+(* Copyright (C) 2003, 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 AssertFailure of string
+(* (* PROFILING *)
+let apply_subst_counter = ref 0
+let apply_subst_context_counter = ref 0
+let apply_subst_metasenv_counter = ref 0
+let lift_counter = ref 0
+let subst_counter = ref 0
+let whd_counter = ref 0
+let are_convertible_counter = ref 0
+let metasenv_length = ref 0
+let context_length = ref 0
+let reset_counters () =
+ apply_subst_counter := 0;
+ apply_subst_context_counter := 0;
+ apply_subst_metasenv_counter := 0;
+ lift_counter := 0;
+ subst_counter := 0;
+ whd_counter := 0;
+ are_convertible_counter := 0;
+ metasenv_length := 0;
+ context_length := 0
+let print_counters () =
+ prerr_endline (Printf.sprintf
+"apply_subst: %d
+apply_subst_context: %d
+apply_subst_metasenv: %d
+lift: %d
+subst: %d
+whd: %d
+are_convertible: %d
+metasenv length: %d (avg = %.2f)
+context length: %d (avg = %.2f)
+"
+ !apply_subst_counter !apply_subst_context_counter
+ !apply_subst_metasenv_counter !lift_counter !subst_counter !whd_counter
+ !are_convertible_counter !metasenv_length
+ ((float !metasenv_length) /. (float !apply_subst_metasenv_counter))
+ !context_length
+ ((float !context_length) /. (float !apply_subst_context_counter))
+ )
+*)
+
exception MetaSubstFailure of string
+exception Uncertain of string
+exception AssertFailure of string
+exception SubstNotFound of int
let debug_print = prerr_endline
-type substitution = (int * Cic.term) list
+type substitution = (int * (Cic.context * Cic.term)) list
+
+let lookup_subst n subst =
+ try
+ List.assoc n subst
+ with Not_found -> raise (SubstNotFound n)
+
+(* clean_up_meta take a metasenv and a term and make every local context
+of each occurrence of a metavariable consistent with its canonical context,
+with respect to the hidden hipothesis *)
+(*
+let clean_up_meta subst metasenv t =
+ let module C = Cic in
+ let rec aux t =
+ match t with
+ C.Rel _
+ | C.Sort _ -> t
+ | C.Implicit _ -> assert false
+ | C.Meta (n,l) as t ->
+ let cc =
+ (try
+ let (cc,_) = lookup_subst n subst in cc
+ with SubstNotFound _ ->
+ try
+ let (_,cc,_) = CicUtil.lookup_meta n metasenv in cc
+ with CicUtil.Meta_not_found _ -> assert false) in
+ let l' =
+ (try
+ List.map2
+ (fun t1 t2 ->
+ match t1,t2 with
+ None , _ -> None
+ | _ , t -> t) cc l
+ with
+ Invalid_argument _ -> assert false) in
+ C.Meta (n, l')
+ | C.Cast (te,ty) -> C.Cast (aux te, aux ty)
+ | C.Prod (name,so,dest) -> C.Prod (name, aux so, aux dest)
+ | C.Lambda (name,so,dest) -> C.Lambda (name, aux so, aux dest)
+ | C.LetIn (name,so,dest) -> C.LetIn (name, aux so, aux dest)
+ | C.Appl l -> C.Appl (List.map aux l)
+ | C.Var (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (fun (uri,t) -> (uri, aux 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 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 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 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 out, aux te, List.map aux pl)
+ | C.Fix (i,fl) ->
+ let fl' =
+ List.map
+ (fun (name,j,ty,bo) -> (name, j, aux ty, aux bo)) fl
+ in
+ C.Fix (i, fl')
+ | C.CoFix (i,fl) ->
+ let fl' =
+ List.map
+ (fun (name,ty,bo) -> (name, aux ty, aux bo)) fl
+ in
+ C.CoFix (i, fl')
+ in
+ aux t *)
(*** Functions to apply a substitution ***)
let module S = CicSubstitution in
function
C.Rel _ as t -> t
- | C.Var _ 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
+ let (context, t) = lookup_subst i subst in
um_aux (S.lift_meta l t)
- with Not_found -> (* not constrained variable, i.e. free in subst*)
+ with SubstNotFound _ -> (* unconstrained variable, i.e. free in subst*)
let l' =
List.map (function None -> None | Some t -> Some (um_aux t)) l
in
;;
let apply_subst =
+(* CSC: old code that never performs beta reduction
let appl_fun um_aux he tl =
let tl' = List.map um_aux tl in
begin
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' =
| he' -> Cic.Appl (he'::tl')
in
begin
- match meta_to_reduce, he with
- Some (mtr,reductions_no), Cic.Meta (m,_) when m = mtr ->
+ match he with
+ Cic.Meta (m,_) ->
let rec beta_reduce =
function
- (n,(Cic.Appl (Cic.Lambda (_,_,t)::he'::tl'))) when n > 0 ->
+ (Cic.Appl (Cic.Lambda (_,_,t)::he'::tl')) ->
let he'' = CicSubstitution.subst he' t in
if tl' = [] then
he''
else
- beta_reduce (n-1,Cic.Appl(he''::tl'))
- | (_,t) -> t
+ beta_reduce (Cic.Appl(he''::tl'))
+ | t -> t
in
- beta_reduce (reductions_no,t')
- | _,_ -> t'
+ beta_reduce t'
+ | _ -> t'
end
in
- apply_subst_gen ~appl_fun
+ fun s t ->
+(* incr apply_subst_counter; *)
+ apply_subst_gen ~appl_fun s t
+;;
let rec apply_subst_context subst context =
+(*
+ incr apply_subst_context_counter;
+ context_length := !context_length + List.length context;
+*)
List.fold_right
(fun item context ->
match item with
context []
let apply_subst_metasenv subst metasenv =
+(*
+ incr apply_subst_metasenv_counter;
+ metasenv_length := !metasenv_length + List.length 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))
+ (fun (i, _, _) -> not (List.mem_assoc 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 =
sprintf "%s_ :? _" (separate i), None::name_context
) context ("",[])
+let ppsubst_unfolded subst =
+ String.concat "\n"
+ (List.map
+ (fun (idx, (c, t)) ->
+ let context,name_context = ppcontext' ~sep:"; " subst c in
+ sprintf "%s |- ?%d:= %s" context idx
+ (ppterm_in_context subst t name_context))
+ subst)
+(*
+ Printf.sprintf "?%d := %s" idx (CicPp.ppterm term))
+ subst) *)
+;;
+
+let ppsubst subst =
+ String.concat "\n"
+ (List.map
+ (fun (idx, (c, t)) ->
+ let context,name_context = ppcontext' ~sep:"; " [] c in
+ sprintf "%s |- ?%d:= %s" context idx
+ (ppterm_in_context [] t name_context))
+ subst)
+;;
+
let ppcontext ?sep subst context = fst (ppcontext' ?sep subst context)
let ppmetasenv ?(sep = "\n") metasenv subst =
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))
+ (fun (i, _, _) -> not (List.mem_assoc i subst))
metasenv))
(* From now on we recreate a kernel abstraction where substitutions are part of
* the calculus *)
let lift subst n term =
+(* incr subst_counter; *)
let term = apply_subst subst term in
try
CicSubstitution.lift n term
raise (MetaSubstFailure ("Lift failure: " ^ Printexc.to_string e))
let subst subst t1 t2 =
+(* incr subst_counter; *)
let t1 = apply_subst subst t1 in
let t2 = apply_subst subst t2 in
try
raise (MetaSubstFailure ("Subst failure: " ^ Printexc.to_string e))
let whd subst context term =
+(* incr whd_counter; *)
let term = apply_subst subst term in
let context = apply_subst_context subst context in
try
Printexc.to_string e))
let are_convertible subst context t1 t2 =
+(* incr are_convertible_counter; *)
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_subst = ref 0.0;;
let tempi_type_of_aux = ref 0.0;;
+ (* assumption: metasenv is already instantiated wrt subst *)
let type_of_aux' metasenv subst context term =
-let time1 = Unix.gettimeofday () in
+ let time1 = Unix.gettimeofday () in
+(* let term = clean_up_meta subst metasenv term 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)
+(* let metasenv = apply_subst_metasenv 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 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
+ let time3 = Unix.gettimeofday () in
+ tempi_type_of_aux_subst := !tempi_type_of_aux_subst +. time3 -. time1 ;
+ tempi_subst := !tempi_subst +. time2 -. time1 ;
+ tempi_type_of_aux := !tempi_type_of_aux +. time3 -. time2 ;
+ res
(**** DELIFT ****)
(* the delift function takes in input a metavariable index, an ordered list of
(List.map
(fun i ->
try
- match List.nth context i with
+ match List.nth context (i-1) with
| None -> assert false
| Some (n, _) -> CicPp.ppname n
with
with Occur ->
more_to_be_restricted, (i :: restricted), None :: tl')
in
- let (more_to_be_restricted, metasenv, subst) =
+ let (more_to_be_restricted, metasenv) = (* restrict metasenv *)
List.fold_right
- (fun (n, context, t) (more, metasenv, subst) ->
+ (fun (n, context, t) (more, metasenv) ->
let to_be_restricted =
List.map snd (List.filter (fun (m, _) -> m = n) to_be_restricted)
in
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))
+ (more @ more_to_be_restricted @ more_to_be_restricted',
+ metasenv')
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)
+ n (names_of_context_indexes context to_be_restricted))))
+ metasenv ([], [])
+ in
+ let (more_to_be_restricted', subst) = (* restrict subst *)
+ List.fold_right
+ (fun (n, (context, term)) (more, subst') ->
+ let to_be_restricted =
+ List.map snd (List.filter (fun (m, _) -> m = n) to_be_restricted)
+ in
+ (try
+ 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
+ let more_to_be_restricted', term' =
+ force_does_not_occur subst restricted term
+ in
+ let subst' = (n, (context', term')) :: subst' in
+ let more = more @ more_to_be_restricted @ more_to_be_restricted' in
+ (more, subst')
+ with Occur ->
+ let error_msg = 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 term)
+ in
+ (* DEBUG
+ prerr_endline error_msg;
+ prerr_endline ("metasenv = \n" ^ (ppmetasenv metasenv subst));
+ prerr_endline ("subst = \n" ^ (ppsubst subst));
+ prerr_endline ("context = \n" ^ (ppcontext subst context)); *)
+ raise (MetaSubstFailure error_msg)))
+ subst ([], [])
in
- match more_to_be_restricted with
+ match more_to_be_restricted @ more_to_be_restricted' with
| [] -> (metasenv, subst)
- | _ -> restrict subst more_to_be_restricted metasenv
+ | l -> restrict subst l metasenv
;;
-(*CSC: maybe we should rename delift in abstract, as I did in my dissertation *)
+(*CSC: maybe we should rename delift in abstract, as I did in my dissertation *)(*Andrea: maybe not*)
+
let delift n subst context metasenv l t =
+(* INVARIANT: we suppose that t is not another occurrence of Meta(n,_),
+ otherwise the occur check does not make sense *)
+(*
+ prerr_endline ("sto deliftando il termine " ^ (CicPp.ppterm t) ^ " rispetto
+ al contesto locale " ^ (CicPp.ppterm (Cic.Meta(0,l))));
+*)
+
let module S = CicSubstitution in
let l =
let (_, canonical_context, _) = CicUtil.lookup_meta n metasenv in
(*CSC: deliftato la regola per il LetIn *)
(*CSC: FALSO! La regola per il LetIn non lo fa *)
else
- (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"))
+ (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
+ (* see the top level invariant *)
+ 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)))
+ i (ppterm subst t)))
else
+ begin
(* 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 =
with
NotInTheList
| MetaSubstFailure _ ->
- to_be_restricted := (i,j)::!to_be_restricted ; None::l1'
+ to_be_restricted := (i,j)::!to_be_restricted ; None::l1'
in
- let l' = deliftl 1 l1 in
- C.Meta(i,l')
+ let l' = deliftl 1 l1 in
+ C.Meta(i,l')
+ end
| C.Sort _ as t -> t
| C.Implicit _ as t -> t
| C.Cast (te,ty) -> C.Cast (deliftaux k te, deliftaux k ty)
(* 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 "!!!!!!!!!!! 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 (MetaSubstFailure (sprintf
+(* debug_print "First Order UnificationFailure during delift" ;
+prerr_endline(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
+ ))); *)
+ raise (Uncertain (sprintf
"Error trying to abstract %s over [%s]: the algorithm only tried to abstract over bound variables"
(ppterm subst t)
(String.concat "; "
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