(* ||M|| This file is part of HELM, an Hypertextual, Electronic ||A|| Library of Mathematics, developed at the Computer Science ||T|| Department, University of Bologna, Italy. ||I|| ||T|| HELM is free software; you can redistribute it and/or ||A|| modify it under the terms of the GNU General Public License \ / version 2 or (at your option) any later version. \ / This software is distributed as is, NO WARRANTY. V_______________________________________________________________ *) (* $Id$ *) exception RefineFailure of (Stdpp.location * string) Lazy.t;; exception Uncertain of (Stdpp.location * string) Lazy.t;; exception AssertFailure of string Lazy.t;; module C = NCic module Ref = NReference type 'a expected_type = [ `XTNone (* unknown *) | `XTSome of 'a (* the given term *) | `XTSort (* any sort *) | `XTInd (* any (co)inductive type *) ] let debug = ref false;; let indent = ref "";; let times = ref [];; let pp s = if !debug then prerr_endline (Printf.sprintf "%-20s" !indent ^ " " ^ Lazy.force s) ;; let inside c = if !debug then begin let time1 = Unix.gettimeofday () in indent := !indent ^ String.make 1 c; times := time1 :: !times; prerr_endline ("{{{" ^ !indent ^ " ") end ;; let outside ok = if !debug then begin let time2 = Unix.gettimeofday () in let time1 = match !times with time1::tl -> times := tl; time1 | [] -> assert false in prerr_endline ("}}} " ^ string_of_float (time2 -. time1)); if not ok then prerr_endline "exception raised!"; try indent := String.sub !indent 0 (String.length !indent -1) with Invalid_argument _ -> indent := "??"; () end ;; let wrap_exc msg = function | NCicUnification.Uncertain _ -> Uncertain msg | NCicUnification.UnificationFailure _ -> RefineFailure msg | NCicTypeChecker.TypeCheckerFailure _ -> RefineFailure msg | e -> raise e ;; let exp_implicit status ~localise metasenv subst context with_type t = function | `Closed -> let metasenv,subst,expty = match with_type with `XTSort | `XTInd | `XTNone -> metasenv,subst,None | `XTSome typ -> let (metasenv,subst),typ = try NCicMetaSubst.delift status ~unify:(fun m s c t1 t2 -> try Some (NCicUnification.unify status m s c t1 t2) with NCicUnification.UnificationFailure _ | NCicUnification.Uncertain _ -> None) metasenv subst context (-1) (0,C.Irl 0) typ with NCicMetaSubst.MetaSubstFailure _ | NCicMetaSubst.Uncertain _ -> raise (RefineFailure (lazy (localise t,"Trying to create a closed meta with a non closed type: " ^ status#ppterm ~metasenv ~subst ~context typ))) in metasenv,subst,Some typ in NCicMetaSubst.mk_meta metasenv [] ?with_type:expty `IsTerm,subst | `Type -> let with_type = match with_type with `XTSome t -> Some t | _ -> None in NCicMetaSubst.mk_meta metasenv context ?with_type `IsType,subst | `Term -> let with_type = match with_type with `XTSome t -> Some t | _ -> None in NCicMetaSubst.mk_meta metasenv context ?with_type `IsTerm,subst | `Tagged s -> let with_type = match with_type with `XTSome t -> Some t | _ -> None in NCicMetaSubst.mk_meta ~attrs:[`Name s] metasenv context ?with_type `IsTerm,subst | `Vector -> raise (RefineFailure (lazy (localise t, "A vector of implicit terms " ^ "can only be used in argument position"))) | _ -> assert false ;; let check_allowed_sort_elimination status localise r orig = let mkapp he arg = match he with | C.Appl l -> C.Appl (l @ [arg]) | t -> C.Appl [t;arg] in (* ctx, ind_type @ lefts, sort_of_ind_ty@lefts, outsort *) let rec aux metasenv subst context ind arity1 arity2 = (*D*)inside 'S'; try let rc = let arity1 = NCicReduction.whd status ~subst context arity1 in pp (lazy(status#ppterm ~subst ~metasenv ~context arity1 ^ " elimsto " ^ status#ppterm ~subst ~metasenv ~context arity2 ^ "\nMENV:\n"^ status#ppmetasenv ~subst metasenv)); match arity1 with | C.Prod (name,so1,de1) (* , t ==?== C.Prod _ *) -> let metasenv, _, meta, _ = NCicMetaSubst.mk_meta metasenv ((name,C.Decl so1)::context) `IsType in let metasenv, subst = try NCicUnification.unify status metasenv subst context arity2 (C.Prod (name, so1, meta)) with exc -> raise (wrap_exc (lazy (localise orig, Printf.sprintf "expected %s, found %s" (* XXX localizzare meglio *) (status#ppterm ~subst ~metasenv ~context (C.Prod (name, so1, meta))) (status#ppterm ~subst ~metasenv ~context arity2))) exc) in aux metasenv subst ((name, C.Decl so1)::context) (mkapp (NCicSubstitution.lift status 1 ind) (C.Rel 1)) de1 meta | C.Sort _ (* , t ==?== C.Prod _ *) -> let metasenv, _, meta, _ = NCicMetaSubst.mk_meta metasenv [] `IsSort in let metasenv, subst = try NCicUnification.unify status metasenv subst context arity2 (C.Prod ("_", ind, meta)) with exc -> raise (wrap_exc (lazy (localise orig, Printf.sprintf "expected %s, found %s" (* XXX localizzare meglio *) (status#ppterm ~subst ~metasenv ~context (C.Prod ("_", ind, meta))) (status#ppterm ~subst ~metasenv ~context arity2))) exc) in (try NCicTypeChecker.check_allowed_sort_elimination status ~metasenv ~subst r context ind arity1 arity2; metasenv, subst with exc -> raise (wrap_exc (lazy (localise orig, "Sort elimination not allowed ")) exc)) | _ -> assert false (*D*)in outside true; rc with exc -> outside false; raise exc in aux ;; (* CSC: temporary thing, waiting for better times *) let mk_fresh_name context name = try let rex = Str.regexp "[0-9']*$" in let rex2 = Str.regexp "'*$" in let basename = Str.global_replace rex "" in let suffix name = ignore (Str.search_forward rex name 0); let n = Str.matched_string name in let n = Str.global_replace rex2 "" n in if n = "" then 0 else int_of_string n in let name' = basename name in let name' = if name' = "_" then "H" else name' in let last = List.fold_left (fun last (name,_) -> if basename name = name' then max last (suffix name) else last ) (-1) context in name' ^ (if last = -1 then "" else string_of_int (last + 1)) with exn -> prerr_endline ("XXX" ^ Printexc.to_string exn); assert false (* let eq, eq_refl = let uri = NUri.uri_of_string "cic:/matita/ng/Plogic/equality/eq.ind" in C.Const (Ref.reference_of_spec uri (Ref.Ind (true,0,2))), C.Const (Ref.reference_of_spec uri Ref.Con (0,1,2)) *) let eq, eq_refl = let uri = NUri.uri_of_string "cic:/matita/basics/jmeq/jmeq.ind" in C.Const (Ref.reference_of_spec uri (Ref.Ind(true,0,2))), C.Const (Ref.reference_of_spec uri (Ref.Con(0,1,2))) let rec typeof (status:#NCicCoercion.status) ?(localise=fun _ -> Stdpp.dummy_loc) metasenv subst context term expty = let force_ty skip_lambda skip_appl metasenv subst context orig t infty expty = (*D*)inside 'F'; try let rc = match expty with | `XTSome expty -> (match t with | C.Implicit _ -> assert false | C.Lambda _ when skip_lambda -> metasenv, subst, t, expty | C.Appl _ when skip_appl -> metasenv, subst, t, expty | _ -> pp (lazy ("forcing infty=expty: "^ (status#ppterm ~metasenv ~subst ~context infty) ^ " === " ^ (status#ppterm ~metasenv ~subst:[] ~context expty))); try let metasenv, subst = (*D*)inside 'U'; try let rc = NCicUnification.unify status metasenv subst context infty expty (*D*)in outside true; rc with exc -> outside false; raise exc in metasenv, subst, t, expty with | NCicUnification.Uncertain _ | NCicUnification.UnificationFailure _ as exc -> try_coercions status ~localise metasenv subst context t orig infty (`XTSome expty) exc) | `XTNone -> metasenv, subst, t, infty | `XTSort -> (match t with | C.Implicit _ -> assert false | _ -> pp (lazy ("forcing infty=any sort: "^ (status#ppterm ~metasenv ~subst ~context infty) ^ " === any sort")); force_to_sort status metasenv subst context t orig localise infty) | `XTInd -> (match t with | C.Implicit _ -> assert false | _ -> pp (lazy ("forcing infty=any (co)inductive type: "^ (status#ppterm ~metasenv ~subst ~context infty) ^ " === any (co)inductive type")); force_to_inductive status metasenv subst context t orig localise infty) (*D*)in outside true; rc with exc -> outside false; raise exc in let rec typeof_aux metasenv subst context expty = fun t as orig -> (*D*)inside 'R'; try let rc = pp (lazy (status#ppterm ~metasenv ~subst ~context t ^ " ::exp:: " ^ match expty with `XTSort -> "Any sort" | `XTInd -> "Any (co)inductive type" | `XTNone -> "None" | `XTSome e -> status#ppterm ~metasenv ~subst ~context e)); let metasenv, subst, t, infty = match t with | C.Rel n -> let infty = (try match List.nth context (n - 1) with | (_,C.Decl ty) -> NCicSubstitution.lift status n ty | (_,C.Def (_,ty)) -> NCicSubstitution.lift status n ty with Failure _ -> raise (RefineFailure (lazy (localise t,"unbound variable")))) in metasenv, subst, t, infty | C.Sort s -> (try metasenv, subst, t, C.Sort (NCicEnvironment.typeof_sort s) with | NCicEnvironment.UntypableSort msg -> raise (RefineFailure (lazy (localise t, Lazy.force msg))) | NCicEnvironment.AssertFailure msg -> raise (AssertFailure msg)) | C.Implicit infos -> let (metasenv,_,t,ty),subst = exp_implicit status ~localise metasenv subst context expty t infos in (match expty with | `XTSome _ -> metasenv, subst, t, ty | _ -> typeof_aux metasenv subst context expty t) | C.Meta (n,l) as t -> let metasenv, ty = try let _,_,_,ty = NCicUtils.lookup_subst n subst in metasenv, ty with NCicUtils.Subst_not_found _ -> NCicMetaSubst.extend_meta metasenv n in metasenv, subst, t, NCicSubstitution.subst_meta status l ty | C.Const _ -> metasenv, subst, t, NCicTypeChecker.typeof status ~subst ~metasenv context t | C.Prod (name,(s as orig_s),(t as orig_t)) -> let metasenv, subst, s, s1 = typeof_aux metasenv subst context `XTSort s in let metasenv, subst, s, s1 = force_to_sort status metasenv subst context s orig_s localise s1 in let context1 = (name,(C.Decl s))::context in let metasenv, subst, t, s2 = typeof_aux metasenv subst context1 `XTSort t in let metasenv, subst, t, s2 = force_to_sort status metasenv subst context1 t orig_t localise s2 in let metasenv, subst, s, t, ty = sort_of_prod status localise metasenv subst context orig_s orig_t (name,s) t (s1,s2) in metasenv, subst, C.Prod(name,s,t), ty | C.Lambda (n,(s as orig_s),t) as orig -> let exp_s, exp_ty_t, force_after = match expty with | `XTSort | `XTInd | `XTNone -> `XTNone, `XTNone, false | `XTSome expty -> match NCicReduction.whd status ~subst context expty with | C.Prod (_,s,t) -> `XTSome s, `XTSome t, false | _ -> `XTNone, `XTNone, true in let (metasenv,subst), s = match exp_s with | `XTSome exp_s -> (* optimized case: implicit and implicitly typed meta * the optimization prevents proliferation of metas *) (match s with | C.Implicit _ -> (metasenv,subst),exp_s | _ -> let metasenv, subst, s = match s with | C.Meta (n,_) when (try (match NCicUtils.lookup_meta n metasenv with | _,_,C.Implicit (`Typeof _) -> true | _ -> false) with | _ -> false) -> metasenv, subst, s | _ -> check_type status ~localise metasenv subst context s in (try pp(lazy("Force source to: "^status#ppterm ~metasenv ~subst ~context exp_s)); NCicUnification.unify ~test_eq_only:true status metasenv subst context s exp_s, s with exc -> raise (wrap_exc (lazy (localise orig_s, Printf.sprintf "Source type %s was expected to be %s" (status#ppterm ~metasenv ~subst ~context s) (status#ppterm ~metasenv ~subst ~context exp_s))) exc))) | `XTNone | `XTSort | `XTInd -> let metasenv, subst, s = check_type status ~localise metasenv subst context s in (metasenv, subst), s in let context_for_t = (n,C.Decl s) :: context in let metasenv, subst, t, ty_t = typeof_aux metasenv subst context_for_t exp_ty_t t in if force_after then force_ty false true metasenv subst context orig (C.Lambda(n,s,t)) (C.Prod (n,s,ty_t)) expty else metasenv, subst, C.Lambda(n,s,t), C.Prod (n,s,ty_t) | C.LetIn (n,ty,t,bo) -> let metasenv, subst, ty = check_type status ~localise metasenv subst context ty in let metasenv, subst, t, _ = typeof_aux metasenv subst context (`XTSome ty) t in let context1 = (n, C.Def (t,ty)) :: context in let metasenv, subst, expty1 = match expty with | `XTSome x -> let m, s, x = NCicUnification.delift_type_wrt_terms status metasenv subst context1 (NCicSubstitution.lift status 1 x) [NCicSubstitution.lift status 1 t] in m, s, `XTSome x | _ -> metasenv, subst, expty in let metasenv, subst, bo, bo_ty = typeof_aux metasenv subst context1 expty1 bo in let bo_ty = NCicSubstitution.subst status ~avoid_beta_redexes:true t bo_ty in metasenv, subst, C.LetIn (n, ty, t, bo), bo_ty | C.Appl ((he as orig_he)::(_::_ as args)) -> let upto = match orig_he with C.Meta _ -> List.length args | _ -> 0 in let hbr t = if upto > 0 then NCicReduction.head_beta_reduce status ~upto t else t in let refine_appl metasenv subst args = let metasenv, subst, he, ty_he = typeof_aux metasenv subst context `XTNone he in let metasenv, subst, t, ty = eat_prods status ~localise force_ty metasenv subst context expty t orig_he he ty_he args in metasenv, subst, hbr t, ty in if args = [C.Implicit `Vector] && expty <> `XTNone then (* we try here to expand the vector a 0 implicits, but we use * the expected type *) try let metasenv, subst, he, ty_he = typeof_aux metasenv subst context expty he in metasenv, subst, hbr he, ty_he with Uncertain _ | RefineFailure _ -> refine_appl metasenv subst args else (* CSC: whd can be useful on he too... *) (match he with C.Const (Ref.Ref (uri1,Ref.Con _)) -> ( match expty with | `XTSome expty -> ( match NCicReduction.whd status ~subst context expty with C.Appl (C.Const (Ref.Ref (uri2,Ref.Ind _) as ref)::expargs) when NUri.eq uri1 uri2 -> (try let _,leftno,_,_,_ = NCicEnvironment.get_checked_indtys status ref in let leftexpargs,_ = HExtlib.split_nth leftno expargs in let rec instantiate metasenv subst revargs args = function [] -> (* some checks are re-done here, but it would be complex to avoid them (e.g. we did not check yet that the constructor is a constructor for that inductive type)*) refine_appl metasenv subst ((List.rev revargs)@args) | (exparg::expargs) as allexpargs -> match args with [] -> raise (Failure "Not enough args") | (C.Implicit `Vector::args) as allargs -> (try instantiate metasenv subst revargs args allexpargs with Sys.Break as exn -> raise exn | _ -> instantiate metasenv subst revargs (C.Implicit `Term :: allargs) allexpargs) | arg::args -> let metasenv,subst,arg,_ = typeof_aux metasenv subst context `XTNone arg in let metasenv,subst = NCicUnification.unify status metasenv subst context arg exparg in instantiate metasenv subst(arg::revargs) args expargs in instantiate metasenv subst [] args leftexpargs with | Sys.Break as exn -> raise exn | _ -> refine_appl metasenv subst args (* to try coercions *)) | _ -> refine_appl metasenv subst args) | `XTNone | `XTSort | `XTInd -> refine_appl metasenv subst args) | _ -> refine_appl metasenv subst args) | C.Appl _ -> raise (AssertFailure (lazy "Appl of length < 2")) | C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as r, outtype,(term as orig_term),pl) as orig -> let _, leftno, itl, _, _ = NCicEnvironment.get_checked_indtys status r in let _, _, arity, cl = List.nth itl tyno in let constructorsno = List.length cl in let _, metasenv, args = NCicMetaSubst.saturate status metasenv subst context arity 0 in let ind = if args = [] then C.Const r else C.Appl (C.Const r::args) in let metasenv, subst, term, _ = typeof_aux metasenv subst context (`XTSome ind) term in let parameters, arguments = HExtlib.split_nth leftno args in let outtype = match outtype with | C.Implicit _ as ot -> let rec aux = function | [] -> C.Lambda ("_",C.Implicit `Type,ot) | _::tl -> C.Lambda ("_",C.Implicit `Type,aux tl) in aux arguments | _ -> outtype in let metasenv, subst, outtype, outsort = typeof_aux metasenv subst context `XTNone outtype in (* this cannot be `XTSort *) (* next lines are to do a subst-expansion of the outtype, so that when it becomes a beta-abstraction, the beta-redex is fired during substitution *) let _,fresh_metanoouttype,newouttype,_ = NCicMetaSubst.mk_meta metasenv context `IsTerm in let subst = (fresh_metanoouttype,([`Name "outtype"],context,outtype,outsort)) ::subst in let outtype = newouttype in (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *) let ind = if parameters = [] then C.Const r else C.Appl ((C.Const r)::parameters) in let metasenv, subst, ind, ind_ty = typeof_aux metasenv subst context `XTNone ind in (* FG: this cannot be `XTSort *) let metasenv, subst = check_allowed_sort_elimination status localise r orig_term metasenv subst context ind ind_ty outsort in (* let's check if the type of branches are right *) if List.length pl <> constructorsno then raise (RefineFailure (lazy (localise orig, "Wrong number of cases in a match"))); (* let metasenv, subst = match expty with | None -> metasenv, subst | Some expty -> NCicUnification.unify status metasenv subst context resty expty in *) let _, metasenv, subst, pl = List.fold_right (fun p (j, metasenv, subst, branches) -> let cons = let cons = Ref.mk_constructor j r in if parameters = [] then C.Const cons else C.Appl (C.Const cons::parameters) in let metasenv, subst, cons, ty_cons = typeof_aux metasenv subst context `XTNone cons in (* FG: this cannot be `XTInd *) let ty_branch = NCicTypeChecker.type_of_branch status ~subst context leftno outtype cons ty_cons in pp (lazy ("TYPEOFBRANCH: " ^ status#ppterm ~metasenv ~subst ~context p ^ " ::inf:: " ^ status#ppterm ~metasenv ~subst ~context ty_branch )); let metasenv, subst, p, _ = typeof_aux metasenv subst context (`XTSome ty_branch) p in j-1, metasenv, subst, p :: branches) pl (List.length pl, metasenv, subst, []) in let resty = C.Appl (outtype::arguments@[term]) in let resty = NCicReduction.head_beta_reduce status ~subst resty in metasenv, subst, C.Match (r, outtype, term, pl),resty | C.Match _ -> assert false in pp (lazy (status#ppterm ~metasenv ~subst ~context t ^ " ::inf:: "^ status#ppterm ~metasenv ~subst ~context infty )); force_ty true true metasenv subst context orig t infty expty (*D*)in outside true; rc with exc -> outside false; raise exc in typeof_aux metasenv subst context expty term and check_type status ~localise metasenv subst context (ty as orig_ty) = let metasenv, subst, ty, sort = typeof status ~localise metasenv subst context ty `XTSort in let metasenv, subst, ty, _ = force_to_sort status metasenv subst context ty orig_ty localise sort in metasenv, subst, ty and try_coercions status ~localise metasenv subst context t orig_t infty expty exc = let cs_subst = NCicSubstitution.subst status ~avoid_beta_redexes:true in try (match expty with `XTSome expty -> pp (lazy "WWW: trying coercions -- preliminary unification"); let metasenv, subst = NCicUnification.unify status metasenv subst context infty expty in metasenv, subst, t, expty | _ -> raise (Failure "Special case XTProd, XTSort or XTInd")) with | exn -> (* we try with a coercion *) let rec first exc = function | [] -> pp (lazy "WWW: no more coercions!"); raise (wrap_exc (lazy let expty = match expty with `XTSome expty -> status#ppterm ~metasenv ~subst ~context expty | `XTSort -> "[[sort]]" | `XTProd -> "[[prod]]" | `XTInd -> "[[ind]]" in (localise orig_t, Printf.sprintf "The term\n%s\nhas type\n%s\nbut is here used with type\n%s" (status#ppterm ~metasenv ~subst ~context t) (status#ppterm ~metasenv ~subst ~context infty) expty)) exc) | (_,metasenv, newterm, newtype, meta)::tl -> try pp (lazy("K=" ^ status#ppterm ~metasenv ~subst ~context newterm)); pp (lazy ( "UNIFICATION in CTX:\n"^ status#ppcontext ~metasenv ~subst context ^ "\nMENV: " ^ status#ppmetasenv metasenv ~subst ^ "\nOF: " ^ status#ppterm ~metasenv ~subst ~context t ^ " === " ^ status#ppterm ~metasenv ~subst ~context meta ^ "\n")); let metasenv, subst = NCicUnification.unify status metasenv subst context t meta in match expty with `XTSome expty -> pp (lazy ( "UNIFICATION in CTX:\n"^ status#ppcontext ~metasenv ~subst context ^ "\nMENV: " ^ status#ppmetasenv metasenv ~subst ^ "\nOF: " ^ status#ppterm ~metasenv ~subst ~context newtype ^ " === " ^ status#ppterm ~metasenv ~subst ~context expty ^ "\n")); let metasenv,subst = NCicUnification.unify status metasenv subst context newtype expty in metasenv, subst, newterm, newtype | `XTSort -> (match NCicReduction.whd status ~subst context newtype with C.Sort _ -> metasenv,subst,newterm,newtype | _ -> first exc tl) | `XTInd -> (match NCicReduction.whd status ~subst context newtype with C.Const (Ref.Ref (_, Ref.Ind _)) -> metasenv,subst,newterm,newtype | _ -> first exc tl) | `XTProd -> (match NCicReduction.whd status ~subst context newtype with C.Prod _ -> metasenv,subst,newterm,newtype | _ -> first exc tl) with | NCicUnification.UnificationFailure _ -> first exc tl | NCicUnification.Uncertain _ as exc -> first exc tl in try pp (lazy "WWW: trying coercions -- inner check"); match infty, expty, t with (* `XTSort|`XTProd|`XTInd + Match not implemented *) | _,`XTSome expty, C.Match (Ref.Ref (_,Ref.Ind (_,_tyno,_leftno)) as r,outty,m,pl) -> (*{{{*) pp (lazy "CASE"); (* {{{ helper functions *) let get_cl_and_left_p refit outty = match refit with | Ref.Ref (_uri, Ref.Ind (_,tyno,_leftno)) -> let _, leftno, itl, _, _ = NCicEnvironment.get_checked_indtys status r in let _, _, ty, cl = List.nth itl tyno in (*let constructorsno = List.length cl in*) let count_pis t = let rec aux ctx t = match NCicReduction.whd status ~subst ~delta:max_int ctx t with | C.Prod (name,src,tgt) -> let ctx = (name, (C.Decl src)) :: ctx in 1 + aux ctx tgt | _ -> 0 in aux [] t in let rec skip_lambda_delifting t n = match t,n with | _,0 -> t | C.Lambda (_,_,t),n -> pp (lazy ("WWW: failing term? "^ status#ppterm ~subst:[] ~metasenv:[] ~context:[] t)); skip_lambda_delifting (* substitute dangling indices with a dummy *) (NCicSubstitution.subst status (C.Sort C.Prop) t) (n - 1) | _ -> assert false in let get_l_r_p n = function | C.Lambda (_,C.Const (Ref.Ref (_,Ref.Ind (_,_,_))),_) -> [],[] | C.Lambda (_,C.Appl (C.Const (Ref.Ref (_,Ref.Ind (_,_,_))) :: args),_) -> HExtlib.split_nth n args | _ -> assert false in let pis = count_pis ty in let rno = pis - leftno in let t = skip_lambda_delifting outty rno in let left_p, _ = get_l_r_p leftno t in let instantiate_with_left cl = List.map (fun ty -> List.fold_left (fun t p -> match t with | C.Prod (_,_,t) -> cs_subst p t | _-> assert false) ty left_p) cl in let cl = instantiate_with_left (List.map (fun (_,_,x) -> x) cl) in cl, left_p, leftno, rno | _ -> raise exn in (*{{{*) pp (lazy "CASE"); let rec keep_lambdas_and_put_expty ctx t bo right_p matched n = match t,n with | _,0 -> let rec mkr n = function | [] -> [] | _::tl -> C.Rel n :: mkr (n+1) tl in pp (lazy ("input replace: " ^ status#ppterm ~context:ctx ~metasenv:[] ~subst:[] bo)); let bo = NCicRefineUtil.replace_lifting status ~equality:(fun _ -> NCicRefineUtil.alpha_equivalence status) ~context:ctx ~what:(matched::right_p) ~with_what:(C.Rel 1::List.rev (mkr 2 right_p)) ~where:bo in pp (lazy ("output replace: " ^ status#ppterm ~context:ctx ~metasenv:[] ~subst:[] bo)); bo | C.Lambda (name, src, tgt),_ -> C.Lambda (name, src, keep_lambdas_and_put_expty ((name, C.Decl src)::ctx) tgt (NCicSubstitution.lift status 1 bo) (List.map (NCicSubstitution.lift status 1) right_p) (NCicSubstitution.lift status 1 matched) (n-1)) | _ -> assert false in let add_params metasenv subst context cty outty mty m i = let rec aux context outty par j mty m = function | C.Prod (name, src, tgt) -> let t,k = aux ((name, C.Decl src) :: context) (NCicSubstitution.lift status 1 outty) (C.Rel j::par) (j+1) (NCicSubstitution.lift status 1 mty) (NCicSubstitution.lift status 1 m) tgt in C.Prod (name, src, t), k | C.Const (Ref.Ref (_,Ref.Ind (_,_,_leftno)) as r) -> let k = let k = C.Const(Ref.mk_constructor i r) in NCicUntrusted.mk_appl k par in (* the type has no parameters, so kty = mty let kty = try NCicTypechecker.typeof ~subst ~metasenv context k with NCicTypeChecker.TypeCheckerFailure _ -> assert false in *) C.Prod ("p", C.Appl [eq; mty; m; mty; k], (NCicSubstitution.lift status 1 (NCicReduction.head_beta_reduce status ~delta:max_int (NCicUntrusted.mk_appl outty [k])))),[mty,m,mty,k] | C.Appl (C.Const (Ref.Ref (_,Ref.Ind (_,_,leftno)) as r)::pl) -> let left_p,_right_p = HExtlib.split_nth leftno pl in (*let has_rights = right_p <> [] in*) let k = let k = C.Const(Ref.mk_constructor i r) in NCicUntrusted.mk_appl k (left_p@par) in let right_p = try match NCicTypeChecker.typeof status ~subst ~metasenv context k with | C.Appl (C.Const (Ref.Ref (_,Ref.Ind (_,_,_)))::args) -> snd (HExtlib.split_nth leftno args) | _ -> assert false with NCicTypeChecker.TypeCheckerFailure _-> assert false in let orig_right_p = match mty with | C.Appl (C.Const (Ref.Ref (_,Ref.Ind (_,_,_)))::args) -> snd (HExtlib.split_nth leftno args) | _ -> assert false in List.fold_right2 (fun x y (tacc,pacc) -> let xty = try NCicTypeChecker.typeof status ~subst ~metasenv context x with NCicTypeChecker.TypeCheckerFailure _ -> assert false in let yty = try NCicTypeChecker.typeof status ~subst ~metasenv context y with NCicTypeChecker.TypeCheckerFailure _ -> assert false in C.Prod ("_", C.Appl [eq;xty;x;yty;y], NCicSubstitution.lift status 1 tacc), (xty,x,yty,y)::pacc) (orig_right_p @ [m]) (right_p @ [k]) (NCicReduction.head_beta_reduce status ~delta:max_int (NCicUntrusted.mk_appl outty (right_p@[k])), []) (* if has_rights then NCicReduction.head_beta_reduce status ~delta:max_int (C.Appl (outty ::right_p @ [k])),k else C.Prod ("p", C.Appl [eq; mty; m; k], (NCicSubstitution.lift status 1 (NCicReduction.head_beta_reduce status ~delta:max_int (C.Appl (outty ::right_p @ [k]))))),k*) | _ -> assert false in aux context outty [] 1 mty m cty in let add_lambda_for_refl_m pbo eqs cty = (* k lives in the right context *) (* if rno <> 0 then pbo else *) let rec aux = function | C.Lambda (name,src,bo), C.Prod (_,_,ty) -> C.Lambda (name,src, (aux (bo,ty))) | t,_ -> snd (List.fold_right (fun (xty,x,yty,y) (n,acc) -> n+1, C.Lambda ("p" ^ string_of_int n, C.Appl [eq; xty; x; yty; y], NCicSubstitution.lift status 1 acc)) eqs (1,t)) (*C.Lambda ("p", C.Appl [eq; mty; m; k],NCicSubstitution.lift status 1 t)*) in aux (pbo,cty) in let add_pi_for_refl_m context new_outty mty m lno rno = (*if rno <> 0 then new_outty else*) let rec aux context mty m = function | C.Lambda (name, src, tgt) -> let context = (name, C.Decl src)::context in C.Lambda (name, src, aux context (NCicSubstitution.lift status 1 mty) (NCicSubstitution.lift status 1 m) tgt) | t -> let lhs = match mty with | C.Appl (_::params) -> (snd (HExtlib.split_nth lno params))@[m] | _ -> [m] in let rhs = List.map (fun x -> C.Rel x) (List.rev (HExtlib.list_seq 1 (rno+2))) in List.fold_right2 (fun x y acc -> let xty = try NCicTypeChecker.typeof status ~subst ~metasenv context x with NCicTypeChecker.TypeCheckerFailure _ -> assert false in let yty = try NCicTypeChecker.typeof status ~subst ~metasenv context y with NCicTypeChecker.TypeCheckerFailure _ -> assert false in C.Prod ("_", C.Appl [eq;xty;x;yty;y], (NCicSubstitution.lift status 1 acc))) lhs rhs t (* C.Prod ("_", C.Appl [eq;mty;m;C.Rel 1], NCicSubstitution.lift status 1 t)*) in aux context mty m new_outty in (* }}} end helper functions *) (* constructors types with left params already instantiated *) let outty = NCicUntrusted.apply_subst status subst context outty in let cl, _left_p, leftno,rno = get_cl_and_left_p r outty in let right_p, mty = try match NCicTypeChecker.typeof status ~subst ~metasenv context m with | (C.Const (Ref.Ref (_,Ref.Ind (_,_,_))) | C.Meta _) as mty -> [], mty | C.Appl ((C.Const (Ref.Ref (_,Ref.Ind (_,_,_)))|C.Meta _)::args) as mty -> snd (HExtlib.split_nth leftno args), mty | _ -> assert false with NCicTypeChecker.TypeCheckerFailure _ -> raise (AssertFailure(lazy "already ill-typed matched term")) in let mty = NCicUntrusted.apply_subst status subst context mty in let outty = NCicUntrusted.apply_subst status subst context outty in let expty = NCicUntrusted.apply_subst status subst context expty in let new_outty = keep_lambdas_and_put_expty context outty expty right_p m (rno+1) in pp (lazy ("CASE: new_outty: " ^ status#ppterm ~context ~metasenv ~subst new_outty)); let _,pl,subst,metasenv = List.fold_right2 (fun cty pbo (i, acc, s, menv) -> pp (lazy ("begin iteration")); (* Pi k_par, (Pi H:m=(K_i left_par k_par)), * (new_)outty right_par (K_i left_par k_par) *) let infty_pbo, _ = add_params menv s context cty outty mty m i in pp (lazy ("CASE: infty_pbo: "^ status#ppterm ~context ~metasenv ~subst infty_pbo)); let expty_pbo, eqs = (* k is (K_i left_par k_par) *) add_params menv s context cty new_outty mty m i in pp (lazy ("CASE: expty_pbo: "^ status#ppterm ~context ~metasenv ~subst expty_pbo)); let pbo = add_lambda_for_refl_m pbo eqs cty in pp (lazy ("CASE: pbo: " ^ status#ppterm ~context ~metasenv ~subst pbo)); let metasenv, subst, pbo, _ = try_coercions status ~localise menv s context pbo orig_t (*??*) infty_pbo (`XTSome expty_pbo) exc in pp (lazy ("CASE: pbo2: " ^ status#ppterm ~context ~metasenv ~subst pbo)); (i-1, pbo::acc, subst, metasenv)) cl pl (List.length pl, [], subst, metasenv) in (*let metasenv, subst = try NCicUnification.unify status metasenv subst context outty new_outty with _ -> raise (RefineFailure (lazy (localise orig_t, "try_coercions"))) in*) let new_outty = add_pi_for_refl_m context new_outty mty m leftno rno in pp (lazy ("CASE: new_outty: " ^ (status#ppterm ~metasenv ~subst ~context new_outty))); let right_tys = List.map (fun t -> NCicTypeChecker.typeof status ~subst ~metasenv context t) right_p in let eqs = List.map2 (fun x y -> C.Appl[eq_refl;x;y]) (right_tys@[mty]) (right_p@[m]) in let t = C.Appl (C.Match(r,new_outty,m,pl) :: eqs) in metasenv, subst, t, expty (*}}}*) | _,`XTSome expty,C.LetIn(name,ty,t,bo) -> pp (lazy "LETIN"); let name' = mk_fresh_name context name in let context_bo = (name', C.Def (t,ty)) :: context in let metasenv, subst, bo2, _ = try_coercions status ~localise metasenv subst context_bo bo orig_t (NCicSubstitution.lift status 1 infty) (`XTSome (NCicSubstitution.lift status 1 expty)) exc in let coerced = C.LetIn (name',ty,t,bo2) in pp (lazy ("LETIN: coerced = " ^ status#ppterm ~metasenv ~subst ~context coerced)); metasenv, subst, coerced, expty | C.Prod (nameprod, src, ty),`XTSome (C.Prod (_, src2, ty2) as expty), _ -> (*{{{*) pp (lazy "LAM"); pp (lazy ("LAM: t = " ^ status#ppterm ~metasenv ~subst ~context t)); let namename = match t with C.Lambda (n,_,_) -> n | _ -> nameprod in let name_con = mk_fresh_name context namename in let context_src2 = ((name_con, C.Decl src2) :: context) in (* contravariant part: the argument of f:src->ty *) let metasenv, subst, rel1, _ = try_coercions status ~localise metasenv subst context_src2 (C.Rel 1) orig_t (NCicSubstitution.lift status 1 src2) (`XTSome (NCicSubstitution.lift status 1 src)) exc in (* covariant part: the result of f(c x); x:src2; (c x):src *) let name_t, bo = match t with | C.Lambda (n,_,bo) -> n, cs_subst rel1 (NCicSubstitution.lift_from status 2 1 bo) | _ -> name_con, NCicUntrusted.mk_appl (NCicSubstitution.lift status 1 t) [rel1] in (* we fix the possible dependency problem in the source ty *) let ty = cs_subst rel1 (NCicSubstitution.lift_from status 2 1 ty) in let metasenv, subst, bo, _ = try_coercions status ~localise metasenv subst context_src2 bo orig_t ty (`XTSome ty2) exc in let coerced = C.Lambda (name_t,src2, bo) in pp (lazy ("LAM: coerced = " ^ status#ppterm ~metasenv ~subst ~context coerced)); metasenv, subst, coerced, expty (*}}}*) | _ -> raise exc with _ -> let expty = match expty with `XTSome expty -> expty | `XTSort -> C.Sort (C.Type (match NCicEnvironment.get_universes () with | x::_ -> x | _ -> assert false)) | `XTProd -> C.Prod ("_",C.Implicit `Type,C.Implicit `Type) | `XTInd -> assert false(*CSC: was not handled, OCaml 4.0 complains. ??? *) in pp(lazy("try_coercion " ^ status#ppterm ~metasenv ~subst ~context infty ^ " |---> " ^ status#ppterm ~metasenv ~subst ~context expty)); first exc (NCicCoercion.look_for_coercion status metasenv subst context infty expty) and force_to_sort status metasenv subst context t orig_t localise ty = try let metasenv, subst, ty = NCicUnification.sortfy status (Failure "sortfy") metasenv subst context ty in metasenv, subst, t, ty with Failure _ -> let msg = (lazy (localise orig_t, "The type of " ^ status#ppterm ~metasenv ~subst ~context t ^ " is not a sort: " ^ status#ppterm ~metasenv ~subst ~context ty)) in let ty = NCicReduction.whd status ~subst context ty in let exn = if NCicUnification.could_reduce status ~subst context ty then Uncertain msg else RefineFailure msg in try_coercions status ~localise metasenv subst context t orig_t ty `XTSort exn and force_to_inductive status metasenv subst context t orig_t localise ty = try let metasenv, subst, ty = NCicUnification.indfy status (Failure "indfy") metasenv subst context ty in metasenv, subst, t, ty with Failure _ -> let msg = (lazy (localise orig_t, "The type of " ^ status#ppterm ~metasenv ~subst ~context t ^ " is not a (co)inductive type: " ^ status#ppterm ~metasenv ~subst ~context ty)) in let ty = NCicReduction.whd status ~subst context ty in (* prerr_endline ("#### " ^ status#ppterm ~metasenv ~subst ~context ty); *) let exn = if NCicUnification.could_reduce status ~subst context ty then Uncertain msg else RefineFailure msg in raise exn (* FG: this should be as follows but the case `XTInd is not imp;emented yet try_coercions status ~localise metasenv subst context t orig_t ty `XTInd exn *) and sort_of_prod status localise metasenv subst context orig_s orig_t (name,s) t (t1, t2) = (* force to sort is done in the Prod case in typeof *) match t1, t2 with | C.Sort _, C.Sort C.Prop -> metasenv, subst, s, t, t2 | C.Sort (C.Type u1), C.Sort (C.Type u2) -> metasenv, subst, s, t, C.Sort (C.Type (NCicEnvironment.max u1 u2)) | C.Sort C.Prop,C.Sort (C.Type _) -> metasenv, subst, s, t, t2 | C.Meta _, C.Sort _ | C.Meta _, C.Meta (_,(_,_)) | C.Sort _, C.Meta (_,(_,_)) -> metasenv, subst, s, t, t2 | x, (C.Sort _ | C.Meta _) | _, x -> let y, context, orig = if x == t1 then s, context, orig_s else t, ((name,C.Decl s)::context), orig_t in raise (RefineFailure (lazy (localise orig,Printf.sprintf "%s is expected to be a type, but its type is %s that is not a sort" (status#ppterm ~subst ~metasenv ~context y) (status#ppterm ~subst ~metasenv ~context x)))) and guess_name status subst ctx ty = let aux initial = "#" ^ String.make 1 initial in match ty with | C.Const (Ref.Ref (u,_)) | C.Appl (C.Const (Ref.Ref (u,_)) :: _) -> aux (String.sub (NUri.name_of_uri u) 0 1).[0] | C.Prod _ -> aux 'f' | C.Meta (n,lc) -> (try let _,_,t,_ = NCicUtils.lookup_subst n subst in guess_name status subst ctx (NCicSubstitution.subst_meta status lc t) with NCicUtils.Subst_not_found _ -> aux 'M') | _ -> aux 'H' and eat_prods status ~localise force_ty metasenv subst context expty orig_t orig_he he ty_he args = (*D*)inside 'E'; try let rc = let rec aux metasenv subst args_so_far he ty_he xxx = (*D*)inside 'V'; try let rc = match xxx with | [] -> let res = NCicUntrusted.mk_appl he (List.rev args_so_far) in pp(lazy("FORCE FINAL APPL: " ^ status#ppterm ~metasenv ~subst ~context res ^ " of type " ^ status#ppterm ~metasenv ~subst ~context ty_he ^ " to type " ^ match expty with `XTSort -> "Any sort" | `XTInd -> "Any (co)inductive type" | `XTNone -> "None" | `XTSome x -> status#ppterm ~metasenv ~subst ~context x)); (* whatever the term is, we force the type. in case of ((Lambda..) ?...) * the application may also be a lambda! *) force_ty false false metasenv subst context orig_t res ty_he expty | C.Implicit `Vector::tl -> let has_some_more_pis x = match NCicReduction.whd status ~subst context x with | C.Meta _ | C.Appl (C.Meta _::_) -> false | _ -> true in (try aux metasenv subst args_so_far he ty_he tl with | Uncertain _ | RefineFailure _ as exc when has_some_more_pis ty_he -> (try aux metasenv subst args_so_far he ty_he (C.Implicit `Term :: C.Implicit `Vector :: tl) with Uncertain msg | RefineFailure msg -> raise (wrap_exc msg exc)) | RefineFailure msg when not (has_some_more_pis ty_he) -> (* instantiating the head could change the has_some_more_pis flag *) raise (Uncertain msg)) | arg::tl -> match NCicReduction.whd status ~subst context ty_he with | C.Prod (_,s,t) -> let metasenv, subst, arg, _ = typeof status ~localise metasenv subst context arg (`XTSome s) in let t = NCicSubstitution.subst status ~avoid_beta_redexes:true arg t in aux metasenv subst (arg :: args_so_far) he t tl | C.Meta _ | C.Appl (C.Meta _ :: _) as t -> let metasenv, subst, arg, ty_arg = typeof status ~localise metasenv subst context arg `XTNone in let name = guess_name status subst context ty_arg in let metasenv, _, meta, _ = NCicMetaSubst.mk_meta metasenv ((name,C.Decl ty_arg) :: context) `IsType in let flex_prod = C.Prod (name, ty_arg, meta) in (* next line grants that ty_args is a type *) let metasenv,subst, flex_prod, _ = typeof status ~localise metasenv subst context flex_prod `XTSort in (* pp (lazy ( "UNIFICATION in CTX:\n"^ status#ppcontext ~metasenv ~subst context ^ "\nOF: " ^ status#ppterm ~metasenv ~subst ~context t ^ " === " ^ status#ppterm ~metasenv ~subst ~context flex_prod ^ "\n")); *) let metasenv, subst = try NCicUnification.unify status metasenv subst context t flex_prod with exc -> raise (wrap_exc (lazy (localise orig_he, Printf.sprintf ("The term %s has an inferred type %s, but is applied to the" ^^ " argument %s of type %s") (status#ppterm ~metasenv ~subst ~context he) (status#ppterm ~metasenv ~subst ~context t) (status#ppterm ~metasenv ~subst ~context arg) (status#ppterm ~metasenv ~subst ~context ty_arg))) (match exc with | NCicUnification.UnificationFailure m -> NCicUnification.Uncertain m | x -> x)) (* XXX coerce to funclass *) in let meta = NCicSubstitution.subst status ~avoid_beta_redexes:true arg meta in aux metasenv subst (arg :: args_so_far) he meta tl | C.Match (_,_,C.Meta _,_) | C.Match (_,_,C.Appl (C.Meta _ :: _),_) | C.Appl (C.Const (Ref.Ref (_, Ref.Fix _)) :: _) -> raise (Uncertain (lazy (localise orig_he, Printf.sprintf ("The term %s is here applied to %d arguments but expects " ^^ "only %d arguments") (status#ppterm ~metasenv ~subst ~context he) (List.length args) (List.length args_so_far)))) | ty -> let metasenv, subst, newhead, newheadty = try_coercions status ~localise metasenv subst context (NCicUntrusted.mk_appl he (List.rev args_so_far)) orig_he ty `XTProd (RefineFailure (lazy (localise orig_he, Printf.sprintf ("The term %s is here applied to %d arguments but expects " ^^ "only %d arguments") (status#ppterm ~metasenv ~subst ~context he) (List.length args) (List.length args_so_far)))) in aux metasenv subst [] newhead newheadty (arg :: tl) (*D*)in outside true; rc with exc -> outside false; raise exc in (* We need to reverse the order of the new created metas since they are pushed on top of the metasenv in the wrong order *) let highest_meta = NCicMetaSubst.maxmeta () in let metasenv, subst, newhead, newheadty = aux metasenv subst [] he ty_he args in let metasenv_old,metasenv_new = List.partition (fun (i,_) -> i <= highest_meta) metasenv in (List.rev metasenv_new) @ metasenv_old, subst, newhead, newheadty (*D*)in outside true; rc with exc -> outside false; raise exc ;; let rec first f l1 l2 = match l1,l2 with | x1::tl1, x2::tl2 -> (try f x1 x2 with Not_found -> first f tl1 tl2) | _ -> raise Not_found ;; let rec find add dt t = if dt == add then t else let dl, l = match dt, t with | C.Meta (_,(_,C.Ctx dl)), C.Meta (_,(_,C.Ctx l)) | C.Appl dl,C.Appl l -> dl,l | C.Lambda (_,ds,dt), C.Lambda (_,s,t) | C.Prod (_,ds,dt), C.Prod (_,s,t) -> [ds;dt],[s;t] | C.LetIn (_,ds,db,dt), C.LetIn (_,s,b,t) -> [ds;db;dt],[s;b;t] | C.Match (_,dot,dt,dl), C.Match (_,ot,t,l) -> (dot::dt::dl),(ot::t::l) | _ -> raise Not_found in first (find add) dl l ;; let relocalise old_localise dt t add = old_localise (try find add dt t with Not_found -> assert false) ;; let undebruijnate status inductive ref t rev_fl = let len = List.length rev_fl in NCicSubstitution.psubst status (fun x -> x) (HExtlib.list_mapi (fun (_,_,rno,_,_,_) i -> let i = len - i - 1 in C.Const (if inductive then Ref.mk_fix i rno ref else Ref.mk_cofix i ref)) rev_fl) t ;; let typeof_obj status ?(localise=fun _ -> Stdpp.dummy_loc) (uri,height,metasenv,subst,obj) = match obj with | C.Constant (relevance, name, bo, ty, attr) -> let metasenv, subst, ty = check_type status ~localise metasenv subst [] ty in let metasenv, subst, bo, ty, height = match bo with | Some bo -> let metasenv, subst, bo, ty = typeof status ~localise metasenv subst [] bo (`XTSome ty) in let height = (* XXX recalculate *) height in metasenv, subst, Some bo, ty, height | None -> metasenv, subst, None, ty, 0 in uri, height, metasenv, subst, C.Constant (relevance, name, bo, ty, attr) | C.Fixpoint (inductive, fl, attr) -> let len = List.length fl in let types, metasenv, subst, rev_fl = List.fold_left (fun (types, metasenv, subst, fl) (relevance,name,k,ty,bo) -> let metasenv, subst, ty = check_type status ~localise metasenv subst [] ty in let dbo = NCicTypeChecker.debruijn status uri len [] ~subst bo in let localise = relocalise localise dbo bo in (name,C.Decl ty)::types, metasenv, subst, (relevance,name,k,ty,dbo,localise)::fl ) ([], metasenv, subst, []) fl (* XXX kl rimosso nel nucleo *) in let metasenv, subst, fl = List.fold_left (fun (metasenv,subst,fl) (relevance,name,k,ty,dbo,localise) -> let metasenv, subst, dbo, ty = typeof status ~localise metasenv subst types dbo (`XTSome ty) in metasenv, subst, (relevance,name,k,ty,dbo)::fl) (metasenv, subst, []) rev_fl in let height = (* XXX recalculate *) height in let fl = List.map (fun (relevance,name,k,ty,dbo) -> let bo = undebruijnate status inductive (Ref.reference_of_spec uri (if inductive then Ref.Fix (0,k,0) else Ref.CoFix 0)) dbo rev_fl in relevance,name,k,ty,bo) fl in uri, height, metasenv, subst, C.Fixpoint (inductive, fl, attr) | C.Inductive (ind, leftno, itl, attr) -> let len = List.length itl in let metasenv,subst,rev_itl,tys = List.fold_left (fun (metasenv,subst,res,ctx) (relevance,n,ty,cl) -> let metasenv, subst, ty = check_type status ~localise metasenv subst [] ty in metasenv,subst,(relevance,n,ty,cl)::res,(n,C.Decl ty)::ctx ) (metasenv,subst,[],[]) itl in let metasenv,subst,itl,_ = List.fold_left (fun (metasenv,subst,res,i) (it_relev,n,ty,cl) -> let context,ty_sort = NCicReduction.split_prods status ~subst [] ~-1 ty in let sx_context_ty_rev,_= HExtlib.split_nth leftno (List.rev context) in let metasenv,subst,cl = List.fold_right (fun (k_relev,n,te) (metasenv,subst,res) -> let k_relev = try snd (HExtlib.split_nth leftno k_relev) with Failure _ -> k_relev in let te = NCicTypeChecker.debruijn status uri len [] ~subst te in let metasenv, subst, te = check_type status ~localise metasenv subst tys te in let context,te = NCicReduction.split_prods status ~subst tys leftno te in let _,chopped_context_rev = HExtlib.split_nth (List.length tys) (List.rev context) in let sx_context_te_rev,_ = HExtlib.split_nth leftno chopped_context_rev in let metasenv,subst,_ = try List.fold_left2 (fun (metasenv,subst,context) item1 item2 -> let (metasenv,subst),convertible = try match item1,item2 with (n1,C.Decl ty1),(n2,C.Decl ty2) -> if n1 = n2 then NCicUnification.unify status ~test_eq_only:true metasenv subst context ty1 ty2,true else (metasenv,subst),false | (n1,C.Def (bo1,ty1)),(n2,C.Def (bo2,ty2)) -> if n1 = n2 then let metasenv,subst = NCicUnification.unify status ~test_eq_only:true metasenv subst context ty1 ty2 in NCicUnification.unify status ~test_eq_only:true metasenv subst context bo1 bo2,true else (metasenv,subst),false | _,_ -> (metasenv,subst),false with | NCicUnification.Uncertain _ | NCicUnification.UnificationFailure _ -> (metasenv,subst),false in let term2 = match item2 with _,C.Decl t -> t | _,C.Def (b,_) -> b in if not convertible then raise (RefineFailure (lazy (localise term2, ("Mismatch between the left parameters of the constructor " ^ "and those of its inductive type")))) else metasenv,subst,item1::context ) (metasenv,subst,tys) sx_context_ty_rev sx_context_te_rev with Invalid_argument "List.fold_left2" -> assert false in let metasenv, subst = let rec aux context (metasenv,subst) = function | C.Meta _ -> metasenv, subst | C.Implicit _ -> metasenv, subst | C.Appl (C.Rel i :: args) when i > List.length context - len -> let lefts, _ = HExtlib.split_nth leftno args in let ctxlen = List.length context in let (metasenv, subst), _ = List.fold_left (fun ((metasenv, subst),l) arg -> NCicUnification.unify status ~test_eq_only:true metasenv subst context arg (C.Rel (ctxlen - len - l)), l+1 ) ((metasenv, subst), 0) lefts in metasenv, subst | t -> NCicUtils.fold (fun e c -> e::c) context aux (metasenv,subst) t in aux context (metasenv,subst) te in let con_sort= NCicTypeChecker.typeof status ~subst ~metasenv context te in (match NCicReduction.whd status ~subst context con_sort, NCicReduction.whd status ~subst [] ty_sort with (C.Sort (C.Type u1) as s1), (C.Sort (C.Type u2) as s2) -> if not (NCicEnvironment.universe_leq u1 u2) then raise (RefineFailure (lazy(localise te, "The type " ^ status#ppterm ~metasenv ~subst ~context s1 ^ " of the constructor is not included in the inductive"^ " type sort " ^ status#ppterm ~metasenv ~subst ~context s2))) | C.Sort _, C.Sort C.Prop | C.Sort _, C.Sort C.Type _ -> () | _, _ -> raise (RefineFailure (lazy (localise te, "Wrong constructor or inductive arity shape")))); (* let's check also the positivity conditions *) if not (NCicTypeChecker.are_all_occurrences_positive status ~subst context uri leftno (i+leftno) leftno (len+leftno) te) then raise (RefineFailure (lazy (localise te, "Non positive occurence in " ^ status#ppterm ~metasenv ~subst ~context te))) else let relsno = List.length itl + leftno in let te = NCicSubstitution.psubst status (fun i -> if i <= leftno then C.Rel i else C.Const (Ref.reference_of_spec uri (Ref.Ind (ind,relsno - i,leftno)))) (HExtlib.list_seq 1 (relsno+1)) te in let te = List.fold_right (fun (name,decl) te -> match decl with C.Decl ty -> C.Prod (name,ty,te) | C.Def (bo,ty) -> C.LetIn (name,ty,bo,te) ) sx_context_te_rev te in metasenv,subst,(k_relev,n,te)::res ) cl (metasenv,subst,[]) in metasenv,subst,(it_relev,n,ty,cl)::res,i+1 ) (metasenv,subst,[],1) rev_itl in uri, height, metasenv, subst, C.Inductive (ind, leftno, itl, attr) ;; (* vim:set foldmethod=marker: *)