+(* 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
-exception MetaSubstFailure of string
+(* PROFILING *)
+(*
+let deref_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 () =
+ debug_print (lazy (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 Lazy.t
+exception Uncertain of string Lazy.t
+exception AssertFailure of string Lazy.t
+exception DeliftingARelWouldCaptureAFreeVariable;;
+
+let debug_print = fun _ -> ()
+
+type substitution = (int * (Cic.context * Cic.term)) list
+
+(*
+let rec deref subst =
+ let third _,_,a = a in
+ function
+ Cic.Meta(n,l) as t ->
+ (try
+ deref subst
+ (CicSubstitution.subst_meta
+ l (third (CicUtil.lookup_subst n subst)))
+ with
+ CicUtil.Subst_not_found _ -> t)
+ | t -> t
+;;
+*)
+
+let lookup_subst = CicUtil.lookup_subst
+;;
+
+
+(* 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 CicUtil.Subst_not_found _ ->
+ 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 *)
-let debug_print = prerr_endline
+(*** Functions to apply a substitution ***)
-type substitution = (int * Cic.term) list
+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,_) = lookup_subst i subst in
+ um_aux (S.subst_meta l t)
+ with CicUtil.Subst_not_found _ ->
+ (* unconstrained 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 _
+ | 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 (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
+ let t' =
+ match um_aux he with
+ Cic.Appl l -> Cic.Appl (l@tl')
+ | he' -> Cic.Appl (he'::tl')
+ in
+ begin
+ match he with
+ Cic.Meta (m,_) -> CicReduction.head_beta_reduce t'
+ | _ -> t'
+ end
+ in
+ 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
+ | 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 =
+(*
+ 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.mem_assoc i subst))
+ metasenv)
+
+(***** Pretty printing functions ******)
+
+let ppterm subst term = CicPp.ppterm (apply_subst subst term)
+
+let ppterm_in_name_context subst term name_context =
+ CicPp.pp (apply_subst subst term) name_context
+
+let ppterm_in_context subst term context =
+ let name_context =
+ List.map (function None -> None | Some (n,_) -> Some n) context
+ in
+ ppterm_in_name_context 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_name_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_name_context subst ty name_context)
+ (ppterm_in_name_context subst bo name_context), (Some n)::name_context
+ | None ->
+ 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_name_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, term) -> Printf.sprintf "?%d := %s" idx (CicPp.ppterm term))
- subst)
+ (fun (idx, (c, t, _)) ->
+ let context,name_context = ppcontext' ~sep:"; " [] c in
+ sprintf "%s |- ?%d:= %s" context idx
+ (ppterm_in_name_context [] t name_context))
+ subst)
+;;
+
+let ppcontext ?sep subst context = fst (ppcontext' ?sep subst context)
+
+let ppmetasenv ?(sep = "\n") subst metasenv =
+ 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_name_context subst t name_context))
+ (List.filter
+ (fun (i, _, _) -> not (List.mem_assoc i subst))
+ metasenv))
+
+let tempi_type_of_aux_subst = ref 0.0;;
+let tempi_subst = ref 0.0;;
+let tempi_type_of_aux = ref 0.0;;
(**** DELIFT ****)
(* the delift function takes in input a metavariable index, an ordered list of
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 r when List.mem (r - k) to_be_restricted -> raise Occur
| C.Rel _
| C.Sort _ as t -> t
- | C.Implicit -> assert false
+ | C.Implicit _ -> assert false
| C.Meta (n, l) ->
- (try
- aux k (CicSubstitution.lift_meta l (List.assoc n subst))
- with Not_found ->
- let l' =
- let i = ref 0 in
- List.map
- (function
- | None -> None
- | Some t ->
- incr i;
- try
- Some (aux k t)
- with Occur ->
- more_to_be_restricted := (n,!i) :: !more_to_be_restricted;
- None)
- l
- in
- 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)
String.concat ", "
(List.map
(fun i ->
- match List.nth context i with
- | None -> assert false
- | Some (n, _) -> CicPp.ppname n)
- indexes)
+ try
+ match List.nth context (i-1) 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
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)
+ 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
let rec erase i to_be_restricted n = function
| [] -> [], to_be_restricted, []
| hd::tl ->
- let restrict_me = List.mem i to_be_restricted in
+ 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
- let more_to_be_restricted, restricted, new_tl =
- erase (i+1) (i :: to_be_restricted) n tl
- in
- more_to_be_restricted, restricted, None :: new_tl
+ more_to_be_restricted, restricted, None:: tl'
else
(try
- let more_to_be_restricted, hd' =
- force_does_not_occur_in_context to_be_restricted hd
- in
- let more_to_be_restricted', restricted, tl' =
- erase (i+1) to_be_restricted n tl
+ 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'
+ more_to_be_restricted @ more_to_be_restricted',
+ restricted, hd' :: tl'
with Occur ->
- let more_to_be_restricted, restricted, tl' =
- erase (i+1) (i :: to_be_restricted) n tl
- in
- more_to_be_restricted, restricted, None :: tl')
+ 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
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
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
- (CicPp.ppterm s)))
- with Not_found -> (more @ more_to_be_restricted, metasenv', subst))
+ (more @ more_to_be_restricted @ more_to_be_restricted',
+ metasenv')
with Occur ->
- raise (MetaSubstFailure (sprintf
+ raise (MetaSubstFailure (lazy (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
- match more_to_be_restricted with
+ let (more_to_be_restricted', subst) = (* restrict subst *)
+ List.fold_right
+ (* TODO: cambiare dopo l'aggiunta del ty *)
+ (fun (n, (context, term,ty)) (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 more_to_be_restricted'', ty' =
+ force_does_not_occur subst restricted ty in
+ let subst' = (n, (context', term',ty')) :: subst' in
+ let more =
+ more @ more_to_be_restricted
+ @ more_to_be_restricted'@more_to_be_restricted'' in
+ (more, subst')
+ with Occur ->
+ let error_msg = lazy (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
+ debug_print (lazy error_msg);
+ debug_print (lazy ("metasenv = \n" ^ (ppmetasenv metasenv subst)));
+ debug_print (lazy ("subst = \n" ^ (ppsubst subst)));
+ debug_print (lazy ("context = \n" ^ (ppcontext subst context))); *)
+ raise (MetaSubstFailure error_msg)))
+ subst ([], [])
+ in
+ 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 =
- 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
+(* INVARIANT: we suppose that t is not another occurrence of Meta(n,_),
+ otherwise the occur check does not make sense *)
+
+(*
+ debug_print (lazy ("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
+ 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
(*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) ->
- (*CSC: The following check seems to be wrong! *)
- (*CSC: B:Set |- ?2 : Set *)
- (*CSC: A:Set ; x:?2[A/B] |- ?1[x/A] =?= x *)
- (*CSC: Why should I restrict ?2 over B? The instantiation *)
- (*CSC: ?1 := A is perfectly reasonable and well-typed. *)
- (*CSC: Thus I comment out the following two lines that *)
- (*CSC: are the incriminated ones. *)
- (*(* It may augment to_be_restricted *)
- ignore (deliftaux k (S.lift m t)) ;*)
- (*CSC: end of bug commented out *)
- 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 (lazy "RelToHiddenHypothesis"))
+ with
+ Failure _ ->
+ raise (MetaSubstFailure (lazy "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 (CicPp.ppterm t)))
- else
- (try
- deliftaux k (S.lift_meta l (List.assoc i subst))
- with Not_found ->
- 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'))
+ (try
+ let (_,t,_) = CicUtil.lookup_subst i subst in
+ deliftaux k (CicSubstitution.subst_meta l1 t)
+ with CicUtil.Subst_not_found _ ->
+ (* see the top level invariant *)
+ if (i = n) then
+ raise (MetaSubstFailure (lazy (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
+ 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 =
+ 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')
+ end)
| C.Sort _ as t -> t
- | C.Implicit 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)
(* 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 (lazy "First Order UnificationFailure during delift") ;
+debug_print(lazy (sprintf
"Error trying to abstract %s over [%s]: the algorithm only tried to abstract over bound variables"
- (CicPp.ppterm t)
+ (ppterm subst t)
(String.concat "; "
(List.map
- (function Some t -> CicPp.ppterm t | None -> "_")
- l))))
+ (function Some t -> ppterm subst t | None -> "_") l
+ )))); *)
+ raise (Uncertain (lazy (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 ****)
-
-let apply_subst_gen ~appl_fun subst term =
- let rec um_aux =
+(* delifts a term t of n levels strating from k, that is changes (Rel m)
+ * to (Rel (m - n)) when m > (k + n). if k <= m < k + n delift fails
+ *)
+let delift_rels_from subst metasenv k n =
+ let rec liftaux subst metasenv k =
let module C = Cic in
- let module S = CicSubstitution in
function
- C.Rel _ as t -> t
- | C.Var _ as t -> t
- | C.Meta (i, l) ->
+ C.Rel m ->
+ if m < k then
+ C.Rel m, subst, metasenv
+ else if m < k + n then
+ raise DeliftingARelWouldCaptureAFreeVariable
+ else
+ C.Rel (m - n), subst, metasenv
+ | C.Var (uri,exp_named_subst) ->
+ let exp_named_subst',subst,metasenv =
+ List.fold_right
+ (fun (uri,t) (l,subst,metasenv) ->
+ let t',subst,metasenv = liftaux subst metasenv k t in
+ (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
+ in
+ C.Var (uri,exp_named_subst'),subst,metasenv
+ | 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
+ let (_, t,_) = lookup_subst i subst in
+ liftaux subst metasenv k (CicSubstitution.subst_meta l t)
+ with CicUtil.Subst_not_found _ ->
+ let l',to_be_restricted,subst,metasenv =
+ let rec aux con l subst metasenv =
+ match l with
+ [] -> [],[],subst,metasenv
+ | he::tl ->
+ let tl',to_be_restricted,subst,metasenv =
+ aux (con + 1) tl subst metasenv in
+ let he',more_to_be_restricted,subst,metasenv =
+ match he with
+ None -> None,[],subst,metasenv
+ | Some t ->
+ try
+ let t',subst,metasenv = liftaux subst metasenv k t in
+ Some t',[],subst,metasenv
+ with
+ DeliftingARelWouldCaptureAFreeVariable ->
+ None,[i,con],subst,metasenv
+ in
+ he'::tl',more_to_be_restricted@to_be_restricted,subst,metasenv
+ in
+ aux 1 l subst metasenv in
+ let metasenv,subst = restrict subst to_be_restricted metasenv in
+ C.Meta(i,l'),subst,metasenv)
+ | C.Sort _ as t -> t,subst,metasenv
+ | C.Implicit _ as t -> t,subst,metasenv
+ | C.Cast (te,ty) ->
+ let te',subst,metasenv = liftaux subst metasenv k te in
+ let ty',subst,metasenv = liftaux subst metasenv k ty in
+ C.Cast (te',ty'),subst,metasenv
+ | C.Prod (n,s,t) ->
+ let s',subst,metasenv = liftaux subst metasenv k s in
+ let t',subst,metasenv = liftaux subst metasenv (k+1) t in
+ C.Prod (n,s',t'),subst,metasenv
+ | C.Lambda (n,s,t) ->
+ let s',subst,metasenv = liftaux subst metasenv k s in
+ let t',subst,metasenv = liftaux subst metasenv (k+1) t in
+ C.Lambda (n,s',t'),subst,metasenv
+ | C.LetIn (n,s,t) ->
+ let s',subst,metasenv = liftaux subst metasenv k s in
+ let t',subst,metasenv = liftaux subst metasenv (k+1) t in
+ C.LetIn (n,s',t'),subst,metasenv
+ | C.Appl l ->
+ let l',subst,metasenv =
+ List.fold_right
+ (fun t (l,subst,metasenv) ->
+ let t',subst,metasenv = liftaux subst metasenv k t in
+ t'::l,subst,metasenv) l ([],subst,metasenv) in
+ C.Appl l',subst,metasenv
| C.Const (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
+ let exp_named_subst',subst,metasenv =
+ List.fold_right
+ (fun (uri,t) (l,subst,metasenv) ->
+ let t',subst,metasenv = liftaux subst metasenv k t in
+ (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
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
+ C.Const (uri,exp_named_subst'),subst,metasenv
+ | C.MutInd (uri,tyno,exp_named_subst) ->
+ let exp_named_subst',subst,metasenv =
+ List.fold_right
+ (fun (uri,t) (l,subst,metasenv) ->
+ let t',subst,metasenv = liftaux subst metasenv k t in
+ (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
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
+ C.MutInd (uri,tyno,exp_named_subst'),subst,metasenv
+ | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
+ let exp_named_subst',subst,metasenv =
+ List.fold_right
+ (fun (uri,t) (l,subst,metasenv) ->
+ let t',subst,metasenv = liftaux subst metasenv k t in
+ (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
in
- C.MutConstruct (uri,typeno,consno,exp_named_subst')
+ C.MutConstruct (uri,tyno,consno,exp_named_subst'),subst,metasenv
| 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')
+ let outty',subst,metasenv = liftaux subst metasenv k outty in
+ let t',subst,metasenv = liftaux subst metasenv k t in
+ let pl',subst,metasenv =
+ List.fold_right
+ (fun t (l,subst,metasenv) ->
+ let t',subst,metasenv = liftaux subst metasenv k t in
+ t'::l,subst,metasenv) pl ([],subst,metasenv)
+ in
+ C.MutCase (sp,i,outty',t',pl'),subst,metasenv
| C.Fix (i, fl) ->
- let fl' =
- List.map (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo)) fl
+ let len = List.length fl in
+ let liftedfl,subst,metasenv =
+ List.fold_right
+ (fun (name, i, ty, bo) (l,subst,metasenv) ->
+ let ty',subst,metasenv = liftaux subst metasenv k ty in
+ let bo',subst,metasenv = liftaux subst metasenv (k+len) bo in
+ (name,i,ty',bo')::l,subst,metasenv
+ ) fl ([],subst,metasenv)
in
- C.Fix (i, fl')
+ C.Fix (i, liftedfl),subst,metasenv
| C.CoFix (i, fl) ->
- let fl' =
- List.map (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo)) fl
+ let len = List.length fl in
+ let liftedfl,subst,metasenv =
+ List.fold_right
+ (fun (name, ty, bo) (l,subst,metasenv) ->
+ let ty',subst,metasenv = liftaux subst metasenv k ty in
+ let bo',subst,metasenv = liftaux subst metasenv (k+len) bo in
+ (name,ty',bo')::l,subst,metasenv
+ ) fl ([],subst,metasenv)
in
- C.CoFix (i, fl')
+ C.CoFix (i, liftedfl),subst,metasenv
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
-
-let ppterm subst term = CicPp.ppterm (apply_subst subst term)
+ liftaux subst metasenv k
-(* 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 delift_rels subst metasenv n t =
+ delift_rels_from subst metasenv 1 n t
+
-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)
+(**** END OF DELIFT ****)
-let ppterm subst term = CicPp.ppterm (apply_subst subst term)
-let ppcontext ?(sep = "\n") subst context =
- String.concat sep
- (List.rev_map (function
- | Some (n, Cic.Decl t) ->
- sprintf "%s : %s" (CicPp.ppname n) (ppterm subst t)
- | Some (n, Cic.Def (t, ty)) ->
- sprintf "%s : %s := %s"
- (CicPp.ppname n)
- (match ty with None -> "_" | Some ty -> ppterm subst ty)
- (ppterm subst t)
- | None -> "_")
- context)
-
-let ppmetasenv ?(sep = "\n") metasenv subst =
- String.concat sep
- (List.map
- (fun (i, c, t) ->
- sprintf "%s |- ?%d: %s" (ppcontext ~sep:"; " subst c) i
- (ppterm subst t))
- (List.filter
- (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
- metasenv))
+(** {2 Format-like pretty printers} *)
-(* UNWIND THE MGU INSIDE THE MGU *)
-(*
-let unwind_subst metasenv subst =
- List.fold_left
- (fun (unwinded,metasenv) (i,_) ->
- let (_,canonical_context,_) = CicUtil.lookup_meta i metasenv in
- let identity_relocation_list =
- CicMkImplicit.identity_relocation_list_for_metavariable canonical_context
- in
- let (_,metasenv',subst') =
- unwind metasenv subst unwinded (Cic.Meta (i,identity_relocation_list))
- in
- subst',metasenv'
- ) ([],metasenv) subst
-*)
+let fpp_gen ppf s =
+ Format.pp_print_string ppf s;
+ Format.pp_print_newline ppf ();
+ Format.pp_print_flush ppf ()
-(* 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 type_of_aux' metasenv subst context term =
- 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
- try
- CicTypeChecker.type_of_aux' metasenv context term
- with CicTypeChecker.TypeCheckerFailure msg ->
- raise (MetaSubstFailure ("Type checker failure: " ^ msg))
+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