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, CastConv 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 *)