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Commit c0f46a4f authored by charguer's avatar charguer
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inprogress

parent 5b7e4812
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TODO
View file @ c0f46a4f
......@@ -3,54 +3,20 @@
URGENT
- record generation breaks circularity through use of "loc" systematically for records
SANITY
- reject programs with constructor names ending with "_"
(e.g. "A_" is already used for type variables *)
- reject variable names and type definition that belongs to the list
builtin_type_constructors
- rename on the fly coq keyword such as exists, forall, etc..
=> requires a list of all coq keywords: see
else if name = "exists" then "exists__"
else if name = "forall" then "forall__"
- prevent rebinding of List
- restriction on not binding "min" and "max" might be a bit restrictive..
COMPILATION
- In the makefile.Coq, when building the .vq and obtaining
"Error: /home/charguer/tlc/src/LibPer.vio: premature end of file. Try to rebuild it."
=> then delete the .vio file
(useful for compilations interrupted using CTRL+C)
=> even better, wrap "coqc -quick" with an atomic commit of its result.
MAJOR TODAY
- record
- array
- notations for primitive ops
- loops
- mutual type defs
record generation breaks circularity through use of "loc" systematically for records
MAJOR NEXT
- record single field and array single cell notation
Notation "x `. f '~>' S" :=
Notation "x `[ i ] '~>' S" :=
- partial application
- xabstract => rename as xgen
......@@ -76,18 +42,7 @@ MAJOR POSTPONED
=> how to shared typed/untyped AST
LATER
- semantics for records|arrays passed by value / passed by reference
TODO
SANITY
- discuss the naming scheme
=> type t --> t_ || x'
......@@ -97,37 +52,51 @@ TODO
=> PB: plus_plus_infix' !
=> var x_ --> forbidden
- reject programs with constructor names ending with "_"
(e.g. "A_" is already used for type variables *)
- reject variable names and type definition that belongs to the list
builtin_type_constructors
- in print_tast and print_past, protect with parenth the infix names being bound
- rename on the fly coq keyword such as exists, forall, etc..
=> requires a list of all coq keywords: see
else if name = "exists" then "exists__"
else if name = "forall" then "forall__"
- make sure that check_var is called where needed
- prevent rebinding of List
- restriction on not binding "min" and "max" might be a bit restrictive..
- need to prevent double-underscore in the names?
- unify the source code in main.ml and makecmj.ml
- check that there are no uses of labels in source files
OTHER LANGUAGES
- semantics for records|arrays passed by value / passed by reference
- make systematic use of || (rm -f $@; exit 1) in cfml calls
- support null pointers
- Ltac xcf_core tt should be able to test whether Spec is a top val, and then do rewrite.
CODE BEAUTIFY
DEPRECATED?
- make sure that check_var is called where needed
- no longer rely on myocamldep
- unify the source code in main.ml and makecmj.ml
- incorrect CF generation for "let n = null"
- check that there are no uses of labels in input source files
- Ltac xcf_core tt
should be able to test whether Spec is a top val, and then do rewrite.
(*
(** Auxiliary function for the special case of compiling pervasives *)
MAKEFILE BEAUTIFY
let add_pervasives_prefix_if_needed p =
if !Clflags.nopervasives then "Pervasives." ^ p else p
let p = add_pervasives_prefix_if_needed p in
- no longer rely on myocamldep
- make systematic use of || (rm -f $@; exit 1) in cfml calls
*)
\ No newline at end of file
- In the makefile.Coq, when building the .vq and obtaining
"Error: /home/charguer/tlc/src/LibPer.vio: premature end of file. Try to rebuild it."
=> then delete the .vio file
(useful for compilations interrupted using CTRL+C)
=> even better, wrap "coqc -quick" with an atomic commit of its result.
examples/BasicDemos/Demo_proof.v
View file @ c0f46a4f
......@@ -7,6 +7,60 @@ Require Import Stdlib.
(********************************************************************)
(* ** Records *)
type 'a sitems = {
mutable nb : int;
mutable items : 'a list; }
Lemma sitems_build n =
{ nb = n; items = [] }
Proof using.
xcf.
Qed.
Lemma sitems_get_nb r =
r.nb
Proof using.
xcf.
Qed.
Lemma sitems_incr_nb r =
r.nb <- r.nb + 1
Proof using.
xcf.
Qed.
Lemma sitems_length_items r =
List.length r.items
Proof using.
xcf.
Qed.
Lemma sitems_push x r =
r.nb <- r.nb + 1;
r.items <- x :: r.items
Proof using.
xcf.
Qed.
(********************************************************************)
(* ** Arrays *)
Lemma array_ops () =
let t = Array.make 3 0 in
let _x = t.(1) in
t.(2) <- 4;
let _y = t.(2) in
let _z = t.(1) in
Array.length t
Proof using.
xcf.
Qed.
(********************************************************************)
(********************************************************************)
......@@ -674,17 +728,6 @@ let order_record () =
Require Import LibInt.
Ltac xgo1_core tt :=
xgo_once tt.
Tactic Notation "x" :=
xgo1_core tt.
Tactic Notation "x" "~" :=
x; xauto~.
Tactic Notation "x" "*" :=
x; xauto*.
Lemma rec_partial_half_spec : forall k n,
n = 2 * k ->
app rec_partial_half [n] \[] \[= k].
......@@ -825,60 +868,6 @@ Qed.
(********************************************************************)
(* ** Records *)
type 'a sitems = {
mutable nb : int;
mutable items : 'a list; }
Lemma sitems_build n =
{ nb = n; items = [] }
Proof using.
xcf.
Qed.
Lemma sitems_get_nb r =
r.nb
Proof using.
xcf.
Qed.
Lemma sitems_incr_nb r =
r.nb <- r.nb + 1
Proof using.
xcf.
Qed.
Lemma sitems_length_items r =
List.length r.items
Proof using.
xcf.
Qed.
Lemma sitems_push x r =
r.nb <- r.nb + 1;
r.items <- x :: r.items
Proof using.
xcf.
Qed.
(********************************************************************)
(* ** Arrays *)
Lemma array_ops () =
let t = Array.make 3 0 in
let _x = t.(1) in
t.(2) <- 4;
let _y = t.(2) in
let _z = t.(1) in
Array.length t
Proof using.
xcf.
Qed.
(********************************************************************)
(* ** While loops *)
......
generator/characteristic.ml
View file @ c0f46a4f
......@@ -611,18 +611,26 @@ let rec cfg_exp env e =
(* TODO: only in purely function setting: | Texp_record (lbl_expr_list, opt_init_expr) -> ret e*)
| Texp_record (lbl_expr_list, opt_init_expr) ->
if opt_init_expr <> None then unsupported loc "record-with"; (* TODO *)
let (pathfront,pathend) = get_record_decomposed_name_for_exp e in
let func = Coq_var (pathfront ^ (record_make_name pathend)) in (* tood: move the underscore *)
if opt_init_expr <> None then unsupported loc "record-with";
let named_args = List.map (fun (p,li,ei) -> (li.lbl_name,ei)) lbl_expr_list in
(* deprecated sorting: let args = List.map snd (list_ksort str_cmp named_args) in *)
let fields_names = extract_label_names_simple e.exp_env e.exp_type in
let build_arg (name, arg) =
let value = coq_apps coq_dyn_at [coq_typ arg; lift arg] in
Coq_tuple [Coq_var (record_field_name name); value]
in
let arg = coq_list (List.map build_arg named_args) in
Cf_record_new (arg)
(* DEPRECATED
let (pathfront,pathend) = get_record_decomposed_name_for_exp e in
let func = Coq_var (pathfront ^ (record_make_name pathend)) in
let fields_names = extract_label_names_scimple e.exp_env e.exp_type in
let args =
try List.map (fun name -> List.assoc name named_args) fields_names
with Not_found -> failwith "some fields are missing in a record construction"
in
let tprod = coq_prod (List.map coq_typ args) in
Cf_app ([tprod], loc_type, func, [Coq_tuple (List.map lift args)])
*)
| Texp_apply (funct, oargs) when exp_is_inlined_primitive funct oargs -> ret e
......@@ -752,10 +760,7 @@ let rec cfg_exp env e =
end
| Texp_array args ->
let ccons = Coq_var (get_builtin_constructor "::") in
let cnil = Coq_var (get_builtin_constructor "[]") in
let arg = List.fold_right (fun arg acc ->
coq_apps ccons [lift arg; acc]) args cnil in
let arg = coq_list (List.map lift args) in
let targ = (* ['a], obtained by extraction from ['a array]. *)
match btyp_of_typ_exp e.exp_type with
| Btyp_constr (id,[t]) when Path.name id = "array" -> lift_btyp t
......@@ -769,14 +774,24 @@ let rec cfg_exp env e =
| Texp_field (arg, p, lbl) ->
let tr = coq_typ e in
let ts = coq_typ arg in (* todo: check it is always 'loc' *)
let func = Coq_var "CFML.CFApp.record_get" in
let field = Coq_var (record_field_name lbl.lbl_name) in
Cf_app ([ts; coq_nat], tr, func, [lift arg; field])
(* DEPRECATED
let func = Coq_var (record_field_get_name lbl.lbl_name) in
Cf_app ([ts], tr, func, [lift arg])
*)
| Texp_setfield(arg, p, lbl, newval) ->
let ts1 = coq_typ arg in (* todo: check it is always 'loc' *)
let ts2 = coq_typ newval in
let func = Coq_var "CFML.CFApp.record_get" in
let field = Coq_var (record_field_name lbl.lbl_name) in
Cf_app ([ts1; coq_nat; ts2], coq_unit, func, [lift arg; field; lift newval])
(* DEPRECATED
let func = Coq_var (record_field_set_name lbl.lbl_name) in
Cf_app ([ts1;ts2], coq_unit, func, [lift arg; lift newval])
Cf_app ([ts1;ts2], coq_unit, func, [lift arg; lift newval])
*)
| Texp_try(body, pat_expr_list) -> unsupported loc "try expression"
| Texp_variant(l, arg) -> unsupported loc "variant expression"
......@@ -1008,15 +1023,25 @@ and cfg_type_record (name,dec) =
in
let type_abbrev = Coqtop_def ((type_constr_name x, Coq_wild), coq_fun_types params loc_type) in
[ type_abbrev ],
(* DEPRECATED BUT KEEP FOR FUTURE USE
[ Coqtop_record top ]
@ (implicit_decl)
@ [ Coqtop_hint_constructors ([record_structure_name x], "typeclass_instances") ]
@ record_functions x (record_constructor_name x) (record_repr_name x) params fields_names fields_types
@
*)
record_functions x (record_constructor_name x) (record_repr_name x) params fields_names fields_types
(* todo: move le "_of" *)
(** Auxiliary function to generate stuff for records *)
and record_functions name record_constr repr_name params fields_names fields_types =
and record_functions name record_constr repr_name params fields_names fields_types =
let build_field_name_def i field_name =
Coqtop_def ((field_name, coq_nat), Coq_nat i)
in
let fields_names_def = list_mapi build_field_name_def fields_names in
fields_names_def
(* DEPRECATED BUT KEEP FOR FUTURE USE
let nth i l = List.nth l i in
let n = List.length fields_names in
let indices = list_nat n in
......@@ -1030,7 +1055,7 @@ and record_functions name record_constr repr_name params fields_names fields_typ
[ Coqtop_param (nth i get_names, val_type);
Coqtop_param (nth i set_names, val_type) ] in
let logicals = List.map str_capitalize_1 fields_names (* for_indices (fun i -> sprintf "A%d" (i+1)) *) in
let logicals = List.map str_capitalize_1 fields_names in
let reprs = for_indices (fun i -> sprintf "_T%d" (i+1)) in
let abstracts = for_indices (fun i -> sprintf "_X%d" (i+1)) in
let concretes = for_indices (fun i -> sprintf "x%d" (i+1)) in
......@@ -1050,6 +1075,7 @@ and record_functions name record_constr repr_name params fields_names fields_typ
let tconcretes = List.map (fun i -> nth i concretes, nth i fields_types) indices in
let tloc = (loc, loc_type) in
let repr_args = tparams @ tlogicals @ treprs @ tabstracts @ [tloc] in
let hcore = heap_is_single vloc (coq_apps (coq_var_at record_constr) (vparams @ vconcretes)) in
let helems_items = for_indices (fun i -> hdata (nth i vconcretes) (Coq_app (nth i vreprs, nth i vabstracts))) in
......@@ -1198,12 +1224,12 @@ and record_functions name record_constr repr_name params fields_names fields_typ
@ [ repr_def ]
@ repr_convert_focus_unfocus
@ fields_convert_focus_unfocus
(* TODO: revive *)
(*
@ new_spec
@ (List.concat (List.map get_set_spec indices))
@ (List.concat (List.map get_spec_focus indices))
@ (List.concat (List.map set_spec_unfocus indices)) *)
@ (List.concat (List.map set_spec_unfocus indices))
END DEPRECATED *)
......
generator/coq.ml
View file @ c0f46a4f
......@@ -25,7 +25,6 @@ and coq =
| Coq_var of var
| Coq_nat of int
| Coq_int of int
| Coq_list of coq list
| Coq_app of coq * coq
| Coq_impl of coq * coq
| Coq_lettuple of coqs * coq * coq
......@@ -38,6 +37,7 @@ and coq =
| Coq_record of (var * coq) list
| Coq_tag of string * coq list * string option * coq
| Coq_annot of coq * coq
(* DEPRECATED ; maybe future ? | Coq_list of coq list *)
and coqs = coq list
......@@ -136,8 +136,8 @@ let coq_unit =
let coq_int =
Coq_var "Coq.ZArith.BinInt.Z"
let coq_list xs =
Coq_list xs
let coq_nat =
Coq_var "Coq.Init.Datatypes.nat"
let coq_bool =
Coq_var "Coq.Init.Datatypes.bool"
......@@ -230,6 +230,24 @@ let coq_prod cs =
| [c] -> c
| c0::cs' -> List.fold_left (fun acc c -> coq_apps (Coq_var "Coq.Init.Datatypes.prod") [acc;c]) c0 cs'
(** List [c1 :: c2 :: .. :: cN] *)
let coq_list xs =
let ccons = Coq_var (Renaming.get_builtin_constructor "::") in
let cnil = Coq_var (Renaming.get_builtin_constructor "[]") in
List.fold_right (fun arg acc ->
coq_apps ccons [arg; acc]) xs cnil
(* DEPRECATED ; maybe future ?
let coq_list xs =
Coq_list xs
*)
(* DEPRECATED
let ccons = get_builtin_constructor "::" in
let cnil = get_builtin_constructor "[]" in
let cnil = "Coq.Lists.List.nil" in
let ccons = "Coq.Lists.List.cons" in
*)
(** Logic combinators *)
let coq_eq c1 c2 =
......
generator/formula.ml
View file @ c0f46a4f
......@@ -10,6 +10,7 @@ type cf =
| Cf_fail
| Cf_assert of cf
| Cf_done
| Cf_record_new of coq
| Cf_app of coqs * coq * coq * coqs
| Cf_body of var * vars * typed_vars * coq * cf
| Cf_let of typed_var * cf * cf
......
generator/formula.mli
View file @ c0f46a4f
......@@ -19,6 +19,8 @@ type cf =
(* Assert Q *)
| Cf_done
(* Done *)
| Cf_record_new of coq
(* AppNew [.. (fi, @dyn Ai xi) .. ] *)
| Cf_app of coqs * coq * coq * coqs
(* App f [.. (@dyn Ai xi) .. ] (B:=B) *)
| Cf_body of var * vars * typed_vars * coq * cf
......
generator/formula_to_coq.ml
View file @ c0f46a4f
......@@ -46,6 +46,10 @@ let rec coqtops_of_imp_cf cf =
| Cf_done ->
funhq "tag_done" coq_true
| Cf_record_new (arg) ->
(* AppNew [.. (fi, @dyn Ai xi) .. ] *)
coq_tag "tag_record_new" (coq_apps (Coq_var "CFML.CFApp.app_record_new") [arg])
| Cf_app (ts, tret, f, vs) -> (* TODO: maybe make the return type explicit? *)
(* old: let arity = List.length vs in *)
assert (List.length ts = List.length vs);
......
generator/print_coq.ml
View file @ c0f46a4f
......@@ -134,10 +134,11 @@ let rec expr0 = function
parens (string (string_of_int n)) ^^ string "%nat"
| Coq_int n ->
parens (string (string_of_int n)) ^^ string "%Z"
(* DEPRECATED ; maybe future ?
| Coq_list cs ->
(* TODO: *)
if (cs = []) then string "nil" else
if (cs = []) then string cnil else
parens ((separate_map (string "::" ^^ break 1) expr0 cs) ^^ string "::nil")
*)
| Coq_wild ->
string "_"
| Coq_prop ->
......
generator/renaming.ml
View file @ c0f46a4f
......@@ -318,10 +318,14 @@ let record_field_name name =
(** Convention for naming record accessor function *)
let record_field_get_name name =
let record_field_name name =
name ^ "'"
(* TODO: avoid names ending with a quote in caml code *)
let record_field_get_name name = (* DEPRECATED *)
name ^ "__get"
let record_field_set_name name =
let record_field_set_name name = (* DEPRECATED *)
name ^ "__set"
(** Convention for naming record accessor function specifications *)
......
lib/coq/CFApp.v
View file @ c0f46a4f
This diff is collapsed.
lib/coq/CFHeaps.v
View file @ c0f46a4f
......@@ -1069,7 +1069,7 @@ Tactic Notation "xunfold_clean" :=
(** [xunfold E] unfolds all occurences of the representation
predicate [E].
Limitation: won't work if E has more than 7 arguments.
Limitation: won't work if E has more than 12 arguments.
Implementation: converts all occurences of hdata to hdata',
then unfolds these occurences one by one, and considers
......@@ -1090,6 +1090,11 @@ Tactic Notation "xunfold" constr(E) :=
| |- context [ hdata' (E _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _ _ _ _ _ _) _ ] => constr:(true)
| _ => constr:(false)
end in
match ok with
......@@ -1099,6 +1104,7 @@ Tactic Notation "xunfold" constr(E) :=
clear h;
unfold E.
(** [xunfold E] unfolds a specific occurence of the representation
predicate [E]. TODO: still needs to unfold [E] by hand. *)
......@@ -1121,6 +1127,11 @@ Tactic Notation "xunfold" constr(E) "at" constr(n) :=
| |- context [ hdata' (E' _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E' _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E' _ _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _ _ _ _ _ _) _ ] => constr:(true)
| _ => constr:(false)
end in
match ok with
......@@ -1141,6 +1152,128 @@ Tactic Notation "xunfold" constr(E) "at" constr(n) :=
clear E'.
(********************************************************************)
(* ** DEPRECATED OLD XUNFOLD
Tactic Notation "ltac_set" "(" ident(X) ":=" constr(E) ")" "at" constr(K) :=
match nat_from_number K with
| 1%nat => set (X := E) at 1
| 2%nat => set (X := E) at 2
| 3%nat => set (X := E) at 3
| 4%nat => set (X := E) at 4
| 5%nat => set (X := E) at 5
| 6%nat => set (X := E) at 6
| 7%nat => set (X := E) at 7
| 8%nat => set (X := E) at 8
| 9%nat => set (X := E) at 9
| 10%nat => set (X := E) at 10
| 11%nat => set (X := E) at 11
| 12%nat => set (X := E) at 12
| 13%nat => set (X := E) at 13
| _ => fail "ltac_set: arity not supported"
end.
(** [xunfold at n] unfold the definition of the arrow [~>]
at the occurence [n] in the goal. *)
Definition hdata' (A:Type) (S:A->hprop) (x:A) : hprop := S x.
Tactic Notation "xunfold" "at" constr(n) :=
let h := fresh "temp" in
ltac_set (h := hdata) at n;
change h with hdata';
unfold hdata';
clear h.
(** [xunfold_clean] simplifies instances of
[p ~> (fun _ => _)] by unfolding the arrow,
but only when the body does not captures
locally-bound variables.
TODO: deprecated *)
Tactic Notation "xunfold_clean" :=
try match goal with |- context C [?p ~> ?E] =>
match E with (fun _ => _) =>
let E' := eval cbv beta in (E p) in
let G' := context C [E'] in
let G := match goal with |- ?G => G end in
change G with G' end end.
(** [xunfold E] unfolds all occurences of the representation
predicate [E].
Limitation: won't work if E has more than 7 arguments.
Implementation: converts all occurences of hdata to hdata',
then unfolds these occurences one by one, and considers
them for unfolding. *)
Tactic Notation "xunfold" constr(E) :=
change hdata with hdata';
let h := fresh "temp" in
set (h := hdata');
repeat (
unfold h at 1;
let ok := match goal with
| |- context [ hdata' (E) _ ] => constr:(true)
| |- context [ hdata' (E _) _ ] => constr:(true)
| |- context [ hdata' (E _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E _ _ _ _ _ _ _) _ ] => constr:(true)
| _ => constr:(false)
end in
match ok with
| true => unfold hdata'
| false => change hdata' with hdata
end);
clear h;
unfold E.
(** [xunfold E] unfolds a specific occurence of the representation
predicate [E]. TODO: still needs to unfold [E] by hand. *)
Tactic Notation "xunfold" constr(E) "at" constr(n) :=
let n := nat_from_number n in
change hdata with hdata';
let h := fresh "temp" in
set (h := hdata');
let E' := fresh "tempR" in
set (E' := E);
let rec aux n :=
try (
unfold h at 1;
let ok := match goal with
| |- context [ hdata' (E') _ ] => constr:(true)
| |- context [ hdata' (E' _) _ ] => constr:(true)
| |- context [ hdata' (E' _ _) _ ] => constr:(true)
| |- context [ hdata' (E' _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E' _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E' _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E' _ _ _ _ _ _) _ ] => constr:(true)
| |- context [ hdata' (E' _ _ _ _ _ _ _) _ ] => constr:(true)
| _ => constr:(false)
end in
match ok with
| true =>
match n with
| (S O)%nat =>
unfold hdata'
| (S ?n')%nat => change hdata' with hdata; aux n'
end
| false => change hdata' with hdata; aux n
end)
in
aux n;
unfold h;
clear h;
change hdata' with hdata;
unfold E';
clear E'.
*)
(********************************************************************)
(* ** Other tactics *)
......
lib/coq/CFPrint.v
View file @ c0f46a4f
......@@ -16,6 +16,7 @@ Require Export CFApp.
Inductive tag_type : Type :=
| tag_ret
| tag_apply
| tag_record_new
| tag_val
| tag_fun
| tag_let
......@@ -156,6 +157,8 @@ Notation "'!Ret' P" := (tag tag_ret (local P))
(at level 69) : tag_scope.
Notation "'!App' P" := (tag tag_apply P)
(at level 95) : tag_scope.
Notation "'!RecordNew' P" := (tag tag_record_new P)
(at level 95) : tag_scope.
Notation "'!Val' P" := (tag tag_val (local P))
(at level 95) : tag_scope.
Notation "'!Fun' P" := (tag tag_fun (local P))
......@@ -266,7 +269,7 @@ Open Scope charac.
(********************************************************************)
(** App and LetApp and SeqApp*)