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|
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'
|
