nar 0.0.8

Narc, a dependently-typed programming language with dependent pattern matching
Documentation 
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use std::rc::Rc;

use voile_util::{meta::MetaSolution, uid::DBI};

use crate::syntax::{
    common::{Bind, Let},
    core::{
        subst::{def_app, PrimSubst, Subst},
        Closure, Elim, Term, Val, ValData,
    },
    pat::{Copat, Pat},
};

/// Reducible expressions.
/// [Agda](https://hackage.haskell.org/package/Agda-2.6.0.1/docs/src/Agda.TypeChecking.Substitute.Class.html#Subst).
pub trait RedEx<T: Sized = Self, A = Term>: Sized {
    /// Apply a substitution to a redex.
    fn reduce_dbi(self, subst: Rc<PrimSubst<A>>) -> T;
}

impl RedEx for Term {
    fn reduce_dbi(self, subst: Rc<Subst>) -> Term {
        match self {
            Term::Whnf(n) => n.reduce_dbi(subst),
            Term::Redex(f, id, args) => def_app(f, id, vec![], args.reduce_dbi(subst)),
        }
    }
}

impl RedEx for Elim {
    fn reduce_dbi(self, subst: Rc<Subst>) -> Elim {
        match self {
            Elim::App(term) => Elim::app(term.reduce_dbi(subst)),
            e => e,
        }
    }
}

impl<R, T: RedEx<R>> RedEx<MetaSolution<R>> for MetaSolution<T> {
    fn reduce_dbi(self, subst: Rc<Subst>) -> MetaSolution<R> {
        use MetaSolution::*;
        match self {
            Solved(t) => Solved(Box::new(t.reduce_dbi(subst))),
            Inlined => Inlined,
            Unsolved => Unsolved,
        }
    }
}

impl<R, T: RedEx<R>> RedEx<Bind<R>> for Bind<T> {
    fn reduce_dbi(self, subst: Rc<Subst>) -> Bind<R> {
        self.map_term(|t| t.reduce_dbi(subst))
    }
}

impl<R, T: RedEx<R>> RedEx<Let<R>> for Let<T> {
    fn reduce_dbi(self, subst: Rc<Subst>) -> Let<R> {
        let bind = self.bind.reduce_dbi(subst.clone());
        Let::new(bind, self.val.reduce_dbi(subst))
    }
}

impl RedEx for ValData {
    fn reduce_dbi(self, subst: Rc<Subst>) -> Self {
        ValData::new(self.kind, self.def, self.args.reduce_dbi(subst))
    }
}

impl RedEx<Term> for Val {
    fn reduce_dbi(self, subst: Rc<Subst>) -> Term {
        match self {
            Val::Pi(arg, closure) => Term::pi2(
                arg.unboxed().reduce_dbi(subst.clone()).boxed(),
                closure.reduce_dbi(subst),
            ),
            Val::Cons(name, a) => Term::cons(name, a.reduce_dbi(subst)),
            Val::Type(n) => Term::universe(n),
            Val::Data(info) => Term::data(info.reduce_dbi(subst)),
            Val::Meta(m, a) => Term::meta(m, a.reduce_dbi(subst)),
            Val::Var(f, args) => subst.lookup(f).apply_elim(args.reduce_dbi(subst)),
            Val::Axiom(a) => Term::Whnf(Val::Axiom(a)),
            Val::Refl => Term::reflexivity(),
            Val::Id(ty, a, b) => Term::identity(
                ty.reduce_dbi(subst.clone()),
                a.reduce_dbi(subst.clone()),
                b.reduce_dbi(subst),
            ),
        }
    }
}

impl RedEx for Closure {
    fn reduce_dbi(self, subst: Rc<Subst>) -> Self {
        match self {
            Closure::Plain(body) => Self::plain(body.reduce_dbi(subst.lift_by(DBI(1)))),
        }
    }
}

/// For `Tele`.
impl<R, T: RedEx<R>> RedEx<Vec<R>> for Vec<T> {
    fn reduce_dbi(self, subst: Rc<Subst>) -> Vec<R> {
        self.into_iter()
            .map(|e| e.reduce_dbi(subst.clone()))
            .collect()
    }
}

impl<A, B, X: RedEx<A>, Y: RedEx<B>> RedEx<(A, B)> for (X, Y) {
    fn reduce_dbi(self, subst: Rc<Subst>) -> (A, B) {
        let (x, y) = self;
        (x.reduce_dbi(subst.clone()), y.reduce_dbi(subst))
    }
}

impl<Ix, R, T: RedEx<R>> RedEx<Copat<Ix, R>> for Copat<Ix, T> {
    fn reduce_dbi(self, subst: Rc<Subst>) -> Copat<Ix, R> {
        match self {
            Copat::App(a) => Copat::App(a.reduce_dbi(subst)),
            Copat::Proj(p) => Copat::Proj(p),
        }
    }
}

impl<Ix, R, T: RedEx<R>> RedEx<Pat<Ix, R>> for Pat<Ix, T> {
    fn reduce_dbi(self, subst: Rc<Subst>) -> Pat<Ix, R> {
        match self {
            Pat::Refl => Pat::Refl,
            Pat::Absurd => Pat::Absurd,
            Pat::Var(v) => Pat::Var(v),
            Pat::Cons(f, c, pats) => Pat::Cons(f, c, pats.reduce_dbi(subst)),
            Pat::Forced(t) => Pat::Forced(t.reduce_dbi(subst)),
        }
    }
}