src/HOL/Nominal/nominal_fresh_fun.ML
author wenzelm
Tue Aug 14 23:22:51 2007 +0200 (2007-08-14)
changeset 24271 499608101177
parent 23368 ad690b9bca1c
child 24558 419f7cde7f59
permissions -rw-r--r--
avoid low-level tsig;
     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 in the library *)
    10 
    11 (* A tactical which applies a list of int -> tactic to the corresponding subgoals present after the application of another tactic. 
    12 T THENL [A,B,C] is equivalent to T THEN (C 3 THEN B 2 THEN A 1) 
    13 *)
    14 
    15 infix 1 THENL
    16 
    17 fun tac THENL tacs =
    18  tac THEN
    19   (EVERY (map  (fn (tac,i) => tac i) (rev tacs ~~ (length tacs downto 1))))
    20 
    21 (* A tactical to test if a tactic completly solve a subgoal *)
    22 
    23 fun SOLVEI t = t THEN_ALL_NEW (fn i => no_tac);
    24 
    25 (* A version of TRY for int -> tactic *)
    26 
    27 fun TRY' tac i =  TRY (tac i);
    28 
    29 fun gen_res_inst_tac_term instf tyinst tinst elim th i st =
    30   let
    31     val thy = theory_of_thm st;
    32     val cgoal = nth (cprems_of st) (i - 1);
    33     val {maxidx, ...} = rep_cterm cgoal;
    34     val j = maxidx + 1;
    35     val tyinst' = map (apfst (Logic.incr_tvar j)) tyinst;
    36     val ps = Logic.strip_params (term_of cgoal);
    37     val Ts = map snd ps;
    38     val tinst' = map (fn (t, u) =>
    39       (head_of (Logic.incr_indexes (Ts, j) t),
    40        list_abs (ps, u))) tinst;
    41     val th' = instf
    42       (map (pairself (ctyp_of thy)) tyinst')
    43       (map (pairself (cterm_of thy)) tinst')
    44       (Thm.lift_rule cgoal th)
    45   in
    46     compose_tac (elim, th', nprems_of th) i st
    47   end handle Subscript => Seq.empty;
    48 
    49 val res_inst_tac_term = 
    50   gen_res_inst_tac_term (curry Thm.instantiate);
    51 
    52 val res_inst_tac_term' = 
    53   gen_res_inst_tac_term (K Drule.cterm_instantiate) [];
    54 
    55 fun cut_inst_tac_term' tinst th =
    56   res_inst_tac_term' tinst false (Tactic.make_elim_preserve th);
    57 
    58 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."); 
    59 
    60 (* End of function waiting to be
    61  in the library *)
    62 
    63 (* The theorems needed that are known at
    64 compile time. *)
    65 
    66 val at_exists_fresh' = thm "at_exists_fresh'";
    67 val fresh_fun_app' = thm "fresh_fun_app'";
    68 val fresh_prod = thm "fresh_prod";
    69 
    70 (* A tactic to generate a name fresh for 
    71 all the free variables and parameters of the goal *)
    72 
    73 fun generate_fresh_tac atom_name i thm =
    74  let 
    75    val thy = theory_of_thm thm;
    76 (* the parsing function returns a qualified name, we get back the base name *)
    77    val atom_basename = Sign.base_name atom_name;
    78    val goal = List.nth(prems_of thm, i-1);
    79    val ps = Logic.strip_params goal;
    80    val Ts = rev (map snd ps);
    81    fun is_of_fs_name T = Sign.of_sort thy (T, Sign.intern_sort thy ["fs_"^atom_basename]); 
    82 (* rebuild de bruijn indices *)
    83    val bvs = map_index (Bound o fst) ps;
    84 (* select variables of the right class *)
    85    val vs = filter (fn t => is_of_fs_name (fastype_of1 (Ts, t)))
    86      (term_frees goal @ bvs);
    87 (* build the tuple *)
    88    val s = (Library.foldr1 (fn (v, s) =>
    89      HOLogic.pair_const (fastype_of1 (Ts, v)) (fastype_of1 (Ts, s)) $ v $ s) vs) handle _ => HOLogic.unit ;
    90    val fs_name_thm = get_dyn_thm thy ("fs_"^atom_basename^"1") atom_basename;
    91    val at_name_inst_thm = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
    92    val exists_fresh' = at_name_inst_thm RS at_exists_fresh';
    93 (* find the variable we want to instantiate *)
    94    val x = hd (term_vars (prop_of exists_fresh'));
    95  in 
    96    (cut_inst_tac_term' [(x,s)] exists_fresh' 1 THEN
    97    rtac fs_name_thm 1 THEN
    98    etac exE 1) thm
    99   handle Empty  => all_tac thm (* if we collected no variables then we do nothing *)
   100   end;
   101 
   102 fun get_inner_fresh_fun (Bound j) = NONE
   103   | get_inner_fresh_fun (v as Free _) = NONE 
   104   | get_inner_fresh_fun (v as Var _)  = NONE
   105   | get_inner_fresh_fun (Const _) = NONE
   106   | get_inner_fresh_fun (Abs (_, _, t)) = get_inner_fresh_fun t 
   107   | get_inner_fresh_fun (Const ("Nominal.fresh_fun",Type("fun",[Type ("fun",[Type (T,_),_]),_])) $ u) = SOME T 
   108   | get_inner_fresh_fun (t $ u) = 
   109      let val a = get_inner_fresh_fun u in
   110      if a = NONE then get_inner_fresh_fun t else a 
   111      end;
   112 
   113 (* This tactic generates a fresh name 
   114 of the atom type given by the inner most fresh_fun *)
   115 
   116 fun generate_fresh_fun_tac i thm =
   117   let
   118     val goal = List.nth(prems_of thm, i-1);
   119     val atom_name_opt = get_inner_fresh_fun goal;
   120   in
   121   case atom_name_opt of 
   122     NONE => all_tac thm
   123   | SOME atom_name  => generate_fresh_tac atom_name i thm               
   124   end
   125 
   126 (* Two substitution tactics which looks for the inner most occurence in 
   127    one assumption or in the conclusion *)
   128 
   129 val search_fun     = curry (Seq.flat o (uncurry EqSubst.searchf_bt_unify_valid));
   130 val search_fun_asm = EqSubst.skip_first_asm_occs_search EqSubst.searchf_bt_unify_valid;
   131 
   132 fun subst_inner_tac           ctx = EqSubst.eqsubst_tac' ctx search_fun;
   133 fun subst_inner_asm_tac_aux i ctx = EqSubst.eqsubst_asm_tac' ctx search_fun_asm i;
   134 
   135 (* A tactic to substitute in the first assumption 
   136    which contains an occurence. *)
   137 
   138 fun subst_inner_asm_tac ctx th =  curry (curry (FIRST' (map uncurry (map uncurry (map subst_inner_asm_tac_aux (1 upto Thm.nprems_of th)))))) ctx th;
   139 
   140 fun fresh_fun_tac no_asm i thm = 
   141   (* Find the variable we instantiate *)
   142   let
   143     val thy = theory_of_thm thm;
   144     val ctx = Context.init_proof thy;
   145     val ss = simpset_of thy;
   146     val abs_fresh = PureThy.get_thms thy (Name "abs_fresh");
   147     val fresh_perm_app = PureThy.get_thms thy (Name "fresh_perm_app");
   148     val ss' = ss addsimps fresh_prod::abs_fresh;
   149     val ss'' = ss' addsimps fresh_perm_app;
   150     val x = hd (tl (term_vars (prop_of exI)));
   151     val goal = nth (prems_of thm) (i-1);
   152     val atom_name_opt = get_inner_fresh_fun goal;
   153     val n = List.length (Logic.strip_params goal);
   154     (* Here we rely on the fact that the variable introduced by generate_fresh_tac is the last one in the list, the inner one *)
   155   in
   156   case atom_name_opt of 
   157     NONE => all_tac thm
   158   | SOME atom_name  =>    
   159   let 
   160     val atom_basename = Sign.base_name atom_name;
   161     val pt_name_inst = get_dyn_thm thy ("pt_"^atom_basename^"_inst") atom_basename;
   162     val at_name_inst = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
   163     fun inst_fresh vars params i st =
   164    let val vars' = term_vars (prop_of st);
   165        val thy = theory_of_thm st;
   166    in case vars' \\ vars of 
   167      [x] => Seq.single (Thm.instantiate ([],[(cterm_of thy x,cterm_of thy (list_abs (params,Bound 0)))]) st)
   168     | _ => error "fresh_fun_simp: Too many variables, please report."
   169   end
   170   in
   171   ((fn st =>
   172   let 
   173     val vars = term_vars (prop_of st);
   174     val params = Logic.strip_params (nth (prems_of st) (i-1))
   175     (* The tactics which solve the subgoals generated 
   176        by the conditionnal rewrite rule. *)
   177     val post_rewrite_tacs =  
   178           [rtac pt_name_inst,
   179            rtac at_name_inst,
   180            TRY' (SOLVEI (NominalPermeq.finite_guess_tac ss'')),
   181            inst_fresh vars params THEN'
   182            (TRY' (SOLVEI (NominalPermeq.fresh_guess_tac ss''))) THEN'
   183            (TRY' (SOLVEI (asm_full_simp_tac ss'')))] 
   184   in 
   185    ((if no_asm then no_tac else
   186     (subst_inner_asm_tac ctx fresh_fun_app' i THENL post_rewrite_tacs)) 
   187     ORELSE
   188     (subst_inner_tac     ctx fresh_fun_app' i THENL post_rewrite_tacs)) st
   189   end)) thm
   190   
   191   end
   192   end
   193 
   194 (* syntax for options, given "(no_asm)" will give back true, without
   195    gives back false *)
   196 val options_syntax =
   197     (Args.parens (Args.$$$ "no_asm") >> (K true)) ||
   198      (Scan.succeed false);
   199 
   200 val setup_generate_fresh =
   201   Method.goal_args_ctxt' Args.tyname (fn ctxt => generate_fresh_tac) 
   202 
   203 val setup_fresh_fun_simp =
   204   Method.simple_args options_syntax 
   205   (fn b => fn _ => Method.SIMPLE_METHOD (fresh_fun_tac b 1))