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|
(************************************************************************)
(* 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 *)
(************************************************************************)
(* $Id$ *)
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
module type S = sig
(*s Coercions. *)
(* [inh_app_fun env isevars j] coerces [j] to a function; i.e. it
inserts a coercion into [j], if needed, in such a way it gets as
type a product; it returns [j] if no coercion is applicable *)
val inh_app_fun :
env -> evar_defs -> unsafe_judgment -> evar_defs * unsafe_judgment
(* [inh_coerce_to_sort env isevars j] coerces [j] to a type; i.e. it
inserts a coercion into [j], if needed, in such a way it gets as
type a sort; it fails if no coercion is applicable *)
val inh_coerce_to_sort : loc ->
env -> evar_defs -> unsafe_judgment -> evar_defs * unsafe_type_judgment
(* [inh_conv_coerce_to loc env isevars j t] coerces [j] to an object of type
[t]; i.e. it inserts a coercion into [j], if needed, in such a way [t] and
[j.uj_type] are convertible; it fails if no coercion is applicable *)
val inh_conv_coerce_to : loc ->
env -> evar_defs -> unsafe_judgment -> types -> evar_defs * unsafe_judgment
(* [inh_pattern_coerce_to loc env isevars pat ind1 ind2] coerces the Cases
pattern [pat] typed in [ind1] into a pattern typed in [ind2];
raises [Not_found] if no coercion found *)
val inh_pattern_coerce_to :
loc -> Rawterm.cases_pattern -> inductive -> inductive -> Rawterm.cases_pattern
end
module Default = struct
(* Typing operations dealing with coercions *)
exception NoCoercion
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 � faire hnf_constr *)
match kind_of_term (whd_betadeltaiota env Evd.empty typ) with
| Prod (_,c1,c2) ->
(* Typage garanti par l'appel � 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 *)
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 � 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 -> (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 hj =
let hj' =
try
let t1,i1 = class_of1 env (evars_of isevars) c1 in
let t2,i2 = class_of1 env (evars_of isevars) hj.uj_type in
let p = lookup_path_between (i2,i1) in
apply_coercion env p hj t2
with Not_found -> raise NoCoercion
in
try (the_conv_x_leq env hj'.uj_type c1 isevars, hj')
with Reduction.NotConvertible -> raise NoCoercion
let rec inh_conv_coerce_to_fail env isevars hj c1 =
let {uj_val = v; uj_type = t} = hj in
try (the_conv_x_leq env t c1 isevars, hj)
with Reduction.NotConvertible ->
(try
inh_coerce_to_fail env isevars c1 hj
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' = whd_betadeltaiota env (evars_of isevars) v in
let (evd',b) =
match kind_of_term v' with
| Lambda (_,v1,v2) ->
(try the_conv_x env v1 u1 isevars, true (* leq v1 u1? *)
with Reduction.NotConvertible -> (isevars, false))
| _ -> (isevars,false) in
if b
then
let (x,v1,v2) = destLambda v' in
let env1 = push_rel (x,None,v1) env in
let (evd'',h2) = inh_conv_coerce_to_fail env1 evd'
{uj_val = v2; uj_type = t2 } u2 in
(evd'',{ uj_val = mkLambda (x, v1, h2.uj_val);
uj_type = mkProd (x, v1, h2.uj_type) })
else
(* 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',h1) =
inh_conv_coerce_to_fail env1 isevars
{uj_val = mkRel 1; uj_type = (lift 1 u1) }
(lift 1 t1) in
let (evd'',h2) = inh_conv_coerce_to_fail env1 evd'
{ uj_val = mkApp (lift 1 v, [|h1.uj_val|]);
uj_type = subst1 h1.uj_val t2 }
u2
in
(evd'',
{ uj_val = mkLambda (name, u1, h2.uj_val);
uj_type = mkProd (name, u1, h2.uj_type) })
| _ -> 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 t =
let (evd',cj') =
try
inh_conv_coerce_to_fail env isevars cj t
with NoCoercion ->
let sigma = evars_of isevars in
error_actual_type_loc loc env sigma cj t
in
(evd',{ uj_val = cj'.uj_val; uj_type = t })
end
|
