use std::collections::BTreeMap;
use std::hash::Hash;
pub trait NameTrait: Eq + Ord + PartialOrd + Hash + Clone {}
#[derive(Debug, Clone, Ord, PartialOrd, Eq, PartialEq)]
pub enum Expression<Name: NameTrait> {
Unit,
One,
Type,
Void,
Var(Name),
Sum(Branch<Name>),
Function(Branch<Name>),
Pi(Pattern<Name>, Box<Expression<Name>>, Box<Expression<Name>>),
Sigma(Pattern<Name>, Box<Expression<Name>>, Box<Expression<Name>>),
Lambda(Pattern<Name>, Box<Expression<Name>>),
First(Box<Expression<Name>>),
Second(Box<Expression<Name>>),
Application(Box<Expression<Name>>, Box<Expression<Name>>),
Pair(Box<Expression<Name>>, Box<Expression<Name>>),
Constructor(Name, Box<Expression<Name>>),
Declaration(Box<Declaration<Name>>, Box<Expression<Name>>),
}
type Branch<Name> = BTreeMap<Name, Box<Expression<Name>>>;
#[derive(Debug, Clone)]
pub enum Value<Name: NameTrait> {
Lambda(Closure<Name>),
Unit,
One,
Type,
Pi(Box<Value<Name>>, Closure<Name>),
Sigma(Box<Value<Name>>, Closure<Name>),
Pair(Box<Value<Name>>, Box<Value<Name>>),
Constructor(Name, Box<Value<Name>>),
Function(SClosure<Name>),
Sum(SClosure<Name>),
Neutral(Neutral<Name>),
}
#[derive(Debug, Clone)]
pub enum Neutral<Name: NameTrait> {
Generated(u32),
Application(Box<Neutral<Name>>, Box<Value<Name>>),
First(Box<Neutral<Name>>),
Second(Box<Neutral<Name>>),
Function(Box<SClosure<Name>>, Box<Neutral<Name>>),
}
#[derive(Debug, Clone, Ord, PartialOrd, Eq, PartialEq)]
pub enum Pattern<Name: NameTrait> {
Pair(Box<Pattern<Name>>, Box<Pattern<Name>>),
Unit,
Var(Name),
}
#[derive(Debug, Clone, Ord, PartialOrd, Eq, PartialEq)]
pub enum Declaration<Name: NameTrait> {
Simple(Pattern<Name>, Expression<Name>, Expression<Name>),
Recursive(Pattern<Name>, Expression<Name>, Expression<Name>),
}
#[derive(Debug, Clone)]
pub enum Telescope<Name: NameTrait> {
Nil,
UpDec(Box<Telescope<Name>>, Declaration<Name>),
UpVar(Box<Telescope<Name>>, Pattern<Name>, Value<Name>),
}
#[derive(Debug, Clone)]
pub enum Closure<Name: NameTrait> {
Choice(Pattern<Name>, Expression<Name>, Box<Telescope<Name>>),
Function(Box<Closure<Name>>, Name),
}
type SClosure<Name> = (Box<Branch<Name>>, Box<Telescope<Name>>);