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Datei: indfun.ml Sprache: SML

Original von: Coq^©

open CErrors
open Sorts
open Util
open Names
open Constr
open Context
open EConstr
open Pp
open Indfun_common
open Libnames
open Globnames
open Glob_term
open Declarations
open Tactypes
open Decl_kinds

module RelDecl = Context.Rel.Declaration

let is_rec_info sigma scheme_info =
  let test_branche min acc decl =
    acc || (
      let new_branche =
it_mkProd_or_LetIn mkProp (fst (decompose_prod_assum sigma (RelDecl.get_type decl))) in
      let free_rels_in_br = Termops.free_rels sigma new_branche in
      let max = min + scheme_info.Tactics.npredicates in
      Int.Set.exists (fun i -> i >= min && i< max) free_rels_in_br
    )
  in
  List.fold_left_i test_branche 1 false (List.rev scheme_info.Tactics.branches)

let choose_dest_or_ind scheme_info args =
  Proofview.tclBIND Proofview.tclEVARMAP (fun sigma ->
  Tactics.induction_destruct (is_rec_info sigma scheme_info) false args)

let functional_induction with_clean c princl pat =
  let res =
    fun g ->
    let sigma = Tacmach.project g in
    let f,args = decompose_app sigma c in
    let princ,bindings, princ_type,g' =
      match princl with
      | None -> (* No principle is given let's find the good one *)
  begin
    match EConstr.kind sigma f with
    | Const (c',u) ->
       let princ_option =
  let finfo = (* we first try to find out a graph on f *)
    try find_Function_infos c'
    with Not_found ->
      user_err  (str "Cannot find induction information on "++
                                       Printer.pr_leconstr_env (Tacmach.pf_env g) sigma (mkConst c') )
  in
                match Tacticals.elimination_sort_of_goal g with
                | InSProp -> finfo.sprop_lemma
  | InProp -> finfo.prop_lemma
  | InSet -> finfo.rec_lemma
  | InType -> finfo.rect_lemma
       in
       let princ,g' = (* then we get the principle *)
  try
    let g',princ =
      Tacmach.pf_eapply (Evd.fresh_global) g  (Globnames.ConstRef (Option.get princ_option )) in
    princ,g'
  with Option.IsNone ->
    (*i If there is not default lemma defined then,
  we cross our finger and try to find a lemma named f_ind
  (or f_rec, f_rect) i*)
    let princ_name =
      Indrec.make_elimination_ident
        (Label.to_id (Constant.label c'))
        (Tacticals.elimination_sort_of_goal g)
    in
    try
      let princ_ref = const_of_id princ_name in
      let (a,b) = Tacmach.pf_eapply (Evd.fresh_global) g princ_ref in
      (b,a)
      (* mkConst(const_of_id princ_name ),g (\* FIXME *\) *)
    with Not_found -> (* This one is neither defined ! *)
      user_err  (str "Cannot find induction principle for "
                                     ++ Printer.pr_leconstr_env (Tacmach.pf_env g) sigma (mkConst c') )
       in
              (princ,NoBindings,Tacmach.pf_unsafe_type_of g' princ,g')
    | _ -> raise (UserError(None,str "functional induction must be used with a function" ))
  end
      | Some ((princ,binding)) ->
  princ,binding,Tacmach.pf_unsafe_type_of g princ,g
    in
    let sigma = Tacmach.project g' in
    let princ_infos = Tactics.compute_elim_sig (Tacmach.project g') princ_type in
    let args_as_induction_constr =
      let c_list =
if princ_infos.Tactics.farg_in_concl
then [c] else []
      in
      if List.length args + List.length c_list = 0
      then user_err Pp.(str "Cannot recognize a valid functional scheme" );
      let encoded_pat_as_patlist =
        List.make (List.length args + List.length c_list - 1) None @ [pat]
      in
      List.map2
        (fun c pat ->
          ((None,
            Tactics.ElimOnConstr (fun env sigma -> (sigma,(c,NoBindings)))),
           (None,pat),
           None))
        (args@c_list)
        encoded_pat_as_patlist
    in
    let princ' = Some (princ,bindings) in
    let princ_vars =
      List.fold_right
(fun a acc -> try Id.Set.add (destVar sigma a) acc with DestKO -> acc)
args
Id.Set.empty
    in
    let old_idl = List.fold_right Id.Set.add (Tacmach.pf_ids_of_hyps g) Id.Set.empty in
    let old_idl = Id.Set.diff old_idl princ_vars in
    let subst_and_reduce g =
      if with_clean
      then
let idl =
   List.filter (fun id -> not (Id.Set.mem id old_idl))
     (Tacmach.pf_ids_of_hyps g)
in
let flag =
   Genredexpr.Cbv
     {Redops.all_flags
      with Genredexpr.rDelta = false;
     }
in
Tacticals.tclTHEN
   (Tacticals.tclMAP (fun id -> Tacticals.tclTRY (Proofview.V82.of_tactic (Equality.subst_gen (do_rewrite_dependent ()) [id]))) idl )
   (Proofview.V82.of_tactic (Tactics.reduce flag Locusops.allHypsAndConcl))
   g
      else Tacticals.tclIDTAC g
    in
    Tacticals.tclTHEN
      (Proofview.V82.of_tactic (choose_dest_or_ind
  princ_infos
  (args_as_induction_constr,princ')))
      subst_and_reduce
      g'
  in res

let rec abstract_glob_constr c = function
  | [] -> c
  | Constrexpr.CLocalDef (x,b,t)::bl -> Constrexpr_ops.mkLetInC(x,b,t,abstract_glob_constr c bl)
  | Constrexpr.CLocalAssum (idl,k,t)::bl ->
      List.fold_right (fun x b -> Constrexpr_ops.mkLambdaC([x],k,t,b)) idl
        (abstract_glob_constr c bl)
  | Constrexpr.CLocalPattern _::bl -> assert false

let interp_casted_constr_with_implicits env sigma impls c  =
  Constrintern.intern_gen Pretyping.WithoutTypeConstraint env sigma ~impls c

(*
   Construct a fixpoint as a Glob_term
   and not as a constr
*)

let build_newrecursive
    lnameargsardef  =
  let env0 = Global.env() in
  let sigma = Evd.from_env env0 in
  let (rec_sign,rec_impls) =
    List.fold_left
      (fun (env,impls) (({CAst.v=recname},_),bl,arityc,_) ->
        let arityc = Constrexpr_ops.mkCProdN bl arityc in
        let arity,ctx = Constrintern.interp_type env0 sigma arityc in
        let evd = Evd.from_env env0 in
        let evd, (_, (_, impls')) = Constrintern.interp_context_evars ~program_mode:false env evd bl in
        let impl = Constrintern.compute_internalization_data env0 evd Constrintern.Recursive arity impls' in
        let open Context.Named.Declaration in
        let r = Sorts.Relevant in (* TODO relevance *)
        (EConstr.push_named (LocalAssum (make_annot recname r,arity)) env, Id.Map.add recname impl impls))
      (env0,Constrintern.empty_internalization_env) lnameargsardef in
  let recdef =
    (* Declare local notations *)
    let f (_,bl,_,def) =
      let def = abstract_glob_constr def bl in
      interp_casted_constr_with_implicits
        rec_sign sigma rec_impls def
    in
    States.with_state_protection (List.map f) lnameargsardef
  in
  recdef,rec_impls

let build_newrecursive l =
  let l' = List.map
    (fun ((fixna,_,bll,ar,body_opt),lnot) ->
       match body_opt with
  | Some body ->
      (fixna,bll,ar,body)
  | None -> user_err ~hdr:"Function" (str "Body of Function must be given")
    ) l
  in
  build_newrecursive l'

let error msg = user_err Pp.(str msg)

(* Checks whether or not the mutual bloc is recursive *)
let is_rec names =
  let names = List.fold_right Id.Set.add names Id.Set.empty in
  let check_id id names =  Id.Set.mem id names in
  let rec lookup names gt = match DAst.get gt with
    | GVar(id) -> check_id id names
    | GRef _ | GEvar _ | GPatVar _ | GSort _ |  GHole _ | GInt _ -> false
    | GCast(b,_) -> lookup names b
    | GRec _ -> error "GRec not handled"
    | GIf(b,_,lhs,rhs) ->
(lookup names b) || (lookup names lhs) || (lookup names rhs)
    | GProd(na,_,t,b) | GLambda(na,_,t,b) ->
lookup names t || lookup (Nameops.Name.fold_right Id.Set.remove na names) b
    | GLetIn(na,b,t,c) ->
lookup names b || Option.cata (lookup names) true t || lookup (Nameops.Name.fold_right Id.Set.remove na names) c
    | GLetTuple(nal,_,t,b) -> lookup names t ||
lookup
   (List.fold_left
      (fun acc na -> Nameops.Name.fold_right Id.Set.remove na acc)
      names
      nal
   )
   b
    | GApp(f,args) -> List.exists (lookup names) (f::args)
    | GCases(_,_,el,brl) ->
List.exists (fun (e,_) -> lookup names e) el ||
   List.exists (lookup_br names) brl
  and lookup_br names {CAst.v=(idl,_,rt)} =
    let new_names = List.fold_right Id.Set.remove idl names in
    lookup new_names rt
  in
  lookup names

let rec local_binders_length = function
  (* Assume that no `{ ... } contexts occur *)
  | [] -> 0
  | Constrexpr.CLocalDef _::bl -> 1 + local_binders_length bl
  | Constrexpr.CLocalAssum (idl,_,_)::bl -> List.length idl + local_binders_length bl
  | Constrexpr.CLocalPattern _::bl -> assert false

let prepare_body ((name,_,args,types,_),_) rt =
  let n = local_binders_length args in
(*   Pp.msgnl (str "nb lambda to chop : " ++ str (string_of_int n) ++ fnl () ++Printer.pr_glob_constr rt); *)
  let fun_args,rt' = chop_rlambda_n n rt in
  (fun_args,rt')

let process_vernac_interp_error e =
  fst (ExplainErr.process_vernac_interp_error (e, Exninfo.null))

let warn_funind_cannot_build_inversion =
  CWarnings.create ~name:"funind-cannot-build-inversion" ~category:"funind"
    (fun e' -> strbrk "Cannot build inversion information" ++
                 if do_observe () then (fnl() ++ CErrors.print e') else mt ())

let derive_inversion fix_names =
  try
    let evd' = Evd.from_env (Global.env ()) in
    (* we first transform the fix_names identifier into their corresponding constant *)
    let evd',fix_names_as_constant =
      List.fold_right
(fun id (evd,l) ->
  let evd,c =
    Evd.fresh_global
      (Global.env ()) evd (Constrintern.locate_reference (Libnames.qualid_of_ident id)) in
        let (cst, u) = destConst evd c in
  evd, (cst, EInstance.kind evd u) :: l
)
fix_names
(evd',[])
    in
    (*
       Then we check that the graphs have been defined
       If one of the graphs haven't been defined
       we do nothing
    *)
    List.iter (fun c -> ignore (find_Function_infos (fst c))) fix_names_as_constant ;
    try
      let evd', lind =
List.fold_right
   (fun id (evd,l) ->
    let evd,id =
      Evd.fresh_global
        (Global.env ()) evd
        (Constrintern.locate_reference (Libnames.qualid_of_ident (mk_rel_id id)))
    in
           evd,(fst (destInd evd id))::l
   )
   fix_names
   (evd',[])
      in
      Invfun.derive_correctness
Functional_principles_types.make_scheme
fix_names_as_constant
lind;
      with e when CErrors.noncritical e ->
      let e' = process_vernac_interp_error e in
      warn_funind_cannot_build_inversion e'
  with e when CErrors.noncritical e ->
    let e' = process_vernac_interp_error e in
    warn_funind_cannot_build_inversion e'

let warn_cannot_define_graph =
  CWarnings.create ~name:"funind-cannot-define-graph" ~category:"funind"
    (fun (names,error) -> strbrk "Cannot define graph(s) for " ++
      h 1 names ++ error)

let warn_cannot_define_principle =
  CWarnings.create ~name:"funind-cannot-define-principle" ~category:"funind"
  (fun (names,error) -> strbrk "Cannot define induction principle(s) for "++
      h 1 names ++ error)

let warning_error names e =
  let e = process_vernac_interp_error e in
  let e_explain e =
    match e with
      | ToShow e ->
let e = process_vernac_interp_error e in
spc () ++ CErrors.print e
      | _ ->
if do_observe ()
then
   let e = process_vernac_interp_error e in
   (spc () ++ CErrors.print e)
else mt ()
  in
  match e with
    | Building_graph e ->
       let names = prlist_with_sep (fun _ -> str","++spc ()) Ppconstr.pr_id names in
       warn_cannot_define_graph (names,e_explain e)
    | Defining_principle e ->
       let names = prlist_with_sep (fun _ -> str","++spc ()) Ppconstr.pr_id names in
       warn_cannot_define_principle (names,e_explain e)
    | _ -> raise e

let error_error names e =
  let e = process_vernac_interp_error e in
  let e_explain e =
    match e with
      | ToShow e -> spc () ++ CErrors.print e
      | _ -> if do_observe () then (spc () ++ CErrors.print e) else mt ()
  in
  match e with
    | Building_graph e ->
user_err
   (str "Cannot define graph(s) for " ++
      h 1 (prlist_with_sep (fun _ -> str","++spc ()) Ppconstr.pr_id names) ++
      e_explain e)
    | _ -> raise e

let generate_principle (evd:Evd.evar_map ref) pconstants on_error
    is_general do_built (fix_rec_l:(Vernacexpr.fixpoint_expr * Vernacexpr.decl_notation list) list) recdefs  interactive_proof
    (continue_proof : int -> Names.Constant.t array -> EConstr.constr array -> int ->
      Tacmach.tactic) : unit =
  let names = List.map (function (({CAst.v=name},_),_,_,_,_),_ -> name) fix_rec_l in
  let fun_bodies = List.map2 prepare_body fix_rec_l recdefs in
  let funs_args = List.map fst fun_bodies in
  let funs_types =  List.map (function ((_,_,_,types,_),_) -> types) fix_rec_l in
  try
    (* We then register the Inductive graphs of the functions  *)
    Glob_term_to_relation.build_inductive !evd pconstants funs_args funs_types recdefs;
    if do_built
    then
      begin
(*i The next call to mk_rel_id is valid since we have just construct the graph
   Ensures by : do_built
i*)
        let f_R_mut = qualid_of_ident @@ mk_rel_id (List.nth names 0) in
let ind_kn =
   fst (locate_with_msg
                 (pr_qualid f_R_mut++str ": Not an inductive type!")
   locate_ind
   f_R_mut)
in
let fname_kn (((fname,_),_,_,_,_),_) =
   let f_ref = qualid_of_ident ?loc:fname.CAst.loc fname.CAst.v in
          locate_with_msg
            (pr_qualid f_ref++str ": Not an inductive type!")
     locate_constant
     f_ref
in
let funs_kn = Array.of_list (List.map fname_kn fix_rec_l) in
let _ =
   List.map_i
     (fun i x ->
      let princ = Indrec.lookup_eliminator (ind_kn,i) (InProp) in
      let env = Global.env () in
      let evd = ref (Evd.from_env env) in
      let evd',uprinc = Evd.fresh_global env !evd princ in
             let _ = evd := evd' in
             let sigma, princ_type = Typing.type_of ~refresh:true env !evd uprinc in
             evd := sigma;
      let princ_type = EConstr.Unsafe.to_constr princ_type in
          Functional_principles_types.generate_functional_principle
        evd
   interactive_proof
   princ_type
   None
   None
   (Array.of_list pconstants)
   (* funs_kn *)
   i
   (continue_proof  0 [|funs_kn.(i)|])
     )
     0
     fix_rec_l
in
Array.iter (add_Function is_general) funs_kn;
()
      end
  with e when CErrors.noncritical e ->
    on_error names e

let register_struct ~pstate is_rec (fixpoint_exprl:(Vernacexpr.fixpoint_expr * Vernacexpr.decl_notation list) list) =
  match fixpoint_exprl with
    | [(({CAst.v=fname},pl),_,bl,ret_type,body),_] when not is_rec ->
      let body = match body with | Some body -> body | None -> user_err ~hdr:"Function" (str "Body of Function must be given") in
      ComDefinition.do_definition ~ontop:pstate
        ~program_mode:false
fname
        (Decl_kinds.Global,false,Decl_kinds.Definition) pl
        bl None body (Some ret_type);
       let evd,rev_pconstants =
  List.fold_left
           (fun (evd,l) ((({CAst.v=fname},_),_,_,_,_),_) ->
     let evd,c =
       Evd.fresh_global
  (Global.env ()) evd (Constrintern.locate_reference (Libnames.qualid_of_ident fname)) in
            let (cst, u) = destConst evd c in
            let u = EInstance.kind evd u in
            evd,((cst, u) :: l)
    )
    (Evd.from_env (Global.env ()),[])
    fixpoint_exprl
       in
       pstate, evd,List.rev rev_pconstants
    | _ ->
      let pstate = ComFixpoint.do_fixpoint ~ontop:pstate Global false fixpoint_exprl in
       let evd,rev_pconstants =
  List.fold_left
           (fun (evd,l) ((({CAst.v=fname},_),_,_,_,_),_) ->
     let evd,c =
       Evd.fresh_global
  (Global.env ()) evd (Constrintern.locate_reference (Libnames.qualid_of_ident fname)) in
            let (cst, u) = destConst evd c in
            let u = EInstance.kind evd u in
            evd,((cst, u) :: l)
    )
    (Evd.from_env (Global.env ()),[])
    fixpoint_exprl
       in
       pstate,evd,List.rev rev_pconstants

let generate_correction_proof_wf f_ref tcc_lemma_ref
    is_mes functional_ref eq_ref rec_arg_num rec_arg_type nb_args relation
    (_: int) (_:Names.Constant.t array) (_:EConstr.constr array) (_:int) : Tacmach.tactic =
  Functional_principles_proofs.prove_principle_for_gen
    (f_ref,functional_ref,eq_ref)
    tcc_lemma_ref is_mes  rec_arg_num rec_arg_type relation

let register_wf ?(is_mes=false) fname rec_impls wf_rel_expr wf_arg using_lemmas args ret_type body
    pre_hook
    =
  let type_of_f = Constrexpr_ops.mkCProdN args ret_type in
  let rec_arg_num =
    let names =
      List.map
        CAst.(with_val (fun x -> x))
(Constrexpr_ops.names_of_local_assums args)
    in
   List.index Name.equal (Name wf_arg) names
  in
  let unbounded_eq =
    let f_app_args =
      CAst.make @@ Constrexpr.CAppExpl(
         (None,qualid_of_ident fname,None) ,
  (List.map
     (function
               | {CAst.v=Anonymous} -> assert false
               | {CAst.v=Name e} -> (Constrexpr_ops.mkIdentC e)
     )
     (Constrexpr_ops.names_of_local_assums args)
  )
)
    in
    CAst.make @@ Constrexpr.CApp ((None,Constrexpr_ops.mkRefC (qualid_of_string "Logic.eq")),
      [(f_app_args,None);(body,None)])
  in
  let eq = Constrexpr_ops.mkCProdN args unbounded_eq in
  let hook ((f_ref,_) as fconst) tcc_lemma_ref (functional_ref,_) (eq_ref,_) rec_arg_num rec_arg_type
      nb_args relation =
    try
      pre_hook [fconst]
(generate_correction_proof_wf f_ref tcc_lemma_ref is_mes
    functional_ref eq_ref rec_arg_num rec_arg_type nb_args relation
);
      derive_inversion [fname]
    with e when CErrors.noncritical e ->
      (* No proof done *)
      ()
  in
  Recdef.recursive_definition
    is_mes fname rec_impls
    type_of_f
    wf_rel_expr
    rec_arg_num
    eq
    hook
    using_lemmas

let register_mes fname rec_impls wf_mes_expr wf_rel_expr_opt wf_arg using_lemmas args ret_type body =
  let wf_arg_type,wf_arg =
    match wf_arg with
      | None ->
   begin
     match args with
              | [Constrexpr.CLocalAssum ([{CAst.v=Name x}],k,t)] -> t,x
       | _ -> error "Recursive argument must be specified"
   end
      | Some wf_args ->
   try
     match
       List.find
  (function
     | Constrexpr.CLocalAssum(l,k,t) ->
         List.exists
                         (function {CAst.v=Name id} -> Id.equal id wf_args | _ -> false)
    l
     | _ -> false
  )
  args
     with
       | Constrexpr.CLocalAssum(_,k,t)  ->     t,wf_args
       | _ -> assert false
   with Not_found -> assert false
  in
  let wf_rel_from_mes,is_mes =
    match wf_rel_expr_opt with
      | None ->
   let ltof =
     let make_dir l = DirPath.make (List.rev_map Id.of_string l) in
            Libnames.qualid_of_path
              (Libnames.make_path (make_dir ["Arith";"Wf_nat"]) (Id.of_string "ltof"))
          in
   let fun_from_mes =
     let applied_mes =
       Constrexpr_ops.mkAppC(wf_mes_expr,[Constrexpr_ops.mkIdentC wf_arg])    in
            Constrexpr_ops.mkLambdaC ([CAst.make @@ Name wf_arg],Constrexpr_ops.default_binder_kind,wf_arg_type,applied_mes)
   in
   let wf_rel_from_mes =
     Constrexpr_ops.mkAppC(Constrexpr_ops.mkRefC  ltof,[wf_arg_type;fun_from_mes])
   in
   wf_rel_from_mes,true
      | Some wf_rel_expr ->
   let wf_rel_with_mes =
     let a = Names.Id.of_string "___a" in
     let b = Names.Id.of_string "___b" in
     Constrexpr_ops.mkLambdaC(
              [CAst.make @@ Name a; CAst.make @@ Name b],
       Constrexpr.Default Explicit,
       wf_arg_type,
       Constrexpr_ops.mkAppC(wf_rel_expr,
          [
    Constrexpr_ops.mkAppC(wf_mes_expr,[Constrexpr_ops.mkIdentC a]);
    Constrexpr_ops.mkAppC(wf_mes_expr,[Constrexpr_ops.mkIdentC b])
          ])
         )
   in
   wf_rel_with_mes,false
  in
  register_wf ~is_mes:is_mes fname rec_impls wf_rel_from_mes wf_arg
    using_lemmas args ret_type body

let map_option f = function
  | None -> None
  | Some v -> Some (f v)

open Constrexpr

let rec rebuild_bl aux bl typ =
match bl,typ with
   | [], _ -> List.rev aux,typ
   | (CLocalAssum(nal,bk,_))::bl',typ ->
      rebuild_nal aux bk bl' nal typ
   | (CLocalDef(na,_,_))::bl',{ CAst.v = CLetIn(_,nat,ty,typ') } ->
     rebuild_bl (Constrexpr.CLocalDef(na,nat,ty)::aux)
       bl' typ'
   | _ -> assert false
and rebuild_nal aux bk bl' nal typ =
match nal,typ with
   | _,{ CAst.v = CProdN([],typ) } -> rebuild_nal aux bk bl' nal typ
   | [], _ -> rebuild_bl aux bl' typ
          | na::nal,{ CAst.v = CProdN(CLocalAssum(na'::nal',bk',nal't)::rest,typ') } ->
             if Name.equal (na.CAst.v) (na'.CAst.v) || Name.is_anonymous (na'.CAst.v)
      then
        let assum = CLocalAssum([na],bk,nal't) in
               let new_rest = if nal' = [] then rest else (CLocalAssum(nal',bk',nal't)::rest) in
        rebuild_nal
   (assum::aux)
   bk
   bl'
   nal
   (CAst.make @@ CProdN(new_rest,typ'))
      else
        let assum = CLocalAssum([na'],bk,nal't) in
               let new_rest = if nal' = [] then rest else (CLocalAssum(nal',bk',nal't)::rest) in
        rebuild_nal
   (assum::aux)
   bk
   bl'
   (na::nal)
   (CAst.make @@ CProdN(new_rest,typ'))
   | _ ->
      assert false

let rebuild_bl aux bl typ = rebuild_bl aux bl typ

let recompute_binder_list (fixpoint_exprl : (Vernacexpr.fixpoint_expr * Vernacexpr.decl_notation list) list) =
  let fixl,ntns = ComFixpoint.extract_fixpoint_components ~structonly:false fixpoint_exprl in
  let ((_,_,_,typel),_,ctx,_) = ComFixpoint.interp_fixpoint ~cofix:false fixl ntns in
  let constr_expr_typel =
    with_full_print (List.map (fun c -> Constrextern.extern_constr false (Global.env ()) (Evd.from_ctx ctx) (EConstr.of_constr c))) typel in
  let fixpoint_exprl_with_new_bl =
    List.map2 (fun ((lna,rec_order_opt,bl,ret_typ,opt_body),notation_list) fix_typ ->

      let new_bl',new_ret_type = rebuild_bl [] bl fix_typ in
      (((lna,rec_order_opt,new_bl',new_ret_type,opt_body),notation_list):(Vernacexpr.fixpoint_expr * Vernacexpr.decl_notation list))
    )
      fixpoint_exprl constr_expr_typel
  in
  fixpoint_exprl_with_new_bl


let do_generate_principle ~pstate pconstants on_error register_built interactive_proof
    (fixpoint_exprl:(Vernacexpr.fixpoint_expr * Vernacexpr.decl_notation list) list) : Proof_global.t option =
  List.iter (fun (_,l) -> if not (List.is_empty l) then error "Function does not support notations for now") fixpoint_exprl;
  let pstate, _is_struct =
    match fixpoint_exprl with
      | [((_,Some {CAst.v = Constrexpr.CWfRec (wf_x,wf_rel)},_,_,_),_) as fixpoint_expr] ->
          let (((({CAst.v=name},pl),_,args,types,body)),_)  as fixpoint_expr =
     match recompute_binder_list [fixpoint_expr] with
       | [e] -> e
       | _ -> assert false
   in
   let fixpoint_exprl = [fixpoint_expr] in
   let body = match body with | Some body -> body | None -> user_err ~hdr:"Function" (str "Body of Function must be given") in
   let recdefs,rec_impls = build_newrecursive fixpoint_exprl in
   let using_lemmas = [] in
   let pre_hook pconstants =
     generate_principle
       (ref (Evd.from_env (Global.env ())))
       pconstants
       on_error
       true
       register_built
       fixpoint_exprl
       recdefs
       true
   in
   if register_built
          then register_wf name rec_impls wf_rel wf_x.CAst.v using_lemmas args types body pre_hook, false
          else pstate, false
      |[((_,Some {CAst.v = Constrexpr.CMeasureRec(wf_x,wf_mes,wf_rel_opt)},_,_,_),_) as fixpoint_expr] ->
          let (((({CAst.v=name},_),_,args,types,body)),_)  as fixpoint_expr =
     match recompute_binder_list [fixpoint_expr] with
       | [e] -> e
       | _ -> assert false
   in
   let fixpoint_exprl = [fixpoint_expr] in
   let recdefs,rec_impls = build_newrecursive fixpoint_exprl in
   let using_lemmas = [] in
   let body = match body with | Some body -> body | None -> user_err ~hdr:"Function" (str "Body of Function must be given") in
   let pre_hook pconstants =
     generate_principle
       (ref (Evd.from_env (Global.env ())))
       pconstants
       on_error
       true
       register_built
       fixpoint_exprl
       recdefs
       true
   in
   if register_built
          then register_mes name rec_impls wf_mes wf_rel_opt (map_option (fun x -> x.CAst.v) wf_x) using_lemmas args types body pre_hook, true
          else pstate, true
      | _ ->
          List.iter (function ((_na,ord,_args,_body,_type),_not) ->
         match ord with
                         | Some { CAst.v = (Constrexpr.CMeasureRec _ | Constrexpr.CWfRec _) } ->
        error
          ("Cannot use mutual definition with well-founded recursion or measure")
    | _ -> ()
      )
     fixpoint_exprl;
let fixpoint_exprl = recompute_binder_list fixpoint_exprl in
let fix_names =
          List.map (function ((({CAst.v=name},_),_,_,_,_),_) -> name) fixpoint_exprl
in
(* ok all the expressions are structural *)
   let recdefs,rec_impls = build_newrecursive fixpoint_exprl in
let is_rec = List.exists (is_rec fix_names) recdefs in
        let pstate,evd,pconstants =
   if register_built
          then register_struct ~pstate is_rec fixpoint_exprl
          else pstate, Evd.from_env (Global.env ()), pconstants
in
let evd = ref evd in
generate_principle
   (ref !evd)
   pconstants
   on_error
   false
   register_built
   fixpoint_exprl
   recdefs
   interactive_proof
   (Functional_principles_proofs.prove_princ_for_struct evd interactive_proof);
          if register_built then
            begin derive_inversion fix_names; end;
          pstate, true
  in
  pstate

let rec add_args id new_args = CAst.map (function
  | CRef (qid,_) as b ->
    if qualid_is_ident qid && Id.equal (qualid_basename qid) id then
      CAppExpl((None,qid,None),new_args)
    else b
  | CFix  _  | CCoFix _ -> anomaly ~label:"add_args " (Pp.str "todo.")
  | CProdN(nal,b1) ->
        CProdN(List.map (function  CLocalAssum (nal,k,b2) -> CLocalAssum (nal,k,add_args id new_args b2)
                                 | CLocalDef (na,b1,t) -> CLocalDef (na,add_args id new_args b1,Option.map (add_args id new_args) t)
                                 | CLocalPattern _ -> user_err (Pp.str "pattern with quote not allowed here.")) nal,
      add_args id new_args  b1)
  | CLambdaN(nal,b1) ->
      CLambdaN(List.map (function  CLocalAssum (nal,k,b2) -> CLocalAssum (nal,k,add_args id new_args b2)
                                 | CLocalDef (na,b1,t) -> CLocalDef (na,add_args id new_args b1,Option.map (add_args id new_args) t)
                                 | CLocalPattern _ -> user_err (Pp.str "pattern with quote not allowed here.")) nal,
        add_args id new_args  b1)
  | CLetIn(na,b1,t,b2) ->
      CLetIn(na,add_args id new_args b1,Option.map (add_args id new_args) t,add_args id new_args b2)
  | CAppExpl((pf,qid,us),exprl) ->
    if qualid_is_ident qid && Id.equal (qualid_basename qid) id then
      CAppExpl((pf,qid,us),new_args@(List.map (add_args id new_args) exprl))
    else CAppExpl((pf,qid,us),List.map (add_args id new_args) exprl)
  | CApp((pf,b),bl) ->
      CApp((pf,add_args id new_args b),
    List.map (fun (e,o) -> add_args id new_args e,o) bl)
  | CCases(sty,b_option,cel,cal) ->
      CCases(sty,Option.map (add_args id new_args) b_option,
      List.map (fun (b,na,b_option) ->
    add_args id new_args b,
    na, b_option) cel,
             List.map CAst.(map (fun (cpl,e) -> (cpl,add_args id new_args e))) cal
     )
  | CLetTuple(nal,(na,b_option),b1,b2) ->
      CLetTuple(nal,(na,Option.map (add_args id new_args) b_option),
  add_args id new_args b1,
  add_args id new_args b2
        )

  | CIf(b1,(na,b_option),b2,b3) ->
      CIf(add_args id new_args b1,
   (na,Option.map (add_args id new_args) b_option),
   add_args id new_args b2,
   add_args id new_args b3
  )
  | CHole _
  | CPatVar _
  | CEvar _
  | CPrim _
  | CSort _ as b -> b
  | CCast(b1,b2)  ->
      CCast(add_args id new_args b1,
            Glob_ops.map_cast_type (add_args id new_args) b2)
  | CRecord pars ->
      CRecord (List.map (fun (e,o) -> e, add_args id new_args o) pars)
  | CNotation _ -> anomaly ~label:"add_args " (Pp.str "CNotation.")
  | CGeneralization _ -> anomaly ~label:"add_args " (Pp.str "CGeneralization.")
  | CDelimiters _ -> anomaly ~label:"add_args " (Pp.str "CDelimiters.")
  )
exception Stop of  Constrexpr.constr_expr

(* [chop_n_arrow n t] chops the [n] first arrows in [t]
   Acts on Constrexpr.constr_expr
*)
let rec chop_n_arrow n t =
  if n <= 0
  then t (* If we have already removed all the arrows then return the type *)
  else (* If not we check the form of [t] *)
    match t.CAst.v with
      | Constrexpr.CProdN(nal_ta',t') -> (* If we have a forall, two results are possible :
     either we need to discard more than the number of arrows contained
     in this product declaration then we just recall [chop_n_arrow] on
     the remaining number of arrow to chop and [t'] we discard it and
     recall [chop_n_arrow], either this product contains more arrows
     than the number we need to chop and then we return the new type
  *)
   begin
     try
       let new_n =
  let rec aux (n:int) = function
      [] -> n
                | CLocalAssum(nal,k,t'')::nal_ta' ->
      let nal_l = List.length nal in
      if n >= nal_l
      then
        aux (n - nal_l) nal_ta'
      else
        let new_t' = CAst.make @@
   Constrexpr.CProdN(
                                        CLocalAssum((snd (List.chop n nal)),k,t'')::nal_ta',t')
        in
        raise (Stop new_t')
                | _ -> anomaly (Pp.str "Not enough products.")
  in
  aux n nal_ta'
     in
       chop_n_arrow new_n t'
     with Stop t -> t
   end
      | _ -> anomaly (Pp.str "Not enough products.")

let rec get_args b t : Constrexpr.local_binder_expr list *
    Constrexpr.constr_expr * Constrexpr.constr_expr =
  match b.CAst.v with
    | Constrexpr.CLambdaN (CLocalAssum(nal,k,ta) as d::rest, b') ->
begin
          let n = List.length nal in
          let nal_tas,b'',t'' = get_args (CAst.make ?loc:b.CAst.loc @@ Constrexpr.CLambdaN (rest,b')) (chop_n_arrow n t) in
          d :: nal_tas, b'',t''
end
    | Constrexpr.CLambdaN ([], b) -> [],b,t
    | _ -> [],b,t

let make_graph ~pstate (f_ref : GlobRef.t) =
  let sigma, env = Option.cata Pfedit.get_current_context
      (let e = Global.env () in Evd.from_env e, e) pstate in
  let c,c_body =
    match f_ref with
    | ConstRef c ->
      begin try c,Global.lookup_constant c
        with Not_found ->
          raise (UserError (None,str "Cannot find " ++ Printer.pr_leconstr_env env sigma (mkConst c)) )
      end
    | _ -> raise (UserError (None, str "Not a function reference") )
  in
  (match Global.body_of_constant_body c_body with
     | None -> error "Cannot build a graph over an axiom!"
     | Some (body, _) ->
       let env = Global.env () in
  let extern_body,extern_type =
    with_full_print (fun () ->
  (Constrextern.extern_constr false env sigma (EConstr.of_constr body),
   Constrextern.extern_type false env sigma
                   (EConstr.of_constr (*FIXME*) c_body.const_type)
  )
      )
      ()
  in
  let (nal_tas,b,t)  = get_args extern_body extern_type in
  let expr_list =
    match b.CAst.v with
    | Constrexpr.CFix(l_id,fixexprl) ->
      let l =
        List.map
          (fun (id,recexp,bl,t,b) ->
             let { CAst.loc; v=rec_id } = match Option.get recexp with
               | { CAst.v = CStructRec id } -> id
               | { CAst.v = CWfRec (id,_) } -> id
               | { CAst.v = CMeasureRec (oid,_,_) } -> Option.get oid
             in
             let new_args =
               List.flatten
                 (List.map
                    (function
                      | Constrexpr.CLocalDef (na,_,_)-> []
                      | Constrexpr.CLocalAssum (nal,_,_) ->
                        List.map
                          (fun {CAst.loc;v=n} -> CAst.make ?loc @@
                            CRef(Libnames.qualid_of_ident ?loc @@ Nameops.Name.get_id n,None))
                          nal
                      | Constrexpr.CLocalPattern _ -> assert false
                    )
                    nal_tas
                 )
             in
             let b' = add_args id.CAst.v new_args b in
             ((((id,None), ( Some (CAst.make (CStructRec (CAst.make rec_id)))),nal_tas@bl,t,Some b'),[]):(Vernacexpr.fixpoint_expr * Vernacexpr.decl_notation list))
          )
                      fixexprl
                  in
                  l
      | _ ->
  let id = Label.to_id (Constant.label c) in
                 [((CAst.make id,None),None,nal_tas,t,Some b),[]]
  in
         let mp = Constant.modpath c in
         let pstate = do_generate_principle ~pstate [c,Univ.Instance.empty] error_error  false false expr_list in
  (* We register the infos *)
  List.iter
           (fun ((({CAst.v=id},_),_,_,_,_),_) -> add_Function false (Constant.make2 mp (Label.of_id id)))
           expr_list;
         pstate)

let do_generate_principle = do_generate_principle [] warning_error true

¤ Dauer der Verarbeitung: 0.31 Sekunden (vorverarbeitet) ¤

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