numerical-program.md

Your first numerical program

This tutorial uses the alpha.2 numerical implementation. Build the current source with cargo build --locked --offline, then verify cargo run -- --version. An older alpha.1 executable accepts floats but does not implement vectors. For current downloads, use the latest prerelease, which includes these kernels and the later module system.

Construct data and read an element

bind samples = [1.0, 2.0, 3.0];
print(len(samples), samples[0]);
print(sum(samples), mean(samples));

Exact stdout is 3 1.0 then 6.0 2.0, each followed by LF. Elements must be floats: use 1.0 rather than 1. There is no implicit integer conversion. samples[0] is the first element; index 3 is outside this vector.

Replace a value without changing its copies

var weights = fill(0.5, 3);
bind snapshot = weights;
weights = scale(weights, 2.0);
print(snapshot);
print(weights);

This prints [0.5, 0.5, 0.5] and [1.0, 1.0, 1.0]. Fill takes a float value first, then an integer count. A mutable binding permits replacing the whole vector. Elements remain immutable, and copies/pending prints keep their original values. Use add/scale/clamp to create a result rather than assigning an element.

Put numerical work in a typed function

pure funcra squared_error(predicted: vector, expected: vector) -> float
    needs len(predicted) > 0;
    needs len(predicted) == len(expected);
{
    return mse(predicted, expected);
}

bind inputs = [1.0, 2.0, 3.0];
bind targets = [2.0, 4.0, 6.0];
bind predictions = scale(inputs, 2.0);
print(dot(inputs, inputs));
print(squared_error(expected: targets, predicted: predictions));

Exact stdout is 14.0 then 0.0. Named arguments work for user functions; native kernels require positional arguments. The contracts make this function's nonempty/equal-length requirements explicit. A failing contract or kernel writes no pending program output to either stream.

Check probabilities with a tolerance

bind probabilities = softmax([1000.0, 1001.0, 1002.0]);
bind total = sum(probabilities);
print(total > 0.999999999999 and total < 1.000000000001);
print(probabilities[0] < probabilities[1] and probabilities[1] < probabilities[2]);

Both lines print true. Softmax shifts by the maximum to avoid an overflowing exponential. Nontrivial exponential results can vary slightly between platforms, so use numerical tolerances rather than asserting their exact printed digits.

Run a complete calculation with limits

Coefficient fitting combines vectors, an explicit squared-error gradient, 40 iterations and a typed loss function. Both fixture lines are true. Its derivative is written in the program.

cargo run -- run examples/coefficient_fit.srp
cargo run -- check --max-steps 200000 --max-capture-bytes 1048576 examples/coefficient_fit.srp

Check executes the selected calculations and enforces the same quotas while remaining silent. Work limits also bound cumulative vector payload allocation; they are not a total process-memory cap. See budgets, the vector reference and numerical errors.