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-rw-r--r--contrib/subtac/FixSub.v22
-rw-r--r--contrib/subtac/Utils.v34
-rw-r--r--contrib/subtac/context.ml35
-rw-r--r--contrib/subtac/context.mli5
-rw-r--r--contrib/subtac/eterm.ml168
-rw-r--r--contrib/subtac/eterm.mli20
-rw-r--r--contrib/subtac/g_eterm.ml427
-rw-r--r--contrib/subtac/g_subtac.ml462
-rw-r--r--contrib/subtac/subtac.ml203
-rw-r--r--contrib/subtac/subtac.mli14
-rw-r--r--contrib/subtac/subtac_coercion.ml485
-rw-r--r--contrib/subtac/subtac_coercion.mli1
-rw-r--r--contrib/subtac/subtac_command.ml422
-rw-r--r--contrib/subtac/subtac_command.mli42
-rw-r--r--contrib/subtac/subtac_errors.ml24
-rw-r--r--contrib/subtac/subtac_errors.mli15
-rw-r--r--contrib/subtac/subtac_interp_fixpoint.ml219
-rw-r--r--contrib/subtac/subtac_interp_fixpoint.mli39
-rw-r--r--contrib/subtac/subtac_pretyping.ml150
-rw-r--r--contrib/subtac/subtac_pretyping.mli12
-rw-r--r--contrib/subtac/subtac_utils.ml246
-rw-r--r--contrib/subtac/subtac_utils.mli85
22 files changed, 2330 insertions, 0 deletions
diff --git a/contrib/subtac/FixSub.v b/contrib/subtac/FixSub.v
new file mode 100644
index 00000000..bbf722db
--- /dev/null
+++ b/contrib/subtac/FixSub.v
@@ -0,0 +1,22 @@
+Require Import Wf.
+
+Section Well_founded.
+Variable A : Set.
+Variable R : A -> A -> Prop.
+Hypothesis Rwf : well_founded R.
+
+Section FixPoint.
+
+Variable P : A -> Set.
+
+Variable F_sub : forall x:A, (forall y: { y : A | R y x }, P (proj1_sig y)) -> P x.
+
+Fixpoint Fix_F_sub (x : A) (r : Acc R x) {struct r} : P x :=
+ F_sub x (fun y: { y : A | R y x} => Fix_F_sub (proj1_sig y)
+ (Acc_inv r (proj1_sig y) (proj2_sig y))).
+
+Definition Fix_sub (x : A) := Fix_F_sub x (Rwf x).
+
+End FixPoint.
+
+End Well_founded.
diff --git a/contrib/subtac/Utils.v b/contrib/subtac/Utils.v
new file mode 100644
index 00000000..9acb10ae
--- /dev/null
+++ b/contrib/subtac/Utils.v
@@ -0,0 +1,34 @@
+Set Implicit Arguments.
+
+Definition ex_pi1 (A : Prop) (P : A -> Prop) (t : ex P) : A.
+intros.
+induction t.
+exact x.
+Defined.
+
+Check proj1_sig.
+Lemma subset_simpl : forall (A : Set) (P : A -> Prop)
+ (t : sig P), P (proj1_sig t).
+Proof.
+intros.
+induction t.
+ simpl ; auto.
+Qed.
+
+Lemma ex_pi2 : forall (A : Prop) (P : A -> Prop) (t : ex P),
+ P (ex_pi1 t).
+intros A P.
+dependent inversion t.
+simpl.
+exact p.
+Defined.
+
+Notation "'forall' { x : A | P } , Q" :=
+ (forall x:{x:A|P}, Q)
+ (at level 200, x ident, right associativity).
+
+Notation "'fun' { x : A | P } => Q" :=
+ (fun x:{x:A|P} => Q)
+ (at level 200, x ident, right associativity).
+
+Notation "( x & y )" := (@existS _ _ x y) : core_scope.
diff --git a/contrib/subtac/context.ml b/contrib/subtac/context.ml
new file mode 100644
index 00000000..236b0ea5
--- /dev/null
+++ b/contrib/subtac/context.ml
@@ -0,0 +1,35 @@
+open Term
+open Names
+
+type t = rel_declaration list (* name, optional coq interp, algorithmic type *)
+
+let assoc n t =
+ let _, term, typ = List.find (fun (x, _, _) -> x = n) t in
+ term, typ
+
+let assoc_and_index x l =
+ let rec aux i = function
+ (y, term, typ) :: tl -> if x = y then i, term, typ else aux (succ i) tl
+ | [] -> raise Not_found
+ in aux 0 l
+
+let id_of_name = function
+ Name id -> id
+ | Anonymous -> raise (Invalid_argument "id_of_name")
+(*
+
+let subst_ctx ctx c =
+ let rec aux ((ctx, n, c) as acc) = function
+ (name, None, typ) :: tl ->
+ aux (((id_of_name name, None, rel_to_vars ctx typ) :: ctx),
+ pred n, c) tl
+ | (name, Some term, typ) :: tl ->
+ let t' = Term.substnl [term] n c in
+ aux (ctx, n, t') tl
+ | [] -> acc
+ in
+ let (x, _, z) = aux ([], pred (List.length ctx), c) (List.rev ctx) in
+ (x, rel_to_vars x z)
+*)
+
+let subst_env env c = (env, c)
diff --git a/contrib/subtac/context.mli b/contrib/subtac/context.mli
new file mode 100644
index 00000000..671d6f36
--- /dev/null
+++ b/contrib/subtac/context.mli
@@ -0,0 +1,5 @@
+type t = Term.rel_declaration list
+val assoc : 'a -> ('a * 'b * 'c) list -> 'b * 'c
+val assoc_and_index : 'a -> ('a * 'b * 'c) list -> int * 'b * 'c
+val id_of_name : Names.name -> Names.identifier
+val subst_env : 'a -> 'b -> 'a * 'b
diff --git a/contrib/subtac/eterm.ml b/contrib/subtac/eterm.ml
new file mode 100644
index 00000000..5703c0ef
--- /dev/null
+++ b/contrib/subtac/eterm.ml
@@ -0,0 +1,168 @@
+(**
+ - Get types of existentials ;
+ - Flatten dependency tree (prefix order) ;
+ - Replace existentials by De Bruijn indices in term, applied to the right arguments ;
+ - Apply term prefixed by quantification on "existentials".
+*)
+
+open Term
+open Names
+open Evd
+open List
+open Pp
+open Util
+
+let reverse_array arr =
+ Array.of_list (List.rev (Array.to_list arr))
+
+let trace s =
+ if !Options.debug then msgnl s
+ else ()
+
+(** Utilities to find indices in lists *)
+let list_index x l =
+ let rec aux i = function
+ k :: tl -> if k = x then i else aux (succ i) tl
+ | [] -> raise Not_found
+ in aux 0 l
+
+let list_assoc_index x l =
+ let rec aux i = function
+ (k, _, v) :: tl -> if k = x then i else aux (succ i) tl
+ | [] -> raise Not_found
+ in aux 0 l
+
+(** Substitute evar references in t using De Bruijn indices,
+ where n binders were passed through. *)
+let subst_evars evs n t =
+ let evar_info id =
+ let rec aux i = function
+ (k, h, v) :: tl -> if k = id then (i, h, v) else aux (succ i) tl
+ | [] -> raise Not_found
+ in
+ let (idx, hyps, v) = aux 0 evs in
+ n + idx + 1, hyps
+ in
+ let rec substrec depth c = match kind_of_term c with
+ | Evar (k, args) ->
+ (try
+ let index, hyps = evar_info k in
+ trace (str "Evar " ++ int k ++ str " found, applied to " ++ int (Array.length args) ++ str "arguments," ++
+ int (List.length hyps) ++ str " hypotheses");
+
+ let ex = mkRel (index + depth) in
+ (* Evar arguments are created in inverse order,
+ and we must not apply to defined ones (i.e. LetIn's)
+ *)
+ let args =
+ let rec aux hyps args acc =
+ match hyps, args with
+ ((_, None, _) :: tlh), (c :: tla) ->
+ aux tlh tla ((map_constr_with_binders succ substrec depth c) :: acc)
+ | ((_, Some _, _) :: tlh), (_ :: tla) ->
+ aux tlh tla acc
+ | [], [] -> acc
+ | _, _ -> failwith "subst_evars: invalid argument"
+ in aux hyps (Array.to_list args) []
+ in
+ mkApp (ex, Array.of_list args)
+ with Not_found ->
+ anomaly ("eterm: existential variable " ^ string_of_int k ^ " not found"))
+ | _ -> map_constr_with_binders succ substrec depth c
+ in
+ substrec 0 t
+
+(** Substitute variable references in t using De Bruijn indices,
+ where n binders were passed through. *)
+let subst_vars acc n t =
+ let var_index id =
+ let idx = list_index id acc in
+ idx + 1
+ in
+ let rec substrec depth c = match kind_of_term c with
+ | Var v -> (try mkRel (depth + (var_index v)) with Not_found -> c)
+ | _ -> map_constr_with_binders succ substrec depth c
+ in
+ substrec 0 t
+
+(** Rewrite type of an evar ([ H1 : t1, ... Hn : tn |- concl ])
+ to a product : forall H1 : t1, ..., forall Hn : tn, concl.
+ Changes evars and hypothesis references to De Bruijn indices.
+*)
+let etype_of_evar evs ev hyps =
+ let rec aux acc n = function
+ (id, copt, t) :: tl ->
+ let t' = subst_evars evs n t in
+ let t'' = subst_vars acc 0 t' in
+ mkNamedProd_or_LetIn (id, copt, t'') (aux (id :: acc) (succ n) tl)
+ | [] ->
+ let t' = subst_evars evs n ev.evar_concl in
+ subst_vars acc 0 t'
+ in aux [] 0 (rev hyps)
+
+
+open Tacticals
+
+let eterm_term evm t tycon =
+ (* 'Serialize' the evars, we assume that the types of the existentials
+ refer to previous existentials in the list only *)
+ let evl = to_list evm in
+ let evts =
+ (* Remove existential variables in types and build the corresponding products *)
+ fold_right
+ (fun (id, ev) l ->
+ let hyps = Environ.named_context_of_val ev.evar_hyps in
+ let y' = (id, hyps, etype_of_evar l ev hyps) in
+ y' :: l)
+ evl []
+ in
+ let t' = (* Substitute evar refs in the term by De Bruijn indices *)
+ subst_evars evts 0 t
+ in
+ let evar_names =
+ List.map (fun (id, _, c) -> (id_of_string ("Evar" ^ string_of_int id)), c) evts
+ in
+ let evar_bl =
+ List.map (fun (id, c) -> Name id, None, c) evar_names
+ in
+ let anon_evar_bl = List.map (fun (_, x, y) -> (Anonymous, x, y)) evar_bl in
+ (* Generalize over the existential variables *)
+ let t'' = Termops.it_mkLambda_or_LetIn t' evar_bl
+ and tycon = option_app
+ (fun typ -> Termops.it_mkProd_wo_LetIn typ anon_evar_bl) tycon
+ in
+ let _declare_evar (id, c) =
+ let id = id_of_string ("Evar" ^ string_of_int id) in
+ ignore(Declare.declare_variable id (Names.empty_dirpath, Declare.SectionLocalAssum c,
+ Decl_kinds.IsAssumption Decl_kinds.Definitional))
+ in
+ let _declare_assert acc (id, c) =
+ let id = id_of_string ("Evar" ^ string_of_int id) in
+ tclTHEN acc (Tactics.assert_tac false (Name id) c)
+ in
+ trace (str "Term given to eterm" ++ spc () ++
+ Termops.print_constr_env (Global.env ()) t);
+ trace (str "Term constructed in eterm" ++ spc () ++
+ Termops.print_constr_env (Global.env ()) t'');
+ ignore(option_app
+ (fun typ ->
+ trace (str "Type :" ++ spc () ++
+ Termops.print_constr_env (Global.env ()) typ))
+ tycon);
+ t'', tycon, evar_names
+
+let mkMetas n =
+ let rec aux i acc =
+ if i > 0 then aux (pred i) (Evarutil.mk_new_meta () :: acc)
+ else acc
+ in aux n []
+
+let eterm evm t (tycon : types option) =
+ let t, tycon, evs = eterm_term evm t tycon in
+ match tycon with
+ Some typ -> Tactics.apply_term (mkCast (t, DEFAULTcast, typ)) []
+ | None -> Tactics.apply_term t (mkMetas (List.length evs))
+
+open Tacmach
+
+let etermtac (evm, t) = eterm evm t None
diff --git a/contrib/subtac/eterm.mli b/contrib/subtac/eterm.mli
new file mode 100644
index 00000000..fbe2ac1d
--- /dev/null
+++ b/contrib/subtac/eterm.mli
@@ -0,0 +1,20 @@
+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+
+(*i $Id: eterm.mli 8688 2006-04-07 15:08:12Z msozeau $ i*)
+
+open Tacmach
+open Term
+open Evd
+open Names
+
+val mkMetas : int -> constr list
+
+val eterm_term : evar_map -> constr -> types option -> constr * types option * (identifier * types) list
+
+val etermtac : open_constr -> tactic
diff --git a/contrib/subtac/g_eterm.ml4 b/contrib/subtac/g_eterm.ml4
new file mode 100644
index 00000000..d9dd42cd
--- /dev/null
+++ b/contrib/subtac/g_eterm.ml4
@@ -0,0 +1,27 @@
+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+(**************************************************************************)
+(* *)
+(* Omega: a solver of quantifier-free problems in Presburger Arithmetic *)
+(* *)
+(* Pierre Crégut (CNET, Lannion, France) *)
+(* *)
+(**************************************************************************)
+
+(*i camlp4deps: "parsing/grammar.cma" i*)
+
+(* $Id: g_eterm.ml4 8654 2006-03-22 15:36:58Z msozeau $ *)
+
+open Eterm
+
+TACTIC EXTEND eterm
+ [ "eterm" ] -> [
+ (fun gl ->
+ let evm = Tacmach.project gl and t = Tacmach.pf_concl gl in
+ Eterm.etermtac (evm, t) gl) ]
+END
diff --git a/contrib/subtac/g_subtac.ml4 b/contrib/subtac/g_subtac.ml4
new file mode 100644
index 00000000..c3f2a24d
--- /dev/null
+++ b/contrib/subtac/g_subtac.ml4
@@ -0,0 +1,62 @@
+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+
+(*
+ Syntax for the subtac terms and types.
+ Elaborated from correctness/psyntax.ml4 by Jean-Christophe Filliâtre *)
+
+(* $Id: g_subtac.ml4 8688 2006-04-07 15:08:12Z msozeau $ *)
+
+(*i camlp4deps: "parsing/grammar.cma" i*)
+
+open Options
+open Util
+open Names
+open Nameops
+open Vernacentries
+open Reduction
+open Term
+open Libnames
+open Topconstr
+
+(* We define new entries for programs, with the use of this module
+ * Subtac. These entries are named Subtac.<foo>
+ *)
+
+module Gram = Pcoq.Gram
+module Vernac = Pcoq.Vernac_
+
+module SubtacGram =
+struct
+ let gec s = Gram.Entry.create ("Subtac."^s)
+ (* types *)
+ let subtac_gallina_loc : Vernacexpr.vernac_expr located Gram.Entry.e = gec "subtac_gallina_loc"
+end
+
+open SubtacGram
+open Util
+
+GEXTEND Gram
+ GLOBAL: subtac_gallina_loc;
+
+ subtac_gallina_loc:
+ [ [ g = Vernac.gallina -> loc, g ] ]
+ ;
+ END
+
+type gallina_loc_argtype = (Vernacexpr.vernac_expr located, constr_expr, Tacexpr.raw_tactic_expr) Genarg.abstract_argument_type
+
+let (wit_subtac_gallina_loc : gallina_loc_argtype),
+ (globwit_subtac_gallina_loc : gallina_loc_argtype),
+ (rawwit_subtac_gallina_loc : gallina_loc_argtype) =
+ Genarg.create_arg "subtac_gallina_loc"
+
+VERNAC COMMAND EXTEND Subtac
+[ "Program" subtac_gallina_loc(g) ] ->
+ [ Subtac.subtac g ]
+END
diff --git a/contrib/subtac/subtac.ml b/contrib/subtac/subtac.ml
new file mode 100644
index 00000000..84b7d39b
--- /dev/null
+++ b/contrib/subtac/subtac.ml
@@ -0,0 +1,203 @@
+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+
+(* $Id: subtac.ml 8688 2006-04-07 15:08:12Z msozeau $ *)
+
+open Global
+open Pp
+open Util
+open Names
+open Sign
+open Evd
+open Term
+open Termops
+open Reductionops
+open Environ
+open Type_errors
+open Typeops
+open Libnames
+open Classops
+open List
+open Recordops
+open Evarutil
+open Pretype_errors
+open Rawterm
+open Evarconv
+open Pattern
+open Dyn
+open Vernacexpr
+
+open Subtac_coercion
+open Subtac_utils
+open Coqlib
+open Printer
+open Subtac_errors
+open Context
+open Eterm
+
+let require_library dirpath =
+ let qualid = (dummy_loc, qualid_of_dirpath (dirpath_of_string dirpath)) in
+ Library.require_library [qualid] None
+
+let subtac_one_fixpoint env isevars (f, decl) =
+ let ((id, n, bl, typ, body), decl) =
+ Subtac_interp_fixpoint.rewrite_fixpoint env [] (f, decl)
+ in
+ let _ = trace (str "Working on a single fixpoint rewritten as: " ++ spc () ++
+ Ppconstr.pr_constr_expr body)
+ in ((id, n, bl, typ, body), decl)
+
+
+let subtac_fixpoint isevars l =
+ (* TODO: Copy command.build_recursive *)
+ ()
+(*
+let save id const (locality,kind) hook =
+ let {const_entry_body = pft;
+ const_entry_type = tpo;
+ const_entry_opaque = opacity } = const in
+ let l,r = match locality with
+ | Local when Lib.sections_are_opened () ->
+ let k = logical_kind_of_goal_kind kind in
+ let c = SectionLocalDef (pft, tpo, opacity) in
+ let _ = declare_variable id (Lib.cwd(), c, k) in
+ (Local, VarRef id)
+ | Local ->
+ let k = logical_kind_of_goal_kind kind in
+ let kn = declare_constant id (DefinitionEntry const, k) in
+ (Global, ConstRef kn)
+ | Global ->
+ let k = logical_kind_of_goal_kind kind in
+ let kn = declare_constant id (DefinitionEntry const, k) in
+ (Global, ConstRef kn) in
+ Pfedit.delete_current_proof ();
+ hook l r;
+ definition_message id
+
+let save_named opacity =
+ let id,(const,persistence,hook) = Pfedit.cook_proof () in
+ let const = { const with const_entry_opaque = opacity } in
+ save id const persistence hook
+
+let check_anonymity id save_ident =
+ if atompart_of_id id <> "Unnamed_thm" then
+ error "This command can only be used for unnamed theorem"
+(*
+ message("Overriding name "^(string_of_id id)^" and using "^save_ident)
+*)
+
+let save_anonymous opacity save_ident =
+ let id,(const,persistence,hook) = Pfedit.cook_proof () in
+ let const = { const with const_entry_opaque = opacity } in
+ check_anonymity id save_ident;
+ save save_ident const persistence hook
+
+let save_anonymous_with_strength kind opacity save_ident =
+ let id,(const,_,hook) = Pfedit.cook_proof () in
+ let const = { const with const_entry_opaque = opacity } in
+ check_anonymity id save_ident;
+ (* we consider that non opaque behaves as local for discharge *)
+ save save_ident const (Global, Proof kind) hook
+
+let subtac_end_proof = function
+ | Admitted -> admit ()
+ | Proved (is_opaque,idopt) ->
+ if_verbose show_script ();
+ match idopt with
+ | None -> save_named is_opaque
+ | Some ((_,id),None) -> save_anonymous is_opaque id
+ | Some ((_,id),Some kind) -> save_anonymous_with_strength kind is_opaque id
+
+ *)
+
+let subtac (loc, command) =
+ check_required_library ["Coq";"Init";"Datatypes"];
+ check_required_library ["Coq";"Init";"Specif"];
+ require_library "Coq.subtac.FixSub";
+ require_library "Coq.subtac.Utils";
+ try
+ match command with
+ VernacDefinition (defkind, (locid, id), expr, hook) ->
+ let env = Global.env () in
+ let isevars = ref (create_evar_defs Evd.empty) in
+ (match expr with
+ ProveBody (bl, c) ->
+ let evm, c, ctyp = Subtac_pretyping.subtac_process env isevars id bl c None in
+ trace (str "Starting proof");
+ Command.start_proof id goal_kind c hook;
+ trace (str "Started proof");
+
+ | DefineBody (bl, _, c, tycon) ->
+ let evm, c, ctyp = Subtac_pretyping.subtac_process env isevars id bl c tycon in
+ let tac = Eterm.etermtac (evm, c) in
+ trace (str "Starting proof");
+ Command.start_proof id goal_kind ctyp hook;
+ trace (str "Started proof");
+ Pfedit.by tac)
+ | VernacFixpoint (l, b) ->
+ let _ = trace (str "Building fixpoint") in
+ ignore(Subtac_command.build_recursive l b)
+ (*| VernacEndProof e ->
+ subtac_end_proof e*)
+
+ | _ -> user_err_loc (loc,"", str ("Invalid Program command"))
+ with
+ | Typing_error e ->
+ msg_warning (str "Type error in Program tactic:");
+ let cmds =
+ (match e with
+ | NonFunctionalApp (loc, x, mux, e) ->
+ str "non functional application of term " ++
+ e ++ str " to function " ++ x ++ str " of (mu) type " ++ mux
+ | NonSigma (loc, t) ->
+ str "Term is not of Sigma type: " ++ t
+ | NonConvertible (loc, x, y) ->
+ str "Unconvertible terms:" ++ spc () ++
+ x ++ spc () ++ str "and" ++ spc () ++ y
+ | IllSorted (loc, t) ->
+ str "Term is ill-sorted:" ++ spc () ++ t
+ )
+ in msg_warning cmds
+
+ | Subtyping_error e ->
+ msg_warning (str "(Program tactic) Subtyping error:");
+ let cmds =
+ match e with
+ | UncoercibleInferType (loc, x, y) ->
+ str "Uncoercible terms:" ++ spc ()
+ ++ x ++ spc () ++ str "and" ++ spc () ++ y
+ | UncoercibleInferTerm (loc, x, y, tx, ty) ->
+ str "Uncoercible terms:" ++ spc ()
+ ++ tx ++ spc () ++ str "of" ++ spc () ++ str "type" ++ spc () ++ x
+ ++ str "and" ++ spc() ++ ty ++ spc () ++ str "of" ++ spc () ++ str "type" ++ spc () ++ y
+ | UncoercibleRewrite (x, y) ->
+ str "Uncoercible terms:" ++ spc ()
+ ++ x ++ spc () ++ str "and" ++ spc () ++ y
+ in msg_warning cmds
+
+ | Type_errors.TypeError (env, e) ->
+ debug 2 (Himsg.explain_type_error env e)
+
+ | Pretype_errors.PretypeError (env, e) ->
+ debug 2 (Himsg.explain_pretype_error env e)
+
+ | Stdpp.Exc_located (loc, e) ->
+ debug 2 (str "Parsing exception: ");
+ (match e with
+ | Type_errors.TypeError (env, e) ->
+ debug 2 (Himsg.explain_type_error env e)
+
+ | Pretype_errors.PretypeError (env, e) ->
+ debug 2 (Himsg.explain_pretype_error env e)
+
+ | e -> msg_warning (str "Unexplained exception: " ++ Cerrors.explain_exn e))
+
+ | e ->
+ msg_warning (str "Uncatched exception: " ++ Cerrors.explain_exn e)
+
+
diff --git a/contrib/subtac/subtac.mli b/contrib/subtac/subtac.mli
new file mode 100644
index 00000000..a0d2fb2b
--- /dev/null
+++ b/contrib/subtac/subtac.mli
@@ -0,0 +1,14 @@
+val require_library : string -> unit
+val subtac_one_fixpoint :
+ 'a ->
+ 'b ->
+ (Names.identifier * (int * Topconstr.recursion_order_expr) *
+ Topconstr.local_binder list * Topconstr.constr_expr *
+ Topconstr.constr_expr) *
+ 'c ->
+ (Names.identifier * (int * Topconstr.recursion_order_expr) *
+ Topconstr.local_binder list * Topconstr.constr_expr *
+ Topconstr.constr_expr) *
+ 'c
+val subtac_fixpoint : 'a -> 'b -> unit
+val subtac : Util.loc * Vernacexpr.vernac_expr -> unit
diff --git a/contrib/subtac/subtac_coercion.ml b/contrib/subtac/subtac_coercion.ml
new file mode 100644
index 00000000..7c8ea2d6
--- /dev/null
+++ b/contrib/subtac/subtac_coercion.ml
@@ -0,0 +1,485 @@
+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+(* $Id: subtac_coercion.ml 8695 2006-04-10 16:33:52Z msozeau $ *)
+
+open Util
+open Names
+open Term
+open Reductionops
+open Environ
+open Typeops
+open Pretype_errors
+open Classops
+open Recordops
+open Evarutil
+open Evarconv
+open Retyping
+open Evd
+
+open Global
+open Subtac_utils
+open Coqlib
+open Printer
+open Subtac_errors
+open Context
+open Eterm
+open Pp
+
+let pair_of_array a = (a.(0), a.(1))
+let make_name s = Name (id_of_string s)
+
+module Coercion = struct
+
+ exception NoSubtacCoercion
+
+ let rec disc_subset x =
+ match kind_of_term x with
+ | App (c, l) ->
+ (match kind_of_term c with
+ Ind i ->
+ let len = Array.length l in
+ let sig_ = Lazy.force sig_ in
+ if len = 2 && i = Term.destInd sig_.typ
+ then
+ let (a, b) = pair_of_array l in
+ Some (a, b)
+ else None
+ | _ -> None)
+ | _ -> None
+
+ and disc_exist env x =
+ trace (str "Disc_exist: " ++ my_print_constr env x);
+ match kind_of_term x with
+ | App (c, l) ->
+ (match kind_of_term c with
+ Construct c ->
+ if c = Term.destConstruct (Lazy.force sig_).intro
+ then Some (l.(0), l.(1), l.(2), l.(3))
+ else None
+ | _ -> None)
+ | _ -> None
+
+
+ let disc_proj_exist env x =
+ trace (str "disc_proj_exist: " ++ my_print_constr env x);
+ match kind_of_term x with
+ | App (c, l) ->
+ (if Term.eq_constr c (Lazy.force sig_).proj1
+ && Array.length l = 3
+ then disc_exist env l.(2)
+ else None)
+ | _ -> None
+
+
+ let sort_rel s1 s2 =
+ match s1, s2 with
+ Prop Pos, Prop Pos -> Prop Pos
+ | Prop Pos, Prop Null -> Prop Null
+ | Prop Null, Prop Null -> Prop Null
+ | Prop Null, Prop Pos -> Prop Pos
+ | Type _, Prop Pos -> Prop Pos
+ | Type _, Prop Null -> Prop Null
+ | _, Type _ -> s2
+
+ let hnf env isevars c = whd_betadeltaiota env (evars_of !isevars) c
+
+ let rec mu env isevars t =
+ let rec aux v =
+ match disc_subset v with
+ Some (u, p) ->
+ let f, ct = aux u in
+ (Some (fun x ->
+ app_opt f (mkApp ((Lazy.force sig_).proj1,
+ [| u; p; x |]))),
+ ct)
+ | None -> (None, t)
+ in aux t
+
+ and coerce loc env isevars (x : Term.constr) (y : Term.constr)
+ : (Term.constr -> Term.constr) option
+ =
+ let x = nf_evar (evars_of !isevars) x and y = nf_evar (evars_of !isevars) y in
+ trace (str "Coerce called for " ++ (my_print_constr env x) ++
+ str " and "++ my_print_constr env y ++
+ str " with evars: " ++ spc () ++
+ my_print_evardefs !isevars);
+ let rec coerce_unify env x y =
+ trace (str "coerce_unify from " ++ (my_print_constr env x) ++
+ str " to "++ my_print_constr env y);
+ try
+ isevars := the_conv_x_leq env x y !isevars;
+ trace (str "Unified " ++ (my_print_constr env x) ++
+ str " and "++ my_print_constr env y);
+ None
+ with Reduction.NotConvertible -> coerce' env (hnf env isevars x) (hnf env isevars y)
+ and coerce' env x y : (Term.constr -> Term.constr) option =
+ let subco () = subset_coerce env isevars x y in
+ trace (str "coerce' from " ++ (my_print_constr env x) ++
+ str " to "++ my_print_constr env y);
+ match (kind_of_term x, kind_of_term y) with
+ | Sort s, Sort s' ->
+ (match s, s' with
+ Prop x, Prop y when x = y -> None
+ | Prop _, Type _ -> None
+ | Type x, Type y when x = y -> None (* false *)
+ | _ -> subco ())
+ | Prod (name, a, b), Prod (name', a', b') ->
+ let c1 = coerce_unify env a' a in
+ let env' = push_rel (name', None, a') env in
+ let c2 = coerce_unify env' b b' in
+ (match c1, c2 with
+ None, None -> failwith "subtac.coerce': Should have detected equivalence earlier"
+ | _, _ ->
+ Some
+ (fun f ->
+ mkLambda (name', a',
+ app_opt c2
+ (mkApp (Term.lift 1 f,
+ [| app_opt c1 (mkRel 1) |])))))
+
+ | App (c, l), App (c', l') ->
+ (match kind_of_term c, kind_of_term c' with
+ Ind i, Ind i' -> (* Sigma types *)
+ let len = Array.length l in
+ let existS = Lazy.force existS in
+ let prod = Lazy.force prod in
+ if len = Array.length l' && len = 2 && i = i'
+ then
+ if i = Term.destInd existS.typ
+ then
+ begin
+ debug 1 (str "In coerce sigma types");
+ let (a, pb), (a', pb') =
+ pair_of_array l, pair_of_array l'
+ in
+ let c1 = coerce_unify env a a' in
+ let rec remove_head a c =
+ match kind_of_term c with
+ | Lambda (n, t, t') -> c, t'
+ (*| Prod (n, t, t') -> t'*)
+ | Evar (k, args) ->
+ let (evs, t) = Evarutil.define_evar_as_lambda !isevars (k,args) in
+ isevars := evs;
+ let (n, dom, rng) = destLambda t in
+ let (domk, args) = destEvar dom in
+ isevars := evar_define domk a !isevars;
+ t, rng
+ | _ -> raise NoSubtacCoercion
+ in
+ let (pb, b), (pb', b') = remove_head a pb, remove_head a' pb' in
+ let env' = push_rel (make_name "x", None, a) env in
+ let c2 = coerce_unify env' b b' in
+ match c1, c2 with
+ None, None ->
+ trace (str "No coercion needed");
+ None
+ | _, _ ->
+ Some
+ (fun x ->
+ let x, y =
+ app_opt c1 (mkApp (existS.proj1,
+ [| a; pb; x |])),
+ app_opt c2 (mkApp (existS.proj2,
+ [| a; pb; x |]))
+ in
+ mkApp (existS.intro, [| a'; pb'; x ; y |]))
+ end
+ else if i = Term.destInd prod.typ then
+ begin
+ debug 1 (str "In coerce prod types");
+ let (a, b), (a', b') =
+ pair_of_array l, pair_of_array l'
+ in
+ let c1 = coerce_unify env a a' in
+ let c2 = coerce_unify env b b' in
+ match c1, c2 with
+ None, None -> None
+ | _, _ ->
+ Some
+ (fun x ->
+ let x, y =
+ app_opt c1 (mkApp (prod.proj1,
+ [| a; b; x |])),
+ app_opt c2 (mkApp (prod.proj2,
+ [| a; b; x |]))
+ in
+ mkApp (prod.intro, [| a'; b'; x ; y |]))
+ end
+ else subco ()
+ else subco ()
+ | _ -> subco ())
+ | _, _ -> subco ()
+
+ and subset_coerce env isevars x y =
+ match disc_subset x with
+ Some (u, p) ->
+ let c = coerce_unify env u y in
+ let f x =
+ app_opt c (mkApp ((Lazy.force sig_).proj1,
+ [| u; p; x |]))
+ in Some f
+ | None ->
+ match disc_subset y with
+ Some (u, p) ->
+ let c = coerce_unify env x u in
+ Some
+ (fun x ->
+ let cx = app_opt c x in
+ let evar = make_existential dummy_loc env isevars (mkApp (p, [| cx |]))
+ in
+ (mkApp
+ ((Lazy.force sig_).intro,
+ [| u; p; cx; evar |])))
+ | None ->
+ raise NoSubtacCoercion
+ (*isevars := Evd.add_conv_pb (Reduction.CONV, x, y) !isevars;
+ None*)
+ in coerce_unify env x y
+
+ let coerce_itf loc env isevars v t c1 =
+ let evars = ref isevars in
+ let coercion = coerce loc env evars t c1 in
+ !evars, option_app (app_opt coercion) v, t
+
+ (* Taken from pretyping/coercion.ml *)
+
+ (* Typing operations dealing with coercions *)
+
+ let class_of1 env sigma t = class_of env sigma (nf_evar sigma t)
+
+ (* Here, funj is a coercion therefore already typed in global context *)
+ let apply_coercion_args env argl funj =
+ let rec apply_rec acc typ = function
+ | [] -> { uj_val = applist (j_val funj,argl);
+ uj_type = typ }
+ | h::restl ->
+ (* On devrait pouvoir s'arranger pour qu'on n'ait pas à faire hnf_constr *)
+ match kind_of_term (whd_betadeltaiota env Evd.empty typ) with
+ | Prod (_,c1,c2) ->
+ (* Typage garanti par l'appel à app_coercion*)
+ apply_rec (h::acc) (subst1 h c2) restl
+ | _ -> anomaly "apply_coercion_args"
+ in
+ apply_rec [] funj.uj_type argl
+
+ (* appliquer le chemin de coercions de patterns p *)
+ exception NoCoercion
+
+ let apply_pattern_coercion loc pat p =
+ List.fold_left
+ (fun pat (co,n) ->
+ let f i = if i<n then Rawterm.PatVar (loc, Anonymous) else pat in
+ Rawterm.PatCstr (loc, co, list_tabulate f (n+1), Anonymous))
+ pat p
+
+ (* raise Not_found if no coercion found *)
+ let inh_pattern_coerce_to loc pat ind1 ind2 =
+ let i1 = inductive_class_of ind1 in
+ let i2 = inductive_class_of ind2 in
+ let p = lookup_pattern_path_between (i1,i2) in
+ apply_pattern_coercion loc pat p
+
+ (* appliquer le chemin de coercions p à hj *)
+
+ let apply_coercion env p hj typ_cl =
+ try
+ fst (List.fold_left
+ (fun (ja,typ_cl) i ->
+ let fv,isid = coercion_value i in
+ let argl = (class_args_of typ_cl)@[ja.uj_val] in
+ let jres = apply_coercion_args env argl fv in
+ (if isid then
+ { uj_val = ja.uj_val; uj_type = jres.uj_type }
+ else
+ jres),
+ jres.uj_type)
+ (hj,typ_cl) p)
+ with _ -> anomaly "apply_coercion"
+
+ let inh_app_fun env isevars j =
+ let t = whd_betadeltaiota env (evars_of isevars) j.uj_type in
+ match kind_of_term t with
+ | Prod (_,_,_) -> (isevars,j)
+ | Evar ev when not (is_defined_evar isevars ev) ->
+ let (isevars',t) = define_evar_as_arrow isevars ev in
+ (isevars',{ uj_val = j.uj_val; uj_type = t })
+ | _ ->
+ (try
+ let t,i1 = class_of1 env (evars_of isevars) j.uj_type in
+ let p = lookup_path_to_fun_from i1 in
+ (isevars,apply_coercion env p j t)
+ with Not_found ->
+ try
+ let coercef, t = mu env isevars t in
+ (isevars, { uj_val = app_opt coercef j.uj_val; uj_type = t })
+ with NoSubtacCoercion | NoCoercion ->
+ (isevars,j))
+
+ let inh_tosort_force loc env isevars j =
+ try
+ let t,i1 = class_of1 env (evars_of isevars) j.uj_type in
+ let p = lookup_path_to_sort_from i1 in
+ let j1 = apply_coercion env p j t in
+ (isevars,type_judgment env (j_nf_evar (evars_of isevars) j1))
+ with Not_found ->
+ error_not_a_type_loc loc env (evars_of isevars) j
+
+ let inh_coerce_to_sort loc env isevars j =
+ let typ = whd_betadeltaiota env (evars_of isevars) j.uj_type in
+ match kind_of_term typ with
+ | Sort s -> (isevars,{ utj_val = j.uj_val; utj_type = s })
+ | Evar ev when not (is_defined_evar isevars ev) ->
+ let (isevars',s) = define_evar_as_sort isevars ev in
+ (isevars',{ utj_val = j.uj_val; utj_type = s })
+ | _ ->
+ inh_tosort_force loc env isevars j
+
+ let inh_coerce_to_fail env isevars c1 v t =
+ let v', t' =
+ try
+ let t1,i1 = class_of1 env (evars_of isevars) c1 in
+ let t2,i2 = class_of1 env (evars_of isevars) t in
+ let p = lookup_path_between (i2,i1) in
+ match v with
+ Some v ->
+ let j = apply_coercion env p {uj_val = v; uj_type = t} t2 in
+ Some j.uj_val, j.uj_type
+ | None -> None, t
+ with Not_found -> raise NoCoercion
+ in
+ try (the_conv_x_leq env t' c1 isevars, v', t')
+ with Reduction.NotConvertible -> raise NoCoercion
+
+ let rec inh_conv_coerce_to_fail loc env isevars v t c1 =
+ (try
+ trace (str "inh_conv_coerce_to_fail called for " ++
+ Termops.print_constr_env env t ++ str " and "++ spc () ++
+ Termops.print_constr_env env c1 ++ str " with evars: " ++ spc () ++
+ Evd.pr_evar_defs isevars ++ str " in env: " ++ spc () ++
+ Termops.print_env env);
+ with _ -> ());
+ try (the_conv_x_leq env t c1 isevars, v, t)
+ with Reduction.NotConvertible ->
+ (try
+ inh_coerce_to_fail env isevars c1 v t
+ with NoCoercion ->
+ (match kind_of_term (whd_betadeltaiota env (evars_of isevars) t),
+ kind_of_term (whd_betadeltaiota env (evars_of isevars) c1) with
+ | Prod (_,t1,t2), Prod (name,u1,u2) ->
+ let v' = option_app (whd_betadeltaiota env (evars_of isevars)) v in
+ let (evd',b) =
+ match v' with
+ Some v' ->
+ (match kind_of_term v' with
+ | Lambda (x,v1,v2) ->
+ (try the_conv_x env v1 u1 isevars, Some (x, v1, v2) (* leq v1 u1? *)
+ with Reduction.NotConvertible -> (isevars, None))
+ | _ -> (isevars, None))
+ | None -> (isevars, None)
+ in
+ (match b with
+ Some (x, v1, v2) ->
+ let env1 = push_rel (x,None,v1) env in
+ let (evd'', v2', t2') = inh_conv_coerce_to_fail loc env1 evd'
+ (Some v2) t2 u2 in
+ (evd'', option_app (fun v2' -> mkLambda (x, v1, v2')) v2',
+ mkProd (x, v1, t2'))
+ | None ->
+ (* Mismatch on t1 and u1 or not a lambda: we eta-expand *)
+ (* we look for a coercion c:u1->t1 s.t. [name:u1](v' (c x)) *)
+ (* has type (name:u1)u2 (with v' recursively obtained) *)
+ let name = (match name with
+ | Anonymous -> Name (id_of_string "x")
+ | _ -> name) in
+ let env1 = push_rel (name,None,u1) env in
+ let (evd', v1', t1') =
+ inh_conv_coerce_to_fail loc env1 isevars
+ (Some (mkRel 1)) (lift 1 u1) (lift 1 t1)
+ in
+ let (evd'', v2', t2') =
+ let v2 =
+ match v with
+ Some v -> option_app (fun v1' -> mkApp (lift 1 v, [|v1'|])) v1'
+ | None -> None
+ and evd', t2 =
+ match v1' with
+ Some v1' -> evd', subst1 v1' t2
+ | None ->
+ let evd', ev = new_evar evd' env ~src:(loc, InternalHole) t1' in
+ evd', subst1 ev t2
+ in
+ inh_conv_coerce_to_fail loc env1 evd' v2 t2 u2
+ in
+ (evd'', option_app (fun v2' -> mkLambda (name, u1, v2')) v2',
+ mkProd (name, u1, t2')))
+ | _ -> raise NoCoercion))
+
+
+ (* Look for cj' obtained from cj by inserting coercions, s.t. cj'.typ = t *)
+ let inh_conv_coerce_to loc env isevars cj ((n, t) as tycon) =
+ (try
+ trace (str "Subtac_coercion.inh_conv_coerce_to called for " ++
+ Termops.print_constr_env env cj.uj_type ++ str " and "++ spc () ++
+ Evarutil.pr_tycon_type env tycon ++ str " with evars: " ++ spc () ++
+ Evd.pr_evar_defs isevars ++ str " in env: " ++ spc () ++
+ Termops.print_env env);
+ with _ -> ());
+ match n with
+ None ->
+ let (evd', val', type') =
+ try
+ inh_conv_coerce_to_fail loc env isevars (Some cj.uj_val) cj.uj_type t
+ with NoCoercion ->
+ let sigma = evars_of isevars in
+ try
+ coerce_itf loc env isevars (Some cj.uj_val) cj.uj_type t
+ with NoSubtacCoercion ->
+ error_actual_type_loc loc env sigma cj t
+ in
+ let val' = match val' with Some v -> v | None -> assert(false) in
+ (evd',{ uj_val = val'; uj_type = t })
+ | Some (init, cur) ->
+ (isevars, cj)
+
+ let inh_conv_coerces_to loc env isevars t ((abs, t') as tycon) =
+ (try
+ trace (str "Subtac_coercion.inh_conv_coerces_to called for " ++
+ Termops.print_constr_env env t ++ str " and "++ spc () ++
+ Evarutil.pr_tycon_type env tycon ++ str " with evars: " ++ spc () ++
+ Evd.pr_evar_defs isevars ++ str " in env: " ++ spc () ++
+ Termops.print_env env);
+ with _ -> ());
+ let nabsinit, nabs =
+ match abs with
+ None -> 0, 0
+ | Some (init, cur) -> init, cur
+ in
+ let (rels, rng) =
+ (* a little more effort to get products is needed *)
+ try decompose_prod_n nabs t
+ with _ ->
+ trace (str "decompose_prod_n failed");
+ raise (Invalid_argument "Subtac_coercion.inh_conv_coerces_to")
+ in
+ (* The final range free variables must have been replaced by evars, we accept only that evars
+ in rng are applied to free vars. *)
+ if noccur_with_meta 0 (succ nabsinit) rng then (
+ trace (str "No occur between 0 and " ++ int (succ nabsinit));
+ let env', t, t' =
+ let env' = List.fold_right (fun (n, t) env -> push_rel (n, None, t) env) rels env in
+ env', rng, lift nabs t'
+ in
+ try
+ pi1 (try inh_conv_coerce_to_fail loc env' isevars None t t'
+ with NoCoercion ->
+ coerce_itf loc env' isevars None t t')
+ with NoSubtacCoercion ->
+ let sigma = evars_of isevars in
+ error_cannot_coerce env' sigma (t, t'))
+ else isevars
+end
diff --git a/contrib/subtac/subtac_coercion.mli b/contrib/subtac/subtac_coercion.mli
new file mode 100644
index 00000000..53a8d213
--- /dev/null
+++ b/contrib/subtac/subtac_coercion.mli
@@ -0,0 +1 @@
+module Coercion : Coercion.S
diff --git a/contrib/subtac/subtac_command.ml b/contrib/subtac/subtac_command.ml
new file mode 100644
index 00000000..1b92c691
--- /dev/null
+++ b/contrib/subtac/subtac_command.ml
@@ -0,0 +1,422 @@
+open Closure
+open RedFlags
+open Declarations
+open Entries
+open Dyn
+open Libobject
+open Pattern
+open Matching
+open Pp
+open Rawterm
+open Sign
+open Tacred
+open Util
+open Names
+open Nameops
+open Libnames
+open Nametab
+open Pfedit
+open Proof_type
+open Refiner
+open Tacmach
+open Tactic_debug
+open Topconstr
+open Term
+open Termops
+open Tacexpr
+open Safe_typing
+open Typing
+open Hiddentac
+open Genarg
+open Decl_kinds
+open Mod_subst
+open Printer
+open Inductiveops
+open Syntax_def
+open Environ
+open Tactics
+open Tacticals
+open Tacinterp
+open Vernacexpr
+open Notation
+
+module SPretyping = Subtac_pretyping.Pretyping
+open Subtac_utils
+open Pretyping
+
+(*********************************************************************)
+(* Functions to parse and interpret constructions *)
+
+let evar_nf isevars c =
+ isevars := Evarutil.nf_evar_defs !isevars;
+ Evarutil.nf_isevar !isevars c
+
+let interp_gen kind isevars env
+ ?(impls=([],[])) ?(allow_soapp=false) ?(ltacvars=([],[]))
+ c =
+ let c' = Constrintern.intern_gen (kind=IsType) ~impls ~allow_soapp ~ltacvars (Evd.evars_of !isevars) env c in
+ let c' = Subtac_interp_fixpoint.rewrite_cases env c' in
+ msgnl (str "Pretyping " ++ my_print_constr_expr c);
+ let c' = SPretyping.pretype_gen isevars env ([],[]) kind c' in
+ evar_nf isevars c'
+
+let interp_constr isevars env c =
+ interp_gen (OfType None) isevars env c
+
+let interp_type isevars env ?(impls=([],[])) c =
+ interp_gen IsType isevars env ~impls c
+
+let interp_casted_constr isevars env ?(impls=([],[])) c typ =
+ interp_gen (OfType (Some typ)) isevars env ~impls c
+
+let interp_open_constr isevars env c =
+ msgnl (str "Pretyping " ++ my_print_constr_expr c);
+ let c = Constrintern.intern_constr (Evd.evars_of !isevars) env c in
+ let c' = SPretyping.pretype_gen isevars env ([], []) (OfType None) c in
+ evar_nf isevars c'
+
+let interp_constr_judgment isevars env c =
+ let j =
+ SPretyping.understand_judgment_tcc isevars env
+ (Constrintern.intern_constr (Evd.evars_of !isevars) env c)
+ in
+ { uj_val = evar_nf isevars j.uj_val; uj_type = evar_nf isevars j.uj_type }
+
+let locate_if_isevar loc na = function
+ | RHole _ ->
+ (try match na with
+ | Name id -> Reserve.find_reserved_type id
+ | Anonymous -> raise Not_found
+ with Not_found -> RHole (loc, Evd.BinderType na))
+ | x -> x
+
+let interp_binder sigma env na t =
+ let t = Constrintern.intern_gen true (Evd.evars_of !sigma) env t in
+ SPretyping.understand_type (Evd.evars_of !sigma) env (locate_if_isevar (loc_of_rawconstr t) na t)
+
+
+let interp_context sigma env params =
+ List.fold_left
+ (fun (env,params) d -> match d with
+ | LocalRawAssum ([_,na],(CHole _ as t)) ->
+ let t = interp_binder sigma env na t in
+ let d = (na,None,t) in
+ (push_rel d env, d::params)
+ | LocalRawAssum (nal,t) ->
+ let t = interp_type sigma env t in
+ let ctx = list_map_i (fun i (_,na) -> (na,None,lift i t)) 0 nal in
+ let ctx = List.rev ctx in
+ (push_rel_context ctx env, ctx@params)
+ | LocalRawDef ((_,na),c) ->
+ let c = interp_constr_judgment sigma env c in
+ let d = (na, Some c.uj_val, c.uj_type) in
+ (push_rel d env,d::params))
+ (env,[]) params
+
+(* try to find non recursive definitions *)
+
+let list_chop_hd i l = match list_chop i l with
+ | (l1,x::l2) -> (l1,x,l2)
+ | _ -> assert false
+
+let collect_non_rec env =
+ let rec searchrec lnonrec lnamerec ldefrec larrec nrec =
+ try
+ let i =
+ list_try_find_i
+ (fun i f ->
+ if List.for_all (fun (_, _, def) -> not (occur_var env f def)) ldefrec
+ then i else failwith "try_find_i")
+ 0 lnamerec
+ in
+ let (lf1,f,lf2) = list_chop_hd i lnamerec in
+ let (ldef1,def,ldef2) = list_chop_hd i ldefrec in
+ let (lar1,ar,lar2) = list_chop_hd i larrec in
+ let newlnv =
+ try
+ match list_chop i nrec with
+ | (lnv1,_::lnv2) -> (lnv1@lnv2)
+ | _ -> [] (* nrec=[] for cofixpoints *)
+ with Failure "list_chop" -> []
+ in
+ searchrec ((f,def,ar)::lnonrec)
+ (lf1@lf2) (ldef1@ldef2) (lar1@lar2) newlnv
+ with Failure "try_find_i" ->
+ (List.rev lnonrec,
+ (Array.of_list lnamerec, Array.of_list ldefrec,
+ Array.of_list larrec, Array.of_list nrec))
+ in
+ searchrec []
+
+let definition_message id =
+ Options.if_verbose message ((string_of_id id) ^ " is defined")
+
+let recursive_message v =
+ match Array.length v with
+ | 0 -> error "no recursive definition"
+ | 1 -> (Printer.pr_global v.(0) ++ str " is recursively defined")
+ | _ -> hov 0 (prvect_with_sep pr_coma Printer.pr_global v ++
+ spc () ++ str "are recursively defined")
+
+let filter_map f l =
+ let rec aux acc = function
+ hd :: tl -> (match f hd with Some t -> aux (t :: acc) tl
+ | None -> aux acc tl)
+ | [] -> List.rev acc
+ in aux [] l
+
+let list_of_local_binders l =
+ let rec aux acc = function
+ Topconstr.LocalRawDef (n, c) :: tl -> aux ((n, Some c, None) :: acc) tl
+ | Topconstr.LocalRawAssum (nl, c) :: tl ->
+ aux (List.fold_left (fun acc n -> (n, None, Some c) :: acc) acc nl) tl
+ | [] -> List.rev acc
+ in aux [] l
+
+let build_recursive (lnameargsardef:(fixpoint_expr * decl_notation) list) boxed =
+ let sigma = Evd.empty
+ and env0 = Global.env()
+ in
+ let lnameargsardef =
+ (*List.map (fun (f, d) -> Subtac_interp_fixpoint.rewrite_fixpoint env0 protos (f, d))*)
+ lnameargsardef
+ in
+ let lrecnames = List.map (fun ((f,_,_,_,_),_) -> f) lnameargsardef
+ and nv = List.map (fun ((_,n,_,_,_),_) -> n) lnameargsardef
+ in
+ (* Build the recursive context and notations for the recursive types *)
+ let (rec_sign,rec_impls,arityl) =
+ List.fold_left
+ (fun (env,impls,arl) ((recname,(n, ro),bl,arityc,body),_) ->
+ let isevars = ref (Evd.create_evar_defs sigma) in
+ match ro with
+ CStructRec ->
+ let arityc = Command.generalize_constr_expr arityc bl in
+ let arity = interp_type isevars env0 arityc in
+ let impl =
+ if Impargs.is_implicit_args()
+ then Impargs.compute_implicits env0 arity
+ else [] in
+ let impls' =(recname,([],impl,compute_arguments_scope arity))::impls in
+ (Environ.push_named (recname,None,arity) env, impls', (isevars, None, arity)::arl)
+ | CWfRec r ->
+ let _ = trace (str "Rewriting fixpoint: " ++ Ppconstr.pr_id recname ++
+ Ppconstr.pr_binders bl ++ str " : " ++
+ Ppconstr.pr_constr_expr arityc ++ str " := " ++ spc () ++
+ Ppconstr.pr_constr_expr body)
+ in
+ let env', binders_rel = interp_context isevars env0 bl in
+ let after, ((argname, _, argtyp) as arg), before = list_chop_hd n binders_rel in
+ let argid = match argname with Name n -> n | _ -> assert(false) in
+ let after' = List.map (fun (n, c, t) -> (n, option_app (lift 1) c, lift 1 t)) after in
+ let envwf = push_rel_context before env0 in
+ let wf_rel = interp_constr isevars envwf r in
+ let accarg_id = id_of_string ("Acc_" ^ string_of_id argid) in
+ let accarg = (Name accarg_id, None, mkApp (Lazy.force acc_inv, [| argtyp; wf_rel; mkRel 1 |])) in
+ let argid' = id_of_string (string_of_id argid ^ "'") in
+ let before_length, after_length = List.length before, List.length after in
+ let full_length = before_length + 1 + after_length in
+ let wfarg len = (Name argid, None,
+ mkSubset (Name argid') argtyp
+ (mkApp (wf_rel, [|mkRel 1; mkRel (len + 1)|])))
+ in
+ let new_bl = after' @ (accarg :: arg :: before)
+ and intern_bl = after @ (wfarg (before_length + 1) :: before)
+ in
+ let intern_env = push_rel_context intern_bl env0 in
+ let env' = push_rel_context new_bl env0 in
+ let arity = interp_type isevars intern_env arityc in
+ let intern_arity = it_mkProd_or_LetIn arity intern_bl in
+ let arity' = interp_type isevars env' arityc in
+ let arity' = it_mkProd_or_LetIn arity' new_bl in
+ let fun_bl = after @ ((Name recname, None, intern_arity) :: arg :: before) in
+ let _ =
+ let pr c = my_print_constr env c in
+ let prr = Printer.pr_rel_context env in
+ trace (str "Fun bl: " ++ prr fun_bl ++ spc () ++
+ str "Intern bl" ++ prr intern_bl ++ spc () ++
+ str "Extern bl" ++ prr new_bl ++ spc () ++
+ str "Intern arity: " ++ pr intern_arity)
+ in
+ let impl =
+ if Impargs.is_implicit_args()
+ then Impargs.compute_implicits intern_env arity'
+ else [] in
+ let impls' = (recname,([],impl,compute_arguments_scope arity'))::impls in
+ (Environ.push_named (recname,None,arity') env, impls',
+ (isevars, Some (full_length - n, argtyp, wf_rel, fun_bl, intern_bl, intern_arity), arity')::arl))
+ (env0,[],[]) lnameargsardef in
+ let arityl = List.rev arityl in
+ let notations =
+ List.fold_right (fun (_,ntnopt) l -> option_cons ntnopt l)
+ lnameargsardef [] in
+
+ let recdef =
+
+ (* Declare local notations *)
+ let fs = States.freeze() in
+ let def =
+ try
+ List.iter (fun (df,c,scope) -> (* No scope for tmp notation *)
+ Metasyntax.add_notation_interpretation df rec_impls c None) notations;
+ List.map2
+ (fun ((_,_,bl,_,def),_) (isevars, info, arity) ->
+ match info with
+ None ->
+ let def = abstract_constr_expr def bl in
+ isevars, info, interp_casted_constr isevars rec_sign ~impls:([],rec_impls)
+ def arity
+ | Some (n, artyp, wfrel, fun_bl, intern_bl, intern_arity) ->
+ let rec_sign = push_rel_context fun_bl rec_sign in
+ let cstr = interp_casted_constr isevars rec_sign ~impls:([],rec_impls)
+ def intern_arity
+ in isevars, info, it_mkLambda_or_LetIn cstr fun_bl)
+ lnameargsardef arityl
+ with e ->
+ States.unfreeze fs; raise e in
+ States.unfreeze fs; def
+ in
+
+ let (lnonrec,(namerec,defrec,arrec,nvrec)) =
+ collect_non_rec env0 lrecnames recdef arityl nv in
+ let nvrec' = Array.map fst nvrec in(* ignore rec order *)
+ let declare arrec defrec =
+ let recvec =
+ Array.map (subst_vars (List.rev (Array.to_list namerec))) defrec in
+ let recdecls = (Array.map (fun id -> Name id) namerec, arrec, recvec) in
+ let rec declare i fi =
+ trace (str "Declaring: " ++ pr_id fi ++ spc () ++
+ my_print_constr env0 (recvec.(i)));
+ let ce =
+ { const_entry_body = mkFix ((nvrec',i),recdecls);
+ const_entry_type = Some arrec.(i);
+ const_entry_opaque = false;
+ const_entry_boxed = boxed} in
+ let kn = Declare.declare_constant fi (DefinitionEntry ce,IsDefinition Fixpoint)
+ in (ConstRef kn)
+ in
+ (* declare the recursive definitions *)
+ let lrefrec = Array.mapi declare namerec in
+ Options.if_verbose ppnl (recursive_message lrefrec);
+
+
+ (*(* The others are declared as normal definitions *)
+ let var_subst id = (id, Constrintern.global_reference id) in
+ let _ =
+ List.fold_left
+ (fun subst (f,def,t) ->
+ let ce = { const_entry_body = replace_vars subst def;
+ const_entry_type = Some t;
+ const_entry_opaque = false;
+ const_entry_boxed = boxed } in
+ let _ =
+ Declare.declare_constant f (DefinitionEntry ce,IsDefinition Definition)
+ in
+ warning ((string_of_id f)^" is non-recursively defined");
+ (var_subst f) :: subst)
+ (List.map var_subst (Array.to_list namerec))
+ lnonrec
+ in*)
+ List.iter (fun (df,c,scope) ->
+ Metasyntax.add_notation_interpretation df [] c scope) notations
+ in
+ let declare l =
+ let recvec = Array.of_list l
+ and arrec = Array.map pi3 arrec
+ in declare arrec recvec
+ in
+ let recdefs = Array.length defrec in
+ trace (int recdefs ++ str " recursive definitions");
+ (* Solve remaining evars *)
+ let rec collect_evars i acc =
+ if i < recdefs then
+ let (isevars, info, def) = defrec.(i) in
+ let _ = trace (str "In solve evars, isevars is: " ++ Evd.pr_evar_defs !isevars) in
+ let def = evar_nf isevars def in
+ let isevars = Evd.undefined_evars !isevars in
+ let _ = trace (str "In solve evars, undefined is: " ++ Evd.pr_evar_defs isevars) in
+ let evm = Evd.evars_of isevars in
+ let _, _, typ = arrec.(i) in
+ let id = namerec.(i) in
+ let evars_def, evars_typ, evars = Eterm.eterm_term evm def (Some typ) in
+ (* Generalize by the recursive prototypes *)
+ let def =
+ Termops.it_mkNamedLambda_or_LetIn def (Environ.named_context rec_sign)
+ and typ =
+ Termops.it_mkNamedProd_or_LetIn typ (Environ.named_context rec_sign)
+ in
+ (*let evars_typ = match evars_typ with Some t -> t | None -> assert(false) in*)
+ (*let fi = id_of_string (string_of_id id ^ "_evars") in*)
+ (*let ce =
+ { const_entry_body = evars_def;
+ const_entry_type = Some evars_typ;
+ const_entry_opaque = false;
+ const_entry_boxed = boxed} in
+ let kn = Declare.declare_constant fi (DefinitionEntry ce,IsDefinition Definition) in
+ definition_message fi;
+ trace (str (string_of_id fi) ++ str " is defined");*)
+ let evar_sum =
+ if evars = [] then None
+ else
+ let sum = Subtac_utils.build_dependent_sum evars in
+ trace (str "Evars sum: " ++ my_print_constr env0 (pi1 sum));
+ Some sum
+ in
+ collect_evars (succ i) ((id, evars_def, evar_sum) :: acc)
+ else acc
+ in
+ let defs = collect_evars 0 [] in
+
+ (* Solve evars then create the definitions *)
+ let real_evars =
+ filter_map (fun (id, kn, sum) ->
+ match sum with Some (sumg, sumtac, _) -> Some (id, kn, sumg, sumtac) | None -> None)
+ defs
+ in
+ Subtac_utils.and_tac real_evars
+ (fun f _ gr ->
+ let _ = trace (str "Got a proof of: " ++ pr_global gr) in
+ let constant = match gr with Libnames.ConstRef c -> c
+ | _ -> assert(false)
+ in
+ try
+ (*let value = Environ.constant_value (Global.env ()) constant in*)
+ let pis = f (mkConst constant) in
+ trace (str "Accessors: " ++
+ List.fold_right (fun (_, _, _, c) acc -> my_print_constr env0 c ++ spc () ++ acc)
+ pis (mt()));
+ trace (str "Applied existentials: " ++
+ (List.fold_right
+ (fun (id, kn, sumg, pi) acc ->
+ let args = Subtac_utils.destruct_ex pi sumg in
+ my_print_constr env0 (mkApp (kn, Array.of_list args)))
+ pis (mt ())));
+ let rec aux pis acc = function
+ (id, kn, sum) :: tl ->
+ (match sum with
+ None -> aux pis (kn :: acc) tl
+ | Some (sumg, _, _) ->
+ let (id, kn, sumg, pi), pis = List.hd pis, List.tl pis in
+ let args = Subtac_utils.destruct_ex pi sumg in
+ let args =
+ List.map (fun c ->
+ try Reductionops.whd_betadeltaiota (Global.env ()) Evd.empty c
+ with Not_found ->
+ trace (str "Not_found while reducing " ++
+ my_print_constr (Global.env ()) c);
+ c
+ ) args
+ in
+ let _, newdef = decompose_lam_n (recdefs + List.length args) kn in
+ let constr = Term.substl (mkRel 1 :: List.rev args) newdef in
+ aux pis (constr :: acc) tl)
+ | [] -> List.rev acc
+ in
+ declare (aux pis [] defs)
+ with Environ.NotEvaluableConst cer ->
+ match cer with
+ Environ.NoBody -> trace (str "Constant has no body")
+ | Environ.Opaque -> trace (str "Constant is opaque")
+ )
+
+
diff --git a/contrib/subtac/subtac_command.mli b/contrib/subtac/subtac_command.mli
new file mode 100644
index 00000000..e1bbbbb5
--- /dev/null
+++ b/contrib/subtac/subtac_command.mli
@@ -0,0 +1,42 @@
+open Pretyping
+open Evd
+open Environ
+open Term
+open Topconstr
+open Names
+open Libnames
+open Pp
+open Vernacexpr
+open Constrintern
+
+val interp_gen :
+ typing_constraint ->
+ evar_defs ref ->
+ env ->
+ ?impls:full_implicits_env ->
+ ?allow_soapp:bool ->
+ ?ltacvars:ltac_sign ->
+ constr_expr -> constr
+val interp_constr :
+ evar_defs ref ->
+ env -> constr_expr -> constr
+val interp_type :
+ evar_defs ref ->
+ env ->
+ ?impls:full_implicits_env ->
+ constr_expr -> constr
+val interp_casted_constr :
+ evar_defs ref ->
+ env ->
+ ?impls:full_implicits_env ->
+ constr_expr -> types -> constr
+val interp_open_constr :
+ evar_defs ref -> env -> constr_expr -> constr
+val interp_constr_judgment :
+ evar_defs ref ->
+ env ->
+ constr_expr -> unsafe_judgment
+val list_chop_hd : int -> 'a list -> 'a list * 'a * 'a list
+val recursive_message : global_reference array -> std_ppcmds
+val build_recursive :
+ (fixpoint_expr * decl_notation) list -> bool -> unit
diff --git a/contrib/subtac/subtac_errors.ml b/contrib/subtac/subtac_errors.ml
new file mode 100644
index 00000000..3bbfe22b
--- /dev/null
+++ b/contrib/subtac/subtac_errors.ml
@@ -0,0 +1,24 @@
+open Util
+open Pp
+open Printer
+
+type term_pp = Pp.std_ppcmds
+
+type subtyping_error =
+ | UncoercibleInferType of loc * term_pp * term_pp
+ | UncoercibleInferTerm of loc * term_pp * term_pp * term_pp * term_pp
+ | UncoercibleRewrite of term_pp * term_pp
+
+type typing_error =
+ | NonFunctionalApp of loc * term_pp * term_pp * term_pp
+ | NonConvertible of loc * term_pp * term_pp
+ | NonSigma of loc * term_pp
+ | IllSorted of loc * term_pp
+
+exception Subtyping_error of subtyping_error
+exception Typing_error of typing_error
+
+exception Debug_msg of string
+
+let typing_error e = raise (Typing_error e)
+let subtyping_error e = raise (Subtyping_error e)
diff --git a/contrib/subtac/subtac_errors.mli b/contrib/subtac/subtac_errors.mli
new file mode 100644
index 00000000..8d75b9c0
--- /dev/null
+++ b/contrib/subtac/subtac_errors.mli
@@ -0,0 +1,15 @@
+type term_pp = Pp.std_ppcmds
+type subtyping_error =
+ UncoercibleInferType of Util.loc * term_pp * term_pp
+ | UncoercibleInferTerm of Util.loc * term_pp * term_pp * term_pp * term_pp
+ | UncoercibleRewrite of term_pp * term_pp
+type typing_error =
+ NonFunctionalApp of Util.loc * term_pp * term_pp * term_pp
+ | NonConvertible of Util.loc * term_pp * term_pp
+ | NonSigma of Util.loc * term_pp
+ | IllSorted of Util.loc * term_pp
+exception Subtyping_error of subtyping_error
+exception Typing_error of typing_error
+exception Debug_msg of string
+val typing_error : typing_error -> 'a
+val subtyping_error : subtyping_error -> 'a
diff --git a/contrib/subtac/subtac_interp_fixpoint.ml b/contrib/subtac/subtac_interp_fixpoint.ml
new file mode 100644
index 00000000..599dbe39
--- /dev/null
+++ b/contrib/subtac/subtac_interp_fixpoint.ml
@@ -0,0 +1,219 @@
+open Global
+open Pp
+open Util
+open Names
+open Sign
+open Evd
+open Term
+open Termops
+open Reductionops
+open Environ
+open Type_errors
+open Typeops
+open Libnames
+open Classops
+open List
+open Recordops
+open Evarutil
+open Pretype_errors
+open Rawterm
+open Evarconv
+open Pattern
+open Dyn
+open Topconstr
+
+open Subtac_coercion
+open Subtac_utils
+open Coqlib
+open Printer
+open Subtac_errors
+open Context
+open Eterm
+
+
+let mkAppExplC (f, args) = CAppExpl (dummy_loc, (None, f), args)
+
+let mkSubset name typ prop =
+ mkAppExplC (sig_ref,
+ [ typ; mkLambdaC ([name], typ, prop) ])
+
+let mkProj1 u p x =
+ mkAppExplC (proj1_sig_ref, [ u; p; x ])
+
+let mkProj2 u p x =
+ mkAppExplC (proj2_sig_ref, [ u; p; x ])
+
+let list_of_local_binders l =
+ let rec aux acc = function
+ Topconstr.LocalRawDef (n, c) :: tl -> aux ((n, c) :: acc) tl
+ | Topconstr.LocalRawAssum (nl, c) :: tl ->
+ aux (List.fold_left (fun acc n -> (n, c) :: acc) acc nl) tl
+ | [] -> List.rev acc
+ in aux [] l
+
+let abstract_constr_expr_bl abs c bl =
+ List.fold_right (fun (n, t) c -> abs ([n], t, c)) bl c
+
+let pr_binder_list b =
+ List.fold_right (fun ((loc, name), t) acc -> Nameops.pr_name name ++ str " : " ++
+ Ppconstr.pr_constr_expr t ++ spc () ++ acc) b (mt ())
+
+
+let rec rewrite_rec_calls l c = c
+
+let rewrite_fixpoint env l (f, decl) =
+ let (id, (n, ro), bl, typ, body) = f in
+ let body = rewrite_rec_calls l body in
+ match ro with
+ CStructRec -> ((id, (n, ro), bl, typ, body), decl)
+ | CWfRec wfrel ->
+ let bls = list_of_local_binders bl in
+ let _ = trace (str "Rewriting fixpoint: " ++ Ppconstr.pr_id id ++
+ Ppconstr.pr_binders bl ++ str " : " ++
+ Ppconstr.pr_constr_expr typ ++ str " := " ++ spc () ++
+ Ppconstr.pr_constr_expr body)
+ in
+ let before, after = list_chop n bls in
+ let _ = trace (str "Binders before the recursion arg: " ++ spc () ++
+ pr_binder_list before ++ str "; after the recursion arg: " ++
+ pr_binder_list after)
+ in
+ let ((locn, name) as lnid, ntyp), after = match after with
+ hd :: tl -> hd, tl
+ | _ -> assert(false) (* Rec arg must be in after *)
+ in
+ let nid = match name with
+ Name id -> id
+ | Anonymous -> assert(false) (* Rec arg _must_ be named *)
+ in
+ let _wfproof =
+ let _wf_rel = mkAppExplC (well_founded_ref, [ntyp; wfrel]) in
+ (*make_existential_expr dummy_loc before wf_rel*)
+ mkRefC lt_wf_ref
+ in
+ let nid', accproofid =
+ let nid = string_of_id nid in
+ id_of_string (nid ^ "'"), id_of_string ("Acc_" ^ nid)
+ in
+ let lnid', laccproofid = (dummy_loc, Name nid'), (dummy_loc, Name accproofid) in
+ let wf_prop = (mkAppC (wfrel, [ mkIdentC nid'; mkIdentC nid ])) in
+ let lam_wf_prop = mkLambdaC ([lnid'], ntyp, wf_prop) in
+ let typnid' = mkSubset lnid' ntyp wf_prop in
+ let internal_type =
+ abstract_constr_expr_bl mkProdC
+ (mkProdC ([lnid'], typnid',
+ mkLetInC (lnid, mkProj1 ntyp lam_wf_prop (mkIdentC nid'),
+ abstract_constr_expr_bl mkProdC typ after)))
+ before
+ in
+ let body' =
+ let body =
+ (* cast or we will loose some info at pretyping time as body
+ is a function *)
+ CCast (dummy_loc, body, DEFAULTcast, typ)
+ in
+ let body' = (* body abstracted by rec call *)
+ mkLambdaC ([(dummy_loc, Name id)], internal_type, body)
+ in
+ mkAppC (body',
+ [mkLambdaC
+ ([lnid'], typnid',
+ mkAppC (mkIdentC id,
+ [mkProj1 ntyp lam_wf_prop (mkIdentC nid');
+ (mkAppExplC (acc_inv_ref,
+ [ ntyp; wfrel;
+ mkIdentC nid;
+ mkIdentC accproofid;
+ mkProj1 ntyp lam_wf_prop (mkIdentC nid');
+ mkProj2 ntyp lam_wf_prop (mkIdentC nid') ])) ]))])
+ in
+ let acctyp = mkAppExplC (acc_ref, [ ntyp; wfrel; mkIdentC nid ]) in
+ let bl' =
+ let rec aux acc = function
+ Topconstr.LocalRawDef _ as x :: tl ->
+ aux (x :: acc) tl
+ | Topconstr.LocalRawAssum (bl, typ) as assum :: tl ->
+ let rec aux' bl' = function
+ ((loc, name') as x) :: tl ->
+ if name' = name then
+ (if tl = [] then [] else [LocalRawAssum (tl, typ)]) @
+ LocalRawAssum ([(dummy_loc, Name accproofid)], acctyp) ::
+ [LocalRawAssum (List.rev (x :: bl'), typ)]
+ else aux' (x :: bl') tl
+ | [] -> [assum]
+ in aux (aux' [] bl @ acc) tl
+ | [] -> List.rev acc
+ in aux [] bl
+ in
+ let _ = trace (str "Rewrote fixpoint: " ++ Ppconstr.pr_id id ++
+ Ppconstr.pr_binders bl' ++ str " : " ++
+ Ppconstr.pr_constr_expr typ ++ str " := " ++ spc () ++
+ Ppconstr.pr_constr_expr body')
+ in (id, (succ n, ro), bl', typ, body'), decl
+
+let list_mapi f =
+ let rec aux i = function
+ hd :: tl -> f i hd :: aux (succ i) tl
+ | [] -> []
+ in aux 0
+
+let rewrite_cases_aux (loc, po, tml, eqns) =
+ let tml = list_mapi (fun i (c, (n, opt)) -> c,
+ ((match n with
+ Name id -> (match c with
+ | RVar (_, id') when id = id' ->
+ Name (id_of_string (string_of_id id ^ "'"))
+ | _ -> n)
+ | Anonymous -> Name (id_of_string ("x" ^ string_of_int i))),
+ opt)) tml
+ in
+ let mkHole = RHole (dummy_loc, InternalHole) in
+ let mkeq c n = RApp (dummy_loc, RRef (dummy_loc, (Lazy.force eqind_ref)),
+ [mkHole; c; n])
+ in
+ let eqs_types =
+ List.map
+ (fun (c, (n, _)) ->
+ let id = match n with Name id -> id | _ -> assert false in
+ let heqid = id_of_string ("Heq" ^ string_of_id id) in
+ Name heqid, mkeq c (RVar (dummy_loc, id)))
+ tml
+ in
+ let po =
+ List.fold_right
+ (fun (n,t) acc ->
+ RProd (dummy_loc, Anonymous, t, acc))
+ eqs_types (match po with
+ Some e -> e
+ | None -> mkHole)
+ in
+ let eqns =
+ List.map (fun (loc, idl, cpl, c) ->
+ let c' =
+ List.fold_left
+ (fun acc (n, t) ->
+ RLambda (dummy_loc, n, mkHole, acc))
+ c eqs_types
+ in (loc, idl, cpl, c'))
+ eqns
+ in
+ let mk_refl_equal c = RApp (dummy_loc, RRef (dummy_loc, Lazy.force refl_equal_ref),
+ [mkHole; c])
+ in
+ let refls = List.map (fun (c, _) -> mk_refl_equal c) tml in
+ let case = RCases (loc,Some po,tml,eqns) in
+ let app = RApp (dummy_loc, case, refls) in
+ app
+
+let rec rewrite_cases c =
+ match c with
+ RCases _ -> let c' = map_rawconstr rewrite_cases c in
+ (match c' with
+ | RCases (x, y, z, w) -> rewrite_cases_aux (x,y,z,w)
+ | _ -> assert(false))
+ | _ -> map_rawconstr rewrite_cases c
+
+let rewrite_cases env c =
+ let c' = rewrite_cases c in
+ let _ = trace (str "Rewrote cases: " ++ spc () ++ my_print_rawconstr env c') in
+ c'
diff --git a/contrib/subtac/subtac_interp_fixpoint.mli b/contrib/subtac/subtac_interp_fixpoint.mli
new file mode 100644
index 00000000..b0de0641
--- /dev/null
+++ b/contrib/subtac/subtac_interp_fixpoint.mli
@@ -0,0 +1,39 @@
+val mkAppExplC :
+ Libnames.reference * Topconstr.constr_expr list -> Topconstr.constr_expr
+val mkSubset :
+ Names.name Util.located ->
+ Topconstr.constr_expr -> Topconstr.constr_expr -> Topconstr.constr_expr
+val mkProj1 :
+ Topconstr.constr_expr ->
+ Topconstr.constr_expr -> Topconstr.constr_expr -> Topconstr.constr_expr
+val mkProj2 :
+ Topconstr.constr_expr ->
+ Topconstr.constr_expr -> Topconstr.constr_expr -> Topconstr.constr_expr
+val list_of_local_binders :
+ Topconstr.local_binder list ->
+ (Names.name Util.located * Topconstr.constr_expr) list
+val pr_binder_list :
+ (('a * Names.name) * Topconstr.constr_expr) list -> Pp.std_ppcmds
+val rewrite_rec_calls : 'a -> 'b -> 'b
+val rewrite_fixpoint :
+ 'a ->
+ 'b ->
+ (Names.identifier * (int * Topconstr.recursion_order_expr) *
+ Topconstr.local_binder list * Topconstr.constr_expr *
+ Topconstr.constr_expr) *
+ 'c ->
+ (Names.identifier * (int * Topconstr.recursion_order_expr) *
+ Topconstr.local_binder list * Topconstr.constr_expr *
+ Topconstr.constr_expr) *
+ 'c
+val list_mapi : (int -> 'a -> 'b) -> 'a list -> 'b list
+val rewrite_cases_aux :
+ Util.loc * Rawterm.rawconstr option *
+ (Rawterm.rawconstr *
+ (Names.name * (Util.loc * Names.inductive * Names.name list) option))
+ list *
+ (Util.loc * Names.identifier list * Rawterm.cases_pattern list *
+ Rawterm.rawconstr)
+ list -> Rawterm.rawconstr
+
+val rewrite_cases : Environ.env -> Rawterm.rawconstr -> Rawterm.rawconstr
diff --git a/contrib/subtac/subtac_pretyping.ml b/contrib/subtac/subtac_pretyping.ml
new file mode 100644
index 00000000..104a0a58
--- /dev/null
+++ b/contrib/subtac/subtac_pretyping.ml
@@ -0,0 +1,150 @@
+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+
+(* $Id: subtac_pretyping.ml 8688 2006-04-07 15:08:12Z msozeau $ *)
+
+open Global
+open Pp
+open Util
+open Names
+open Sign
+open Evd
+open Term
+open Termops
+open Reductionops
+open Environ
+open Type_errors
+open Typeops
+open Libnames
+open Classops
+open List
+open Recordops
+open Evarutil
+open Pretype_errors
+open Rawterm
+open Evarconv
+open Pattern
+open Dyn
+
+open Subtac_coercion
+open Subtac_utils
+open Coqlib
+open Printer
+open Subtac_errors
+open Context
+open Eterm
+
+module Pretyping = Pretyping.Pretyping_F(Subtac_coercion.Coercion)
+
+open Pretyping
+
+let _ = Pretyping.allow_anonymous_refs := true
+
+type recursion_info = {
+ arg_name: name;
+ arg_type: types; (* A *)
+ args_after : rel_context;
+ wf_relation: constr; (* R : A -> A -> Prop *)
+ wf_proof: constr; (* : well_founded R *)
+ f_type: types; (* f: A -> Set *)
+ f_fulltype: types; (* Type with argument and wf proof product first *)
+}
+
+let my_print_rec_info env t =
+ str "Name: " ++ Nameops.pr_name t.arg_name ++ spc () ++
+ str "Arg type: " ++ my_print_constr env t.arg_type ++ spc () ++
+ str "Wf relation: " ++ my_print_constr env t.wf_relation ++ spc () ++
+ str "Wf proof: " ++ my_print_constr env t.wf_proof ++ spc () ++
+ str "Abbreviated Type: " ++ my_print_constr env t.f_type ++ spc () ++
+ str "Full type: " ++ my_print_constr env t.f_fulltype
+(* trace (str "pretype for " ++ (my_print_rawconstr env c) ++ *)
+(* str " and tycon "++ my_print_tycon env tycon ++ *)
+(* str " in environment: " ++ my_print_env env); *)
+
+let merge_evms x y =
+ Evd.fold (fun ev evi evm -> Evd.add evm ev evi) x y
+
+let interp env isevars c tycon =
+ let j = pretype tycon env isevars ([],[]) c in
+ let evm = evars_of !isevars in
+ nf_evar evm j.uj_val, nf_evar evm j.uj_type
+
+let find_with_index x l =
+ let rec aux i = function
+ (y, _, _) as t :: tl -> if x = y then i, t else aux (succ i) tl
+ | [] -> raise Not_found
+ in aux 0 l
+
+let list_split_at index l =
+ let rec aux i acc = function
+ hd :: tl when i = index -> (List.rev acc), tl
+ | hd :: tl -> aux (succ i) (hd :: acc) tl
+ | [] -> failwith "list_split_at: Invalid argument"
+ in aux 0 [] l
+
+open Vernacexpr
+
+let coqintern evd env : Topconstr.constr_expr -> Rawterm.rawconstr = Constrintern.intern_constr (evars_of evd) env
+let coqinterp evd env : Topconstr.constr_expr -> Term.constr = Constrintern.interp_constr (evars_of evd) env
+
+let env_with_binders env isevars l =
+ let rec aux ((env, rels) as acc) = function
+ Topconstr.LocalRawDef ((loc, name), def) :: tl ->
+ let rawdef = coqintern !isevars env def in
+ let coqdef, deftyp = interp env isevars rawdef empty_tycon in
+ let reldecl = (name, Some coqdef, deftyp) in
+ aux (push_rel reldecl env, reldecl :: rels) tl
+ | Topconstr.LocalRawAssum (bl, typ) :: tl ->
+ let rawtyp = coqintern !isevars env typ in
+ let coqtyp, typtyp = interp env isevars rawtyp empty_tycon in
+ let acc =
+ List.fold_left (fun (env, rels) (loc, name) ->
+ let reldecl = (name, None, coqtyp) in
+ (push_rel reldecl env,
+ reldecl :: rels))
+ (env, rels) bl
+ in aux acc tl
+ | [] -> acc
+ in aux (env, []) l
+
+let subtac_process env isevars id l c tycon =
+ let evars () = evars_of !isevars in
+ let _ = trace (str "Creating env with binders") in
+ let env_binders, binders_rel = env_with_binders env isevars l in
+ let _ = trace (str "New env created:" ++ my_print_context env_binders) in
+ let tycon =
+ match tycon with
+ None -> empty_tycon
+ | Some t ->
+ let t = coqintern !isevars env_binders t in
+ let _ = trace (str "Internalized specification: " ++ my_print_rawconstr env_binders t) in
+ let coqt, ttyp = interp env_binders isevars t empty_tycon in
+ let _ = trace (str "Interpreted type: " ++ my_print_constr env_binders coqt) in
+ mk_tycon coqt
+ in
+ let c = coqintern !isevars env_binders c in
+ let _ = trace (str "Internalized term: " ++ my_print_rawconstr env c) in
+ let coqc, ctyp = interp env_binders isevars c tycon in
+ let _ = trace (str "Interpreted term: " ++ my_print_constr env_binders coqc ++ spc () ++
+ str "Coq type: " ++ my_print_constr env_binders ctyp)
+ in
+ let _ = trace (str "Original evar map: " ++ Evd.pr_evar_map (evars ())) in
+
+ let fullcoqc = it_mkLambda_or_LetIn coqc binders_rel
+ and fullctyp = it_mkProd_or_LetIn ctyp binders_rel
+ in
+ let fullcoqc = Evarutil.nf_evar (evars_of !isevars) fullcoqc in
+ let fullctyp = Evarutil.nf_evar (evars_of !isevars) fullctyp in
+
+ let _ = trace (str "After evar normalization: " ++ spc () ++
+ str "Coq term: " ++ my_print_constr env fullcoqc ++ spc ()
+ ++ str "Coq type: " ++ my_print_constr env fullctyp)
+ in
+ let evm = non_instanciated_map env isevars in
+ let _ = trace (str "Non instanciated evars map: " ++ Evd.pr_evar_map evm) in
+ evm, fullcoqc, fullctyp
diff --git a/contrib/subtac/subtac_pretyping.mli b/contrib/subtac/subtac_pretyping.mli
new file mode 100644
index 00000000..97e56ecb
--- /dev/null
+++ b/contrib/subtac/subtac_pretyping.mli
@@ -0,0 +1,12 @@
+open Term
+open Environ
+open Names
+open Sign
+open Evd
+open Global
+open Topconstr
+
+module Pretyping : Pretyping.S
+
+val subtac_process : env -> evar_defs ref -> identifier -> local_binder list ->
+ constr_expr -> constr_expr option -> evar_map * constr * types
diff --git a/contrib/subtac/subtac_utils.ml b/contrib/subtac/subtac_utils.ml
new file mode 100644
index 00000000..6c165dad
--- /dev/null
+++ b/contrib/subtac/subtac_utils.ml
@@ -0,0 +1,246 @@
+open Evd
+open Libnames
+open Coqlib
+open Term
+open Names
+open Util
+
+(****************************************************************************)
+(* Library linking *)
+
+let contrib_name = "subtac"
+
+let subtac_dir = [contrib_name]
+let fix_sub_module = "FixSub"
+let utils_module = "Utils"
+let fixsub_module = subtac_dir @ [fix_sub_module]
+let utils_module = subtac_dir @ [utils_module]
+let init_constant dir s = gen_constant contrib_name dir s
+let init_reference dir s = gen_reference contrib_name dir s
+
+let fixsub = lazy (init_constant fixsub_module "Fix_sub")
+let ex_pi1 = lazy (init_constant utils_module "ex_pi1")
+let ex_pi2 = lazy (init_constant utils_module "ex_pi2")
+
+let make_ref s = Qualid (dummy_loc, (qualid_of_string s))
+let well_founded_ref = make_ref "Init.Wf.Well_founded"
+let acc_ref = make_ref "Init.Wf.Acc"
+let acc_inv_ref = make_ref "Init.Wf.Acc_inv"
+let fix_sub_ref = make_ref "Coq.subtac.FixSub.Fix_sub"
+let lt_wf_ref = make_ref "Coq.Wf_nat.lt_wf"
+let sig_ref = make_ref "Init.Specif.sig"
+let proj1_sig_ref = make_ref "Init.Specif.proj1_sig"
+let proj2_sig_ref = make_ref "Init.Specif.proj2_sig"
+
+let build_sig () =
+ { proj1 = init_constant ["Init"; "Specif"] "proj1_sig";
+ proj2 = init_constant ["Init"; "Specif"] "proj2_sig";
+ elim = init_constant ["Init"; "Specif"] "sig_rec";
+ intro = init_constant ["Init"; "Specif"] "exist";
+ typ = init_constant ["Init"; "Specif"] "sig" }
+
+let sig_ = lazy (build_sig ())
+
+let eqind = lazy (init_constant ["Init"; "Logic"] "eq")
+let eqind_ref = lazy (init_reference ["Init"; "Logic"] "eq")
+let refl_equal_ref = lazy (init_reference ["Init"; "Logic"] "refl_equal")
+
+let ex_ind = lazy (init_constant ["Init"; "Logic"] "ex")
+let ex_intro = lazy (init_reference ["Init"; "Logic"] "ex_intro")
+
+let proj1 = lazy (init_constant ["Init"; "Logic"] "proj1")
+let proj2 = lazy (init_constant ["Init"; "Logic"] "proj2")
+
+let boolind = lazy (init_constant ["Init"; "Datatypes"] "bool")
+let sumboolind = lazy (init_constant ["Init"; "Specif"] "sumbool")
+let natind = lazy (init_constant ["Init"; "Datatypes"] "nat")
+let intind = lazy (init_constant ["ZArith"; "binint"] "Z")
+let existSind = lazy (init_constant ["Init"; "Specif"] "sigS")
+
+let existS = lazy (build_sigma_set ())
+
+let prod = lazy (build_prod ())
+
+
+(* orders *)
+let well_founded = lazy (init_constant ["Init"; "Wf"] "well_founded")
+let fix = lazy (init_constant ["Init"; "Wf"] "Fix")
+let acc = lazy (init_constant ["Init"; "Wf"] "Acc")
+let acc_inv = lazy (init_constant ["Init"; "Wf"] "Acc_inv")
+
+let extconstr = Constrextern.extern_constr true (Global.env ())
+let extsort s = Constrextern.extern_constr true (Global.env ()) (mkSort s)
+
+open Pp
+
+let my_print_constr = Termops.print_constr_env
+let my_print_constr_expr = Ppconstr.pr_constr_expr
+let my_print_context = Termops.print_rel_context
+let my_print_env = Termops.print_env
+let my_print_rawconstr = Printer.pr_rawconstr_env
+let my_print_evardefs = Evd.pr_evar_defs
+
+let my_print_tycon_type = Evarutil.pr_tycon_type
+
+
+let debug n s =
+ if !Options.debug then
+ msgnl s
+ else ()
+
+let debug_msg n s =
+ if !Options.debug then s
+ else mt ()
+
+let trace s =
+ if !Options.debug then msgnl s
+ else ()
+
+let wf_relations = Hashtbl.create 10
+
+let std_relations () =
+ let add k v = Hashtbl.add wf_relations k v in
+ add (init_constant ["Init"; "Peano"] "lt")
+ (lazy (init_constant ["Arith"; "Wf_nat"] "lt_wf"))
+
+let std_relations = Lazy.lazy_from_fun std_relations
+
+type binders = Topconstr.local_binder list
+
+let app_opt c e =
+ match c with
+ Some constr -> constr e
+ | None -> e
+
+let print_args env args =
+ Array.fold_right (fun a acc -> my_print_constr env a ++ spc () ++ acc) args (str "")
+
+let make_existential loc env isevars c =
+ let evar = Evarutil.e_new_evar isevars env ~src:(loc, QuestionMark) c in
+ let (key, args) = destEvar evar in
+ debug 2 (str "Constructed evar " ++ int key ++ str " applied to args: " ++
+ print_args env args);
+ evar
+
+let make_existential_expr loc env c =
+ let key = Evarutil.new_untyped_evar () in
+ let evar = Topconstr.CEvar (loc, key) in
+ debug 2 (str "Constructed evar " ++ int key);
+ evar
+
+let string_of_hole_kind = function
+ | ImplicitArg _ -> "ImplicitArg"
+ | BinderType _ -> "BinderType"
+ | QuestionMark -> "QuestionMark"
+ | CasesType -> "CasesType"
+ | InternalHole -> "InternalHole"
+ | TomatchTypeParameter _ -> "TomatchTypeParameter"
+
+let non_instanciated_map env evd =
+ let evm = evars_of !evd in
+ List.fold_left
+ (fun evm (key, evi) ->
+ let (loc,k) = evar_source key !evd in
+ debug 2 (str "evar " ++ int key ++ str " has kind " ++
+ str (string_of_hole_kind k));
+ match k with
+ QuestionMark -> Evd.add evm key evi
+ | _ ->
+ debug 2 (str " and is an implicit");
+ Pretype_errors.error_unsolvable_implicit loc env evm k)
+ Evd.empty (Evarutil.non_instantiated evm)
+
+let global_kind = Decl_kinds.IsDefinition Decl_kinds.Definition
+let goal_kind = Decl_kinds.Global, Decl_kinds.DefinitionBody Decl_kinds.Definition
+
+let global_fix_kind = Decl_kinds.IsDefinition Decl_kinds.Fixpoint
+let goal_fix_kind = Decl_kinds.Global, Decl_kinds.DefinitionBody Decl_kinds.Fixpoint
+
+open Tactics
+open Tacticals
+
+let build_dependent_sum l =
+ let rec aux (acc, tac, typ) = function
+ (n, t) :: tl ->
+ let t' = mkLambda (Name n, t, typ) in
+ trace (str ("treating " ^ string_of_id n) ++
+ str "assert: " ++ my_print_constr (Global.env ()) t);
+ let tac' =
+ tclTHEN (assert_tac true (Name n) t)
+ (tclTHENLIST
+ [intros;
+ (tclTHENSEQ
+ [tclTRY (constructor_tac (Some 1) 1
+ (Rawterm.ImplicitBindings [mkVar n]));
+ tac]);
+ ])
+ in
+ aux (mkApp (Lazy.force ex_ind, [| t; t'; |]), tac', t') tl
+ | [] -> acc, tac, typ
+ in
+ match l with
+ (_, hd) :: tl -> aux (hd, intros, hd) tl
+ | [] -> raise (Invalid_argument "build_dependent_sum")
+
+open Proof_type
+open Tacexpr
+
+let mkProj1 a b c =
+ mkApp (Lazy.force proj1, [| a; b; c |])
+
+let mkProj2 a b c =
+ mkApp (Lazy.force proj2, [| a; b; c |])
+
+let mk_ex_pi1 a b c =
+ mkApp (Lazy.force ex_pi1, [| a; b; c |])
+
+let mk_ex_pi2 a b c =
+ mkApp (Lazy.force ex_pi2, [| a; b; c |])
+
+
+let mkSubset name typ prop =
+ mkApp ((Lazy.force sig_).typ,
+ [| typ; mkLambda (name, typ, prop) |])
+
+let and_tac l hook =
+ let andc = Coqlib.build_coq_and () in
+ let rec aux ((accid, goal, tac, extract) as acc) = function
+ | [] -> (* Singleton *) acc
+
+ | (id, x, elgoal, eltac) :: tl ->
+ let tac' = tclTHEN simplest_split (tclTHENLIST [tac; eltac]) in
+ let proj = fun c -> mkProj2 goal elgoal c in
+ let extract = List.map (fun (id, x, y, f) -> (id, x, y, (fun c -> f (mkProj1 goal elgoal c)))) extract in
+ aux ((string_of_id id) ^ "_" ^ accid, mkApp (andc, [| goal; elgoal |]), tac',
+ (id, x, elgoal, proj) :: extract) tl
+
+ in
+ let and_proof_id, and_goal, and_tac, and_extract =
+ match l with
+ | [] -> raise (Invalid_argument "and_tac: empty list of goals")
+ | (hdid, x, hdg, hdt) :: tl -> aux (string_of_id hdid, hdg, hdt, [hdid, x, hdg, (fun c -> c)]) tl
+ in
+ let and_proofid = id_of_string (and_proof_id ^ "_and_proof") in
+ Command.start_proof and_proofid goal_kind and_goal
+ (hook (fun c -> List.map (fun (id, x, t, f) -> (id, x, t, f c)) and_extract));
+ trace (str "Started and proof");
+ Pfedit.by and_tac;
+ trace (str "Applied and tac")
+
+
+let destruct_ex ext ex =
+ let rec aux c acc =
+ match kind_of_term c with
+ App (f, args) ->
+ (match kind_of_term f with
+ Ind i when i = Term.destInd (Lazy.force ex_ind) && Array.length args = 2 ->
+ let (dom, rng) =
+ try (args.(0), args.(1))
+ with _ -> assert(false)
+ in
+ (mk_ex_pi1 dom rng acc) :: aux rng (mk_ex_pi2 dom rng acc)
+ | _ -> [acc])
+ | _ -> [acc]
+ in aux ex ext
+
+
diff --git a/contrib/subtac/subtac_utils.mli b/contrib/subtac/subtac_utils.mli
new file mode 100644
index 00000000..92a995c8
--- /dev/null
+++ b/contrib/subtac/subtac_utils.mli
@@ -0,0 +1,85 @@
+open Term
+open Libnames
+open Coqlib
+open Environ
+open Pp
+open Evd
+open Decl_kinds
+open Topconstr
+open Rawterm
+open Util
+open Evarutil
+open Names
+
+val contrib_name : string
+val subtac_dir : string list
+val fix_sub_module : string
+val fixsub_module : string list
+val init_constant : string list -> string -> constr
+val init_reference : string list -> string -> global_reference
+val fixsub : constr lazy_t
+val make_ref : string -> reference
+val well_founded_ref : reference
+val acc_ref : reference
+val acc_inv_ref : reference
+val fix_sub_ref : reference
+val lt_wf_ref : reference
+val sig_ref : reference
+val proj1_sig_ref : reference
+val proj2_sig_ref : reference
+val build_sig : unit -> coq_sigma_data
+val sig_ : coq_sigma_data lazy_t
+val eqind : constr lazy_t
+val eqind_ref : global_reference lazy_t
+val refl_equal_ref : global_reference lazy_t
+val boolind : constr lazy_t
+val sumboolind : constr lazy_t
+val natind : constr lazy_t
+val intind : constr lazy_t
+val existSind : constr lazy_t
+val existS : coq_sigma_data lazy_t
+val prod : coq_sigma_data lazy_t
+
+val well_founded : constr lazy_t
+val fix : constr lazy_t
+val acc : constr lazy_t
+val acc_inv : constr lazy_t
+val extconstr : constr -> constr_expr
+val extsort : sorts -> constr_expr
+val my_print_constr : env -> constr -> std_ppcmds
+val my_print_constr_expr : constr_expr -> std_ppcmds
+val my_print_evardefs : evar_defs -> std_ppcmds
+val my_print_context : env -> std_ppcmds
+val my_print_env : env -> std_ppcmds
+val my_print_rawconstr : env -> rawconstr -> std_ppcmds
+val my_print_tycon_type : env -> type_constraint_type -> std_ppcmds
+
+
+val debug : int -> std_ppcmds -> unit
+val debug_msg : int -> std_ppcmds -> std_ppcmds
+val trace : std_ppcmds -> unit
+val wf_relations : (constr, constr lazy_t) Hashtbl.t
+
+type binders = local_binder list
+val app_opt : ('a -> 'a) option -> 'a -> 'a
+val print_args : env -> constr array -> std_ppcmds
+val make_existential : loc -> env -> evar_defs ref -> types -> constr
+val make_existential_expr : loc -> 'a -> 'b -> constr_expr
+val string_of_hole_kind : hole_kind -> string
+val non_instanciated_map : env -> evar_defs ref -> evar_map
+val global_kind : logical_kind
+val goal_kind : locality_flag * goal_object_kind
+val global_fix_kind : logical_kind
+val goal_fix_kind : locality_flag * goal_object_kind
+
+val mkSubset : name -> constr -> constr -> constr
+val mkProj1 : constr -> constr -> constr -> constr
+val mkProj1 : constr -> constr -> constr -> constr
+val mk_ex_pi1 : constr -> constr -> constr -> constr
+val mk_ex_pi1 : constr -> constr -> constr -> constr
+
+val build_dependent_sum : (identifier * types) list -> constr * Proof_type.tactic * types
+val and_tac : (identifier * 'a * constr * Proof_type.tactic) list ->
+ ((constr -> (identifier * 'a * constr * constr) list) -> Tacexpr.declaration_hook) -> unit
+
+val destruct_ex : constr -> constr -> constr list
generated by cgit v1.2.3 (git 2.39.1) at 2024-06-13 22:14:24 +0000