src/HOL/Nominal/nominal_fresh_fun.ML
author narboux
Tue Apr 24 14:01:23 2007 +0200 (2007-04-24)
changeset 22774 8c64803fae48
parent 22753 49d7818e6161
child 22787 85e7e32e6004
permissions -rw-r--r--
adds op in front of an infix to fix SML compilation
     1 (*  Title:      HOL/Nominal/nominal_fresh_fun.ML
     2     ID:         $Id$
     3     Authors:    Stefan Berghofer, Julien Narboux, TU Muenchen
     4 
     5 A tactic to generate fresh names.
     6 A tactic to get rid of the fresh_fun.
     7 *)
     8 
     9 (* First some functions that could be
    10  in the library *)
    11 
    12 (* A tactical which applies a list of int -> tactic to the corresponding subgoals present after the application of another tactic. 
    13 T THENL [A,B,C] is equivalent to T THEN (C 3 THEN B 2 THEN A 1) 
    14 *)
    15 
    16 infix 1 THENL
    17 
    18 fun (op THENL) (tac,tacs) =
    19  tac THEN
    20   (EVERY (map  (fn (tac,i) => tac i) (rev tacs ~~ (length tacs downto 1))))
    21 
    22 fun gen_res_inst_tac_term instf tyinst tinst elim th i st =
    23   let
    24     val thy = theory_of_thm st;
    25     val cgoal = nth (cprems_of st) (i - 1);
    26     val {maxidx, ...} = rep_cterm cgoal;
    27     val j = maxidx + 1;
    28     val tyinst' = map (apfst (Logic.incr_tvar j)) tyinst;
    29     val ps = Logic.strip_params (term_of cgoal);
    30     val Ts = map snd ps;
    31     val tinst' = map (fn (t, u) =>
    32       (head_of (Logic.incr_indexes (Ts, j) t),
    33        list_abs (ps, u))) tinst;
    34     val th' = instf
    35       (map (pairself (ctyp_of thy)) tyinst')
    36       (map (pairself (cterm_of thy)) tinst')
    37       (Thm.lift_rule cgoal th)
    38   in
    39     compose_tac (elim, th', nprems_of th) i st
    40   end handle Subscript => Seq.empty;
    41 
    42 val res_inst_tac_term = 
    43   gen_res_inst_tac_term (curry Thm.instantiate);
    44 
    45 val res_inst_tac_term' = 
    46   gen_res_inst_tac_term (K Drule.cterm_instantiate) [];
    47 
    48 fun cut_inst_tac_term' tinst th =
    49   res_inst_tac_term' tinst false (Tactic.make_elim_preserve th);
    50 
    51 fun get_dyn_thm thy name atom_name = (PureThy.get_thm thy (Name name)) handle _ => raise ERROR ("The atom type "^atom_name^" is not defined."); 
    52 
    53 (* End of function waiting to be
    54  in the library *)
    55 
    56 (* The theorems needed that are known at
    57 compile time. *)
    58 
    59 val at_exists_fresh' = thm "at_exists_fresh'";
    60 val fresh_fun_app = thm "fresh_fun_app";
    61 val fresh_prod = thm "fresh_prod";
    62 
    63 (* A tactic to generate a name fresh for 
    64 all the free variables and parameters of the goal *)
    65 
    66 fun generate_fresh_tac atom_name i thm =
    67  let 
    68    val thy = theory_of_thm thm;
    69 (* the parsing function returns a qualified name, we get back the base name *)
    70    val atom_basename = Sign.base_name atom_name;
    71    val goal = List.nth(prems_of thm, i-1);
    72    val ps = Logic.strip_params goal;
    73    val Ts = rev (map snd ps);
    74    fun is_of_fs_name T = Type.of_sort (Sign.tsig_of thy)
    75      (T, Sign.intern_sort thy ["fs_"^atom_basename]); 
    76 (* rebuild de bruijn indices *)
    77    val bvs = map_index (Bound o fst) ps;
    78 (* select variables of the right class *)
    79    val vs = filter (fn t => is_of_fs_name (fastype_of1 (Ts, t)))
    80      (term_frees goal @ bvs);
    81 (* build the tuple *)
    82    val s = Library.foldr1 (fn (v, s) =>
    83      HOLogic.pair_const (fastype_of1 (Ts, v)) (fastype_of1 (Ts, s)) $ v $ s)
    84        vs;
    85    val fs_name_thm = get_dyn_thm thy ("fs_"^atom_basename^"1") atom_basename;
    86    val at_name_inst_thm = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
    87    val exists_fresh' = at_name_inst_thm RS at_exists_fresh';
    88 (* find the variable we want to instantiate *)
    89    val x = hd (term_vars (prop_of exists_fresh'));
    90  in 
    91    (cut_inst_tac_term' [(x,s)] exists_fresh' 1 THEN
    92    rtac fs_name_thm 1 THEN
    93    etac exE 1) thm
    94   handle Empty  => all_tac thm (* if we collected no variables then we do nothing *)
    95   end;
    96 
    97 fun get_inner_fresh_fun (Bound j) = NONE
    98   | get_inner_fresh_fun (v as Free _) = NONE 
    99   | get_inner_fresh_fun (v as Var _)  = NONE
   100   | get_inner_fresh_fun (Const _) = NONE
   101   | get_inner_fresh_fun (Abs (_, _, t)) = get_inner_fresh_fun t 
   102   | get_inner_fresh_fun (Const ("Nominal.fresh_fun",Type("fun",[Type ("fun",[Type (T,_),_]),_])) $ u) = SOME T 
   103   | get_inner_fresh_fun (t $ u) = 
   104      let val a = get_inner_fresh_fun u in
   105      if a = NONE then get_inner_fresh_fun t else a 
   106      end;
   107 
   108 (* This tactic generates a fresh name 
   109 of the atom type given by the inner most fresh_fun *)
   110 
   111 fun generate_fresh_fun_tac i thm =
   112   let
   113     val goal = List.nth(prems_of thm, i-1);
   114     val atom_name_opt = get_inner_fresh_fun goal;
   115   in
   116   case atom_name_opt of 
   117     NONE => all_tac thm
   118   | SOME atom_name  => generate_fresh_tac atom_name i thm               
   119   end
   120 
   121 (* A substitution tactic, FIXME : change the search function to get the inner occurence of fresh_fun (bottom -> up search ) *)
   122 
   123 fun subst_outer_tac ctx = EqSubst.eqsubst_tac' ctx (curry (Seq.flat o (uncurry EqSubst.searchf_lr_unify_valid)));
   124 
   125 fun fresh_fun_tac i thm = 
   126   (* Find the variable we instantiate *)
   127   let
   128     val thy = theory_of_thm thm;
   129     val ctx = Context.init_proof thy;
   130     val ss = simpset_of thy;
   131     val abs_fresh = PureThy.get_thms thy (Name "abs_fresh");
   132     val ss' = ss addsimps fresh_prod::abs_fresh;
   133     val x = hd (tl (term_vars (prop_of exI)));
   134     val goal = List.nth(prems_of thm, i-1);
   135     val atom_name_opt = get_inner_fresh_fun goal;
   136     val n = List.length (Logic.strip_params goal);
   137     (* Here we rely on the fact that the variable introduced by generate_fresh_tac is the last one in the list, the inner one *)
   138   in
   139   case atom_name_opt of 
   140     NONE => all_tac thm
   141   | SOME atom_name  =>    
   142   let 
   143     val atom_basename = Sign.base_name atom_name;
   144     val pt_name_inst = get_dyn_thm thy ("pt_"^atom_basename^"_inst") atom_basename;
   145     val at_name_inst = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
   146     fun tac_a i = 
   147       res_inst_tac_term' [(x,Bound n)] false exI i THEN
   148       asm_full_simp_tac ss' i                      THEN 
   149       NominalPermeq.fresh_guess_tac HOL_ss i;
   150   in
   151   (generate_fresh_tac atom_name i      THEN 
   152    subst_outer_tac ctx fresh_fun_app i THENL 
   153    [rtac pt_name_inst,
   154     rtac at_name_inst, 
   155     (fn i => TRY (NominalPermeq.finite_guess_tac HOL_ss i)),   
   156     tac_a, 
   157     (fn i => TRY (NominalPermeq.fresh_guess_tac  HOL_ss i)),
   158     (fn i => auto_tac (HOL_cs, HOL_ss)) 
   159 ]) thm 
   160   end
   161   end
   162 
   163 val setup_generate_fresh =
   164   Method.goal_args_ctxt' Args.tyname (fn ctxt => generate_fresh_tac) 
   165 
   166 val setup_fresh_fun_simp =
   167   Method.no_args (Method.SIMPLE_METHOD (fresh_fun_tac 1))