--- /dev/null
+(* 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);;
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