Source file parmatch.ml

(**************************************************************************)
(*                                                                        *)
(*                                 OCaml                                  *)
(*                                                                        *)
(*             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 GNU Lesser General Public License version 2.1, with the          *)
(*   special exception on linking described in the file LICENSE.          *)
(*                                                                        *)
(**************************************************************************)

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

open Misc
open Asttypes
open Types
open Typedtree

type 'pattern parmatch_case =
  { pattern : 'pattern;
    has_guard : bool;
    needs_refute : bool;
  }

let typed_case { c_lhs; c_guard; c_rhs } =
  { pattern = c_lhs;
    has_guard = Option.is_some c_guard;
    needs_refute = (c_rhs.exp_desc = Texp_unreachable);
  }

let untyped_case { Parsetree.pc_lhs; pc_guard; pc_rhs } =
  { pattern = pc_lhs;
    has_guard = Option.is_some pc_guard;
    needs_refute = (pc_rhs.pexp_desc = Parsetree.Pexp_unreachable);
  }

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

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

let omega = Patterns.omega
let omegas = Patterns.omegas
let omega_list = Patterns.omega_list

let extra_pat =
  make_pat
    (Tpat_var (Ident.create_local "+", mknoloc "+",
      Uid.internal_not_actually_unique))
    Ctype.none Env.empty


(*******************)
(* Coherence check *)
(*******************)

(* For some of the operations we do in this module, we would like (because it
   simplifies matters) to assume that patterns appearing on a given column in a
   pattern matrix are /coherent/ (think "of the same type").
   Unfortunately that is not always true.

   Consider the following (well-typed) example:
   {[
     type _ t = S : string t | U : unit t

     let f (type a) (t1 : a t) (t2 : a t) (a : a) =
       match t1, t2, a with
       | U, _, () -> ()
       | _, S, "" -> ()
   ]}

   Clearly the 3rd column contains incoherent patterns.

   On the example above, most of the algorithms will explore the pattern matrix
   as illustrated by the following tree:

   {v
                                                   S
                                                -------> | "" |
                             U     | S, "" | __/         | () |
                         --------> | _, () |   \ not S
        | U, _, () | __/                        -------> | () |
        | _, S, "" |   \
                        ---------> | S, "" | ----------> | "" |
                          not U                    S
   v}

   where following an edge labelled by a pattern P means "assuming the value I
   am matching on is filtered by [P] on the column I am currently looking at,
   then the following submatrix is still reachable".

   Notice that at any point of that tree, if the first column of a matrix is
   incoherent, then the branch leading to it can only be taken if the scrutinee
   is ill-typed.
   In the example above the only case where we have a matrix with an incoherent
   first column is when we consider [t1, t2, a] to be [U, S, ...]. However such
   a value would be ill-typed, so we can never actually get there.

   Checking the first column at each step of the recursion and making the
   conscious decision of "aborting" the algorithm whenever the first column
   becomes incoherent, allows us to retain the initial assumption in later
   stages of the algorithms.

   ---

   N.B. two patterns can be considered coherent even though they might not be of
   the same type.

   That's in part because we only care about the "head" of patterns and leave
   checking coherence of subpatterns for the next steps of the algorithm:
   ('a', 'b') and (1, ()) will be deemed coherent because they are both a tuples
   of arity 2 (we'll notice at a later stage the incoherence of 'a' and 1).

   But also because it can be hard/costly to determine exactly whether two
   patterns are of the same type or not (eg. in the example above with _ and S,
   but see also the module [Coherence_illustration] in
   testsuite/tests/basic-more/robustmatch.ml).

   For the moment our weak, loosely-syntactic, coherence check seems to be
   enough and we leave it to each user to consider (and document!) what happens
   when an "incoherence" is not detected by this check.
*)

(* Given the first column of a simplified matrix, this function first looks for
   a "discriminating" pattern on that column (i.e. a non-omega one) and then
   check that every other head pattern in the column is coherent with that one.
*)
let all_coherent column =
  let open Patterns.Head in
  let coherent_heads hp1 hp2 =
    match hp1.pat_desc, hp2.pat_desc with
    | Construct c, Construct c' ->
      c.cstr_consts = c'.cstr_consts
      && c.cstr_nonconsts = c'.cstr_nonconsts
    | Constant c1, Constant c2 -> begin
        match c1, c2 with
        | Const_char _, Const_char _
        | Const_int _, Const_int _
        | Const_int32 _, Const_int32 _
        | Const_int64 _, Const_int64 _
        | Const_nativeint _, Const_nativeint _
        | Const_float _, Const_float _
        | Const_string _, Const_string _ -> true
        | ( Const_char _
          | Const_int _
          | Const_int32 _
          | Const_int64 _
          | Const_nativeint _
          | Const_float _
          | Const_string _), _ -> false
      end
    | Tuple l1, Tuple l2 -> l1 = l2
    | Record (lbl1 :: _), Record (lbl2 :: _) ->
      Array.length lbl1.lbl_all = Array.length lbl2.lbl_all
    | Any, _
    | _, Any
    | Record [], Record []
    | Variant _, Variant _
    | Array _, Array _
    | Lazy, Lazy -> true
    | _, _ -> false
  in
  match
    List.find
      (function
       | { pat_desc = Any } -> false
       | _ -> true)
      column
  with
  | exception Not_found ->
    (* only omegas on the column: the column is coherent. *)
    true
  | discr_pat ->
    List.for_all (coherent_heads discr_pat) column

let first_column simplified_matrix =
  List.map (fun ((head, _args), _rest) -> head) simplified_matrix

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

(* Patterns p and q compatible means:
   there exists value V that matches both, However....

  The case of extension types is dubious, as constructor rebind permits
  that different constructors are the same (and are thus compatible).

  Compilation must take this into account, consider:

  type t = ..
  type t += A|B
  type t += C=A

  let f x y = match x,y with
  | true,A  -> '1'
  | _,C     -> '2'
  | false,A -> '3'
  | _,_     -> '_'

  As C is bound to A the value of f false A is '2' (and not '3' as it would
  be in the absence of rebinding).

  Not considering rebinding, patterns "false,A" and "_,C" are incompatible
  and the compiler can swap the second and third clause, resulting in the
  (more efficiently compiled) matching

  match x,y with
  | true,A  -> '1'
  | false,A -> '3'
  | _,C     -> '2'
  | _,_     -> '_'

  This is not correct: when C is bound to A, "f false A" returns '2' (not '3')


  However, diagnostics do not take constructor rebinding into account.
  Notice, that due to module abstraction constructor rebinding is hidden.

  module X : sig type t = .. type t += A|B end = struct
    type t = ..
    type t += A
    type t += B=A
  end

  open X

  let f x = match x with
  | A -> '1'
  | B -> '2'
  | _ -> '_'

  The second clause above will NOT (and cannot) be flagged as useless.

  Finally, there are two compatibility functions:
   compat p q      ---> 'syntactic compatibility, used for diagnostics.
   may_compat p q --->   a safe approximation of possible compat,
                         for compilation

*)


let is_absent tag row = row_field_repr (get_row_field tag !row) = Rabsent

let is_absent_pat d =
  match d.pat_desc with
  | Patterns.Head.Variant { tag; cstr_row; _ } -> is_absent tag cstr_row
  | _ -> false

let const_compare x y =
  match x,y with
  | Const_float f1, Const_float f2 ->
      Stdlib.compare (float_of_string f1) (float_of_string f2)
  | Const_string (s1, _, _), Const_string (s2, _, _) ->
      String.compare s1 s2
  | (Const_int _
    |Const_char _
    |Const_string (_, _, _)
    |Const_float _
    |Const_int32 _
    |Const_int64 _
    |Const_nativeint _
    ), _ -> Stdlib.compare x y

let records_args l1 l2 =
  (* Invariant: fields are already sorted by Typecore.type_label_a_list *)
  let rec combine r1 r2 l1 l2 = match l1,l2 with
  | [],[] -> List.rev r1, List.rev 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



module Compat
    (Constr:sig
      val equal :
          Types.constructor_description ->
            Types.constructor_description ->
              bool
    end) = struct

  let rec compat p q = match p.pat_desc,q.pat_desc with
(* Variables match any value *)
  | ((Tpat_any|Tpat_var _),_)
  | (_,(Tpat_any|Tpat_var _)) -> true
(* Structural induction *)
  | Tpat_alias (p,_,_,_),_      -> compat p q
  | _,Tpat_alias (q,_,_,_)      -> compat p q
  | Tpat_or (p1,p2,_),_ ->
      (compat p1 q || compat p2 q)
  | _,Tpat_or (q1,q2,_) ->
      (compat p q1 || compat p q2)
(* Constructors, with special case for extension *)
  | Tpat_construct (_, c1, ps1, _), Tpat_construct (_, c2, ps2, _) ->
      Constr.equal c1 c2 && compats ps1 ps2
(* More standard stuff *)
  | Tpat_variant(l1,op1, _), Tpat_variant(l2,op2,_) ->
      l1=l2 && ocompat op1 op2
  | Tpat_constant c1, Tpat_constant c2 ->
      const_compare c1 c2 = 0
  | Tpat_tuple ps, Tpat_tuple qs -> compats ps qs
  | Tpat_lazy p, Tpat_lazy q -> compat p q
  | 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
  | _,_  -> false

  and ocompat op oq = match op,oq with
  | None,None -> true
  | Some p,Some q -> compat p q
  | (None,Some _)|(Some _,None) -> false

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

end

module SyntacticCompat =
  Compat
    (struct
      let equal c1 c2 =  Types.equal_tag c1.cstr_tag c2.cstr_tag
    end)

let compat =  SyntacticCompat.compat
and compats = SyntacticCompat.compats

(* Due to (potential) rebinding, two extension constructors
   of the same arity type may equal *)

exception Empty (* Empty pattern *)

(****************************************)
(* Utilities for retrieving type paths  *)
(****************************************)

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

let get_constructor_type_path ty tenv =
  let ty = Ctype.expand_head tenv (clean_copy ty) in
  match get_desc ty with
  | Tconstr (path,_,_) -> path
  | _ -> assert false

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

(* Check top matching *)
let simple_match d h =
  let open Patterns.Head in
  match d.pat_desc, h.pat_desc with
  | Construct c1, Construct c2 ->
      Types.equal_tag c1.cstr_tag c2.cstr_tag
  | Variant { tag = t1; _ }, Variant { tag = t2 } ->
      t1 = t2
  | Constant c1, Constant c2 -> const_compare c1 c2 = 0
  | Lazy, Lazy -> true
  | Record _, Record _ -> true
  | Tuple len1, Tuple len2
  | Array len1, Array len2 -> len1 = len2
  | _, Any -> true
  | _, _ -> false



(* extract record fields as a whole *)
let record_arg ph =
  let open Patterns.Head in
  match ph.pat_desc with
  | Any -> []
  | Record args -> args
  | _ -> fatal_error "Parmatch.as_record"


let extract_fields lbls arg =
  let get_field pos arg =
    match List.find (fun (lbl,_) -> pos = lbl.lbl_pos) arg with
    | _, p -> p
    | exception Not_found -> omega
  in
  List.map (fun lbl -> get_field lbl.lbl_pos arg) lbls

(* Build argument list when p2 >= p1, where p1 is a simple pattern *)
let simple_match_args discr head args =
  let open Patterns.Head in
  match head.pat_desc with
  | Constant _ -> []
  | Construct _
  | Variant _
  | Tuple _
  | Array _
  | Lazy -> args
  | Record lbls ->  extract_fields (record_arg discr) (List.combine lbls args)
  | Any ->
      begin match discr.pat_desc with
      | Construct cstr -> Patterns.omegas cstr.cstr_arity
      | Variant { has_arg = true }
      | Lazy -> [Patterns.omega]
      | Record lbls ->  omega_list lbls
      | Array len
      | Tuple len -> Patterns.omegas len
      | Variant { has_arg = false }
      | Any
      | Constant _ -> []
      end

(* Consider a pattern matrix whose first column has been simplified to contain
   only _ or a head constructor
     | p1, r1...
     | p2, r2...
     | p3, r3...
     | ...

   We build a normalized /discriminating/ pattern from a pattern [q] by folding
   over the first column of the matrix, "refining" [q] as we go:

   - when we encounter a row starting with [Tuple] or [Lazy] then we
   can stop and return that head, as we cannot refine any further. Indeed,
   these constructors are alone in their signature, so they will subsume
   whatever other head we might find, as well as the head we're threading
   along.

   - when we find a [Record] then it is a bit more involved: it is also alone
   in its signature, however it might only be matching a subset of the
   record fields. We use these fields to refine our accumulator and keep going
   as another row might match on different fields.

   - rows starting with a wildcard do not bring any information, so we ignore
   them and keep going

   - if we encounter anything else (i.e. any other constructor), then we just
   stop and return our accumulator.
*)
let discr_pat q pss =
  let open Patterns.Head in
  let rec refine_pat acc = function
    | [] -> acc
    | ((head, _), _) :: rows ->
      match head.pat_desc with
      | Any -> refine_pat acc rows
      | Tuple _ | Lazy -> head
      | Record lbls ->
        (* N.B. we could make this case "simpler" by refining the record case
           using [all_record_args].
           In which case we wouldn't need to fold over the first column for
           records.
           However it makes the witness we generate for the exhaustivity warning
           less pretty. *)
        let fields =
          List.fold_right (fun lbl r ->
            if List.exists (fun l -> l.lbl_pos = lbl.lbl_pos) r then
              r
            else
              lbl :: r
          ) lbls (record_arg acc)
        in
        let d = { head with pat_desc = Record fields } in
        refine_pat d rows
      | _ -> acc
  in
  let q, _ = deconstruct q in
  match q.pat_desc with
  (* short-circuiting: clearly if we have anything other than [Record] or
     [Any] to start with, we're not going to be able refine at all. So
     there's no point going over the matrix. *)
  | Any | Record _ -> refine_pat q pss
  | _ -> 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,closed)} ->
    let args,rest = read_args omegas r in
    make_pat
      (Tpat_record
         (List.map2 (fun (lid, lbl,_) arg ->
           if
             erase_mutable &&
             (match lbl.lbl_mut with
             | Mutable -> true | Immutable -> false)
           then
             lid, lbl, omega
           else
             lid, lbl, arg)
            omegas args, closed))
      q.pat_type q.pat_env::
    rest
| {pat_desc = Tpat_construct (lid, c, omegas, _)} ->
    let args,rest = read_args omegas r in
    make_pat
      (Tpat_construct (lid, c, args, None))
      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
    let args = if erase_mutable then omegas else args 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 *)
| {pat_desc = (Tpat_var _ | Tpat_alias _ | Tpat_or _); _} ->
    fatal_error "Parmatch.set_args"

let set_args q r = do_set_args ~erase_mutable:false q r
and set_args_erase_mutable q r = do_set_args ~erase_mutable:true q r

(* Given a matrix of non-empty rows
   p1 :: r1...
   p2 :: r2...
   p3 :: r3...

   Simplify the first column [p1 p2 p3] by splitting all or-patterns.
   The result is a list of pairs
     ((pattern head, arguments), rest of row)

   For example,
     x :: r1
     (Some _) as y :: r2
     (None as x) as y :: r3
     (Some x | (None as x)) :: r4
   becomes
     ((   _ , [ ] ), r1)
     (( Some, [_] ), r2)
     (( None, [ ] ), r3)
     (( Some, [x] ), r4)
     (( None, [ ] ), r4)
 *)
let simplify_head_pat ~add_column p ps k =
  let rec simplify_head_pat p ps k =
    match Patterns.General.(view p |> strip_vars).pat_desc with
    | `Or (p1,p2,_) -> simplify_head_pat p1 ps (simplify_head_pat p2 ps k)
    | #Patterns.Simple.view as view ->
       add_column (Patterns.Head.deconstruct { p with pat_desc = view }) ps k
  in simplify_head_pat p ps k

let rec simplify_first_col = function
  | [] -> []
  | [] :: _ -> assert false (* the rows are non-empty! *)
  | (p::ps) :: rows ->
      let add_column p ps k = (p, ps) :: k in
      simplify_head_pat ~add_column p ps (simplify_first_col rows)


(* Builds the specialized matrix of [pss] according to the discriminating
   pattern head [d].
   See section 3.1 of http://moscova.inria.fr/~maranget/papers/warn/warn.pdf

   NOTES:
   - we are polymorphic on the type of matrices we work on, in particular a row
   might not simply be a [pattern list]. That's why we have the [extend_row]
   parameter.
*)
let build_specialized_submatrix ~extend_row discr pss =
  let rec filter_rec = function
    | ((head, args), ps) :: pss ->
        if simple_match discr head
        then extend_row (simple_match_args discr head args) ps :: filter_rec pss
        else filter_rec pss
    | _ -> [] in
  filter_rec pss

(* The "default" and "specialized" matrices of a given matrix.
   See section 3.1 of http://moscova.inria.fr/~maranget/papers/warn/warn.pdf .
*)
type 'matrix specialized_matrices = {
  default : 'matrix;
  constrs : (Patterns.Head.t * 'matrix) list;
}

(* Consider a pattern matrix whose first column has been simplified
   to contain only _ or a head constructor
     | p1, r1...
     | p2, r2...
     | p3, r3...
     | ...

   We split this matrix into a list of /specialized/ sub-matrices, one for
   each head constructor appearing in the first column. For each row whose
   first column starts with a head constructor, remove this head
   column, prepend one column for each argument of the constructor,
   and add the resulting row in the sub-matrix corresponding to this
   head constructor.

   Rows whose left column is omega (the Any pattern _) may match any
   head constructor, so they are added to all sub-matrices.

   In the case where all the rows in the matrix have an omega on their first
   column, then there is only one /specialized/ sub-matrix, formed of all these
   omega rows.
   This matrix is also called the /default/ matrix.

   See the documentation of [build_specialized_submatrix] for an explanation of
   the [extend_row] parameter.
*)
let build_specialized_submatrices ~extend_row discr rows =
  let extend_group discr p args r rs =
    let r = extend_row (simple_match_args discr p args) r in
    (discr, r :: rs)
  in

  (* insert a row of head [p] and rest [r] into the right group

     Note: with this implementation, the order of the groups
     is the order of their first row in the source order.
     This is a nice property to get exhaustivity counter-examples
     in source order.
  *)
  let rec insert_constr head args r = function
    | [] ->
      (* if no group matched this row, it has a head constructor that
         was never seen before; add a new sub-matrix for this head *)
      [extend_group head head args r []]
    | (q0,rs) as bd::env ->
      if simple_match q0 head
      then extend_group q0 head args r rs :: env
      else bd :: insert_constr head args r env
  in

  (* insert a row of head omega into all groups *)
  let insert_omega r env =
    List.map (fun (q0,rs) -> extend_group q0 Patterns.Head.omega [] r rs) env
  in

  let rec form_groups constr_groups omega_tails = function
    | [] -> (constr_groups, omega_tails)
    | ((head, args), tail) :: rest ->
        match head.pat_desc with
        | Patterns.Head.Any ->
            (* note that calling insert_omega here would be wrong
               as some groups may not have been formed yet, if the
               first row with this head pattern comes after in the list *)
            form_groups constr_groups (tail :: omega_tails) rest
        | _ ->
            form_groups
              (insert_constr head args tail constr_groups) omega_tails rest
  in

  let constr_groups, omega_tails =
    let initial_constr_group =
      let open Patterns.Head in
      match discr.pat_desc with
      | Record _ | Tuple _ | Lazy ->
        (* [discr] comes from [discr_pat], and in this case subsumes any of the
           patterns we could find on the first column of [rows]. So it is better
           to use it for our initial environment than any of the normalized
           pattern we might obtain from the first column. *)
        [discr,[]]
      | _ -> []
    in
    form_groups initial_constr_group [] rows
  in

  (* groups are accumulated in reverse order;
     we restore the order of rows in the source code *)
  let default = List.rev omega_tails in
  let constrs =
    List.fold_right insert_omega omega_tails constr_groups
    |> List.map (fun (discr, rs) -> (discr, List.rev rs))
  in
  { default; constrs; }

(* Variant related functions *)

let set_last a =
  let rec loop = function
    | [] -> assert false
    | [_] -> [Patterns.General.erase a]
    | x::l -> x :: loop l
  in
  function
  | (_, []) -> (Patterns.Head.deconstruct a, [])
  | (first, row) -> (first, loop row)

(* mark constructor lines for failure when they are incomplete *)
let mark_partial =
  let zero = make_pat (`Constant (Const_int 0)) Ctype.none Env.empty in
  List.map (fun ((hp, _), _ as ps) ->
    match hp.pat_desc with
    | Patterns.Head.Any -> ps
    | _ -> set_last zero ps
  )

let close_variant env row =
  let Row {fields; more; name=orig_name; closed; fixed} = row_repr row in
  let name, static =
    List.fold_left
      (fun (nm, static) (_tag,f) ->
        match row_field_repr f with
        | Reither(_, _, false) ->
            (* fixed=false means that this tag is not explicitly matched *)
            link_row_field_ext ~inside:f rf_absent;
            (None, static)
        | Reither (_, _, true) -> (nm, false)
        | Rabsent | Rpresent _ -> (nm, static))
      (orig_name, true) fields in
  if not closed || name != orig_name then begin
    let more' = if static then Btype.newgenty Tnil else Btype.newgenvar () in
    (* this unification cannot fail *)
    Ctype.unify env more
      (Btype.newgenty
         (Tvariant
            (create_row ~fields:[] ~more:more'
               ~closed:true ~name ~fixed)))
  end

(*
  Check whether the first column of env makes up a complete signature or
  not. We work on the discriminating pattern heads of each sub-matrix: they
  are not omega/Any.
*)
let full_match closing env =  match env with
| [] -> false
| (discr, _) :: _ ->
  let open Patterns.Head in
  match discr.pat_desc with
  | Any -> assert false
  | Construct { cstr_tag = Cstr_extension _ ; _ } -> false
  | Construct c -> List.length env = c.cstr_consts + c.cstr_nonconsts
  | Variant { type_row; _ } ->
      let fields =
        List.map
          (fun (d, _) ->
            match d.pat_desc with
            | Variant { tag } -> tag
            | _ -> assert false)
          env
      in
      let row = type_row () in
      if closing && not (Btype.has_fixed_explanation row) then
        (* closing=true, we are considering the variant as closed *)
        List.for_all
          (fun (tag,f) ->
            match 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_fields row)
      else
        row_closed row &&
        List.for_all
          (fun (tag,f) ->
            row_field_repr f = Rabsent || List.mem tag fields)
          (row_fields row)
  | Constant Const_char _ ->
      List.length env = 256
  | Constant _
  | Array _ -> false
  | Tuple _
  | Record _
  | Lazy -> true

(* Written as a non-fragile matching, PR#7451 originated from a fragile matching
   below. *)
let should_extend ext env = match ext with
| None -> false
| Some ext -> begin match env with
  | [] -> assert false
  | (p,_)::_ ->
      let open Patterns.Head in
      begin match p.pat_desc with
      | Construct {cstr_tag=(Cstr_constant _|Cstr_block _|Cstr_unboxed)} ->
          let path = get_constructor_type_path p.pat_type p.pat_env in
          Path.same path ext
      | Construct {cstr_tag=(Cstr_extension _)} -> false
      | Constant _ | Tuple _ | Variant _ | Record _ | Array _ | Lazy -> false
      | Any -> assert false
      end
end

(* build a pattern from a constructor description *)
let pat_of_constr ex_pat cstr =
  {ex_pat with pat_desc =
   Tpat_construct (mknoloc (Longident.Lident cstr.cstr_name),
                   cstr, omegas cstr.cstr_arity, None)}

let orify x y = make_pat (Tpat_or (x, y, None)) x.pat_type x.pat_env

let rec orify_many = function
| [] -> assert false
| [x] -> x
| x :: xs -> orify x (orify_many xs)

(* build an or-pattern from a constructor list *)
let pat_of_constrs ex_pat cstrs =
  let ex_pat = Patterns.Head.to_omega_pattern ex_pat in
  if cstrs = [] then raise Empty else
  orify_many (List.map (pat_of_constr ex_pat) cstrs)

let pats_of_type env ty =
  match Ctype.extract_concrete_typedecl env ty with
  | Typedecl (_, path, {type_kind = Type_variant _ | Type_record _}) ->
      begin match Env.find_type_descrs path env with
      | Type_variant (cstrs,_) when List.length cstrs <= 1 ||
        (* Only explode when all constructors are GADTs *)
        List.for_all (fun cd -> cd.cstr_generalized) cstrs ->
          List.map (pat_of_constr (make_pat Tpat_any ty env)) cstrs
      | Type_record (labels, _) ->
          let fields =
            List.map (fun ld ->
              mknoloc (Longident.Lident ld.lbl_name), ld, omega)
              labels
          in
          [make_pat (Tpat_record (fields, Closed)) ty env]
      | _ -> [omega]
      end
  | Has_no_typedecl ->
      begin match get_desc (Ctype.expand_head env ty) with
        Ttuple tl ->
          [make_pat (Tpat_tuple (omegas (List.length tl))) ty env]
      | _ -> [omega]
      end
  | Typedecl (_, _, {type_kind = Type_abstract _ | Type_open})
  | May_have_typedecl -> [omega]

let get_variant_constructors env ty =
  match Ctype.extract_concrete_typedecl env ty with
  | Typedecl (_, path, {type_kind = Type_variant _}) ->
      begin match Env.find_type_descrs path env with
      | Type_variant (cstrs,_) -> cstrs
      | _ -> fatal_error "Parmatch.get_variant_constructors"
      end
  | _ -> fatal_error "Parmatch.get_variant_constructors"

module ConstructorSet = Set.Make(struct
  type t = constructor_description
  let compare c1 c2 = String.compare c1.cstr_name c2.cstr_name
end)

(* Sends back a pattern that complements the given constructors used_constrs *)
let complete_constrs constr used_constrs =
  let c = constr.pat_desc in
  let constrs = get_variant_constructors constr.pat_env c.cstr_res in
  let used_constrs = ConstructorSet.of_list used_constrs in
  let others =
    List.filter
      (fun cnstr -> not (ConstructorSet.mem cnstr used_constrs))
      constrs in
  (* Split constructors to put constant ones first *)
  let const, nonconst =
    List.partition (fun cnstr -> cnstr.cstr_arity = 0) others in
  const @ nonconst

let build_other_constrs env p =
  let open Patterns.Head in
  match p.pat_desc with
  | Construct ({ cstr_tag = Cstr_extension _ }) -> extra_pat
  | Construct
      ({ cstr_tag = Cstr_constant _ | Cstr_block _ | Cstr_unboxed } as c) ->
        let constr = { p with pat_desc = c } in
        let get_constr q =
          match q.pat_desc with
          | Construct c -> c
          | _ -> fatal_error "Parmatch.get_constr" in
        let used_constrs =  List.map (fun (p,_) -> get_constr p) env in
        pat_of_constrs p (complete_constrs constr used_constrs)
  | _ -> extra_pat

(* 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
  the first column of env
*)

let some_private_tag = "<some private tag>"

let build_other ext env =
  match env with
  | [] -> omega
  | (d, _) :: _ ->
      let open Patterns.Head in
      match d.pat_desc with
      | Construct { cstr_tag = Cstr_extension _ } ->
          (* let c = {c with cstr_name = "*extension*"} in *) (* PR#7330 *)
          make_pat
            (Tpat_var (Ident.create_local "*extension*",
                       {txt="*extension*"; loc = d.pat_loc},
                       Uid.internal_not_actually_unique))
            Ctype.none Env.empty
      | Construct _ ->
          begin match ext with
          | Some ext ->
              if Path.same ext (get_constructor_type_path d.pat_type d.pat_env)
              then
                extra_pat
              else
                build_other_constrs env d
          | _ ->
              build_other_constrs env d
          end
      | Variant { cstr_row; type_row } ->
          let tags =
            List.map
              (fun (d, _) ->
                match d.pat_desc with
                | Variant { tag } -> tag
                | _ -> assert false)
              env
            in
            let make_other_pat tag const =
              let arg = if const then None else Some Patterns.omega in
              make_pat (Tpat_variant(tag, arg, cstr_row)) d.pat_type d.pat_env
            in
            let row = type_row () in
            begin match
              List.fold_left
                (fun others (tag,f) ->
                  if List.mem tag tags then others else
                  match 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_fields row)
            with
              [] ->
                let tag =
                  if Btype.has_fixed_explanation row then some_private_tag else
                  let rec mktag tag =
                    if List.mem tag tags then mktag (tag ^ "'") else tag in
                  mktag "AnyOtherTag"
                in make_other_pat tag true
            | pat::other_pats ->
                List.fold_left
                  (fun p_res pat ->
                    make_pat (Tpat_or (pat, p_res, None)) d.pat_type d.pat_env)
                  pat other_pats
            end
      | Constant Const_char _ ->
          let all_chars =
            List.map
              (fun (p,_) -> match p.pat_desc with
              | 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)) d.pat_type d.pat_env
          in
          let rec try_chars = function
            | [] -> Patterns.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]
      | Constant Const_int _ ->
          build_other_constant
            (function Constant(Const_int i) -> i | _ -> assert false)
            (function i -> Tpat_constant(Const_int i))
            0 succ d env
      | Constant Const_int32 _ ->
          build_other_constant
            (function Constant(Const_int32 i) -> i | _ -> assert false)
            (function i -> Tpat_constant(Const_int32 i))
            0l Int32.succ d env
      | Constant Const_int64 _ ->
          build_other_constant
            (function Constant(Const_int64 i) -> i | _ -> assert false)
            (function i -> Tpat_constant(Const_int64 i))
            0L Int64.succ d env
      | Constant Const_nativeint _ ->
          build_other_constant
            (function Constant(Const_nativeint i) -> i | _ -> assert false)
            (function i -> Tpat_constant(Const_nativeint i))
            0n Nativeint.succ d env
      | Constant Const_string _ ->
          build_other_constant
            (function Constant(Const_string (s, _, _)) -> String.length s
                    | _ -> assert false)
            (function i ->
               Tpat_constant
                 (Const_string(String.make i '*',Location.none,None)))
            0 succ d env
      | Constant Const_float _ ->
          build_other_constant
            (function 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) d env
      | Array _ ->
          let all_lengths =
            List.map
              (fun (p,_) -> match p.pat_desc with
              | Array len -> len
              | _ -> 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)) d.pat_type d.pat_env in
          try_arrays 0
      | _ -> Patterns.omega

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 (fun (_,_,x) -> x) lps)
  | Tpat_lazy p
    -> has_instance p

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

(*
  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)

   ---

   In two places in the following function, we check the coherence of the first
   column of (pss + qs).
   If it is incoherent, then we exit early saying that (pss + qs) is not
   satisfiable (which is equivalent to saying "oh, we shouldn't have considered
   that branch, no good result came come from here").

   But what happens if we have a coherent but ill-typed column?
   - we might end up returning [false], which is equivalent to noticing the
   incompatibility: clearly this is fine.
   - if we end up returning [true] then we're saying that [qs] is useful while
   it is not. This is sad but not the end of the world, we're just allowing dead
   code to survive.
*)
let rec satisfiable pss qs = match pss with
| [] -> has_instances qs
| _  ->
    match qs with
    | [] -> false
    | q::qs ->
       match Patterns.General.(view q |> strip_vars).pat_desc with
       | `Or(q1,q2,_) ->
          satisfiable pss (q1::qs) || satisfiable pss (q2::qs)
       | `Any ->
          let pss = simplify_first_col pss in
          if not (all_coherent (first_column pss)) then
            false
          else begin
            let { default; constrs } =
              let q0 = discr_pat Patterns.Simple.omega pss in
              build_specialized_submatrices ~extend_row:(@) q0 pss in
            if not (full_match false constrs) then
              satisfiable default qs
            else
              List.exists
                (fun (p,pss) ->
                   not (is_absent_pat p) &&
                   satisfiable pss
                     (simple_match_args p Patterns.Head.omega [] @ qs))
                constrs
          end
       | `Variant (l,_,r) when is_absent l r -> false
       | #Patterns.Simple.view as view ->
          let q = { q with pat_desc = view } in
          let pss = simplify_first_col pss in
          let hq, qargs = Patterns.Head.deconstruct q in
          if not (all_coherent (hq :: first_column pss)) then
            false
          else begin
              let q0 = discr_pat q pss in
              satisfiable (build_specialized_submatrix ~extend_row:(@) q0 pss)
                (simple_match_args q0 hq qargs @ qs)
            end

(* While [satisfiable] only checks whether the last row of [pss + qs] is
   satisfiable, this function returns the (possibly empty) list of vectors [es]
   which verify:
     1- for all ps in pss, ps # es (ps and es are not compatible)
     2- qs <= es                   (es matches qs)

   This is done to enable GADT handling

   For considerations regarding the coherence check, see the comment on
   [satisfiable] above.  *)
let rec list_satisfying_vectors pss qs =
  match pss with
  | [] -> if has_instances qs then [qs] else []
  | _  ->
      match qs with
      | [] -> []
      | q :: qs ->
         match Patterns.General.(view q |> strip_vars).pat_desc with
         | `Or(q1,q2,_) ->
            list_satisfying_vectors pss (q1::qs) @
            list_satisfying_vectors pss (q2::qs)
         | `Any ->
            let pss = simplify_first_col pss in
            if not (all_coherent (first_column pss)) then
              []
            else begin
              let q0 = discr_pat Patterns.Simple.omega pss in
              let wild default_matrix p =
                List.map (fun qs -> p::qs)
                  (list_satisfying_vectors default_matrix qs)
              in
              match build_specialized_submatrices ~extend_row:(@) q0 pss with
              | { default; constrs = [] } ->
                  (* first column of pss is made of variables only *)
                  wild default omega
              | { default; constrs = ((p,_)::_ as constrs) } ->
                  let for_constrs () =
                    List.flatten (
                      List.map (fun (p,pss) ->
                        if is_absent_pat p then
                          []
                        else
                          let witnesses =
                            list_satisfying_vectors pss
                              (simple_match_args p Patterns.Head.omega [] @ qs)
                          in
                          let p = Patterns.Head.to_omega_pattern p in
                          List.map (set_args p) witnesses
                      ) constrs
                    )
                  in
                  if full_match false constrs then for_constrs () else
                  begin match p.pat_desc with
                  | Construct _ ->
                      (* activate this code
                         for checking non-gadt constructors *)
                      wild default (build_other_constrs constrs p)
                      @ for_constrs ()
                  | _ ->
                      wild default Patterns.omega
                  end
          end
      | `Variant (l, _, r) when is_absent l r -> []
      | #Patterns.Simple.view as view ->
          let q = { q with pat_desc = view } in
          let hq, qargs = Patterns.Head.deconstruct q in
          let pss = simplify_first_col pss in
          if not (all_coherent (hq :: first_column pss)) then
            []
          else begin
            let q0 = discr_pat q pss in
            List.map (set_args (Patterns.Head.to_omega_pattern q0))
              (list_satisfying_vectors
                 (build_specialized_submatrix ~extend_row:(@) q0 pss)
                 (simple_match_args q0 hq qargs @ qs))
          end

(******************************************)
(* 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)
*)

let rec do_match pss qs = match qs with
| [] ->
    begin match pss  with
    | []::_ -> true
    | _ -> false
    end
| q::qs -> match Patterns.General.(view q |> strip_vars).pat_desc with
  | `Or (q1,q2,_) ->
      do_match pss (q1::qs) || do_match pss (q2::qs)
  | `Any ->
      let rec remove_first_column = function
        | (_::ps)::rem -> ps::remove_first_column rem
        | _ -> []
      in
      do_match (remove_first_column pss) qs
  | #Patterns.Simple.view as view ->
      let q = { q with pat_desc = view } in
      let q0, qargs = Patterns.Head.deconstruct q in
      let pss = simplify_first_col pss in
      (* [pss] will (or won't) match [q0 :: qs] regardless of the coherence of
         its first column. *)
      do_match
        (build_specialized_submatrix ~extend_row:(@) q0 pss)
        (qargs @ qs)

(*
let print_pat pat =
  let rec string_of_pat pat =
    match pat.pat_desc with
        Tpat_var _ -> "v"
      | Tpat_any -> "_"
      | Tpat_alias (p, x) -> Printf.sprintf "(%s) as ?"  (string_of_pat p)
      | Tpat_constant n -> "0"
      | Tpat_construct (_, lid, _) ->
        Printf.sprintf "%s" (String.concat "." (Longident.flatten lid.txt))
      | Tpat_lazy p ->
        Printf.sprintf "(lazy %s)" (string_of_pat p)
      | Tpat_or (p1,p2,_) ->
        Printf.sprintf "(%s | %s)" (string_of_pat p1) (string_of_pat p2)
      | Tpat_tuple list ->
        Printf.sprintf "(%s)" (String.concat "," (List.map string_of_pat list))
      | Tpat_variant (_, _, _) -> "variant"
      | Tpat_record (_, _) -> "record"
      | Tpat_array _ -> "array"
  in
  Printf.fprintf stderr "PAT[%s]\n%!" (string_of_pat pat)
*)

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

  This function should be called for exhaustiveness check only.
*)
let rec exhaust (ext:Path.t option) pss n = match pss with
| []    ->  Seq.return (omegas n)
| []::_ ->  Seq.empty
| [(p :: ps)] -> exhaust_single_row ext p ps n
| pss   -> specialize_and_exhaust ext pss n

and exhaust_single_row ext p ps n =
  (* Shortcut: in the single-row case p :: ps we know that all
     counter-examples are either of the form
       counter-example(p) :: omegas
     or
       p :: counter-examples(ps)

     This is very interesting in the case where p contains
     or-patterns, as the non-shortcut path below would do a separate
     search for each constructor of the or-pattern, which can lead to
     an exponential blowup on examples such as

       | (A|B), (A|B), (A|B), (A|B) -> foo

     Note that this shortcut also applies to examples such as

       | A, A, A, A -> foo | (A|B), (A|B), (A|B), (A|B) -> bar

     thanks to the [get_mins] preprocessing step which will drop the
     first row (subsumed by the second). Code with this shape does
     occur naturally when people want to avoid fragile pattern
     matches: if A and B are the only two constructors, this is the
     best way to make a non-fragile distinction between "all As" and
     "at least one B".
  *)
  List.to_seq [Some p; None] |> Seq.flat_map
    (function
      | Some p ->
          let sub_witnesses = exhaust ext [ps] (n - 1) in
          Seq.map (fun row -> p :: row) sub_witnesses
      | None ->
          (* note: calling [exhaust] recursively of p would
             result in an infinite loop in the case n=1 *)
          let p_witnesses = specialize_and_exhaust ext [[p]] 1 in
          Seq.map (fun p_row -> p_row @ omegas (n - 1)) p_witnesses
    )

and specialize_and_exhaust ext pss n =
  let pss = simplify_first_col pss in
  if not (all_coherent (first_column pss)) then
    (* We're considering an ill-typed branch, we won't actually be able to
       produce a well typed value taking that branch. *)
    Seq.empty
  else begin
    (* Assuming the first column is ill-typed but considered coherent, we
       might end up producing an ill-typed witness of non-exhaustivity
       corresponding to the current branch.

       If [exhaust] has been called by [do_check_partial], then the witnesses
       produced get typechecked and the ill-typed ones are discarded.

       If [exhaust] has been called by [do_check_fragile], then it is possible
       we might fail to warn the user that the matching is fragile. See for
       example testsuite/tests/warnings/w04_failure.ml. *)
    let q0 = discr_pat Patterns.Simple.omega pss in
    match build_specialized_submatrices ~extend_row:(@) q0 pss with
    | { default; constrs = [] } ->
        (* first column of pss is made of variables only *)
        let sub_witnesses = exhaust ext default (n-1) in
        let q0 = Patterns.Head.to_omega_pattern q0 in
        Seq.map (fun row -> q0::row) sub_witnesses
    | { default; constrs } ->
        let try_non_omega (p,pss) =
          if is_absent_pat p then
            Seq.empty
          else
            let sub_witnesses =
              exhaust
                ext pss
                (List.length (simple_match_args p Patterns.Head.omega [])
                 + n - 1)
            in
            let p = Patterns.Head.to_omega_pattern p in
            Seq.map (set_args p) sub_witnesses
        in
        let try_omega () =
          if full_match false constrs && not (should_extend ext constrs) then
            Seq.empty
          else
            let sub_witnesses = exhaust ext default (n-1) in
            match build_other ext constrs with
            | exception Empty ->
                (* cannot occur, since constructors don't make
                   a full signature *)
                fatal_error "Parmatch.exhaust"
            | p ->
                Seq.map (fun tail -> p :: tail) sub_witnesses
        in
        (* Lazily compute witnesses for all constructor submatrices
           (Some constr_mat) then the wildcard/default submatrix (None).
           Note that the call to [try_omega ()] is delayed to after
           all constructor matrices have been traversed. *)
        List.map (fun constr_mat -> Some constr_mat) constrs @ [None]
        |> List.to_seq
        |> Seq.flat_map
          (function
            | Some constr_mat -> try_non_omega constr_mat
            | None -> try_omega ())
  end

let exhaust ext pss n =
  exhaust ext pss n
  |> Seq.map (function
     | [x] -> x
     | _ -> assert false)

(*
   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 pss = simplify_first_col pss in
      if not (all_coherent (first_column pss)) then
        true
      else begin
        let q0 = discr_pat Patterns.Simple.omega pss in
        match build_specialized_submatrices ~extend_row:(@) q0 pss with
        | { default; constrs = [] } -> pressure_variants tdefs default
        | { default; constrs } ->
            let rec try_non_omega = function
              | (_p,pss) :: rem ->
                  let ok = pressure_variants tdefs pss in
                  (* The order below matters : we want [pressure_variants] to be
                    called on all the specialized submatrices because we might
                    close some variant in any of them regardless of whether [ok]
                    is true for [pss] or not *)
                  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 default
            else
              let full = full_match true constrs in
              let ok =
                if full then
                  try_non_omega constrs
                else begin
                  let { constrs = partial_constrs; _ } =
                    build_specialized_submatrices ~extend_row:(@) q0
                      (mark_partial pss)
                  in
                  try_non_omega partial_constrs
                end
              in
              begin match constrs, tdefs with
              | [], _
              | _, None -> ()
              | (d, _) :: _, Some env ->
                match d.pat_desc with
                | Variant { type_row; _ } ->
                  let row = type_row () in
                  if Btype.has_fixed_explanation row
                  || pressure_variants None default then ()
                  else close_variant env row
                | _ -> ()
              end;
              ok
      end


(* Yet another satisfiable function *)

(*
   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  (* Mixed, with list of useless ones *)



(* this row type enable column processing inside the matrix
    - left  ->  elements not to be processed,
    - right ->  elements to be processed
*)
type usefulness_row =
  {no_ors : pattern list ; ors : pattern list ; active : pattern 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 is_var p = match Patterns.General.(view p |> strip_vars).pat_desc with
| `Any -> 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

let rec simplify_first_usefulness_col = function
  | [] -> []
  | row :: rows ->
    match row.active with
    | [] -> assert false (* the rows are non-empty! *)
    | p :: ps ->
      let add_column p ps k =
        (p, { row with active = ps }) :: k in
      simplify_head_pat ~add_column p ps
        (simplify_first_usefulness_col rows)

(* Back to normal matrices *)
let make_vector r = List.rev 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 partitioned,  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 ->
    begin match Patterns.General.(view q |> strip_vars).pat_desc with
    | `Any ->
        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)
    | `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)
    | `Variant (l,_,r) when is_absent l r -> (* Ah Jacques... *)
        Unused
    | #Patterns.Simple.view as view ->
        let q = { q with pat_desc = view } in
        (* standard case, filter matrix *)
        let pss = simplify_first_usefulness_col pss in
        let hq, args = Patterns.Head.deconstruct q in
        (* The handling of incoherent matrices is kept in line with
           [satisfiable] *)
        if not (all_coherent (hq :: first_column pss)) then
          Unused
        else begin
          let q0 = discr_pat q pss in
          every_satisfiables
            (build_specialized_submatrix q0 pss
              ~extend_row:(fun ps r -> { r with active = ps @ r.active }))
            {qs with active=simple_match_args q0 hq args @ rem}
        end
    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) -> const_compare c1 c2 = 0
  | Tpat_construct(_,c1,ps,_), Tpat_construct(_,c2,qs,_) ->
      Types.equal_tag 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] removes the elements that are followed by a smaller element.
     An element that is preceded by a smaller element may stay in the list.
     We thus do two passes on the list, which is returned reversed
     the first time. *)
  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 are 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 const_compare c1 c2 = 0 -> 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 (lid,c1,ps1,_), Tpat_construct (_,c2,ps2,_)
      when  Types.equal_tag c1.cstr_tag c2.cstr_tag  ->
        let rs = lubs ps1 ps2 in
        make_pat (Tpat_construct (lid, c1, rs, None))
          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,closed),Tpat_record (l2,_) ->
    let rs = record_lubs l1 l2 in
    make_pat (Tpat_record (rs, closed)) 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 rec lub_rec l1 l2 = match l1,l2 with
  | [],_ -> l2
  | _,[] -> l1
  | (lid1, lbl1,p1)::rem1, (lid2, lbl2,p2)::rem2 ->
      if lbl1.lbl_pos < lbl2.lbl_pos then
        (lid1, lbl1,p1)::lub_rec rem1 l2
      else if lbl2.lbl_pos < lbl1.lbl_pos  then
        (lid2, lbl2,p2)::lub_rec l1 rem2
      else
        (lid1, 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 =
  ignore (pressure_variants
            (Some tdefs)
            (List.map (fun p -> [p; omega]) patl))

let pressure_variants_in_computation_pattern tdefs patl =
  let add_row pss p_opt =
    match p_opt with
    | None -> pss
    | Some p -> p :: pss
  in
  let val_pss, exn_pss =
    List.fold_right (fun pat (vpss, epss)->
      let (vp, ep) = split_pattern pat in
      add_row vpss vp, add_row epss ep
    ) patl ([], [])
  in
  pressure_variants tdefs val_pss;
  pressure_variants tdefs exn_pss

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

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

let rec initial_matrix = function
    [] -> []
  | {has_guard=true} :: rem -> initial_matrix rem
  | {has_guard=false; pattern=p} :: rem -> [p] :: initial_matrix rem

(*
   Build up a working pattern matrix by keeping
   only the patterns which are guarded
*)
let rec initial_only_guarded = function
  | [] -> []
  | { has_guard = false; _} :: rem ->
      initial_only_guarded rem
  | { pattern = pat; _ } :: rem ->
      [pat] :: initial_only_guarded rem


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

(* Whether the counter-example contains an extension pattern *)
let contains_extension pat =
  exists_pattern
    (function
     | {pat_desc=Tpat_var (_, {txt="*extension*"}, _)} -> true
     | _ -> false)
    pat

let do_check_partial ~pred 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
    | [] -> ()
    | _  ->
      if Warnings.is_active Warnings.All_clauses_guarded then
        Location.prerr_warning loc Warnings.All_clauses_guarded
    end ;
    Partial
| ps::_  ->
    let counter_examples =
      exhaust None pss (List.length ps) |> Seq.filter_map pred in
    match counter_examples () with
    | Seq.Nil -> Total
    | Seq.Cons (v, _rest) ->
      if Warnings.is_active (Warnings.Partial_match "") then begin
        let errmsg =
          try
            let buf = Buffer.create 16 in
            let fmt = Format.formatter_of_buffer buf in
            Format.fprintf fmt "%a@?" Printpat.pretty_pat v;
            if do_match (initial_only_guarded casel) [v] then
              Buffer.add_string buf
                "\n(However, some guarded clause may match this value.)";
            if contains_extension v then
              Buffer.add_string buf
                "\nMatching over values of extensible variant types \
                   (the *extension* above)\n\
              must include a wild card pattern in order to be exhaustive."
            ;
            Buffer.contents buf
          with _ ->
            ""
        in
        Location.prerr_warning loc (Warnings.Partial_match errmsg)
      end;
      Partial

(*****************)
(* 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_unit ||
    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 _|Cstr_unboxed)},
                 ps, _) ->
    let path = get_constructor_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_extension _}, 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 exhaustivity check per datatype, considering that
      the type is extended.
*)

let do_check_fragile loc casel pss =
  let exts =
    List.fold_left
      (fun r c -> collect_paths_from_pat r c.pattern)
      [] casel in
  match exts with
  | [] -> ()
  | _ -> match pss with
    | [] -> ()
    | ps::_ ->
        List.iter
          (fun ext ->
            let witnesses = exhaust (Some ext) pss (List.length ps) in
            match witnesses () with
            | Seq.Nil ->
                Location.prerr_warning
                  loc
                  (Warnings.Fragile_match (Path.name ext))
            | Seq.Cons _ -> ())
          exts

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

let check_unused pred casel =
  if Warnings.is_active Warnings.Redundant_case
  || List.exists (fun vc -> vc.needs_refute) casel then
    let rec do_rec pref = function
      | [] -> ()
      | {pattern=q; has_guard; needs_refute=refute} :: rem ->
          let qs = [q] in
            begin try
              let pss =
                (* prev was accumulated in reverse order;
                   restore source order to get ordered counter-examples *)
                List.rev pref
                |> List.filter (compats qs)
                |> get_mins le_pats in
              (* First look for redundant or partially redundant patterns *)
              let r = every_satisfiables (make_rows pss) (make_row qs) in
              (* Do not warn for unused [pat -> .] *)
              if r = Unused && refute then () else
              let r =
                (* Do not refine if either:
                   - we already know the clause is unused
                   - the clause under consideration is not a refutation clause
                     and either:
                     + there are no other lines
                     + we do not care whether the types prevent this clause to
                       be reached.
                     If the clause under consideration *is* a refutation clause
                     then we do need to check more carefully whether it can be
                     refuted or not.  *)
                let skip =
                  r = Unused || (not refute && pref = []) ||
                  not(refute || Warnings.is_active Warnings.Unreachable_case) in
                if skip then r else
                (* Then look for empty patterns *)
                let sfs = list_satisfying_vectors pss qs in
                if sfs = [] then Unused else
                let sfs =
                  List.map (function [u] -> u | _ -> assert false) sfs in
                let u = orify_many sfs in
                (*Format.eprintf "%a@." pretty_val u;*)
                let pattern = {u with pat_loc = q.pat_loc} in
                match pred refute pattern with
                  None when not refute ->
                    Location.prerr_warning q.pat_loc Warnings.Unreachable_case;
                    Used
                | _ -> r
              in
              match r with
              | Unused ->
                  Location.prerr_warning
                    q.pat_loc Warnings.Redundant_case
              | Upartial ps ->
                  List.iter
                    (fun p ->
                      Location.prerr_warning
                        p.pat_loc Warnings.Redundant_subpat)
                    ps
              | Used -> ()
            with Empty | Not_found -> assert false
            end ;

          if has_guard 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

let inactive ~partial pat =
  match partial with
  | Partial -> false
  | Total -> begin
      let rec loop pat =
        match pat.pat_desc with
        | Tpat_lazy _ | Tpat_array _ ->
          false
        | Tpat_any | Tpat_var _ | Tpat_variant (_, None, _) ->
            true
        | Tpat_constant c -> begin
            match c with
            | Const_string _
            | Const_int _ | Const_char _ | Const_float _
            | Const_int32 _ | Const_int64 _ | Const_nativeint _ -> true
          end
        | Tpat_tuple ps | Tpat_construct (_, _, ps, _) ->
            List.for_all (fun p -> loop p) ps
        | Tpat_alias (p,_,_,_) | Tpat_variant (_, Some p, _) ->
            loop p
        | Tpat_record (ldps,_) ->
            List.for_all
              (fun (_, lbl, p) -> lbl.lbl_mut = Immutable && loop p)
              ldps
        | Tpat_or (p,q,_) ->
            loop p && loop q
      in
      loop pat
  end







(*********************************)
(* Exported exhaustiveness check *)
(*********************************)

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

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

(*************************************)
(* Ambiguous variable in or-patterns *)
(*************************************)

(* Specification: ambiguous variables in or-patterns.

   The semantics of or-patterns in OCaml is specified with
   a left-to-right bias: a value [v] matches the pattern [p | q] if it
   matches [p] or [q], but if it matches both, the environment
   captured by the match is the environment captured by [p], never the
   one captured by [q].

   While this property is generally well-understood, one specific case
   where users expect a different semantics is when a pattern is
   followed by a when-guard: [| p when g -> e]. Consider for example:

     | ((Const x, _) | (_, Const x)) when is_neutral x -> branch

   The semantics is clear: match the scrutinee against the pattern, if
   it matches, test the guard, and if the guard passes, take the
   branch.

   However, consider the input [(Const a, Const b)], where [a] fails
   the test [is_neutral f], while [b] passes the test [is_neutral
   b]. With the left-to-right semantics, the clause above is *not*
   taken by its input: matching [(Const a, Const b)] against the
   or-pattern succeeds in the left branch, it returns the environment
   [x -> a], and then the guard [is_neutral a] is tested and fails,
   the branch is not taken. Most users, however, intuitively expect
   that any pair that has one side passing the test will take the
   branch. They assume it is equivalent to the following:

     | (Const x, _) when is_neutral x -> branch
     | (_, Const x) when is_neutral x -> branch

   while it is not.

   The code below is dedicated to finding these confusing cases: the
   cases where a guard uses "ambiguous" variables, that are bound to
   different parts of the scrutinees by different sides of
   a or-pattern. In other words, it finds the cases where the
   specified left-to-right semantics is not equivalent to
   a non-deterministic semantics (any branch can be taken) relatively
   to a specific guard.
*)

let pattern_vars p = Ident.Set.of_list (Typedtree.pat_bound_idents p)

(* Row for ambiguous variable search,
   row is the traditional pattern row,
   varsets contain a list of head variable sets (varsets)

   A given varset contains all the variables that appeared at the head
   of a pattern in the row at some point during traversal: they would
   all be bound to the same value at matching time. On the contrary,
   two variables of different varsets appeared at different places in
   the pattern and may be bound to distinct sub-parts of the matched
   value.

   All rows of a (sub)matrix have rows of the same length,
   but also varsets of the same length.

   Varsets are populated when simplifying the first column
   -- the variables of the head pattern are collected in a new varset.
   For example,
     { row = x :: r1; varsets = s1 }
     { row = (Some _) as y :: r2; varsets  = s2 }
     { row = (None as x) as y :: r3; varsets = s3 }
     { row = (Some x | (None as x)) :: r4 with varsets = s4 }
   becomes
     (_, { row = r1; varsets = {x} :: s1 })
     (Some _, { row = r2; varsets = {y} :: s2 })
     (None, { row = r3; varsets = {x, y} :: s3 })
     (Some x, { row = r4; varsets = {} :: s4 })
     (None, { row = r4; varsets = {x} :: s4 })
*)
type amb_row = { row : pattern list ; varsets : Ident.Set.t list; }

let simplify_head_amb_pat head_bound_variables varsets ~add_column p ps k =
  let rec simpl head_bound_variables varsets p ps k =
    match (Patterns.General.view p).pat_desc with
    | `Alias (p,x,_,_) ->
      simpl (Ident.Set.add x head_bound_variables) varsets p ps k
    | `Var (x,_,_) ->
      simpl (Ident.Set.add x head_bound_variables) varsets Patterns.omega ps k
    | `Or (p1,p2,_) ->
      simpl head_bound_variables varsets p1 ps
        (simpl head_bound_variables varsets p2 ps k)
    | #Patterns.Simple.view as view ->
      add_column (Patterns.Head.deconstruct { p with pat_desc = view })
        { row = ps; varsets = head_bound_variables :: varsets; } k
  in simpl head_bound_variables varsets p ps k

(*
   To accurately report ambiguous variables, one must consider
   that previous clauses have already matched some values.
   Consider for example:

     | (Foo x, Foo y) -> ...
     | ((Foo x, _) | (_, Foo x)) when bar x -> ...

   The second line taken in isolation uses an unstable variable,
   but the discriminating values, of the shape [(Foo v1, Foo v2)],
   would all be filtered by the line above.

   To track this information, the matrices we analyze contain both
   *positive* rows, that describe the rows currently being analyzed
   (of type Varsets.row, so that their varsets are tracked) and
   *negative rows*, that describe the cases already matched against.

   The values matched by a signed matrix are the values matched by
   some of the positive rows but none of the negative rows. In
   particular, a variable is stable if, for any value not matched by
   any of the negative rows, the environment captured by any of the
   matching positive rows is identical.
*)
type ('a, 'b) signed = Positive of 'a | Negative of 'b

let rec simplify_first_amb_col = function
  | [] -> []
  | (Negative [] | Positive { row = []; _ }) :: _  -> assert false
  | Negative (n :: ns) :: rem ->
      let add_column n ns k = (n, Negative ns) :: k in
      simplify_head_pat
        ~add_column n ns (simplify_first_amb_col rem)
  | Positive { row = p::ps; varsets; }::rem ->
      let add_column p ps k = (p, Positive ps) :: k in
      simplify_head_amb_pat
        Ident.Set.empty varsets
        ~add_column p ps (simplify_first_amb_col rem)

(* Compute stable bindings *)

type stable_vars =
  | All
  | Vars of Ident.Set.t

let stable_inter sv1 sv2 = match sv1, sv2 with
  | All, sv | sv, All -> sv
  | Vars s1, Vars s2 -> Vars (Ident.Set.inter s1 s2)

let reduce f = function
| [] -> invalid_arg "reduce"
| x::xs -> List.fold_left f x xs

let rec matrix_stable_vars m = match m with
  | [] -> All
  | ((Positive {row = []; _} | Negative []) :: _) as empty_rows ->
      let exception Negative_empty_row in
      (* if at least one empty row is negative, the matrix matches no value *)
      let get_varsets = function
        | Negative n ->
            (* All rows have the same number of columns;
               if the first row is empty, they all are. *)
            assert (n = []);
            raise Negative_empty_row
        | Positive p ->
            assert (p.row = []);
            p.varsets in
      begin match List.map get_varsets empty_rows with
      | exception Negative_empty_row -> All
      | rows_varsets ->
          let stables_in_varsets =
            reduce (List.map2 Ident.Set.inter) rows_varsets in
          (* The stable variables are those stable at any position *)
          Vars
            (List.fold_left Ident.Set.union Ident.Set.empty stables_in_varsets)
      end
  | m ->
      let is_negative = function
        | Negative _ -> true
        | Positive _ -> false in
      if List.for_all is_negative m then
        (* optimization: quit early if there are no positive rows.
           This may happen often when the initial matrix has many
           negative cases and few positive cases (a small guarded
           clause after a long list of clauses) *)
        All
      else begin
        let m = simplify_first_amb_col m in
        if not (all_coherent (first_column m)) then
          All
        else begin
          (* If the column is ill-typed but deemed coherent, we might
             spuriously warn about some variables being unstable.
             As sad as that might be, the warning can be silenced by
             splitting the or-pattern...  *)
          let submatrices =
            let extend_row columns = function
              | Negative r -> Negative (columns @ r)
              | Positive r -> Positive { r with row = columns @ r.row } in
            let q0 = discr_pat Patterns.Simple.omega m in
            let { default; constrs } =
              build_specialized_submatrices ~extend_row q0 m in
            let non_default = List.map snd constrs in
            if full_match false constrs
            then non_default
            else default :: non_default in
          (* A stable variable must be stable in each submatrix. *)
          let submat_stable = List.map matrix_stable_vars submatrices in
          List.fold_left stable_inter All submat_stable
        end
      end

let pattern_stable_vars ns p =
  matrix_stable_vars
    (List.fold_left (fun m n -> Negative n :: m)
       [Positive {varsets = []; row = [p]}] ns)

(* All identifier paths that appear in an expression that occurs
   as a clause right hand side or guard.
*)

let all_rhs_idents exp =
  let ids = ref Ident.Set.empty in
  let open Tast_iterator in
  let expr_iter iter exp =
    match exp.exp_desc with
    | Texp_ident (path, _lid, _descr) ->
        List.iter (fun id -> ids := Ident.Set.add id !ids) (Path.heads path)
    (* Use default iterator methods for rest of match.*)
    | _ -> Tast_iterator.default_iterator.expr iter exp
  in
  let iterator = {Tast_iterator.default_iterator with expr = expr_iter} in
  iterator.expr iterator exp;
  !ids

let check_ambiguous_bindings =
  let open Warnings in
  let warn0 = Ambiguous_var_in_pattern_guard [] in
  fun cases ->
    if is_active warn0 then
      let check_case ns case = match case with
        | { c_lhs = p; c_guard=None ; _} -> [p]::ns
        | { c_lhs = p; c_guard=Some g; _} ->
            let all =
              Ident.Set.inter (pattern_vars p) (all_rhs_idents g) in
            if not (Ident.Set.is_empty all) then begin
              match pattern_stable_vars ns p with
              | All -> ()
              | Vars stable ->
                  let ambiguous = Ident.Set.diff all stable in
                  if not (Ident.Set.is_empty ambiguous) then begin
                    let pps =
                      Ident.Set.elements ambiguous |> List.map Ident.name in
                    let warn = Ambiguous_var_in_pattern_guard pps in
                    Location.prerr_warning p.pat_loc warn
                  end
            end;
            ns
      in
      ignore (List.fold_left check_case [] cases)

let do_complete_partial ~(pred : pattern -> pattern option) pss =
  (* c/p of [do_check_partial] without the parts concerning the generation of
     the error message or the warning emiting. *)
  match pss with
  | [] -> []
  | ps :: _  ->
    let typecheck p =
      pred p
    in
    exhaust None pss (List.length ps)
    |> Seq.filter_map typecheck
    |> List.of_seq

let complete_partial ~(pred : pattern -> pattern option) pss =
  let pss = get_mins le_pats pss in
  do_complete_partial ~pred pss

let return_unused casel =
  let rec do_rec acc pref = function
    | [] -> acc
    | q :: rem ->
      let qs = [q] in
      let acc =
        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 -> `Unused q :: acc
          | Upartial ps -> `Unused_subs (q, ps) :: acc
          | Used -> acc
        with Empty | Not_found -> assert false
      in
      (* FIXME: we need to know whether there is a guard here, because if there
         is, we dont want to add [[q]] to [pref]. *)
      do_rec acc ([q]::pref) rem
  in
  do_rec [] [] casel