--- /dev/null
+(* 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/.
+ *)
+
+(* $Id$ *)
+
+open Printf
+
+(* 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 *)
+
+(*** 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,_) = 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,ty,t) -> C.LetIn (n, um_aux s, um_aux ty, 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 subst t ->
+(* incr apply_subst_counter; *)
+match subst with
+ [] -> t
+ | _ -> apply_subst_gen ~appl_fun subst t
+;;
+
+let profiler = HExtlib.profile "U/CicMetaSubst.apply_subst"
+let apply_subst s t =
+ profiler.HExtlib.profile (apply_subst s) t
+
+
+let apply_subst_context subst context =
+ match subst with
+ [] -> 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' = 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;
+*)
+match subst with
+ [] -> 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 ~metasenv subst term =
+ CicPp.ppterm ~metasenv (apply_subst subst term)
+
+let ppterm_in_name_context ~metasenv subst term name_context =
+ CicPp.pp ~metasenv (apply_subst subst term) name_context
+
+let ppterm_in_context ~metasenv subst term context =
+ let name_context =
+ List.map (function None -> None | Some (n,_) -> Some n) context
+ in
+ ppterm_in_name_context ~metasenv subst term name_context
+
+let ppterm_in_context_ref = ref ppterm_in_context
+let set_ppterm_in_context f =
+ ppterm_in_context_ref := f
+let use_low_level_ppterm_in_context = ref false
+
+let ppterm_in_context ~metasenv subst term context =
+ if !use_low_level_ppterm_in_context then
+ ppterm_in_context ~metasenv subst term context
+ else
+ !ppterm_in_context_ref ~metasenv subst term context
+
+let ppcontext' ~metasenv ?(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 ~metasenv subst t name_context),
+ (Some n)::name_context
+ | Some (n,Cic.Def (bo,ty)) ->
+ sprintf "%s%s : %s := %s" (separate i) (CicPp.ppname n)
+ (ppterm_in_name_context ~metasenv subst ty name_context)
+ (ppterm_in_name_context ~metasenv subst bo name_context), (Some n)::name_context
+ | None ->
+ sprintf "%s_ :? _" (separate i), None::name_context
+ ) context ("",[])
+
+let ppsubst_unfolded ~metasenv subst =
+ String.concat "\n"
+ (List.map
+ (fun (idx, (c, t,ty)) ->
+ let context,name_context = ppcontext' ~metasenv ~sep:"; " subst c in
+ sprintf "%s |- ?%d : %s := %s" context idx
+(ppterm_in_name_context ~metasenv [] ty name_context)
+ (ppterm_in_name_context ~metasenv subst t name_context))
+ subst)
+(*
+ Printf.sprintf "?%d := %s" idx (CicPp.ppterm term))
+ subst) *)
+;;
+
+let ppsubst ~metasenv subst =
+ String.concat "\n"
+ (List.map
+ (fun (idx, (c, t, ty)) ->
+ let context,name_context = ppcontext' ~metasenv ~sep:"; " [] c in
+ sprintf "%s |- ?%d : %s := %s" context idx (ppterm_in_name_context ~metasenv [] ty name_context)
+ (ppterm_in_name_context ~metasenv [] t name_context))
+ subst)
+;;
+
+let ppcontext ~metasenv ?sep subst context =
+ fst (ppcontext' ~metasenv ?sep subst context)
+
+let ppmetasenv ?(sep = "\n") subst metasenv =
+ String.concat sep
+ (List.map
+ (fun (i, c, t) ->
+ let context,name_context = ppcontext' ~metasenv ~sep:"; " subst c in
+ sprintf "%s |- ?%d: %s" context i
+ (ppterm_in_name_context ~metasenv 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
+ * 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,ty,dest) ->
+ C.LetIn (name, aux k so, aux k ty, 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 =
+ match to_be_restricted with
+ | [] -> metasenv, subst
+ | _ ->
+ let names_of_context_indexes context indexes =
+ String.concat ", "
+ (List.map
+ (fun i ->
+ 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
+ | 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' =
+ let more_to_be_restricted', ty' =
+ force_does_not_occur subst to_be_restricted ty
+ in
+ more_to_be_restricted @ more_to_be_restricted',
+ 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) = (* restrict metasenv *)
+ List.fold_right
+ (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
+ let more_to_be_restricted', t' =
+ force_does_not_occur subst restricted t
+ in
+ let metasenv' = (n, context', t') :: metasenv in
+ (more @ more_to_be_restricted @ more_to_be_restricted',
+ metasenv')
+ with Occur ->
+ 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 ([], [])
+ in
+ 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 ~metasenv 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
+ restrict subst (more_to_be_restricted @ more_to_be_restricted') metasenv
+;;
+
+(*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 *)
+
+(*
+ 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
+ function
+ | C.Rel m as t->
+ if m <=k then
+ t
+ else
+ (try
+ match List.nth context (m-k-1) with
+ Some (_,C.Def (t,_)) ->
+ (try
+ C.Rel ((position (m-k) l) + k)
+ with
+ NotInTheList ->
+ (*CSC: Hmmm. This bit of reduction is not in the spirit of *)
+ (*CSC: first order unification. Does it help or does it harm? *)
+ (*CSC: ANSWER: it hurts performances since it is possible to *)
+ (*CSC: have an exponential explosion of the size of the proof.*)
+ (*CSC: However, without this bit of reduction some "apply" in *)
+ (*CSC: the library fail (e.g. nat/nth_prime.ma). *)
+ 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 ->
+ (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 ~metasenv 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.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,ty,t) ->
+ C.LetIn (n, deliftaux k s, deliftaux k ty, 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 (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"
+ (ppterm subst t)
+ (String.concat "; "
+ (List.map
+ (function Some t -> ppterm subst t | None -> "_") l
+ )))); *)
+ let msg = (lazy (sprintf
+ "Error trying to abstract %s over [%s]: the algorithm only tried to abstract over bound variables"
+ (ppterm ~metasenv subst t)
+ (String.concat "; "
+ (List.map
+ (function Some t -> ppterm ~metasenv subst t | None -> "_")
+ l))))
+ in
+ if
+ List.exists
+ (function
+ Some t -> CicUtil.is_meta_closed (apply_subst subst t)
+ | None -> true) l
+ then
+ raise (Uncertain msg)
+ else
+ raise (MetaSubstFailure msg)
+ in
+ let (metasenv, subst) = restrict subst !to_be_restricted metasenv in
+ res, metasenv, subst
+;;
+
+(* 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
+ function
+ C.Rel m as t ->
+ if m < k then
+ t, 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,_) = 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,ty,t) ->
+ let s',subst,metasenv = liftaux subst metasenv k s in
+ let ty',subst,metasenv = liftaux subst metasenv k ty in
+ let t',subst,metasenv = liftaux subst metasenv (k+1) t in
+ C.LetIn (n,s',ty',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',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'),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,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,tyno,consno,exp_named_subst'),subst,metasenv
+ | C.MutCase (sp,i,outty,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 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, liftedfl),subst,metasenv
+ | C.CoFix (i, 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, liftedfl),subst,metasenv
+ in
+ liftaux subst metasenv k
+
+let delift_rels subst metasenv n t =
+ delift_rels_from subst metasenv 1 n t
+
+
+(**** 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 ~metasenv:[] subst)
+let fppterm ppf term = fpp_gen ppf (CicPp.ppterm term)
+let fppmetasenv ppf metasenv = fpp_gen ppf (ppmetasenv [] metasenv)
projects / helm.git / blobdiff