type_eval

An R&D project that explores adding evaluation as a first-class-citizen to the typenum crate.

Typenum treats constant values and evaluation the way it ought to be treated:

• Unconcerned with machine representation (u64, usize, i32, etc)
• Specifications in the type-system (fn foo<F: IsGreater<U8>())
• Compile-time and Execution-time code is explicitly separated

The shortfall of typenum, is that evaluation is not provided. The operation ((x + 4) * Y) / Z must be expressed like so:

fn thing<X, Y>()
where
    X: Add<U4>,
    op!(X + U4): Mul<Y>,
    op!((X + U4) * Y): Div<Z>,
    op!(((X + U4) * Y) / Z): Unsigned,
{
    type ResHelper = op!(((X + U4) * Y) / Z);
    println!("the value evaluated to {}", ResHelper::USIZE)
    // Use `ResHelper` as the final type-system evaluation
}

fn main() {
    thing::<X, U4>();
}

This process of saying "the type-values passed in must be able to perform this arithmetic" is now done internally through the *Expr traits (Num/Bool/Ord/other expression traits):

fn thing<E: NumExpr>() {
    // TODO: extract an execution-time value from the type
    println!("the value evaluated to {}", E::Ret)
}

fn main() {
    // todo: actually impl the op! macro:
    // do_thing::<op!(((X + 4) * Y) / Z)>();
    // ...which would expand to:
    do_thing::<Div<Mul<Add<X, U4>, Y>, Z>>();
}

Limitations

Currently negative numbers are not yet implemented.

The strategy for implementing division requires type-resolution capabilities made available in nightly-2024-10-17. This should be improved in the near future.

The following operations are implemented: if, +, -, *, /, <<, >>, <, >, <=, >=, ==, cmp

The error output is in a messy binary form. The plan is to make this more readable.

Future work

In very approximate order of priority:

• Runtime number expression
• Robust property/fuzz testing
• negative numbers
• Move from binary to decimal representation
• More readable errors
• implementation of an op macro (replace IF<LT<X, Y>, Add<Div<X, U2>, Y>, Z> with op!(if X < Y {(X + 2)/ Y} else {Z}))
• Explore use of struct U238... instead of type U238 = ...
• Usable in place of a usize type in declaring array lengths.
• match expression impl
• closure expression impl
• any-type expression (i.e. Bool/Num/Ord expressions all impl the generic expression)
• Upstreaming into a nursary/nightly feature.