 as a dependency. Replace src/main.ch with this program:

module Demo.Main
import Nautilus.Distributions (normal_cdf)
def black_scholes_call(spot: f32, strike: f32, rate: f32, vol: f32, t_years: f32) -> f32 = {
  ln_ratio = log(div(spot, strike))
  half_vol_sq = mul(cast(0.5, f32), mul(vol, vol))
  d1_num = add(ln_ratio, mul(add(rate, half_vol_sq), t_years))
  vol_sqrt_t = mul(vol, sqrt(t_years))
  d1 = div(d1_num, vol_sqrt_t)
  d2 = sub(d1, vol_sqrt_t)
  zero = cast(0.0, f32)
  one = cast(1.0, f32)
  nd1 = normal_cdf(d1, zero, one)
  nd2 = normal_cdf(d2, zero, one)
  neg_rt = neg(mul(rate, t_years))
  discount = exp(neg_rt)
  sub(mul(spot, nd1), mul(mul(strike, discount), nd2))
}
price = black_scholes_call(cast(100.0, f32), cast(100.0, f32), cast(0.05, f32), cast(0.2, f32), cast(1.0, f32))

The inputs are a spot and strike of 100, a 5% annual rate, 20% volatility, and one year to expiry. normal_cdf(d1, zero, one) evaluates the standard normal distribution at d1; it takes the value, mean, and standard deviation.

Check and evaluate

From the demo directory, run:

chelis fmt --inplace src/main.ch
chelis check src/main.ch
chelis eval --file src/main.ch

chelis check should report a score of 1 and an empty error list. The evaluator prints price = 10.450577 for this example. Formatting comes first because both check and eval --file enforce Chelis's source style gate.

For machine-readable output, add --json to the evaluation command. Its roots array contains the price result; the f32 value is encoded in the bits field.

To build the Reef package, run chelis reef build. To compile the program for the C target, run chelis build src/main.ch --target c --output out/. The command creates the out/main executable and retains the generated C and runtime files under out/; it does not run the calculation.

Reading the program

• The file is src/main.ch, so its module name is Demo.Main. The import names the Nautilus module and the one function this program uses.
• Unsuffixed floating literals have f32 precision. The explicit cast calls make that choice visible here; Chelis does not promote a value to f64 implicitly.
• Math uses named functions such as add, mul, and log.
• price is a top-level value, which gives chelis eval a result to print. Defining a function alone does not evaluate it.

For the pricing formula and its domain, see Black-Scholes pricing.