Show off type functions in rust with an example of 'type constructors'

type_fns.rs

// emulates the type of a function from types 'E' to sequence-like types
pub trait SeqTypeFn<E> { type Result : SeqLike<E>; }

// sequence-like interface
pub trait SeqLike<E>{
    fn new() -> Self;
    fn push(self,e:E) -> Self;
    fn first(&self) -> Option<&E>;
}

// List type - pushes to front
pub struct ListConstructor;
pub enum List<E>{
    Nil, Cons(E,Box<List<E>>)
}
impl<E> SeqTypeFn<E> for ListConstructor {
    type Result = List<E>;
}
impl<E> SeqLike<E> for List<E> {
    fn new() -> Self { List::Nil }
    fn push(self,e:E) -> Self { List::Cons(e,Box::new(self)) }
    fn first(&self) -> Option<&E> {
        match *self{
            List::Nil => None,
            List::Cons(ref e,_) => Some(e),
        }
    }
}

// Vect type - pushes to end
pub struct VectConstructor;
pub struct Vect<E>(Vec<E>);
impl<E> SeqTypeFn<E> for VectConstructor {
    type Result = Vect<E>;
}
impl<E> SeqLike<E> for Vect<E> {
    fn new() -> Self { Vect(Vec::new()) }
    fn push(self,e:E) -> Self {
        let mut v = self.0;
        v.push(e);
        Vect(v)
    }
    fn first(&self) -> Option<&E> { self.0.first() }
}

fn main() {
    // four similar code blocks 
    
    // list usize
    type T1 = <ListConstructor as SeqTypeFn<usize>>::Result;
    let a = T1::new();
    let a = a.push(1).push(2);
    let a = a.first();
    println!("list first usize: {:?}",a);
    
    // vect usize
    type T2 = <VectConstructor as SeqTypeFn<usize>>::Result;
    let a = T2::new();
    let a = a.push(1).push(2);
    let a = a.first();
    println!("vect first usize: {:?}",a);
    
    // list char
    type T3 = <ListConstructor as SeqTypeFn<char>>::Result;
    let a = T3::new();
    let a = a.push('1').push('2');
    let a = a.first();
    println!("list first char: {:?}",a);
    
    // vect char
    type T4 = <VectConstructor as SeqTypeFn<char>>::Result;
    let a = T4::new();
    let a = a.push('1').push('2');
    let a = a.first();
    println!("vect first char: {:?}",a);   
}