(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2013     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)
open Pp
open Errors
open Term
open Vars
open Environ
open Reduction
open Univ
open Declarations
open Names
open Inductive
open Util
open Unix
open Nativecode
open Inductiveops
open Closure
open Nativevalues
open Nativelambda

(** This module implements normalization by evaluation to OCaml code *)

let evars_of_evar_map evd =
  { evars_val = Evd.existential_opt_value evd;
    evars_typ = Evd.existential_type evd;
    evars_metas = Evd.meta_type evd }

exception Find_at of int

let invert_tag cst tag reloc_tbl =
  try
    for j = 0 to Array.length reloc_tbl - 1 do
      let tagj,arity = reloc_tbl.(j) in
      if Int.equal tag tagj && (cst && Int.equal arity 0 || not(cst || Int.equal arity 0)) then
	raise (Find_at j)
      else ()
    done;raise Not_found
  with Find_at j -> (j+1)

let decompose_prod env t =
  let (name,dom,codom as res) = destProd (whd_betadeltaiota env t) in
  match name with
  | Anonymous -> (Name (id_of_string "x"),dom,codom)
  | _ -> res

let app_type env c =
  let t = whd_betadeltaiota env c in
  try destApp t with DestKO -> (t,[||])

 
let find_rectype_a env c =
  let (t, l) = app_type env c in
  match kind_of_term t with
  | Ind ind -> (ind, l)
  | _ -> raise Not_found

(* Instantiate inductives and parameters in constructor type *)

let type_constructor mind mib typ params = 
  let s = ind_subst mind mib in
  let ctyp = substl s typ in
  let nparams = Array.length params in
  if Int.equal nparams 0 then ctyp
  else
    let _,ctyp = decompose_prod_n nparams ctyp in   
    substl (List.rev (Array.to_list params)) ctyp

let construct_of_constr_notnative const env tag (mind, _ as ind) allargs =
  let mib,mip = lookup_mind_specif env ind in
  let nparams = mib.mind_nparams in
  let i = invert_tag const tag mip.mind_reloc_tbl in
  let params = Array.sub allargs 0 nparams in
  let ctyp = type_constructor mind mib (mip.mind_nf_lc.(i-1)) params in
  (mkApp(mkConstruct(ind,i), params), ctyp)
 

let construct_of_constr const env tag typ =
  let t, l = app_type env typ in
  match kind_of_term t with
  | Ind ind -> 
      construct_of_constr_notnative const env tag ind l
  | _ -> assert false

let construct_of_constr_const env tag typ = 
  fst (construct_of_constr true env tag typ)

let construct_of_constr_block = construct_of_constr false

let build_branches_type env (mind,_ as _ind) mib mip params dep p =
  let rtbl = mip.mind_reloc_tbl in
  (* [build_one_branch i cty] construit le type de la ieme branche (commence
     a 0) et les lambda correspondant aux realargs *)
  let build_one_branch i cty =
    let typi = type_constructor mind mib cty params in
    let decl,indapp = Term.decompose_prod typi in
    let ind,cargs = find_rectype_a env indapp in
    let nparams = Array.length params in
    let carity = snd (rtbl.(i)) in
    let crealargs = Array.sub cargs nparams (Array.length cargs - nparams) in
    let codom = 
      let papp = mkApp(lift (List.length decl) p,crealargs) in
      if dep then
	let cstr = ith_constructor_of_inductive ind (i+1) in
        let relargs = Array.init carity (fun i -> mkRel (carity-i)) in
	let dep_cstr = mkApp(mkApp(mkConstruct cstr,params),relargs) in
	mkApp(papp,[|dep_cstr|])
      else papp
    in 
    decl, codom
  in Array.mapi build_one_branch mip.mind_nf_lc

let build_case_type dep p realargs c = 
  if dep then mkApp(mkApp(p, realargs), [|c|])
  else mkApp(p, realargs)

(* TODO move this function *)
let type_of_rel env n = 
  let (_,_,ty) = lookup_rel n env in
  lift n ty

let type_of_prop = mkSort type1_sort

let type_of_sort s = 
  match s with
  | Prop _ -> type_of_prop
  | Type u -> mkType (Univ.super u)

let type_of_var env id = 
  try let (_,_,ty) = lookup_named id env in ty
  with Not_found ->
    anomaly ~label:"type_of_var" (str "variable " ++ Id.print id ++ str " unbound")

let sort_of_product env domsort rangsort =
  match (domsort, rangsort) with
    (* Product rule (s,Prop,Prop) *)
    | (_,       Prop Null)  -> rangsort
    (* Product rule (Prop/Set,Set,Set) *)
    | (Prop _,  Prop Pos) -> rangsort
    (* Product rule (Type,Set,?) *)
    | (Type u1, Prop Pos) ->
        begin match engagement env with
        | Some ImpredicativeSet ->
          (* Rule is (Type,Set,Set) in the Set-impredicative calculus *)
          rangsort
        | _ ->
          (* Rule is (Type_i,Set,Type_i) in the Set-predicative calculus *)
          Type (sup u1 type0_univ)
        end
    (* Product rule (Prop,Type_i,Type_i) *)
    | (Prop Pos,  Type u2)  -> Type (sup type0_univ u2)
    (* Product rule (Prop,Type_i,Type_i) *)
    | (Prop Null, Type _)  -> rangsort
    (* Product rule (Type_i,Type_i,Type_i) *)
    | (Type u1, Type u2) -> Type (sup u1 u2)

(* normalisation of values *)

let branch_of_switch lvl ans bs = 
  let tbl = ans.asw_reloc in
  let branch i = 
    let tag,arity = tbl.(i) in
    let ci = 
      if Int.equal arity 0 then mk_const tag
      else mk_block tag (mk_rels_accu lvl arity) in
    bs ci in
  Array.init (Array.length tbl) branch

let rec nf_val env v typ =
  match kind_of_value v with
  | Vaccu accu -> nf_accu env accu
  | Vfun f -> 
      let lvl = nb_rel env in
      let name,dom,codom = 
	try decompose_prod env typ
	with DestKO ->
          Errors.anomaly
            (Pp.strbrk "Returned a functional value in a type not recognized as a product type.")
      in
      let env = push_rel (name,None,dom) env in
      let body = nf_val env (f (mk_rel_accu lvl)) codom in
      mkLambda(name,dom,body)
  | Vconst n -> construct_of_constr_const env n typ
  | Vblock b ->
      let capp,ctyp = construct_of_constr_block env (block_tag b) typ in
      let args = nf_bargs env b ctyp in
      mkApp(capp,args)

and nf_type env v =
  match kind_of_value v with
  | Vaccu accu -> nf_accu env accu
  | _ -> assert false

and nf_type_sort env v =
  match kind_of_value v with
  | Vaccu accu -> 
      let t,s = nf_accu_type env accu in
      let s = try destSort s with DestKO -> assert false in
      t, s
  | _ -> assert false

and nf_accu env accu =
  let atom = atom_of_accu accu in
  if Int.equal (accu_nargs accu) 0 then nf_atom env atom
  else
    let a,typ = nf_atom_type env atom in
    let _, args = nf_args env accu typ in
    mkApp(a,Array.of_list args)

and nf_accu_type env accu =
  let atom = atom_of_accu accu in
  if Int.equal (accu_nargs accu) 0 then nf_atom_type env atom
  else
    let a,typ = nf_atom_type env atom in
    let t, args = nf_args env accu typ in
    mkApp(a,Array.of_list args), t

and nf_args env accu t =
  let aux arg (t,l) = 
    let _,dom,codom =
      try decompose_prod env t with
	DestKO ->
	Errors.anomaly
	  (Pp.strbrk "Returned a functional value in a type not recognized as a product type.")
    in
    let c = nf_val env arg dom in
    (subst1 c codom, c::l)
  in
  let t,l = List.fold_right aux (args_of_accu accu) (t,[]) in
  t, List.rev l

and nf_bargs env b t =
  let t = ref t in
  let len = block_size b in
  Array.init len
    (fun i ->
      let _,dom,codom =
	try decompose_prod env !t with
	  DestKO ->
	  Errors.anomaly
	    (Pp.strbrk "Returned a functional value in a type not recognized as a product type.")
      in
      let c = nf_val env (block_field b i) dom in
      t := subst1 c codom; c)

and nf_atom env atom =
  match atom with
  | Arel i -> mkRel (nb_rel env - i)
  | Aconstant cst -> mkConst cst
  | Aind ind -> mkInd ind
  | Asort s -> mkSort s
  | Avar id -> mkVar id
  | Aprod(n,dom,codom) ->
      let dom = nf_type env dom in
      let vn = mk_rel_accu (nb_rel env) in
      let env = push_rel (n,None,dom) env in
      let codom = nf_type env (codom vn) in
      mkProd(n,dom,codom)
  | Ameta (mv,_) -> mkMeta mv
  | Aevar (ev,_) -> mkEvar ev
  | _ -> fst (nf_atom_type env atom)

and nf_atom_type env atom =
  match atom with
  | Arel i ->
      let n = (nb_rel env - i) in
      mkRel n, type_of_rel env n
  | Aconstant cst ->
      mkConst cst, Typeops.type_of_constant env cst
  | Aind ind ->
      mkInd ind, Inductiveops.type_of_inductive env ind 
  | Asort s ->
      mkSort s, type_of_sort s
  | Avar id ->
      mkVar id, type_of_var env id
  | Acase(ans,accu,p,bs) ->
      let a,ta = nf_accu_type env accu in
      let (mind,_ as ind),allargs = find_rectype_a env ta in
      let (mib,mip) = Inductive.lookup_mind_specif env ind in
      let nparams = mib.mind_nparams in
      let params,realargs = Array.chop nparams allargs in
      let pT = 
	hnf_prod_applist env 
	  (Inductiveops.type_of_inductive env ind) (Array.to_list params) in
      let pT = whd_betadeltaiota env pT in
      let dep, p = nf_predicate env ind mip params p pT in
      (* Calcul du type des branches *)
      let btypes = build_branches_type env ind mib mip params dep p in
      (* calcul des branches *)
      let bsw = branch_of_switch (nb_rel env) ans bs in
      let mkbranch i v =
	let decl,codom = btypes.(i) in
	let env = 
	  List.fold_right 
	    (fun (name,t) env -> push_rel (name,None,t) env) decl env in
	let b = nf_val env v codom in
	compose_lam decl b 
      in 
      let branchs = Array.mapi mkbranch bsw in
      let tcase = build_case_type dep p realargs a in
      let ci = ans.asw_ci in
      mkCase(ci, p, a, branchs), tcase 
  | Afix(tt,ft,rp,s) ->
      let tt = Array.map (nf_type env) tt in
      let name = Array.map (fun _ -> (Name (id_of_string "Ffix"))) tt in
      let lvl = nb_rel env in
      let fargs = mk_rels_accu lvl (Array.length ft) in
      let env = push_rec_types (name,tt,[||]) env in
      let ft = Array.mapi (fun i v -> nf_val env (napply v fargs) tt.(i)) ft in
      mkFix((rp,s),(name,tt,ft)), tt.(s)
  | Acofix(tt,ft,s,_) | Acofixe(tt,ft,s,_) ->
      let tt = Array.map (nf_type env) tt in
      let name = Array.map (fun _ -> (Name (id_of_string "Fcofix"))) tt in
      let lvl = nb_rel env in
      let fargs = mk_rels_accu lvl (Array.length ft) in
      let env = push_rec_types (name,tt,[||]) env in
      let ft = Array.mapi (fun i v -> nf_val env (napply v fargs) tt.(i)) ft in
      mkCoFix(s,(name,tt,ft)), tt.(s)
  | Aprod(n,dom,codom) ->
      let dom,s1 = nf_type_sort env dom in
      let vn = mk_rel_accu (nb_rel env) in
      let env = push_rel (n,None,dom) env in
      let codom,s2 = nf_type_sort env (codom vn) in
      mkProd(n,dom,codom), mkSort (sort_of_product env s1 s2)
  | Aevar(ev,ty) ->
     let ty = nf_type env ty in
     mkEvar ev, ty
  | Ameta(mv,ty) ->
     let ty = nf_type env ty in
     mkMeta mv, ty

and  nf_predicate env ind mip params v pT =
  match kind_of_value v, kind_of_term pT with
  | Vfun f, Prod _ ->
      let k = nb_rel env in
      let vb = f (mk_rel_accu k) in
      let name,dom,codom =
	try decompose_prod env pT with
	  DestKO ->
	  Errors.anomaly
	    (Pp.strbrk "Returned a functional value in a type not recognized as a product type.")
      in
      let dep,body = 
	nf_predicate (push_rel (name,None,dom) env) ind mip params vb codom in
      dep, mkLambda(name,dom,body)
  | Vfun f, _ -> 
      let k = nb_rel env in
      let vb = f (mk_rel_accu k) in
      let name = Name (id_of_string "c") in
      let n = mip.mind_nrealargs in
      let rargs = Array.init n (fun i -> mkRel (n-i)) in
      let params = if Int.equal n 0 then params else Array.map (lift n) params in
      let dom = mkApp(mkInd ind,Array.append params rargs) in
      let body = nf_type (push_rel (name,None,dom) env) vb in
      true, mkLambda(name,dom,body)
  | _, _ -> false, nf_type env v

let native_norm env sigma c ty =  
  if !Flags.no_native_compiler then
    error "Native_compute reduction has been disabled"
  else
  let penv = Environ.pre_env env in 
  (*
  Format.eprintf "Numbers of free variables (named): %i\n" (List.length vl1);
  Format.eprintf "Numbers of free variables (rel): %i\n" (List.length vl2);
  *)
  let ml_filename, prefix = Nativelib.get_ml_filename () in
  let code, upd = mk_norm_code penv sigma prefix c in
  match Nativelib.compile ml_filename code with
    | 0,fn ->
        if !Flags.debug then Pp.msg_debug (Pp.str "Running norm ...");
        let t0 = Sys.time () in
        Nativelib.call_linker ~fatal:true prefix fn (Some upd);
        let t1 = Sys.time () in
        let time_info = Format.sprintf "Evaluation done in %.5f@." (t1 -. t0) in
        if !Flags.debug then Pp.msg_debug (Pp.str time_info);
        let res = nf_val env !Nativelib.rt1 ty in
        let t2 = Sys.time () in
        let time_info = Format.sprintf "Reification done in %.5f@." (t2 -. t1) in
        if !Flags.debug then Pp.msg_debug (Pp.str time_info);
        res
    | _ -> anomaly (Pp.str "Compilation failure")