src/HOL/Nominal/nominal_fresh_fun.ML
author narboux
Mon May 21 16:19:56 2007 +0200 (2007-05-21)
changeset 23054 d1bbe5afa279
parent 22792 2443ae6dac7d
child 23065 ab28e8398670
permissions -rw-r--r--
change fresh_fun_simp to treat occurences in assumptions and try to solve the generated subgoals
narboux@22729
     1
(*  Title:      HOL/Nominal/nominal_fresh_fun.ML
narboux@22729
     2
    ID:         $Id$
narboux@22729
     3
    Authors:    Stefan Berghofer, Julien Narboux, TU Muenchen
narboux@22729
     4
narboux@22729
     5
A tactic to generate fresh names.
narboux@22729
     6
A tactic to get rid of the fresh_fun.
narboux@22729
     7
*)
narboux@22729
     8
narboux@22729
     9
(* First some functions that could be
narboux@22729
    10
 in the library *)
narboux@22729
    11
narboux@22774
    12
(* A tactical which applies a list of int -> tactic to the corresponding subgoals present after the application of another tactic. 
narboux@22774
    13
T THENL [A,B,C] is equivalent to T THEN (C 3 THEN B 2 THEN A 1) 
narboux@22774
    14
*)
narboux@22753
    15
narboux@22753
    16
infix 1 THENL
narboux@22753
    17
narboux@22792
    18
fun tac THENL tacs =
narboux@22753
    19
 tac THEN
narboux@22753
    20
  (EVERY (map  (fn (tac,i) => tac i) (rev tacs ~~ (length tacs downto 1))))
narboux@22753
    21
narboux@23054
    22
fun SOLVEI t = t THEN_ALL_NEW (fn i => no_tac);
narboux@23054
    23
fun TRY' tac i =  TRY (tac i);
narboux@23054
    24
narboux@22729
    25
fun gen_res_inst_tac_term instf tyinst tinst elim th i st =
narboux@22729
    26
  let
narboux@22729
    27
    val thy = theory_of_thm st;
narboux@22729
    28
    val cgoal = nth (cprems_of st) (i - 1);
narboux@22729
    29
    val {maxidx, ...} = rep_cterm cgoal;
narboux@22729
    30
    val j = maxidx + 1;
narboux@22729
    31
    val tyinst' = map (apfst (Logic.incr_tvar j)) tyinst;
narboux@22729
    32
    val ps = Logic.strip_params (term_of cgoal);
narboux@22729
    33
    val Ts = map snd ps;
narboux@22729
    34
    val tinst' = map (fn (t, u) =>
narboux@22729
    35
      (head_of (Logic.incr_indexes (Ts, j) t),
narboux@22729
    36
       list_abs (ps, u))) tinst;
narboux@22729
    37
    val th' = instf
narboux@22729
    38
      (map (pairself (ctyp_of thy)) tyinst')
narboux@22729
    39
      (map (pairself (cterm_of thy)) tinst')
narboux@22729
    40
      (Thm.lift_rule cgoal th)
narboux@22729
    41
  in
narboux@22729
    42
    compose_tac (elim, th', nprems_of th) i st
narboux@22729
    43
  end handle Subscript => Seq.empty;
narboux@22729
    44
narboux@22729
    45
val res_inst_tac_term = 
narboux@22729
    46
  gen_res_inst_tac_term (curry Thm.instantiate);
narboux@22729
    47
narboux@22729
    48
val res_inst_tac_term' = 
narboux@22729
    49
  gen_res_inst_tac_term (K Drule.cterm_instantiate) [];
narboux@22729
    50
narboux@22729
    51
fun cut_inst_tac_term' tinst th =
narboux@22729
    52
  res_inst_tac_term' tinst false (Tactic.make_elim_preserve th);
narboux@22729
    53
narboux@22729
    54
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."); 
narboux@22729
    55
narboux@22729
    56
(* End of function waiting to be
narboux@22729
    57
 in the library *)
narboux@22729
    58
narboux@22729
    59
(* The theorems needed that are known at
narboux@22729
    60
compile time. *)
narboux@22729
    61
narboux@22729
    62
val at_exists_fresh' = thm "at_exists_fresh'";
narboux@22787
    63
val fresh_fun_app' = thm "fresh_fun_app'";
narboux@22729
    64
val fresh_prod = thm "fresh_prod";
narboux@22729
    65
narboux@22729
    66
(* A tactic to generate a name fresh for 
narboux@22729
    67
all the free variables and parameters of the goal *)
narboux@22729
    68
narboux@22729
    69
fun generate_fresh_tac atom_name i thm =
narboux@22729
    70
 let 
narboux@22729
    71
   val thy = theory_of_thm thm;
narboux@22729
    72
(* the parsing function returns a qualified name, we get back the base name *)
narboux@22729
    73
   val atom_basename = Sign.base_name atom_name;
narboux@22729
    74
   val goal = List.nth(prems_of thm, i-1);
narboux@22729
    75
   val ps = Logic.strip_params goal;
narboux@22729
    76
   val Ts = rev (map snd ps);
narboux@22729
    77
   fun is_of_fs_name T = Type.of_sort (Sign.tsig_of thy)
narboux@22729
    78
     (T, Sign.intern_sort thy ["fs_"^atom_basename]); 
narboux@22729
    79
(* rebuild de bruijn indices *)
narboux@22729
    80
   val bvs = map_index (Bound o fst) ps;
narboux@22729
    81
(* select variables of the right class *)
narboux@22729
    82
   val vs = filter (fn t => is_of_fs_name (fastype_of1 (Ts, t)))
narboux@22729
    83
     (term_frees goal @ bvs);
narboux@22729
    84
(* build the tuple *)
narboux@22729
    85
   val s = Library.foldr1 (fn (v, s) =>
narboux@22729
    86
     HOLogic.pair_const (fastype_of1 (Ts, v)) (fastype_of1 (Ts, s)) $ v $ s)
narboux@22729
    87
       vs;
narboux@22729
    88
   val fs_name_thm = get_dyn_thm thy ("fs_"^atom_basename^"1") atom_basename;
narboux@22729
    89
   val at_name_inst_thm = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
narboux@22729
    90
   val exists_fresh' = at_name_inst_thm RS at_exists_fresh';
narboux@22729
    91
(* find the variable we want to instantiate *)
narboux@22729
    92
   val x = hd (term_vars (prop_of exists_fresh'));
narboux@22729
    93
 in 
narboux@22729
    94
   (cut_inst_tac_term' [(x,s)] exists_fresh' 1 THEN
narboux@22729
    95
   rtac fs_name_thm 1 THEN
narboux@22729
    96
   etac exE 1) thm
narboux@22729
    97
  handle Empty  => all_tac thm (* if we collected no variables then we do nothing *)
narboux@22729
    98
  end;
narboux@22729
    99
narboux@22729
   100
fun get_inner_fresh_fun (Bound j) = NONE
narboux@22729
   101
  | get_inner_fresh_fun (v as Free _) = NONE 
narboux@22729
   102
  | get_inner_fresh_fun (v as Var _)  = NONE
narboux@22729
   103
  | get_inner_fresh_fun (Const _) = NONE
narboux@22729
   104
  | get_inner_fresh_fun (Abs (_, _, t)) = get_inner_fresh_fun t 
narboux@22729
   105
  | get_inner_fresh_fun (Const ("Nominal.fresh_fun",Type("fun",[Type ("fun",[Type (T,_),_]),_])) $ u) = SOME T 
narboux@22729
   106
  | get_inner_fresh_fun (t $ u) = 
narboux@22729
   107
     let val a = get_inner_fresh_fun u in
narboux@22729
   108
     if a = NONE then get_inner_fresh_fun t else a 
narboux@22729
   109
     end;
narboux@22729
   110
narboux@22729
   111
(* This tactic generates a fresh name 
narboux@22729
   112
of the atom type given by the inner most fresh_fun *)
narboux@22729
   113
narboux@22729
   114
fun generate_fresh_fun_tac i thm =
narboux@22729
   115
  let
narboux@22729
   116
    val goal = List.nth(prems_of thm, i-1);
narboux@22729
   117
    val atom_name_opt = get_inner_fresh_fun goal;
narboux@22729
   118
  in
narboux@22729
   119
  case atom_name_opt of 
narboux@22729
   120
    NONE => all_tac thm
narboux@22729
   121
  | SOME atom_name  => generate_fresh_tac atom_name i thm               
narboux@22729
   122
  end
narboux@22729
   123
narboux@22729
   124
(* A substitution tactic, FIXME : change the search function to get the inner occurence of fresh_fun (bottom -> up search ) *)
narboux@22729
   125
narboux@23054
   126
val search_fun     = curry (Seq.flat o (uncurry EqSubst.searchf_lr_unify_valid));
narboux@23054
   127
val search_fun_asm = EqSubst.skip_first_asm_occs_search EqSubst.searchf_lr_unify_valid;
narboux@23054
   128
narboux@23054
   129
fun subst_outer_tac           ctx = EqSubst.eqsubst_tac' ctx search_fun;
narboux@23054
   130
fun subst_outer_asm_tac_aux i ctx = EqSubst.eqsubst_asm_tac' ctx search_fun_asm i;
narboux@23054
   131
narboux@23054
   132
fun subst_outer_asm_tac ctx th =  curry (curry (FIRST' (map uncurry (map uncurry (map subst_outer_asm_tac_aux (1 upto Thm.nprems_of th)))))) ctx th;
narboux@22729
   133
narboux@22729
   134
fun fresh_fun_tac i thm = 
narboux@22729
   135
  (* Find the variable we instantiate *)
narboux@22729
   136
  let
narboux@22729
   137
    val thy = theory_of_thm thm;
narboux@22729
   138
    val ctx = Context.init_proof thy;
narboux@22729
   139
    val ss = simpset_of thy;
narboux@22729
   140
    val abs_fresh = PureThy.get_thms thy (Name "abs_fresh");
narboux@23054
   141
    val fresh_perm_app = PureThy.get_thms thy (Name "fresh_perm_app");
narboux@22729
   142
    val ss' = ss addsimps fresh_prod::abs_fresh;
narboux@23054
   143
    val ss'' = ss' addsimps fresh_perm_app;
narboux@22729
   144
    val x = hd (tl (term_vars (prop_of exI)));
narboux@22787
   145
    val goal = nth (prems_of thm) (i-1);
narboux@22729
   146
    val atom_name_opt = get_inner_fresh_fun goal;
narboux@22729
   147
    val n = List.length (Logic.strip_params goal);
narboux@22729
   148
    (* Here we rely on the fact that the variable introduced by generate_fresh_tac is the last one in the list, the inner one *)
narboux@22729
   149
  in
narboux@22729
   150
  case atom_name_opt of 
narboux@22729
   151
    NONE => all_tac thm
narboux@22729
   152
  | SOME atom_name  =>    
narboux@22729
   153
  let 
narboux@22729
   154
    val atom_basename = Sign.base_name atom_name;
narboux@22729
   155
    val pt_name_inst = get_dyn_thm thy ("pt_"^atom_basename^"_inst") atom_basename;
narboux@22729
   156
    val at_name_inst = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
narboux@22787
   157
    fun inst_fresh vars params i st =
narboux@22787
   158
   let val vars' = term_vars (prop_of st);
narboux@22787
   159
       val thy = theory_of_thm st;
narboux@22787
   160
   in case vars' \\ vars of 
narboux@22787
   161
     [x] => Seq.single (Thm.instantiate ([],[(cterm_of thy x,cterm_of thy (list_abs (params,Bound 0)))]) st)
narboux@22787
   162
    | _ => error "fresh_fun_simp: Too many variables, please report."
narboux@22787
   163
  end
narboux@22729
   164
  in
narboux@22787
   165
  ( (* generate_fresh_tac atom_name i      THEN *) 
narboux@22787
   166
  (fn st =>
narboux@22787
   167
  let 
narboux@22787
   168
    val vars = term_vars (prop_of st);
narboux@22787
   169
    val params = Logic.strip_params (nth (prems_of st) (i-1))
narboux@23054
   170
    val post_rewrite_tacs =  
narboux@23054
   171
          [rtac pt_name_inst,
narboux@23054
   172
           rtac at_name_inst,
narboux@23054
   173
           TRY' (SOLVEI (NominalPermeq.finite_guess_tac ss'')),
narboux@23054
   174
           inst_fresh vars params THEN'
narboux@23054
   175
           (TRY' (SOLVEI (NominalPermeq.fresh_guess_tac ss''))) THEN'
narboux@23054
   176
           (TRY' (SOLVEI (asm_full_simp_tac ss'')))] 
narboux@23054
   177
  in 
narboux@23054
   178
   ((subst_outer_asm_tac ctx fresh_fun_app' i THENL post_rewrite_tacs) ORELSE 
narboux@23054
   179
    (subst_outer_tac     ctx fresh_fun_app' i THENL post_rewrite_tacs)) st
narboux@22787
   180
  end)) thm
narboux@22787
   181
  
narboux@22729
   182
  end
narboux@22729
   183
  end
narboux@22729
   184
narboux@22729
   185
val setup_generate_fresh =
narboux@22729
   186
  Method.goal_args_ctxt' Args.tyname (fn ctxt => generate_fresh_tac) 
narboux@22729
   187
narboux@22729
   188
val setup_fresh_fun_simp =
narboux@22729
   189
  Method.no_args (Method.SIMPLE_METHOD (fresh_fun_tac 1))