Quellcode-Bibliothek

^© Kompilation durch diese Firma

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Datei: top.pvs Sprache: PVS

Original von: Coq^©

(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

module CVars = Vars

open Pp
open CErrors
open Util
open Names
open Nameops
open Constr
open Context
open Termops
open Environ
open EConstr
open Vars
open Namegen
open Declarations
open Inductiveops
open Reductionops
open Type_errors
open Glob_term
open Glob_ops
open Retyping
open Pretype_errors
open Evarutil
open Evardefine
open Evarsolve
open Evarconv
open Evd
open Context.Rel.Declaration
open GlobEnv

module RelDecl = Context.Rel.Declaration
module NamedDecl = Context.Named.Declaration

(* Pattern-matching errors *)

type pattern_matching_error =
  | BadPattern of constructor * constr
  | BadConstructor of constructor * inductive
  | WrongNumargConstructor of constructor * int
  | WrongNumargInductive of inductive * int
  | UnusedClause of cases_pattern list
  | NonExhaustive of cases_pattern list
  | CannotInferPredicate of (constr * types) array

exception PatternMatchingError of env * evar_map * pattern_matching_error

let raise_pattern_matching_error ?loc (env,sigma,te) =
  Loc.raise ?loc (PatternMatchingError(env,sigma,te))

let error_bad_pattern ?loc env sigma cstr ind =
  raise_pattern_matching_error ?loc
    (env, sigma, BadPattern (cstr,ind))

let error_bad_constructor ?loc env cstr ind =
  raise_pattern_matching_error ?loc
    (env, Evd.empty, BadConstructor (cstr,ind))

let error_wrong_numarg_constructor ?loc env c n =
  raise_pattern_matching_error ?loc (env, Evd.empty, WrongNumargConstructor(c,n))

let error_wrong_numarg_inductive ?loc env c n =
  raise_pattern_matching_error ?loc (env, Evd.empty, WrongNumargInductive(c,n))

let list_try_compile f l =
  let rec aux errors = function
  | [] -> if errors = [] then anomaly (str "try_find_f.") else iraise (List.last errors)
  | h::t ->
      try f h
      with UserError _ | TypeError _ | PretypeError _ | PatternMatchingError _ as e ->
     let e = CErrors.push e in
     aux (e::errors) t in
  aux [] l

let force_name =
  let nx = Name default_dependent_ident in function Anonymous -> nx | na -> na

(************************************************************************)
(*            Pattern-matching compilation (Cases)                      *)
(************************************************************************)

(************************************************************************)
(* Configuration, errors and warnings *)

open Pp

let msg_may_need_inversion () =
  strbrk "Found a matching with no clauses on a term unknown to have an empty inductive type."

(* Utils *)
let make_anonymous_patvars n =
  List.make n (DAst.make @@ PatVar Anonymous)

(* We have x1:t1...xn:tn,xi':ti,y1..yk |- c and re-generalize
   over xi:ti to get x1:t1...xn:tn,xi':ti,y1..yk |- c[xi:=xi'] *)

let relocate_rel n1 n2 k j = if Int.equal j (n1 + k) then n2+k else j

let rec relocate_index sigma n1 n2 k t =
  match EConstr.kind sigma t with
  | Rel j when Int.equal j (n1 + k) -> mkRel (n2+k)
  | Rel j when j < n1+k -> t
  | Rel j when j > n1+k -> t
  | _ -> EConstr.map_with_binders sigma succ (relocate_index sigma n1 n2) k t

(**********************************************************************)
(* Structures used in compiling pattern-matching *)

let (!!) env = GlobEnv.env env

type 'a rhs =
    { rhs_env    : GlobEnv.t;
      rhs_vars   : Id.Set.t;
      avoid_ids  : Id.Set.t;
      it         : 'a option}

type 'a equation =
    { patterns     : cases_pattern list;
      rhs          : 'a rhs;
      alias_stack  : Name.t list;
      eqn_loc      : Loc.t option;
      used         : bool ref }

type 'a matrix = 'a equation list

(* 1st argument of IsInd is the original ind before extracting the summary *)
type tomatch_type =
  | IsInd of types * inductive_type * Name.t list
  | NotInd of constr option * types

(* spiwack: The first argument of [Pushed] is [true] for initial
   Pushed and [false] otherwise. Used to decide whether the term being
   matched on must be aliased in the variable case (only initial
   Pushed need to be aliased). The first argument of [Alias] is [true]
   if the alias was introduced by an initial pushed and [false]
   otherwise.*)
type tomatch_status =
  | Pushed of (bool*((constr * tomatch_type) * int list * Name.t))
  | Alias of (bool*(Name.t * constr * (constr * types)))
  | NonDepAlias
  | Abstract of int * rel_declaration

type tomatch_stack = tomatch_status list

(* We keep a constr for aliases and a cases_pattern for error message *)

type pattern_history =
  | Top
  | MakeConstructor of constructor * pattern_continuation

and pattern_continuation =
  | Continuation of int * cases_pattern list * pattern_history
  | Result of cases_pattern list

let start_history n = Continuation (n, [], Top)

let feed_history arg = function
  | Continuation (n, l, h) when n>=1 ->
      Continuation (n-1, arg :: l, h)
  | Continuation (n, _, _) ->
      anomaly (str "Bad number of expected remaining patterns: " ++ int n ++ str ".")
  | Result _ ->
      anomaly (Pp.str "Exhausted pattern history.")

(* This is for non exhaustive error message *)

let rec glob_pattern_of_partial_history args2 = function
  | Continuation (n, args1, h) ->
      let args3 = make_anonymous_patvars (n - (List.length args2)) in
      build_glob_pattern (List.rev_append args1 (args2@args3)) h
  | Result pl -> pl

and build_glob_pattern args = function
  | Top -> args
  | MakeConstructor (pci, rh) ->
      glob_pattern_of_partial_history
[DAst.make @@ PatCstr (pci, args, Anonymous)] rh

let complete_history = glob_pattern_of_partial_history []

(* This is to build glued pattern-matching history and alias bodies *)

let pop_history_pattern = function
  | Continuation (0, l, Top) ->
      Result (List.rev l)
  | Continuation (0, l, MakeConstructor (pci, rh)) ->
      feed_history (DAst.make @@ PatCstr (pci,List.rev l,Anonymous)) rh
  | _ ->
      anomaly (Pp.str "Constructor not yet filled with its arguments.")

let pop_history h =
  feed_history (DAst.make @@ PatVar Anonymous) h

(* Builds a continuation expecting [n] arguments and building [ci] applied
   to this [n] arguments *)

let push_history_pattern n pci cont =
  Continuation (n, [], MakeConstructor (pci, cont))

(* A pattern-matching problem has the following form:

   env, evd |- match terms_to_tomatch return pred with mat end

  where terms_to_match is some sequence of "instructions" (t1 ... tp)

  and mat is some matrix

   (p11 ... p1n -> rhs1)
   (    ...            )
   (pm1 ... pmn -> rhsm)

  Terms to match: there are 3 kinds of instructions

  - "Pushed" terms to match are typed in [env]; these are usually just
    Rel(n) except for the initial terms given by user; in Pushed ((c,tm),deps,na),
    [c] is the reference to the term (which is a Rel or an initial term), [tm] is
    its type (telling whether we know if it is an inductive type or not),
    [deps] is the list of terms to abstract before matching on [c] (these are
    rels too)
  - "Abstract" instructions mean that an abstraction has to be inserted in the
    current branch to build (this means a pattern has been detected dependent
    in another one and a generalization is necessary to ensure well-typing)
    Abstract instructions extend the [env] in which the other instructions
    are typed
  - "Alias" instructions mean an alias has to be inserted (this alias
    is usually removed at the end, except when its type is not the
    same as the type of the matched term from which it comes -
    typically because the inductive types are "real" parameters)
  - "NonDepAlias" instructions mean the completion of a matching over
    a term to match as for Alias but without inserting this alias
    because there is no dependency in it

  Right-hand sides:

  They consist of a raw term to type in an environment specific to the
  clause they belong to: the names of declarations are those of the
  variables present in the patterns. Therefore, they come with their
  own [rhs_env] (actually it is the same as [env] except for the names
  of variables).

*)

type 'a pattern_matching_problem =
    { env       : GlobEnv.t;
      pred      : constr;
      tomatch   : tomatch_stack;
      history   : pattern_continuation;
      mat       : 'a matrix;
      caseloc   : Loc.t option;
      casestyle : case_style;
      typing_function: type_constraint -> GlobEnv.t -> evar_map -> 'a option -> evar_map * unsafe_judgment }

(*--------------------------------------------------------------------------*
* A few functions to infer the inductive type from the patterns instead of *
* checking that the patterns correspond to the ind. type of the            *
* destructurated object. Allows type inference of examples like            *
*  match n with O => true | _ => false end                                 *
*  match x in I with C => true | _ => false end                            *
*--------------------------------------------------------------------------*)

(* Computing the inductive type from the matrix of patterns *)

(* We use the "in I" clause to coerce the terms to match and otherwise
   use the constructor to know in which type is the matching problem

   Note that insertion of coercions inside nested patterns is done
   each time the matrix is expanded *)

let rec find_row_ind = function
    [] -> None
  | p :: l ->
    match DAst.get p with
    | PatVar _ -> find_row_ind l
    | PatCstr(c,_,_) -> Some (p.CAst.loc,c)

let inductive_template env sigma tmloc ind =
  let sigma, indu = Evd.fresh_inductive_instance env sigma ind in
  let arsign = inductive_alldecls_env env indu in
  let indu = on_snd EInstance.make indu in
  let hole_source i = match tmloc with
    | Some loc -> Loc.tag ~loc @@ Evar_kinds.TomatchTypeParameter (ind,i)
    | None     -> Loc.tag      @@ Evar_kinds.TomatchTypeParameter (ind,i) in
   let (sigma, _, evarl, _) =
    List.fold_right
      (fun decl (sigma, subst, evarl, n) ->
match decl with
        | LocalAssum (na,ty) ->
            let ty = EConstr.of_constr ty in
     let ty' = substl subst ty in
            let sigma, e =
              Evarutil.new_evar env ~src:(hole_source n) ~typeclass_candidate:false sigma ty'
            in
            (sigma, e::subst,e::evarl,n+1)
| LocalDef (na,b,ty) ->
            let b = EConstr.of_constr b in
            (sigma, substl subst b::subst,evarl,n+1))
      arsign (sigma, [], [], 1) in
   sigma, applist (mkIndU indu,List.rev evarl)

let try_find_ind env sigma typ realnames =
  let (IndType(indf,realargs) as ind) = find_rectype env sigma typ in
  let names =
    match realnames with
      | Some names -> names
      | None ->
          let ind = fst (fst (dest_ind_family indf)) in
          List.make (inductive_nrealdecls ind) Anonymous in
  IsInd (typ,ind,names)

let inh_coerce_to_ind env sigma0 loc ty tyi =
  let sigma, expected_typ = inductive_template env sigma0 loc tyi in
  (* Try to refine the type with inductive information coming from the
     constructor and renounce if not able to give more information *)
  (* devrait être indifférent d'exiger leq ou pas puisque pour
     un inductif cela doit être égal *)
  match Evarconv.unify_leq_delay env sigma expected_typ ty with
  | sigma -> sigma
  | exception Evarconv.UnableToUnify _ -> sigma0

let binding_vars_of_inductive sigma = function
  | NotInd _ -> []
  | IsInd (_,IndType(_,realargs),_) -> List.filter (isRel sigma) realargs

let set_tomatch_realnames names = function
  | NotInd _ as t -> t
  | IsInd (typ,ind,_) -> IsInd (typ,ind,names)

let extract_inductive_data env sigma decl =
  match decl with
  | LocalAssum (_,t) ->
    let tmtyp =
      try try_find_ind env sigma t None
      with Not_found -> NotInd (None,t) in
    let tmtypvars = binding_vars_of_inductive sigma tmtyp in
    (tmtyp,tmtypvars)
  | LocalDef (_,_,t) ->
    (NotInd (None, t), [])

let unify_tomatch_with_patterns env sigma loc typ pats realnames =
  match find_row_ind pats with
    | None -> sigma, NotInd (None,typ)
    | Some (_,(ind,_)) ->
        let sigma = inh_coerce_to_ind env sigma loc typ ind in
        try sigma, try_find_ind env sigma typ realnames
        with Not_found -> sigma, NotInd (None,typ)

let find_tomatch_tycon env sigma loc = function
  (* Try if some 'in I ...' is present and can be used as a constraint *)
  | Some {CAst.v=(ind,realnal)} ->
      let sigma, tycon = inductive_template env sigma loc ind in
      sigma, mk_tycon tycon, Some (List.rev realnal)
  | None ->
      sigma, empty_tycon, None

let make_return_predicate_ltac_lvar env sigma na tm c =
  (* If we have an [x as x return ...] clause and [x] expands to [c],
     we have to update the status of [x] in the substitution:
     - if [c] is a variable [id'], then [x] should now become [id']
     - otherwise, [x] should be hidden *)
  match na, DAst.get tm with
  | Name id, (GVar id' | GRef (Globnames.VarRef id', _)) when Id.equal id id' ->
     let expansion = match kind sigma c with
       | Var id' -> Name id'
       | _ -> Anonymous in
       GlobEnv.hide_variable env expansion id
  | _ -> env

let is_patvar pat =
  match DAst.get pat with
  | PatVar _ -> true
  | _ -> false

let coerce_row ~program_mode typing_fun env sigma pats (tomatch,(na,indopt)) =
  let loc = loc_of_glob_constr tomatch in
  let sigma, tycon, realnames = find_tomatch_tycon !!env sigma loc indopt in
  let sigma, j = typing_fun tycon env sigma tomatch in
  let sigma, j = Coercion.inh_coerce_to_base ?loc:(loc_of_glob_constr tomatch) ~program_mode !!env sigma j in
  let typ = nf_evar sigma j.uj_type in
  let env = make_return_predicate_ltac_lvar env sigma na tomatch j.uj_val in
  let sigma, t =
    if realnames = None && pats <> [] && List.for_all is_patvar pats then
      sigma, NotInd (None,typ)
    else
    try sigma, try_find_ind !!env sigma typ realnames
    with Not_found ->
      unify_tomatch_with_patterns !!env sigma loc typ pats realnames
  in
  ((env, sigma), (j.uj_val,t))

let coerce_to_indtype ~program_mode typing_fun env sigma matx tomatchl =
  let pats = List.map (fun r ->  r.patterns) matx in
  let matx' = match matrix_transpose pats with
    | [] -> List.map (fun _ -> []) tomatchl (* no patterns at all *)
    | m -> m in
  let (env, sigma), tms = List.fold_left2_map (fun (env, sigma) -> coerce_row ~program_mode typing_fun env sigma) (env, sigma) matx' tomatchl in
  env, sigma, tms

(************************************************************************)
(* Utils *)

let mkExistential ?(src=(Loc.tag Evar_kinds.InternalHole)) env sigma =
  let sigma, (e, u) = Evarutil.new_type_evar env sigma ~src:src univ_flexible_alg in
  sigma, e

let adjust_tomatch_to_pattern ~program_mode sigma pb ((current,typ),deps,dep) =
  (* Ideally, we could find a common inductive type to which both the
     term to match and the patterns coerce *)
  (* In practice, we coerce the term to match if it is not already an
     inductive type and it is not dependent; moreover, we use only
     the first pattern type and forget about the others *)
  let typ,names =
    match typ with IsInd(t,_,names) -> t,Some names | NotInd(_,t) -> t,None in
  let tmtyp =
    try try_find_ind !!(pb.env) sigma typ names
    with Not_found -> NotInd (None,typ) in
  match tmtyp with
  | NotInd (None,typ) ->
      let tm1 = List.map (fun eqn -> List.hd eqn.patterns) pb.mat in
      (match find_row_ind tm1 with
        | None -> sigma, (current, tmtyp)
        | Some (loc,(ind,_)) ->
            let sigma, indt = inductive_template !!(pb.env) sigma None ind in
            let sigma, current =
              if List.is_empty deps && isEvar sigma typ then
       (* Don't insert coercions if dependent; only solve evars *)
                match Evarconv.unify_leq_delay !!(pb.env) sigma indt typ with
                | exception Evarconv.UnableToUnify _ -> sigma, current
                | sigma -> sigma, current
       else
                let sigma, j = Coercion.inh_conv_coerce_to ?loc ~program_mode true !!(pb.env) sigma (make_judge current typ) indt in
                sigma, j.uj_val
            in
            sigma, (current, try_find_ind !!(pb.env) sigma indt names))
  | _ -> sigma, (current, tmtyp)

let type_of_tomatch = function
  | IsInd (t,_,_) -> t
  | NotInd (_,t) -> t

let map_tomatch_type f = function
  | IsInd (t,ind,names) -> IsInd (f t,map_inductive_type f ind,names)
  | NotInd (c,t) -> NotInd (Option.map f c, f t)

let liftn_tomatch_type n depth = map_tomatch_type (Vars.liftn n depth)
let lift_tomatch_type n = liftn_tomatch_type n 1

(**********************************************************************)
(* Utilities on patterns *)

let current_pattern eqn =
  match eqn.patterns with
    | pat::_ -> pat
    | [] -> anomaly (Pp.str "Empty list of patterns.")

let remove_current_pattern eqn =
  match eqn.patterns with
    | pat::pats ->
{ eqn with
     patterns = pats;
     alias_stack = alias_of_pat pat :: eqn.alias_stack }
    | [] -> anomaly (Pp.str "Empty list of patterns.")

let push_current_pattern ~program_mode sigma (cur,ty) eqn =
  let hypnaming = if program_mode then ProgramNaming else KeepUserNameAndRenameExistingButSectionNames in
  match eqn.patterns with
    | pat::pats ->
        let r = Sorts.Relevant in (* TODO relevance *)
        let _,rhs_env = push_rel ~hypnaming sigma (LocalDef (make_annot (alias_of_pat pat) r,cur,ty)) eqn.rhs.rhs_env in
{ eqn with
            rhs = { eqn.rhs with rhs_env = rhs_env };
     patterns = pats }
    | [] -> anomaly (Pp.str "Empty list of patterns.")

(* spiwack: like [push_current_pattern] but does not introduce an
   alias in rhs_env. Aliasing binders are only useful for variables at
   the root of a pattern matching problem (initial push), so we
   distinguish the cases. *)
let push_noalias_current_pattern eqn =
  match eqn.patterns with
  | _::pats ->
      { eqn with patterns = pats }
  | [] -> anomaly (Pp.str "push_noalias_current_pattern: Empty list of patterns.")

let prepend_pattern tms eqn = {eqn with patterns = [email protected] }

(**********************************************************************)
(* Well-formedness tests *)
(* Partial check on patterns *)

exception NotAdjustable

let rec adjust_local_defs ?loc = function
  | (pat :: pats, LocalAssum _ :: decls) ->
      pat :: adjust_local_defs ?loc (pats,decls)
  | (pats, LocalDef _ :: decls) ->
      (DAst.make ?loc @@ PatVar Anonymous) :: adjust_local_defs ?loc (pats,decls)
  | [], [] -> []
  | _ -> raise NotAdjustable

let check_and_adjust_constructor env ind cstrs pat = match DAst.get pat with
  | PatVar _ -> pat
  | PatCstr (((_,i) as cstr),args,alias) ->
      let loc = pat.CAst.loc in
      (* Check it is constructor of the right type *)
      let ind' = inductive_of_constructor cstr in
      if eq_ind ind' ind then
(* Check the constructor has the right number of args *)
let ci = cstrs.(i-1) in
let nb_args_constr = ci.cs_nargs in
if Int.equal (List.length args) nb_args_constr then pat
else
   try
     let args' = adjust_local_defs ?loc (args, List.rev ci.cs_args)
     in DAst.make ?loc @@ PatCstr (cstr, args', alias)
   with NotAdjustable ->
     error_wrong_numarg_constructor ?loc env cstr nb_args_constr
      else
(* Try to insert a coercion *)
try
   Coercion.inh_pattern_coerce_to ?loc env pat ind' ind
with Not_found ->
   error_bad_constructor ?loc env cstr ind

let check_all_variables env sigma typ mat =
  List.iter
    (fun eqn ->
      let pat = current_pattern eqn in
      match DAst.get pat with
       | PatVar id -> ()
       | PatCstr (cstr_sp,_,_) ->
          let loc = pat.CAst.loc in
    error_bad_pattern ?loc env sigma cstr_sp typ)
    mat

let check_unused_pattern env eqn =
  if not !(eqn.used) then
    raise_pattern_matching_error ?loc:eqn.eqn_loc (env, Evd.empty, UnusedClause eqn.patterns)

let set_used_pattern eqn = eqn.used := true

let extract_rhs pb =
  match pb.mat with
    | [] -> user_err ~hdr:"build_leaf" (msg_may_need_inversion())
    | eqn::_ ->
set_used_pattern eqn;
        eqn.rhs

(**********************************************************************)
(* Functions to deal with matrix factorization *)

let occur_in_rhs na rhs =
  match na with
    | Anonymous -> false
    | Name id -> Id.Set.mem id rhs.rhs_vars

let is_dep_patt_in eqn pat = match DAst.get pat with
  | PatVar name -> occur_in_rhs name eqn.rhs
  | PatCstr _ -> true

let mk_dep_patt_row ~program_mode (pats,_,eqn) =
  if program_mode then List.map (fun _ -> true) pats
  else List.map (is_dep_patt_in eqn) pats

let dependencies_in_pure_rhs ~program_mode nargs eqns =
  if List.is_empty eqns then
    List.make nargs (not program_mode)  (* Only "_" patts *) else
  let deps_rows = List.map (mk_dep_patt_row ~program_mode) eqns in
  let deps_columns = matrix_transpose deps_rows in
  List.map (List.exists (fun x -> x)) deps_columns

let dependent_decl sigma a =
  function
  | LocalAssum (na,t) -> dependent sigma a t
  | LocalDef (na,c,t) -> dependent sigma a t || dependent sigma a c

let rec dep_in_tomatch sigma n = function
  | (Pushed _ | Alias _ | NonDepAlias) :: l -> dep_in_tomatch sigma n l
  | Abstract (_,d) :: l -> RelDecl.exists (fun c -> not (noccurn sigma n c)) d || dep_in_tomatch sigma (n+1) l
  | [] -> false

let dependencies_in_rhs ~program_mode sigma nargs current tms eqns =
  match EConstr.kind sigma current with
  | Rel n when dep_in_tomatch sigma n tms -> List.make nargs true
  | _ -> dependencies_in_pure_rhs ~program_mode nargs eqns

(* Computing the matrix of dependencies *)

(* [find_dependency_list tmi [d(i+1);...;dn]] computes in which
   declarations [d(i+1);...;dn] the term [tmi] is dependent in.

   [find_dependencies_signature (used1,...,usedn) ((tm1,d1),...,(tmn,dn))]
   returns [(deps1,...,depsn)] where [depsi] is a subset of tm(i+1),..,tmn
   denoting in which of the d(i+1)...dn, the term tmi is dependent.
*)

let rec find_dependency_list sigma tmblock = function
  | [] -> []
  | (used,tdeps,tm,d)::rest ->
      let deps = find_dependency_list sigma tmblock rest in
      if used && List.exists (fun x -> dependent_decl sigma x d) tmblock
      then
        match EConstr.kind sigma tm with
        | Rel n -> List.add_set Int.equal n (List.union Int.equal deps tdeps)
        | _ -> List.union Int.equal deps tdeps
      else deps

let find_dependencies sigma is_dep_or_cstr_in_rhs (tm,(_,tmtypleaves),d) nextlist =
  let deps = find_dependency_list sigma (tm::tmtypleaves) nextlist in
  if is_dep_or_cstr_in_rhs || not (List.is_empty deps)
  then ((true ,deps,tm,d)::nextlist)
  else ((false,[]  ,tm,d)::nextlist)

let find_dependencies_signature sigma deps_in_rhs typs =
  let l = List.fold_right2 (find_dependencies sigma) deps_in_rhs typs [] in
  List.map (fun (_,deps,_,_) -> deps) l

(* Assume we had terms t1..tq to match in a context xp:Tp,...,x1:T1 |-
   and xn:Tn has just been regeneralized into x:Tn so that the terms
   to match are now to be considered in the context xp:Tp,...,x1:T1,x:Tn |-.

   [relocate_index_tomatch n 1 tomatch] updates t1..tq so that
   former references to xn1 are now references to x. Note that t1..tq
   are already adjusted to the context xp:Tp,...,x1:T1,x:Tn |-.

   [relocate_index_tomatch 1 n tomatch] will go the way back.
*)

let relocate_index_tomatch sigma n1 n2 =
  let rec genrec depth = function
  | [] ->
      []
  | Pushed (b,((c,tm),l,na)) :: rest ->
      let c = relocate_index sigma n1 n2 depth c in
      let tm = map_tomatch_type (relocate_index sigma n1 n2 depth) tm in
      let l = List.map (relocate_rel n1 n2 depth) l in
      Pushed (b,((c,tm),l,na)) :: genrec depth rest
  | Alias (initial,(na,c,d)) :: rest ->
      (* [c] is out of relocation scope *)
      Alias (initial,(na,c,map_pair (relocate_index sigma n1 n2 depth) d)) :: genrec depth rest
  | NonDepAlias :: rest ->
      NonDepAlias :: genrec depth rest
  | Abstract (i,d) :: rest ->
      let i = relocate_rel n1 n2 depth i in
      Abstract (i, RelDecl.map_constr (fun c -> relocate_index sigma n1 n2 depth c) d)
      :: genrec (depth+1) rest in
  genrec 0

(* [replace_tomatch n c tomatch] replaces [Rel n] by [c] in [tomatch] *)

let rec replace_term sigma n c k t =
  if isRel sigma t && Int.equal (destRel sigma t) (n + k) then Vars.lift k c
  else EConstr.map_with_binders sigma succ (replace_term sigma n c) k t

let length_of_tomatch_type_sign na t =
  let l = match na with
  | Anonymous -> 0
  | Name _ -> 1
  in
  match t with
  | NotInd _ -> l
  | IsInd (_, _, names) -> List.length names + l

let replace_tomatch sigma n c =
  let rec replrec depth = function
  | [] -> []
  | Pushed (initial,((b,tm),l,na)) :: rest ->
      let b = replace_term sigma n c depth b in
      let tm = map_tomatch_type (replace_term sigma n c depth) tm in
      List.iter (fun i -> if Int.equal i (n + depth) then anomaly (Pp.str "replace_tomatch.")) l;
      Pushed (initial,((b,tm),l,na)) :: replrec depth rest
  | Alias (initial,(na,b,d)) :: rest ->
      (* [b] is out of replacement scope *)
      Alias (initial,(na,b,map_pair (replace_term sigma n c depth) d)) :: replrec depth rest
  | NonDepAlias  :: rest ->
      NonDepAlias :: replrec depth rest
  | Abstract (i,d) :: rest ->
      Abstract (i, RelDecl.map_constr (fun t -> replace_term sigma n c depth t) d)
      :: replrec (depth+1) rest in
  replrec 0

(* [liftn_tomatch_stack]: a term to match has just been substituted by
   some constructor t = (ci x1...xn) and the terms x1 ... xn have been
   added to match; all pushed terms to match must be lifted by n
   (knowing that [Abstract] introduces a binder in the list of pushed
   terms to match).
*)

let rec liftn_tomatch_stack n depth = function
  | [] -> []
  | Pushed (initial,((c,tm),l,na))::rest ->
      let c = liftn n depth c in
      let tm = liftn_tomatch_type n depth tm in
      let l = List.map (fun i -> if i<depth then i else i+n) l in
      Pushed (initial,((c,tm),l,na))::(liftn_tomatch_stack n depth rest)
  | Alias (initial,(na,c,d))::rest ->
      Alias (initial,(na,liftn n depth c,map_pair (liftn n depth) d))
      ::(liftn_tomatch_stack n depth rest)
  | NonDepAlias  :: rest ->
      NonDepAlias :: liftn_tomatch_stack n depth rest
  | Abstract (i,d)::rest ->
      let i = if i<depth then i else i+n in
      Abstract (i, RelDecl.map_constr (liftn n depth) d)
      ::(liftn_tomatch_stack n (depth+1) rest)

let lift_tomatch_stack n = liftn_tomatch_stack n 1

(* if [current] has type [I(p1...pn u1...um)] and we consider the case
   of constructor [ci] of type [I(p1...pn u'1...u'm)], then the
   default variable [name] is expected to have which type?
   Rem: [current] is [(Rel i)] except perhaps for initial terms to match *)

(************************************************************************)
(* Some heuristics to get names for variables pushed in pb environment *)
(* Typical requirement:

   [match y with (S (S x)) => x | x => x end] should be compiled into
   [match y with O => y | (S n) => match n with O => y | (S x) => x end end]

   and [match y with (S (S n)) => n | n => n end] into
   [match y with O => y | (S n0) => match n0 with O => y | (S n) => n end end]

   i.e. user names should be preserved and created names should not
   interfere with user names

   The exact names here are not important for typing (because they are
   put in pb.env and not in the rhs.rhs_env of branches. However,
   whether a name is Anonymous or not may have an effect on whether a
   generalization is done or not.
*)

let merge_name get_name obj = function
  | Anonymous -> get_name obj
  | na -> na

let merge_names get_name = List.map2 (merge_name get_name)

let get_names avoid env sigma sign eqns =
  let names1 = List.make (Context.Rel.length sign) Anonymous in
  (* If any, we prefer names used in pats, from top to bottom *)
  let names2,aliasname =
    List.fold_right
      (fun (pats,pat_alias,eqn) (names,aliasname) ->
        (merge_names alias_of_pat pats names,
         merge_name (fun x -> x) pat_alias aliasname))
      eqns (names1,Anonymous) in
  (* Otherwise, we take names from the parameters of the constructor but
     avoiding conflicts with user ids *)
  let allvars =
    List.fold_left (fun l (_,_,eqn) -> Id.Set.union l eqn.rhs.avoid_ids)
      avoid eqns in
  let names3,_ =
    List.fold_left2
      (fun (l,avoid) d na ->
  let na =
    merge_name
             (fun decl ->
                let na = get_name decl in
                let t = get_type decl in
                Name (next_name_away (named_hd env sigma t na) avoid))
      d na
  in
         (na::l,Id.Set.add (Name.get_id na) avoid))
      ([],allvars) (List.rev sign) names2 in
  names3,aliasname

(*****************************************************************)
(* Recovering names for variables pushed to the rhs' environment *)
(* We just factorized a match over a matrix of equations         *)
(* "C xi1 .. xin as xi" as a single match over "C y1 .. yn as y" *)
(* We now replace the names y1 .. yn y by the actual names       *)
(* xi1 .. xin xi to be found in the i-th clause of the matrix    *)

let recover_initial_subpattern_names = List.map2 RelDecl.set_name

let recover_and_adjust_alias_names (_,avoid) names sign =
  let rec aux = function
  | [],[] ->
      []
  | x::names, LocalAssum (x',t)::sign ->
      (x, LocalAssum ({x' with binder_name=alias_of_pat x},t)) :: aux (names,sign)
  | names, (LocalDef (na,_,_) as decl)::sign ->
      (DAst.make @@ PatVar na.binder_name, decl) :: aux (names,sign)
  | _ -> assert false
  in
  List.split (aux (names,sign))

let push_rels_eqn ~hypnaming sigma sign eqn =
  {eqn with
     rhs = {eqn.rhs with rhs_env = snd (push_rel_context ~hypnaming sigma sign eqn.rhs.rhs_env) } }

let push_rels_eqn_with_names sigma sign eqn =
  let subpats = List.rev (List.firstn (List.length sign) eqn.patterns) in
  let subpatnames = List.map alias_of_pat subpats in
  let sign = recover_initial_subpattern_names subpatnames sign in
  push_rels_eqn sigma sign eqn

let push_generalized_decl_eqn ~hypnaming env sigma n decl eqn =
  match RelDecl.get_name decl with
  | Anonymous ->
      push_rels_eqn ~hypnaming sigma [decl] eqn
  | Name _ ->
      push_rels_eqn ~hypnaming sigma [RelDecl.set_name (RelDecl.get_name (Environ.lookup_rel n !!(eqn.rhs.rhs_env))) decl] eqn

let drop_alias_eqn eqn =
  { eqn with alias_stack = List.tl eqn.alias_stack }

let push_alias_eqn sigma alias eqn =
  let aliasname = List.hd eqn.alias_stack in
  let eqn = drop_alias_eqn eqn in
  let alias = RelDecl.set_name aliasname alias in
  push_rels_eqn sigma [alias] eqn

(**********************************************************************)
(* Functions to deal with elimination predicate *)

(* Inferring the predicate *)
(*
The problem to solve is the following:

We match Gamma |- t : I(u01..u0q) against the following constructors:

  Gamma, x11...x1p1 |- C1(x11..x1p1) : I(u11..u1q)
   ...
  Gamma, xn1...xnpn |- Cn(xn1..xnp1) : I(un1..unq)

Assume the types in the branches are the following

  Gamma, x11...x1p1 |- branch1 : T1
   ...
  Gamma, xn1...xnpn |- branchn : Tn

Assume the type of the global case expression is Gamma |- T

The predicate has the form phi = [y1..yq][z:I(y1..yq)]psi and it has to
satisfy the following n+1 equations:

  Gamma, x11...x1p1 |- (phi u11..u1q (C1 x11..x1p1))  =  T1
   ...
  Gamma, xn1...xnpn |- (phi un1..unq (Cn xn1..xnpn))  =  Tn
  Gamma             |- (phi u01..u0q t)               =  T

Some hints:

- Clearly, if xij occurs in Ti, then, a "match z with (Ci xi1..xipi)
  => ... end"  or a "psi(yk)", with psi extracting xij from uik, should be
  inserted somewhere in Ti.

- If T is undefined, an easy solution is to insert a "match z with
  (Ci xi1..xipi) => ... end" in front of each Ti

- Otherwise, T1..Tn and T must be step by step unified, if some of them
  diverge, then try to replace the diverging subterm by one of y1..yq or z.

- The main problem is what to do when an existential variables is encountered

*)

(* Propagation of user-provided predicate through compilation steps *)

let rec map_predicate f k ccl = function
  | [] -> f k ccl
  | Pushed (_,((_,tm),_,na)) :: rest ->
      let k' = length_of_tomatch_type_sign na tm in
      map_predicate f (k+k') ccl rest
  | (Alias _ | NonDepAlias) :: rest ->
      map_predicate f k ccl rest
  | Abstract _ :: rest ->
      map_predicate f (k+1) ccl rest

let noccur_predicate_between sigma n = map_predicate (noccur_between sigma n)

let liftn_predicate n = map_predicate (liftn n)

let lift_predicate n = liftn_predicate n 1

let regeneralize_index_predicate sigma n = map_predicate (relocate_index sigma n 1) 0

let substnl_predicate sigma = map_predicate (substnl sigma)

(* This is parallel bindings *)
let subst_predicate (subst,copt) ccl tms =
  let sigma = match copt with
    | None -> subst
    | Some c -> c::subst in
  substnl_predicate sigma 0 ccl tms

let specialize_predicate_var (cur,typ,dep) env tms ccl =
  let c = match dep with
  | Anonymous -> None
  | Name _ -> Some cur
  in
  let l =
    match typ with
    | IsInd (_, IndType (_, _), []) -> []
    | IsInd (_, IndType (indf, realargs), names) ->
       let arsign,_ = get_arity env indf in
       let arsign = List.map EConstr.of_rel_decl arsign in
       subst_of_rel_context_instance arsign realargs
    | NotInd _ -> [] in
  subst_predicate (l,c) ccl tms

(*****************************************************************************)
(* We have pred = [X:=realargs;x:=c]P typed in Gamma1, x:I(realargs), Gamma2 *)
(* and we want to abstract P over y:t(x) typed in the same context to get    *)
(*                                                                           *)
(*    pred' = [X:=realargs;x':=c](y':t(x'))P[y:=y']                          *)
(*                                                                           *)
(* We first need to lift t(x) s.t. it is typed in Gamma, X:=rargs, x'        *)
(* then we have to replace x by x' in t(x) and y by y' in P                  *)
(*****************************************************************************)
let generalize_predicate sigma (names,na) ny d tms ccl =
  let () = match na with
  | Anonymous -> anomaly (Pp.str "Undetected dependency.")
  | _ -> () in
  let p = List.length names + 1 in
  let ccl = lift_predicate 1 ccl tms in
  regeneralize_index_predicate sigma (ny+p+1) ccl tms

(*****************************************************************************)
(* We just matched over cur:ind(realargs) in the following matching problem  *)
(*                                                                           *)
(*   env |- match cur tms return ccl with ... end                            *)
(*                                                                           *)
(* and we want to build the predicate corresponding to the individual        *)
(* matching over cur                                                         *)
(*                                                                           *)
(*    pred = fun X:realargstyps x:ind(X)] PI tms.ccl                         *)
(*                                                                           *)
(* where pred is computed by abstract_predicate and PI tms.ccl by            *)
(* extract_predicate                                                         *)
(*****************************************************************************)
let rec extract_predicate ccl = function
  | (Alias _ | NonDepAlias)::tms ->
      (* substitution already done in build_branch *)
      extract_predicate ccl tms
  | Abstract (i,d)::tms ->
      mkProd_wo_LetIn d (extract_predicate ccl tms)
  | Pushed (_,((cur,NotInd _),_,na))::tms ->
      begin match na with
      | Anonymous -> extract_predicate ccl tms
      | Name _ ->
        let tms = lift_tomatch_stack 1 tms in
        let pred = extract_predicate ccl tms in
        subst1 cur pred
      end
  | Pushed (_,((cur,IsInd (_,IndType(_,realargs),_)),_,na))::tms ->
      let realargs = List.rev realargs in
      let k, nrealargs = match na with
      | Anonymous -> 0, realargs
      | Name _ -> 1, (cur :: realargs)
      in
      let tms = lift_tomatch_stack (List.length realargs + k) tms in
      let pred = extract_predicate ccl tms in
      substl nrealargs pred
  | [] ->
      ccl

let abstract_predicate env sigma indf cur realargs (names,na) tms ccl =
  let sign = make_arity_signature !!env sigma true indf in
  (* n is the number of real args + 1 (+ possible let-ins in sign) *)
  let n = List.length sign in
  (* Before abstracting we generalize over cur and on those realargs *)
  (* that are rels, consistently with the specialization made in     *)
  (* build_branch                                                    *)
  let tms = List.fold_right2 (fun par arg tomatch ->
    match EConstr.kind sigma par with
    | Rel i -> relocate_index_tomatch sigma (i+n) (destRel sigma arg) tomatch
    | _ -> tomatch) (realargs@[cur]) (Context.Rel.to_extended_list EConstr.mkRel 0 sign)
       (lift_tomatch_stack n tms) in
  (* Pred is already dependent in the current term to match (if      *)
  (* (na<>Anonymous) and its realargs; we just need to adjust it to  *)
  (* full sign if dep in cur is not taken into account               *)
  let ccl = match na with
  | Anonymous -> lift_predicate 1 ccl tms
  | Name _ -> ccl
  in
  let pred = extract_predicate ccl tms in
  (* Build the predicate properly speaking *)
  let sign = List.map2 set_name (na::names) sign in
  it_mkLambda_or_LetIn_name !!env sigma pred sign

(* [expand_arg] is used by [specialize_predicate]
   if Yk denotes [Xk;xk] or [Xk],
   it replaces gamma, x1...xn, x1...xk Yk+1...Yn |- pred
   by gamma, x1...xn, x1...xk-1 [Xk;xk] Yk+1...Yn |- pred (if dep) or
   by gamma, x1...xn, x1...xk-1 [Xk] Yk+1...Yn |- pred (if not dep) *)

let expand_arg tms (p,ccl) ((_,t),_,na) =
  let k = length_of_tomatch_type_sign na t in
  (p+k,liftn_predicate (k-1) (p+1) ccl tms)

let use_unit_judge env evd =
  let j, ctx = coq_unit_judge !!env in
  let evd' = Evd.merge_context_set Evd.univ_flexible evd ctx in
    evd', j

let add_assert_false_case pb tomatch =
  let pats = List.map (fun _ -> DAst.make @@ PatVar Anonymous) tomatch in
  let aliasnames =
    List.map_filter (function Alias _ | NonDepAlias -> Some Anonymous | _ -> None) tomatch
  in
  [ { patterns = pats;
      rhs = { rhs_env = pb.env;
       rhs_vars = Id.Set.empty;
       avoid_ids = Id.Set.empty;
       it = None };
      alias_stack = Anonymous::aliasnames;
      eqn_loc = None;
      used = ref false } ]

let adjust_impossible_cases sigma pb pred tomatch submat =
  match submat with
  | [] ->
    (* FIXME: This breaks if using evar-insensitive primitives. In particular,
       this means that the Evd.define below may redefine an already defined
       evar. See e.g. first definition of test for bug #3388. *)
    let pred = EConstr.Unsafe.to_constr pred in
    begin match Constr.kind pred with
    | Evar (evk,_) when snd (evar_source evk sigma) == Evar_kinds.ImpossibleCase ->
        let sigma =
          if not (Evd.is_defined sigma evk) then
            let sigma, default = use_unit_judge pb.env sigma in
            let sigma = Evd.define evk default.uj_type sigma in
            sigma
          else sigma
        in
        sigma, add_assert_false_case pb tomatch
    | _ ->
        sigma, submat
    end
  | _ ->
    sigma, submat

(*****************************************************************************)
(* Let  pred = PI [X;x:I(X)]. PI tms. P  be a typing predicate for the       *)
(* following pattern-matching problem:                                       *)
(*                                                                           *)
(*  Gamma |- match Pushed(c:I(V)) as x in I(X), tms return pred with...end   *)
(*                                                                           *)
(* where the branch with constructor Ci:(x1:T1)...(xn:Tn)->I(realargsi)      *)
(* is considered. Assume each Ti is some Ii(argsi) with Ti:PI Ui. sort_i     *)
(* We let subst = X:=realargsi;x:=Ci(x1,...,xn) and replace pred by          *)
(*                                                                           *)
(* pred' = PI [X1:Ui;x1:I1(X1)]...[Xn:Un;xn:In(Xn)]. (PI tms. P)[subst]      *)
(*                                                                           *)
(* s.t. the following well-typed sub-pattern-matching problem is obtained    *)
(*                                                                           *)
(* Gamma,x'1..x'n |-                                                         *)
(*   match                                                                   *)
(*      Pushed(x'1) as x1 in I(X1),                                          *)
(*      ..,                                                                  *)
(*      Pushed(x'n) as xn in I(Xn),                                          *)
(*      tms                                                                  *)
(*      return pred'                                                         *)
(*   with .. end                                                             *)
(*                                                                           *)
(*****************************************************************************)
let specialize_predicate newtomatchs (names,depna) arsign cs tms ccl =
  (* Assume some gamma st: gamma |- PI [X,x:I(X)]. PI tms. ccl *)
  let nrealargs = List.length names in
  let l = match depna with Anonymous -> 0 | Name _ -> 1 in
  let k = nrealargs + l in
  (* We adjust pred st: gamma, x1..xn |- PI [X,x:I(X)]. PI tms. ccl' *)
  (* so that x can later be instantiated by Ci(x1..xn) *)
  (* and X by the realargs for Ci *)
  let n = cs.cs_nargs in
  let ccl' = liftn_predicate n (k+1) ccl tms in
  (* We prepare the substitution of X and x:I(X) *)
  let realargsi =
    if not (Int.equal nrealargs 0) then
      CVars.subst_of_rel_context_instance arsign (Array.to_list cs.cs_concl_realargs)
    else
      [] in
  let realargsi = List.map EConstr.of_constr realargsi in
  let copti = match depna with
  | Anonymous -> None
  | Name _ -> Some (EConstr.of_constr (build_dependent_constructor cs))
  in
  (* The substituends realargsi, copti are all defined in gamma, x1...xn *)
  (* We need _parallel_ bindings to get gamma, x1...xn |- PI tms. ccl'' *)
  (* Note: applying the substitution in tms is not important (is it sure?) *)
  let ccl'' =
    whd_betaiota Evd.empty (subst_predicate (realargsi, copti) ccl' tms) in
  (* We adjust ccl st: gamma, x'1..x'n, x1..xn, tms |- ccl'' *)
  let ccl''' = liftn_predicate n (n+1) ccl'' tms in
  (* We finally get gamma,x'1..x'n,x |- [X1;x1:I(X1)]..[Xn;xn:I(Xn)]pred'''*)
  snd (List.fold_left (expand_arg tms) (1,ccl''') newtomatchs)

let find_predicate loc env sigma p current (IndType (indf,realargs)) dep tms =
  let pred = abstract_predicate env sigma indf current realargs dep tms p in
  (pred, whd_betaiota sigma
           (applist (pred, realargs@[current])))

(* Take into account that a type has been discovered to be inductive, leading
   to more dependencies in the predicate if the type has indices *)
let adjust_predicate_from_tomatch tomatch (current,typ as ct) pb =
  let ((_,oldtyp),deps,na) = tomatch in
  match typ, oldtyp with
  | IsInd (_,_,names), NotInd _ ->
      let k = match na with
      | Anonymous -> 1
      | Name _ -> 2
      in
      let n = List.length names in
      { pb with pred = liftn_predicate n k pb.pred pb.tomatch },
      (ct,List.map (fun i -> if i >= k then i+n else i) deps,na)
  | _ ->
      pb, (ct,deps,na)

(* Remove commutative cuts that turn out to be non-dependent after
   some evars have been instantiated *)

let rec ungeneralize sigma n ng body =
  match EConstr.kind sigma body with
  | Lambda (_,_,c) when Int.equal ng 0 ->
      subst1 (mkRel n) c
  | Lambda (na,t,c) ->
      (* We traverse an inner generalization *)
      mkLambda (na,t,ungeneralize sigma (n+1) (ng-1) c)
  | LetIn (na,b,t,c) ->
      (* We traverse an alias *)
      mkLetIn (na,b,t,ungeneralize sigma (n+1) ng c)
  | Case (ci,p,c,brs) ->
      (* We traverse a split *)
      let p =
        let sign,p = decompose_lam_assum sigma p in
        let sign2,p = decompose_prod_n_assum sigma ng p in
        let p = prod_applist sigma p [mkRel (n+List.length sign+ng)] in
        it_mkLambda_or_LetIn (it_mkProd_or_LetIn p sign2) sign in
      mkCase (ci,p,c,Array.map2 (fun q c ->
        let sign,b = decompose_lam_n_decls sigma q c in
        it_mkLambda_or_LetIn (ungeneralize sigma (n+q) ng b) sign)
        ci.ci_cstr_ndecls brs)
  | App (f,args) ->
      (* We traverse an inner generalization *)
      assert (isCase sigma f);
      mkApp (ungeneralize sigma n (ng+Array.length args) f,args)
  | _ -> assert false

let ungeneralize_branch sigma n k (sign,body) cs =
  (sign,ungeneralize sigma (n+cs.cs_nargs) k body)

let rec is_dependent_generalization sigma ng body =
  match EConstr.kind sigma body with
  | Lambda (_,_,c) when Int.equal ng 0 ->
      not (noccurn sigma 1 c)
  | Lambda (na,t,c) ->
      (* We traverse an inner generalization *)
      is_dependent_generalization sigma (ng-1) c
  | LetIn (na,b,t,c) ->
      (* We traverse an alias *)
      is_dependent_generalization sigma ng c
  | Case (ci,p,c,brs) ->
      (* We traverse a split *)
      Array.exists2 (fun q c ->
        let _,b = decompose_lam_n_decls sigma q c in
        is_dependent_generalization sigma ng b)
        ci.ci_cstr_ndecls brs
  | App (g,args) ->
      (* We traverse an inner generalization *)
      assert (isCase sigma g);
      is_dependent_generalization sigma (ng+Array.length args) g
  | _ -> assert false

let is_dependent_branch sigma k (_,br) =
  is_dependent_generalization sigma k br

let postprocess_dependencies evd tocheck brs tomatch pred deps cs =
  let rec aux k brs tomatch pred tocheck deps = match deps, tomatch with
  | [], _ -> brs,tomatch,pred,[]
  | n::deps, Abstract (i,d) :: tomatch ->
      let d = map_constr (fun c -> nf_evar evd c) d in
      let is_d = match d with LocalAssum _ -> false | LocalDef _ -> true in
      if is_d || List.exists (fun c -> dependent_decl evd (lift k c) d) tocheck
                 && Array.exists (is_dependent_branch evd k) brs then
        (* Dependency in the current term to match and its dependencies is real *)
        let brs,tomatch,pred,inst = aux (k+1) brs tomatch pred (mkRel n::tocheck) deps in
        let inst = match d with
        | LocalAssum _ -> mkRel n :: inst
        | _ -> inst
        in
        brs, Abstract (i,d) :: tomatch, pred, inst
      else
        (* Finally, no dependency remains, so, we can replace the generalized *)
        (* terms by its actual value in both the remaining terms to match and *)
        (* the bodies of the Case *)
        let pred = lift_predicate (-1) pred tomatch in
        let tomatch = relocate_index_tomatch evd 1 (n+1) tomatch in
        let tomatch = lift_tomatch_stack (-1) tomatch in
        let brs = Array.map2 (ungeneralize_branch evd n k) brs cs in
        aux k brs tomatch pred tocheck deps
  | _ -> assert false
  in aux 0 brs tomatch pred tocheck deps

(************************************************************************)
(* Sorting equations by constructor *)

let rec irrefutable env pat = match DAst.get pat with
  | PatVar name -> true
  | PatCstr (cstr,args,_) ->
      let ind = inductive_of_constructor cstr in
      let (_,mip) = Inductive.lookup_mind_specif env ind in
      let one_constr = Int.equal (Array.length mip.mind_user_lc) 1 in
      one_constr && List.for_all (irrefutable env) args

let first_clause_irrefutable env = function
  | eqn::mat -> List.for_all (irrefutable env) eqn.patterns
  | _ -> false

let group_equations pb ind current cstrs mat =
  let mat =
    if first_clause_irrefutable !!(pb.env) mat then [List.hd mat] else mat in
  let brs = Array.make (Array.length cstrs) [] in
  let only_default = ref None in
  let _ =
    List.fold_right (* To be sure it's from bottom to top *)
      (fun eqn () ->
  let rest = remove_current_pattern eqn in
  let pat = current_pattern eqn in
         match DAst.get (check_and_adjust_constructor !!(pb.env) ind cstrs pat) with
    | PatVar name ->
        (* This is a default clause that we expand *)
        for i=1 to Array.length cstrs do
   let args = make_anonymous_patvars cstrs.(i-1).cs_nargs in
   brs.(i-1) <- (args, name, rest) :: brs.(i-1)
        done;
        if !only_default == None then only_default := Some true
    | PatCstr (((_,i)),args,name) ->
        (* This is a regular clause *)
        only_default := Some false;
        brs.(i-1) <- (args, name, rest) :: brs.(i-1)) mat () in
  (brs,Option.default false !only_default)

(************************************************************************)
(* Here starts the pattern-matching compilation algorithm *)

(* Abstracting over dependent subterms to match *)
let rec generalize_problem names sigma pb = function
  | [] -> pb, []
  | i::l ->
      let pb',deps = generalize_problem names sigma pb l in
      let d = map_constr (lift i) (lookup_rel i !!(pb.env)) in
      begin match d with
      | LocalDef ({binder_name=Anonymous},_,_) -> pb', deps
      | _ ->
  (* for better rendering *)
        let d = RelDecl.map_type (fun c -> whd_betaiota sigma c) d in
        let tomatch = lift_tomatch_stack 1 pb'.tomatch in
        let tomatch = relocate_index_tomatch sigma (i+1) 1 tomatch in
        { pb' with
            tomatch = Abstract (i,d) :: tomatch;
            pred = generalize_predicate sigma names i d pb'.tomatch pb'.pred  },
        i::deps
      end

(* No more patterns: typing the right-hand side of equations *)
let build_leaf sigma pb =
  let rhs = extract_rhs pb in
  let sigma, j = pb.typing_function (mk_tycon pb.pred) rhs.rhs_env sigma rhs.it in
  sigma, j_nf_evar sigma j

(* Build the sub-pattern-matching problem for a given branch "C x1..xn as x" *)
(* spiwack: the [initial] argument keeps track whether the branch is a
   toplevel branch ([true]) or a deep one ([false]). *)
let build_branch ~program_mode initial current realargs deps (realnames,curname) sigma pb arsign eqns const_info =
  (* We remember that we descend through constructor C *)
  let history =
    push_history_pattern const_info.cs_nargs (fst const_info.cs_cstr) pb.history in

  (* We prepare the matching on x1:T1 .. xn:Tn using some heuristic to *)
  (* build the name x1..xn from the names present in the equations *)
  (* that had matched constructor C *)
  let cs_args = const_info.cs_args in
  let cs_args = List.map (fun d -> map_rel_decl EConstr.of_constr d) cs_args in
  let names,aliasname = get_names (GlobEnv.vars_of_env pb.env) !!(pb.env) sigma cs_args eqns in
  let typs = List.map2 RelDecl.set_name names cs_args
  in

  (* Beta-iota-normalize types to better compatibility of refine with 8.4 behavior *)
  (* This is a bit too strong I think, in the sense that what we would *)
  (* really like is to have beta-iota reduction only at the positions where *)
  (* parameters are substituted *)
  let typs = List.map (map_type (nf_betaiota !!(pb.env) sigma)) typs in

  (* We build the matrix obtained by expanding the matching on *)
  (* "C x1..xn as x" followed by a residual matching on eqn into *)
  (* a matching on "x1 .. xn eqn" *)
  let submat = List.map (fun (tms,_,eqn) -> prepend_pattern tms eqn) eqns in

  (* We adjust the terms to match in the context they will be once the *)
  (* context [x1:T1,..,xn:Tn] will have been pushed on the current env *)
  let typs' =
    List.map_i (fun i d -> (mkRel i, map_constr (lift i) d)) 1 typs in

  let hypnaming = if program_mode then ProgramNaming else KeepUserNameAndRenameExistingButSectionNames in
  let typs,extenv = push_rel_context ~hypnaming sigma typs pb.env in

  let typs' =
    List.map (fun (c,d) ->
      (c,extract_inductive_data !!extenv sigma d,d)) typs' in

  (* We compute over which of x(i+1)..xn and x matching on xi will need a *)
  (* generalization *)
  let dep_sign =
    find_dependencies_signature sigma
      (dependencies_in_rhs ~program_mode sigma const_info.cs_nargs current pb.tomatch eqns)
      (List.rev typs') in

  (* The dependent term to subst in the types of the remaining UnPushed
     terms is relative to the current context enriched by topushs *)
  let ci = EConstr.of_constr (build_dependent_constructor const_info) in

  (* Current context Gamma has the form Gamma1;cur:I(realargs);Gamma2 *)
  (* We go from Gamma |- PI tms. pred to                              *)
  (* Gamma;x1..xn;curalias:I(x1..xn) |- PI tms'. pred'                *)
  (* where, in tms and pred, those realargs that are vars are         *)
  (* replaced by the corresponding xi and cur replaced by curalias    *)
  let cirealargs = Array.map_to_list EConstr.of_constr const_info.cs_concl_realargs in

  (* Do the specialization for terms to match *)
  let tomatch = List.fold_right2 (fun par arg tomatch ->
    match EConstr.kind sigma par with
    | Rel i -> replace_tomatch sigma (i+const_info.cs_nargs) arg tomatch
    | _ -> tomatch) (current::realargs) (ci::cirealargs)
      (lift_tomatch_stack const_info.cs_nargs pb.tomatch) in

  let pred_is_not_dep =
    noccur_predicate_between sigma 1 (List.length realnames + 1) pb.pred tomatch in

  let typs' =
    List.map2
      (fun (tm, (tmtyp,_), decl) deps ->
        let na = RelDecl.get_name decl in
let na = match curname, na with
| Name _, Anonymous -> curname
| Name _, Name _ -> na
| Anonymous, _ ->
     if List.is_empty deps && pred_is_not_dep then Anonymous else force_name na in
((tm,tmtyp),deps,na))
      typs' (List.rev dep_sign) in

  (* Do the specialization for the predicate *)
  let pred =
    specialize_predicate typs' (realnames,curname) arsign const_info tomatch pb.pred in

  let currents = List.map (fun x -> Pushed (false,x)) typs' in

  let alias = match aliasname with
  | Anonymous ->
      NonDepAlias
  | Name _ ->
      let cur_alias = lift const_info.cs_nargs current in
      let ind =
        mkApp (
          applist (mkIndU (inductive_of_constructor (fst const_info.cs_cstr), EInstance.make (snd const_info.cs_cstr)),
                   List.map (EConstr.of_constr %> lift const_info.cs_nargs) const_info.cs_params),
          Array.map EConstr.of_constr const_info.cs_concl_realargs) in
      Alias (initial,(aliasname,cur_alias,(ci,ind))) in

  let tomatch = List.rev_append (alias :: currents) tomatch in

  let sigma, submat = adjust_impossible_cases sigma pb pred tomatch submat in
  let () = match submat with
  | [] ->
    raise_pattern_matching_error (!!(pb.env), Evd.empty, NonExhaustive (complete_history history))
  | _ -> ()
  in

  sigma, typs,
  { pb with
      env = extenv;
      tomatch = tomatch;
      pred = pred;
      history = history;
      mat = List.map (push_rels_eqn_with_names ~hypnaming sigma typs) submat }

(**********************************************************************
INVARIANT:

  pb = { env, pred, tomatch, mat, ...}
  tomatch = list of Pushed (c:T), Abstract (na:T), Alias (c:T) or NonDepAlias

  all terms and types in Pushed, Abstract and Alias are relative to env
  enriched by the Abstract coming before

*)

(**********************************************************************)
(* Main compiling descent *)
let compile ~program_mode sigma pb =
  let rec compile sigma pb =
    match pb.tomatch with
      | Pushed cur :: rest -> match_current sigma { pb with tomatch = rest } cur
      | Alias (initial,x) :: rest -> compile_alias initial sigma pb x rest
      | NonDepAlias :: rest -> compile_non_dep_alias sigma pb rest
      | Abstract (i,d) :: rest -> compile_generalization sigma pb i d rest
      | [] -> build_leaf sigma pb

(* Case splitting *)
  and match_current sigma pb (initial,tomatch) =
    let sigma, tm = adjust_tomatch_to_pattern ~program_mode sigma pb tomatch in
    let pb,tomatch = adjust_predicate_from_tomatch tomatch tm pb in
    let ((current,typ),deps,dep) = tomatch in
    match typ with
      | NotInd (_,typ) ->
          check_all_variables !!(pb.env) sigma typ pb.mat;
          compile_all_variables initial tomatch sigma pb
      | IsInd (_,(IndType(indf,realargs) as indt),names) ->
let mind,_ = dest_ind_family indf in
          let mind = Tacred.check_privacy !!(pb.env) mind in
          let cstrs = get_constructors !!(pb.env) indf in
          let arsign, _ = get_arity !!(pb.env) indf in
let eqns,onlydflt = group_equations pb (fst mind) current cstrs pb.mat in
          let no_cstr = Int.equal (Array.length cstrs) 0 in
if (not no_cstr || not (List.is_empty pb.mat)) && onlydflt then
            compile_all_variables initial tomatch sigma pb
else
   (* We generalize over terms depending on current term to match *)
            let pb,deps = generalize_problem (names,dep) sigma pb deps in

   (* We compile branches *)
            let fold_br sigma eqn cstr =
              compile_branch initial current realargs (names,dep) deps sigma pb arsign eqn cstr
            in
            let sigma, brvals = Array.fold_left2_map fold_br sigma eqns cstrs in
   (* We build the (elementary) case analysis *)
            let depstocheck = current::binding_vars_of_inductive sigma typ in
            let brvals,tomatch,pred,inst =
              postprocess_dependencies sigma depstocheck
                brvals pb.tomatch pb.pred deps cstrs in
            let brvals = Array.map (fun (sign,body) ->
              it_mkLambda_or_LetIn body sign) brvals in
            let (pred,typ) =
              find_predicate pb.caseloc pb.env sigma
                pred current indt (names,dep) tomatch
            in
            let rci = Typing.check_allowed_sort !!(pb.env) sigma mind current pred in
            let ci = make_case_info !!(pb.env) (fst mind) rci pb.casestyle in
            let pred = nf_betaiota !!(pb.env) sigma pred in
            let case = make_case_or_project !!(pb.env) sigma indf ci pred current brvals in
            let sigma, _ = Typing.type_of !!(pb.env) sigma pred in
            sigma, { uj_val = applist (case, inst);
              uj_type = prod_applist sigma typ inst }

  (* Building the sub-problem when all patterns are variables. Case
     where [current] is an initially pushed term. *)
  and shift_problem ((current,t),_,na) sigma pb =
    let ty = type_of_tomatch t in
    let tomatch = lift_tomatch_stack 1 pb.tomatch in
    let pred = specialize_predicate_var (current,t,na) !!(pb.env) pb.tomatch pb.pred in
    let env = Name.fold_left (fun env id -> hide_variable env Anonymous id) pb.env na in
    let hypnaming = if program_mode then ProgramNaming else KeepUserNameAndRenameExistingButSectionNames in
    let pb =
      { pb with
         env = snd (push_rel ~hypnaming sigma (LocalDef (annotR na,current,ty)) env);
         tomatch = tomatch;
         pred = lift_predicate 1 pred tomatch;
         history = pop_history pb.history;
         mat = List.map (push_current_pattern ~program_mode sigma (current,ty)) pb.mat } in
    let sigma, j = compile sigma pb in
    sigma, { uj_val = subst1 current j.uj_val;
      uj_type = subst1 current j.uj_type }

  (* Building the sub-problem when all patterns are variables,
     non-initial case. Variables which appear as subterms of constructor
     are already introduced in the context, we avoid creating aliases to
     themselves by treating this case specially. *)
  and pop_problem ((current,t),_,na) sigma pb =
    let pred = specialize_predicate_var (current,t,na) !!(pb.env) pb.tomatch pb.pred in
    let pb =
      { pb with
         pred = pred;
         history = pop_history pb.history;
         mat = List.map push_noalias_current_pattern pb.mat } in
    compile sigma pb

  (* Building the sub-problem when all patterns are variables. *)
  and compile_all_variables initial cur sigma pb =
    if initial then shift_problem cur sigma pb
    else pop_problem cur sigma pb

  (* Building the sub-problem when all patterns are variables *)
  and compile_branch initial current realargs names deps sigma pb arsign eqns cstr =
    let sigma, sign, pb = build_branch ~program_mode initial current realargs deps names sigma pb arsign eqns cstr in
    let sigma, j = compile sigma pb in
    sigma, (sign, j.uj_val)

  (* Abstract over a declaration before continuing splitting *)
  and compile_generalization sigma pb i d rest =
    let hypnaming = if program_mode then ProgramNaming else KeepUserNameAndRenameExistingButSectionNames in
    let pb =
      { pb with
         env = snd (push_rel ~hypnaming sigma d pb.env);
         tomatch = rest;
         mat = List.map (push_generalized_decl_eqn ~hypnaming pb.env sigma i d) pb.mat } in
    let sigma, j = compile sigma pb in
    sigma, { uj_val = mkLambda_or_LetIn d j.uj_val;
      uj_type = mkProd_wo_LetIn d j.uj_type }

  (* spiwack: the [initial] argument keeps track whether the alias has
     been introduced by a toplevel branch ([true]) or a deep one
     ([false]). *)
  and compile_alias initial sigma pb (na,orig,(expanded,expanded_typ)) rest =
    let hypnaming = if program_mode then ProgramNaming else KeepUserNameAndRenameExistingButSectionNames in
    let f c t =
      let r = Retyping.relevance_of_type !!(pb.env) sigma t in
      let alias = LocalDef (make_annot na r,c,t) in
      let pb =
        { pb with
           env = snd (push_rel ~hypnaming sigma alias pb.env);
           tomatch = lift_tomatch_stack 1 rest;
           pred = lift_predicate 1 pb.pred pb.tomatch;
           history = pop_history_pattern pb.history;
           mat = List.map (push_alias_eqn ~hypnaming sigma alias) pb.mat } in
      let sigma, j = compile sigma pb in
      sigma, { uj_val =
          if isRel sigma c || isVar sigma c || count_occurrences sigma (mkRel 1) j.uj_val <= 1 then
            subst1 c j.uj_val
          else
            mkLetIn (make_annot na r,c,t,j.uj_val);
        uj_type = subst1 c j.uj_type } in
    (* spiwack: when an alias appears on a deep branch, its non-expanded
       form is automatically a variable of the same name. We avoid
       introducing such superfluous aliases so that refines are elegant. *)
    let just_pop sigma =
      let pb =
        { pb with
          tomatch = rest;
          history = pop_history_pattern pb.history;
          mat = List.map drop_alias_eqn pb.mat } in
      compile sigma pb
    in
    (* If the "match" was originally over a variable, as in "match x with
       O => true | n => n end", we give preference to non-expansion in
       the default clause (i.e. "match x with O => true | n => n end"
       rather than "match x with O => true | S p => S p end";
       computationally, this avoids reallocating constructors in cbv
       evaluation; the drawback is that it might duplicate the instances
       of the term to match when the corresponding variable is
       substituted by a non-evaluated expression *)
    if not program_mode && (isRel sigma orig || isVar sigma orig) then
      (* Try to compile first using non expanded alias *)
      try
        if initial then f orig (Retyping.get_type_of !!(pb.env) sigma orig)
        else just_pop sigma
      with e when precatchable_exception e ->
      (* Try then to compile using expanded alias *)
      (* Could be needed in case of dependent return clause *)
      f expanded expanded_typ
    else
      (* Try to compile first using expanded alias *)
      try f expanded expanded_typ
      with e when precatchable_exception e ->
      (* Try then to compile using non expanded alias *)
      (* Could be needed in case of a recursive call which requires to
         be on a variable for size reasons *)
      if initial then f orig (Retyping.get_type_of !!(pb.env) sigma orig)
      else just_pop sigma

  (* Remember that a non-trivial pattern has been consumed *)
  and compile_non_dep_alias sigma pb rest =
    let pb =
      { pb with
         tomatch = rest;
         history = pop_history_pattern pb.history;
         mat = List.map drop_alias_eqn pb.mat } in
    compile sigma pb
  in
  compile sigma pb

(* pour les alias des initiaux, enrichir les env de ce qu'il faut et
substituer après par les initiaux *)

(**************************************************************************)
(* Preparation of the pattern-matching problem                            *)

(* builds the matrix of equations testing that each eqn has n patterns
* and linearizing the _ patterns.
* Syntactic correctness has already been done in constrintern *)
let matx_of_eqns env eqns =
  let build_eqn {CAst.loc;v=(ids,initial_lpat,initial_rhs)} =
    let avoid = ids_of_named_context_val (named_context_val !!env) in
    let avoid = List.fold_left (fun accu id -> Id.Set.add id accu) avoid ids in
    let rhs =
      { rhs_env = env;
        rhs_vars = free_glob_vars initial_rhs;
avoid_ids = avoid;
it = Some initial_rhs } in
    { patterns = initial_lpat;
      alias_stack = [];
      eqn_loc = loc;
      used = ref false;
      rhs = rhs }
--> --------------------

--> maximum size reached

--> --------------------

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