X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Fng_kernel%2FnCicTypeChecker.ml;h=96b2f9186fcc7ebfcec7714e9a35f6d1fe66df0a;hb=c22f39a5d5afc0ef55beb221e00e2e6703b13d90;hp=ca943a828fd421a6cc630716cf9f786c41bb6555;hpb=a3ba13b9503a2c0dd89b89b489899362d17b3f3a;p=helm.git diff --git a/helm/software/components/ng_kernel/nCicTypeChecker.ml b/helm/software/components/ng_kernel/nCicTypeChecker.ml index ca943a828..c4c2af477 100644 --- a/helm/software/components/ng_kernel/nCicTypeChecker.ml +++ b/helm/software/components/ng_kernel/nCicTypeChecker.ml @@ -1,6 +1,1382 @@ +(* + ||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_______________________________________________________________ *) + +(* $Id$ *) + +module C = NCic +module Ref = NReference +module R = NCicReduction +module S = NCicSubstitution +module U = NCicUtils +module E = NCicEnvironment +module PP = NCicPp exception TypeCheckerFailure of string Lazy.t exception AssertFailure of string Lazy.t -(* typechecks the object, raising an exception if illtyped *) -let typecheck_obj obj = () +(* +let raise = function + | TypeCheckerFailure s as e -> prerr_endline (Lazy.force s); raise e + | e -> raise e +;; +*) + +type recf_entry = + | Evil of int (* rno *) + | UnfFix of bool list (* fixed arguments *) + | Safe +;; + +let is_dangerous i l = + List.exists (function (j,Evil _) when j=i -> true | _ -> false) l +;; + +let is_unfolded i l = + List.exists (function (j,UnfFix _) when j=i -> true | _ -> false) l +;; + +let is_safe i l = + List.exists (function (j,Safe) when j=i -> true | _ -> false) l +;; + +let get_recno i l = + try match List.assoc i l with Evil rno -> rno | _ -> assert false + with Not_found -> assert false +;; + +let get_fixed_args i l = + try match List.assoc i l with UnfFix fa -> fa | _ -> assert false + with Not_found -> assert false +;; + +let shift_k e (c,rf,x) = e::c,List.map (fun (k,v) -> k+1,v) rf,x+1;; + +(* for debugging only +let string_of_recfuns ~subst ~metasenv ~context l = + let pp = PP.ppterm ~subst ~metasenv ~context in + let safe, rest = List.partition (function (_,Safe) -> true | _ -> false) l in + let dang,unf = List.partition (function (_,UnfFix _)-> false | _->true)rest in + "\n\tsafes: "^String.concat "," (List.map (fun (i,_)->pp (C.Rel i)) safe) ^ + "\n\tfix : "^String.concat "," + (List.map + (function (i,UnfFix l)-> pp(C.Rel i)^"/"^String.concat "," (List.map + string_of_bool l) + | _ ->assert false) unf) ^ + "\n\trec : "^String.concat "," + (List.map + (function (i,Evil rno)->pp(C.Rel i)^"/"^string_of_int rno + | _ -> assert false) dang) +;; +*) + +let fixed_args bos j n nn = + let rec aux k acc = function + | C.Appl (C.Rel i::args) when i-k > n && i-k <= nn -> + let rec combine l1 l2 = + match l1,l2 with + [],[] -> [] + | he1::tl1, he2::tl2 -> (he1,he2)::combine tl1 tl2 + | _::tl, [] -> (false,C.Rel ~-1)::combine tl [] (* dummy term *) + | [],_::_ -> assert false + in + let lefts, _ = HExtlib.split_nth (min j (List.length args)) args in + List.map (fun ((b,x),i) -> b && x = C.Rel (k-i)) + (HExtlib.list_mapi (fun x i -> x,i) (combine acc lefts)) + | t -> U.fold (fun _ k -> k+1) k aux acc t + in + List.fold_left (aux 0) + (let rec f = function 0 -> [] | n -> true :: f (n-1) in f j) bos +;; + +let debruijn uri number_of_types ~subst context = +(* manca la subst! *) + let rec aux k t = + match t with + | C.Meta (i,(s,l)) -> + (try + let _,_,term,_ = U.lookup_subst i subst in + let ts = S.subst_meta (0,l) term in + let ts' = aux (k-s) ts in + if ts == ts' then t else ts' + with U.Subst_not_found _ -> + match l with + C.Ctx l -> + let l1 = HExtlib.sharing_map (aux (k-s)) l in + if l1 == l then t else C.Meta (i,(s,C.Ctx l1)) + | _ -> t) + | C.Const (Ref.Ref (uri1,(Ref.Fix (no,_,_) | Ref.CoFix no))) + | C.Const (Ref.Ref (uri1,Ref.Ind (_,no,_))) when NUri.eq uri uri1 -> + C.Rel (k + number_of_types - no) + | t -> U.map (fun _ k -> k+1) k aux t + in + aux (List.length context) +;; + +let sort_of_prod ~metasenv ~subst context (name,s) t (t1, t2) = + let t1 = R.whd ~subst context t1 in + let t2 = R.whd ~subst ((name,C.Decl s)::context) t2 in + match t1, t2 with + | C.Sort _, C.Sort C.Prop -> t2 + | C.Sort (C.Type u1), C.Sort (C.Type u2) -> + C.Sort (C.Type (NCicEnvironment.max u1 u2)) + | C.Sort C.Prop,C.Sort (C.Type _) -> t2 + | C.Meta (_,(_,(C.Irl 0 | C.Ctx []))), C.Sort _ -> t2 + | C.Meta (_,(_,(C.Irl 0 | C.Ctx []))), C.Meta (i,(_,(C.Irl 0 | C.Ctx []))) + | C.Sort _, C.Meta (i,(_,(C.Irl 0 | C.Ctx []))) -> + NCic.Meta (i,(0, C.Irl 0)) + | x, (C.Sort _ | C.Meta (_,(_,(C.Irl 0 | C.Ctx [])))) + | _, x -> + let y, context = + if x == t1 then s, context else t, ((name,C.Decl s)::context) + in + raise (TypeCheckerFailure (lazy (Printf.sprintf + "%s is expected to be a type, but its type is %s that is not a sort" + (PP.ppterm ~subst ~metasenv ~context y) + (PP.ppterm ~subst ~metasenv ~context x)))) +;; + +(* instantiate_parameters ps (x1:T1)...(xn:Tn)C *) +(* returns ((x_|ps|:T_|ps|)...(xn:Tn)C){ps_1 / x1 ; ... ; ps_|ps| / x_|ps|} *) +let rec instantiate_parameters params c = + match c, params with + | c,[] -> c + | C.Prod (_,_,ta), he::tl -> instantiate_parameters tl (S.subst he ta) + | _,_ -> raise (AssertFailure (lazy "1")) +;; + +let specialize_inductive_type_constrs ~subst context ty_term = + match R.whd ~subst context ty_term with + | C.Const (Ref.Ref (_,Ref.Ind _) as ref) + | C.Appl (C.Const (Ref.Ref (_,Ref.Ind _) as ref) :: _ ) as ty -> + let args = match ty with C.Appl (_::tl) -> tl | _ -> [] in + let _, leftno, itl, _, i = E.get_checked_indtys ref in + let left_args,_ = HExtlib.split_nth leftno args in + let _,_,_,cl = List.nth itl i in + List.map + (fun (rel,name,ty) -> rel, name, instantiate_parameters left_args ty) cl + | _ -> assert false +;; + +let specialize_and_abstract_constrs ~subst r_uri r_len context ty_term = + let cl = specialize_inductive_type_constrs ~subst context ty_term in + let len = List.length context in + let context_dcl = + match E.get_checked_obj r_uri with + | _,_,_,_, C.Inductive (_,_,tys,_) -> + context @ List.map (fun (_,name,arity,_) -> name,C.Decl arity) tys + | _ -> assert false + in + context_dcl, + List.map (fun (_,id,ty) -> id, debruijn r_uri r_len ~subst context ty) cl, + len, len + r_len +;; + +exception DoesOccur;; + +let does_not_occur ~subst context n nn t = + let rec aux k _ = function + | C.Rel m when m > n+k && m <= nn+k -> raise DoesOccur + | C.Rel m when m <= k || m > nn+k -> () + | C.Rel m -> + (try match List.nth context (m-1-k) with + | _,C.Def (bo,_) -> aux (n-m) () bo + | _ -> () + with Failure _ -> assert false) + | C.Meta (_,(_,(C.Irl 0 | C.Ctx []))) -> (* closed meta *) () + | C.Meta (mno,(s,l)) -> + (try + (* possible optimization here: try does_not_occur on l and + perform substitution only if DoesOccur is raised *) + let _,_,term,_ = U.lookup_subst mno subst in + aux (k-s) () (S.subst_meta (0,l) term) + with U.Subst_not_found _ -> match l with + | C.Irl len -> if not (n+k >= s+len || s > nn+k) then raise DoesOccur + | C.Ctx lc -> List.iter (aux (k-s) ()) lc) + | t -> U.fold (fun _ k -> k + 1) k aux () t + in + try aux 0 () t; true + with DoesOccur -> false +;; + +let rec eat_lambdas ~subst ~metasenv context n te = + match (n, R.whd ~subst context te) with + | (0, _) -> (te, context) + | (n, C.Lambda (name,so,ta)) when n > 0 -> + eat_lambdas ~subst ~metasenv ((name,(C.Decl so))::context) (n - 1) ta + | (n, te) -> + raise (AssertFailure (lazy (Printf.sprintf "eat_lambdas (%d, %s)" n + (PP.ppterm ~subst ~metasenv ~context te)))) +;; + +let rec eat_or_subst_lambdas + ~subst ~metasenv n te to_be_subst args (context,_,_ as k) += + match n, R.whd ~subst context te, to_be_subst, args with + | (n, C.Lambda (_,_,ta),true::to_be_subst,arg::args) when n > 0 -> + eat_or_subst_lambdas ~subst ~metasenv (n - 1) (S.subst arg ta) + to_be_subst args k + | (n, C.Lambda (name,so,ta),false::to_be_subst,_::args) when n > 0 -> + eat_or_subst_lambdas ~subst ~metasenv (n - 1) ta to_be_subst args + (shift_k (name,(C.Decl so)) k) + | (_, te, _, _) -> te, k +;; + +let check_homogeneous_call ~subst context indparamsno n uri reduct tl = + let last = + List.fold_left + (fun k x -> + if k = 0 then 0 + else + match R.whd ~subst context x with + | C.Rel m when m = n - (indparamsno - k) -> k - 1 + | _ -> raise (TypeCheckerFailure (lazy + ("Argument "^string_of_int (indparamsno - k + 1) ^ " (of " ^ + string_of_int indparamsno ^ " fixed) is not homogeneous in "^ + "appl:\n"^ PP.ppterm ~context ~subst ~metasenv:[] reduct)))) + indparamsno tl + in + if last <> 0 then + raise (TypeCheckerFailure + (lazy ("Non-positive occurence in mutual inductive definition(s) [2]"^ + NUri.string_of_uri uri))) +;; + +(* Inductive types being checked for positivity have *) +(* indexes x s.t. n < x <= nn. *) +let rec weakly_positive ~subst context n nn uri indparamsno posuri te = + (*CSC: Not very nice. *) + let dummy = C.Sort C.Prop in + (*CSC: to be moved in cicSubstitution? *) + let rec subst_inductive_type_with_dummy _ = function + | C.Const (Ref.Ref (uri',Ref.Ind (true,0,_))) when NUri.eq uri' uri -> dummy + | C.Appl ((C.Const (Ref.Ref (uri',Ref.Ind (true,0,lno))))::tl) + when NUri.eq uri' uri -> + let _, rargs = HExtlib.split_nth lno tl in + if rargs = [] then dummy else C.Appl (dummy :: rargs) + | t -> U.map (fun _ x->x) () subst_inductive_type_with_dummy t + in + (* this function has the same semantics of are_all_occurrences_positive + but the i-th context entry role is played by dummy and some checks + are skipped because we already know that are_all_occurrences_positive + of uri in te. *) + let rec aux context n nn te = + match R.whd ~subst context te with + | t when t = dummy -> true + | C.Appl (te::rargs) when te = dummy -> + List.for_all (does_not_occur ~subst context n nn) rargs + | C.Prod (name,source,dest) when + does_not_occur ~subst ((name,C.Decl source)::context) 0 1 dest -> + (* dummy abstraction, so we behave as in the anonimous case *) + strictly_positive ~subst context n nn indparamsno posuri source && + aux ((name,C.Decl source)::context) (n + 1) (nn + 1) dest + | C.Prod (name,source,dest) -> + does_not_occur ~subst context n nn source && + aux ((name,C.Decl source)::context) (n + 1) (nn + 1) dest + | _ -> + raise (TypeCheckerFailure (lazy "Malformed inductive constructor type")) + in + aux context n nn (subst_inductive_type_with_dummy () te) + +and strictly_positive ~subst context n nn indparamsno posuri te = + match R.whd ~subst context te with + | t when does_not_occur ~subst context n nn t -> true + | C.Rel _ when indparamsno = 0 -> true + | C.Appl ((C.Rel m)::tl) as reduct when m > n && m <= nn -> + check_homogeneous_call ~subst context indparamsno n posuri reduct tl; + List.for_all (does_not_occur ~subst context n nn) tl + | C.Prod (name,so,ta) -> + does_not_occur ~subst context n nn so && + strictly_positive ~subst ((name,C.Decl so)::context) (n+1) (nn+1) + indparamsno posuri ta + | C.Appl (C.Const (Ref.Ref (uri,Ref.Ind _) as r)::tl) -> + let _,paramsno,tyl,_,i = E.get_checked_indtys r in + let _,name,ity,cl = List.nth tyl i in + let ok = List.length tyl = 1 in + let params, arguments = HExtlib.split_nth paramsno tl in + let lifted_params = List.map (S.lift 1) params in + let cl = + List.map (fun (_,_,te) -> instantiate_parameters lifted_params te) cl + in + ok && + List.for_all (does_not_occur ~subst context n nn) arguments && + List.for_all + (weakly_positive ~subst ((name,C.Decl ity)::context) (n+1) (nn+1) + uri indparamsno posuri) cl + | _ -> false + +(* the inductive type indexes are s.t. n < x <= nn *) +and are_all_occurrences_positive ~subst context uri indparamsno i n nn te = + match R.whd ~subst context te with + | C.Appl ((C.Rel m)::tl) as reduct when m = i -> + check_homogeneous_call ~subst context indparamsno n uri reduct tl; + List.for_all (does_not_occur ~subst context n nn) tl + | C.Rel m when m = i -> + if indparamsno = 0 then + true + else + raise (TypeCheckerFailure + (lazy ("Non-positive occurence in mutual inductive definition(s) [3]"^ + NUri.string_of_uri uri))) + | C.Prod (name,source,dest) when + does_not_occur ~subst ((name,C.Decl source)::context) 0 1 dest -> + strictly_positive ~subst context n nn indparamsno uri source && + are_all_occurrences_positive ~subst + ((name,C.Decl source)::context) uri indparamsno + (i+1) (n + 1) (nn + 1) dest + | C.Prod (name,source,dest) -> + if not (does_not_occur ~subst context n nn source) then + raise (TypeCheckerFailure (lazy ("Non-positive occurrence in "^ + PP.ppterm ~context ~metasenv:[] ~subst te))); + are_all_occurrences_positive ~subst ((name,C.Decl source)::context) + uri indparamsno (i+1) (n + 1) (nn + 1) dest + | _ -> + raise + (TypeCheckerFailure (lazy ("Malformed inductive constructor type " ^ + (NUri.string_of_uri uri)))) +;; + +exception NotGuarded of string Lazy.t;; + +let type_of_branch ~subst context leftno outty cons tycons = + let rec aux liftno context cons tycons = + match R.whd ~subst context tycons with + | C.Const (Ref.Ref (_,Ref.Ind _)) -> C.Appl [S.lift liftno outty ; cons] + | C.Appl (C.Const (Ref.Ref (_,Ref.Ind _))::tl) -> + let _,arguments = HExtlib.split_nth leftno tl in + C.Appl (S.lift liftno outty::arguments@[cons]) + | C.Prod (name,so,de) -> + let cons = + match S.lift 1 cons with + | C.Appl l -> C.Appl (l@[C.Rel 1]) + | t -> C.Appl [t ; C.Rel 1] + in + C.Prod (name,so, aux (liftno+1) ((name,(C.Decl so))::context) cons de) + | t -> raise (AssertFailure + (lazy ("type_of_branch, the contructor has type: " ^ NCicPp.ppterm + ~metasenv:[] ~context:[] ~subst:[] t))) + in + aux 0 context cons tycons +;; + + +let rec typeof ~subst ~metasenv context term = + let rec typeof_aux context = + fun t -> (*prerr_endline (PP.ppterm ~metasenv ~subst ~context t);*) + match t with + | C.Rel n -> + (try + match List.nth context (n - 1) with + | (_,C.Decl ty) -> S.lift n ty + | (_,C.Def (_,ty)) -> S.lift n ty + with Failure _ -> + raise (TypeCheckerFailure (lazy ("unbound variable " ^ string_of_int n + ^" under: " ^ NCicPp.ppcontext ~metasenv ~subst context)))) + | C.Sort (C.Type [false,u]) -> C.Sort (C.Type [true, u]) + | C.Sort (C.Type _) -> + raise (AssertFailure (lazy ("Cannot type an inferred type: "^ + NCicPp.ppterm ~subst ~metasenv ~context t))) + | C.Sort _ -> C.Sort (C.Type NCicEnvironment.type0) + | C.Implicit _ -> raise (AssertFailure (lazy "Implicit found")) + | C.Meta (n,l) as t -> + let canonical_ctx,ty = + try + let _,c,_,ty = U.lookup_subst n subst in c,ty + with U.Subst_not_found _ -> try + let _,c,ty = U.lookup_meta n metasenv in c, ty +(* match ty with C.Implicit _ -> assert false | _ -> c,ty *) + with U.Meta_not_found _ -> + raise (AssertFailure (lazy (Printf.sprintf + "%s not found in:\n%s" (PP.ppterm ~subst ~metasenv ~context t) + (PP.ppmetasenv ~subst metasenv) + ))) + in + check_metasenv_consistency t ~subst ~metasenv context canonical_ctx l; + S.subst_meta l ty + | C.Const ref -> type_of_constant ref + | C.Prod (name,s,t) -> + let sort1 = typeof_aux context s in + let sort2 = typeof_aux ((name,(C.Decl s))::context) t in + sort_of_prod ~metasenv ~subst context (name,s) t (sort1,sort2) + | C.Lambda (n,s,t) -> + let sort = typeof_aux context s in + (match R.whd ~subst context sort with + | C.Meta _ | C.Sort _ -> () + | _ -> + raise + (TypeCheckerFailure (lazy (Printf.sprintf + ("Not well-typed lambda-abstraction: " ^^ + "the source %s should be a type; instead it is a term " ^^ + "of type %s") (PP.ppterm ~subst ~metasenv ~context s) + (PP.ppterm ~subst ~metasenv ~context sort))))); + let ty = typeof_aux ((n,(C.Decl s))::context) t in + C.Prod (n,s,ty) + | C.LetIn (n,ty,t,bo) -> + let ty_t = typeof_aux context t in + let _ = typeof_aux context ty in + if not (R.are_convertible ~metasenv ~subst context ty_t ty) then + raise + (TypeCheckerFailure + (lazy (Printf.sprintf + "The type of %s is %s but it is expected to be %s" + (PP.ppterm ~subst ~metasenv ~context t) + (PP.ppterm ~subst ~metasenv ~context ty_t) + (PP.ppterm ~subst ~metasenv ~context ty)))) + else + let ty_bo = typeof_aux ((n,C.Def (t,ty))::context) bo in + S.subst ~avoid_beta_redexes:true t ty_bo + | C.Appl (he::(_::_ as args)) -> + let ty_he = typeof_aux context he in + let args_with_ty = List.map (fun t -> t, typeof_aux context t) args in + eat_prods ~subst ~metasenv context he ty_he args_with_ty + | C.Appl _ -> raise (AssertFailure (lazy "Appl of length < 2")) + | C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as r,outtype,term,pl) -> + let outsort = typeof_aux context outtype in + let _,leftno,itl,_,_ = E.get_checked_indtys r in + let constructorsno = + let _,_,_,cl = List.nth itl tyno in List.length cl + in + let parameters, arguments = + let ty = R.whd ~subst context (typeof_aux context term) in + let r',tl = + match ty with + C.Const (Ref.Ref (_,Ref.Ind _) as r') -> r',[] + | C.Appl (C.Const (Ref.Ref (_,Ref.Ind _) as r') :: tl) -> r',tl + | _ -> + raise + (TypeCheckerFailure (lazy (Printf.sprintf + "Case analysis: analysed term %s is not an inductive one" + (PP.ppterm ~subst ~metasenv ~context term)))) in + if not (Ref.eq r r') then + raise + (TypeCheckerFailure (lazy (Printf.sprintf + ("Case analysys: analysed term type is %s, but is expected " ^^ + "to be (an application of) %s") + (PP.ppterm ~subst ~metasenv ~context ty) + (PP.ppterm ~subst ~metasenv ~context (C.Const r'))))) + else + try HExtlib.split_nth leftno tl + with + Failure _ -> + raise (TypeCheckerFailure (lazy (Printf.sprintf + "%s is partially applied" + (PP.ppterm ~subst ~metasenv ~context ty)))) in + (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *) + let sort_of_ind_type = + if parameters = [] then C.Const r + else C.Appl ((C.Const r)::parameters) in + let type_of_sort_of_ind_ty = typeof_aux context sort_of_ind_type in + check_allowed_sort_elimination ~subst ~metasenv r context + sort_of_ind_type type_of_sort_of_ind_ty outsort; + (* let's check if the type of branches are right *) + if List.length pl <> constructorsno then + raise (TypeCheckerFailure (lazy ("Wrong number of cases in a match"))); + let j,branches_ok,p_ty, exp_p_ty = + List.fold_left + (fun (j,b,old_p_ty,old_exp_p_ty) p -> + if b then + 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 ty_p = typeof_aux context p in + let ty_cons = typeof_aux context cons in + let ty_branch = + type_of_branch ~subst context leftno outtype cons ty_cons + in + j+1, R.are_convertible ~metasenv ~subst context ty_p ty_branch, + ty_p, ty_branch + else + j,false,old_p_ty,old_exp_p_ty + ) (1,true,C.Sort C.Prop,C.Sort C.Prop) pl + in + if not branches_ok then + raise + (TypeCheckerFailure + (lazy (Printf.sprintf ("Branch for constructor %s :=\n%s\n"^^ + "has type %s\nnot convertible with %s") + (PP.ppterm ~subst ~metasenv ~context + (C.Const (Ref.mk_constructor (j-1) r))) + (PP.ppterm ~metasenv ~subst ~context (List.nth pl (j-2))) + (PP.ppterm ~metasenv ~subst ~context p_ty) + (PP.ppterm ~metasenv ~subst ~context exp_p_ty)))); + let res = outtype::arguments@[term] in + R.head_beta_reduce (C.Appl res) + | C.Match _ -> assert false + + (* check_metasenv_consistency checks that the "canonical" context of a + metavariable is consitent - up to relocation via the relocation list l - + with the actual context *) + and check_metasenv_consistency + ~subst ~metasenv term context canonical_context l + = + match l with + | shift, C.Irl n -> + let context = snd (HExtlib.split_nth shift context) in + let rec compare = function + | 0,_,[] -> () + | 0,_,_::_ + | _,_,[] -> + raise (AssertFailure (lazy (Printf.sprintf + "(2) Local and canonical context %s have different lengths" + (PP.ppterm ~subst ~context ~metasenv term)))) + | m,[],_::_ -> + raise (TypeCheckerFailure (lazy (Printf.sprintf + "Unbound variable -%d in %s" m + (PP.ppterm ~subst ~metasenv ~context term)))) + | m,t::tl,ct::ctl -> + (match t,ct with + (_,C.Decl t1), (_,C.Decl t2) + | (_,C.Def (t1,_)), (_,C.Def (t2,_)) + | (_,C.Def (_,t1)), (_,C.Decl t2) -> + if not (R.are_convertible ~metasenv ~subst tl t1 t2) then + raise + (TypeCheckerFailure + (lazy (Printf.sprintf + ("Not well typed metavariable local context for %s: " ^^ + "%s expected, which is not convertible with %s") + (PP.ppterm ~subst ~metasenv ~context term) + (PP.ppterm ~subst ~metasenv ~context t2) + (PP.ppterm ~subst ~metasenv ~context t1)))) + | _,_ -> + raise + (TypeCheckerFailure (lazy (Printf.sprintf + ("Not well typed metavariable local context for %s: " ^^ + "a definition expected, but a declaration found") + (PP.ppterm ~subst ~metasenv ~context term))))); + compare (m - 1,tl,ctl) + in + compare (n,context,canonical_context) + | shift, lc_kind -> + (* we avoid useless lifting by shortening the context*) + let l,context = (0,lc_kind), snd (HExtlib.split_nth shift context) in + let lifted_canonical_context = + let rec lift_metas i = function + | [] -> [] + | (n,C.Decl t)::tl -> + (n,C.Decl (S.subst_meta l (S.lift i t)))::(lift_metas (i+1) tl) + | (n,C.Def (t,ty))::tl -> + (n,C.Def ((S.subst_meta l (S.lift i t)), + S.subst_meta l (S.lift i ty)))::(lift_metas (i+1) tl) + in + lift_metas 1 canonical_context in + let l = U.expand_local_context lc_kind in + try + List.iter2 + (fun t ct -> + match (t,ct) with + | t, (_,C.Def (ct,_)) -> + (*CSC: the following optimization is to avoid a possibly expensive + reduction that can be easily avoided and that is quite + frequent. However, this is better handled using levels to + control reduction *) + let optimized_t = + match t with + | C.Rel n -> + (try + match List.nth context (n - 1) with + | (_,C.Def (te,_)) -> S.lift n te + | _ -> t + with Failure _ -> t) + | _ -> t + in + if not (R.are_convertible ~metasenv ~subst context optimized_t ct) + then + raise + (TypeCheckerFailure + (lazy (Printf.sprintf + ("Not well typed metavariable local context: " ^^ + "expected a term convertible with %s, found %s") + (PP.ppterm ~subst ~metasenv ~context ct) + (PP.ppterm ~subst ~metasenv ~context t)))) + | t, (_,C.Decl ct) -> + let type_t = typeof_aux context t in + if not (R.are_convertible ~metasenv ~subst context type_t ct) then + raise (TypeCheckerFailure + (lazy (Printf.sprintf + ("Not well typed metavariable local context: "^^ + "expected a term of type %s, found %s of type %s") + (PP.ppterm ~subst ~metasenv ~context ct) + (PP.ppterm ~subst ~metasenv ~context t) + (PP.ppterm ~subst ~metasenv ~context type_t)))) + ) l lifted_canonical_context + with + | Invalid_argument "List.iter2" -> + raise (AssertFailure (lazy (Printf.sprintf + "(1) Local and canonical context %s have different lengths" + (PP.ppterm ~subst ~metasenv ~context term)))) + + in + typeof_aux context term + +and check_allowed_sort_elimination ~subst ~metasenv r = + let mkapp he arg = + match he with + | C.Appl l -> C.Appl (l @ [arg]) + | t -> C.Appl [t;arg] in + let rec aux context ind arity1 arity2 = + let arity1 = R.whd ~subst context arity1 in + let arity2 = R.whd ~subst context arity2 in + match arity1,arity2 with + | C.Prod (name,so1,de1), C.Prod (_,so2,de2) -> + if not (R.are_convertible ~metasenv ~subst context so1 so2) then + raise (TypeCheckerFailure (lazy (Printf.sprintf + "In outtype: expected %s, found %s" + (PP.ppterm ~subst ~metasenv ~context so1) + (PP.ppterm ~subst ~metasenv ~context so2) + ))); + aux ((name, C.Decl so1)::context) + (mkapp (S.lift 1 ind) (C.Rel 1)) de1 de2 + | C.Sort _, C.Prod (name,so,ta) -> + if not (R.are_convertible ~metasenv ~subst context so ind) then + raise (TypeCheckerFailure (lazy (Printf.sprintf + "In outtype: expected %s, found %s" + (PP.ppterm ~subst ~metasenv ~context ind) + (PP.ppterm ~subst ~metasenv ~context so) + ))); + (match arity1, R.whd ~subst ((name,C.Decl so)::context) ta with + | (C.Sort C.Type _, C.Sort _) + | (C.Sort C.Prop, C.Sort C.Prop) -> () + | (C.Sort C.Prop, C.Sort C.Type _) -> + (* TODO: we should pass all these parameters since we + * have them already *) + let _,leftno,itl,_,i = E.get_checked_indtys r in + let itl_len = List.length itl in + let _,itname,ittype,cl = List.nth itl i in + let cl_len = List.length cl in + (* is it a singleton, non recursive and non informative + definition or an empty one? *) + if not + (cl_len = 0 || + (itl_len = 1 && cl_len = 1 && + let _,_,constrty = List.hd cl in + is_non_recursive_singleton + ~subst r itname ittype constrty && + is_non_informative ~metasenv ~subst leftno constrty)) + then + raise (TypeCheckerFailure (lazy + ("Sort elimination not allowed"))); + | _,_ -> ()) + | _,_ -> () + in + aux + +and eat_prods ~subst ~metasenv context he ty_he args_with_ty = + let rec aux ty_he = function + | [] -> ty_he + | (arg, ty_arg)::tl -> + match R.whd ~subst context ty_he with + | C.Prod (_,s,t) -> + if R.are_convertible ~metasenv ~subst context ty_arg s then + aux (S.subst ~avoid_beta_redexes:true arg t) tl + else + raise + (TypeCheckerFailure + (lazy (Printf.sprintf + ("Appl: wrong application of %s: the argument %s has type"^^ + "\n%s\nbut it should have type \n%s\nContext:\n%s\n") + (PP.ppterm ~subst ~metasenv ~context he) + (PP.ppterm ~subst ~metasenv ~context arg) + (PP.ppterm ~subst ~metasenv ~context ty_arg) + (PP.ppterm ~subst ~metasenv ~context s) + (PP.ppcontext ~subst ~metasenv context)))) + | _ -> + raise + (TypeCheckerFailure + (lazy (Printf.sprintf + "Appl: %s is not a function, it cannot be applied" + (PP.ppterm ~subst ~metasenv ~context + (let res = List.length tl in + let eaten = List.length args_with_ty - res in + (C.Appl + (he::List.map fst + (fst (HExtlib.split_nth eaten args_with_ty))))))))) + in + aux ty_he args_with_ty + +and is_non_recursive_singleton ~subst (Ref.Ref (uri,_)) iname ity cty = + let ctx = [iname, C.Decl ity] in + let cty = debruijn uri 1 [] ~subst cty in + let len = List.length ctx in + let rec aux ctx n nn t = + match R.whd ~subst ctx t with + | C.Prod (name, src, tgt) -> + does_not_occur ~subst ctx n nn src && + aux ((name, C.Decl src) :: ctx) (n+1) (nn+1) tgt + | C.Rel k | C.Appl (C.Rel k :: _) when k = nn -> true + | _ -> assert false + in + aux ctx (len-1) len cty + +and is_non_informative ~metasenv ~subst paramsno c = + let rec aux context c = + match R.whd ~subst context c with + | C.Prod (n,so,de) -> + let s = typeof ~metasenv ~subst context so in + s = C.Sort C.Prop && aux ((n,(C.Decl so))::context) de + | _ -> true in + let context',dx = NCicReduction.split_prods ~subst [] paramsno c in + aux context' dx + +and check_mutual_inductive_defs uri ~metasenv ~subst leftno tyl = + (* let's check if the arity of the inductive types are well formed *) + List.iter (fun (_,_,x,_) -> ignore (typeof ~subst ~metasenv [] x)) tyl; + (* let's check if the types of the inductive constructors are well formed. *) + let len = List.length tyl in + let tys = List.rev_map (fun (_,n,ty,_) -> (n,(C.Decl ty))) tyl in + ignore + (List.fold_right + (fun (it_relev,_,ty,cl) i -> + let context,ty_sort = NCicReduction.split_prods ~subst [] ~-1 ty in + let sx_context_ty_rev,_ = HExtlib.split_nth leftno (List.rev context) in + List.iter + (fun (k_relev,_,te) -> + let k_relev = + try snd (HExtlib.split_nth leftno k_relev) + with Failure _ -> k_relev in + let te = debruijn uri len [] ~subst te in + let context,te = NCicReduction.split_prods ~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 + (try + ignore (List.fold_left2 + (fun context item1 item2 -> + let convertible = + match item1,item2 with + (_,C.Decl ty1),(_,C.Decl ty2) -> + R.are_convertible ~metasenv ~subst context ty1 ty2 + | (_,C.Def (bo1,ty1)),(_,C.Def (bo2,ty2)) -> + R.are_convertible ~metasenv ~subst context ty1 ty2 && + R.are_convertible ~metasenv ~subst context bo1 bo2 + | _,_ -> false + in + if not convertible then + raise (TypeCheckerFailure (lazy + ("Mismatch between the left parameters of the constructor " ^ + "and those of its inductive type"))) + else + item1::context + ) [] sx_context_ty_rev sx_context_te_rev) + with Invalid_argument "List.fold_left2" -> assert false); + let con_sort = typeof ~subst ~metasenv context te in + (match R.whd ~subst context con_sort, R.whd ~subst [] ty_sort with + (C.Sort (C.Type u1) as s1), (C.Sort (C.Type u2) as s2) -> + if not (E.universe_leq u1 u2) then + raise + (TypeCheckerFailure + (lazy ("The type " ^ PP.ppterm ~metasenv ~subst ~context s1^ + " of the constructor is not included in the inductive" ^ + " type sort " ^ PP.ppterm ~metasenv ~subst ~context s2))) + | C.Sort _, C.Sort C.Prop + | C.Sort _, C.Sort C.Type _ -> () + | _, _ -> + raise + (TypeCheckerFailure + (lazy ("Wrong constructor or inductive arity shape")))); + (* let's check also the positivity conditions *) + if + not + (are_all_occurrences_positive ~subst context uri leftno + (i+leftno) leftno (len+leftno) te) + then + raise + (TypeCheckerFailure + (lazy ("Non positive occurence in "^NUri.string_of_uri + uri))) + else check_relevance ~subst ~metasenv context k_relev te) + cl; + check_relevance ~subst ~metasenv [] it_relev ty; + i+1) + tyl 1) + +and check_relevance ~subst ~metasenv context relevance ty = + let error context ty = + raise (TypeCheckerFailure + (lazy ("Wrong relevance declaration: " ^ + String.concat "," (List.map string_of_bool relevance)^ + "\nfor type: "^PP.ppterm ~metasenv ~subst ~context ty))) + in + let rec aux context relevance ty = + match R.whd ~subst context ty with + | C.Prod (name,so,de) -> + let sort = typeof ~subst ~metasenv context so in + (match (relevance,R.whd ~subst context sort) with + | [],_ -> () + | false::tl,C.Sort C.Prop -> aux ((name,(C.Decl so))::context) tl de + | true::_,C.Sort C.Prop + | false::_,C.Sort _ + | false::_,C.Meta _ -> error context ty + | true::tl,C.Sort _ + | true::tl,C.Meta _ -> aux ((name,(C.Decl so))::context) tl de + | _ -> raise (AssertFailure (lazy (Printf.sprintf + "Prod: the type %s of the source of %s is not a sort" + (PP.ppterm ~subst ~metasenv ~context sort) + (PP.ppterm ~subst ~metasenv ~context so))))) + | _ -> (match relevance with + | [] -> () + | _::_ -> error context ty) + in aux context relevance ty + +and guarded_by_destructors r_uri r_len ~subst ~metasenv context recfuns t = + let recursor f k t = U.fold shift_k k (fun k () -> f k) () t in + let rec aux (context, recfuns, x as k) t = +(* + prerr_endline ("GB:\n" ^ + PP.ppcontext ~subst ~metasenv context^ + PP.ppterm ~metasenv ~subst ~context t^ + string_of_recfuns ~subst ~metasenv ~context recfuns); +*) + try + match t with + | C.Rel m as t when is_dangerous m recfuns -> + raise (NotGuarded (lazy + (PP.ppterm ~subst ~metasenv ~context t ^ + " is a partial application of a fix"))) + | C.Appl ((C.Rel m)::tl) as t when is_dangerous m recfuns -> + let rec_no = get_recno m recfuns in + if not (List.length tl > rec_no) then + raise (NotGuarded (lazy + (PP.ppterm ~context ~subst ~metasenv t ^ + " is a partial application of a fix"))) + else + let rec_arg = List.nth tl rec_no in + if not (is_really_smaller r_uri r_len ~subst ~metasenv k rec_arg) then + raise (NotGuarded (lazy (Printf.sprintf ("Recursive call %s, %s is not" + ^^ " smaller.\ncontext:\n%s") (PP.ppterm ~context ~subst ~metasenv + t) (PP.ppterm ~context ~subst ~metasenv rec_arg) + (PP.ppcontext ~subst ~metasenv context)))); + List.iter (aux k) tl + | C.Appl ((C.Rel m)::tl) when is_unfolded m recfuns -> + let fixed_args = get_fixed_args m recfuns in + HExtlib.list_iter_default2 + (fun x b -> if not b then aux k x) tl false fixed_args + | C.Rel m -> + (match List.nth context (m-1) with + | _,C.Decl _ -> () + | _,C.Def (bo,_) -> aux k (S.lift m bo)) + | C.Meta _ -> () + | C.Appl (C.Const ((Ref.Ref (uri,Ref.Fix (i,recno,_))) as r)::args) -> + if List.exists (fun t -> try aux k t;false with NotGuarded _ -> true) args + then + let fl,_,_ = E.get_checked_fixes_or_cofixes r in + let ctx_tys, bos = + List.split (List.map (fun (_,name,_,ty,bo) -> (name, C.Decl ty), bo) fl) + in + let fl_len = List.length fl in + let bos = List.map (debruijn uri fl_len context ~subst) bos in + let j = List.fold_left min max_int (List.map (fun (_,_,i,_,_)->i) fl) in + let ctx_len = List.length context in + (* we may look for fixed params not only up to j ... *) + let fa = fixed_args bos j ctx_len (ctx_len + fl_len) in + HExtlib.list_iter_default2 + (fun x b -> if not b then aux k x) args false fa; + let context = context@ctx_tys in + let ctx_len = List.length context in + let extra_recfuns = + HExtlib.list_mapi (fun _ i -> ctx_len - i, UnfFix fa) ctx_tys + in + let new_k = context, extra_recfuns@recfuns, x in + let bos_and_ks = + HExtlib.list_mapi + (fun bo fno -> + let bo_and_k = + eat_or_subst_lambdas ~subst ~metasenv j bo fa args new_k + in + if + fno = i && + List.length args > recno && + (*case where the recursive argument is already really_smaller *) + is_really_smaller r_uri r_len ~subst ~metasenv k + (List.nth args recno) + then + let bo,(context, _, _ as new_k) = bo_and_k in + let bo, context' = + eat_lambdas ~subst ~metasenv context (recno + 1 - j) bo in + let new_context_part,_ = + HExtlib.split_nth (List.length context' - List.length context) + context' in + let k = List.fold_right shift_k new_context_part new_k in + let context, recfuns, x = k in + let k = context, (1,Safe)::recfuns, x in + bo,k + else + bo_and_k + ) bos + in + List.iter (fun (bo,k) -> aux k bo) bos_and_ks + | C.Match (Ref.Ref (_,Ref.Ind (true,_,_)),outtype,term,pl) as t -> + (match R.whd ~subst context term with + | C.Rel m | C.Appl (C.Rel m :: _ ) as t when is_safe m recfuns || m = x -> + let ty = typeof ~subst ~metasenv context term in + let dc_ctx, dcl, start, stop = + specialize_and_abstract_constrs ~subst r_uri r_len context ty in + let args = match t with C.Appl (_::tl) -> tl | _ -> [] in + aux k outtype; + List.iter (aux k) args; + List.iter2 + (fun p (_,dc) -> + let rl = recursive_args ~subst ~metasenv dc_ctx start stop dc in + let p, k = get_new_safes ~subst k p rl in + aux k p) + pl dcl + | _ -> recursor aux k t) + | t -> recursor aux k t + with + NotGuarded _ as exc -> + let t' = R.whd ~delta:0 ~subst context t in + if t = t' then raise exc + else aux k t' + in + try aux (context, recfuns, 1) t + with NotGuarded s -> raise (TypeCheckerFailure s) + +and guarded_by_constructors ~subst ~metasenv context t indURI indlen nn = + let rec aux context n nn h te = + match R.whd ~subst context te with + | C.Rel m when m > n && m <= nn -> h + | C.Rel _ | C.Meta _ -> true + | C.Sort _ + | C.Implicit _ + | C.Prod _ + | C.Const (Ref.Ref (_,Ref.Ind _)) + | C.LetIn _ -> raise (AssertFailure (lazy "17")) + | C.Lambda (name,so,de) -> + does_not_occur ~subst context n nn so && + aux ((name,C.Decl so)::context) (n + 1) (nn + 1) h de + | C.Appl ((C.Rel m)::tl) when m > n && m <= nn -> + h && List.for_all (does_not_occur ~subst context n nn) tl + | C.Const (Ref.Ref (_,Ref.Con _)) -> true + | C.Appl (C.Const (Ref.Ref (_, Ref.Con (_,j,paramsno))) :: tl) as t -> + let ty_t = typeof ~subst ~metasenv context t in + let dc_ctx, dcl, start, stop = + specialize_and_abstract_constrs ~subst indURI indlen context ty_t in + let _, dc = List.nth dcl (j-1) in +(* + prerr_endline (PP.ppterm ~subst ~metasenv ~context:dc_ctx dc); + prerr_endline (PP.ppcontext ~subst ~metasenv dc_ctx); + *) + let rec_params = recursive_args ~subst ~metasenv dc_ctx start stop dc in + let rec analyse_instantiated_type rec_spec args = + match rec_spec, args with + | h::rec_spec, he::args -> + aux context n nn h he && analyse_instantiated_type rec_spec args + | _,[] -> true + | _ -> raise (AssertFailure (lazy + ("Too many args for constructor: " ^ String.concat " " + (List.map (fun x-> PP.ppterm ~subst ~metasenv ~context x) args)))) + in + let _, args = HExtlib.split_nth paramsno tl in + analyse_instantiated_type rec_params args + | C.Appl ((C.Match (_,out,te,pl))::_) + | C.Match (_,out,te,pl) as t -> + let tl = match t with C.Appl (_::tl) -> tl | _ -> [] in + List.for_all (does_not_occur ~subst context n nn) tl && + does_not_occur ~subst context n nn out && + does_not_occur ~subst context n nn te && + List.for_all (aux context n nn h) pl +(* IMPOSSIBLE unsless we allow to pass cofix to other fix/cofix as we do for + higher order fix in g_b_destructors. + + | C.Const (Ref.Ref (u,(Ref.Fix _| Ref.CoFix _)) as ref) + | C.Appl(C.Const (Ref.Ref(u,(Ref.Fix _| Ref.CoFix _)) as ref) :: _) as t -> + let tl = match t with C.Appl (_::tl) -> tl | _ -> [] in + let fl,_,_ = E.get_checked_fixes_or_cofixes ref in + let len = List.length fl in + let tys = List.map (fun (_,n,_,ty,_) -> n, C.Decl ty) fl in + List.for_all (does_not_occur ~subst context n nn) tl && + List.for_all + (fun (_,_,_,_,bo) -> + aux (context@tys) n nn h (debruijn u len context bo)) + fl +*) + | C.Const _ + | C.Appl _ as t -> does_not_occur ~subst context n nn t + in + aux context 0 nn false t + +and recursive_args ~subst ~metasenv context n nn te = + match R.whd ~subst context te with + | C.Rel _ | C.Appl _ | C.Const _ -> [] + | C.Prod (name,so,de) -> + (not (does_not_occur ~subst context n nn so)) :: + (recursive_args ~subst ~metasenv + ((name,(C.Decl so))::context) (n+1) (nn + 1) de) + | t -> + raise (AssertFailure (lazy ("recursive_args:" ^ PP.ppterm ~subst + ~metasenv ~context:[] t))) + +and get_new_safes ~subst (context, recfuns, x as k) p rl = + match R.whd ~subst context p, rl with + | C.Lambda (name,so,ta), b::tl -> + let recfuns = (if b then [0,Safe] else []) @ recfuns in + get_new_safes ~subst + (shift_k (name,(C.Decl so)) (context, recfuns, x)) ta tl + | C.Meta _ as e, _ | e, [] -> e, k + | _ -> raise (AssertFailure (lazy "Ill formed pattern")) + +and is_really_smaller + r_uri r_len ~subst ~metasenv (context, recfuns, x as k) te += + match R.whd ~subst context te with + | C.Rel m when is_safe m recfuns -> true + | C.Lambda (name, s, t) -> + is_really_smaller r_uri r_len ~subst ~metasenv (shift_k (name,C.Decl s) k) t + | C.Appl (he::_) -> + is_really_smaller r_uri r_len ~subst ~metasenv k he + | C.Rel _ + | C.Const (Ref.Ref (_,Ref.Con _)) -> false + | C.Appl [] + | C.Const (Ref.Ref (_,Ref.Fix _)) -> assert false + | C.Meta _ -> true + | C.Match (Ref.Ref (_,Ref.Ind (isinductive,_,_)),_,term,pl) -> + (match term with + | C.Rel m | C.Appl (C.Rel m :: _ ) when is_safe m recfuns || m = x -> + if not isinductive then + List.for_all (is_really_smaller r_uri r_len ~subst ~metasenv k) pl + else + let ty = typeof ~subst ~metasenv context term in + let dc_ctx, dcl, start, stop = + specialize_and_abstract_constrs ~subst r_uri r_len context ty in + List.for_all2 + (fun p (_,dc) -> + let rl = recursive_args ~subst ~metasenv dc_ctx start stop dc in + let e, k = get_new_safes ~subst k p rl in + is_really_smaller r_uri r_len ~subst ~metasenv k e) + pl dcl + | _ -> List.for_all (is_really_smaller r_uri r_len ~subst ~metasenv k) pl) + | _ -> assert false + +and returns_a_coinductive ~subst context ty = + match R.whd ~subst context ty with + | C.Const (Ref.Ref (uri,Ref.Ind (false,_,_)) as ref) + | C.Appl (C.Const (Ref.Ref (uri,Ref.Ind (false,_,_)) as ref)::_) -> + let _, _, itl, _, _ = E.get_checked_indtys ref in + Some (uri,List.length itl) + | C.Prod (n,so,de) -> + returns_a_coinductive ~subst ((n,C.Decl so)::context) de + | _ -> None + +and type_of_constant ((Ref.Ref (uri,_)) as ref) = + let error () = + raise (TypeCheckerFailure (lazy "Inconsistent cached infos in reference")) + in + match E.get_checked_obj uri, ref with + | (_,_,_,_,C.Inductive(isind1,lno1,tl,_)),Ref.Ref(_,Ref.Ind (isind2,i,lno2))-> + if isind1 <> isind2 || lno1 <> lno2 then error (); + let _,_,arity,_ = List.nth tl i in arity + | (_,_,_,_,C.Inductive (_,lno1,tl,_)), Ref.Ref (_,Ref.Con (i,j,lno2)) -> + if lno1 <> lno2 then error (); + let _,_,_,cl = List.nth tl i in + let _,_,arity = List.nth cl (j-1) in + arity + | (_,_,_,_,C.Fixpoint (false,fl,_)), Ref.Ref (_,Ref.CoFix i) -> + let _,_,_,arity,_ = List.nth fl i in + arity + | (_,h1,_,_,C.Fixpoint (true,fl,_)), Ref.Ref (_,Ref.Fix (i,recno2,h2)) -> + let _,_,recno1,arity,_ = List.nth fl i in + if h1 <> h2 || recno1 <> recno2 then error (); + arity + | (_,_,_,_,C.Constant (_,_,None,ty,_)), Ref.Ref (_,Ref.Decl) -> ty + | (_,h1,_,_,C.Constant (_,_,Some _,ty,_)), Ref.Ref (_,Ref.Def h2) -> + if h1 <> h2 then error (); + ty + | _ -> + raise (AssertFailure + (lazy ("type_of_constant: environment/reference: " ^ + Ref.string_of_reference ref))) + +and get_relevance ~metasenv ~subst context t args = + let ty = typeof ~subst ~metasenv context t in + let rec aux context ty = function + | [] -> [] + | arg::tl -> match R.whd ~subst context ty with + | C.Prod (_,so,de) -> + let sort = typeof ~subst ~metasenv context so in + let new_ty = S.subst ~avoid_beta_redexes:true arg de in + (*prerr_endline ("so: " ^ PP.ppterm ~subst ~metasenv:[] + ~context so); + prerr_endline ("sort: " ^ PP.ppterm ~subst ~metasenv:[] + ~context sort);*) + (match R.whd ~subst context sort with + | C.Sort C.Prop -> + false::(aux context new_ty tl) + | C.Sort _ + | C.Meta _ -> true::(aux context new_ty tl) + | _ -> raise (TypeCheckerFailure (lazy (Printf.sprintf + "Prod: the type %s of the source of %s is not a sort" + (PP.ppterm ~subst ~metasenv ~context sort) + (PP.ppterm ~subst ~metasenv ~context so))))) + | _ -> + raise + (TypeCheckerFailure + (lazy (Printf.sprintf + "Appl: %s is not a function, it cannot be applied" + (PP.ppterm ~subst ~metasenv ~context + (let res = List.length tl in + let eaten = List.length args - res in + (C.Appl + (t::fst + (HExtlib.split_nth eaten args)))))))) + in aux context ty args +;; + +let typecheck_context ~metasenv ~subst context = + ignore + (List.fold_right + (fun d context -> + begin + match d with + _,C.Decl t -> ignore (typeof ~metasenv ~subst:[] context t) + | name,C.Def (te,ty) -> + ignore (typeof ~metasenv ~subst:[] context ty); + let ty' = typeof ~metasenv ~subst:[] context te in + if not (R.are_convertible ~metasenv ~subst context ty' ty) then + raise (AssertFailure (lazy (Printf.sprintf ( + "the type of the definiens for %s in the context is not "^^ + "convertible with the declared one.\n"^^ + "inferred type:\n%s\nexpected type:\n%s") + name (PP.ppterm ~subst ~metasenv ~context ty') + (PP.ppterm ~subst ~metasenv ~context ty)))) + end; + d::context + ) context []) +;; + +let typecheck_metasenv metasenv = + ignore + (List.fold_left + (fun metasenv (i,(_,context,ty) as conj) -> + if List.mem_assoc i metasenv then + raise (TypeCheckerFailure (lazy ("duplicate meta " ^ string_of_int i ^ + " in metasenv"))); + typecheck_context ~metasenv ~subst:[] context; + ignore (typeof ~metasenv ~subst:[] context ty); + metasenv @ [conj] + ) [] metasenv) +;; + +let typecheck_subst ~metasenv subst = + ignore + (List.fold_left + (fun subst (i,(_,context,ty,bo) as conj) -> + if List.mem_assoc i subst then + raise (AssertFailure (lazy ("duplicate meta " ^ string_of_int i ^ + " in substitution"))); + if List.mem_assoc i metasenv then + raise (AssertFailure (lazy ("meta " ^ string_of_int i ^ + " is both in the metasenv and in the substitution"))); + typecheck_context ~metasenv ~subst context; + ignore (typeof ~metasenv ~subst context ty); + let ty' = typeof ~metasenv ~subst context bo in + if not (R.are_convertible ~metasenv ~subst context ty' ty) then + raise (AssertFailure (lazy (Printf.sprintf ( + "the type of the definiens for %d in the substitution is not "^^ + "convertible with the declared one.\n"^^ + "inferred type:\n%s\nexpected type:\n%s") + i + (PP.ppterm ~subst ~metasenv ~context ty') + (PP.ppterm ~subst ~metasenv ~context ty)))); + subst @ [conj] + ) [] subst) +;; + +let height_of_term tl = + let h = ref 0 in + let get_height (NReference.Ref (uri,_)) = + let _,height,_,_,_ = NCicEnvironment.get_checked_obj uri in + height in + let rec aux = + function + NCic.Meta (_,(_,NCic.Ctx l)) -> List.iter aux l + | NCic.Meta _ -> () + | NCic.Rel _ + | NCic.Sort _ -> () + | NCic.Implicit _ -> assert false + | NCic.Const nref -> h := max !h (get_height nref) + | NCic.Prod (_,t1,t2) + | NCic.Lambda (_,t1,t2) -> aux t1; aux t2 + | NCic.LetIn (_,s,ty,t) -> aux s; aux ty; aux t + | NCic.Appl l -> List.iter aux l + | NCic.Match (_,outty,t,pl) -> aux outty; aux t; List.iter aux pl + in + List.iter aux tl; + 1 + !h +;; + +let height_of_obj_kind uri ~subst = + function + NCic.Inductive _ + | NCic.Constant (_,_,None,_,_) + | NCic.Fixpoint (false,_,_) -> 0 + | NCic.Fixpoint (true,ifl,_) -> + let iflno = List.length ifl in + height_of_term + (List.fold_left + (fun l (_,_,_,ty,bo) -> + let bo = debruijn uri iflno [] ~subst bo in + ty::bo::l + ) [] ifl) + | NCic.Constant (_,_,Some bo,ty,_) -> height_of_term [bo;ty] +;; + +let typecheck_obj (uri,height,metasenv,subst,kind) = +(*height must be checked since it is not only an optimization during reduction*) + let iheight = height_of_obj_kind uri ~subst kind in + if height <> iheight then + raise (TypeCheckerFailure (lazy (Printf.sprintf + "the declared object height (%d) is not the inferred one (%d)" + height iheight))); + typecheck_metasenv metasenv; + typecheck_subst ~metasenv subst; + match kind with + | C.Constant (relevance,_,Some te,ty,_) -> + let _ = typeof ~subst ~metasenv [] ty in + let ty_te = typeof ~subst ~metasenv [] te in + if not (R.are_convertible ~metasenv ~subst [] ty_te ty) then + raise (TypeCheckerFailure (lazy (Printf.sprintf ( + "the type of the body is not convertible with the declared one.\n"^^ + "inferred type:\n%s\nexpected type:\n%s") + (PP.ppterm ~subst ~metasenv ~context:[] ty_te) + (PP.ppterm ~subst ~metasenv ~context:[] ty)))); + check_relevance ~subst ~metasenv [] relevance ty + (*check_relevance ~in_type:false ~subst ~metasenv relevance te*) + | C.Constant (relevance,_,None,ty,_) -> + ignore (typeof ~subst ~metasenv [] ty); + check_relevance ~subst ~metasenv [] relevance ty + | C.Inductive (_, leftno, tyl, _) -> + check_mutual_inductive_defs uri ~metasenv ~subst leftno tyl + | C.Fixpoint (inductive,fl,_) -> + let types, kl = + List.fold_left + (fun (types,kl) (relevance,name,k,ty,_) -> + let _ = typeof ~subst ~metasenv [] ty in + check_relevance ~subst ~metasenv [] relevance ty; + ((name,C.Decl ty)::types, k::kl) + ) ([],[]) fl + in + let len = List.length types in + let dfl, kl = + List.split (List.map2 + (fun (_,_,_,_,bo) rno -> + let dbo = debruijn uri len [] ~subst bo in + dbo, Evil rno) + fl kl) + in + List.iter2 (fun (_,_,x,ty,_) bo -> + let ty_bo = typeof ~subst ~metasenv types bo in + if not (R.are_convertible ~metasenv ~subst types ty_bo ty) + then raise (TypeCheckerFailure (lazy ("(Co)Fix: ill-typed bodies"))) + else + if inductive then begin + let m, context = eat_lambdas ~subst ~metasenv types (x + 1) bo in + let r_uri, r_len = + let he = + match List.hd context with _,C.Decl t -> t | _ -> assert false + in + match R.whd ~subst (List.tl context) he with + | C.Const (Ref.Ref (uri,Ref.Ind _) as ref) + | C.Appl (C.Const (Ref.Ref (uri,Ref.Ind _) as ref) :: _) -> + let _,_,itl,_,_ = E.get_checked_indtys ref in + uri, List.length itl + | _ -> assert false + in + (* guarded by destructors conditions D{f,k,x,M} *) + let rec enum_from k = + function [] -> [] | v::tl -> (k,v)::enum_from (k+1) tl + in + guarded_by_destructors r_uri r_len + ~subst ~metasenv context (enum_from (x+2) kl) m + end else + match returns_a_coinductive ~subst [] ty with + | None -> + raise (TypeCheckerFailure + (lazy "CoFix: does not return a coinductive type")) + | Some (r_uri, r_len) -> + (* guarded by constructors conditions C{f,M} *) + if not + (guarded_by_constructors ~subst ~metasenv types bo r_uri r_len len) + then + raise (TypeCheckerFailure + (lazy "CoFix: not guarded by constructors")) + ) fl dfl +;; + +(* trust *) + +let trust = ref (fun _ -> false);; +let set_trust f = trust := f +let trust_obj obj = !trust obj + + +(* web interface stuff *) + +let logger = + ref (function (`Start_type_checking _|`Type_checking_completed _|`Type_checking_interrupted _|`Type_checking_failed _|`Trust_obj _) -> ()) +;; + +let set_logger f = logger := f;; + +let typecheck_obj obj = + let u,_,_,_,_ = obj in + try + !logger (`Start_type_checking u); + typecheck_obj obj; + !logger (`Type_checking_completed u) + with + Sys.Break as e -> + !logger (`Type_checking_interrupted u); + raise e + | e -> + !logger (`Type_checking_failed u); + raise e +;; + +E.set_typecheck_obj + (fun obj -> + if trust_obj obj then + let u,_,_,_,_ = obj in + !logger (`Trust_obj u) + else + typecheck_obj obj) +;; + +let _ = NCicReduction.set_get_relevance get_relevance;; + + +let indent = ref 0;; +let debug = true;; +let logger = + let do_indent () = String.make !indent ' ' in + (function + | `Start_type_checking s -> + if debug then + prerr_endline (do_indent () ^ "Start: " ^ NUri.string_of_uri s); + incr indent + | `Type_checking_completed s -> + decr indent; + if debug then + prerr_endline (do_indent () ^ "End: " ^ NUri.string_of_uri s) + | `Type_checking_interrupted s -> + decr indent; + if debug then + prerr_endline (do_indent () ^ "Break: " ^ NUri.string_of_uri s) + | `Type_checking_failed s -> + decr indent; + if debug then + prerr_endline (do_indent () ^ "Fail: " ^ NUri.string_of_uri s) + | `Trust_obj s -> + if debug then + prerr_endline (do_indent () ^ "Trust: " ^ NUri.string_of_uri s)) +;; +(* let _ = set_logger logger ;; *) +(* EOF *)