X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=components%2Fcic_proof_checking%2FcicTypeChecker.ml;fp=components%2Fcic_proof_checking%2FcicTypeChecker.ml;h=44cf6d24ad1c03bda2f5a61605fb092b4537a3c9;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/components/cic_proof_checking/cicTypeChecker.ml b/components/cic_proof_checking/cicTypeChecker.ml new file mode 100644 index 000000000..44cf6d24a --- /dev/null +++ b/components/cic_proof_checking/cicTypeChecker.ml @@ -0,0 +1,2181 @@ +(* Copyright (C) 2000, HELM Team. + * + * This file is part of HELM, an Hypertextual, Electronic + * Library of Mathematics, developed at the Computer Science + * Department, University of Bologna, Italy. + * + * HELM is free software; you can redistribute it and/or + * modify it under the terms of the GNU General Public License + * as published by the Free Software Foundation; either version 2 + * of the License, or (at your option) any later version. + * + * HELM is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with HELM; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, + * MA 02111-1307, USA. + * + * For details, see the HELM World-Wide-Web page, + * http://cs.unibo.it/helm/. + *) + +(* $Id$ *) + +(* TODO factorize functions to frequent errors (e.g. "Unknwon mutual inductive + * ...") *) + +open Printf + +exception AssertFailure of string Lazy.t;; +exception TypeCheckerFailure of string Lazy.t;; + +let fdebug = ref 0;; +let debug t context = + let rec debug_aux t i = + let module C = Cic in + let module U = UriManager in + CicPp.ppobj (C.Variable ("DEBUG", None, t, [], [])) ^ "\n" ^ i + in + if !fdebug = 0 then + raise (TypeCheckerFailure (lazy (List.fold_right debug_aux (t::context) ""))) +;; + +let debug_print = fun _ -> ();; + +let rec split l n = + match (l,n) with + (l,0) -> ([], l) + | (he::tl, n) -> let (l1,l2) = split tl (n-1) in (he::l1,l2) + | (_,_) -> + raise (TypeCheckerFailure (lazy "Parameters number < left parameters number")) +;; + +(* XXX: bug *) +let ugraph_convertibility ug1 ug2 ul2 = true;; + +let check_and_clean_ugraph inferred_ugraph unchecked_ugraph uri obj = + match unchecked_ugraph with + | Some (ug,ul) -> + if not (ugraph_convertibility inferred_ugraph ug ul) then + raise (TypeCheckerFailure (lazy + ("inferred univ graph not equal with declared ugraph"))) + else + ug,ul,obj + | None -> + CicUnivUtils.clean_and_fill uri obj inferred_ugraph +;; + +let debrujin_constructor ?(cb=fun _ _ -> ()) ?(check_exp_named_subst=true) uri number_of_types context = + let rec aux k t = + let module C = Cic in + let res = + match t with + C.Rel n as t when n <= k -> t + | C.Rel _ -> + raise (TypeCheckerFailure (lazy "unbound variable found in constructor type")) + | C.Var (uri,exp_named_subst) -> + let exp_named_subst' = + List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst + in + C.Var (uri,exp_named_subst') + | C.Meta (i,l) -> + let l' = List.map (function None -> None | Some t -> Some (aux k t)) l in + C.Meta (i,l') + | C.Sort _ + | C.Implicit _ as t -> t + | C.Cast (te,ty) -> C.Cast (aux k te, aux k ty) + | C.Prod (n,s,t) -> C.Prod (n, aux k s, aux (k+1) t) + | C.Lambda (n,s,t) -> C.Lambda (n, aux k s, aux (k+1) t) + | C.LetIn (n,s,ty,t) -> C.LetIn (n, aux k s, aux k ty, aux (k+1) t) + | C.Appl l -> C.Appl (List.map (aux k) l) + | C.Const (uri,exp_named_subst) -> + let exp_named_subst' = + List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst + in + C.Const (uri,exp_named_subst') + | C.MutInd (uri',tyno,exp_named_subst) when UriManager.eq uri uri' -> + if check_exp_named_subst && exp_named_subst != [] then + raise (TypeCheckerFailure + (lazy ("non-empty explicit named substitution is applied to "^ + "a mutual inductive type which is being defined"))) ; + C.Rel (k + number_of_types - tyno) ; + | C.MutInd (uri',tyno,exp_named_subst) -> + let exp_named_subst' = + List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst + in + C.MutInd (uri',tyno,exp_named_subst') + | C.MutConstruct (uri,tyno,consno,exp_named_subst) -> + let exp_named_subst' = + List.map (function (uri,t) -> (uri,aux k t)) exp_named_subst + in + C.MutConstruct (uri,tyno,consno,exp_named_subst') + | C.MutCase (sp,i,outty,t,pl) -> + C.MutCase (sp, i, aux k outty, aux k t, + List.map (aux k) pl) + | C.Fix (i, fl) -> + let len = List.length fl in + let liftedfl = + List.map + (fun (name, i, ty, bo) -> (name, i, aux k ty, aux (k+len) bo)) + fl + in + C.Fix (i, liftedfl) + | C.CoFix (i, fl) -> + let len = List.length fl in + let liftedfl = + List.map + (fun (name, ty, bo) -> (name, aux k ty, aux (k+len) bo)) + fl + in + C.CoFix (i, liftedfl) + in + cb t res; + res + in + aux (List.length context) +;; + +exception CicEnvironmentError;; + +let rec type_of_constant ~logger uri orig_ugraph = + let module C = Cic in + let module R = CicReduction in + let module U = UriManager in + let cobj,ugraph = + match CicEnvironment.is_type_checked ~trust:true orig_ugraph uri with + CicEnvironment.CheckedObj (cobj,ugraph') -> cobj,ugraph' + | CicEnvironment.UncheckedObj (uobj,unchecked_ugraph) -> + logger#log (`Start_type_checking uri) ; + (* let's typecheck the uncooked obj *) + let inferred_ugraph = + match uobj with + C.Constant (_,Some te,ty,_,_) -> + let _,ugraph = type_of ~logger ty CicUniv.empty_ugraph in + let type_of_te,ugraph = type_of ~logger te ugraph in + let b,ugraph = R.are_convertible [] type_of_te ty ugraph in + if not b then + raise (TypeCheckerFailure (lazy (sprintf + "the constant %s is not well typed because the type %s of the body is not convertible to the declared type %s" + (U.string_of_uri uri) (CicPp.ppterm type_of_te) + (CicPp.ppterm ty)))) + else + ugraph + | C.Constant (_,None,ty,_,_) -> + (* only to check that ty is well-typed *) + let _,ugraph = type_of ~logger ty CicUniv.empty_ugraph in + ugraph + | C.CurrentProof (_,conjs,te,ty,_,_) -> + let _,ugraph = + List.fold_left + (fun (metasenv,ugraph) ((_,context,ty) as conj) -> + let _,ugraph = + type_of_aux' ~logger metasenv context ty ugraph + in + (metasenv @ [conj],ugraph) + ) ([],CicUniv.empty_ugraph) conjs + in + let _,ugraph = type_of_aux' ~logger conjs [] ty ugraph in + let type_of_te,ugraph = type_of_aux' ~logger conjs [] te ugraph in + let b,ugraph = R.are_convertible [] type_of_te ty ugraph in + if not b then + raise (TypeCheckerFailure (lazy (sprintf + "the current proof %s is not well typed because the type %s of the body is not convertible to the declared type %s" + (U.string_of_uri uri) (CicPp.ppterm type_of_te) + (CicPp.ppterm ty)))) + else + ugraph + | _ -> + raise + (TypeCheckerFailure (lazy ("Unknown constant:" ^ U.string_of_uri uri))) + in + let ugraph, ul, obj = check_and_clean_ugraph inferred_ugraph unchecked_ugraph uri uobj in + CicEnvironment.set_type_checking_info uri (obj, ugraph, ul); + logger#log (`Type_checking_completed uri) ; + match CicEnvironment.is_type_checked ~trust:false orig_ugraph uri with + CicEnvironment.CheckedObj (cobj,ugraph') -> cobj,ugraph' + | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError + in + match cobj,ugraph with + (C.Constant (_,_,ty,_,_)),g -> ty,g + | (C.CurrentProof (_,_,_,ty,_,_)),g -> ty,g + | _ -> + raise (TypeCheckerFailure (lazy ("Unknown constant:" ^ U.string_of_uri uri))) + +and type_of_variable ~logger uri orig_ugraph = + let module C = Cic in + let module R = CicReduction in + let module U = UriManager in + (* 0 because a variable is never cooked => no partial cooking at one level *) + match CicEnvironment.is_type_checked ~trust:true orig_ugraph uri with + | CicEnvironment.CheckedObj ((C.Variable (_,_,ty,_,_)),ugraph') -> ty,ugraph' + | CicEnvironment.UncheckedObj + (C.Variable (_,bo,ty,_,_) as uobj, unchecked_ugraph) + -> + logger#log (`Start_type_checking uri) ; + (* only to check that ty is well-typed *) + let _,ugraph = type_of ~logger ty CicUniv.empty_ugraph in + let inferred_ugraph = + match bo with + None -> ugraph + | Some bo -> + let ty_bo,ugraph = type_of ~logger bo ugraph in + let b,ugraph = R.are_convertible [] ty_bo ty ugraph in + if not b then + raise (TypeCheckerFailure + (lazy ("Unknown variable:" ^ U.string_of_uri uri))) + else + ugraph + in + let ugraph, ul, obj = + check_and_clean_ugraph inferred_ugraph unchecked_ugraph uri uobj + in + CicEnvironment.set_type_checking_info uri (obj, ugraph, ul); + logger#log (`Type_checking_completed uri) ; + (match CicEnvironment.is_type_checked ~trust:false orig_ugraph uri with + CicEnvironment.CheckedObj((C.Variable(_,_,ty,_,_)),ugraph)->ty,ugraph + | CicEnvironment.CheckedObj _ + | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError) + | _ -> + raise (TypeCheckerFailure (lazy + ("Unknown variable:" ^ U.string_of_uri uri))) + +and does_not_occur ?(subst=[]) context n nn te = + let module C = Cic in + match te with + C.Rel m when m > n && m <= nn -> false + | C.Rel m -> + (try + (match List.nth context (m-1) with + Some (_,C.Def (bo,_)) -> + does_not_occur ~subst context n nn (CicSubstitution.lift m bo) + | _ -> true) + with + Failure _ -> assert false) + | C.Sort _ + | C.Implicit _ -> true + | C.Meta (mno,l) -> + List.fold_right + (fun x i -> + match x with + None -> i + | Some x -> i && does_not_occur ~subst context n nn x) l true && + (try + let (canonical_context,term,ty) = CicUtil.lookup_subst mno subst in + does_not_occur ~subst context n nn (CicSubstitution.subst_meta l term) + with + CicUtil.Subst_not_found _ -> true) + | C.Cast (te,ty) -> + does_not_occur ~subst context n nn te && + does_not_occur ~subst context n nn ty + | C.Prod (name,so,dest) -> + does_not_occur ~subst context n nn so && + does_not_occur ~subst ((Some (name,(C.Decl so)))::context) (n + 1) + (nn + 1) dest + | C.Lambda (name,so,dest) -> + does_not_occur ~subst context n nn so && + does_not_occur ~subst ((Some (name,(C.Decl so)))::context) (n+1) (nn+1) + dest + | C.LetIn (name,so,ty,dest) -> + does_not_occur ~subst context n nn so && + does_not_occur ~subst context n nn ty && + does_not_occur ~subst ((Some (name,(C.Def (so,ty))))::context) + (n + 1) (nn + 1) dest + | C.Appl l -> + List.for_all (does_not_occur ~subst context n nn) l + | C.Var (_,exp_named_subst) + | C.Const (_,exp_named_subst) + | C.MutInd (_,_,exp_named_subst) + | C.MutConstruct (_,_,_,exp_named_subst) -> + List.for_all (fun (_,x) -> does_not_occur ~subst context n nn x) + exp_named_subst + | C.MutCase (_,_,out,te,pl) -> + does_not_occur ~subst context n nn out && + does_not_occur ~subst context n nn te && + List.for_all (does_not_occur ~subst context n nn) pl + | C.Fix (_,fl) -> + let len = List.length fl in + let n_plus_len = n + len in + let nn_plus_len = nn + len in + let tys,_ = + List.fold_left + (fun (types,len) (n,_,ty,_) -> + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, + len+1) + ) ([],0) fl + in + List.fold_right + (fun (_,_,ty,bo) i -> + i && does_not_occur ~subst context n nn ty && + does_not_occur ~subst (tys @ context) n_plus_len nn_plus_len bo + ) fl true + | C.CoFix (_,fl) -> + let len = List.length fl in + let n_plus_len = n + len in + let nn_plus_len = nn + len in + let tys,_ = + List.fold_left + (fun (types,len) (n,ty,_) -> + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, + len+1) + ) ([],0) fl + in + List.fold_right + (fun (_,ty,bo) i -> + i && does_not_occur ~subst context n nn ty && + does_not_occur ~subst (tys @ context) n_plus_len nn_plus_len bo + ) fl true + +(*CSC l'indice x dei tipi induttivi e' t.c. n < x <= nn *) +(*CSC questa funzione e' simile alla are_all_occurrences_positive, ma fa *) +(*CSC dei controlli leggermente diversi. Viene invocata solamente dalla *) +(*CSC strictly_positive *) +(*CSC definizione (giusta???) tratta dalla mail di Hugo ;-) *) +and weakly_positive context n nn uri te = + let module C = Cic in +(*CSC: Che schifo! Bisogna capire meglio e trovare una soluzione ragionevole!*) + let dummy_mutind = + C.MutInd (HelmLibraryObjects.Datatypes.nat_URI,0,[]) + in + (*CSC: mettere in cicSubstitution *) + let rec subst_inductive_type_with_dummy_mutind = + function + C.MutInd (uri',0,_) when UriManager.eq uri' uri -> + dummy_mutind + | C.Appl ((C.MutInd (uri',0,_))::tl) when UriManager.eq uri' uri -> + dummy_mutind + | C.Cast (te,ty) -> subst_inductive_type_with_dummy_mutind te + | C.Prod (name,so,ta) -> + C.Prod (name, subst_inductive_type_with_dummy_mutind so, + subst_inductive_type_with_dummy_mutind ta) + | C.Lambda (name,so,ta) -> + C.Lambda (name, subst_inductive_type_with_dummy_mutind so, + subst_inductive_type_with_dummy_mutind ta) + | C.LetIn (name,so,ty,ta) -> + C.LetIn (name, subst_inductive_type_with_dummy_mutind so, + subst_inductive_type_with_dummy_mutind ty, + subst_inductive_type_with_dummy_mutind ta) + | C.Appl tl -> + C.Appl (List.map subst_inductive_type_with_dummy_mutind tl) + | C.MutCase (uri,i,outtype,term,pl) -> + C.MutCase (uri,i, + subst_inductive_type_with_dummy_mutind outtype, + subst_inductive_type_with_dummy_mutind term, + List.map subst_inductive_type_with_dummy_mutind pl) + | C.Fix (i,fl) -> + C.Fix (i,List.map (fun (name,i,ty,bo) -> (name,i, + subst_inductive_type_with_dummy_mutind ty, + subst_inductive_type_with_dummy_mutind bo)) fl) + | C.CoFix (i,fl) -> + C.CoFix (i,List.map (fun (name,ty,bo) -> (name, + subst_inductive_type_with_dummy_mutind ty, + subst_inductive_type_with_dummy_mutind bo)) fl) + | C.Const (uri,exp_named_subst) -> + let exp_named_subst' = + List.map + (function (uri,t) -> (uri,subst_inductive_type_with_dummy_mutind t)) + exp_named_subst + in + C.Const (uri,exp_named_subst') + | C.Var (uri,exp_named_subst) -> + let exp_named_subst' = + List.map + (function (uri,t) -> (uri,subst_inductive_type_with_dummy_mutind t)) + exp_named_subst + in + C.Var (uri,exp_named_subst') + | C.MutInd (uri,typeno,exp_named_subst) -> + let exp_named_subst' = + List.map + (function (uri,t) -> (uri,subst_inductive_type_with_dummy_mutind t)) + exp_named_subst + in + C.MutInd (uri,typeno,exp_named_subst') + | C.MutConstruct (uri,typeno,consno,exp_named_subst) -> + let exp_named_subst' = + List.map + (function (uri,t) -> (uri,subst_inductive_type_with_dummy_mutind t)) + exp_named_subst + in + C.MutConstruct (uri,typeno,consno,exp_named_subst') + | t -> t + in + match CicReduction.whd context te with +(* + C.Appl ((C.MutInd (uri',0,_))::tl) when UriManager.eq uri' uri -> true +*) + C.Appl ((C.MutInd (uri',_,_))::tl) when UriManager.eq uri' uri -> true + | C.MutInd (uri',0,_) when UriManager.eq uri' uri -> true + | C.Prod (name,source,dest) when + does_not_occur ((Some (name,(C.Decl source)))::context) 0 1 dest -> + (* dummy abstraction, so we behave as in the anonimous case *) + strictly_positive context n nn + (subst_inductive_type_with_dummy_mutind source) && + weakly_positive ((Some (name,(C.Decl source)))::context) + (n + 1) (nn + 1) uri dest + | C.Prod (name,source,dest) -> + does_not_occur context n nn + (subst_inductive_type_with_dummy_mutind source)&& + weakly_positive ((Some (name,(C.Decl source)))::context) + (n + 1) (nn + 1) uri dest + | _ -> + raise (TypeCheckerFailure (lazy "Malformed inductive constructor type")) + +(* instantiate_parameters ps (x1:T1)...(xn:Tn)C *) +(* returns ((x_|ps|:T_|ps|)...(xn:Tn)C){ps_1 / x1 ; ... ; ps_|ps| / x_|ps|} *) +and instantiate_parameters params c = + let module C = Cic in + match (c,params) with + (c,[]) -> c + | (C.Prod (_,_,ta), he::tl) -> + instantiate_parameters tl + (CicSubstitution.subst he ta) + | (C.Cast (te,_), _) -> instantiate_parameters params te + | (t,l) -> raise (AssertFailure (lazy "1")) + +and strictly_positive context n nn te = + let module C = Cic in + let module U = UriManager in + match CicReduction.whd context te with + | t when does_not_occur context n nn t -> true + | C.Rel _ -> true + | C.Cast (te,ty) -> + (*CSC: bisogna controllare ty????*) + strictly_positive context n nn te + | C.Prod (name,so,ta) -> + does_not_occur context n nn so && + strictly_positive ((Some (name,(C.Decl so)))::context) (n+1) (nn+1) ta + | C.Appl ((C.Rel m)::tl) when m > n && m <= nn -> + List.fold_right (fun x i -> i && does_not_occur context n nn x) tl true + | C.Appl ((C.MutInd (uri,i,exp_named_subst))::_) + | (C.MutInd (uri,i,exp_named_subst)) as t -> + let tl = match t with C.Appl (_::tl) -> tl | _ -> [] in + let (ok,paramsno,ity,cl,name) = + let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in + match o with + C.InductiveDefinition (tl,_,paramsno,_) -> + let (name,_,ity,cl) = List.nth tl i in + (List.length tl = 1, paramsno, ity, cl, name) + (* (true, paramsno, ity, cl, name) *) + | _ -> + raise + (TypeCheckerFailure + (lazy ("Unknown inductive type:" ^ U.string_of_uri uri))) + in + let (params,arguments) = split tl paramsno in + let lifted_params = List.map (CicSubstitution.lift 1) params in + let cl' = + List.map + (fun (_,te) -> + instantiate_parameters lifted_params + (CicSubstitution.subst_vars exp_named_subst te) + ) cl + in + ok && + List.fold_right + (fun x i -> i && does_not_occur context n nn x) + arguments true && + List.fold_right + (fun x i -> + i && + weakly_positive + ((Some (C.Name name,(Cic.Decl ity)))::context) (n+1) (nn+1) uri + x + ) cl' true + | t -> false + +(* the inductive type indexes are s.t. n < x <= nn *) +and are_all_occurrences_positive context uri indparamsno i n nn te = + let module C = Cic in + match CicReduction.whd context te with + C.Appl ((C.Rel m)::tl) when m = i -> + (*CSC: riscrivere fermandosi a 0 *) + (* let's check if the inductive type is applied at least to *) + (* indparamsno parameters *) + let last = + List.fold_left + (fun k x -> + if k = 0 then 0 + else + match CicReduction.whd context x with + C.Rel m when m = n - (indparamsno - k) -> k - 1 + | _ -> + raise (TypeCheckerFailure + (lazy + ("Non-positive occurence in mutual inductive definition(s) [1]" ^ + UriManager.string_of_uri uri))) + ) indparamsno tl + in + if last = 0 then + List.fold_right (fun x i -> i && does_not_occur context n nn x) tl true + else + raise (TypeCheckerFailure + (lazy ("Non-positive occurence in mutual inductive definition(s) [2]"^ + UriManager.string_of_uri uri))) + | C.Rel m when m = i -> + if indparamsno = 0 then + true + else + raise (TypeCheckerFailure + (lazy ("Non-positive occurence in mutual inductive definition(s) [3]"^ + UriManager.string_of_uri uri))) + | C.Prod (name,source,dest) when + does_not_occur ((Some (name,(C.Decl source)))::context) 0 1 dest -> + (* dummy abstraction, so we behave as in the anonimous case *) + strictly_positive context n nn source && + are_all_occurrences_positive + ((Some (name,(C.Decl source)))::context) uri indparamsno + (i+1) (n + 1) (nn + 1) dest + | C.Prod (name,source,dest) -> + does_not_occur context n nn source && + are_all_occurrences_positive ((Some (name,(C.Decl source)))::context) + uri indparamsno (i+1) (n + 1) (nn + 1) dest + | _ -> + raise + (TypeCheckerFailure (lazy ("Malformed inductive constructor type " ^ + (UriManager.string_of_uri uri)))) + +(* Main function to checks the correctness of a mutual *) +(* inductive block definition. This is the function *) +(* exported to the proof-engine. *) +and typecheck_mutual_inductive_defs ~logger uri (itl,_,indparamsno) ugraph = + let module U = UriManager in + (* let's check if the arity of the inductive types are well *) + (* formed *) + let ugrap1 = List.fold_left + (fun ugraph (_,_,x,_) -> let _,ugraph' = + type_of ~logger x ugraph in ugraph') + ugraph itl in + + (* let's check if the types of the inductive constructors *) + (* are well formed. *) + (* In order not to use type_of_aux we put the types of the *) + (* mutual inductive types at the head of the types of the *) + (* constructors using Prods *) + let len = List.length itl in + let tys = + List.map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) itl in + let _,ugraph2 = + List.fold_right + (fun (_,_,_,cl) (i,ugraph) -> + let ugraph'' = + List.fold_left + (fun ugraph (name,te) -> + let debrujinedte = debrujin_constructor uri len [] te in + let augmented_term = + List.fold_right + (fun (name,_,ty,_) i -> Cic.Prod (Cic.Name name, ty, i)) + itl debrujinedte + in + let _,ugraph' = type_of ~logger augmented_term ugraph in + (* let's check also the positivity conditions *) + if + not + (are_all_occurrences_positive tys uri indparamsno i 0 len + debrujinedte) + then + begin + prerr_endline (UriManager.string_of_uri uri); + prerr_endline (string_of_int (List.length tys)); + raise + (TypeCheckerFailure + (lazy ("Non positive occurence in " ^ U.string_of_uri uri))) end + else + ugraph' + ) ugraph cl in + (i + 1),ugraph'' + ) itl (1,ugrap1) + in + ugraph2 + +(* Main function to checks the correctness of a mutual *) +(* inductive block definition. *) +and check_mutual_inductive_defs uri obj ugraph = + match obj with + Cic.InductiveDefinition (itl, params, indparamsno, _) -> + typecheck_mutual_inductive_defs uri (itl,params,indparamsno) ugraph + | _ -> + raise (TypeCheckerFailure ( + lazy ("Unknown mutual inductive definition:" ^ + UriManager.string_of_uri uri))) + +and type_of_mutual_inductive_defs ~logger uri i orig_ugraph = + let module C = Cic in + let module R = CicReduction in + let module U = UriManager in + let cobj,ugraph1 = + match CicEnvironment.is_type_checked ~trust:true orig_ugraph uri with + CicEnvironment.CheckedObj (cobj,ugraph') -> cobj,ugraph' + | CicEnvironment.UncheckedObj (uobj,unchecked_ugraph) -> + logger#log (`Start_type_checking uri) ; + let inferred_ugraph = + check_mutual_inductive_defs ~logger uri uobj CicUniv.empty_ugraph + in + let ugraph, ul, obj = check_and_clean_ugraph inferred_ugraph unchecked_ugraph uri uobj in + CicEnvironment.set_type_checking_info uri (obj,ugraph,ul); + logger#log (`Type_checking_completed uri) ; + (match CicEnvironment.is_type_checked ~trust:false orig_ugraph uri with + CicEnvironment.CheckedObj (cobj,ugraph') -> (cobj,ugraph') + | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError + ) + in + match cobj with + | C.InductiveDefinition (dl,_,_,_) -> + let (_,_,arity,_) = List.nth dl i in + arity,ugraph1 + | _ -> + raise (TypeCheckerFailure + (lazy ("Unknown mutual inductive definition:" ^ U.string_of_uri uri))) + +and type_of_mutual_inductive_constr ~logger uri i j orig_ugraph = + let module C = Cic in + let module R = CicReduction in + let module U = UriManager in + let cobj,ugraph1 = + match CicEnvironment.is_type_checked ~trust:true orig_ugraph uri with + CicEnvironment.CheckedObj (cobj,ugraph') -> cobj,ugraph' + | CicEnvironment.UncheckedObj (uobj,unchecked_ugraph) -> + logger#log (`Start_type_checking uri) ; + let inferred_ugraph = + check_mutual_inductive_defs ~logger uri uobj CicUniv.empty_ugraph + in + let ugraph, ul, obj = check_and_clean_ugraph inferred_ugraph unchecked_ugraph uri uobj in + CicEnvironment.set_type_checking_info uri (obj, ugraph, ul); + logger#log (`Type_checking_completed uri) ; + (match + CicEnvironment.is_type_checked ~trust:false orig_ugraph uri + with + CicEnvironment.CheckedObj (cobj,ugraph') -> cobj,ugraph' + | CicEnvironment.UncheckedObj _ -> + raise CicEnvironmentError) + in + match cobj with + C.InductiveDefinition (dl,_,_,_) -> + let (_,_,_,cl) = List.nth dl i in + let (_,ty) = List.nth cl (j-1) in + ty,ugraph1 + | _ -> + raise (TypeCheckerFailure + (lazy ("Unknown mutual inductive definition:" ^ UriManager.string_of_uri uri))) + +and recursive_args context n nn te = + let module C = Cic in + match CicReduction.whd context te with + C.Rel _ + | C.MutInd _ -> [] + | C.Var _ + | C.Meta _ + | C.Sort _ + | C.Implicit _ + | C.Cast _ (*CSC ??? *) -> + raise (AssertFailure (lazy "3")) (* due to type-checking *) + | C.Prod (name,so,de) -> + (not (does_not_occur context n nn so)) :: + (recursive_args ((Some (name,(C.Decl so)))::context) (n+1) (nn + 1) de) + | C.Lambda _ + | C.LetIn _ -> + raise (AssertFailure (lazy "4")) (* due to type-checking *) + | C.Appl _ -> [] + | C.Const _ -> raise (AssertFailure (lazy "5")) + | C.MutConstruct _ + | C.MutCase _ + | C.Fix _ + | C.CoFix _ -> raise (AssertFailure (lazy "6")) (* due to type-checking *) + +and get_new_safes ~subst context p rl safes n nn x = + let module C = Cic in + let module U = UriManager in + let module R = CicReduction in + match R.whd ~subst context p, rl with + | C.Lambda (name,so,ta), b::tl -> + let safes = List.map (fun x -> x + 1) safes in + let safes = if b then 1::safes else safes in + get_new_safes ~subst ((Some (name,(C.Decl so)))::context) + ta tl safes (n+1) (nn+1) (x+1) + | C.MutConstruct _ as e, _ + | (C.Rel _ as e), _ + | e, [] -> (e,safes,n,nn,x,context) + | p,_::_ -> + raise + (AssertFailure (lazy + (Printf.sprintf "Get New Safes: p=%s" (CicPp.ppterm p)))) + +and split_prods ~subst context n te = + let module C = Cic in + let module R = CicReduction in + match (n, R.whd ~subst context te) with + (0, _) -> context,te + | (n, C.Prod (name,so,ta)) when n > 0 -> + split_prods ~subst ((Some (name,(C.Decl so)))::context) (n - 1) ta + | (_, _) -> raise (AssertFailure (lazy "8")) + +and eat_lambdas ~subst context n te = + let module C = Cic in + let module R = CicReduction in + match (n, R.whd ~subst context te) with + (0, _) -> (te, 0, context) + | (n, C.Lambda (name,so,ta)) when n > 0 -> + let (te, k, context') = + eat_lambdas ~subst ((Some (name,(C.Decl so)))::context) (n - 1) ta + in + (te, k + 1, context') + | (n, te) -> + raise (AssertFailure (lazy (sprintf "9 (%d, %s)" n (CicPp.ppterm te)))) + +and specialize_inductive_type ~logger ~subst ~metasenv context t = + let ty,_= type_of_aux' ~logger ~subst metasenv context t CicUniv.oblivion_ugraph in + match CicReduction.whd ~subst context ty with + | Cic.MutInd (uri,_,exp) + | Cic.Appl (Cic.MutInd (uri,_,exp) :: _) as ty -> + let args = match ty with Cic.Appl (_::tl) -> tl | _ -> [] in + let o,_ = CicEnvironment.get_obj CicUniv.oblivion_ugraph uri in + (match o with + | Cic.InductiveDefinition (tl,_,paramsno,_) -> + let left_args,_ = HExtlib.split_nth paramsno args in + List.map (fun (name, isind, arity, cl) -> + let arity = CicSubstitution.subst_vars exp arity in + let arity = instantiate_parameters left_args arity in + let cl = + List.map + (fun (id,ty) -> + let ty = CicSubstitution.subst_vars exp ty in + id, instantiate_parameters left_args ty) + cl + in + name, isind, arity, cl) + tl + | _ -> assert false) + | _ -> assert false + +and check_is_really_smaller_arg + ~logger ~metasenv ~subst rec_uri rec_uri_len context n nn kl x safes te += + let module C = Cic in + let module U = UriManager in + (*CSC: we could perform beta-iota(-zeta?) immediately, and + delta only on-demand when it fails without *) + match CicReduction.whd ~subst context te with + C.Rel m when List.mem m safes -> true + | C.Rel _ + | C.MutConstruct _ + | C.Const _ + | C.Var _ -> false + | C.Appl (he::_) -> + check_is_really_smaller_arg rec_uri rec_uri_len + ~logger ~metasenv ~subst context n nn kl x safes he + | C.Lambda (name,ty,ta) -> + check_is_really_smaller_arg rec_uri rec_uri_len + ~logger ~metasenv ~subst (Some (name,Cic.Decl ty)::context) + (n+1) (nn+1) kl (x+1) (List.map (fun n -> n+1) safes) ta + | C.MutCase (uri,i,outtype,term,pl) -> + (match term with + | C.Rel m | C.Appl ((C.Rel m)::_) when List.mem m safes || m = x -> + let tys = + specialize_inductive_type ~logger ~subst ~metasenv context term + in + let tys_ctx = + List.map (fun (name,_,ty,_) -> Some (Cic.Name name, Cic.Decl ty)) tys + in + let _,isinductive,_,cl = List.nth tys i in + if not isinductive then + List.for_all + (check_is_really_smaller_arg rec_uri rec_uri_len + ~logger ~metasenv ~subst context n nn kl x safes) + pl + else + List.for_all2 + (fun p (_,c) -> + let rec_params = + let c = + debrujin_constructor ~check_exp_named_subst:false + rec_uri rec_uri_len context c in + let len_ctx = List.length context in + recursive_args (context@tys_ctx) len_ctx (len_ctx+rec_uri_len) c + in + let (e, safes',n',nn',x',context') = + get_new_safes ~subst context p rec_params safes n nn x + in + check_is_really_smaller_arg rec_uri rec_uri_len + ~logger ~metasenv ~subst context' n' nn' kl x' safes' e + ) pl cl + | _ -> + List.for_all + (check_is_really_smaller_arg + rec_uri rec_uri_len ~logger ~metasenv ~subst + context n nn kl x safes) pl + ) + | C.Fix (_, fl) -> + let len = List.length fl in + let n_plus_len = n + len + and nn_plus_len = nn + len + and x_plus_len = x + len + and tys,_ = + List.fold_left + (fun (types,len) (n,_,ty,_) -> + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, + len+1) + ) ([],0) fl + and safes' = List.map (fun x -> x + len) safes in + List.for_all + (fun (_,_,_,bo) -> + check_is_really_smaller_arg + rec_uri rec_uri_len ~logger ~metasenv ~subst + (tys@context) n_plus_len nn_plus_len kl + x_plus_len safes' bo + ) fl + | t -> + raise (AssertFailure (lazy ("An inhabitant of an inductive type in normal form cannot have this shape: " ^ CicPp.ppterm t))) + +and guarded_by_destructors + ~logger ~metasenv ~subst rec_uri rec_uri_len context n nn kl x safes t += + let module C = Cic in + let module U = UriManager in + match CicReduction.whd ~subst context t with + C.Rel m when m > n && m <= nn -> false + | C.Rel m -> + (match List.nth context (m-1) with + Some (_,C.Decl _) -> true + | Some (_,C.Def (bo,_)) -> + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes + (CicSubstitution.lift m bo) + | None -> raise (TypeCheckerFailure (lazy "Reference to deleted hypothesis")) + ) + | C.Meta _ + | C.Sort _ + | C.Implicit _ -> true + | C.Cast (te,ty) -> + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes te && + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes ty + | C.Prod (name,so,ta) -> + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes so && + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst ((Some (name,(C.Decl so)))::context) + (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta + | C.Lambda (name,so,ta) -> + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes so && + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst ((Some (name,(C.Decl so)))::context) + (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta + | C.LetIn (name,so,ty,ta) -> + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes so && + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes ty && + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst ((Some (name,(C.Def (so,ty))))::context) + (n+1) (nn+1) kl (x+1) (List.map (fun x -> x + 1) safes) ta + | C.Appl ((C.Rel m)::tl) when m > n && m <= nn -> + let k = List.nth kl (m - n - 1) in + if not (List.length tl > k) then false + else + List.for_all + (guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes) tl && + check_is_really_smaller_arg + rec_uri rec_uri_len + ~logger ~metasenv ~subst context n nn kl x safes (List.nth tl k) + | C.Var (_,exp_named_subst) + | C.Const (_,exp_named_subst) + | C.MutInd (_,_,exp_named_subst) + | C.MutConstruct (_,_,_,exp_named_subst) -> + List.for_all + (fun (_,t) -> guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes t) + exp_named_subst + | C.MutCase (uri,i,outtype,term,pl) -> + (match CicReduction.whd ~subst context term with + | C.Rel m + | C.Appl ((C.Rel m)::_) as t when List.mem m safes || m = x -> + let tl = match t with C.Appl (_::tl) -> tl | _ -> [] in + List.for_all + (guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes) + tl && + let tys = + specialize_inductive_type ~logger ~subst ~metasenv context t + in + let tys_ctx = + List.map + (fun (name,_,ty,_) -> Some (Cic.Name name, Cic.Decl ty)) tys + in + let _,isinductive,_,cl = List.nth tys i in + if not isinductive then + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes outtype && + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes term && + List.for_all + (guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes) + pl + else + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes outtype && + List.for_all2 + (fun p (_,c) -> + let rec_params = + let c = + debrujin_constructor ~check_exp_named_subst:false + rec_uri rec_uri_len context c in + let len_ctx = List.length context in + recursive_args (context@tys_ctx) len_ctx (len_ctx+rec_uri_len) c + in + let (e, safes',n',nn',x',context') = + get_new_safes ~subst context p rec_params safes n nn x + in + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context' n' nn' kl x' safes' e + ) pl cl + | _ -> + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes outtype && + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes term && + (*CSC: manca ??? il controllo sul tipo di term? *) + List.fold_right + (fun p i -> i && guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes p) + pl true + ) + | C.Appl (C.Fix (fixno, fl)::_) | C.Fix (fixno,fl) as t-> + let l = match t with C.Appl (_::tl) -> tl | _ -> [] in + let len = List.length fl in + let n_plus_len = n + len in + let nn_plus_len = nn + len in + let x_plus_len = x + len in + let tys,_ = + List.fold_left + (fun (types,len) (n,_,ty,_) -> + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, + len+1) + ) ([],0) fl in + let safes' = List.map (fun x -> x + len) safes in + List.for_all + (guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes) l && + snd (List.fold_left + (fun (fixno',i) (_,recno,ty,bo) -> + fixno'+1, + i && + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x_plus_len safes' ty && + if + fixno' = fixno && + List.length l > recno && + (*case where the recursive argument is already really_smaller *) + check_is_really_smaller_arg + rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes + (List.nth l recno) + then + let bo_without_lambdas,_,context = + eat_lambdas ~subst (tys@context) (recno+1) bo + in + (* we assume the formal argument to be safe *) + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context (n_plus_len+recno+1) + (nn_plus_len+recno+1) kl (x_plus_len+recno+1) + (1::List.map (fun x -> x+recno+1) safes') + bo_without_lambdas + else + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst (tys@context) n_plus_len nn_plus_len + kl x_plus_len safes' bo + ) (0,true) fl) + | C.CoFix (_, fl) -> + let len = List.length fl in + let n_plus_len = n + len + and nn_plus_len = nn + len + and x_plus_len = x + len + and tys,_ = + List.fold_left + (fun (types,len) (n,ty,_) -> + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, + len+1) + ) ([],0) fl + and safes' = List.map (fun x -> x + len) safes in + List.fold_right + (fun (_,ty,bo) i -> + i && + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x_plus_len safes' ty && + guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst (tys@context) n_plus_len nn_plus_len kl + x_plus_len safes' bo + ) fl true + | C.Appl tl -> + List.fold_right + (fun t i -> i && guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes t) + tl true + +(* the boolean h means already protected *) +(* args is the list of arguments the type of the constructor that may be *) +(* found in head position must be applied to. *) +and guarded_by_constructors ~subst context n nn h te args coInductiveTypeURI = + let module C = Cic in + (*CSC: There is a lot of code replication between the cases X and *) + (*CSC: (C.Appl X tl). Maybe it will be better to define a function *) + (*CSC: that maps X into (C.Appl X []) when X is not already a C.Appl *) + match CicReduction.whd ~subst context te with + C.Rel m when m > n && m <= nn -> h + | C.Rel _ -> true + | C.Meta _ + | C.Sort _ + | C.Implicit _ + | C.Cast _ + | C.Prod _ + | C.LetIn _ -> + (* the term has just been type-checked *) + raise (AssertFailure (lazy "17")) + | C.Lambda (name,so,de) -> + does_not_occur ~subst context n nn so && + guarded_by_constructors ~subst ((Some (name,(C.Decl so)))::context) + (n + 1) (nn + 1) h de args coInductiveTypeURI + | C.Appl ((C.Rel m)::tl) when m > n && m <= nn -> + h && + List.fold_right (fun x i -> i && does_not_occur ~subst context n nn x) tl true + | C.Appl ((C.MutConstruct (uri,i,j,exp_named_subst))::tl) -> + let consty = + let obj,_ = + try + CicEnvironment.get_cooked_obj ~trust:false CicUniv.empty_ugraph uri + with Not_found -> assert false + in + match obj with + C.InductiveDefinition (itl,_,_,_) -> + let (_,_,_,cl) = List.nth itl i in + let (_,cons) = List.nth cl (j - 1) in + CicSubstitution.subst_vars exp_named_subst cons + | _ -> + raise (TypeCheckerFailure + (lazy ("Unknown mutual inductive definition:" ^ UriManager.string_of_uri uri))) + in + let rec analyse_branch context ty te = + match CicReduction.whd ~subst context ty with + C.Meta _ -> raise (AssertFailure (lazy "34")) + | C.Rel _ + | C.Var _ + | C.Sort _ -> + does_not_occur ~subst context n nn te + | C.Implicit _ + | C.Cast _ -> + raise (AssertFailure (lazy "24"))(* due to type-checking *) + | C.Prod (name,so,de) -> + analyse_branch ((Some (name,(C.Decl so)))::context) de te + | C.Lambda _ + | C.LetIn _ -> + raise (AssertFailure (lazy "25"))(* due to type-checking *) + | C.Appl ((C.MutInd (uri,_,_))::_) when uri == coInductiveTypeURI -> + guarded_by_constructors ~subst context n nn true te [] + coInductiveTypeURI + | C.Appl ((C.MutInd (uri,_,_))::_) -> + guarded_by_constructors ~subst context n nn true te tl + coInductiveTypeURI + | C.Appl _ -> + does_not_occur ~subst context n nn te + | C.Const _ -> raise (AssertFailure (lazy "26")) + | C.MutInd (uri,_,_) when uri == coInductiveTypeURI -> + guarded_by_constructors ~subst context n nn true te [] + coInductiveTypeURI + | C.MutInd _ -> + does_not_occur ~subst context n nn te + | C.MutConstruct _ -> raise (AssertFailure (lazy "27")) + (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *) + (*CSC: in head position. *) + | C.MutCase _ + | C.Fix _ + | C.CoFix _ -> + raise (AssertFailure (lazy "28"))(* due to type-checking *) + in + let rec analyse_instantiated_type context ty l = + match CicReduction.whd ~subst context ty with + C.Rel _ + | C.Var _ + | C.Meta _ + | C.Sort _ + | C.Implicit _ + | C.Cast _ -> raise (AssertFailure (lazy "29"))(* due to type-checking *) + | C.Prod (name,so,de) -> + begin + match l with + [] -> true + | he::tl -> + analyse_branch context so he && + analyse_instantiated_type + ((Some (name,(C.Decl so)))::context) de tl + end + | C.Lambda _ + | C.LetIn _ -> + raise (AssertFailure (lazy "30"))(* due to type-checking *) + | C.Appl _ -> + List.fold_left + (fun i x -> i && does_not_occur ~subst context n nn x) true l + | C.Const _ -> raise (AssertFailure (lazy "31")) + | C.MutInd _ -> + List.fold_left + (fun i x -> i && does_not_occur ~subst context n nn x) true l + | C.MutConstruct _ -> raise (AssertFailure (lazy "32")) + (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *) + (*CSC: in head position. *) + | C.MutCase _ + | C.Fix _ + | C.CoFix _ -> + raise (AssertFailure (lazy "33"))(* due to type-checking *) + in + let rec instantiate_type args consty = + function + [] -> true + | tlhe::tltl as l -> + let consty' = CicReduction.whd ~subst context consty in + match args with + he::tl -> + begin + match consty' with + C.Prod (_,_,de) -> + let instantiated_de = CicSubstitution.subst he de in + (*CSC: siamo sicuri che non sia troppo forte? *) + does_not_occur ~subst context n nn tlhe & + instantiate_type tl instantiated_de tltl + | _ -> + (*CSC:We do not consider backbones with a MutCase, a *) + (*CSC:FixPoint, a CoFixPoint and so on in head position.*) + raise (AssertFailure (lazy "23")) + end + | [] -> analyse_instantiated_type context consty' l + (* These are all the other cases *) + in + instantiate_type args consty tl + | C.Appl ((C.CoFix (_,fl))::tl) -> + List.fold_left (fun i x -> i && does_not_occur ~subst context n nn x) true tl && + let len = List.length fl in + let n_plus_len = n + len + and nn_plus_len = nn + len + (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *) + and tys,_ = + List.fold_left + (fun (types,len) (n,ty,_) -> + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, + len+1) + ) ([],0) fl + in + List.fold_right + (fun (_,ty,bo) i -> + i && does_not_occur ~subst context n nn ty && + guarded_by_constructors ~subst (tys@context) n_plus_len nn_plus_len + h bo args coInductiveTypeURI + ) fl true + | C.Appl ((C.MutCase (_,_,out,te,pl))::tl) -> + List.fold_left (fun i x -> i && does_not_occur ~subst context n nn x) true tl && + does_not_occur ~subst context n nn out && + does_not_occur ~subst context n nn te && + List.fold_right + (fun x i -> + i && + guarded_by_constructors ~subst context n nn h x args + coInductiveTypeURI + ) pl true + | C.Appl l -> + List.fold_right (fun x i -> i && does_not_occur ~subst context n nn x) l true + | C.Var (_,exp_named_subst) + | C.Const (_,exp_named_subst) -> + List.fold_right + (fun (_,x) i -> i && does_not_occur ~subst context n nn x) exp_named_subst true + | C.MutInd _ -> assert false + | C.MutConstruct (_,_,_,exp_named_subst) -> + List.fold_right + (fun (_,x) i -> i && does_not_occur ~subst context n nn x) exp_named_subst true + | C.MutCase (_,_,out,te,pl) -> + does_not_occur ~subst context n nn out && + does_not_occur ~subst context n nn te && + List.fold_right + (fun x i -> + i && + guarded_by_constructors ~subst context n nn h x args + coInductiveTypeURI + ) pl true + | C.Fix (_,fl) -> + let len = List.length fl in + let n_plus_len = n + len + and nn_plus_len = nn + len + (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *) + and tys,_ = + List.fold_left + (fun (types,len) (n,_,ty,_) -> + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, + len+1) + ) ([],0) fl + in + List.fold_right + (fun (_,_,ty,bo) i -> + i && does_not_occur ~subst context n nn ty && + does_not_occur ~subst (tys@context) n_plus_len nn_plus_len bo + ) fl true + | C.CoFix (_,fl) -> + let len = List.length fl in + let n_plus_len = n + len + and nn_plus_len = nn + len + (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *) + and tys,_ = + List.fold_left + (fun (types,len) (n,ty,_) -> + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, + len+1) + ) ([],0) fl + in + List.fold_right + (fun (_,ty,bo) i -> + i && does_not_occur ~subst context n nn ty && + guarded_by_constructors ~subst (tys@context) n_plus_len nn_plus_len + h bo + args coInductiveTypeURI + ) fl true + +and check_allowed_sort_elimination ~subst ~metasenv ~logger context uri i + need_dummy ind arity1 arity2 ugraph = + let module C = Cic in + let module U = UriManager in + let arity1 = CicReduction.whd ~subst context arity1 in + let rec check_allowed_sort_elimination_aux ugraph context arity2 need_dummy = + match arity1, CicReduction.whd ~subst context arity2 with + (C.Prod (name,so1,de1), C.Prod (_,so2,de2)) -> + let b,ugraph1 = + CicReduction.are_convertible ~subst ~metasenv context so1 so2 ugraph in + if b then + check_allowed_sort_elimination ~subst ~metasenv ~logger + ((Some (name,C.Decl so1))::context) uri i + need_dummy (C.Appl [CicSubstitution.lift 1 ind ; C.Rel 1]) de1 de2 + ugraph1 + else + false,ugraph1 + | (C.Sort _, C.Prod (name,so,ta)) when not need_dummy -> + let b,ugraph1 = + CicReduction.are_convertible ~subst ~metasenv context so ind ugraph in + if not b then + false,ugraph1 + else + check_allowed_sort_elimination_aux ugraph1 + ((Some (name,C.Decl so))::context) ta true + | (C.Sort C.Prop, C.Sort C.Prop) when need_dummy -> true,ugraph + | (C.Sort C.Prop, C.Sort C.Set) + | (C.Sort C.Prop, C.Sort C.CProp) + | (C.Sort C.Prop, C.Sort (C.Type _) ) when need_dummy -> + (let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in + match o with + C.InductiveDefinition (itl,_,paramsno,_) -> + let itl_len = List.length itl in + let (name,_,ty,cl) = List.nth itl i in + let cl_len = List.length cl in + if (cl_len = 0 || (itl_len = 1 && cl_len = 1)) then + let non_informative,ugraph = + if cl_len = 0 then true,ugraph + else + is_non_informative ~logger [Some (C.Name name,C.Decl ty)] + paramsno (snd (List.nth cl 0)) ugraph + in + (* is it a singleton or empty non recursive and non informative + definition? *) + non_informative, ugraph + else + false,ugraph + | _ -> + raise (TypeCheckerFailure + (lazy ("Unknown mutual inductive definition:" ^ + UriManager.string_of_uri uri))) + ) + | (C.Sort C.Set, C.Sort C.Prop) when need_dummy -> true , ugraph + | (C.Sort C.CProp, C.Sort C.Prop) when need_dummy -> true , ugraph + | (C.Sort C.Set, C.Sort C.Set) when need_dummy -> true , ugraph + | (C.Sort C.Set, C.Sort C.CProp) when need_dummy -> true , ugraph + | (C.Sort C.CProp, C.Sort C.Set) when need_dummy -> true , ugraph + | (C.Sort C.CProp, C.Sort C.CProp) when need_dummy -> true , ugraph + | ((C.Sort C.Set, C.Sort (C.Type _)) | (C.Sort C.CProp, C.Sort (C.Type _))) + when need_dummy -> + (let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in + match o with + C.InductiveDefinition (itl,_,paramsno,_) -> + let tys = + List.map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) itl + in + let (_,_,_,cl) = List.nth itl i in + (List.fold_right + (fun (_,x) (i,ugraph) -> + if i then + is_small ~logger tys paramsno x ugraph + else + false,ugraph + ) cl (true,ugraph)) + | _ -> + raise (TypeCheckerFailure + (lazy ("Unknown mutual inductive definition:" ^ + UriManager.string_of_uri uri))) + ) + | (C.Sort (C.Type _), C.Sort _) when need_dummy -> true , ugraph + | (_,_) -> false,ugraph + in + check_allowed_sort_elimination_aux ugraph context arity2 need_dummy + +and type_of_branch ~subst context argsno need_dummy outtype term constype = + let module C = Cic in + let module R = CicReduction in + match R.whd ~subst context constype with + C.MutInd (_,_,_) -> + if need_dummy then + outtype + else + C.Appl [outtype ; term] + | C.Appl (C.MutInd (_,_,_)::tl) -> + let (_,arguments) = split tl argsno + in + if need_dummy && arguments = [] then + outtype + else + C.Appl (outtype::arguments@(if need_dummy then [] else [term])) + | C.Prod (name,so,de) -> + let term' = + match CicSubstitution.lift 1 term with + C.Appl l -> C.Appl (l@[C.Rel 1]) + | t -> C.Appl [t ; C.Rel 1] + in + C.Prod (name,so,type_of_branch ~subst + ((Some (name,(C.Decl so)))::context) argsno need_dummy + (CicSubstitution.lift 1 outtype) term' de) + | _ -> raise (AssertFailure (lazy "20")) + +(* 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 ~logger ~subst metasenv context + canonical_context l ugraph += + let module C = Cic in + let module R = CicReduction in + let module S = CicSubstitution in + let lifted_canonical_context = + let rec aux i = + function + [] -> [] + | (Some (n,C.Decl t))::tl -> + (Some (n,C.Decl (S.subst_meta l (S.lift i t))))::(aux (i+1) tl) + | None::tl -> None::(aux (i+1) tl) + | (Some (n,C.Def (t,ty)))::tl -> + (Some (n,C.Def ((S.subst_meta l (S.lift i t)),S.subst_meta l (S.lift i ty))))::(aux (i+1) tl) + in + aux 1 canonical_context + in + List.fold_left2 + (fun ugraph t ct -> + match (t,ct) with + | _,None -> ugraph + | Some t,Some (_,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 + Cic.Rel n -> + (try + match List.nth context (n - 1) with + Some (_,C.Def (te,_)) -> S.lift n te + | _ -> t + with + Failure _ -> t) + | _ -> t + in +(*if t <> optimized_t && optimized_t = ct then prerr_endline "!!!!!!!!!!!!!!!" +else if t <> optimized_t then prerr_endline ("@@ " ^ CicPp.ppterm t ^ " ==> " ^ CicPp.ppterm optimized_t ^ " <==> " ^ CicPp.ppterm ct);*) + let b,ugraph1 = + R.are_convertible ~subst ~metasenv context optimized_t ct ugraph + in + if not b then + raise + (TypeCheckerFailure + (lazy (sprintf "Not well typed metavariable local context: expected a term convertible with %s, found %s" (CicPp.ppterm ct) (CicPp.ppterm t)))) + else + ugraph1 + | Some t,Some (_,C.Decl ct) -> + let type_t,ugraph1 = + type_of_aux' ~logger ~subst metasenv context t ugraph + in + let b,ugraph2 = + R.are_convertible ~subst ~metasenv context type_t ct ugraph1 + in + if not b then + raise (TypeCheckerFailure + (lazy (sprintf "Not well typed metavariable local context: expected a term of type %s, found %s of type %s" + (CicPp.ppterm ct) (CicPp.ppterm t) + (CicPp.ppterm type_t)))) + else + ugraph2 + | None, _ -> + raise (TypeCheckerFailure + (lazy ("Not well typed metavariable local context: "^ + "an hypothesis, that is not hidden, is not instantiated"))) + ) ugraph l lifted_canonical_context + + +(* + type_of_aux' is just another name (with a different scope) + for type_of_aux +*) + +and type_of_aux' ~logger ?(subst = []) metasenv context t ugraph = + let rec type_of_aux ~logger context t ugraph = + let module C = Cic in + let module R = CicReduction in + let module S = CicSubstitution in + let module U = UriManager in + match t with + C.Rel n -> + (try + match List.nth context (n - 1) with + Some (_,C.Decl t) -> S.lift n t,ugraph + | Some (_,C.Def (_,ty)) -> S.lift n ty,ugraph + | None -> raise + (TypeCheckerFailure (lazy "Reference to deleted hypothesis")) + with + Failure _ -> + raise (TypeCheckerFailure (lazy "unbound variable")) + ) + | C.Var (uri,exp_named_subst) -> + incr fdebug ; + let ugraph1 = + check_exp_named_subst ~logger ~subst context exp_named_subst ugraph + in + let ty,ugraph2 = type_of_variable ~logger uri ugraph1 in + let ty1 = CicSubstitution.subst_vars exp_named_subst ty in + decr fdebug ; + ty1,ugraph2 + | C.Meta (n,l) -> + (try + let (canonical_context,term,ty) = CicUtil.lookup_subst n subst in + let ugraph1 = + check_metasenv_consistency ~logger + ~subst metasenv context canonical_context l ugraph + in + (* assuming subst is well typed !!!!! *) + ((CicSubstitution.subst_meta l ty), ugraph1) + (* type_of_aux context (CicSubstitution.subst_meta l term) *) + with CicUtil.Subst_not_found _ -> + let (_,canonical_context,ty) = CicUtil.lookup_meta n metasenv in + let ugraph1 = + check_metasenv_consistency ~logger + ~subst metasenv context canonical_context l ugraph + in + ((CicSubstitution.subst_meta l ty),ugraph1)) + (* TASSI: CONSTRAINTS *) + | C.Sort (C.Type t) -> + let t' = CicUniv.fresh() in + (try + let ugraph1 = CicUniv.add_gt t' t ugraph in + (C.Sort (C.Type t')),ugraph1 + with + CicUniv.UniverseInconsistency msg -> raise (TypeCheckerFailure msg)) + | C.Sort s -> (C.Sort (C.Type (CicUniv.fresh ()))),ugraph + | C.Implicit _ -> raise (AssertFailure (lazy "Implicit found")) + | C.Cast (te,ty) as t -> + let _,ugraph1 = type_of_aux ~logger context ty ugraph in + let ty_te,ugraph2 = type_of_aux ~logger context te ugraph1 in + let b,ugraph3 = + R.are_convertible ~subst ~metasenv context ty_te ty ugraph2 + in + if b then + ty,ugraph3 + else + raise (TypeCheckerFailure + (lazy (sprintf "Invalid cast %s" (CicPp.ppterm t)))) + | C.Prod (name,s,t) -> + let sort1,ugraph1 = type_of_aux ~logger context s ugraph in + let sort2,ugraph2 = + type_of_aux ~logger ((Some (name,(C.Decl s)))::context) t ugraph1 + in + sort_of_prod ~subst context (name,s) (sort1,sort2) ugraph2 + | C.Lambda (n,s,t) -> + let sort1,ugraph1 = type_of_aux ~logger context s ugraph in + (match R.whd ~subst context sort1 with + C.Meta _ + | C.Sort _ -> () + | _ -> + raise + (TypeCheckerFailure (lazy (sprintf + "Not well-typed lambda-abstraction: the source %s should be a type; instead it is a term of type %s" (CicPp.ppterm s) + (CicPp.ppterm sort1)))) + ) ; + let type2,ugraph2 = + type_of_aux ~logger ((Some (n,(C.Decl s)))::context) t ugraph1 + in + (C.Prod (n,s,type2)),ugraph2 + | C.LetIn (n,s,ty,t) -> + (* only to check if s is well-typed *) + let ty',ugraph1 = type_of_aux ~logger context s ugraph in + let _,ugraph1 = type_of_aux ~logger context ty ugraph1 in + let b,ugraph1 = + R.are_convertible ~subst ~metasenv context ty ty' ugraph1 + in + if not b then + raise + (TypeCheckerFailure + (lazy (sprintf + "The type of %s is %s but it is expected to be %s" + (CicPp.ppterm s) (CicPp.ppterm ty') (CicPp.ppterm ty)))) + else + (* The type of a LetIn is a LetIn. Extremely slow since the computed + LetIn is later reduced and maybe also re-checked. + (C.LetIn (n,s, type_of_aux ((Some (n,(C.Def s)))::context) t)) + *) + (* The type of the LetIn is reduced. Much faster than the previous + solution. Moreover the inferred type is probably very different + from the expected one. + (CicReduction.whd ~subst context + (C.LetIn (n,s, type_of_aux ((Some (n,(C.Def s)))::context) t))) + *) + (* One-step LetIn reduction. Even faster than the previous solution. + Moreover the inferred type is closer to the expected one. *) + let ty1,ugraph2 = + type_of_aux ~logger + ((Some (n,(C.Def (s,ty))))::context) t ugraph1 + in + (CicSubstitution.subst ~avoid_beta_redexes:true s ty1),ugraph2 + | C.Appl (he::tl) when List.length tl > 0 -> + let hetype,ugraph1 = type_of_aux ~logger context he ugraph in + let tlbody_and_type,ugraph2 = + List.fold_right ( + fun x (l,ugraph) -> + let ty,ugraph1 = type_of_aux ~logger context x ugraph in + (*let _,ugraph1 = type_of_aux ~logger context ty ugraph1 in*) + ((x,ty)::l,ugraph1)) + tl ([],ugraph1) + in + (* TASSI: questa c'era nel mio... ma non nel CVS... *) + (* let _,ugraph2 = type_of_aux context hetype ugraph2 in *) + eat_prods ~subst context hetype tlbody_and_type ugraph2 + | C.Appl _ -> raise (AssertFailure (lazy "Appl: no arguments")) + | C.Const (uri,exp_named_subst) -> + incr fdebug ; + let ugraph1 = + check_exp_named_subst ~logger ~subst context exp_named_subst ugraph + in + let cty,ugraph2 = type_of_constant ~logger uri ugraph1 in + let cty1 = + CicSubstitution.subst_vars exp_named_subst cty + in + decr fdebug ; + cty1,ugraph2 + | C.MutInd (uri,i,exp_named_subst) -> + incr fdebug ; + let ugraph1 = + check_exp_named_subst ~logger ~subst context exp_named_subst ugraph + in + (* TASSI: da me c'era anche questa, ma in CVS no *) + let mty,ugraph2 = type_of_mutual_inductive_defs ~logger uri i ugraph1 in + (* fine parte dubbia *) + let cty = + CicSubstitution.subst_vars exp_named_subst mty + in + decr fdebug ; + cty,ugraph2 + | C.MutConstruct (uri,i,j,exp_named_subst) -> + let ugraph1 = + check_exp_named_subst ~logger ~subst context exp_named_subst ugraph + in + (* TASSI: idem come sopra *) + let mty,ugraph2 = + type_of_mutual_inductive_constr ~logger uri i j ugraph1 + in + let cty = + CicSubstitution.subst_vars exp_named_subst mty + in + cty,ugraph2 + | C.MutCase (uri,i,outtype,term,pl) -> + let outsort,ugraph1 = type_of_aux ~logger context outtype ugraph in + let (need_dummy, k) = + let rec guess_args context t = + let outtype = CicReduction.whd ~subst context t in + match outtype with + C.Sort _ -> (true, 0) + | C.Prod (name, s, t) -> + let (b, n) = + guess_args ((Some (name,(C.Decl s)))::context) t in + if n = 0 then + (* last prod before sort *) + match CicReduction.whd ~subst context s with +(*CSC: for _ see comment below about the missing named_exp_subst ?????????? *) + C.MutInd (uri',i',_) when U.eq uri' uri && i' = i -> + (false, 1) +(*CSC: for _ see comment below about the missing named_exp_subst ?????????? *) + | C.Appl ((C.MutInd (uri',i',_)) :: _) + when U.eq uri' uri && i' = i -> (false, 1) + | _ -> (true, 1) + else + (b, n + 1) + | _ -> + raise + (TypeCheckerFailure + (lazy (sprintf + "Malformed case analasys' output type %s" + (CicPp.ppterm outtype)))) + in +(* + let (parameters, arguments, exp_named_subst),ugraph2 = + let ty,ugraph2 = type_of_aux context term ugraph1 in + match R.whd ~subst context ty with + (*CSC manca il caso dei CAST *) +(*CSC: ma servono i parametri (uri,i)? Se si', perche' non serve anche il *) +(*CSC: parametro exp_named_subst? Se no, perche' non li togliamo? *) +(*CSC: Hint: nella DTD servono per gli stylesheet. *) + C.MutInd (uri',i',exp_named_subst) as typ -> + if U.eq uri uri' && i = i' then + ([],[],exp_named_subst),ugraph2 + else + raise + (TypeCheckerFailure + (lazy (sprintf + ("Case analysys: analysed term type is %s, but is expected to be (an application of) %s#1/%d{_}") + (CicPp.ppterm typ) (U.string_of_uri uri) i))) + | C.Appl + ((C.MutInd (uri',i',exp_named_subst) as typ):: tl) as typ' -> + if U.eq uri uri' && i = i' then + let params,args = + split tl (List.length tl - k) + in (params,args,exp_named_subst),ugraph2 + else + raise + (TypeCheckerFailure + (lazy (sprintf + ("Case analysys: analysed term type is %s, "^ + "but is expected to be (an application of) "^ + "%s#1/%d{_}") + (CicPp.ppterm typ') (U.string_of_uri uri) i))) + | _ -> + raise + (TypeCheckerFailure + (lazy (sprintf + ("Case analysis: "^ + "analysed term %s is not an inductive one") + (CicPp.ppterm term)))) +*) + let (b, k) = guess_args context outsort in + if not b then (b, k - 1) else (b, k) in + let (parameters, arguments, exp_named_subst),ugraph2 = + let ty,ugraph2 = type_of_aux ~logger context term ugraph1 in + match R.whd ~subst context ty with + C.MutInd (uri',i',exp_named_subst) as typ -> + if U.eq uri uri' && i = i' then + ([],[],exp_named_subst),ugraph2 + else raise + (TypeCheckerFailure + (lazy (sprintf + ("Case analysys: analysed term type is %s (%s#1/%d{_}), but is expected to be (an application of) %s#1/%d{_}") + (CicPp.ppterm typ) (U.string_of_uri uri') i' (U.string_of_uri uri) i))) + | C.Appl ((C.MutInd (uri',i',exp_named_subst) as typ):: tl) -> + if U.eq uri uri' && i = i' then + let params,args = + split tl (List.length tl - k) + in (params,args,exp_named_subst),ugraph2 + else raise + (TypeCheckerFailure + (lazy (sprintf + ("Case analysys: analysed term type is %s (%s#1/%d{_}), but is expected to be (an application of) %s#1/%d{_}") + (CicPp.ppterm typ) (U.string_of_uri uri') i' (U.string_of_uri uri) i))) + | _ -> + raise + (TypeCheckerFailure + (lazy (sprintf + "Case analysis: analysed term %s is not an inductive one" + (CicPp.ppterm term)))) + in + (* + let's control if the sort elimination is allowed: + [(I q1 ... qr)|B] + *) + let sort_of_ind_type = + if parameters = [] then + C.MutInd (uri,i,exp_named_subst) + else + C.Appl ((C.MutInd (uri,i,exp_named_subst))::parameters) + in + let type_of_sort_of_ind_ty,ugraph3 = + type_of_aux ~logger context sort_of_ind_type ugraph2 in + let b,ugraph4 = + check_allowed_sort_elimination ~subst ~metasenv ~logger context uri i + need_dummy sort_of_ind_type type_of_sort_of_ind_ty outsort ugraph3 + in + if not b then + raise + (TypeCheckerFailure (lazy ("Case analysis: sort elimination not allowed"))); + (* let's check if the type of branches are right *) + let parsno,constructorsno = + let obj,_ = + try + CicEnvironment.get_cooked_obj ~trust:false CicUniv.empty_ugraph uri + with Not_found -> assert false + in + match obj with + C.InductiveDefinition (il,_,parsno,_) -> + let _,_,_,cl = + try List.nth il i with Failure _ -> assert false + in + parsno, List.length cl + | _ -> + raise (TypeCheckerFailure + (lazy ("Unknown mutual inductive definition:" ^ + UriManager.string_of_uri uri))) + in + if List.length pl <> constructorsno then + raise (TypeCheckerFailure + (lazy ("Wrong number of cases in case analysis"))) ; + let (_,branches_ok,ugraph5) = + List.fold_left + (fun (j,b,ugraph) p -> + if b then + let cons = + if parameters = [] then + (C.MutConstruct (uri,i,j,exp_named_subst)) + else + (C.Appl + (C.MutConstruct (uri,i,j,exp_named_subst)::parameters)) + in + let ty_p,ugraph1 = type_of_aux ~logger context p ugraph in + let ty_cons,ugraph3 = type_of_aux ~logger context cons ugraph1 in + (* 2 is skipped *) + let ty_branch = + type_of_branch ~subst context parsno need_dummy outtype cons + ty_cons in + let b1,ugraph4 = + R.are_convertible + ~subst ~metasenv context ty_p ty_branch ugraph3 + in +(* Debugging code +if not b1 then +begin +prerr_endline ("\n!OUTTYPE= " ^ CicPp.ppterm outtype); +prerr_endline ("!CONS= " ^ CicPp.ppterm cons); +prerr_endline ("!TY_CONS= " ^ CicPp.ppterm ty_cons); +prerr_endline ("#### " ^ CicPp.ppterm ty_p ^ "\n<==>\n" ^ CicPp.ppterm ty_branch); +end; +*) + if not b1 then + debug_print (lazy + ("#### " ^ CicPp.ppterm ty_p ^ + " <==> " ^ CicPp.ppterm ty_branch)); + (j + 1,b1,ugraph4) + else + (j,false,ugraph) + ) (1,true,ugraph4) pl + in + if not branches_ok then + raise + (TypeCheckerFailure (lazy "Case analysys: wrong branch type")); + let arguments' = + if not need_dummy then outtype::arguments@[term] + else outtype::arguments in + let outtype = + if need_dummy && arguments = [] then outtype + else CicReduction.head_beta_reduce (C.Appl arguments') + in + outtype,ugraph5 + | C.Fix (i,fl) -> + let types,kl,ugraph1,len = + List.fold_left + (fun (types,kl,ugraph,len) (n,k,ty,_) -> + let _,ugraph1 = type_of_aux ~logger context ty ugraph in + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, + k::kl,ugraph1,len+1) + ) ([],[],ugraph,0) fl + in + let ugraph2 = + List.fold_left + (fun ugraph (name,x,ty,bo) -> + let ty_bo,ugraph1 = + type_of_aux ~logger (types@context) bo ugraph + in + let b,ugraph2 = + R.are_convertible ~subst ~metasenv (types@context) + ty_bo (CicSubstitution.lift len ty) ugraph1 in + if b then + begin + let (m, eaten, context') = + eat_lambdas ~subst (types @ context) (x + 1) bo + in + let rec_uri, rec_uri_len = + let he = + match List.hd context' with + Some (_,Cic.Decl he) -> he + | _ -> assert false + in + match CicReduction.whd ~subst (List.tl context') he with + | Cic.MutInd (uri,_,_) + | Cic.Appl (Cic.MutInd (uri,_,_)::_) -> + uri, + (match + CicEnvironment.get_obj + CicUniv.oblivion_ugraph uri + with + | Cic.InductiveDefinition (tl,_,_,_), _ -> + List.length tl + | _ -> assert false) + | _ -> assert false + in + (* + let's control the guarded by + destructors conditions D{f,k,x,M} + *) + if not (guarded_by_destructors ~logger ~metasenv ~subst + rec_uri rec_uri_len context' eaten (len + eaten) kl + 1 [] m) + then + raise + (TypeCheckerFailure + (lazy ("Fix: not guarded by destructors:"^CicPp.ppterm t))) + else + ugraph2 + end + else + raise (TypeCheckerFailure (lazy ("Fix: ill-typed bodies"))) + ) ugraph1 fl in + (*CSC: controlli mancanti solo su D{f,k,x,M} *) + let (_,_,ty,_) = List.nth fl i in + ty,ugraph2 + | C.CoFix (i,fl) -> + let types,ugraph1,len = + List.fold_left + (fun (l,ugraph,len) (n,ty,_) -> + let _,ugraph1 = + type_of_aux ~logger context ty ugraph in + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::l, + ugraph1,len+1) + ) ([],ugraph,0) fl + in + let ugraph2 = + List.fold_left + (fun ugraph (_,ty,bo) -> + let ty_bo,ugraph1 = + type_of_aux ~logger (types @ context) bo ugraph + in + let b,ugraph2 = + R.are_convertible ~subst ~metasenv (types @ context) ty_bo + (CicSubstitution.lift len ty) ugraph1 + in + if b then + begin + (* let's control that the returned type is coinductive *) + match returns_a_coinductive ~subst context ty with + None -> + raise + (TypeCheckerFailure + (lazy "CoFix: does not return a coinductive type")) + | Some uri -> + (* + let's control the guarded by constructors + conditions C{f,M} + *) + if not (guarded_by_constructors ~subst + (types @ context) 0 len false bo [] uri) then + raise + (TypeCheckerFailure + (lazy "CoFix: not guarded by constructors")) + else + ugraph2 + end + else + raise + (TypeCheckerFailure (lazy "CoFix: ill-typed bodies")) + ) ugraph1 fl + in + let (_,ty,_) = List.nth fl i in + ty,ugraph2 + + and check_exp_named_subst ~logger ~subst context = + let rec check_exp_named_subst_aux ~logger esubsts l ugraph = + match l with + [] -> ugraph + | ((uri,t) as item)::tl -> + let ty_uri,ugraph1 = type_of_variable ~logger uri ugraph in + let typeofvar = + CicSubstitution.subst_vars esubsts ty_uri in + let typeoft,ugraph2 = type_of_aux ~logger context t ugraph1 in + let b,ugraph3 = + CicReduction.are_convertible ~subst ~metasenv + context typeoft typeofvar ugraph2 + in + if b then + check_exp_named_subst_aux ~logger (esubsts@[item]) tl ugraph3 + else + begin + CicReduction.fdebug := 0 ; + ignore + (CicReduction.are_convertible + ~subst ~metasenv context typeoft typeofvar ugraph2) ; + fdebug := 0 ; + debug typeoft [typeofvar] ; + raise (TypeCheckerFailure (lazy "Wrong Explicit Named Substitution")) + end + in + check_exp_named_subst_aux ~logger [] + + and sort_of_prod ~subst context (name,s) (t1, t2) ugraph = + let module C = Cic in + let t1' = CicReduction.whd ~subst context t1 in + let t2' = CicReduction.whd ~subst ((Some (name,C.Decl s))::context) t2 in + match (t1', t2') with + (C.Sort s1, C.Sort s2) + when (s2 = C.Prop or s2 = C.Set or s2 = C.CProp) -> + (* different from Coq manual!!! *) + C.Sort s2,ugraph + | (C.Sort (C.Type t1), C.Sort (C.Type t2)) -> + (* TASSI: CONSRTAINTS: the same in doubletypeinference, cicrefine *) + let t' = CicUniv.fresh() in + (try + let ugraph1 = CicUniv.add_ge t' t1 ugraph in + let ugraph2 = CicUniv.add_ge t' t2 ugraph1 in + C.Sort (C.Type t'),ugraph2 + with + CicUniv.UniverseInconsistency msg -> raise (TypeCheckerFailure msg)) + | (C.Sort _,C.Sort (C.Type t1)) -> + (* TASSI: CONSRTAINTS: the same in doubletypeinference, cicrefine *) + C.Sort (C.Type t1),ugraph (* c'e' bisogno di un fresh? *) + | (C.Meta _, C.Sort _) -> t2',ugraph + | (C.Meta _, (C.Meta (_,_) as t)) + | (C.Sort _, (C.Meta (_,_) as t)) when CicUtil.is_closed t -> + t2',ugraph + | (_,_) -> raise (TypeCheckerFailure (lazy (sprintf + "Prod: expected two sorts, found = %s, %s" (CicPp.ppterm t1') + (CicPp.ppterm t2')))) + + and eat_prods ~subst context hetype l ugraph = + (*CSC: siamo sicuri che le are_convertible non lavorino con termini non *) + (*CSC: cucinati *) + match l with + [] -> hetype,ugraph + | (hete, hety)::tl -> + (match (CicReduction.whd ~subst context hetype) with + Cic.Prod (n,s,t) -> + let b,ugraph1 = +(*if (match hety,s with Cic.Sort _,Cic.Sort _ -> false | _,_ -> true) && hety <> s then( +prerr_endline ("AAA22: " ^ CicPp.ppterm hete ^ ": " ^ CicPp.ppterm hety ^ " <==> " ^ CicPp.ppterm s); let res = CicReduction.are_convertible ~subst ~metasenv context hety s ugraph in prerr_endline "#"; res) else*) + CicReduction.are_convertible + ~subst ~metasenv context hety s ugraph + in + if b then + begin + CicReduction.fdebug := -1 ; + eat_prods ~subst context + (CicSubstitution.subst ~avoid_beta_redexes:true hete t) + tl ugraph1 + (*TASSI: not sure *) + end + else + begin + CicReduction.fdebug := 0 ; + ignore (CicReduction.are_convertible + ~subst ~metasenv context s hety ugraph) ; + fdebug := 0 ; + debug s [hety] ; + raise + (TypeCheckerFailure + (lazy (sprintf + ("Appl: wrong parameter-type, expected %s, found %s") + (CicPp.ppterm hetype) (CicPp.ppterm s)))) + end + | _ -> + raise (TypeCheckerFailure + (lazy "Appl: this is not a function, it cannot be applied")) + ) + + and returns_a_coinductive ~subst context ty = + let module C = Cic in + match CicReduction.whd ~subst context ty with + C.MutInd (uri,i,_) -> + (*CSC: definire una funzioncina per questo codice sempre replicato *) + let obj,_ = + try + CicEnvironment.get_cooked_obj ~trust:false CicUniv.empty_ugraph uri + with Not_found -> assert false + in + (match obj with + C.InductiveDefinition (itl,_,_,_) -> + let (_,is_inductive,_,_) = List.nth itl i in + if is_inductive then None else (Some uri) + | _ -> + raise (TypeCheckerFailure + (lazy ("Unknown mutual inductive definition:" ^ + UriManager.string_of_uri uri))) + ) + | C.Appl ((C.MutInd (uri,i,_))::_) -> + (let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in + match o with + C.InductiveDefinition (itl,_,_,_) -> + let (_,is_inductive,_,_) = List.nth itl i in + if is_inductive then None else (Some uri) + | _ -> + raise (TypeCheckerFailure + (lazy ("Unknown mutual inductive definition:" ^ + UriManager.string_of_uri uri))) + ) + | C.Prod (n,so,de) -> + returns_a_coinductive ~subst ((Some (n,C.Decl so))::context) de + | _ -> None + + in +(*CSC +debug_print (lazy ("INIZIO TYPE_OF_AUX " ^ CicPp.ppterm t)) ; flush stderr ; +let res = +*) + type_of_aux ~logger context t ugraph +(* +in debug_print (lazy "FINE TYPE_OF_AUX") ; flush stderr ; res +*) + +(* is a small constructor? *) +(*CSC: ottimizzare calcolando staticamente *) +and is_small_or_non_informative ~condition ~logger context paramsno c ugraph = + let rec is_small_or_non_informative_aux ~logger context c ugraph = + let module C = Cic in + match CicReduction.whd context c with + C.Prod (n,so,de) -> + let s,ugraph1 = type_of_aux' ~logger [] context so ugraph in + let b = condition s in + if b then + is_small_or_non_informative_aux + ~logger ((Some (n,(C.Decl so)))::context) de ugraph1 + else + false,ugraph1 + | _ -> true,ugraph (*CSC: we trust the type-checker *) + in + let (context',dx) = split_prods ~subst:[] context paramsno c in + is_small_or_non_informative_aux ~logger context' dx ugraph + +and is_small ~logger = + is_small_or_non_informative + ~condition:(fun s -> s=Cic.Sort Cic.Prop || s=Cic.Sort Cic.Set) + ~logger + +and is_non_informative ~logger = + is_small_or_non_informative + ~condition:(fun s -> s=Cic.Sort Cic.Prop) + ~logger + +and type_of ~logger t ugraph = +(*CSC +debug_print (lazy ("INIZIO TYPE_OF_AUX' " ^ CicPp.ppterm t)) ; flush stderr ; +let res = +*) + type_of_aux' ~logger [] [] t ugraph +(*CSC +in debug_print (lazy "FINE TYPE_OF_AUX'") ; flush stderr ; res +*) +;; + +let typecheck_obj0 ~logger uri (obj,unchecked_ugraph) = + let module C = Cic in + let ugraph = CicUniv.empty_ugraph in + let inferred_ugraph = + match obj with + | C.Constant (_,Some te,ty,_,_) -> + let _,ugraph = type_of ~logger ty ugraph in + let ty_te,ugraph = type_of ~logger te ugraph in + let b,ugraph = (CicReduction.are_convertible [] ty_te ty ugraph) in + if not b then + raise (TypeCheckerFailure + (lazy + ("the type of the body is not the one expected:\n" ^ + CicPp.ppterm ty_te ^ "\nvs\n" ^ + CicPp.ppterm ty))) + else + ugraph + | C.Constant (_,None,ty,_,_) -> + (* only to check that ty is well-typed *) + let _,ugraph = type_of ~logger ty ugraph in + ugraph + | C.CurrentProof (_,conjs,te,ty,_,_) -> + (* this block is broken since the metasenv should + * be topologically sorted before typing metas *) + ignore(assert false); + let _,ugraph = + List.fold_left + (fun (metasenv,ugraph) ((_,context,ty) as conj) -> + let _,ugraph = + type_of_aux' ~logger metasenv context ty ugraph + in + metasenv @ [conj],ugraph + ) ([],ugraph) conjs + in + let _,ugraph = type_of_aux' ~logger conjs [] ty ugraph in + let type_of_te,ugraph = + type_of_aux' ~logger conjs [] te ugraph + in + let b,ugraph = CicReduction.are_convertible [] type_of_te ty ugraph in + if not b then + raise (TypeCheckerFailure (lazy (sprintf + "the current proof is not well typed because the type %s of the body is not convertible to the declared type %s" + (CicPp.ppterm type_of_te) (CicPp.ppterm ty)))) + else + ugraph + | C.Variable (_,bo,ty,_,_) -> + (* only to check that ty is well-typed *) + let _,ugraph = type_of ~logger ty ugraph in + (match bo with + None -> ugraph + | Some bo -> + let ty_bo,ugraph = type_of ~logger bo ugraph in + let b,ugraph = CicReduction.are_convertible [] ty_bo ty ugraph in + if not b then + raise (TypeCheckerFailure + (lazy "the body is not the one expected")) + else + ugraph + ) + | (C.InductiveDefinition _ as obj) -> + check_mutual_inductive_defs ~logger uri obj ugraph + in + check_and_clean_ugraph inferred_ugraph unchecked_ugraph uri obj +;; + +let typecheck uri = + let module C = Cic in + let module R = CicReduction in + let module U = UriManager in + let logger = new CicLogger.logger in + match CicEnvironment.is_type_checked ~trust:false CicUniv.empty_ugraph uri with + | CicEnvironment.CheckedObj (cobj,ugraph') -> cobj,ugraph' + | CicEnvironment.UncheckedObj (uobj,unchecked_ugraph) -> + (* let's typecheck the uncooked object *) + logger#log (`Start_type_checking uri) ; + let ugraph, ul, obj = typecheck_obj0 ~logger uri (uobj,unchecked_ugraph) in + CicEnvironment.set_type_checking_info uri (obj,ugraph,ul); + logger#log (`Type_checking_completed uri); + match CicEnvironment.is_type_checked ~trust:false CicUniv.empty_ugraph uri with + | CicEnvironment.CheckedObj (cobj,ugraph') -> cobj,ugraph' + | _ -> raise CicEnvironmentError +;; + +let typecheck_obj ~logger uri obj = + let ugraph,univlist,obj = typecheck_obj0 ~logger uri (obj,None) in + CicEnvironment.add_type_checked_obj uri (obj,ugraph,univlist) + +(** wrappers which instantiate fresh loggers *) + +let profiler = HExtlib.profile "K/CicTypeChecker.type_of_aux'" + +let type_of_aux' ?(subst = []) metasenv context t ugraph = + let logger = new CicLogger.logger in + profiler.HExtlib.profile + (type_of_aux' ~logger ~subst metasenv context t) ugraph + +let typecheck_obj uri obj = + let logger = new CicLogger.logger in + typecheck_obj ~logger uri obj + +(* check_allowed_sort_elimination uri i s1 s2 + This function is used outside the kernel to determine in advance whether + a MutCase will be allowed or not. + [uri,i] is the type of the term to match + [s1] is the sort of the term to eliminate (i.e. the head of the arity + of the inductive type [uri,i]) + [s2] is the sort of the goal (i.e. the head of the type of the outtype + of the MutCase) *) +let check_allowed_sort_elimination uri i s1 s2 = + fst (check_allowed_sort_elimination ~subst:[] ~metasenv:[] + ~logger:(new CicLogger.logger) [] uri i true + (Cic.Implicit None) (* never used *) (Cic.Sort s1) (Cic.Sort s2) + CicUniv.empty_ugraph) +;; + +Deannotate.type_of_aux' := + fun context t -> + ignore ( + List.fold_right + (fun el context -> + (match el with + None -> () + | Some (_,Cic.Decl ty) -> + ignore (type_of_aux' [] context ty CicUniv.empty_ugraph) + | Some (_,Cic.Def (bo,ty)) -> + ignore (type_of_aux' [] context ty CicUniv.empty_ugraph); + ignore (type_of_aux' [] context bo CicUniv.empty_ugraph)); + el::context + ) context []); + fst (type_of_aux' [] context t CicUniv.empty_ugraph);;