open Printf
exception RefineFailure of string;;
-
-exception Impossible of int;;
-exception NotRefinable of string;;
exception Uncertain of string;;
-exception WrongUriToConstant of string;;
-exception WrongUriToVariable of string;;
-exception ListTooShort;;
-exception WrongUriToMutualInductiveDefinitions of string;;
-exception RelToHiddenHypothesis;;
-exception WrongArgumentNumber;;
+exception AssertFailure of string;;
-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 (NotRefinable ("\n" ^ List.fold_right debug_aux (t::context) ""))
- (*print_endline ("\n" ^ List.fold_right debug_aux (t::context) "") ; flush stdout*)
-;;
+let debug_print = fun _ -> ()
-let debug_print = prerr_endline
+let fo_unif_subst subst context metasenv t1 t2 ugraph =
+ try
+ CicUnification.fo_unif_subst subst context metasenv t1 t2 ugraph
+ with
+ (CicUnification.UnificationFailure msg) -> raise (RefineFailure msg)
+ | (CicUnification.Uncertain msg) -> raise (Uncertain msg)
+;;
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 ListTooShort
+ | (_,_) -> raise (AssertFailure "split: list too short")
;;
-let rec type_of_constant uri =
- let module C = Cic in
- let module R = CicReduction in
- let module U = UriManager in
- match CicEnvironment.get_cooked_obj uri with
- C.Constant (_,_,ty,_) -> ty
- | C.CurrentProof (_,_,_,ty,_) -> ty
- | _ -> raise (WrongUriToConstant (U.string_of_uri uri))
+let rec type_of_constant uri ugraph =
+ let module C = Cic in
+ let module R = CicReduction in
+ let module U = UriManager in
+ (*
+ let obj =
+ try
+ CicEnvironment.get_cooked_obj uri
+ with Not_found -> assert false
+ in
+ *)
+ let obj,u= CicEnvironment.get_obj ugraph uri in
+ match obj with
+ C.Constant (_,_,ty,_,_) -> ty,u
+ | C.CurrentProof (_,_,_,ty,_,_) -> ty,u
+ | _ ->
+ raise
+ (RefineFailure ("Unknown constant definition " ^ U.string_of_uri uri))
+
+and type_of_variable uri ugraph =
+ let module C = Cic in
+ let module R = CicReduction in
+ let module U = UriManager in
+ (*
+ let obj =
+ try
+ CicEnvironment.get_cooked_obj uri
+ with Not_found -> assert false
+ in
+ *)
+ let obj,u = CicEnvironment.get_obj ugraph uri in
+ match obj with
+ C.Variable (_,_,ty,_,_) -> ty,u
+ | _ ->
+ raise
+ (RefineFailure
+ ("Unknown variable definition " ^ UriManager.string_of_uri uri))
-and type_of_variable uri =
- let module C = Cic in
- let module R = CicReduction in
- let module U = UriManager in
- match CicEnvironment.get_cooked_obj uri with
- C.Variable (_,_,ty,_) -> ty
- | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
+and type_of_mutual_inductive_defs uri i ugraph =
+ let module C = Cic in
+ let module R = CicReduction in
+ let module U = UriManager in
+ (*
+ let obj =
+ try
+ CicEnvironment.get_cooked_obj uri
+ with Not_found -> assert false
+ in
+ *)
+ let obj,u = CicEnvironment.get_obj ugraph uri in
+ match obj with
+ C.InductiveDefinition (dl,_,_,_) ->
+ let (_,_,arity,_) = List.nth dl i in
+ arity,u
+ | _ ->
+ raise
+ (RefineFailure
+ ("Unknown mutual inductive definition " ^ U.string_of_uri uri))
-and type_of_mutual_inductive_defs uri i =
- let module C = Cic in
- let module R = CicReduction in
- let module U = UriManager in
- match CicEnvironment.get_cooked_obj uri with
- C.InductiveDefinition (dl,_,_) ->
- let (_,_,arity,_) = List.nth dl i in
- arity
- | _ -> raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
+and type_of_mutual_inductive_constr uri i j ugraph =
+ let module C = Cic in
+ let module R = CicReduction in
+ let module U = UriManager in
+ (*
+ let obj =
+ try
+ CicEnvironment.get_cooked_obj uri
+ with Not_found -> assert false
+ in
+ *)
+ let obj,u = CicEnvironment.get_obj ugraph uri in
+ match obj with
+ C.InductiveDefinition (dl,_,_,_) ->
+ let (_,_,_,cl) = List.nth dl i in
+ let (_,ty) = List.nth cl (j-1) in
+ ty,u
+ | _ ->
+ raise
+ (RefineFailure
+ ("Unkown mutual inductive definition " ^ U.string_of_uri uri))
-and type_of_mutual_inductive_constr uri i j =
- let module C = Cic in
- let module R = CicReduction in
- let module U = UriManager in
- match CicEnvironment.get_cooked_obj uri with
- C.InductiveDefinition (dl,_,_) ->
- let (_,_,_,cl) = List.nth dl i in
- let (_,ty) = List.nth cl (j-1) in
- ty
- | _ -> raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
(* type_of_aux' is just another name (with a different scope) for type_of_aux *)
try to synthesize it from the above information, that is in general
a second order unification problem. *)
-and check_branch n context metasenv subst left_args_no actualtype term expectedtype =
+and check_branch n context metasenv subst left_args_no actualtype term expectedtype ugraph =
let module C = Cic in
- let module R = CicMetaSubst in
- let module Un = CicUnification in
- match R.whd subst context expectedtype with
- C.MutInd (_,_,_) ->
- (n,context,actualtype, [term]), subst, metasenv
- | C.Appl (C.MutInd (_,_,_)::tl) ->
- let (_,arguments) = split tl left_args_no in
- (n,context,actualtype, arguments@[term]), subst, metasenv
- | C.Prod (name,so,de) ->
- (* we expect that the actual type of the branch has the due
- number of Prod *)
- (match R.whd subst context actualtype with
- C.Prod (name',so',de') ->
- let subst, metasenv =
- Un.fo_unif_subst subst context metasenv so so' in
- 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
- (* we should also check that the name variable is anonymous in
- the actual type de' ?? *)
- check_branch (n+1) ((Some (name,(C.Decl so)))::context) metasenv subst left_args_no de' term' de
- | _ -> raise WrongArgumentNumber)
- | _ -> raise (NotRefinable "Prod or MutInd expected")
+ (* let module R = CicMetaSubst in *)
+ let module R = CicReduction in
+ match R.whd ~subst context expectedtype with
+ C.MutInd (_,_,_) ->
+ (n,context,actualtype, [term]), subst, metasenv, ugraph
+ | C.Appl (C.MutInd (_,_,_)::tl) ->
+ let (_,arguments) = split tl left_args_no in
+ (n,context,actualtype, arguments@[term]), subst, metasenv, ugraph
+ | C.Prod (name,so,de) ->
+ (* we expect that the actual type of the branch has the due
+ number of Prod *)
+ (match R.whd ~subst context actualtype with
+ C.Prod (name',so',de') ->
+ let subst, metasenv, ugraph1 =
+ fo_unif_subst subst context metasenv so so' ugraph in
+ 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
+ (* we should also check that the name variable is anonymous in
+ the actual type de' ?? *)
+ check_branch (n+1)
+ ((Some (name,(C.Decl so)))::context)
+ metasenv subst left_args_no de' term' de ugraph1
+ | _ -> raise (AssertFailure "Wrong number of arguments"))
+ | _ -> raise (AssertFailure "Prod or MutInd expected")
-and type_of_aux' metasenv context t =
- let rec type_of_aux subst metasenv context =
- let module C = Cic in
- let module S = CicSubstitution in
- let module U = UriManager in
- let module Un = CicUnification in
- function
- C.Rel n ->
- (try
- match List.nth context (n - 1) with
- Some (_,C.Decl t) -> S.lift n t,subst,metasenv
- | Some (_,C.Def (_,Some ty)) -> S.lift n ty,subst,metasenv
- | Some (_,C.Def (bo,None)) ->
- type_of_aux subst metasenv context (S.lift n bo)
- | None -> raise RelToHiddenHypothesis
- with
- _ -> raise (NotRefinable "Not a close term")
- )
- | C.Var (uri,exp_named_subst) ->
- incr fdebug ;
- let subst',metasenv' =
- check_exp_named_subst subst metasenv context exp_named_subst in
- let ty =
- CicSubstitution.subst_vars exp_named_subst (type_of_variable uri)
- in
- decr fdebug ;
- ty,subst',metasenv'
- | C.Meta (n,l) ->
- let (_,canonical_context,ty) = CicUtil.lookup_meta n metasenv in
- let subst',metasenv' =
- check_metasenv_consistency n subst metasenv context canonical_context l
- in
- CicSubstitution.lift_meta l ty, subst', metasenv'
- | C.Sort s ->
- C.Sort C.Type, (*CSC manca la gestione degli universi!!! *)
- subst,metasenv
- | C.Implicit -> raise (Impossible 21)
- | C.Cast (te,ty) ->
- let _,subst',metasenv' =
- type_of_aux subst metasenv context ty in
- let inferredty,subst'',metasenv'' =
- type_of_aux subst' metasenv' context te
- in
- (try
- let subst''',metasenv''' =
- Un.fo_unif_subst subst'' context metasenv'' inferredty ty
- in
- ty,subst''',metasenv'''
- with
- _ -> raise (NotRefinable "Cast"))
- | C.Prod (name,s,t) ->
- let sort1,subst',metasenv' = type_of_aux subst metasenv context s in
- let sort2,subst'',metasenv'' =
- type_of_aux subst' metasenv' ((Some (name,(C.Decl s)))::context) t
- in
- sort_of_prod subst'' metasenv'' context (name,s) (sort1,sort2),
- subst'',metasenv''
- | C.Lambda (n,s,t) ->
- let sort1,subst',metasenv' = type_of_aux subst metasenv context s in
- let type2,subst'',metasenv'' =
- type_of_aux subst' metasenv' ((Some (n,(C.Decl s)))::context) t
- in
- let sort2,subst''',metasenv''' =
- type_of_aux subst'' metasenv''((Some (n,(C.Decl s)))::context) type2
- in
- (* only to check if the product is well-typed *)
- let _ =
- sort_of_prod subst''' metasenv''' context (n,s) (sort1,sort2)
- in
- C.Prod (n,s,type2),subst''',metasenv'''
- | C.LetIn (n,s,t) ->
- (* only to check if s is well-typed *)
- let ty,subst',metasenv' = type_of_aux subst metasenv context s in
- let inferredty,subst'',metasenv'' =
- type_of_aux subst' metasenv' ((Some (n,(C.Def (s,Some ty))))::context) t
- in
- (* One-step LetIn reduction. Even faster than the previous solution.
- Moreover the inferred type is closer to the expected one. *)
- CicSubstitution.subst s inferredty,subst',metasenv'
- | C.Appl (he::tl) when List.length tl > 0 ->
- let hetype,subst',metasenv' = type_of_aux subst metasenv context he in
- let tlbody_and_type,subst'',metasenv'' =
- List.fold_right
- (fun x (res,subst,metasenv) ->
- let ty,subst',metasenv' =
- type_of_aux subst metasenv context x
- in
- (x, ty)::res,subst',metasenv'
- ) tl ([],subst',metasenv')
- in
- eat_prods subst'' metasenv'' context hetype tlbody_and_type
- | C.Appl _ -> raise (NotRefinable "Appl: no arguments")
- | C.Const (uri,exp_named_subst) ->
- incr fdebug ;
- let subst',metasenv' =
- check_exp_named_subst subst metasenv context exp_named_subst in
- let cty =
- CicSubstitution.subst_vars exp_named_subst (type_of_constant uri)
- in
- decr fdebug ;
- cty,subst',metasenv'
- | C.MutInd (uri,i,exp_named_subst) ->
- incr fdebug ;
- let subst',metasenv' =
- check_exp_named_subst subst metasenv context exp_named_subst in
- let cty =
- CicSubstitution.subst_vars exp_named_subst
- (type_of_mutual_inductive_defs uri i)
- in
- decr fdebug ;
- cty,subst',metasenv'
- | C.MutConstruct (uri,i,j,exp_named_subst) ->
- let subst',metasenv' =
- check_exp_named_subst subst metasenv context exp_named_subst in
- let cty =
- CicSubstitution.subst_vars exp_named_subst
- (type_of_mutual_inductive_constr uri i j)
- in
- cty,subst',metasenv'
- | C.MutCase (uri, i, outtype, term, pl) ->
- (* first, get the inductive type (and noparams) in the environment *)
- let (_,b,arity,constructors), expl_params, no_left_params =
- match CicEnvironment.get_cooked_obj ~trust:true uri with
- C.InductiveDefinition (l,expl_params,parsno) ->
- List.nth l i , expl_params, parsno
- | _ ->
- raise
- (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri)) in
- let rec count_prod t =
- match CicMetaSubst.whd subst context t with
- C.Prod (_, _, t) -> 1 + (count_prod t)
- | _ -> 0 in
- let no_args = count_prod arity in
- (* now, create a "generic" MutInd *)
- let metasenv,left_args =
- CicMkImplicit.n_fresh_metas metasenv context no_left_params in
- let metasenv,right_args =
- let no_right_params = no_args - no_left_params in
- if no_right_params < 0 then assert false
- else CicMkImplicit.n_fresh_metas metasenv context no_right_params in
- let metasenv,exp_named_subst =
- CicMkImplicit.fresh_subst metasenv context expl_params in
- let expected_type =
- if no_args = 0 then
- C.MutInd (uri,i,exp_named_subst)
- else
- C.Appl (C.MutInd (uri,i,exp_named_subst)::(left_args @ right_args))
- in
- (* check consistency with the actual type of term *)
- let actual_type,subst,metasenv =
- type_of_aux subst metasenv context term in
- let _, subst, metasenv =
- type_of_aux subst metasenv context expected_type
- in
- let actual_type = CicMetaSubst.whd subst context actual_type in
- let subst,metasenv =
- Un.fo_unif_subst subst context metasenv expected_type actual_type
- in
- (* TODO: check if the sort elimination is allowed: [(I q1 ... qr)|B] *)
- let (_,outtypeinstances,subst,metasenv) =
- List.fold_left
- (fun (j,outtypeinstances,subst,metasenv) p ->
- let constructor =
- if left_args = [] then
- (C.MutConstruct (uri,i,j,exp_named_subst))
- else
- (C.Appl (C.MutConstruct (uri,i,j,exp_named_subst)::left_args))
- in
- let actual_type,subst,metasenv =
- type_of_aux subst metasenv context p in
- let expected_type, subst, metasenv =
- type_of_aux subst metasenv context constructor in
- let outtypeinstance,subst,metasenv =
- check_branch
- 0 context metasenv subst
- no_left_params actual_type constructor expected_type in
- (j+1,outtypeinstance::outtypeinstances,subst,metasenv))
- (1,[],subst,metasenv) pl in
- (* we are left to check that the outype matches his instances.
- The easy case is when the outype is specified, that amount
- to a trivial check. Otherwise, we should guess a type from
- its instances *)
- (* easy case *)
- let _, subst, metasenv =
- type_of_aux subst metasenv context
- (C.Appl ((outtype :: right_args) @ [term]))
- in
- let (subst,metasenv) =
- List.fold_left
- (fun (subst,metasenv) (constructor_args_no,context,instance,args) ->
- let instance' =
- let appl =
- let outtype' =
- CicSubstitution.lift constructor_args_no outtype
- in
- C.Appl (outtype'::args)
- in
-(*
- (* if appl is not well typed then the type_of below solves the
- * problem *)
- let (_, subst, metasenv) =
- type_of_aux subst metasenv context appl
- in
-*)
- CicMetaSubst.whd subst context appl
- in
- Un.fo_unif_subst subst context metasenv instance instance')
- (subst,metasenv) outtypeinstances in
- CicMetaSubst.whd subst
- context (C.Appl(outtype::right_args@[term])),subst,metasenv
- | C.Fix (i,fl) ->
- let subst,metasenv,types =
- List.fold_left
- (fun (subst,metasenv,types) (n,_,ty,_) ->
- let _,subst',metasenv' = type_of_aux subst metasenv context ty in
- subst',metasenv', Some (C.Name n,(C.Decl ty)) :: types
- ) (subst,metasenv,[]) fl
- in
- let len = List.length types in
- let context' = types@context in
- let subst,metasenv =
- List.fold_left
- (fun (subst,metasenv) (name,x,ty,bo) ->
- let ty_of_bo,subst,metasenv =
- type_of_aux subst metasenv context' bo
+and type_of_aux' metasenv context t ugraph =
+ let rec type_of_aux subst metasenv context t ugraph =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module U = UriManager in
+ match t with
+ (* function *)
+ C.Rel n ->
+ (try
+ match List.nth context (n - 1) with
+ Some (_,C.Decl ty) ->
+ t,S.lift n ty,subst,metasenv, ugraph
+ | Some (_,C.Def (_,Some ty)) ->
+ t,S.lift n ty,subst,metasenv, ugraph
+ | Some (_,C.Def (bo,None)) ->
+ type_of_aux subst metasenv context (S.lift n bo) ugraph
+ | None -> raise (RefineFailure "Rel to hidden hypothesis")
+ with
+ _ -> raise (RefineFailure "Not a close term")
+ )
+ | C.Var (uri,exp_named_subst) ->
+ let exp_named_subst',subst',metasenv',ugraph1 =
+ check_exp_named_subst
+ subst metasenv context exp_named_subst ugraph
+ in
+ let ty_uri,ugraph1 = type_of_variable uri ugraph in
+ let ty =
+ CicSubstitution.subst_vars exp_named_subst' ty_uri
+ in
+ C.Var (uri,exp_named_subst'),ty,subst',metasenv',ugraph1
+ | C.Meta (n,l) ->
+ (try
+ let (canonical_context, term,ty) =
+ CicUtil.lookup_subst n subst
+ in
+ let l',subst',metasenv',ugraph1 =
+ check_metasenv_consistency n subst metasenv context
+ canonical_context l ugraph
+ in
+ (* trust or check ??? *)
+ C.Meta (n,l'),CicSubstitution.subst_meta l' ty,
+ subst', metasenv', ugraph1
+ (* type_of_aux subst metasenv
+ context (CicSubstitution.subst_meta l term) *)
+ with CicUtil.Subst_not_found _ ->
+ let (_,canonical_context,ty) = CicUtil.lookup_meta n metasenv in
+ let l',subst',metasenv', ugraph1 =
+ check_metasenv_consistency n subst metasenv context
+ canonical_context l ugraph
+ in
+ C.Meta (n,l'),CicSubstitution.subst_meta l' ty,
+ subst', metasenv',ugraph1)
+ | C.Sort (C.Type tno) ->
+ let tno' = CicUniv.fresh() in
+ let ugraph1 = CicUniv.add_gt tno' tno ugraph in
+ t,(C.Sort (C.Type tno')),subst,metasenv,ugraph1
+ | C.Sort _ ->
+ t,C.Sort (C.Type (CicUniv.fresh())),subst,metasenv,ugraph
+ | C.Implicit _ -> raise (AssertFailure "21")
+ | C.Cast (te,ty) ->
+ let ty',_,subst',metasenv',ugraph1 =
+ type_of_aux subst metasenv context ty ugraph
+ in
+ let te',inferredty,subst'',metasenv'',ugraph2 =
+ type_of_aux subst' metasenv' context te ugraph1
+ in
+ (try
+ let subst''',metasenv''',ugraph3 =
+ fo_unif_subst subst'' context metasenv''
+ inferredty ty ugraph2
+ in
+ C.Cast (te',ty'),ty',subst''',metasenv''',ugraph3
+ with
+ _ -> raise (RefineFailure "Cast"))
+ | C.Prod (name,s,t) ->
+ let s',sort1,subst',metasenv',ugraph1 =
+ type_of_aux subst metasenv context s ugraph
+ in
+ let t',sort2,subst'',metasenv'',ugraph2 =
+ type_of_aux subst' metasenv'
+ ((Some (name,(C.Decl s')))::context) t ugraph1
+ in
+ let sop,subst''',metasenv''',ugraph3 =
+ sort_of_prod subst'' metasenv''
+ context (name,s') (sort1,sort2) ugraph2
+ in
+ C.Prod (name,s',t'),sop,subst''',metasenv''',ugraph3
+ | C.Lambda (n,s,t) ->
+ let s',sort1,subst',metasenv',ugraph1 =
+ type_of_aux subst metasenv context s ugraph
+ in
+ (match CicReduction.whd ~subst:subst' context sort1 with
+ C.Meta _
+ | C.Sort _ -> ()
+ | _ ->
+ raise (RefineFailure (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 t',type2,subst'',metasenv'',ugraph2 =
+ type_of_aux subst' metasenv'
+ ((Some (n,(C.Decl s')))::context) t ugraph1
+ in
+ C.Lambda (n,s',t'),C.Prod (n,s',type2),
+ subst'',metasenv'',ugraph2
+ | C.LetIn (n,s,t) ->
+ (* only to check if s is well-typed *)
+ let s',ty,subst',metasenv',ugraph1 =
+ type_of_aux subst metasenv context s ugraph
+ in
+ let t',inferredty,subst'',metasenv'',ugraph2 =
+ type_of_aux subst' metasenv'
+ ((Some (n,(C.Def (s',Some ty))))::context) t ugraph1
+ in
+ (* One-step LetIn reduction.
+ * Even faster than the previous solution.
+ * Moreover the inferred type is closer to the expected one.
+ *)
+ C.LetIn (n,s',t'),CicSubstitution.subst s' inferredty,
+ subst'',metasenv'',ugraph2
+ | C.Appl (he::((_::_) as tl)) ->
+ let he',hetype,subst',metasenv',ugraph1 =
+ type_of_aux subst metasenv context he ugraph
+ in
+ let tlbody_and_type,subst'',metasenv'',ugraph2 =
+ List.fold_right
+ (fun x (res,subst,metasenv,ugraph) ->
+ let x',ty,subst',metasenv',ugraph1 =
+ type_of_aux subst metasenv context x ugraph
+ in
+ (x', ty)::res,subst',metasenv',ugraph1
+ ) tl ([],subst',metasenv',ugraph1)
+ in
+ let tl',applty,subst''',metasenv''',ugraph3 =
+ eat_prods subst'' metasenv'' context
+ hetype tlbody_and_type ugraph2
+ in
+ C.Appl (he'::tl'), applty,subst''',metasenv''',ugraph3
+ | C.Appl _ -> raise (RefineFailure "Appl: no arguments")
+ | C.Const (uri,exp_named_subst) ->
+ let exp_named_subst',subst',metasenv',ugraph1 =
+ check_exp_named_subst subst metasenv context
+ exp_named_subst ugraph in
+ let ty_uri,ugraph2 = type_of_constant uri ugraph1 in
+ let cty =
+ CicSubstitution.subst_vars exp_named_subst' ty_uri
+ in
+ C.Const (uri,exp_named_subst'),cty,subst',metasenv',ugraph2
+ | C.MutInd (uri,i,exp_named_subst) ->
+ let exp_named_subst',subst',metasenv',ugraph1 =
+ check_exp_named_subst subst metasenv context
+ exp_named_subst ugraph
+ in
+ let ty_uri,ugraph2 = type_of_mutual_inductive_defs uri i ugraph1 in
+ let cty =
+ CicSubstitution.subst_vars exp_named_subst' ty_uri in
+ C.MutInd (uri,i,exp_named_subst'),cty,subst',metasenv',ugraph2
+ | C.MutConstruct (uri,i,j,exp_named_subst) ->
+ let exp_named_subst',subst',metasenv',ugraph1 =
+ check_exp_named_subst subst metasenv context
+ exp_named_subst ugraph
+ in
+ let ty_uri,ugraph2 =
+ type_of_mutual_inductive_constr uri i j ugraph1
+ in
+ let cty =
+ CicSubstitution.subst_vars exp_named_subst' ty_uri
+ in
+ C.MutConstruct (uri,i,j,exp_named_subst'),cty,subst',
+ metasenv',ugraph2
+ | C.MutCase (uri, i, outtype, term, pl) ->
+ (* first, get the inductive type (and noparams)
+ * in the environment *)
+ let (_,b,arity,constructors), expl_params, no_left_params,ugraph =
+ let obj,u = CicEnvironment.get_obj ugraph uri in
+ match obj with
+ C.InductiveDefinition (l,expl_params,parsno,_) ->
+ List.nth l i , expl_params, parsno, u
+ | _ ->
+ raise
+ (RefineFailure
+ ("Unkown mutual inductive definition " ^
+ U.string_of_uri uri))
in
- Un.fo_unif_subst subst context' metasenv
- ty_of_bo (CicMetaSubst.lift subst len ty)
- ) (subst,metasenv) fl in
- let (_,_,ty,_) = List.nth fl i in
- ty,subst,metasenv
- | C.CoFix (i,fl) ->
- let subst,metasenv,types =
- List.fold_left
- (fun (subst,metasenv,types) (n,ty,_) ->
- let _,subst',metasenv' = type_of_aux subst metasenv context ty in
- subst',metasenv', Some (C.Name n,(C.Decl ty)) :: types
- ) (subst,metasenv,[]) fl
- in
- let len = List.length types in
- let context' = types@context in
- let subst,metasenv =
- List.fold_left
- (fun (subst,metasenv) (name,ty,bo) ->
- let ty_of_bo,subst,metasenv =
- type_of_aux subst metasenv context' bo
+ let rec count_prod t =
+ match CicReduction.whd ~subst context t with
+ C.Prod (_, _, t) -> 1 + (count_prod t)
+ | _ -> 0
+ in
+ let no_args = count_prod arity in
+ (* now, create a "generic" MutInd *)
+ let metasenv,left_args =
+ CicMkImplicit.n_fresh_metas metasenv subst context no_left_params
+ in
+ let metasenv,right_args =
+ let no_right_params = no_args - no_left_params in
+ if no_right_params < 0 then assert false
+ else CicMkImplicit.n_fresh_metas
+ metasenv subst context no_right_params
+ in
+ let metasenv,exp_named_subst =
+ CicMkImplicit.fresh_subst metasenv subst context expl_params in
+ let expected_type =
+ if no_args = 0 then
+ C.MutInd (uri,i,exp_named_subst)
+ else
+ C.Appl
+ (C.MutInd (uri,i,exp_named_subst)::(left_args @ right_args))
+ in
+ (* check consistency with the actual type of term *)
+ let term',actual_type,subst,metasenv,ugraph1 =
+ type_of_aux subst metasenv context term ugraph in
+ let expected_type',_, subst, metasenv,ugraph2 =
+ type_of_aux subst metasenv context expected_type ugraph1
+ in
+ let actual_type = CicReduction.whd ~subst context actual_type in
+ let subst,metasenv,ugraph3 =
+ fo_unif_subst subst context metasenv
+ expected_type' actual_type ugraph2
+ in
+ let rec instantiate_prod t =
+ function
+ [] -> t
+ | he::tl ->
+ match CicReduction.whd ~subst context t with
+ C.Prod (_,_,t') ->
+ instantiate_prod (CicSubstitution.subst he t') tl
+ | _ -> assert false
in
- Un.fo_unif_subst subst context' metasenv
- ty_of_bo (CicMetaSubst.lift subst len ty)
- ) (subst,metasenv) fl in
-
- let (_,ty,_) = List.nth fl i in
- ty,subst,metasenv
+ let arity_instantiated_with_left_args =
+ instantiate_prod arity left_args in
+ (* TODO: check if the sort elimination
+ * is allowed: [(I q1 ... qr)|B] *)
+ let (pl',_,outtypeinstances,subst,metasenv,ugraph4) =
+ List.fold_left
+ (fun (pl,j,outtypeinstances,subst,metasenv,ugraph) p ->
+ let constructor =
+ if left_args = [] then
+ (C.MutConstruct (uri,i,j,exp_named_subst))
+ else
+ (C.Appl
+ (C.MutConstruct (uri,i,j,exp_named_subst)::left_args))
+ in
+ let p',actual_type,subst,metasenv,ugraph1 =
+ type_of_aux subst metasenv context p ugraph
+ in
+ let constructor',expected_type, subst, metasenv,ugraph2 =
+ type_of_aux subst metasenv context constructor ugraph1
+ in
+ let outtypeinstance,subst,metasenv,ugraph3 =
+ check_branch 0 context metasenv subst no_left_params
+ actual_type constructor' expected_type ugraph2
+ in
+ (pl @ [p'],j+1,
+ outtypeinstance::outtypeinstances,subst,metasenv,ugraph3))
+ ([],1,[],subst,metasenv,ugraph3) pl
+ in
+
+ (* we are left to check that the outype matches his instances.
+ The easy case is when the outype is specified, that amount
+ to a trivial check. Otherwise, we should guess a type from
+ its instances
+ *)
+
+ (match outtype with
+ | C.Meta (n,l) ->
+ (let candidate,ugraph5,metasenv,subst =
+ let exp_name_subst, metasenv =
+ let o,_ =
+ CicEnvironment.get_obj CicUniv.empty_ugraph uri
+ in
+ let uris = CicUtil.params_of_obj o in
+ List.fold_right (
+ fun uri (acc,metasenv) ->
+ let metasenv',new_meta =
+ CicMkImplicit.mk_implicit metasenv subst context
+ in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable
+ context
+ in
+ (uri, Cic.Meta(new_meta,irl))::acc, metasenv'
+ ) uris ([],metasenv)
+ in
+ let ty =
+ match left_args,right_args with
+ [],[] -> Cic.MutInd(uri, i, exp_name_subst)
+ | _,_ ->
+ let rec mk_right_args =
+ function
+ 0 -> []
+ | n -> (Cic.Rel n)::(mk_right_args (n - 1))
+ in
+ let right_args_no = List.length right_args in
+ let lifted_left_args =
+ List.map (CicSubstitution.lift right_args_no) left_args
+ in
+ Cic.Appl (Cic.MutInd(uri,i,exp_name_subst)::
+ (lifted_left_args @ mk_right_args right_args_no))
+ in
+ let fresh_name =
+ FreshNamesGenerator.mk_fresh_name ~subst metasenv
+ context Cic.Anonymous ~typ:ty
+ in
+ match outtypeinstances with
+ | [] ->
+ let extended_context =
+ let rec add_right_args =
+ function
+ Cic.Prod (name,ty,t) ->
+ Some (name,Cic.Decl ty)::(add_right_args t)
+ | _ -> []
+ in
+ (Some (fresh_name,Cic.Decl ty))::
+ (List.rev
+ (add_right_args arity_instantiated_with_left_args))@
+ context
+ in
+ let metasenv,new_meta =
+ CicMkImplicit.mk_implicit metasenv subst extended_context
+ in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable
+ extended_context
+ in
+ let rec add_lambdas b =
+ function
+ Cic.Prod (name,ty,t) ->
+ Cic.Lambda (name,ty,(add_lambdas b t))
+ | _ -> Cic.Lambda (fresh_name, ty, b)
+ in
+ let candidate =
+ add_lambdas (Cic.Meta (new_meta,irl))
+ arity_instantiated_with_left_args
+ in
+ (Some candidate),ugraph4,metasenv,subst
+ | (constructor_args_no,_,instance,_)::tl ->
+ try
+ let instance',subst,metasenv =
+ CicMetaSubst.delift_rels subst metasenv
+ constructor_args_no instance
+ in
+ let candidate,ugraph,metasenv,subst =
+ List.fold_left (
+ fun (candidate_oty,ugraph,metasenv,subst)
+ (constructor_args_no,_,instance,_) ->
+ match candidate_oty with
+ | None -> None,ugraph,metasenv,subst
+ | Some ty ->
+ try
+ let instance',subst,metasenv =
+ CicMetaSubst.delift_rels subst metasenv
+ constructor_args_no instance
+ in
+ let subst,metasenv,ugraph =
+ fo_unif_subst subst context metasenv
+ instance' ty ugraph
+ in
+ candidate_oty,ugraph,metasenv,subst
+ with
+ CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable
+ | CicUnification.UnificationFailure _
+ | CicUnification.Uncertain _ ->
+ None,ugraph,metasenv,subst
+ ) (Some instance',ugraph4,metasenv,subst) tl
+ in
+ match candidate with
+ | None -> None, ugraph,metasenv,subst
+ | Some t ->
+ let rec add_lambdas n b =
+ function
+ Cic.Prod (name,ty,t) ->
+ Cic.Lambda (name,ty,(add_lambdas (n + 1) b t))
+ | _ ->
+ Cic.Lambda (fresh_name, ty,
+ CicSubstitution.lift (n + 1) t)
+ in
+ Some
+ (add_lambdas 0 t arity_instantiated_with_left_args),
+ ugraph,metasenv,subst
+ with CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
+ None,ugraph4,metasenv,subst
+ in
+ match candidate with
+ | None -> raise (Uncertain "can't solve an higher order unification problem")
+ | Some candidate ->
+ let subst,metasenv,ugraph =
+ fo_unif_subst subst context metasenv
+ candidate outtype ugraph5
+ in
+ C.MutCase (uri, i, outtype, term', pl'),
+ CicReduction.head_beta_reduce
+ (CicMetaSubst.apply_subst subst
+ (Cic.Appl (outtype::right_args@[term']))),
+ subst,metasenv,ugraph)
+ | _ -> (* easy case *)
+ let _,_, subst, metasenv,ugraph5 =
+ type_of_aux subst metasenv context
+ (C.Appl ((outtype :: right_args) @ [term'])) ugraph4
+ in
+ let (subst,metasenv,ugraph6) =
+ List.fold_left
+ (fun (subst,metasenv,ugraph)
+ (constructor_args_no,context,instance,args) ->
+ let instance' =
+ let appl =
+ let outtype' =
+ CicSubstitution.lift constructor_args_no outtype
+ in
+ C.Appl (outtype'::args)
+ in
+ CicReduction.whd ~subst context appl
+ in
+ fo_unif_subst subst context metasenv
+ instance instance' ugraph)
+ (subst,metasenv,ugraph5) outtypeinstances
+ in
+ C.MutCase (uri, i, outtype, term', pl'),
+ CicReduction.head_beta_reduce
+ (CicMetaSubst.apply_subst subst
+ (C.Appl(outtype::right_args@[term]))),
+ subst,metasenv,ugraph6)
+ | C.Fix (i,fl) ->
+ let fl_ty',subst,metasenv,types,ugraph1 =
+ List.fold_left
+ (fun (fl,subst,metasenv,types,ugraph) (n,_,ty,_) ->
+ let ty',_,subst',metasenv',ugraph1 =
+ type_of_aux subst metasenv context ty ugraph
+ in
+ fl @ [ty'],subst',metasenv',
+ Some (C.Name n,(C.Decl ty')) :: types, ugraph
+ ) ([],subst,metasenv,[],ugraph) fl
+ in
+ let len = List.length types in
+ let context' = types@context in
+ let fl_bo',subst,metasenv,ugraph2 =
+ List.fold_left
+ (fun (fl,subst,metasenv,ugraph) (name,x,ty,bo) ->
+ let bo',ty_of_bo,subst,metasenv,ugraph1 =
+ type_of_aux subst metasenv context' bo ugraph
+ in
+ let subst',metasenv',ugraph' =
+ fo_unif_subst subst context' metasenv
+ ty_of_bo (CicSubstitution.lift len ty) ugraph1
+ in
+ fl @ [bo'] , subst',metasenv',ugraph'
+ ) ([],subst,metasenv,ugraph1) fl
+ in
+ let (_,_,ty,_) = List.nth fl i in
+ (* now we have the new ty in fl_ty', the new bo in fl_bo',
+ * and we want the new fl with bo' and ty' injected in the right
+ * place.
+ *)
+ let rec map3 f l1 l2 l3 =
+ match l1,l2,l3 with
+ | [],[],[] -> []
+ | h1::tl1,h2::tl2,h3::tl3 -> (f h1 h2 h3) :: (map3 f tl1 tl2 tl3)
+ | _ -> assert false
+ in
+ let fl'' = map3 (fun ty' bo' (name,x,ty,bo) -> (name,x,ty',bo') )
+ fl_ty' fl_bo' fl
+ in
+ C.Fix (i,fl''),ty,subst,metasenv,ugraph2
+ | C.CoFix (i,fl) ->
+ let fl_ty',subst,metasenv,types,ugraph1 =
+ List.fold_left
+ (fun (fl,subst,metasenv,types,ugraph) (n,ty,_) ->
+ let ty',_,subst',metasenv',ugraph1 =
+ type_of_aux subst metasenv context ty ugraph
+ in
+ fl @ [ty'],subst',metasenv',
+ Some (C.Name n,(C.Decl ty')) :: types, ugraph1
+ ) ([],subst,metasenv,[],ugraph) fl
+ in
+ let len = List.length types in
+ let context' = types@context in
+ let fl_bo',subst,metasenv,ugraph2 =
+ List.fold_left
+ (fun (fl,subst,metasenv,ugraph) (name,ty,bo) ->
+ let bo',ty_of_bo,subst,metasenv,ugraph1 =
+ type_of_aux subst metasenv context' bo ugraph
+ in
+ let subst',metasenv',ugraph' =
+ fo_unif_subst subst context' metasenv
+ ty_of_bo (CicSubstitution.lift len ty) ugraph1
+ in
+ fl @ [bo'],subst',metasenv',ugraph'
+ ) ([],subst,metasenv,ugraph1) fl
+ in
+ let (_,ty,_) = List.nth fl i in
+ (* now we have the new ty in fl_ty', the new bo in fl_bo',
+ * and we want the new fl with bo' and ty' injected in the right
+ * place.
+ *)
+ let rec map3 f l1 l2 l3 =
+ match l1,l2,l3 with
+ | [],[],[] -> []
+ | h1::tl1,h2::tl2,h3::tl3 -> (f h1 h2 h3) :: (map3 f tl1 tl2 tl3)
+ | _ -> assert false
+ in
+ let fl'' = map3 (fun ty' bo' (name,ty,bo) -> (name,ty',bo') )
+ fl_ty' fl_bo' fl
+ in
+ C.CoFix (i,fl''),ty,subst,metasenv,ugraph2
- (* 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
- metano subst metasenv context canonical_context l
- =
- let module C = Cic in
- let module R = CicReduction in
- let module S = CicSubstitution in
+ (* 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
+ metano 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.lift_meta l (S.lift i t))))::(aux (i+1) tl)
- | (Some (n,C.Def (t,None)))::tl ->
- (Some (n,C.Def ((S.lift_meta l (S.lift i t)),None)))::(aux (i+1) tl)
- | None::tl -> None::(aux (i+1) tl)
- | (Some (n,C.Def (t,Some ty)))::tl ->
- (Some (n,
- C.Def ((S.lift_meta l (S.lift i t)),
- Some (S.lift_meta l (S.lift i ty))))) :: (aux (i+1) tl)
- in
- aux 1 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)
+ | (Some (n,C.Def (t,None)))::tl ->
+ (Some (n,C.Def ((S.subst_meta l (S.lift i t)),None)))::(aux (i+1) tl)
+ | None::tl -> None::(aux (i+1) tl)
+ | (Some (n,C.Def (t,Some ty)))::tl ->
+ (Some (n,
+ C.Def ((S.subst_meta l (S.lift i t)),
+ Some (S.subst_meta l (S.lift i ty))))) :: (aux (i+1) tl)
+ in
+ aux 1 canonical_context
in
- List.fold_left2
- (fun (subst,metasenv) t ct ->
- match (t,ct) with
- _,None ->
- subst,metasenv
- | Some t,Some (_,C.Def (ct,_)) ->
- (try
- CicUnification.fo_unif_subst subst context metasenv t ct
- with _ -> raise (NotRefinable (sprintf "The local context is not consistent with the canonical context, since %s cannot be unified with %s" (CicMetaSubst.ppterm subst t) (CicMetaSubst.ppterm subst ct))))
- | Some t,Some (_,C.Decl ct) ->
- let inferredty,subst',metasenv' =
- type_of_aux subst metasenv context t
+ try
+ List.fold_left2
+ (fun (l,subst,metasenv,ugraph) t ct ->
+ match (t,ct) with
+ _,None ->
+ l @ [None],subst,metasenv,ugraph
+ | Some t,Some (_,C.Def (ct,_)) ->
+ let subst',metasenv',ugraph' =
+ (try
+ fo_unif_subst subst context metasenv t ct ugraph
+ with e -> raise (RefineFailure (sprintf "The local context is not consistent with the canonical context, since %s cannot be unified with %s. Reason: %s" (CicMetaSubst.ppterm subst t) (CicMetaSubst.ppterm subst ct) (match e with AssertFailure msg -> msg | _ -> (Printexc.to_string e)))))
+ in
+ l @ [Some t],subst',metasenv',ugraph'
+ | Some t,Some (_,C.Decl ct) ->
+ let t',inferredty,subst',metasenv',ugraph1 =
+ type_of_aux subst metasenv context t ugraph
+ in
+ let subst'',metasenv'',ugraph2 =
+ (try
+ fo_unif_subst
+ subst' context metasenv' inferredty ct ugraph1
+ with e -> raise (RefineFailure (sprintf "The local context is not consistent with the canonical context, since the type %s of %s cannot be unified with the expected type %s. Reason: %s" (CicMetaSubst.ppterm subst' inferredty) (CicMetaSubst.ppterm subst' t) (CicMetaSubst.ppterm subst' ct) (match e with AssertFailure msg -> msg | _ -> (Printexc.to_string e)))))
+ in
+ l @ [Some t'], subst'',metasenv'',ugraph2
+ | None, Some _ ->
+ raise (RefineFailure (sprintf
+ "Not well typed metavariable instance %s: the local context does not instantiate an hypothesis even if the hypothesis is not restricted in the canonical context %s"
+ (CicMetaSubst.ppterm subst (Cic.Meta (metano, l)))
+ (CicMetaSubst.ppcontext subst canonical_context)))
+ ) ([],subst,metasenv,ugraph) l lifted_canonical_context
+ with
+ Invalid_argument _ ->
+ raise
+ (RefineFailure
+ (sprintf
+ "Not well typed metavariable instance %s: the length of the local context does not match the length of the canonical context %s"
+ (CicMetaSubst.ppterm subst (Cic.Meta (metano, l)))
+ (CicMetaSubst.ppcontext subst canonical_context)))
+
+ and check_exp_named_subst metasubst metasenv context tl ugraph =
+ let rec check_exp_named_subst_aux metasubst metasenv substs tl ugraph =
+ match tl with
+ [] -> [],metasubst,metasenv,ugraph
+ | ((uri,t) as subst)::tl ->
+ let ty_uri,ugraph1 = type_of_variable uri ugraph in
+ let typeofvar =
+ CicSubstitution.subst_vars substs ty_uri in
+ (* CSC: why was this code here? it is wrong
+ (match CicEnvironment.get_cooked_obj ~trust:false uri with
+ Cic.Variable (_,Some bo,_,_) ->
+ raise
+ (RefineFailure
+ "A variable with a body can not be explicit substituted")
+ | Cic.Variable (_,None,_,_) -> ()
+ | _ ->
+ raise
+ (RefineFailure
+ ("Unkown variable definition " ^ UriManager.string_of_uri uri))
+ ) ;
+ *)
+ let t',typeoft,metasubst',metasenv',ugraph2 =
+ type_of_aux metasubst metasenv context t ugraph1
+ in
+ let metasubst'',metasenv'',ugraph3 =
+ try
+ fo_unif_subst
+ metasubst' context metasenv' typeoft typeofvar ugraph2
+ with _ ->
+ raise (RefineFailure
+ ("Wrong Explicit Named Substitution: " ^
+ CicMetaSubst.ppterm metasubst' typeoft ^
+ " not unifiable with " ^
+ CicMetaSubst.ppterm metasubst' typeofvar))
+ in
+ (* FIXME: no mere tail recursive! *)
+ let exp_name_subst, metasubst''', metasenv''', ugraph4 =
+ check_exp_named_subst_aux
+ metasubst'' metasenv'' (substs@[subst]) tl ugraph3
in
- (try
- CicUnification.fo_unif_subst
- subst' context metasenv' inferredty ct
- with _ -> raise (NotRefinable (sprintf "The local context is not consistent with the canonical context, since the type %s of %s cannot be unified with the expected type %s" (CicMetaSubst.ppterm subst' inferredty) (CicMetaSubst.ppterm subst' t) (CicMetaSubst.ppterm subst' ct))))
- | None, Some _ ->
- raise (NotRefinable (sprintf
- "Not well typed metavariable instance %s: the local context does not instantiate an hypothesis even if the hypothesis is not restricted in the canonical context %s"
- (CicMetaSubst.ppterm subst (Cic.Meta (metano, l)))
- (CicMetaSubst.ppcontext subst canonical_context)))
- ) (subst,metasenv) l lifted_canonical_context
+ ((uri,t')::exp_name_subst), metasubst''', metasenv''', ugraph4
+ in
+ check_exp_named_subst_aux metasubst metasenv [] tl ugraph
- and check_exp_named_subst metasubst metasenv context =
- let rec check_exp_named_subst_aux metasubst metasenv substs =
- function
- [] -> metasubst,metasenv
- | ((uri,t) as subst)::tl ->
- let typeofvar =
- CicSubstitution.subst_vars substs (type_of_variable uri) in
- (match CicEnvironment.get_cooked_obj ~trust:false uri with
- Cic.Variable (_,Some bo,_,_) ->
- raise
- (NotRefinable
- "A variable with a body can not be explicit substituted")
- | Cic.Variable (_,None,_,_) -> ()
- | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
- ) ;
- let typeoft,metasubst',metasenv' =
- type_of_aux metasubst metasenv context t
- in
- try
- let metasubst'',metasenv'' =
- CicUnification.fo_unif_subst
- metasubst' context metasenv' typeoft typeofvar
- in
- check_exp_named_subst_aux metasubst'' metasenv'' (substs@[subst]) tl
- with _ ->
- raise (NotRefinable "Wrong Explicit Named Substitution")
- in
- check_exp_named_subst_aux metasubst metasenv []
- and sort_of_prod subst metasenv context (name,s) (t1, t2) =
- let module C = Cic in
- let t1'' = CicMetaSubst.whd subst context t1 in
- let t2'' = CicMetaSubst.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 than Coq manual!!! *)
- C.Sort s2
- | (C.Sort s1, C.Sort s2) ->
- (*CSC manca la gestione degli universi!!! *)
- C.Sort C.Type
- | (C.Meta _,_) | (_,C.Meta _) ->
- (* TODO how can we force the meta to become a sort? If we don't we
- * brake the invariant that refine produce only well typed terms *)
- (* TODO if we check the non meta term and if it is a sort then we are
- * likely to know the exact value of the result e.g. if the rhs is a
- * Sort (Prop | Set | CProp) then the result is the rhs *)
- (C.Sort C.Type)
-(* t2'' *)
- | (_,_) ->
- raise (NotRefinable (sprintf
- "Two types were expected, found %s (that reduces to %s) and %s (that reduces to %s)"
- (CicPp.ppterm t1) (CicPp.ppterm t1'') (CicPp.ppterm t2)
- (CicPp.ppterm t2'')))
+ and sort_of_prod subst metasenv context (name,s) (t1, t2) ugraph =
+ let module C = Cic in
+ let context_for_t2 = (Some (name,C.Decl s))::context in
+ let t1'' = CicReduction.whd ~subst context t1 in
+ let t2'' = CicReduction.whd ~subst context_for_t2 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 than Coq manual!!! *)
+ C.Sort s2,subst,metasenv,ugraph
+ | (C.Sort (C.Type t1), C.Sort (C.Type t2)) ->
+ (* TASSI: CONSRTAINTS: the same in cictypechecker, doubletypeinference *)
+ let t' = CicUniv.fresh() in
+ let ugraph1 = CicUniv.add_ge t' t1 ugraph in
+ let ugraph2 = CicUniv.add_ge t' t2 ugraph1 in
+ C.Sort (C.Type t'),subst,metasenv,ugraph2
+ | (C.Sort _,C.Sort (C.Type t1)) ->
+ (* TASSI: CONSRTAINTS: the same in cictypechecker, doubletypeinference *)
+ C.Sort (C.Type t1),subst,metasenv,ugraph
+ | (C.Meta _, C.Sort _) -> t2'',subst,metasenv,ugraph
+ | (C.Sort _,C.Meta _) | (C.Meta _,C.Meta _) ->
+ (* TODO how can we force the meta to become a sort? If we don't we
+ * brake the invariant that refine produce only well typed terms *)
+ (* TODO if we check the non meta term and if it is a sort then we are
+ * likely to know the exact value of the result e.g. if the rhs is a
+ * Sort (Prop | Set | CProp) then the result is the rhs *)
+ let (metasenv,idx) =
+ CicMkImplicit.mk_implicit_sort metasenv subst in
+ let (subst, metasenv,ugraph1) =
+ fo_unif_subst subst context_for_t2 metasenv (C.Meta (idx,[])) t2'' ugraph
+ in
+ t2'',subst,metasenv,ugraph1
+ | (_,_) ->
+ raise (RefineFailure (sprintf
+ "Two sorts were expected, found %s (that reduces to %s) and %s (that reduces to %s)"
+ (CicPp.ppterm t1) (CicPp.ppterm t1'') (CicPp.ppterm t2)
+ (CicPp.ppterm t2'')))
- and eat_prods subst metasenv context hetype tlbody_and_type =
- let rec aux context' args (resty,subst,metasenv) =
- function
- [] -> resty,subst,metasenv
- | (arg,argty)::tl ->
- let args' =
- List.map
- (function
- None -> assert false
- | Some t -> Some (CicMetaSubst.lift subst 1 t)
- ) args in
- let argty' = CicMetaSubst.lift subst (List.length args) argty in
- let context'' = Some (Cic.Anonymous, Cic.Decl argty') :: context' in
- let (metasenv, idx) =
- CicMkImplicit.mk_implicit metasenv (context'' @ context) in
- let irl =
- (Some (Cic.Rel 1))::args' @
- (CicMkImplicit.identity_relocation_list_for_metavariable ~start:2
- context)
- in
- let newmeta = Cic.Meta (idx, irl) in
- let prod =
- Cic.Prod
- (FreshNamesGenerator.mk_fresh_name
- (CicMetaSubst.apply_subst_metasenv subst metasenv)
- (CicMetaSubst.apply_subst_context subst context)
- Cic.Anonymous
- (CicMetaSubst.apply_subst subst argty),
- argty, newmeta) in
- let (_, subst, metasenv) = type_of_aux subst metasenv context prod in
- let (subst, metasenv) =
- CicUnification.fo_unif_subst subst context metasenv resty prod
- in
- aux context'' (Some arg :: args)
- (CicMetaSubst.subst subst arg newmeta, subst, metasenv) tl
- in
- aux [] [] (hetype,subst,metasenv) tlbody_and_type
+ and eat_prods subst metasenv context hetype tlbody_and_type ugraph =
+ let rec mk_prod metasenv context =
+ function
+ [] ->
+ let (metasenv, idx) =
+ CicMkImplicit.mk_implicit_type metasenv subst context
+ in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
+ in
+ metasenv,Cic.Meta (idx, irl)
+ | (_,argty)::tl ->
+ let (metasenv, idx) =
+ CicMkImplicit.mk_implicit_type metasenv subst context
+ in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
+ in
+ let meta = Cic.Meta (idx,irl) in
+ let name =
+ (* The name must be fresh for context. *)
+ (* Nevertheless, argty is well-typed only in context. *)
+ (* Thus I generate a name (name_hint) in context and *)
+ (* then I generate a name --- using the hint name_hint *)
+ (* --- that is fresh in (context'@context). *)
+ let name_hint =
+ (* Cic.Name "pippo" *)
+ FreshNamesGenerator.mk_fresh_name ~subst metasenv
+ (* (CicMetaSubst.apply_subst_metasenv subst metasenv) *)
+ (CicMetaSubst.apply_subst_context subst context)
+ Cic.Anonymous
+ ~typ:(CicMetaSubst.apply_subst subst argty)
+ in
+ (* [] and (Cic.Sort Cic.prop) are dummy: they will not be used *)
+ FreshNamesGenerator.mk_fresh_name ~subst
+ [] context name_hint ~typ:(Cic.Sort Cic.Prop)
+ in
+ let metasenv,target =
+ mk_prod metasenv ((Some (name, Cic.Decl meta))::context) tl
+ in
+ metasenv,Cic.Prod (name,meta,target)
+ in
+ let metasenv,hetype' = mk_prod metasenv context tlbody_and_type in
+ let (subst, metasenv,ugraph1) =
+ try
+ fo_unif_subst subst context metasenv hetype hetype' ugraph
+ with exn ->
+ debug_print (Printf.sprintf "hetype=%s\nhetype'=%s\nmetasenv=%s\nsubst=%s"
+ (CicPp.ppterm hetype)
+ (CicPp.ppterm hetype')
+ (CicMetaSubst.ppmetasenv metasenv [])
+ (CicMetaSubst.ppsubst subst));
+ raise exn
- in
- let ty,subst',metasenv' =
- type_of_aux [] metasenv context t
+ in
+ let rec eat_prods metasenv subst context hetype ugraph =
+ function
+ | [] -> [],metasenv,subst,hetype,ugraph
+ | (hete, hety)::tl ->
+ (match hetype with
+ Cic.Prod (n,s,t) ->
+ let arg,subst,metasenv,ugraph1 =
+ try
+ let subst,metasenv,ugraph1 =
+ fo_unif_subst subst context metasenv hety s ugraph
+ in
+ hete,subst,metasenv,ugraph1
+ with exn ->
+ (* we search a coercion from hety to s *)
+ let coer = CoercGraph.look_for_coercion
+ (CicMetaSubst.apply_subst subst hety)
+ (CicMetaSubst.apply_subst subst s)
+ in
+ match coer with
+ | None -> raise exn
+ | Some c ->
+ (Cic.Appl [ c ; hete ]), subst, metasenv, ugraph
+ in
+ let coerced_args,metasenv',subst',t',ugraph2 =
+ eat_prods metasenv subst context
+ (* (CicMetaSubst.subst subst hete t) tl *)
+ (CicSubstitution.subst hete t) ugraph1 tl
+ in
+ arg::coerced_args,metasenv',subst',t',ugraph2
+ | _ -> assert false
+ )
+ in
+ let coerced_args,metasenv,subst,t,ugraph2 =
+ eat_prods metasenv subst context hetype' ugraph1 tlbody_and_type
+ in
+ coerced_args,t,subst,metasenv,ugraph2
in
- (FreshNamesGenerator.clean_dummy_dependent_types
- (CicMetaSubst.apply_subst subst' t),
- FreshNamesGenerator.clean_dummy_dependent_types
- (CicMetaSubst.apply_subst subst' ty),
- CicMetaSubst.apply_subst_metasenv subst' metasenv')
+
+ (* eat prods ends here! *)
+
+ let t',ty,subst',metasenv',ugraph1 =
+ type_of_aux [] metasenv context t ugraph
+ in
+ let substituted_t = CicMetaSubst.apply_subst subst' t' in
+ let substituted_ty = CicMetaSubst.apply_subst subst' ty in
+ (* Andrea: ho rimesso qui l'applicazione della subst al
+ metasenv dopo che ho droppato l'invariante che il metsaenv
+ e' sempre istanziato *)
+ let substituted_metasenv =
+ CicMetaSubst.apply_subst_metasenv subst' metasenv' in
+ (* metasenv' *)
+ (* substituted_t,substituted_ty,substituted_metasenv *)
+ (* ANDREA: spostare tutta questa robaccia da un altra parte *)
+ let cleaned_t =
+ FreshNamesGenerator.clean_dummy_dependent_types substituted_t in
+ let cleaned_ty =
+ FreshNamesGenerator.clean_dummy_dependent_types substituted_ty in
+ let cleaned_metasenv =
+ List.map
+ (function (n,context,ty) ->
+ let ty' = FreshNamesGenerator.clean_dummy_dependent_types ty in
+ let context' =
+ List.map
+ (function
+ None -> None
+ | Some (n, Cic.Decl t) ->
+ Some (n,
+ Cic.Decl (FreshNamesGenerator.clean_dummy_dependent_types t))
+ | Some (n, Cic.Def (bo,ty)) ->
+ let bo' = FreshNamesGenerator.clean_dummy_dependent_types bo in
+ let ty' =
+ match ty with
+ None -> None
+ | Some ty ->
+ Some (FreshNamesGenerator.clean_dummy_dependent_types ty)
+ in
+ Some (n, Cic.Def (bo',ty'))
+ ) context
+ in
+ (n,context',ty')
+ ) substituted_metasenv
+ in
+ (cleaned_t,cleaned_ty,cleaned_metasenv,ugraph1)
;;
-(* DEBUGGING ONLY *)
+let type_of_aux' metasenv context term ugraph =
+ try
+ type_of_aux' metasenv context term ugraph
+ with
+ CicUniv.UniverseInconsistency msg -> raise (RefineFailure msg)
+
+(*CSC: this is a very very rough approximation; to be finished *)
+let are_all_occurrences_positive uri =
+ let rec aux =
+ (*CSC: here we should do a whd; but can we do that? *)
+ function
+ Cic.Appl (Cic.MutInd (uri',_,_)::_) when uri = uri' -> ()
+ | Cic.MutInd (uri',_,_) when uri = uri' -> ()
+ | Cic.Prod (_,_,t) -> aux t
+ | _ -> raise (RefineFailure "not well formed constructor type")
+ in
+ aux
+
+let typecheck metasenv uri obj =
+ let ugraph = CicUniv.empty_ugraph in
+ match obj with
+ Cic.Constant (name,Some bo,ty,args,attrs) ->
+ let bo',boty,metasenv,ugraph = type_of_aux' metasenv [] bo ugraph in
+ let ty',_,metasenv,ugraph = type_of_aux' metasenv [] ty ugraph in
+ let subst,metasenv,ugraph = fo_unif_subst [] [] metasenv boty ty' ugraph in
+ let bo' = CicMetaSubst.apply_subst subst bo' in
+ let ty' = CicMetaSubst.apply_subst subst ty' in
+ let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
+ Cic.Constant (name,Some bo',ty',args,attrs),metasenv,ugraph
+ | Cic.Constant (name,None,ty,args,attrs) ->
+ let ty',_,metasenv,ugraph = type_of_aux' metasenv [] ty ugraph in
+ Cic.Constant (name,None,ty',args,attrs),metasenv,ugraph
+ | Cic.CurrentProof (name,metasenv',bo,ty,args,attrs) ->
+ assert (metasenv' = metasenv);
+ (* Here we do not check the metasenv for correctness *)
+ let bo',boty,metasenv,ugraph = type_of_aux' metasenv [] bo ugraph in
+ let ty',sort,metasenv,ugraph = type_of_aux' metasenv [] ty ugraph in
+ begin
+ match sort with
+ Cic.Sort _
+ (* instead of raising Uncertain, let's hope that the meta will become
+ a sort *)
+ | Cic.Meta _ -> ()
+ | _ -> raise (RefineFailure "The term provided is not a type")
+ end;
+ let subst,metasenv,ugraph = fo_unif_subst [] [] metasenv boty ty' ugraph in
+ let bo' = CicMetaSubst.apply_subst subst bo' in
+ let ty' = CicMetaSubst.apply_subst subst ty' in
+ let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
+ Cic.CurrentProof (name,metasenv,bo',ty',args,attrs),metasenv,ugraph
+ | Cic.Variable _ -> assert false (* not implemented *)
+ | Cic.InductiveDefinition (tys,args,paramsno,attrs) ->
+ (*CSC: this code is greately simplified and many many checks are missing *)
+ (*CSC: e.g. the constructors are not required to build their own types, *)
+ (*CSC: the arities are not required to have as type a sort, etc. *)
+ let uri = match uri with Some uri -> uri | None -> assert false in
+ let typesno = List.length tys in
+ (* first phase: we fix only the types *)
+ let metasenv,ugraph,tys =
+ List.fold_right
+ (fun (name,b,ty,cl) (metasenv,ugraph,res) ->
+ let ty',_,metasenv,ugraph = type_of_aux' metasenv [] ty ugraph in
+ metasenv,ugraph,(name,b,ty',cl)::res
+ ) tys (metasenv,ugraph,[]) in
+ let con_context =
+ List.rev_map (fun (name,_,ty,_)-> Some (Cic.Name name,Cic.Decl ty)) tys in
+ (* second phase: we fix only the constructors *)
+ let metasenv,ugraph,tys =
+ List.fold_right
+ (fun (name,b,ty,cl) (metasenv,ugraph,res) ->
+ let metasenv,ugraph,cl' =
+ List.fold_right
+ (fun (name,ty) (metasenv,ugraph,res) ->
+ let ty = CicTypeChecker.debrujin_constructor uri typesno ty in
+ let ty',_,metasenv,ugraph =
+ type_of_aux' metasenv con_context ty ugraph in
+ let undebrujin t =
+ snd
+ (List.fold_right
+ (fun (name,_,_,_) (i,t) ->
+ (* here the explicit_named_substituion is assumed to be *)
+ (* of length 0 *)
+ let t' = Cic.MutInd (uri,i,[]) in
+ let t = CicSubstitution.subst t' t in
+ i - 1,t
+ ) tys (typesno - 1,t)) in
+ let ty' = undebrujin ty' in
+ metasenv,ugraph,(name,ty')::res
+ ) cl (metasenv,ugraph,[])
+ in
+ metasenv,ugraph,(name,b,ty,cl')::res
+ ) tys (metasenv,ugraph,[]) in
+ (* third phase: we check the positivity condition *)
+ List.iter
+ (fun (_,_,_,cl) ->
+ List.iter (fun (_,ty) -> are_all_occurrences_positive uri ty) cl
+ ) tys ;
+ Cic.InductiveDefinition (tys,args,paramsno,attrs),metasenv,ugraph
+
+(* DEBUGGING ONLY
let type_of_aux' metasenv context term =
try
- let (t,ty,m) = type_of_aux' metasenv context term in
- debug_print
- ("@@@ REFINE SUCCESSFUL: " ^ CicPp.ppterm t ^ " : " ^ CicPp.ppterm ty);
-(*
+ let (t,ty,m) =
+ type_of_aux' metasenv context term in
+ debug_print
+ ("@@@ REFINE SUCCESSFUL: " ^ CicPp.ppterm t ^ " : " ^ CicPp.ppterm ty);
debug_print
- ("@@@ REFINE SUCCESSFUL (metasenv):\n" ^ CicMetaSubst.ppmetasenv m s);
-*)
+ ("@@@ REFINE SUCCESSFUL (metasenv):\n" ^ CicMetaSubst.ppmetasenv ~sep:";" m []);
(t,ty,m)
with
- | CicUnification.AssertFailure msg as e ->
- debug_print "@@@ REFINE FAILED: CicUnification.AssertFailure:";
- debug_print msg;
+ | RefineFailure msg as e ->
+ debug_print ("@@@ REFINE FAILED: " ^ msg);
raise e
- | CicUnification.UnificationFailure msg as e ->
- debug_print "@@@ REFINE FAILED: CicUnification.UnificationFailure:";
- debug_print msg;
+ | Uncertain msg as e ->
+ debug_print ("@@@ REFINE UNCERTAIN: " ^ msg);
raise e
- | e ->
- debug_print ("@@@ REFINE FAILED: " ^ Printexc.to_string e) ;
- raise e
-;;
-
+;; *)
projects / helm.git / blobdiff