Crate typed_sf

Expand description

Type-level implementation of SF. Prooving that type-system turing-complete. Higtly inspired by this article.

Features

typed-sf supports “no_std” feature with limitations. Runtime representation of List’s and State’s unavaliable (they are using Vec to represent theyself).

Full list of unsupported features:

List::val() (That includes Nil and Cons).
RuntimeState.
StateTrait::val() (That includes State and DefaultState).

Also where is “require_docs” feature which forbids undocumented pub items. If You want to contrubute, feel free to turn off this default feature.

How it works

First, where’s some traits what i’m calling type-level enums (Bit, List). Have a look at it:

enum Bit {
    True,
    False
}

impl Bit {
    fn neg(self) -> Bit {
        match self {
            Bit::True => Bit::False,
            Bit::False => Bit::True
        }
    }
}

assert_eq!(Bit::True, Bit::False.neg());
assert_eq!(Bit::False, Bit::True.neg());

trait Bit {
    type Neg: Bit;
    fn real() -> bool;
}
struct True;
struct False;

impl Bit for True {
    type Neg = False;
    fn real() -> bool { true }
}

impl Bit for False {
    type Neg = True;
    fn real() -> bool { false }
}

assert_eq!(True::real(), <False as Bit>::Neg::real());
assert_eq!(False::real(), <True as Bit>::Neg::real());

Of course, what’s more bolierplate, but also instead of matching in runtime, compiler solves type-equasions in compile-time for us.

To type-encode functions i’m using something like this:

// A and B are arguments to 'function'.
trait Call<A, B> { type Return; }

struct Sum;
struct Diff;

impl<A, B> Call<A, B> for Sum
where
    A: Add<B>
{
    type Return = <A as Add<B>>::Output;
}

impl<A, B> Call<A, B> for Diff
where
    A: Sub<B>
{
    type Return = <A as Sub<B>>::Output;
}

type Apply<A, Fn, B> = <Fn as Call<A, B>>::Return;

What we can use later as:

struct X;
struct Y;
struct XaddY;
struct XsubY;

impl Add<Y> for X {
    type Output = XaddY;
}
impl Sub<Y> for X {
    type Output = XsubY;
}

/* Add `::val() -> Self` function to all types... */

assert_eq!(
    <Apply<X, Sum, Y>>::val(),
    XaddY::val()
);

assert_eq!(
    <Apply<X, Diff, Y>>::val(),
    XsubY::val()
);

That’s basically how Runner<Left, Value, Right> works. But commands such as Left takes an generic argument, so it runs next command on modified state which does same and so on…

Examples

Basic usage

type SetTrue<Next = EOF> = Cycle<Flip, Flip<Next>>;
// [*<<[*]*>>>] // Move any-sized chunk of True's 2 cells left
type prog = Cycle<Flip<Left<Left<SetTrue<Right<Right<Right>>>>>>>;
type result = Run<
    prog,
    State<Nil, True, Cons<True, Nil>>
>;

assert_eq!(
    <result as StateTrait>::val(),
    (vec![true, true, false, false], false, Vec::new())
); //                 ^^^^^^^^^^^^
   // Some waste, honestly don't why it is here...