ocaml/typing/parmatch.ml

(***********************************************************************)
(*                                                                     *)
(*                           Objective Caml                            *)
(*                                                                     *)
(*            Xavier Leroy, projet Cristal, INRIA Rocquencourt         *)
(*                                                                     *)
(*  Copyright 1996 Institut National de Recherche en Informatique et   *)
(*  en Automatique.  All rights reserved.  This file is distributed    *)
(*  under the terms of the Q Public License version 1.0.               *)
(*                                                                     *)
(***********************************************************************)

(* $Id$ *)

(* Detection of partial matches and unused match cases. *)

open Misc
open Asttypes
open Types
open Typedtree

(*************************************)
(* Utilities for building patterns   *)
(*************************************)

let make_pat desc ty tenv =
  {pat_desc = desc; pat_loc = Location.none;
   pat_type = ty ; pat_env = tenv }

let omega = make_pat Tpat_any Ctype.none Env.empty

let extra_pat =
  make_pat (Tpat_var (Ident.create "+")) Ctype.none Env.empty

let rec omegas i =
  if i <= 0 then [] else omega :: omegas (i-1)

let omega_list l = List.map (fun _ -> omega) l

let zero = make_pat (Tpat_constant (Const_int 0)) Ctype.none Env.empty

(***********************)
(* Compatibility check *)
(***********************)

(* p and q compatible means, there exists V that matches both *)

let is_absent tag row = Btype.row_field tag !row = Rabsent

let is_absent_pat p = match p.pat_desc with
| Tpat_variant (tag, _, row) -> is_absent tag row
| _ -> false

let sort_fields args =
  Sort.list
    (fun (lbl1,_) (lbl2,_) -> lbl1.lbl_pos <= lbl2.lbl_pos)
    args

let records_args l1 l2 =
  let l1 = sort_fields l1
  and l2 = sort_fields l2 in
  let rec combine r1 r2 l1 l2 = match l1,l2 with
  | [],[] -> r1,r2
  | [],(_,p2)::rem2 -> combine (omega::r1) (p2::r2) [] rem2
  | (_,p1)::rem1,[] -> combine (p1::r1) (omega::r2) rem1 []
  | (lbl1,p1)::rem1, (lbl2,p2)::rem2 ->
      if lbl1.lbl_pos < lbl2.lbl_pos then
        combine (p1::r1) (omega::r2) rem1 l2
      else if lbl1.lbl_pos > lbl2.lbl_pos then
        combine (omega::r1) (p2::r2) l1 rem2
      else (* same label on both sides *)
        combine (p1::r1) (p2::r2) rem1 rem2 in
  combine [] [] l1 l2


let rec compat p q =
  match p.pat_desc,q.pat_desc with
  | Tpat_alias (p,_),_      -> compat p q
  | _,Tpat_alias (q,_)      -> compat p q
  | (Tpat_any|Tpat_var _),_ -> true
  | _,(Tpat_any|Tpat_var _) -> true
  | Tpat_or (p1,p2,_),_     -> compat p1 q || compat p2 q
  | _,Tpat_or (q1,q2,_)     -> compat p q1 || compat p q2
  | Tpat_constant c1, Tpat_constant c2 -> c1=c2
  | Tpat_tuple ps, Tpat_tuple qs -> compats ps qs
  | Tpat_lazy p, Tpat_lazy q -> compat p q
  | Tpat_construct (c1,ps1), Tpat_construct (c2,ps2) ->
      c1.cstr_tag = c2.cstr_tag && compats ps1 ps2
  | Tpat_variant(l1,Some p1, r1), Tpat_variant(l2,Some p2,_) ->
      l1=l2 && compat p1 p2
  | Tpat_variant (l1,None,r1), Tpat_variant(l2,None,_) ->
      l1 = l2
  | Tpat_variant (_, None, _), Tpat_variant (_,Some _, _) -> false
  | Tpat_variant (_, Some _, _), Tpat_variant (_, None, _) -> false
  | Tpat_record l1,Tpat_record l2 ->
      let ps,qs = records_args l1 l2 in
      compats ps qs
  | Tpat_array ps, Tpat_array qs ->
      List.length ps = List.length qs &&
      compats ps qs
  | _,_  ->
      assert false

and compats ps qs = match ps,qs with
| [], [] -> true
| p::ps, q::qs -> compat p q && compats ps qs
| _,_    -> assert false

(****************************************)
(* Utilities for retrieving constructor *)
(* and record label names               *)
(****************************************)

exception Empty (* Empty pattern *)

(* May need a clean copy, cf. PR#4745 *)
let clean_copy ty =
  if ty.level = Btype.generic_level then ty
  else Subst.type_expr Subst.identity ty

let get_type_path ty tenv =
  let ty = Ctype.repr (Ctype.expand_head tenv (clean_copy ty)) in
  match ty.desc with
  | Tconstr (path,_,_) -> path
  | _ -> fatal_error "Parmatch.get_type_path"

let rec get_type_descr ty tenv =
  match (Ctype.repr ty).desc with
  | Tconstr (path,_,_) -> Env.find_type path tenv
  | _ -> fatal_error "Parmatch.get_type_descr"

let rec get_constr tag ty tenv =
  match get_type_descr ty tenv with
  | {type_kind=Type_variant constr_list} ->
      Datarepr.find_constr_by_tag tag constr_list
  | {type_manifest = Some _} ->
      get_constr tag (Ctype.expand_head_once tenv (clean_copy ty)) tenv
  | _ -> fatal_error "Parmatch.get_constr"

let find_label lbl lbls =
  try
    let name,_,_ = List.nth lbls lbl.lbl_pos in
    name
  with Failure "nth" -> "*Unkown label*"

let rec get_record_labels ty tenv =
  match get_type_descr ty tenv with
  | {type_kind = Type_record(lbls, rep)} -> lbls
  | {type_manifest = Some _} ->
      get_record_labels (Ctype.expand_head_once tenv (clean_copy ty)) tenv
  | _ -> fatal_error "Parmatch.get_record_labels"


(*************************************)
(* Values as patterns pretty printer *)
(*************************************)

open Format
;;

let get_constr_name tag ty tenv  = match tag with
| Cstr_exception path -> Path.name path
| _ ->
  try
    let name,_ = get_constr tag ty tenv in name
  with
  | Datarepr.Constr_not_found -> "*Unknown constructor*"

let is_cons tag v  = match get_constr_name tag v.pat_type v.pat_env with
| "::" -> true
| _ -> false


let rec pretty_val ppf v = match v.pat_desc with
  | Tpat_any -> fprintf ppf "_"
  | Tpat_var x -> Ident.print ppf x
  | Tpat_constant (Const_int i) -> fprintf ppf "%d" i
  | Tpat_constant (Const_char c) -> fprintf ppf "%C" c
  | Tpat_constant (Const_string s) -> fprintf ppf "%S" s
  | Tpat_constant (Const_float f) -> fprintf ppf "%s" f
  | Tpat_constant (Const_int32 i) -> fprintf ppf "%ldl" i
  | Tpat_constant (Const_int64 i) -> fprintf ppf "%LdL" i
  | Tpat_constant (Const_nativeint i) -> fprintf ppf "%ndn" i
  | Tpat_tuple vs ->
      fprintf ppf "@[(%a)@]" (pretty_vals ",") vs
  | Tpat_construct ({cstr_tag=tag},[]) ->
      let name = get_constr_name tag v.pat_type v.pat_env in
      fprintf ppf "%s" name
  | Tpat_construct ({cstr_tag=tag},[w]) ->
      let name = get_constr_name tag v.pat_type v.pat_env in
      fprintf ppf "@[<2>%s@ %a@]" name pretty_arg w
  | Tpat_construct ({cstr_tag=tag},vs) ->
      let name = get_constr_name tag v.pat_type v.pat_env in
      begin match (name, vs) with
        ("::", [v1;v2]) ->
          fprintf ppf "@[%a::@,%a@]" pretty_car v1 pretty_cdr v2
      |  _ ->
          fprintf ppf "@[<2>%s@ @[(%a)@]@]" name (pretty_vals ",") vs
      end
  | Tpat_variant (l, None, _) ->
      fprintf ppf "`%s" l
  | Tpat_variant (l, Some w, _) ->
      fprintf ppf "@[<2>`%s@ %a@]" l pretty_arg w
  | Tpat_record lvs ->
      fprintf ppf "@[{%a}@]"
        (pretty_lvals (get_record_labels v.pat_type v.pat_env))
        (List.filter
           (function
             | (_,{pat_desc=Tpat_any}) -> false (* do not show lbl=_ *)
             | _ -> true) lvs)
  | Tpat_array vs ->
      fprintf ppf "@[[| %a |]@]" (pretty_vals " ;") vs
  | Tpat_lazy v ->
      fprintf ppf "@[<2>lazy@ %a@]" pretty_arg v
  | Tpat_alias (v,x) ->
      fprintf ppf "@[(%a@ as %a)@]" pretty_val v Ident.print x
  | Tpat_or (v,w,_)    ->
      fprintf ppf "@[(%a|@,%a)@]" pretty_or v pretty_or w

and pretty_car ppf v = match v.pat_desc with
| Tpat_construct ({cstr_tag=tag}, [_ ; _])
    when is_cons tag v ->
      fprintf ppf "(%a)" pretty_val v
| _ -> pretty_val ppf v

and pretty_cdr ppf v = match v.pat_desc with
| Tpat_construct ({cstr_tag=tag}, [v1 ; v2])
    when is_cons tag v ->
      fprintf ppf "%a::@,%a" pretty_car v1 pretty_cdr v2
| _ -> pretty_val ppf v

and pretty_arg ppf v = match v.pat_desc with
| Tpat_construct (_,_::_) -> fprintf ppf "(%a)" pretty_val v
|  _ -> pretty_val ppf v

and pretty_or ppf v = match v.pat_desc with
| Tpat_or (v,w,_) ->
    fprintf ppf "%a|@,%a" pretty_or v pretty_or w
| _ -> pretty_val ppf v

and pretty_vals sep ppf = function
  | [] -> ()
  | [v] -> pretty_val ppf v
  | v::vs ->
      fprintf ppf "%a%s@ %a" pretty_val v sep (pretty_vals sep) vs

and pretty_lvals lbls ppf = function
  | [] -> ()
  | [lbl,v] ->
      let name = find_label lbl lbls in
      fprintf ppf "%s=%a" name pretty_val v
  | (lbl,v)::rest ->
      let name = find_label lbl lbls in
      fprintf ppf "%s=%a;@ %a" name pretty_val v (pretty_lvals lbls) rest

let top_pretty ppf v =
  fprintf ppf "@[%a@]@?" pretty_val v


let prerr_pat v =
  top_pretty str_formatter v ;
  prerr_string (flush_str_formatter ())


(****************************)
(* Utilities for matching   *)
(****************************)

(* Check top matching *)
let simple_match p1 p2 =
  match p1.pat_desc, p2.pat_desc with
  | Tpat_construct(c1, _), Tpat_construct(c2, _) ->
      c1.cstr_tag = c2.cstr_tag
  | Tpat_variant(l1, _, _), Tpat_variant(l2, _, _) ->
      l1 = l2
  | Tpat_constant(Const_float s1), Tpat_constant(Const_float s2) ->
      float_of_string s1 = float_of_string s2
  | Tpat_constant(c1), Tpat_constant(c2) -> c1 = c2
  | Tpat_tuple _, Tpat_tuple _ -> true
  | Tpat_lazy _, Tpat_lazy _ -> true
  | Tpat_record _ , Tpat_record _ -> true
  | Tpat_array p1s, Tpat_array p2s -> List.length p1s = List.length p2s
  | _, (Tpat_any | Tpat_var(_)) -> true
  | _, _ -> false




(* extract record fields as a whole *)
let record_arg p = match p.pat_desc with
| Tpat_any -> []
| Tpat_record args -> args
| _ -> fatal_error "Parmatch.as_record"


(* Raise Not_found when pos is not present in arg *)


let get_field pos arg =
  let _,p = List.find (fun (lbl,_) -> pos = lbl.lbl_pos) arg in
  p


let extract_fields omegas arg =
  List.map
    (fun (lbl,_) ->
      try
        get_field lbl.lbl_pos arg
      with Not_found -> omega)
    omegas



let sort_record p = match p.pat_desc with
| Tpat_record args ->
    make_pat
      (Tpat_record (sort_fields args))
      p.pat_type p.pat_env
| _ -> p

let all_record_args lbls = match lbls with
| ({lbl_all=lbl_all},_)::_ ->
    let t =
      Array.map
        (fun lbl -> lbl,omega) lbl_all in
    List.iter
      (fun ((lbl,_) as x) ->  t.(lbl.lbl_pos) <- x)
      lbls ;
    Array.to_list t
|  _ -> fatal_error "Parmatch.all_record_args"


(* Build argument list when p2 >= p1, where p1 is a simple pattern *)
let rec simple_match_args p1 p2 = match p2.pat_desc with
| Tpat_alias (p2,_) -> simple_match_args p1 p2
| Tpat_construct(cstr, args) -> args
| Tpat_variant(lab, Some arg, _) -> [arg]
| Tpat_tuple(args)  -> args
| Tpat_record(args) ->  extract_fields (record_arg p1) args
| Tpat_array(args) -> args
| Tpat_lazy arg -> [arg]
| (Tpat_any | Tpat_var(_)) ->
    begin match p1.pat_desc with
      Tpat_construct(_, args) -> omega_list args
    | Tpat_variant(_, Some _, _) -> [omega]
    | Tpat_tuple(args) -> omega_list args
    | Tpat_record(args) ->  omega_list args
    | Tpat_array(args) ->  omega_list args
    | Tpat_lazy _ -> [omega]
    | _ -> []
    end
| _ -> []

(*
  Normalize a pattern ->
   all arguments are omega (simple pattern) and no more variables
*)

let rec normalize_pat q = match q.pat_desc with
  | Tpat_any | Tpat_constant _ -> q
  | Tpat_var _ -> make_pat Tpat_any q.pat_type q.pat_env
  | Tpat_alias (p,_) -> normalize_pat p
  | Tpat_tuple (args) ->
      make_pat (Tpat_tuple (omega_list args)) q.pat_type q.pat_env
  | Tpat_construct  (c,args) ->
      make_pat (Tpat_construct (c,omega_list args)) q.pat_type q.pat_env
  | Tpat_variant (l, arg, row) ->
      make_pat (Tpat_variant (l, may_map (fun _ -> omega) arg, row))
        q.pat_type q.pat_env
  | Tpat_array (args) ->
      make_pat (Tpat_array (omega_list args))  q.pat_type q.pat_env
  | Tpat_record (largs) ->
      make_pat (Tpat_record (List.map (fun (lbl,_) -> lbl,omega) largs))
        q.pat_type q.pat_env
  | Tpat_lazy _ ->
      make_pat (Tpat_lazy omega) q.pat_type q.pat_env
  | Tpat_or _ -> fatal_error "Parmatch.normalize_pat"


(*
  Build normalized (cf. supra) discriminating pattern,
  in the non-data type case
*)

let discr_pat q pss =

  let rec acc_pat acc pss = match pss with
    ({pat_desc = Tpat_alias (p,_)}::ps)::pss ->
        acc_pat acc ((p::ps)::pss)
  | ({pat_desc = Tpat_or (p1,p2,_)}::ps)::pss ->
        acc_pat acc ((p1::ps)::(p2::ps)::pss)
  | ({pat_desc = (Tpat_any | Tpat_var _)}::_)::pss ->
        acc_pat acc pss
  | (({pat_desc = Tpat_tuple _} as p)::_)::_ -> normalize_pat p
  | (({pat_desc = Tpat_lazy _} as p)::_)::_ -> normalize_pat p
  | (({pat_desc = Tpat_record largs} as p)::_)::pss ->
      let new_omegas =
        List.fold_left
          (fun r (lbl,_) ->
            try
              let _ = get_field lbl.lbl_pos r in
              r
            with Not_found ->
              (lbl,omega)::r)
          (record_arg acc)
          largs in
      acc_pat
        (make_pat (Tpat_record new_omegas) p.pat_type p.pat_env)
        pss
  | _ -> acc in

  match normalize_pat q with
  | {pat_desc= (Tpat_any | Tpat_record _)} as q ->
      sort_record (acc_pat q pss)
  | q -> q

(*
   In case a matching value is found, set actual arguments
   of the matching pattern.
*)

let rec read_args xs r = match xs,r with
| [],_ -> [],r
| _::xs, arg::rest ->
   let args,rest = read_args xs rest in
   arg::args,rest
| _,_ ->
    fatal_error "Parmatch.read_args"

let do_set_args erase_mutable q r = match q with
| {pat_desc = Tpat_tuple omegas} ->
    let args,rest = read_args omegas r in
    make_pat (Tpat_tuple args) q.pat_type q.pat_env::rest
| {pat_desc = Tpat_record omegas} ->
    let args,rest = read_args omegas r in
    make_pat
      (Tpat_record
         (List.map2 (fun (lbl,_) arg ->
           if
             erase_mutable &&
             (match lbl.lbl_mut with
             | Mutable -> true | Immutable -> false)
           then
             lbl, omega
           else
             lbl,arg)
            omegas args))
      q.pat_type q.pat_env::
    rest
| {pat_desc = Tpat_construct (c,omegas)} ->
    let args,rest = read_args omegas r in
    make_pat
      (Tpat_construct (c,args)) q.pat_type q.pat_env::
    rest
| {pat_desc = Tpat_variant (l, omega, row)} ->
    let arg, rest =
      match omega, r with
        Some _, a::r -> Some a, r
      | None, r -> None, r
      | _ -> assert false
    in
    make_pat
      (Tpat_variant (l, arg, row)) q.pat_type q.pat_env::
    rest
| {pat_desc = Tpat_lazy omega} ->
    begin match r with
      arg::rest ->
        make_pat (Tpat_lazy arg) q.pat_type q.pat_env::rest
    | _ -> fatal_error "Parmatch.do_set_args (lazy)"
    end
| {pat_desc = Tpat_array omegas} ->
    let args,rest = read_args omegas r in
    make_pat
      (Tpat_array args) q.pat_type q.pat_env::
    rest
| {pat_desc=Tpat_constant _|Tpat_any} ->
    q::r (* case any is used in matching.ml *)
| _ -> fatal_error "Parmatch.set_args"

let set_args q r = do_set_args false q r
and set_args_erase_mutable q r = do_set_args true q r

(* filter pss acording to pattern q *)
let filter_one q pss =
  let rec filter_rec = function
      ({pat_desc = Tpat_alias(p,_)}::ps)::pss ->
        filter_rec ((p::ps)::pss)
    | ({pat_desc = Tpat_or(p1,p2,_)}::ps)::pss ->
        filter_rec ((p1::ps)::(p2::ps)::pss)
    | (p::ps)::pss ->
        if simple_match q p
        then (simple_match_args q p @ ps) :: filter_rec pss
        else filter_rec pss
    | _ -> [] in
  filter_rec pss

(*
  Filter pss in the ``extra case''. This applies :
  - According to an extra constructor (datatype case, non-complete signature).
  - Acordinng to anything (all-variables case).
*)
let filter_extra pss =
  let rec filter_rec = function
      ({pat_desc = Tpat_alias(p,_)}::ps)::pss ->
        filter_rec ((p::ps)::pss)
    | ({pat_desc = Tpat_or(p1,p2,_)}::ps)::pss ->
        filter_rec ((p1::ps)::(p2::ps)::pss)
    | ({pat_desc = (Tpat_any | Tpat_var(_))} :: qs) :: pss ->
        qs :: filter_rec pss
    | _::pss  -> filter_rec pss
    | [] -> [] in
  filter_rec pss

(*
  Pattern p0 is the discriminating pattern,
  returns [(q0,pss0) ; ... ; (qn,pssn)]
  where the qi's are simple patterns and the pssi's are
  matched matrices.

  NOTES
   * (qi,[]) is impossible.
   * In the case when matching is useless (all-variable case),
     returns []
*)

let filter_all pat0 pss =

  let rec insert q qs env =
    match env with
      [] ->
        let q0 = normalize_pat q in
        [q0, [simple_match_args q0 q @ qs]]
    | ((q0,pss) as c)::env ->
        if simple_match q0 q
        then (q0, ((simple_match_args q0 q @ qs) :: pss)) :: env
        else c :: insert q qs env in

  let rec filter_rec env = function
    ({pat_desc = Tpat_alias(p,_)}::ps)::pss ->
      filter_rec env ((p::ps)::pss)
  | ({pat_desc = Tpat_or(p1,p2,_)}::ps)::pss ->
      filter_rec env ((p1::ps)::(p2::ps)::pss)
  | ({pat_desc = (Tpat_any | Tpat_var(_))}::_)::pss ->
      filter_rec env pss
  | (p::ps)::pss ->
      filter_rec (insert p ps env) pss
  | _ -> env

  and filter_omega env = function
    ({pat_desc = Tpat_alias(p,_)}::ps)::pss ->
      filter_omega env ((p::ps)::pss)
  | ({pat_desc = Tpat_or(p1,p2,_)}::ps)::pss ->
      filter_omega env ((p1::ps)::(p2::ps)::pss)
  | ({pat_desc = (Tpat_any | Tpat_var(_))}::ps)::pss ->
      filter_omega
        (List.map (fun (q,qss) -> (q,(simple_match_args q omega @ ps) :: qss)) env)
        pss
  | _::pss -> filter_omega env pss
  | [] -> env in

  filter_omega
    (filter_rec
      (match pat0.pat_desc with
        (Tpat_record(_) | Tpat_tuple(_) | Tpat_lazy(_)) -> [pat0,[]]
      | _ -> [])
      pss)
    pss

(* Variant related functions *)

let rec set_last a = function
    [] -> []
  | [_] -> [a]
  | x::l -> x :: set_last a l

(* mark constructor lines for failure when they are incomplete *)
let rec mark_partial = function
    ({pat_desc = Tpat_alias(p,_)}::ps)::pss ->
      mark_partial ((p::ps)::pss)
  | ({pat_desc = Tpat_or(p1,p2,_)}::ps)::pss ->
      mark_partial ((p1::ps)::(p2::ps)::pss)
  | ({pat_desc = (Tpat_any | Tpat_var(_))} :: _ as ps) :: pss ->
      ps :: mark_partial pss
  | ps::pss  ->
      (set_last zero ps) :: mark_partial pss
  | [] -> []

let close_variant env row =
  let row = Btype.row_repr row in
  let nm =
    List.fold_left
      (fun nm (tag,f) ->
        match Btype.row_field_repr f with
        | Reither(_, _, false, e) ->
            (* m=false means that this tag is not explicitly matched *)
            Btype.set_row_field e Rabsent;
            None
        | Rabsent | Reither (_, _, true, _) | Rpresent _ -> nm)
      row.row_name row.row_fields in
  if not row.row_closed || nm != row.row_name then begin
    (* this unification cannot fail *)
    Ctype.unify env row.row_more
      (Btype.newgenty
         (Tvariant {row with row_fields = []; row_more = Btype.newgenvar();
                    row_closed = true; row_name = nm}))
  end

let row_of_pat pat =
  match Ctype.expand_head pat.pat_env pat.pat_type with
    {desc = Tvariant row} -> Btype.row_repr row
  | _ -> assert false

(*
  Check whether the first column of env makes up a complete signature or
  not.
*)

let full_match closing env =  match env with
| ({pat_desc = Tpat_construct ({cstr_tag=Cstr_exception _},_)},_)::_ ->
    false
| ({pat_desc = Tpat_construct(c,_)},_) :: _ ->
    List.length env = c.cstr_consts + c.cstr_nonconsts
| ({pat_desc = Tpat_variant _} as p,_) :: _ ->
    let fields =
      List.map
        (function ({pat_desc = Tpat_variant (tag, _, _)}, _) -> tag
          | _ -> assert false)
        env
    in
    let row = row_of_pat p in
    if closing && not row.row_fixed then
      (* closing=true, we are considering the variant as closed *)
      List.for_all
        (fun (tag,f) ->
          match Btype.row_field_repr f with
            Rabsent | Reither(_, _, false, _) -> true
          | Reither (_, _, true, _)
              (* m=true, do not discard matched tags, rather warn *)
          | Rpresent _ -> List.mem tag fields)
        row.row_fields
    else
      row.row_closed &&
      List.for_all
        (fun (tag,f) ->
          Btype.row_field_repr f = Rabsent || List.mem tag fields)
        row.row_fields
| ({pat_desc = Tpat_constant(Const_char _)},_) :: _ ->
    List.length env = 256
| ({pat_desc = Tpat_constant(_)},_) :: _ -> false
| ({pat_desc = Tpat_tuple(_)},_) :: _ -> true
| ({pat_desc = Tpat_record(_)},_) :: _ -> true
| ({pat_desc = Tpat_array(_)},_) :: _ -> false
| ({pat_desc = Tpat_lazy(_)},_) :: _ -> true
| _ -> fatal_error "Parmatch.full_match"

let extendable_match env = match env with
| ({pat_desc = Tpat_construct({cstr_tag=(Cstr_constant _|Cstr_block _)},_)} as p,_) :: _ ->
    let path = get_type_path p.pat_type p.pat_env in
    not
      (Path.same path Predef.path_bool ||
      Path.same path Predef.path_list ||
      Path.same path Predef.path_option)
| _ -> false


let should_extend ext env = match ext with
| None -> false
| Some ext -> match env with
  | ({pat_desc =
       Tpat_construct({cstr_tag=(Cstr_constant _|Cstr_block _)},_)} as p,_)
    :: _ ->
      let path = get_type_path p.pat_type p.pat_env in
      Path.same path ext
  | _ -> false

(* complement constructor tags *)
let complete_tags nconsts nconstrs tags =
  let seen_const = Array.create nconsts false
  and seen_constr = Array.create nconstrs false in
  List.iter
    (function
      | Cstr_constant i -> seen_const.(i) <- true
      | Cstr_block i -> seen_constr.(i) <- true
      | _  -> assert false)
    tags ;
  let r = ref [] in
  for i = 0 to nconsts-1 do
    if not seen_const.(i) then
      r := Cstr_constant i :: !r
  done ;
  for i = 0 to nconstrs-1 do
    if not seen_constr.(i) then
      r := Cstr_block i :: !r
  done ;
  !r

(* build a pattern from a constructor list *)
let pat_of_constr ex_pat cstr =
 {ex_pat with pat_desc = Tpat_construct (cstr,omegas cstr.cstr_arity)}

let rec pat_of_constrs ex_pat = function
| [] -> raise Empty
| [cstr] -> pat_of_constr ex_pat cstr
| cstr::rem ->
    {ex_pat with
    pat_desc=
      Tpat_or
        (pat_of_constr ex_pat cstr,
         pat_of_constrs ex_pat rem, None)}

(* Sends back a pattern that complements constructor tags all_tag *)
let complete_constrs p all_tags = match p.pat_desc with
| Tpat_construct (c,_) ->
    begin try
      let not_tags = complete_tags  c.cstr_consts c.cstr_nonconsts all_tags in
      List.map
        (fun tag ->
          let _,targs = get_constr tag p.pat_type p.pat_env in
          {c with
      cstr_tag = tag ;
      cstr_args = targs ;
      cstr_arity = List.length targs})
        not_tags
with
| Datarepr.Constr_not_found ->
    fatal_error "Parmatch.complete_constr: constr_not_found"
    end
| _ -> fatal_error "Parmatch.complete_constr"


(* Auxiliary for build_other *)

let build_other_constant proj make first next p env =
  let all = List.map (fun (p, _) -> proj p.pat_desc) env in
  let rec try_const i =
    if List.mem i all
    then try_const (next i)
    else make_pat (make i) p.pat_type p.pat_env
  in try_const first

(*
  Builds a pattern that is incompatible with all patterns in
  in the first column of env
*)

let build_other ext env =  match env with
| ({pat_desc = Tpat_construct ({cstr_tag=Cstr_exception _} as c,_)},_)
  ::_ ->
    make_pat
      (Tpat_construct
         ({c with
           cstr_tag=(Cstr_exception
            (Path.Pident (Ident.create "*exception*")))},
          []))
      Ctype.none Env.empty
| ({pat_desc = Tpat_construct (_,_)} as p,_) :: _ ->
    begin match ext with
    | Some ext when Path.same ext (get_type_path p.pat_type p.pat_env) ->
        extra_pat
    | _ ->
        let get_tag = function
          | {pat_desc = Tpat_construct (c,_)} -> c.cstr_tag
          | _ -> fatal_error "Parmatch.get_tag" in
        let all_tags =  List.map (fun (p,_) -> get_tag p) env in
        pat_of_constrs p (complete_constrs p all_tags)
    end
| ({pat_desc = Tpat_variant (_,_,r)} as p,_) :: _ ->
    let tags =
      List.map
        (function ({pat_desc = Tpat_variant (tag, _, _)}, _) -> tag
                | _ -> assert false)
        env
    in
    let row = row_of_pat p in
    let make_other_pat tag const =
      let arg = if const then None else Some omega in
      make_pat (Tpat_variant(tag, arg, r)) p.pat_type p.pat_env in
    begin match
      List.fold_left
        (fun others (tag,f) ->
          if List.mem tag tags then others else
          match Btype.row_field_repr f with
            Rabsent (* | Reither _ *) -> others
          (* This one is called after erasing pattern info *)
          | Reither (c, _, _, _) -> make_other_pat tag c :: others
          | Rpresent arg -> make_other_pat tag (arg = None) :: others)
        [] row.row_fields
    with
      [] ->
        make_other_pat "AnyExtraTag" true
    | pat::other_pats ->
        List.fold_left
          (fun p_res pat ->
            make_pat (Tpat_or (pat, p_res, None)) p.pat_type p.pat_env)
          pat other_pats
    end
| ({pat_desc = Tpat_constant(Const_char _)} as p,_) :: _ ->
    let all_chars =
      List.map
        (fun (p,_) -> match p.pat_desc with
        | Tpat_constant (Const_char c) -> c
        | _ -> assert false)
        env in

    let rec find_other i imax =
      if i > imax then raise Not_found
      else
        let ci = Char.chr i in
        if List.mem ci all_chars then
          find_other (i+1) imax
        else
          make_pat (Tpat_constant (Const_char ci)) p.pat_type p.pat_env in
    let rec try_chars = function
      | [] -> omega
      | (c1,c2) :: rest ->
          try
            find_other (Char.code c1) (Char.code c2)
          with
          | Not_found -> try_chars rest in

    try_chars
      [ 'a', 'z' ; 'A', 'Z' ; '0', '9' ;
        ' ', '~' ; Char.chr 0 , Char.chr 255]

| ({pat_desc=(Tpat_constant (Const_int _))} as p,_) :: _ ->
    build_other_constant
      (function Tpat_constant(Const_int i) -> i | _ -> assert false)
      (function i -> Tpat_constant(Const_int i))
      0 succ p env
| ({pat_desc=(Tpat_constant (Const_int32 _))} as p,_) :: _ ->
    build_other_constant
      (function Tpat_constant(Const_int32 i) -> i | _ -> assert false)
      (function i -> Tpat_constant(Const_int32 i))
      0l Int32.succ p env
| ({pat_desc=(Tpat_constant (Const_int64 _))} as p,_) :: _ ->
    build_other_constant
      (function Tpat_constant(Const_int64 i) -> i | _ -> assert false)
      (function i -> Tpat_constant(Const_int64 i))
      0L Int64.succ p env
| ({pat_desc=(Tpat_constant (Const_nativeint _))} as p,_) :: _ ->
    build_other_constant
      (function Tpat_constant(Const_nativeint i) -> i | _ -> assert false)
      (function i -> Tpat_constant(Const_nativeint i))
      0n Nativeint.succ p env
| ({pat_desc=(Tpat_constant (Const_string _))} as p,_) :: _ ->
    build_other_constant
      (function Tpat_constant(Const_string s) -> String.length s
              | _ -> assert false)
      (function i -> Tpat_constant(Const_string(String.make i '*')))
      0 succ p env
| ({pat_desc=(Tpat_constant (Const_float _))} as p,_) :: _ ->
    build_other_constant
      (function Tpat_constant(Const_float f) -> float_of_string f
              | _ -> assert false)
      (function f -> Tpat_constant(Const_float (string_of_float f)))
      0.0 (fun f -> f +. 1.0) p env

| ({pat_desc = Tpat_array args} as p,_)::_ ->
    let all_lengths =
      List.map
        (fun (p,_) -> match p.pat_desc with
        | Tpat_array args -> List.length args
        | _ -> assert false)
        env in
    let rec try_arrays l =
      if List.mem l all_lengths then try_arrays (l+1)
      else
        make_pat
          (Tpat_array (omegas l))
          p.pat_type p.pat_env in
    try_arrays 0
| [] -> omega
| _ -> omega

(*
  Core function :
  Is the last row of pattern matrix pss + qs satisfiable ?
  That is :
    Does there exists at least one value vector, es such that :
     1- for all ps in pss ps # es (ps and es are not compatible)
     2- qs <= es                  (es matches qs)
*)

let rec has_instance p = match p.pat_desc with
  | Tpat_variant (l,_,r) when is_absent l r -> false
  | Tpat_any | Tpat_var _ | Tpat_constant _ | Tpat_variant (_,None,_) -> true
  | Tpat_alias (p,_) | Tpat_variant (_,Some p,_) -> has_instance p
  | Tpat_or (p1,p2,_) -> has_instance p1 || has_instance p2
  | Tpat_construct (_,ps) | Tpat_tuple ps | Tpat_array ps -> has_instances ps
  | Tpat_record lps -> has_instances (List.map snd lps)
  | Tpat_lazy p -> has_instance p

and has_instances = function
  | [] -> true
  | q::rem -> has_instance q && has_instances rem

let rec satisfiable pss qs = match pss with
| [] -> has_instances qs
| _  ->
    match qs with
    | [] -> false
    | {pat_desc = Tpat_or(q1,q2,_)}::qs ->
        satisfiable pss (q1::qs) || satisfiable pss (q2::qs)
    | {pat_desc = Tpat_alias(q,_)}::qs ->
          satisfiable pss (q::qs)
    | {pat_desc = (Tpat_any | Tpat_var(_))}::qs ->
        let q0 = discr_pat omega pss in
        begin match filter_all q0 pss with
          (* first column of pss is made of variables only *)
        | [] -> satisfiable (filter_extra pss) qs
        | constrs  ->
            if full_match false constrs then
              List.exists
                (fun (p,pss) ->
                  not (is_absent_pat p) &&
                  satisfiable pss (simple_match_args p omega @ qs))
                constrs
            else
              satisfiable (filter_extra pss) qs
        end
    | {pat_desc=Tpat_variant (l,_,r)}::_ when is_absent l r -> false
    | q::qs ->
        let q0 = discr_pat q pss in
        satisfiable (filter_one q0 pss) (simple_match_args q0 q @ qs)

(*
  Now another satisfiable function that additionally
  supplies an example of a matching value.

  This function should be called for exhaustiveness check only.
*)

type 'a result =
  | Rnone           (* No matching value *)
  | Rsome of 'a     (* This matching value *)

let rec try_many f = function
  | [] -> Rnone
  | x::rest ->
      begin match f x with
      | Rnone -> try_many f rest
      | r -> r
      end

let rec exhaust ext pss n = match pss with
| []    ->  Rsome (omegas n)
| []::_ ->  Rnone
| pss   ->
    let q0 = discr_pat omega pss in
    begin match filter_all q0 pss with
          (* first column of pss is made of variables only *)
    | [] ->
        begin match exhaust ext (filter_extra pss) (n-1) with
        | Rsome r -> Rsome (q0::r)
        | r -> r
      end
    | constrs ->
        let try_non_omega (p,pss) =
          if is_absent_pat p then
            Rnone
          else
            match
              exhaust
                ext pss (List.length (simple_match_args p omega) + n - 1)
            with
            | Rsome r -> Rsome (set_args p r)
            | r       -> r in
        if
          full_match false constrs && not (should_extend ext constrs)
        then
          try_many try_non_omega constrs
        else
          (*
             D = filter_extra pss is the default matrix
             as it is included in pss, one can avoid
             recursive calls on specialized matrices,
             Essentially :
             * D exhaustive => pss exhaustive
             * D non-exhaustive => we have a non-filtered value
          *)
          let r =  exhaust ext (filter_extra pss) (n-1) in
          match r with
          | Rnone -> Rnone
          | Rsome r ->
              try
                Rsome (build_other ext constrs::r)
              with
      (* cannot occur, since constructors don't make a full signature *)
              | Empty -> fatal_error "Parmatch.exhaust"
    end

(*
   Another exhaustiveness check, enforcing variant typing.
   Note that it does not check exact exhaustiveness, but whether a
   matching could be made exhaustive by closing all variant types.
   When this is true of all other columns, the current column is left
   open (even if it means that the whole matching is not exhaustive as
   a result).
   When this is false for the matrix minus the current column, and the
   current column is composed of variant tags, we close the variant
   (even if it doesn't help in making the matching exhaustive).
*)

let rec pressure_variants tdefs = function
  | []    -> false
  | []::_ -> true
  | pss   ->
      let q0 = discr_pat omega pss in
      begin match filter_all q0 pss with
        [] -> pressure_variants tdefs (filter_extra pss)
      | constrs ->
          let rec try_non_omega = function
              (p,pss) :: rem ->
                let ok = pressure_variants tdefs pss in
                try_non_omega rem && ok
            | [] -> true
          in
          if full_match (tdefs=None) constrs then
            try_non_omega constrs
          else if tdefs = None then
            pressure_variants None (filter_extra pss)
          else
            let full = full_match true constrs in
            let ok =
              if full then try_non_omega constrs
              else try_non_omega (filter_all q0 (mark_partial pss))
            in
            begin match constrs, tdefs with
              ({pat_desc=Tpat_variant _} as p,_):: _, Some env ->
                let row = row_of_pat p in
                if row.row_fixed
                || pressure_variants None (filter_extra pss) then ()
                else close_variant env row
            | _ -> ()
            end;
            ok
      end


(* Yet another satisfiable fonction *)

(*
   This time every_satisfiable pss qs checks the
   utility of every expansion of qs.
   Expansion means expansion of or-patterns inside qs
*)

type answer =
  | Used                                (* Useful pattern *)
  | Unused                              (* Useless pattern *)
  | Upartial of Typedtree.pattern list  (* Neither, with list of useless pattern *)


let pretty_pat p =
  top_pretty Format.str_formatter p ;
  prerr_string (Format.flush_str_formatter ())

type matrix = pattern list list

let pretty_line ps =
  List.iter
    (fun p ->
      top_pretty Format.str_formatter p ;
      prerr_string " <" ;
      prerr_string (Format.flush_str_formatter ()) ;
      prerr_string ">")
    ps

let pretty_matrix pss =
  prerr_endline "begin matrix" ;
  List.iter
    (fun ps ->
      pretty_line ps ;
      prerr_endline "")
    pss ;
  prerr_endline "end matrix"

(* this row type enable column processing inside the matrix
    - left  ->  elements not to be processed,
    - right ->  elements to be processed
*)
type 'a row = {no_ors : 'a list ; ors : 'a list ; active : 'a list}


let pretty_row {ors=ors ; no_ors=no_ors; active=active} =
  pretty_line ors ; prerr_string " *" ;
  pretty_line no_ors ; prerr_string " *" ;
  pretty_line active

let pretty_rows rs =
  prerr_endline "begin matrix" ;
  List.iter
    (fun r ->
      pretty_row r ;
      prerr_endline "")
    rs ;
  prerr_endline "end matrix"

(* Initial build *)
let make_row ps = {ors=[] ; no_ors=[]; active=ps}

let make_rows pss = List.map make_row pss


(* Useful to detect and expand  or pats inside as pats *)
let rec unalias p = match p.pat_desc with
| Tpat_alias (p,_) -> unalias p
| _ -> p


let is_var p = match (unalias p).pat_desc with
| Tpat_any|Tpat_var _ -> true
| _                   -> false

let is_var_column rs =
  List.for_all
    (fun r -> match r.active with
    | p::_ -> is_var p
    | []   -> assert false)
    rs

(* Standard or-args for left-to-right matching *)
let rec or_args p = match p.pat_desc with
| Tpat_or (p1,p2,_) -> p1,p2
| Tpat_alias (p,_)  -> or_args p
| _                 -> assert false

(* Just remove current column *)
let remove r = match r.active with
| _::rem -> {r with active=rem}
| []     -> assert false

let remove_column rs = List.map remove rs

(* Current column has been processed *)
let push_no_or r = match r.active with
| p::rem -> { r with no_ors = p::r.no_ors ; active=rem}
| [] -> assert false

let push_or r = match r.active with
| p::rem -> { r with ors = p::r.ors ; active=rem}
| [] -> assert false

let push_or_column rs = List.map push_or rs
and push_no_or_column rs = List.map push_no_or rs

(* Those are adaptations of the previous homonymous functions that
   work on the current column, instead of the first column
*)

let discr_pat q rs =
  discr_pat q (List.map (fun r -> r.active) rs)

let filter_one q rs =
  let rec filter_rec rs = match rs with
  | [] -> []
  | r::rem ->
      match r.active with
      | [] -> assert false
      | {pat_desc = Tpat_alias(p,_)}::ps ->
          filter_rec ({r with active = p::ps}::rem)
      | {pat_desc = Tpat_or(p1,p2,_)}::ps ->
          filter_rec
            ({r with active = p1::ps}::
             {r with active = p2::ps}::
             rem)
      | p::ps ->
          if simple_match q p then
            {r with active=simple_match_args q p @ ps} :: filter_rec rem
          else
            filter_rec rem in
  filter_rec rs


(* Back to normal matrices *)
let make_vector r = r.no_ors

let make_matrix rs = List.map make_vector rs


(* Standard union on answers *)
let union_res r1 r2 = match r1, r2 with
| (Unused,_)
| (_, Unused) -> Unused
| Used,_    -> r2
| _, Used   -> r1
| Upartial u1, Upartial u2 -> Upartial (u1@u2)

(* propose or pats for expansion *)
let extract_elements qs =
  let rec do_rec seen = function
    | [] -> []
    | q::rem ->
        {no_ors= List.rev_append seen rem @ qs.no_ors ;
        ors=[] ;
        active = [q]}::
        do_rec (q::seen) rem in
  do_rec [] qs.ors

(* idem for matrices *)
let transpose rs = match rs with
| [] -> assert false
| r::rem ->
    let i = List.map (fun x -> [x]) r in
    List.fold_left
      (List.map2 (fun r x -> x::r))
      i rem

let extract_columns pss qs = match pss with
| [] -> List.map (fun _ -> []) qs.ors
| _  ->
  let rows = List.map extract_elements pss in
  transpose rows

(* Core function
   The idea is to first look for or patterns (recursive case), then
   check or-patterns argument usefulness (terminal case)
*)

let rec every_satisfiables pss qs = match qs.active with
| []     ->
    (* qs is now partitionned,  check usefulness *)
    begin match qs.ors with
    | [] -> (* no or-patterns *)
        if satisfiable (make_matrix pss) (make_vector qs) then
          Used
        else
          Unused
    | _  -> (* n or-patterns -> 2n expansions *)
        List.fold_right2
          (fun pss qs r -> match r with
          | Unused -> Unused
          | _ ->
              match qs.active with
              | [q] ->
                  let q1,q2 = or_args q in
                  let r_loc = every_both pss qs q1 q2 in
                  union_res r r_loc
              | _   -> assert false)
          (extract_columns pss qs) (extract_elements qs)
          Used
    end
| q::rem ->
    let uq = unalias q in
    begin match uq.pat_desc with
    | Tpat_any | Tpat_var _ ->
        if is_var_column pss then
(* forget about ``all-variable''  columns now *)
          every_satisfiables (remove_column pss) (remove qs)
        else
(* otherwise this is direct food for satisfiable *)
          every_satisfiables (push_no_or_column pss) (push_no_or qs)
    | Tpat_or (q1,q2,_) ->
        if
          q1.pat_loc.Location.loc_ghost &&
          q2.pat_loc.Location.loc_ghost
        then
(* syntactically generated or-pats should not be expanded *)
          every_satisfiables (push_no_or_column pss) (push_no_or qs)
        else
(* this is a real or-pattern *)
          every_satisfiables (push_or_column pss) (push_or qs)
    | Tpat_variant (l,_,r) when is_absent l r -> (* Ah Jacques... *)
        Unused
    | _ ->
(* standard case, filter matrix *)
        let q0 = discr_pat q pss in
        every_satisfiables
          (filter_one q0 pss)
          {qs with active=simple_match_args q0 q @ rem}
    end

(*
  This function ``every_both'' performs the usefulness check
  of or-pat q1|q2.
  The trick is to call every_satisfied twice with
  current active columns restricted to q1 and q2,
  That way,
  - others orpats in qs.ors will not get expanded.
  - all matching work performed on qs.no_ors is not performed again.
  *)
and every_both pss qs q1 q2 =
  let qs1 = {qs with active=[q1]}
  and qs2 =  {qs with active=[q2]} in
  let r1 = every_satisfiables pss qs1
  and r2 =  every_satisfiables (if compat q1 q2 then qs1::pss else pss) qs2 in
  match r1 with
  | Unused ->
      begin match r2 with
      | Unused -> Unused
      | Used   -> Upartial [q1]
      | Upartial u2 -> Upartial (q1::u2)
      end
  | Used ->
      begin match r2 with
      | Unused -> Upartial [q2]
      | _      -> r2
      end
  | Upartial u1 ->
      begin match r2 with
      | Unused -> Upartial (u1@[q2])
      | Used   -> r1
      | Upartial u2 -> Upartial (u1 @ u2)
      end




(* le_pat p q  means, forall V,  V matches q implies V matches p *)
let rec le_pat p q =
  match (p.pat_desc, q.pat_desc) with
  | (Tpat_var _|Tpat_any),_ -> true
  | Tpat_alias(p,_), _ -> le_pat p q
  | _, Tpat_alias(q,_) -> le_pat p q
  | Tpat_constant(c1), Tpat_constant(c2) -> c1 = c2
  | Tpat_construct(c1,ps), Tpat_construct(c2,qs) ->
      c1.cstr_tag = c2.cstr_tag && le_pats ps qs
  | Tpat_variant(l1,Some p1,_), Tpat_variant(l2,Some p2,_) ->
      (l1 = l2 && le_pat p1 p2)
  | Tpat_variant(l1,None,r1), Tpat_variant(l2,None,_) ->
      l1 = l2
  | Tpat_variant(_,_,_), Tpat_variant(_,_,_) -> false
  | Tpat_tuple(ps), Tpat_tuple(qs) -> le_pats ps qs
  | Tpat_lazy p, Tpat_lazy q -> le_pat p q
  | Tpat_record l1, Tpat_record l2 ->
      let ps,qs = records_args l1 l2 in
      le_pats ps qs
  | Tpat_array(ps), Tpat_array(qs) ->
      List.length ps = List.length qs && le_pats ps qs
(* In all other cases, enumeration is performed *)
  | _,_  -> not (satisfiable [[p]] [q])

and le_pats ps qs =
  match ps,qs with
    p::ps, q::qs -> le_pat p q && le_pats ps qs
  | _, _         -> true

let get_mins le ps =
  let rec select_rec r = function
      [] -> r
    | p::ps ->
        if List.exists (fun p0 -> le p0 p) ps
        then select_rec r ps
        else select_rec (p::r) ps in
  select_rec [] (select_rec [] ps)

(*
  lub p q is a pattern that matches all values matched by p and q
  may raise Empty, when p and q and not compatible
*)

let rec lub p q = match p.pat_desc,q.pat_desc with
| Tpat_alias (p,_),_      -> lub p q
| _,Tpat_alias (q,_)      -> lub p q
| (Tpat_any|Tpat_var _),_ -> q
| _,(Tpat_any|Tpat_var _) -> p
| Tpat_or (p1,p2,_),_     -> orlub p1 p2 q
| _,Tpat_or (q1,q2,_)     -> orlub q1 q2 p (* Thanks god, lub is commutative *)
| Tpat_constant c1, Tpat_constant c2 when c1=c2 -> p
| Tpat_tuple ps, Tpat_tuple qs ->
    let rs = lubs ps qs in
    make_pat (Tpat_tuple rs) p.pat_type p.pat_env
| Tpat_lazy p, Tpat_lazy q ->
    let r = lub p q in
    make_pat (Tpat_lazy r) p.pat_type p.pat_env
| Tpat_construct (c1,ps1), Tpat_construct (c2,ps2)
      when  c1.cstr_tag = c2.cstr_tag  ->
        let rs = lubs ps1 ps2 in
        make_pat (Tpat_construct (c1,rs)) p.pat_type p.pat_env
| Tpat_variant(l1,Some p1,row), Tpat_variant(l2,Some p2,_)
          when  l1=l2 ->
            let r=lub p1 p2 in
            make_pat (Tpat_variant (l1,Some r,row)) p.pat_type p.pat_env
| Tpat_variant (l1,None,row), Tpat_variant(l2,None,_)
              when l1 = l2 -> p
| Tpat_record l1,Tpat_record l2 ->
    let rs = record_lubs l1 l2 in
    make_pat (Tpat_record rs) p.pat_type p.pat_env
| Tpat_array ps, Tpat_array qs
      when List.length ps = List.length qs ->
        let rs = lubs ps qs in
        make_pat (Tpat_array rs) p.pat_type p.pat_env
| _,_  ->
    raise Empty

and orlub p1 p2 q =
  try
    let r1 = lub p1 q in
    try
      {q with pat_desc=(Tpat_or (r1,lub p2 q,None))}
  with
  | Empty -> r1
with
| Empty -> lub p2 q

and record_lubs l1 l2 =
  let l1 = sort_fields l1 and l2 = sort_fields l2 in
  let rec lub_rec l1 l2 = match l1,l2 with
  | [],_ -> l2
  | _,[] -> l1
  | (lbl1,p1)::rem1, (lbl2,p2)::rem2 ->
      if lbl1.lbl_pos < lbl2.lbl_pos then
        (lbl1,p1)::lub_rec rem1 l2
      else if lbl2.lbl_pos < lbl1.lbl_pos  then
        (lbl2,p2)::lub_rec l1 rem2
      else
        (lbl1,lub p1 p2)::lub_rec rem1 rem2 in
  lub_rec l1 l2

and lubs ps qs = match ps,qs with
| p::ps, q::qs -> lub p q :: lubs ps qs
| _,_ -> []


(******************************)
(* Exported variant closing   *)
(******************************)

(* Apply pressure to variants *)

let pressure_variants tdefs patl =
  let pss = List.map (fun p -> [p;omega]) patl in
  ignore (pressure_variants (Some tdefs) pss)

(*****************************)
(* Utilities for diagnostics *)
(*****************************)

(*
  Build up a working pattern matrix by forgetting
  about guarded patterns
*)

let has_guard act =   match act.exp_desc with
| Texp_when(_, _) -> true
| _ -> false


let rec initial_matrix = function
    [] -> []
  | (pat, act) :: rem ->
      if has_guard act
      then
        initial_matrix rem
      else
        [pat] :: initial_matrix rem

(******************************************)
(* Look for a row that matches some value *)
(******************************************)

(*
  Useful for seeing if the example of
  non-matched value can indeed be matched
  (by a guarded clause)
*)



exception NoGuard

let rec initial_all no_guard = function
  | [] ->
      if no_guard then
        raise NoGuard
      else
        []
  | (pat, act) :: rem ->
      ([pat], pat.pat_loc) :: initial_all (no_guard && not (has_guard act)) rem


let rec do_filter_var = function
  | (_::ps,loc)::rem -> (ps,loc)::do_filter_var rem
  | _ -> []

let do_filter_one q pss =
  let rec filter_rec = function
    | ({pat_desc = Tpat_alias(p,_)}::ps,loc)::pss ->
        filter_rec ((p::ps,loc)::pss)
    | ({pat_desc = Tpat_or(p1,p2,_)}::ps,loc)::pss ->
        filter_rec ((p1::ps,loc)::(p2::ps,loc)::pss)
    | (p::ps,loc)::pss ->
        if simple_match q p
        then (simple_match_args q p @ ps, loc) :: filter_rec pss
        else filter_rec pss
    | _ -> [] in
  filter_rec pss

let rec do_match pss qs = match qs with
| [] ->
    begin match pss  with
    | ([],loc)::_ -> Some loc
    | _ -> None
    end
| q::qs -> match q with
  | {pat_desc = Tpat_or (q1,q2,_)} ->
      begin match do_match pss (q1::qs) with
      | None -> do_match pss (q2::qs)
      | r -> r
      end
  | {pat_desc = Tpat_any} ->
      do_match (do_filter_var pss) qs
  | _ ->
      let q0 = normalize_pat q in
      do_match (do_filter_one q0 pss) (simple_match_args q0 q @ qs)


let check_partial_all v casel =
  try
    let pss = initial_all true casel in
    do_match pss [v]
  with
  | NoGuard -> None

(************************)
(* Exhaustiveness check *)
(************************)

let do_check_partial loc casel pss = match pss with
| [] ->
        (*
          This can occur
          - For empty matches generated by ocamlp4 (no warning)
          - when all patterns have guards (then, casel <> [])
          (specific warning)
          Then match MUST be considered non-exhaustive,
          otherwise compilation of PM is broken.
          *)
    begin match casel with
    | [] -> ()
    | _  -> Location.prerr_warning loc Warnings.All_clauses_guarded
    end ;
    Partial
| ps::_  ->
    begin match exhaust None pss (List.length ps) with
    | Rnone -> Total
    | Rsome [v] ->
        let errmsg =
          try
            let buf = Buffer.create 16 in
            let fmt = formatter_of_buffer buf in
            top_pretty fmt v;
            begin match check_partial_all v casel with
            | None -> ()
            | Some _ ->
                  (* This is 'Some loc', where loc is the location of
                     a possibly matching clause.
                     Forget about loc, because printing two locations
                     is a pain in the top-level *)
                Buffer.add_string buf
                  "\n(However, some guarded clause may match this value.)"
            end ;
            Buffer.contents buf
          with _ ->
            "" in
        Location.prerr_warning loc (Warnings.Partial_match errmsg) ;
        Partial
    | _ ->
        fatal_error "Parmatch.check_partial"
    end


(*****************)
(* Fragile check *)
(*****************)

(* Collect all data types in a pattern *)

let rec add_path path = function
  | [] -> [path]
  | x::rem as paths ->
      if Path.same path x then paths
      else x::add_path path rem

let extendable_path path =
  not
    (Path.same path Predef.path_bool ||
    Path.same path Predef.path_list ||
    Path.same path Predef.path_option)

let rec collect_paths_from_pat r p = match p.pat_desc with
| Tpat_construct({cstr_tag=(Cstr_constant _|Cstr_block _)},ps) ->
    let path =  get_type_path p.pat_type p.pat_env in
    List.fold_left
      collect_paths_from_pat
      (if extendable_path path then add_path path r else r)
      ps
| Tpat_any|Tpat_var _|Tpat_constant _| Tpat_variant (_,None,_) -> r
| Tpat_tuple ps | Tpat_array ps
| Tpat_construct ({cstr_tag=Cstr_exception _}, ps)->
    List.fold_left collect_paths_from_pat r ps
| Tpat_record lps ->
    List.fold_left
      (fun r (_,p) -> collect_paths_from_pat r p)
      r lps
| Tpat_variant (_, Some p, _) | Tpat_alias (p,_) -> collect_paths_from_pat r p
| Tpat_or (p1,p2,_) ->
    collect_paths_from_pat (collect_paths_from_pat r p1) p2
| Tpat_lazy p ->
    collect_paths_from_pat r p


(*
  Actual fragile check
   1. Collect data types in the patterns of the match.
   2. One exhautivity check per datatype, considering that
      the type is extended.
*)

let do_check_fragile loc casel pss =
  let exts =
    List.fold_left
      (fun r (p,_) -> collect_paths_from_pat r p)
      [] casel in
  match exts with
  | [] -> ()
  | _ -> match pss with
    | [] -> ()
    | ps::_ ->
        List.iter
          (fun ext ->
            match exhaust (Some ext) pss (List.length ps) with
            | Rnone ->
                Location.prerr_warning
                  loc
                  (Warnings.Fragile_match (Path.name ext))
            | Rsome _ -> ())
          exts


(********************************)
(* Exported exhustiveness check *)
(********************************)

(*
   Fragile check is performed when required and
   on exhaustive matches only.
*)

let check_partial loc casel =
  if Warnings.is_active (Warnings.Partial_match "") then begin
    let pss = initial_matrix casel in
    let pss = get_mins le_pats pss in
    let total = do_check_partial loc casel pss in
    if
      total = Total && Warnings.is_active (Warnings.Fragile_match "")
    then begin
      do_check_fragile loc casel pss
    end ;
    total
  end else
    Partial


(********************************)
(* Exported unused clause check *)
(********************************)

let check_unused tdefs casel =
  if Warnings.is_active Warnings.Unused_match then
    let rec do_rec pref = function
      | [] -> ()
      | (q,act)::rem ->
          let qs = [q] in
            begin try
              let pss =
                  get_mins le_pats (List.filter (compats qs) pref) in
              let r = every_satisfiables (make_rows pss) (make_row qs) in
              match r with
              | Unused ->
                  Location.prerr_warning
                    q.pat_loc Warnings.Unused_match
              | Upartial ps ->
                  List.iter
                    (fun p ->
                      Location.prerr_warning
                        p.pat_loc Warnings.Unused_pat)
                    ps
              | Used -> ()
            with e -> assert false
            end ;

          if has_guard act then
            do_rec pref rem
          else
            do_rec ([q]::pref) rem in

    do_rec [] casel

(*********************************)
(* Exported irrefutability tests *)
(*********************************)

let irrefutable pat = le_pat pat omega

(* An inactive pattern is a pattern whose matching needs only
   trivial computations (tag/equality tests).
   Patterns containing (lazy _) subpatterns are active. *)

let rec inactive pat = match pat with
| Tpat_lazy _ ->
    false
| Tpat_any | Tpat_var _ | Tpat_constant _ | Tpat_variant (_, None, _) ->
    true
| Tpat_tuple ps | Tpat_construct (_, ps) | Tpat_array ps ->
    List.for_all (fun p -> inactive p.pat_desc) ps
| Tpat_alias (p,_) | Tpat_variant (_, Some p, _) ->
    inactive p.pat_desc
| Tpat_record ldps ->
    List.exists (fun (_, p) -> inactive p.pat_desc) ldps
| Tpat_or (p,q,_) ->
    inactive p.pat_desc && inactive q.pat_desc


(* A `fluid' pattern is both irrefutable and inactive *)

let fluid pat = irrefutable pat && inactive pat.pat_desc