src/HOL/Nominal/nominal_fresh_fun.ML
author narboux
Thu May 24 12:00:47 2007 +0200 (2007-05-24)
changeset 23091 c91530f18d9c
parent 23065 ab28e8398670
child 23094 f1df8d2da98a
permissions -rw-r--r--
add an option in fresh_fun_simp to prevent rewriting in assumptions
     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 = Type.of_sort (Sign.tsig_of thy)
    82      (T, Sign.intern_sort thy ["fs_"^atom_basename]); 
    83 (* rebuild de bruijn indices *)
    84    val bvs = map_index (Bound o fst) ps;
    85 (* select variables of the right class *)
    86    val vs = filter (fn t => is_of_fs_name (fastype_of1 (Ts, t)))
    87      (term_frees goal @ bvs);
    88 (* build the tuple *)
    89    val s = Library.foldr1 (fn (v, s) =>
    90      HOLogic.pair_const (fastype_of1 (Ts, v)) (fastype_of1 (Ts, s)) $ v $ s)
    91        vs;
    92    val fs_name_thm = get_dyn_thm thy ("fs_"^atom_basename^"1") atom_basename;
    93    val at_name_inst_thm = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
    94    val exists_fresh' = at_name_inst_thm RS at_exists_fresh';
    95 (* find the variable we want to instantiate *)
    96    val x = hd (term_vars (prop_of exists_fresh'));
    97  in 
    98    (cut_inst_tac_term' [(x,s)] exists_fresh' 1 THEN
    99    rtac fs_name_thm 1 THEN
   100    etac exE 1) thm
   101   handle Empty  => all_tac thm (* if we collected no variables then we do nothing *)
   102   end;
   103 
   104 fun get_inner_fresh_fun (Bound j) = NONE
   105   | get_inner_fresh_fun (v as Free _) = NONE 
   106   | get_inner_fresh_fun (v as Var _)  = NONE
   107   | get_inner_fresh_fun (Const _) = NONE
   108   | get_inner_fresh_fun (Abs (_, _, t)) = get_inner_fresh_fun t 
   109   | get_inner_fresh_fun (Const ("Nominal.fresh_fun",Type("fun",[Type ("fun",[Type (T,_),_]),_])) $ u) = SOME T 
   110   | get_inner_fresh_fun (t $ u) = 
   111      let val a = get_inner_fresh_fun u in
   112      if a = NONE then get_inner_fresh_fun t else a 
   113      end;
   114 
   115 (* This tactic generates a fresh name 
   116 of the atom type given by the inner most fresh_fun *)
   117 
   118 fun generate_fresh_fun_tac i thm =
   119   let
   120     val goal = List.nth(prems_of thm, i-1);
   121     val atom_name_opt = get_inner_fresh_fun goal;
   122   in
   123   case atom_name_opt of 
   124     NONE => all_tac thm
   125   | SOME atom_name  => generate_fresh_tac atom_name i thm               
   126   end
   127 
   128 (* Two substitution tactics which looks for the inner most occurence in 
   129    one assumption or in the conclusion *)
   130 
   131 val search_fun     = curry (Seq.flat o (uncurry EqSubst.searchf_bt_unify_valid));
   132 val search_fun_asm = EqSubst.skip_first_asm_occs_search EqSubst.searchf_bt_unify_valid;
   133 
   134 fun subst_inner_tac           ctx = EqSubst.eqsubst_tac' ctx search_fun;
   135 fun subst_inner_asm_tac_aux i ctx = EqSubst.eqsubst_asm_tac' ctx search_fun_asm i;
   136 
   137 (* A tactic to substitute in the first assumption 
   138    which contains an occurence. *)
   139 
   140 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;
   141 
   142 fun fresh_fun_tac no_asm i thm = 
   143   (* Find the variable we instantiate *)
   144   let
   145     val thy = theory_of_thm thm;
   146     val ctx = Context.init_proof thy;
   147     val ss = simpset_of thy;
   148     val abs_fresh = PureThy.get_thms thy (Name "abs_fresh");
   149     val fresh_perm_app = PureThy.get_thms thy (Name "fresh_perm_app");
   150     val ss' = ss addsimps fresh_prod::abs_fresh;
   151     val ss'' = ss' addsimps fresh_perm_app;
   152     val x = hd (tl (term_vars (prop_of exI)));
   153     val goal = nth (prems_of thm) (i-1);
   154     val atom_name_opt = get_inner_fresh_fun goal;
   155     val n = List.length (Logic.strip_params goal);
   156     (* Here we rely on the fact that the variable introduced by generate_fresh_tac is the last one in the list, the inner one *)
   157   in
   158   case atom_name_opt of 
   159     NONE => all_tac thm
   160   | SOME atom_name  =>    
   161   let 
   162     val atom_basename = Sign.base_name atom_name;
   163     val pt_name_inst = get_dyn_thm thy ("pt_"^atom_basename^"_inst") atom_basename;
   164     val at_name_inst = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
   165     fun inst_fresh vars params i st =
   166    let val vars' = term_vars (prop_of st);
   167        val thy = theory_of_thm st;
   168    in case vars' \\ vars of 
   169      [x] => Seq.single (Thm.instantiate ([],[(cterm_of thy x,cterm_of thy (list_abs (params,Bound 0)))]) st)
   170     | _ => error "fresh_fun_simp: Too many variables, please report."
   171   end
   172   in
   173   ((fn st =>
   174   let 
   175     val vars = term_vars (prop_of st);
   176     val params = Logic.strip_params (nth (prems_of st) (i-1))
   177     (* The tactics which solve the subgoals generated 
   178        by the conditionnal rewrite rule. *)
   179     val post_rewrite_tacs =  
   180           [rtac pt_name_inst,
   181            rtac at_name_inst,
   182            TRY' (SOLVEI (NominalPermeq.finite_guess_tac ss'')),
   183            inst_fresh vars params THEN'
   184            (TRY' (SOLVEI (NominalPermeq.fresh_guess_tac ss''))) THEN'
   185            (TRY' (SOLVEI (asm_full_simp_tac ss'')))] 
   186   in 
   187    ((if no_asm then 
   188     (subst_inner_asm_tac ctx fresh_fun_app' i THENL post_rewrite_tacs)
   189     else 
   190      no_tac) 
   191     ORELSE
   192     (subst_inner_tac     ctx fresh_fun_app' i THENL post_rewrite_tacs)) st
   193   end)) thm
   194   
   195   end
   196   end
   197 
   198 (* syntax for options, given "(no_asm)" will give back true, without
   199    gives back false *)
   200 val options_syntax =
   201     (Args.parens (Args.$$$ "no_asm") >> (K true)) ||
   202      (Scan.succeed false);
   203 
   204 val setup_generate_fresh =
   205   Method.goal_args_ctxt' Args.tyname (fn ctxt => generate_fresh_tac) 
   206 
   207 val setup_fresh_fun_simp =
   208   Method.simple_args options_syntax 
   209   (fn b => fn _ => Method.SIMPLE_METHOD (fresh_fun_tac b 1))