Demonstrate searching a type-level list in rust

listsearch.rs

#![allow(dead_code)]
struct True;
struct False;
impl IsEqual<False> for True {type Out=False;}
impl IsEqual<False> for False {type Out=True;}
impl IsEqual<True> for True {type Out=True;}
impl IsEqual<True> for False {type Out=False;}

trait Nat {fn inst()->usize;}
struct Zero;
impl Nat for Zero {fn inst()->usize{0}}
struct Succ<N>(N);
impl<N:Nat> Nat for Succ<N> {fn inst()->usize{1+N::inst()}}
trait Greater<N> {}
impl<N> Greater<Zero> for Succ<N> {}
impl<N1,N2> Greater<Succ<N2>> for Succ<N1> where
    N1: Greater<N2>,
{}
trait IsEqual<N> {type Out;}
impl IsEqual<Zero> for Zero {type Out=True;}
impl<N> IsEqual<Zero> for Succ<N> {type Out=False;}
impl<N> IsEqual<Succ<N>> for Zero {type Out=False;}
impl<B,N1,N2> IsEqual<Succ<N2>> for Succ<N1> where
    N1: IsEqual<N2,Out=B>,
{type Out=B;}


trait List {}

struct Nil;
impl List for Nil {}
struct Cons<E,L:List>(E,L);
impl<E,L:List> List for Cons<E,L> {}

trait Contains<E,N> {}

impl<E,L:List> Contains<E,Zero> for Cons<E,L> {}
impl<E,F,N,L:List> Contains<E,Succ<N>> for Cons<F,L> where L:Contains<E,N> {}

trait Closest<E> {type D;}
trait CBranch<B,E> {type D;}

impl<D,R,E,F,L:List> Closest<E> for Cons<F,L> where
    E:IsEqual<F,Out=R>,
    Self:CBranch<R,E,D=D>,
{type D=D;}
impl<E,F,L:List> CBranch<True,E> for Cons<F,L> {type D=Zero;}
impl<E,F,N,L:List> CBranch<False,E> for Cons<F,L> where
    L:Closest<E,D=N>,
{type D=Succ<N>;}

fn main() {
    fn closest<N:Nat,L:Closest<False,D=N>>(_:L) -> usize {N::inst()}

    //let a = Nil;println!("{:?}",closest(a));
    let a = Cons(False,Nil);println!("{:?}",closest(a));
    //let a = Cons(True,Nil);println!("{:?}",closest(a));
    //let a = Cons(True,Cons(True,Nil));println!("{:?}",closest(a));
    let a = Cons(True,Cons(False,Nil));println!("{:?}",closest(a));
    let a = Cons(False,Cons(True,Nil));println!("{:?}",closest(a));
    let a = Cons(False,Cons(False,Nil));println!("{:?}",closest(a));
    
    let a = Cons(True,Cons(True,Cons(False,Cons(True,Cons(False,Nil)))));println!("{:?}",closest(a));

}