+++ /dev/null
-(* Copyright (C) 2004, 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/.
- *)
-
-open Printf
-
-exception MetaSubstFailure of string
-exception Uncertain of string
-exception AssertFailure of string
-
-let debug_print = prerr_endline
-
-type substitution = (int * Cic.term) list
-
-(*** Functions to apply a substitution ***)
-
-let apply_subst_gen ~appl_fun subst term =
- let rec um_aux =
- let module C = Cic in
- let module S = CicSubstitution in
- function
- C.Rel _ as t -> t
- | C.Var (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
- in
- C.Var (uri, exp_named_subst')
- | C.Meta (i, l) ->
- (try
- let t = List.assoc i subst in
- um_aux (S.lift_meta l t)
- with Not_found -> (* not constrained variable, i.e. free in subst*)
- let l' =
- List.map (function None -> None | Some t -> Some (um_aux t)) l
- in
- C.Meta (i,l'))
- | C.Sort _ as t -> t
- | C.Implicit _ -> assert false
- | 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 (hd :: tl) -> appl_fun um_aux hd tl
- | C.Appl _ -> assert false
- | C.Const (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
- in
- C.Const (uri, exp_named_subst')
- | C.MutInd (uri,typeno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri, t) -> (uri, um_aux 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 (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
- in
- C.MutConstruct (uri,typeno,consno,exp_named_subst')
- | C.MutCase (sp,i,outty,t,pl) ->
- let pl' = List.map um_aux pl in
- C.MutCase (sp, i, um_aux outty, um_aux t, pl')
- | C.Fix (i, fl) ->
- let fl' =
- List.map (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo)) fl
- in
- C.Fix (i, fl')
- | C.CoFix (i, fl) ->
- let fl' =
- List.map (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo)) fl
- in
- C.CoFix (i, fl')
- in
- um_aux term
-;;
-
-let apply_subst =
- let appl_fun um_aux he tl =
- let tl' = List.map um_aux tl in
- begin
- match um_aux he with
- Cic.Appl l -> Cic.Appl (l@tl')
- | he' -> Cic.Appl (he'::tl')
- end
- in
- apply_subst_gen ~appl_fun
-;;
-
-(* 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 meta_to_reduce =
- let appl_fun um_aux he tl =
- let tl' = List.map um_aux tl in
- let t' =
- match um_aux he with
- Cic.Appl l -> Cic.Appl (l@tl')
- | he' -> Cic.Appl (he'::tl')
- in
- begin
- match meta_to_reduce, he with
- Some (mtr,reductions_no), Cic.Meta (m,_) when m = mtr ->
- let rec beta_reduce =
- function
- (n,(Cic.Appl (Cic.Lambda (_,_,t)::he'::tl'))) when n > 0 ->
- let he'' = CicSubstitution.subst he' t in
- if tl' = [] then
- he''
- else
- beta_reduce (n-1,Cic.Appl(he''::tl'))
- | (_,t) -> t
- in
- beta_reduce (reductions_no,t')
- | _,_ -> t'
- end
- in
- apply_subst_gen ~appl_fun
-
-let rec apply_subst_context subst context =
- List.fold_right
- (fun item context ->
- match item with
- | Some (n, Cic.Decl t) ->
- let t' = apply_subst subst t in
- Some (n, Cic.Decl t') :: context
- | Some (n, Cic.Def (t, ty)) ->
- let ty' =
- match ty with
- | None -> None
- | Some ty -> Some (apply_subst subst ty)
- in
- let t' = apply_subst subst t in
- Some (n, Cic.Def (t', ty')) :: context
- | None -> None :: context)
- context []
-
-let apply_subst_metasenv subst metasenv =
- List.map
- (fun (n, context, ty) ->
- (n, apply_subst_context subst context, apply_subst subst ty))
- (List.filter
- (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
- metasenv)
-
-(***** Pretty printing functions ******)
-
-let ppsubst subst =
- String.concat "\n"
- (List.map
- (fun (idx, term) -> Printf.sprintf "?%d := %s" idx (CicPp.ppterm term))
- subst)
-;;
-
-let ppterm subst term = CicPp.ppterm (apply_subst subst term)
-
-let ppterm_in_context subst term name_context =
- CicPp.pp (apply_subst subst term) name_context
-
-let ppcontext' ?(sep = "\n") subst context =
- let separate s = if s = "" then "" else s ^ sep in
- List.fold_right
- (fun context_entry (i,name_context) ->
- match context_entry with
- Some (n,Cic.Decl t) ->
- sprintf "%s%s : %s" (separate i) (CicPp.ppname n)
- (ppterm_in_context subst t name_context), (Some n)::name_context
- | Some (n,Cic.Def (bo,ty)) ->
- sprintf "%s%s : %s := %s" (separate i) (CicPp.ppname n)
- (match ty with
- None -> "_"
- | Some ty -> ppterm_in_context subst ty name_context)
- (ppterm_in_context subst bo name_context), (Some n)::name_context
- | None ->
- sprintf "%s_ :? _" (separate i), None::name_context
- ) context ("",[])
-
-let ppcontext ?sep subst context = fst (ppcontext' ?sep subst context)
-
-let ppmetasenv ?(sep = "\n") metasenv subst =
- String.concat sep
- (List.map
- (fun (i, c, t) ->
- let context,name_context = ppcontext' ~sep:"; " subst c in
- sprintf "%s |- ?%d: %s" context i
- (ppterm_in_context subst t name_context))
- (List.filter
- (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
- metasenv))
-
-(* From now on we recreate a kernel abstraction where substitutions are part of
- * the calculus *)
-
-let lift subst n term =
- let term = apply_subst subst term in
- try
- CicSubstitution.lift n term
- with e ->
- raise (MetaSubstFailure ("Lift failure: " ^ Printexc.to_string e))
-
-let subst subst t1 t2 =
- let t1 = apply_subst subst t1 in
- let t2 = apply_subst subst t2 in
- try
- CicSubstitution.subst t1 t2
- with e ->
- raise (MetaSubstFailure ("Subst failure: " ^ Printexc.to_string e))
-
-let whd subst context term =
- let term = apply_subst subst term in
- let context = apply_subst_context subst context in
- try
- CicReduction.whd context term
- with e ->
- raise (MetaSubstFailure ("Weak head reduction failure: " ^
- Printexc.to_string e))
-
-let are_convertible subst context t1 t2 =
- let context = apply_subst_context subst context in
- let t1 = apply_subst subst t1 in
- let t2 = apply_subst subst t2 in
- CicReduction.are_convertible context t1 t2
-
-let tempi_type_of_aux_subst = ref 0.0;;
-let tempi_type_of_aux = ref 0.0;;
-
-let type_of_aux' metasenv subst context term =
-let time1 = Unix.gettimeofday () in
- let term = apply_subst subst term in
- let context = apply_subst_context subst context in
- let metasenv =
- List.map
- (fun (i, c, t) -> (i, apply_subst_context subst c, apply_subst subst t))
- (List.filter
- (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
- metasenv)
- in
-let time2 = Unix.gettimeofday () in
-let res =
- try
- CicTypeChecker.type_of_aux' metasenv context term
- with CicTypeChecker.TypeCheckerFailure msg ->
- raise (MetaSubstFailure ("Type checker failure: " ^ msg))
-in
-let time3 = Unix.gettimeofday () in
- tempi_type_of_aux_subst := !tempi_type_of_aux_subst +. time3 -. time1 ;
- tempi_type_of_aux := !tempi_type_of_aux +. time2 -. time1 ;
- res
-
-(**** DELIFT ****)
-(* the delift function takes in input a metavariable index, an ordered list of
- * optional terms [t1,...,tn] and a term t, and substitutes every tk = Some
- * (rel(nk)) with rel(k). Typically, the list of optional terms is the explicit
- * substitution that is applied to a metavariable occurrence and the result of
- * the delift function is a term the implicit variable can be substituted with
- * to make the term [t] unifiable with the metavariable occurrence. In general,
- * the problem is undecidable if we consider equivalence in place of alpha
- * convertibility. Our implementation, though, is even weaker than alpha
- * convertibility, since it replace the term [tk] if and only if [tk] is a Rel
- * (missing all the other cases). Does this matter in practice?
- * The metavariable index is the index of the metavariable that must not occur
- * in the term (for occur check).
- *)
-
-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
-;;
-
-exception Occur;;
-
-let rec force_does_not_occur subst to_be_restricted t =
- let module C = Cic in
- let more_to_be_restricted = ref [] in
- let rec aux k = function
- C.Rel r when List.mem (r - k) to_be_restricted -> raise Occur
- | C.Rel _
- | C.Sort _ as t -> t
- | C.Implicit _ -> assert false
- | C.Meta (n, l) ->
- (* we do not retrieve the term associated to ?n in subst since *)
- (* in this way we can restrict if something goes wrong *)
- let l' =
- let i = ref 0 in
- List.map
- (function t ->
- incr i ;
- match t with
- None -> None
- | Some t ->
- try
- Some (aux k t)
- with Occur ->
- more_to_be_restricted := (n,!i) :: !more_to_be_restricted;
- None)
- l
- in
- C.Meta (n, l')
- | C.Cast (te,ty) -> C.Cast (aux k te, aux k ty)
- | C.Prod (name,so,dest) -> C.Prod (name, aux k so, aux (k+1) dest)
- | C.Lambda (name,so,dest) -> C.Lambda (name, aux k so, aux (k+1) dest)
- | C.LetIn (name,so,dest) -> C.LetIn (name, aux k so, aux (k+1) dest)
- | C.Appl l -> C.Appl (List.map (aux k) l)
- | C.Var (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri,t) -> (uri, aux k t)) exp_named_subst
- in
- C.Var (uri, exp_named_subst')
- | C.Const (uri, exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri,t) -> (uri, aux k t)) exp_named_subst
- in
- C.Const (uri, exp_named_subst')
- | C.MutInd (uri,tyno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (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 (fun (uri,t) -> (uri, aux k t)) exp_named_subst
- in
- C.MutConstruct (uri, tyno, consno, exp_named_subst')
- | C.MutCase (uri,tyno,out,te,pl) ->
- C.MutCase (uri, tyno, aux k out, aux k te, List.map (aux k) pl)
- | C.Fix (i,fl) ->
- let len = List.length fl in
- let k_plus_len = k + len in
- let fl' =
- List.map
- (fun (name,j,ty,bo) -> (name, j, aux k ty, aux k_plus_len bo)) fl
- in
- C.Fix (i, fl')
- | C.CoFix (i,fl) ->
- let len = List.length fl in
- let k_plus_len = k + len in
- let fl' =
- List.map
- (fun (name,ty,bo) -> (name, aux k ty, aux k_plus_len bo)) fl
- in
- C.CoFix (i, fl')
- in
- let res = aux 0 t in
- (!more_to_be_restricted, res)
-
-let rec restrict subst to_be_restricted metasenv =
- let names_of_context_indexes context indexes =
- String.concat ", "
- (List.map
- (fun i ->
- try
- match List.nth context i with
- | None -> assert false
- | Some (n, _) -> CicPp.ppname n
- with
- Failure _ -> assert false
- ) indexes)
- in
- let force_does_not_occur_in_context to_be_restricted = function
- | None -> [], None
- | Some (name, Cic.Decl t) ->
- let (more_to_be_restricted, t') =
- force_does_not_occur subst to_be_restricted t
- in
- more_to_be_restricted, Some (name, Cic.Decl t')
- | Some (name, Cic.Def (bo, ty)) ->
- let (more_to_be_restricted, bo') =
- force_does_not_occur subst to_be_restricted bo
- in
- let more_to_be_restricted, ty' =
- match ty with
- | None -> more_to_be_restricted, None
- | Some ty ->
- let more_to_be_restricted', ty' =
- force_does_not_occur subst to_be_restricted ty
- in
- more_to_be_restricted @ more_to_be_restricted',
- Some ty'
- in
- more_to_be_restricted, Some (name, Cic.Def (bo', ty'))
- in
- let rec erase i to_be_restricted n = function
- | [] -> [], to_be_restricted, []
- | hd::tl ->
- let more_to_be_restricted,restricted,tl' =
- erase (i+1) to_be_restricted n tl
- in
- let restrict_me = List.mem i restricted in
- if restrict_me then
- more_to_be_restricted, restricted, None:: tl'
- else
- (try
- let more_to_be_restricted', hd' =
- let delifted_restricted =
- let rec aux =
- function
- [] -> []
- | j::tl when j > i -> (j - i)::aux tl
- | _::tl -> aux tl
- in
- aux restricted
- in
- force_does_not_occur_in_context delifted_restricted hd
- in
- more_to_be_restricted @ more_to_be_restricted',
- restricted, hd' :: tl'
- with Occur ->
- more_to_be_restricted, (i :: restricted), None :: tl')
- in
- let (more_to_be_restricted, metasenv, subst) =
- List.fold_right
- (fun (n, context, t) (more, metasenv, subst) ->
- let to_be_restricted =
- List.map snd (List.filter (fun (m, _) -> m = n) to_be_restricted)
- in
- let (more_to_be_restricted, restricted, context') =
- (* just an optimization *)
- if to_be_restricted = [] then
- [],[],context
- else
- erase 1 to_be_restricted n context
- in
- try
- let more_to_be_restricted', t' =
- force_does_not_occur subst restricted t
- in
- let metasenv' = (n, context', t') :: metasenv in
- (try
- let s = List.assoc n subst in
- try
- let more_to_be_restricted'', s' =
- force_does_not_occur subst restricted s
- in
- let subst' = (n, s') :: (List.remove_assoc n subst) in
- let more =
- more @ more_to_be_restricted @ more_to_be_restricted' @
- more_to_be_restricted''
- in
- (more, metasenv', subst')
- with Occur ->
- raise (MetaSubstFailure (sprintf
- "Cannot restrict the context of the metavariable ?%d over the hypotheses %s since ?%d is already instantiated with %s and at least one of the hypotheses occurs in the substituted term"
- n (names_of_context_indexes context to_be_restricted) n
- (ppterm subst s)))
- with Not_found -> (more @ more_to_be_restricted @ more_to_be_restricted', metasenv', subst))
- with Occur ->
- raise (MetaSubstFailure (sprintf
- "Cannot restrict the context of the metavariable ?%d over the hypotheses %s since metavariable's type depends on at least one of them"
- n (names_of_context_indexes context to_be_restricted))))
- metasenv ([], [], subst)
- in
- match more_to_be_restricted with
- | [] -> (metasenv, subst)
- | _ -> restrict subst more_to_be_restricted metasenv
-;;
-
-(*CSC: maybe we should rename delift in abstract, as I did in my dissertation *)
-let delift n subst context metasenv l t =
- let module S = CicSubstitution in
- let l =
- let (_, canonical_context, _) = CicUtil.lookup_meta n metasenv in
- List.map2 (fun ct lt ->
- match (ct, lt) with
- | None, _ -> None
- | Some _, _ -> lt)
- canonical_context l
- 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 *)
- (*CSC: FALSO! La regola per il LetIn non lo fa *)
- else
- (try
- match List.nth context (m-k-1) with
- Some (_,C.Def (t,_)) ->
- (*CSC: Hmmm. This bit of reduction is not in the spirit of *)
- (*CSC: first order unification. Does it help or does it harm? *)
- deliftaux k (S.lift m t)
- | Some (_,C.Decl t) ->
- C.Rel ((position (m-k) l) + k)
- | None -> raise (MetaSubstFailure "RelToHiddenHypothesis")
- with
- Failure _ ->
- raise (MetaSubstFailure "Unbound variable found in deliftaux")
- )
- | C.Var (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
- in
- C.Var (uri,exp_named_subst')
- | C.Meta (i, l1) as t ->
- if i = n then
- raise (MetaSubstFailure (sprintf
- "Cannot unify the metavariable ?%d with a term that has as subterm %s in which the same metavariable occurs (occur check)"
- i (ppterm subst t)))
- else
- (* I do not consider the term associated to ?i in subst since *)
- (* in this way I can restrict if something goes wrong. *)
- 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
- NotInTheList
- | MetaSubstFailure _ ->
- 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 (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
- in
- C.Const (uri,exp_named_subst')
- | C.MutInd (uri,typeno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,deliftaux k 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,deliftaux k t) exp_named_subst
- in
- C.MutConstruct (uri,typeno,consno,exp_named_subst')
- | C.MutCase (sp,i,outty,t,pl) ->
- C.MutCase (sp, 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 =
- try
- deliftaux 0 t
- with
- NotInTheList ->
- (* This is the case where we fail even first order unification. *)
- (* The reason is that our delift function is weaker than first *)
- (* order (in the sense of alpha-conversion). See comment above *)
- (* related to the delift function. *)
-debug_print "\n!!!!!!!!!!! First Order UnificationFailure, but maybe it could have been successful even in a first order setting (no conversion, only alpha convertibility)! Please, implement a better delift function !!!!!!!!!!!!!!!!" ;
- raise (Uncertain (sprintf
- "Error trying to abstract %s over [%s]: the algorithm only tried to abstract over bound variables"
- (ppterm subst t)
- (String.concat "; "
- (List.map
- (function Some t -> ppterm subst t | None -> "_")
- l))))
- in
- let (metasenv, subst) = restrict subst !to_be_restricted metasenv in
- res, metasenv, subst
-;;
-
-(**** END OF DELIFT ****)
-
-
-(** {2 Format-like pretty printers} *)
-
-let fpp_gen ppf s =
- Format.pp_print_string ppf s;
- Format.pp_print_newline ppf ();
- Format.pp_print_flush ppf ()
-
-let fppsubst ppf subst = fpp_gen ppf (ppsubst subst)
-let fppterm ppf term = fpp_gen ppf (CicPp.ppterm term)
-let fppmetasenv ppf metasenv = fpp_gen ppf (ppmetasenv metasenv [])
-
projects / helm.git / blobdiff