open Bwd
open Bwd.Infix

module S = Syntax
module D = Domain

module Internal =
struct
  module Eff = Algaeff.Reader.Make (struct type nonrec t = D.env end)

  let make_clo body = D.Clo { body; env = Eff.read() }

  let rec inst_clo (D.Clo { body; env }) arg =
    let env = env <: arg in
    Eff.run ~env @@ fun () -> eval body

  and app v w = match v with
    | D.Lam (_, clo) -> inst_clo clo w
    | D.Neutral (hd, frms) ->
      D.Neutral (hd, frms <: D.App w)
    | D.Unfold (hd, frms, v) ->
      D.Unfold (hd, frms <: D.App w, Lazy.map (fun v -> app v w) v)
    | _ -> invalid_arg "Eval.app"

  and fst = function
    | D.Pair (v, _) -> v
    | D.Neutral (hd, frms) ->
      D.Neutral (hd, frms <: D.Fst)
    | D.Unfold (hd, frms, v) ->
      D.Unfold (hd, frms <: D.Fst, Lazy.map (fun v -> fst v) v)
    | _ -> invalid_arg "Eval.fst"

  and snd = function
    | D.Pair (_, v) -> v
    | D.Neutral (hd, frms) ->
      D.Neutral (hd, frms <: D.Snd)
    | D.Unfold (hd, frms, v) ->
      D.Unfold (hd, frms <: D.Snd, Lazy.map (fun v -> snd v) v)
    | _ -> invalid_arg "Eval.snd"

  and bool_elim motive_var motive true_case false_case = function
    | D.True -> true_case
    | D.False -> false_case
    | D.Neutral (hd, frms) ->
      D.Neutral (hd, frms <: D.BoolElim { motive_var; motive; true_case; false_case })
    | D.Unfold (hd, frms, v) ->
      D.Unfold (hd, frms <: D.BoolElim { motive_var; motive; true_case; false_case }, 
                Lazy.map (fun v -> bool_elim motive_var motive true_case false_case v) v)
    | _ -> invalid_arg "Eval.bool_elim"

  and eval = function
    | S.Var i -> Bwd.nth (Eff.read()) i
    | S.Def (p, v) -> D.def p v
    | S.Pi (name, base, fam) -> D.Pi (name, eval base, make_clo fam)
    | S.Lam (name, body) -> D.Lam (name, make_clo body)
    | S.App (a, b) -> app (eval a) (eval b)
    | S.Sg (name, base, fam) -> D.Sg (name, eval base, make_clo fam)
    | S.Pair (a, b) -> D.Pair (eval a, eval b)
    | S.Fst a -> fst (eval a)
    | S.Snd a -> snd (eval a)
    | S.Type -> D.Type
    | S.Bool -> D.Bool
    | S.True -> D.True
    | S.False -> D.False
    | S.BoolElim { motive_var; motive; true_case; false_case; scrut } ->
      bool_elim motive_var (make_clo motive) (eval true_case) (eval false_case) (eval scrut)
end

let eval ~env tm = Internal.Eff.run ~env @@ fun () -> Internal.eval tm
let eval_toplevel tm = eval ~env:Emp tm
let inst_clo = Internal.inst_clo

let rec force_all = function
  | D.Unfold (_, _, v) -> force_all (Lazy.force v)
  | v -> v