+++ /dev/null
-(* Copyright (C) 2000, HELM Team.
- *
- * This file is part of HELM, an Hypertextual, Electronic
- * Library of Mathematics, developed at the Computer Science
- * Department, University of Bologna, Italy.
- *
- * HELM is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * HELM is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with HELM; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- *
- * For details, see the HELM World-Wide-Web page,
- * http://cs.unibo.it/helm/.
- *)
-
-exception UnificationFailed;;
-exception Free;;
-exception OccurCheck;;
-exception RelToHiddenHypothesis;;
-exception OpenTerm;;
-
-(**** DELIFT ****)
-
-(* the delift function takes in input an ordered list of integers [n1,...,nk]
- and a term t, and relocates rel(nk) to k. Typically, the list of integers
- is a parameter of a metavariable occurrence. *)
-
-exception NotInTheList;;
-
-let position n =
- let rec aux k =
- function
- [] -> raise NotInTheList
- | (Some (Cic.Rel m))::_ when m=n -> k
- | _::tl -> aux (k+1) tl in
- aux 1
-;;
-
-let restrict to_be_restricted =
- let rec erase i n =
- function
- [] -> []
- | _::tl when List.mem (n,i) to_be_restricted ->
- None::(erase (i+1) n tl)
- | he::tl -> he::(erase (i+1) n tl) in
- let rec aux =
- function
- [] -> []
- | (n,context,t)::tl -> (n,erase 1 n context,t)::(aux tl) in
- aux
-;;
-
-
-let delift context metasenv l t =
- let module S = CicSubstitution in
- let to_be_restricted = ref [] in
- let rec deliftaux k =
- let module C = Cic in
- function
- C.Rel m ->
- if m <=k then
- C.Rel m (*CSC: che succede se c'e' un Def? Dovrebbe averlo gia' *)
- (*CSC: deliftato la regola per il LetIn *)
- else
- (match List.nth context (m-k-1) with
- Some (_,C.Def t) -> deliftaux k (S.lift m t)
- | Some (_,C.Decl t) ->
- (* It may augment to_be_restricted *)
- ignore (deliftaux k (S.lift m t)) ;
- C.Rel ((position (m-k) l) + k)
- | None -> raise RelToHiddenHypothesis)
- | C.Var _ as t -> t
- | C.Meta (i, l1) as t ->
- let rec deliftl j =
- function
- [] -> []
- | None::tl -> None::(deliftl (j+1) tl)
- | (Some t)::tl ->
- let l1' = (deliftl (j+1) tl) in
- try
- Some (deliftaux k t)::l1'
- with
- RelToHiddenHypothesis
- | NotInTheList ->
- to_be_restricted := (i,j)::!to_be_restricted ; None::l1'
- in
- let l' = deliftl 1 l1 in
- C.Meta(i,l')
- | C.Sort _ as t -> t
- | C.Implicit as t -> t
- | C.Cast (te,ty) -> C.Cast (deliftaux k te, deliftaux k ty)
- | C.Prod (n,s,t) -> C.Prod (n, deliftaux k s, deliftaux (k+1) t)
- | C.Lambda (n,s,t) -> C.Lambda (n, deliftaux k s, deliftaux (k+1) t)
- | C.LetIn (n,s,t) -> C.LetIn (n, deliftaux k s, deliftaux (k+1) t)
- | C.Appl l -> C.Appl (List.map (deliftaux k) l)
- | C.Const _ as t -> t
- | C.MutInd _ as t -> t
- | C.MutConstruct _ as t -> t
- | C.MutCase (sp,cookingsno,i,outty,t,pl) ->
- C.MutCase (sp, cookingsno, i, deliftaux k outty, deliftaux k t,
- List.map (deliftaux k) pl)
- | C.Fix (i, fl) ->
- let len = List.length fl in
- let liftedfl =
- List.map
- (fun (name, i, ty, bo) ->
- (name, i, deliftaux k ty, deliftaux (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, deliftaux k ty, deliftaux (k+len) bo))
- fl
- in
- C.CoFix (i, liftedfl)
- in
- let res = deliftaux 0 t in
- res, restrict !to_be_restricted metasenv
-;;
-
-(**** END OF DELIFT ****)
-
-type substitution = (int * Cic.term) list
-
-(* NUOVA UNIFICAZIONE *)
-(* A substitution is a (int * Cic.term) list that associates a
- metavariable i with its body.
- A metaenv is a (int * Cic.term) list that associate a metavariable
- i with is type.
- fo_unif_new takes a metasenv, a context, two terms t1 and t2 and gives back
- a new substitution which is _NOT_ unwinded. It must be unwinded before
- applying it. *)
-
-let fo_unif_new metasenv context t1 t2 =
- let module C = Cic in
- let module R = CicReduction in
- let module S = CicSubstitution in
- let rec fo_unif_aux subst context metasenv t1 t2 =
- match (t1, t2) with
- (C.Meta (n,ln), C.Meta (m,lm)) when n=m ->
- let ok =
- List.fold_left2
- (fun b t1 t2 ->
- b &&
- match t1,t2 with
- None,_
- | _,None -> true
- | Some t1', Some t2' ->
- (* First possibility: restriction *)
- (* Second possibility: unification *)
- (* Third possibility: convertibility *)
- R.are_convertible context t1' t2'
- ) true ln lm
- in
- if ok then subst,metasenv else
- raise UnificationFailed
- | (C.Meta (n,l), C.Meta (m,_)) when n>m ->
- fo_unif_aux subst context metasenv t2 t1
- | (C.Meta (n,l), t)
- | (t, C.Meta (n,l)) ->
- let subst',metasenv' =
- try
- let oldt = (List.assoc n subst) in
- let lifted_oldt = S.lift_meta l oldt in
- fo_unif_aux subst context metasenv lifted_oldt t
- with Not_found ->
-prerr_endline ("DELIFT2(" ^ CicPp.ppterm t ^ ")") ; flush stderr ;
-List.iter (function (Some t) -> prerr_endline ("l: " ^ CicPp.ppterm t) | None -> prerr_endline " _ ") l ; flush stderr ;
-prerr_endline "<DELIFT2" ; flush stderr ;
- let t',metasenv' = delift context metasenv l t in
- (n, t')::subst, metasenv'
- in
- let (_,_,meta_type) =
- List.find (function (m,_,_) -> m=n) metasenv' in
- let tyt = CicTypeChecker.type_of_aux' metasenv' context t in
- fo_unif_aux subst' context metasenv' (S.lift_meta l meta_type) tyt
- | (C.Rel _, _)
- | (_, C.Rel _)
- | (C.Var _, _)
- | (_, C.Var _)
- | (C.Sort _ ,_)
- | (_, C.Sort _)
- | (C.Implicit, _)
- | (_, C.Implicit) ->
- if R.are_convertible context t1 t2 then subst, metasenv
- else raise UnificationFailed
- | (C.Cast (te,ty), t2) -> fo_unif_aux subst context metasenv te t2
- | (t1, C.Cast (te,ty)) -> fo_unif_aux subst context metasenv t1 te
- | (C.Prod (n1,s1,t1), C.Prod (_,s2,t2)) ->
- let subst',metasenv' = fo_unif_aux subst context metasenv s1 s2 in
- fo_unif_aux subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2
- | (C.Lambda (n1,s1,t1), C.Lambda (_,s2,t2)) ->
- let subst',metasenv' = fo_unif_aux subst context metasenv s1 s2 in
- fo_unif_aux subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2
- | (C.LetIn (_,s1,t1), t2)
- | (t2, C.LetIn (_,s1,t1)) ->
- fo_unif_aux subst context metasenv t2 (S.subst s1 t1)
- | (C.Appl l1, C.Appl l2) ->
- let lr1 = List.rev l1 in
- let lr2 = List.rev l2 in
- let rec fo_unif_l subst metasenv = function
- [],_
- | _,[] -> assert false
- | ([h1],[h2]) ->
- fo_unif_aux subst context metasenv h1 h2
- | ([h],l)
- | (l,[h]) ->
- fo_unif_aux subst context metasenv h (C.Appl (List.rev l))
- | ((h1::l1),(h2::l2)) ->
- let subst', metasenv' =
- fo_unif_aux subst context metasenv h1 h2
- in
- fo_unif_l subst' metasenv' (l1,l2)
- in
- fo_unif_l subst metasenv (lr1, lr2)
- | (C.Const _, _)
- | (_, C.Const _)
- | (C.MutInd _, _)
- | (_, C.MutInd _)
- | (C.MutConstruct _, _)
- | (_, C.MutConstruct _) ->
- if R.are_convertible context t1 t2 then subst, metasenv
- else raise UnificationFailed
- | (C.MutCase (_,_,_,outt1,t1,pl1), C.MutCase (_,_,_,outt2,t2,pl2))->
- let subst', metasenv' =
- fo_unif_aux subst context metasenv outt1 outt2 in
- let subst'',metasenv'' =
- fo_unif_aux subst' context metasenv' t1 t2 in
- List.fold_left2
- (function (subst,metasenv) ->
- fo_unif_aux subst context metasenv
- ) (subst'',metasenv'') pl1 pl2
- | (C.Fix _, _)
- | (_, C.Fix _)
- | (C.CoFix _, _)
- | (_, C.CoFix _) ->
- if R.are_convertible context t1 t2 then subst, metasenv
- else raise UnificationFailed
- | (_,_) -> raise UnificationFailed
- in fo_unif_aux [] context metasenv t1 t2;;
-
-(*CSC: ???????????????
-(* m is the index of a metavariable to restrict, k is nesting depth
-of the occurrence m, and l is its relocation list. canonical_context
-is the context of the metavariable we are instantiating - containing
-m - Only rel in the domain of canonical_context are accessible.
-This function takes in input a metasenv and gives back a metasenv.
-A rel(j) in the canonical context of m, is rel(List.nth l j) for the
-instance of m under consideration, that is rel (List.nth l j) - k
-in canonical_context. *)
-
-let restrict canonical_context m k l =
- let rec erase i =
- function
- [] -> []
- | None::tl -> None::(erase (i+1) tl)
- | he::tl ->
- let i' = (List.nth l (i-1)) in
- if i' <= k
- then he::(erase (i+1) tl) (* local variable *)
- else
- let acc =
- (try List.nth canonical_context (i'-k-1)
- with Failure _ -> None) in
- if acc = None
- then None::(erase (i+1) tl)
- else he::(erase (i+1) tl) in
- let rec aux =
- function
- [] -> []
- | (n,context,t)::tl when n=m -> (n,erase 1 context,t)::tl
- | hd::tl -> hd::(aux tl)
- in
- aux
-;;
-
-
-let check_accessibility metasenv i =
- let module C = Cic in
- let module S = CicSubstitution in
- let (_,canonical_context,_) =
- List.find (function (m,_,_) -> m=i) metasenv in
- List.map
- (function t ->
- let =
- delift canonical_context metasenv ? t
- ) canonical_context
-CSCSCS
-
-
-
- let rec aux metasenv k =
- function
- C.Rel i ->
- if i <= k then
- metasenv
- else
- (try
- match List.nth canonical_context (i-k-1) with
- Some (_,C.Decl t)
- | Some (_,C.Def t) -> aux metasenv k (S.lift i t)
- | None -> raise RelToHiddenHypothesis
- with
- Failure _ -> raise OpenTerm
- )
- | C.Var _ -> metasenv
- | C.Meta (i,l) -> restrict canonical_context i k l metasenv
- | C.Sort _ -> metasenv
- | C.Implicit -> metasenv
- | C.Cast (te,ty) ->
- let metasenv' = aux metasenv k te in
- aux metasenv' k ty
- | C.Prod (_,s,t)
- | C.Lambda (_,s,t)
- | C.LetIn (_,s,t) ->
- let metasenv' = aux metasenv k s in
- aux metasenv' (k+1) t
- | C.Appl l ->
- List.fold_left
- (function metasenv -> aux metasenv k) metasenv l
- | C.Const _
- | C.MutInd _
- | C.MutConstruct _ -> metasenv
- | C.MutCase (_,_,_,outty,t,pl) ->
- let metasenv' = aux metasenv k outty in
- let metasenv'' = aux metasenv' k t in
- List.fold_left
- (function metasenv -> aux metasenv k) metasenv'' pl
- | C.Fix (i, fl) ->
- let len = List.length fl in
- List.fold_left
- (fun metasenv f ->
- let (_,_,ty,bo) = f in
- let metasenv' = aux metasenv k ty in
- aux metasenv' (k+len) bo
- ) metasenv fl
- | C.CoFix (i, fl) ->
- let len = List.length fl in
- List.fold_left
- (fun metasenv f ->
- let (_,ty,bo) = f in
- let metasenv' = aux metasenv k ty in
- aux metasenv' (k+len) bo
- ) metasenv fl
- in aux metasenv 0
-;;
-*)
-
-
-let unwind metasenv subst unwinded t =
- let unwinded = ref unwinded in
- let frozen = ref [] in
- let rec um_aux metasenv =
- let module C = Cic in
- let module S = CicSubstitution in
- function
- C.Rel _ as t -> t,metasenv
- | C.Var _ as t -> t,metasenv
- | C.Meta (i,l) ->
- (try
- S.lift_meta l (List.assoc i !unwinded), metasenv
- with Not_found ->
- if List.mem i !frozen then raise OccurCheck
- else
- let saved_frozen = !frozen in
- frozen := i::!frozen ;
- let res =
- try
- let t = List.assoc i subst in
- let t',metasenv' = um_aux metasenv t in
- let _,metasenv'' =
- let (_,canonical_context,_) =
- List.find (function (m,_,_) -> m=i) metasenv
- in
-prerr_endline ("DELIFT(" ^ CicPp.ppterm t' ^ ")") ; flush stderr ;
-List.iter (function (Some t) -> prerr_endline ("l: " ^ CicPp.ppterm t) | None -> prerr_endline " _ ") l ; flush stderr ;
-prerr_endline "<DELIFT" ; flush stderr ;
- delift canonical_context metasenv' l t'
- in
- unwinded := (i,t')::!unwinded ;
- S.lift_meta l t', metasenv'
- with
- Not_found ->
- (* not constrained variable, i.e. free in subst*)
- let l',metasenv' =
- List.fold_right
- (fun t (tl,metasenv) ->
- match t with
- None -> None::tl,metasenv
- | Some t ->
- let t',metasenv' = um_aux metasenv t in
- (Some t')::tl, metasenv'
- ) l ([],metasenv)
- in
- C.Meta (i,l'), metasenv'
- in
- frozen := saved_frozen ;
- res
- )
- | C.Sort _
- | C.Implicit as t -> t,metasenv
- | C.Cast (te,ty) ->
- let te',metasenv' = um_aux metasenv te in
- let ty',metasenv'' = um_aux metasenv' ty in
- C.Cast (te',ty'),metasenv''
- | C.Prod (n,s,t) ->
- let s',metasenv' = um_aux metasenv s in
- let t',metasenv'' = um_aux metasenv' t in
- C.Prod (n, s', t'), metasenv''
- | C.Lambda (n,s,t) ->
- let s',metasenv' = um_aux metasenv s in
- let t',metasenv'' = um_aux metasenv' t in
- C.Lambda (n, s', t'), metasenv''
- | C.LetIn (n,s,t) ->
- let s',metasenv' = um_aux metasenv s in
- let t',metasenv'' = um_aux metasenv' t in
- C.LetIn (n, s', t'), metasenv''
- | C.Appl (he::tl) ->
- let tl',metasenv' =
- List.fold_right
- (fun t (tl,metasenv) ->
- let t',metasenv' = um_aux metasenv t in
- t'::tl, metasenv'
- ) tl ([],metasenv)
- in
- begin
- match um_aux metasenv' he with
- (C.Appl l, metasenv'') -> C.Appl (l@tl'),metasenv''
- | (he', metasenv'') -> C.Appl (he'::tl'),metasenv''
- end
- | C.Appl _ -> assert false
- | C.Const _
- | C.MutInd _
- | C.MutConstruct _ as t -> t,metasenv
- | C.MutCase (sp,cookingsno,i,outty,t,pl) ->
- let outty',metasenv' = um_aux metasenv outty in
- let t',metasenv'' = um_aux metasenv' t in
- let pl',metasenv''' =
- List.fold_right
- (fun p (pl,metasenv) ->
- let p',metasenv' = um_aux metasenv p in
- p'::pl, metasenv'
- ) pl ([],metasenv'')
- in
- C.MutCase (sp, cookingsno, i, outty', t', pl'),metasenv'''
- | C.Fix (i, fl) ->
- let len = List.length fl in
- let liftedfl,metasenv' =
- List.fold_right
- (fun (name, i, ty, bo) (fl,metasenv) ->
- let ty',metasenv' = um_aux metasenv ty in
- let bo',metasenv'' = um_aux metasenv' bo in
- (name, i, ty', bo')::fl,metasenv''
- ) fl ([],metasenv)
- in
- C.Fix (i, liftedfl),metasenv'
- | C.CoFix (i, fl) ->
- let len = List.length fl in
- let liftedfl,metasenv' =
- List.fold_right
- (fun (name, ty, bo) (fl,metasenv) ->
- let ty',metasenv' = um_aux metasenv ty in
- let bo',metasenv'' = um_aux metasenv' bo in
- (name, ty', bo')::fl,metasenv''
- ) fl ([],metasenv)
- in
- C.CoFix (i, liftedfl),metasenv'
- in
- let t',metasenv' = um_aux metasenv t in
- t',metasenv',!unwinded
-;;
-
-(* apply_subst_reducing subst (Some (mtr,reductions_no)) t *)
-(* performs as (apply_subst subst t) until it finds an application of *)
-(* (META [meta_to_reduce]) that, once unwinding is performed, creates *)
-(* a new beta-redex; in this case up to [reductions_no] consecutive *)
-(* beta-reductions are performed. *)
-(* Hint: this function is usually called when [reductions_no] *)
-(* eta-expansions have been performed and the head of the new *)
-(* application has been unified with (META [meta_to_reduce]): *)
-(* during the unwinding the eta-expansions are undone. *)
-
-let apply_subst_reducing subst meta_to_reduce t =
- let unwinded = ref subst in
- let rec um_aux =
- let module C = Cic in
- let module S = CicSubstitution in
- function
- C.Rel _
- | C.Var _ as t -> t
- | C.Meta (i,l) as t ->
- (try
- S.lift_meta l (List.assoc i !unwinded)
- with Not_found ->
- C.Meta (i,l))
- | C.Sort _ as t -> t
- | C.Implicit as t -> t
- | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
- | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
- | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
- | C.LetIn (n,s,t) -> C.LetIn (n, um_aux s, um_aux t)
- | C.Appl (he::tl) ->
- let tl' = List.map um_aux tl in
- let t' =
- match um_aux he with
- C.Appl l -> C.Appl (l@tl')
- | _ as he' -> C.Appl (he'::tl')
- in
- begin
- match meta_to_reduce,he with
- Some (mtr,reductions_no), C.Meta (m,_) when m = mtr ->
- let rec beta_reduce =
- function
- (n,(C.Appl (C.Lambda (_,_,t)::he'::tl'))) when n > 0 ->
- let he'' = CicSubstitution.subst he' t in
- if tl' = [] then
- he''
- else
- beta_reduce (n-1,C.Appl(he''::tl'))
- | (_,t) -> t
- in
- beta_reduce (reductions_no,t')
- | _,_ -> t'
- end
- | C.Appl _ -> assert false
- | C.Const _ as t -> t
- | C.MutInd _ as t -> t
- | C.MutConstruct _ as t -> t
- | C.MutCase (sp,cookingsno,i,outty,t,pl) ->
- C.MutCase (sp, cookingsno, i, um_aux outty, um_aux t,
- List.map um_aux pl)
- | C.Fix (i, fl) ->
- let len = List.length fl in
- let liftedfl =
- List.map
- (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux 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, um_aux ty, um_aux bo))
- fl
- in
- C.CoFix (i, liftedfl)
- in
- um_aux t
-;;
-
-(* UNWIND THE MGU INSIDE THE MGU *)
-let unwind_subst metasenv subst =
- let identity_relocation_list_for_metavariable i =
- let (_,canonical_context,_) =
- List.find (function (m,_,_) -> m=i) metasenv
- in
- let canonical_context_length = List.length canonical_context in
- let rec aux =
- function
- n when n > canonical_context_length -> []
- | n -> (Some (Cic.Rel n))::(aux (n+1))
- in
- aux 1
- in
- List.fold_left
- (fun (unwinded,metasenv) (i,_) ->
- let identity_relocation_list =
- identity_relocation_list_for_metavariable i
- in
- let (_,metasenv',subst') =
- unwind metasenv subst unwinded (Cic.Meta (i,identity_relocation_list))
- in
- subst',metasenv'
- ) ([],metasenv) subst
-;;
-
-let apply_subst subst t =
- (* metasenv will not be used nor modified. So, let's use a dummy empty one *)
- let metasenv = [] in
- let (t',_,_) = unwind metasenv [] subst t in
- t'
-;;
-
-(* A substitution is a (int * Cic.term) list that associates a *)
-(* metavariable i with its body. *)
-(* metasenv is of type Cic.metasenv *)
-(* fo_unif takes a metasenv, a context, two terms t1 and t2 and gives back *)
-(* a new substitution which is already unwinded and ready to be applied and *)
-(* a new metasenv in which some hypothesis in the contexts of the *)
-(* metavariables may have been restricted. *)
-let fo_unif metasenv context t1 t2 =
-prerr_endline "INIZIO FASE 1" ; flush stderr ;
- let subst_to_unwind,metasenv' = fo_unif_new metasenv context t1 t2 in
-prerr_endline "FINE FASE 1" ; flush stderr ;
-let res =
- unwind_subst metasenv' subst_to_unwind
-in
-prerr_endline "FINE FASE 2" ; flush stderr ; res
-;;
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