src/HOL/Nominal/nominal_fresh_fun.ML
author wenzelm
Sat Mar 22 18:16:54 2014 +0100 (2014-03-22)
changeset 56253 83b3c110f22d
parent 56230 3e449273942a
child 58318 f95754ca7082
permissions -rw-r--r--
more antiquotations;
     1 (*  Title:      HOL/Nominal/nominal_fresh_fun.ML
     2     Authors:    Stefan Berghofer and Julien Narboux, TU Muenchen
     3 
     4 Provides a tactic to generate fresh names and
     5 a tactic to analyse instances of the fresh_fun.
     6 *)
     7 
     8 (* FIXME proper ML structure! *)
     9 
    10 (* FIXME res_inst_tac mostly obsolete, cf. Subgoal.FOCUS *)
    11 
    12 (* FIXME proper SUBGOAL/CSUBGOAL instead of cprems_of etc. *)
    13 fun gen_res_inst_tac_term instf tyinst tinst elim th i st =
    14   let
    15     val thy = theory_of_thm st;
    16     val cgoal = nth (cprems_of st) (i - 1);
    17     val {maxidx, ...} = rep_cterm cgoal;
    18     val j = maxidx + 1;
    19     val tyinst' = map (apfst (Logic.incr_tvar j)) tyinst;
    20     val ps = Logic.strip_params (term_of cgoal);
    21     val Ts = map snd ps;
    22     val tinst' = map (fn (t, u) =>
    23       (head_of (Logic.incr_indexes (Ts, j) t),
    24        fold_rev Term.abs ps u)) tinst;
    25     val th' = instf
    26       (map (pairself (ctyp_of thy)) tyinst')
    27       (map (pairself (cterm_of thy)) tinst')
    28       (Thm.lift_rule cgoal th)
    29   in
    30     compose_tac (elim, th', nprems_of th) i st
    31   end handle General.Subscript => Seq.empty;
    32 (* FIXME proper SUBGOAL/CSUBGOAL instead of cprems_of etc. *)
    33 
    34 val res_inst_tac_term =
    35   gen_res_inst_tac_term (curry Thm.instantiate);
    36 
    37 val res_inst_tac_term' =
    38   gen_res_inst_tac_term (K Drule.cterm_instantiate) [];
    39 
    40 fun cut_inst_tac_term' tinst th =
    41   res_inst_tac_term' tinst false (Rule_Insts.make_elim_preserve th);
    42 
    43 fun get_dyn_thm thy name atom_name =
    44   Global_Theory.get_thm thy name handle ERROR _ =>
    45     error ("The atom type "^atom_name^" is not defined.");
    46 
    47 (* The theorems needed that are known at compile time. *)
    48 val at_exists_fresh' = @{thm "at_exists_fresh'"};
    49 val fresh_fun_app'   = @{thm "fresh_fun_app'"};
    50 val fresh_prod       = @{thm "fresh_prod"};
    51 
    52 (* A tactic to generate a name fresh for  all the free *)
    53 (* variables and parameters of the goal                *)
    54 
    55 fun generate_fresh_tac ctxt atom_name = SUBGOAL (fn (goal, _) =>
    56  let
    57    val thy = Proof_Context.theory_of ctxt;
    58 (* the parsing function returns a qualified name, we get back the base name *)
    59    val atom_basename = Long_Name.base_name atom_name;
    60    val ps = Logic.strip_params goal;
    61    val Ts = rev (map snd ps);
    62    fun is_of_fs_name T = Sign.of_sort thy (T, [Sign.intern_class thy ("fs_"^atom_basename)]);
    63 (* rebuild de bruijn indices *)
    64    val bvs = map_index (Bound o fst) ps;
    65 (* select variables of the right class *)
    66    val vs = filter (fn t => is_of_fs_name (fastype_of1 (Ts, t)))
    67      (Misc_Legacy.term_frees goal @ bvs);
    68 (* build the tuple *)
    69    val s = (Library.foldr1 (fn (v, s) =>
    70        HOLogic.pair_const (fastype_of1 (Ts, v)) (fastype_of1 (Ts, s)) $ v $ s) vs)
    71      handle TERM _ => HOLogic.unit;
    72    val fs_name_thm = get_dyn_thm thy ("fs_"^atom_basename^"1") atom_basename;
    73    val at_name_inst_thm = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
    74    val exists_fresh' = at_name_inst_thm RS at_exists_fresh';
    75 (* find the variable we want to instantiate *)
    76    val x = hd (Misc_Legacy.term_vars (prop_of exists_fresh'));
    77  in
    78    fn st =>
    79    (cut_inst_tac_term' [(x,s)] exists_fresh' 1 THEN
    80    rtac fs_name_thm 1 THEN
    81    etac exE 1) st
    82   handle List.Empty  => all_tac st (* if we collected no variables then we do nothing *)
    83  end) 1;
    84 
    85 fun get_inner_fresh_fun (Bound j) = NONE
    86   | get_inner_fresh_fun (v as Free _) = NONE
    87   | get_inner_fresh_fun (v as Var _)  = NONE
    88   | get_inner_fresh_fun (Const _) = NONE
    89   | get_inner_fresh_fun (Abs (_, _, t)) = get_inner_fresh_fun t
    90   | get_inner_fresh_fun (Const (@{const_name Nominal.fresh_fun},
    91       Type(@{type_name fun},[Type (@{type_name fun},[Type (T,_),_]),_])) $ u) = SOME T
    92   | get_inner_fresh_fun (t $ u) =
    93      let val a = get_inner_fresh_fun u in
    94      if a = NONE then get_inner_fresh_fun t else a
    95      end;
    96 
    97 (* This tactic generates a fresh name of the atom type *)
    98 (* given by the innermost fresh_fun                    *)
    99 
   100 fun generate_fresh_fun_tac ctxt = SUBGOAL (fn (goal, _) =>
   101   let
   102     val atom_name_opt = get_inner_fresh_fun goal;
   103   in
   104   case atom_name_opt of
   105     NONE => all_tac
   106   | SOME atom_name  => generate_fresh_tac ctxt atom_name
   107   end) 1;
   108 
   109 (* Two substitution tactics which looks for the innermost occurence in
   110    one assumption or in the conclusion *)
   111 
   112 val search_fun = curry (Seq.flat o uncurry EqSubst.searchf_bt_unify_valid);
   113 val search_fun_asm = EqSubst.skip_first_asm_occs_search EqSubst.searchf_bt_unify_valid;
   114 
   115 fun subst_inner_tac ctxt = EqSubst.eqsubst_tac' ctxt search_fun;
   116 fun subst_inner_asm_tac_aux i ctxt = EqSubst.eqsubst_asm_tac' ctxt search_fun_asm i;
   117 
   118 (* A tactic to substitute in the first assumption
   119    which contains an occurence. *)
   120 
   121 fun subst_inner_asm_tac ctxt th =
   122   curry (curry (FIRST' (map uncurry (map uncurry (map subst_inner_asm_tac_aux
   123             (1 upto Thm.nprems_of th)))))) ctxt th;
   124 
   125 fun fresh_fun_tac ctxt no_asm = SUBGOAL (fn (goal, i) =>
   126   (* Find the variable we instantiate *)
   127   let
   128     val thy = Proof_Context.theory_of ctxt;
   129     val abs_fresh = Global_Theory.get_thms thy "abs_fresh";
   130     val fresh_perm_app = Global_Theory.get_thms thy "fresh_perm_app";
   131     val simp_ctxt =
   132       ctxt addsimps (fresh_prod :: abs_fresh)
   133       addsimps fresh_perm_app;
   134     val x = hd (tl (Misc_Legacy.term_vars (prop_of exI)));
   135     val atom_name_opt = get_inner_fresh_fun goal;
   136     val n = length (Logic.strip_params goal);
   137     (* Here we rely on the fact that the variable introduced by generate_fresh_tac *)
   138     (* is the last one in the list, the inner one *)
   139   in
   140   case atom_name_opt of
   141     NONE => all_tac
   142   | SOME atom_name =>
   143   let
   144     val atom_basename = Long_Name.base_name atom_name;
   145     val pt_name_inst = get_dyn_thm thy ("pt_"^atom_basename^"_inst") atom_basename;
   146     val at_name_inst = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
   147     fun inst_fresh vars params i st =
   148    let val vars' = Misc_Legacy.term_vars (prop_of st);
   149        val thy = theory_of_thm st;
   150    in case subtract (op =) vars vars' of
   151      [x] =>
   152       Seq.single (Thm.instantiate ([],[(cterm_of thy x,cterm_of thy (fold_rev Term.abs params (Bound 0)))]) st)
   153     | _ => error "fresh_fun_simp: Too many variables, please report."
   154    end
   155   in
   156   ((fn st =>
   157   let
   158     val vars = Misc_Legacy.term_vars (prop_of st);
   159     val params = Logic.strip_params (nth (prems_of st) (i-1))
   160     (* The tactics which solve the subgoals generated
   161        by the conditionnal rewrite rule. *)
   162     val post_rewrite_tacs =
   163           [rtac pt_name_inst,
   164            rtac at_name_inst,
   165            TRY o SOLVED' (NominalPermeq.finite_guess_tac simp_ctxt),
   166            inst_fresh vars params THEN'
   167            (TRY o SOLVED' (NominalPermeq.fresh_guess_tac simp_ctxt)) THEN'
   168            (TRY o SOLVED' (asm_full_simp_tac simp_ctxt))]
   169   in
   170    ((if no_asm then no_tac else
   171     (subst_inner_asm_tac ctxt fresh_fun_app' i THEN (RANGE post_rewrite_tacs i)))
   172     ORELSE
   173     (subst_inner_tac ctxt fresh_fun_app' i THEN (RANGE post_rewrite_tacs i))) st
   174   end))
   175   end
   176   end)
   177