-(* 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 check_homogeneous_call context indparamsno n uri reduct tl =
- let last =
- List.fold_left
- (fun k x ->
- if k = 0 then 0
- else
- match CicReduction.whd context x with
- | Cic.Rel m when m = n - (indparamsno - k) -> k - 1
- | _ -> raise (TypeCheckerFailure (lazy
- ("Argument "^string_of_int (indparamsno - k + 1) ^ " (of " ^
- string_of_int indparamsno ^ " fixed) is not homogeneous in "^
- "appl:\n"^ CicPp.ppterm reduct))))
- indparamsno tl
- in
- if last <> 0 then
- raise (TypeCheckerFailure
- (lazy ("Non-positive occurence in mutual inductive definition(s) [2]"^
- UriManager.string_of_uri uri)))
-;;
-
-
-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
-
-(* Inductive types being checked for positivity have *)
-(* indexes x s.t. n < x <= nn. *)
-and weakly_positive context n nn uri indparamsno posuri te =
- let module C = Cic in
- (*CSC: Not very nice. *)
- let leftno =
- match CicEnvironment.get_obj CicUniv.oblivion_ugraph uri with
- | Cic.InductiveDefinition (_,_,leftno,_), _ -> leftno
- | _ -> assert false
- in
- let dummy = Cic.Sort Cic.Prop in
- (*CSC: to be moved in cicSubstitution? *)
- let rec subst_inductive_type_with_dummy =
- function
- C.MutInd (uri',0,_) when UriManager.eq uri' uri ->
- dummy
- | C.Appl ((C.MutInd (uri',0,_))::tl) when UriManager.eq uri' uri ->
- let _, rargs = HExtlib.split_nth leftno tl in
- if rargs = [] then dummy else Cic.Appl (dummy :: rargs)
- | C.Cast (te,ty) -> subst_inductive_type_with_dummy te
- | C.Prod (name,so,ta) ->
- C.Prod (name, subst_inductive_type_with_dummy so,
- subst_inductive_type_with_dummy ta)
- | C.Lambda (name,so,ta) ->
- C.Lambda (name, subst_inductive_type_with_dummy so,
- subst_inductive_type_with_dummy ta)
- | C.LetIn (name,so,ty,ta) ->
- C.LetIn (name, subst_inductive_type_with_dummy so,
- subst_inductive_type_with_dummy ty,
- subst_inductive_type_with_dummy ta)
- | C.Appl tl ->
- C.Appl (List.map subst_inductive_type_with_dummy tl)
- | C.MutCase (uri,i,outtype,term,pl) ->
- C.MutCase (uri,i,
- subst_inductive_type_with_dummy outtype,
- subst_inductive_type_with_dummy term,
- List.map subst_inductive_type_with_dummy pl)
- | C.Fix (i,fl) ->
- C.Fix (i,List.map (fun (name,i,ty,bo) -> (name,i,
- subst_inductive_type_with_dummy ty,
- subst_inductive_type_with_dummy bo)) fl)
- | C.CoFix (i,fl) ->
- C.CoFix (i,List.map (fun (name,ty,bo) -> (name,
- subst_inductive_type_with_dummy ty,
- subst_inductive_type_with_dummy bo)) fl)
- | C.Const (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map
- (function (uri,t) -> (uri,subst_inductive_type_with_dummy 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 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 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 t))
- exp_named_subst
- in
- C.MutConstruct (uri,typeno,consno,exp_named_subst')
- | t -> t
- in
- (* this function has the same semantics of are_all_occurrences_positive
- but the i-th context entry role is played by dummy and some checks
- are skipped because we already know that are_all_occurrences_positive
- of uri in te. *)
- let rec aux context n nn te =
- match CicReduction.whd context te with
- | C.Appl (C.Sort C.Prop::tl) ->
- List.for_all (does_not_occur context n nn) tl
- | C.Sort C.Prop -> 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 indparamsno posuri source &&
- aux ((Some (name,(C.Decl source)))::context)
- (n + 1) (nn + 1) dest
- | C.Prod (name,source,dest) ->
- does_not_occur context n nn source &&
- aux ((Some (name,(C.Decl source)))::context)
- (n + 1) (nn + 1) dest
- | _ ->
- raise (TypeCheckerFailure (lazy "Malformed inductive constructor type"))
- in
- aux context n nn (subst_inductive_type_with_dummy te)
-
-(* 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 indparamsno posuri 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 _ when indparamsno = 0 -> true
- | C.Cast (te,ty) ->
- (*CSC: bisogna controllare ty????*)
- strictly_positive context n nn indparamsno posuri 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)
- indparamsno posuri ta
- | C.Appl ((C.Rel m)::tl) as reduct when m > n && m <= nn ->
- check_homogeneous_call context indparamsno n posuri reduct tl;
- 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
- indparamsno posuri 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) as reduct when m = i ->
- check_homogeneous_call context indparamsno n uri reduct tl;
- List.fold_right (fun x i -> i && does_not_occur context n nn x) tl true
- | 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 indparamsno uri 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.rev_map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) itl in
- let _,ugraph2 =
- List.fold_right
- (fun (_,_,ty,cl) (i,ugraph) ->
- let _,ty_sort = split_prods ~subst:[] [] ~-1 ty in
- let ugraph'' =
- List.fold_left
- (fun ugraph (name,te) ->
- let te = debrujin_constructor uri len [] te in
- let context,te = split_prods ~subst:[] tys indparamsno te in
- let con_sort,ugraph = type_of_aux' ~logger [] context te ugraph in
- let ugraph =
- match
- CicReduction.whd context con_sort, CicReduction.whd [] ty_sort
- with
- Cic.Sort (Cic.Type u1), Cic.Sort (Cic.Type u2)
- | Cic.Sort (Cic.CProp u1), Cic.Sort (Cic.CProp u2)
- | Cic.Sort (Cic.Type u1), Cic.Sort (Cic.CProp u2)
- | Cic.Sort (Cic.CProp u1), Cic.Sort (Cic.Type u2) ->
- CicUniv.add_ge u2 u1 ugraph
- | Cic.Sort _, Cic.Sort Cic.Prop
- | Cic.Sort _, Cic.Sort Cic.CProp _
- | Cic.Sort _, Cic.Sort Cic.Set
- | Cic.Sort _, Cic.Sort Cic.Type _ -> ugraph
- | a,b ->
- raise
- (TypeCheckerFailure
- (lazy ("Wrong constructor or inductive arity shape: "^
- CicPp.ppterm a ^ " --- " ^ CicPp.ppterm b))) in
- (* let's check also the positivity conditions *)
- if
- not
- (are_all_occurrences_positive context uri indparamsno
- (i+indparamsno) indparamsno (len+indparamsno) te)
- then
- raise
- (TypeCheckerFailure
- (lazy ("Non positive occurence in " ^ U.string_of_uri uri)))
- 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.Sort _) when n <= 0 -> context,te
- | (n, C.Prod (name,so,ta)) ->
- 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, paramsno
- | _ -> 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.fold_left
- (fun (types,len) (n,_,ty,_) ->
- Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
- len+1)
- ([],0) 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
- let t = CicReduction.whd ~delta:false ~subst context t in
- let res =
- match 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.fold_left
- (fun (types,len) (n,_,ty,_) ->
- Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
- len+1)
- ([],0) 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
- in
- if res then res
- else
- let t' = CicReduction.whd ~subst context t in
- if t = t' then
- false
- else
- guarded_by_destructors rec_uri rec_uri_len ~logger ~metasenv ~subst context n nn kl x safes t'
-
-(* 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 ~logger ~subst ~metasenv indURI =
- let module C = Cic in
- let rec aux context n nn h te =
- match CicReduction.whd ~subst context te with
- | C.Rel m when m > n && m <= nn -> h
- | C.Rel _
- | C.Meta _ -> true
- | C.Sort _
- | C.Implicit _
- | C.Cast _
- | C.Prod _
- | C.MutInd _
- | C.LetIn _ -> raise (AssertFailure (lazy "17"))
- | C.Lambda (name,so,de) ->
- does_not_occur ~subst context n nn so &&
- aux ((Some (name,(C.Decl so)))::context) (n + 1) (nn + 1) h de
- | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
- h && List.for_all (does_not_occur ~subst context n nn) tl
- | C.MutConstruct (_,_,_,exp_named_subst) ->
- List.for_all
- (fun (_,x) -> does_not_occur ~subst context n nn x) exp_named_subst
- | C.Appl ((C.MutConstruct (uri,i,j,exp_named_subst))::tl) as t ->
- List.for_all
- (fun (_,x) -> does_not_occur ~subst context n nn x) exp_named_subst &&
- let consty, len_tys, tys_ctx, paramsno =
- let tys, paramsno =
- specialize_inductive_type ~logger ~subst ~metasenv context t in
- let _,_,_,cl = List.nth tys i in
- let _,ty = List.nth cl (j-1) in
- ty, List.length tys,
- fst(List.fold_left
- (fun (types,len) (n,_,ty,_) ->
- Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, len+1)
- ([],0) tys), paramsno
- in
- let rec_params =
- let c =
- debrujin_constructor ~check_exp_named_subst:false
- indURI len_tys context consty
- in
- let len_ctx = List.length context in
- recursive_args (context@tys_ctx) len_ctx (len_ctx+len_tys) c
- in
- let rec analyse_instantiated_type rec_spec args =
- match rec_spec, args with
- | h::rec_spec, he::args ->
- aux context n nn h he &&
- analyse_instantiated_type rec_spec args
- | _,[] -> true
- | _ -> raise (AssertFailure (lazy
- ("Too many args for constructor: " ^ String.concat " "
- (List.map (fun x-> CicPp.ppterm x) args))))
- in
- let left, args = HExtlib.split_nth paramsno tl in
- List.for_all (does_not_occur ~subst context n nn) left &&
- analyse_instantiated_type rec_params args
- | C.Appl ((C.MutCase (_,_,out,te,pl))::_)
- | C.MutCase (_,_,out,te,pl) as t ->
- let tl = match t with C.Appl (_::tl) -> tl | _ -> [] in
- List.for_all (does_not_occur ~subst context n nn) tl &&
- does_not_occur ~subst context n nn out &&
- does_not_occur ~subst context n nn te &&
- List.for_all (aux context n nn h ) pl
- | C.Fix (_,fl)
- | C.Appl (C.Fix (_,fl)::_) as t ->
- let tl = match t with C.Appl (_::tl) -> tl | _ -> [] in
- let len = List.length fl in
- let n_plus_len = n + len
- and nn_plus_len = nn + 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
- in
- List.for_all (does_not_occur ~subst context n nn) tl &&
- List.for_all
- (fun (_,_,ty,bo) ->
- does_not_occur ~subst context n nn ty &&
- aux (tys@context) n_plus_len nn_plus_len h bo)
- fl
- | C.Appl ((C.CoFix (_,fl))::_)
- | C.CoFix (_,fl) as t ->
- let tl = match t with C.Appl (_::tl) -> tl | _ -> [] in
- let len = List.length fl in
- let n_plus_len = n + len
- and nn_plus_len = nn + 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
- in
- List.for_all (does_not_occur ~subst context n nn) tl &&
- List.for_all
- (fun (_,ty,bo) ->
- does_not_occur ~subst context n nn ty &&
- aux (tys@context) n_plus_len nn_plus_len h bo)
- fl
- | C.Var _
- | C.Const _
- | C.Appl _ as t -> does_not_occur ~subst context n nn t
- in
- aux
-
-and is_non_recursive ctx paramsno t uri =
- let t = debrujin_constructor uri 1 [] t in
-(* let ctx, t = split_prods ~subst:[] ctx paramsno t in *)
- let len = List.length ctx in
- let rec aux ctx n nn t =
- match CicReduction.whd ctx t with
- | Cic.Prod (name,src,tgt) ->
- does_not_occur ctx n nn src &&
- aux (Some (name,Cic.Decl src) :: ctx) (n+1) (nn+1) tgt
- | (Cic.Rel k)
- | Cic.Appl (Cic.Rel k :: _) when k = nn -> true
- | t -> assert false
- in
- aux ctx (len-1) len t
-
-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
- let b, ug =
- is_non_informative ~logger [Some (C.Name name,C.Decl ty)]
- paramsno (snd (List.nth cl 0)) ugraph
- in
- b &&
- is_non_recursive [Some (C.Name name,C.Decl ty)]
- paramsno (snd (List.nth cl 0)) uri, ug
- 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.Set, C.Sort C.Set) when need_dummy -> true , ugraph
- | (C.Sort C.Set, C.Sort (C.Type _))
- | (C.Sort C.Set, C.Sort (C.CProp _))
- 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
- | (C.Sort (C.CProp _), 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
-(* FG: DEBUG ONLY
- prerr_endline ("TC: context:\n" ^ CicPp.ppcontext ~metasenv context);
- prerr_endline ("TC: term :\n" ^ CicPp.ppterm ~metasenv t ^ "\n");
-*)
- 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 uri ~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.CProp 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 (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 (C.Prop|C.Set) -> (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 uri ~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 uri ~logger ~subst context exp_named_subst ugraph
- in
- let mty,ugraph2 = type_of_mutual_inductive_defs ~logger uri i ugraph1 in
- 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 uri ~logger ~subst context exp_named_subst ugraph
- in
- 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 ~logger ~subst ~metasenv uri
- (types @ context) 0 len false bo) 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 uri ~logger ~subst context ens ugraph =
- let params =
- let obj,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
- (match obj with
- Cic.Constant (_,_,_,params,_) -> params
- | Cic.Variable (_,_,_,params,_) -> params
- | Cic.CurrentProof (_,_,_,_,params,_) -> params
- | Cic.InductiveDefinition (_,params,_,_) -> params
- ) in
- let rec check_same_order params ens =
- match params,ens with
- | _,[] -> ()
- | [],_::_ ->
- raise (TypeCheckerFailure (lazy "Bad explicit named substitution"))
- | uri::tl,(uri',_)::tl' when UriManager.eq uri uri' ->
- check_same_order tl tl'
- | _::tl,l -> check_same_order tl l
- in
- 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_same_order params ens ;
- check_exp_named_subst_aux ~logger [] ens ugraph
-
- 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 (C.Prop | C.Set)) ->
- (* different from Coq manual!!! *)
- t2',ugraph
- | (C.Sort (C.Type t1 | C.CProp t1), C.Sort (C.Type t2)) ->
- 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.CProp t1 | C.Type t1), C.Sort (C.CProp t2)) ->
- 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.CProp t'),ugraph2
- with
- CicUniv.UniverseInconsistency msg -> raise (TypeCheckerFailure msg))
- | (C.Sort _,C.Sort (C.Type t1)) -> C.Sort (C.Type t1),ugraph
- | (C.Sort _,C.Sort (C.CProp t1)) -> C.Sort (C.CProp t1),ugraph
- | (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 ?(trust=true) 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 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 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);;