open Bwd

module S = Syntax
module D = Domain

module Internal =
struct
  (* keeping track of the context size *)
  module Eff = Algaeff.Reader.Make (struct type t = int end)

  let bind f =
    let arg = D.var (Eff.read()) in
    Eff.scope (fun size -> size + 1) @@ fun () ->
    f arg
    
  let rec quote = function
    | D.Neutral ne -> quote_ne ne
    | D.Pi (name, base, fam) -> S.Pi (name, quote base, quote_clo fam)
    | D.Lam (name, clo) -> S.Lam (name, quote_clo clo)
    | D.Sg (name, base, fam) -> S.Sg (name, quote base, quote_clo fam)
    | D.Pair (v, w) -> S.Pair (quote v, quote w)
    | D.Type -> S.Type
    | D.Bool -> S.Bool
    | D.True -> S.True
    | D.False -> S.False

  and quote_clo clo = bind @@ fun arg -> quote (Eval.inst_clo clo arg)

  and quote_ne (hd, frms) = Bwd.fold_left quote_frm (quote_ne_head hd) frms

  and quote_ne_head (D.Var i) = S.Var (Eff.read() - i - 1) (* converting from levels to indices *)

  and quote_frm hd = function
    | D.App v -> S.App (hd, quote v)
    | D.Fst -> S.Fst hd
    | D.Snd -> S.Snd hd
    | D.BoolElim { motive_var; motive; true_case; false_case } ->
      S.BoolElim {
        motive_var;
        motive = quote_clo motive;
        true_case = quote true_case;
        false_case = quote false_case;
        scrut = hd;
      }
end

let quote ~size v = Internal.Eff.run ~env:size (fun () -> Internal.quote v)
let quote_ne ~size ne = Internal.Eff.run ~env:size (fun () -> Internal.quote_ne ne)