src/HOL/Nominal/nominal_fresh_fun.ML
author wenzelm
Sat Apr 16 16:15:37 2011 +0200 (2011-04-16)
changeset 42361 23f352990944
parent 41519 0940fff556a6
child 42364 8c674b3b8e44
permissions -rw-r--r--
modernized structure Proof_Context;
     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 (* First some functions that should be in the library *)
     9 
    10 fun gen_res_inst_tac_term instf tyinst tinst elim th i st =
    11   let
    12     val thy = theory_of_thm st;
    13     val cgoal = nth (cprems_of st) (i - 1);
    14     val {maxidx, ...} = rep_cterm cgoal;
    15     val j = maxidx + 1;
    16     val tyinst' = map (apfst (Logic.incr_tvar j)) tyinst;
    17     val ps = Logic.strip_params (term_of cgoal);
    18     val Ts = map snd ps;
    19     val tinst' = map (fn (t, u) =>
    20       (head_of (Logic.incr_indexes (Ts, j) t),
    21        list_abs (ps, u))) tinst;
    22     val th' = instf
    23       (map (pairself (ctyp_of thy)) tyinst')
    24       (map (pairself (cterm_of thy)) tinst')
    25       (Thm.lift_rule cgoal th)
    26   in
    27     compose_tac (elim, th', nprems_of th) i st
    28   end handle Subscript => Seq.empty;
    29 
    30 val res_inst_tac_term =
    31   gen_res_inst_tac_term (curry Thm.instantiate);
    32 
    33 val res_inst_tac_term' =
    34   gen_res_inst_tac_term (K Drule.cterm_instantiate) [];
    35 
    36 fun cut_inst_tac_term' tinst th =
    37   res_inst_tac_term' tinst false (RuleInsts.make_elim_preserve th);
    38 
    39 fun get_dyn_thm thy name atom_name =
    40   Global_Theory.get_thm thy name handle ERROR _ =>
    41     error ("The atom type "^atom_name^" is not defined.");
    42 
    43 (* End of function waiting to be in the library :o) *)
    44 
    45 (* The theorems needed that are known at compile time. *)
    46 val at_exists_fresh' = @{thm "at_exists_fresh'"};
    47 val fresh_fun_app'   = @{thm "fresh_fun_app'"};
    48 val fresh_prod       = @{thm "fresh_prod"};
    49 
    50 (* A tactic to generate a name fresh for  all the free *)
    51 (* variables and parameters of the goal                *)
    52 
    53 fun generate_fresh_tac atom_name i thm =
    54  let
    55    val thy = theory_of_thm thm;
    56 (* the parsing function returns a qualified name, we get back the base name *)
    57    val atom_basename = Long_Name.base_name atom_name;
    58    val goal = List.nth(prems_of thm, i-1);
    59    val ps = Logic.strip_params goal;
    60    val Ts = rev (map snd ps);
    61    fun is_of_fs_name T = Sign.of_sort thy (T, [Sign.intern_class thy ("fs_"^atom_basename)]);
    62 (* rebuild de bruijn indices *)
    63    val bvs = map_index (Bound o fst) ps;
    64 (* select variables of the right class *)
    65    val vs = filter (fn t => is_of_fs_name (fastype_of1 (Ts, t)))
    66      (OldTerm.term_frees goal @ bvs);
    67 (* build the tuple *)
    68    val s = (Library.foldr1 (fn (v, s) =>
    69        HOLogic.pair_const (fastype_of1 (Ts, v)) (fastype_of1 (Ts, s)) $ v $ s) vs)
    70      handle TERM _ => HOLogic.unit;
    71    val fs_name_thm = get_dyn_thm thy ("fs_"^atom_basename^"1") atom_basename;
    72    val at_name_inst_thm = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
    73    val exists_fresh' = at_name_inst_thm RS at_exists_fresh';
    74 (* find the variable we want to instantiate *)
    75    val x = hd (OldTerm.term_vars (prop_of exists_fresh'));
    76  in
    77    (cut_inst_tac_term' [(x,s)] exists_fresh' 1 THEN
    78    rtac fs_name_thm 1 THEN
    79    etac exE 1) thm
    80   handle Empty  => all_tac thm (* if we collected no variables then we do nothing *)
    81   end;
    82 
    83 fun get_inner_fresh_fun (Bound j) = NONE
    84   | get_inner_fresh_fun (v as Free _) = NONE
    85   | get_inner_fresh_fun (v as Var _)  = NONE
    86   | get_inner_fresh_fun (Const _) = NONE
    87   | get_inner_fresh_fun (Abs (_, _, t)) = get_inner_fresh_fun t
    88   | get_inner_fresh_fun (Const ("Nominal.fresh_fun",Type("fun",[Type ("fun",[Type (T,_),_]),_])) $ u)
    89                            = SOME T
    90   | get_inner_fresh_fun (t $ u) =
    91      let val a = get_inner_fresh_fun u in
    92      if a = NONE then get_inner_fresh_fun t else a
    93      end;
    94 
    95 (* This tactic generates a fresh name of the atom type *)
    96 (* given by the innermost fresh_fun                    *)
    97 
    98 fun generate_fresh_fun_tac i thm =
    99   let
   100     val goal = List.nth(prems_of thm, i-1);
   101     val atom_name_opt = get_inner_fresh_fun goal;
   102   in
   103   case atom_name_opt of
   104     NONE => all_tac thm
   105   | SOME atom_name  => generate_fresh_tac atom_name i thm
   106   end
   107 
   108 (* Two substitution tactics which looks for the innermost occurence in
   109    one assumption or in the conclusion *)
   110 
   111 val search_fun = curry (Seq.flat o uncurry EqSubst.searchf_bt_unify_valid);
   112 val search_fun_asm = EqSubst.skip_first_asm_occs_search EqSubst.searchf_bt_unify_valid;
   113 
   114 fun subst_inner_tac ctxt = EqSubst.eqsubst_tac' ctxt search_fun;
   115 fun subst_inner_asm_tac_aux i ctxt = EqSubst.eqsubst_asm_tac' ctxt search_fun_asm i;
   116 
   117 (* A tactic to substitute in the first assumption
   118    which contains an occurence. *)
   119 
   120 fun subst_inner_asm_tac ctxt th =
   121   curry (curry (FIRST' (map uncurry (map uncurry (map subst_inner_asm_tac_aux
   122             (1 upto Thm.nprems_of th)))))) ctxt th;
   123 
   124 fun fresh_fun_tac no_asm i thm =
   125   (* Find the variable we instantiate *)
   126   let
   127     val thy = theory_of_thm thm;
   128     val ctxt = Proof_Context.init_global thy;
   129     val ss = global_simpset_of thy;
   130     val abs_fresh = Global_Theory.get_thms thy "abs_fresh";
   131     val fresh_perm_app = Global_Theory.get_thms thy "fresh_perm_app";
   132     val ss' = ss addsimps fresh_prod::abs_fresh;
   133     val ss'' = ss' addsimps fresh_perm_app;
   134     val x = hd (tl (OldTerm.term_vars (prop_of exI)));
   135     val goal = nth (prems_of thm) (i-1);
   136     val atom_name_opt = get_inner_fresh_fun goal;
   137     val n = length (Logic.strip_params goal);
   138     (* Here we rely on the fact that the variable introduced by generate_fresh_tac *)
   139     (* is the last one in the list, the inner one *)
   140   in
   141   case atom_name_opt of
   142     NONE => all_tac thm
   143   | SOME atom_name =>
   144   let
   145     val atom_basename = Long_Name.base_name atom_name;
   146     val pt_name_inst = get_dyn_thm thy ("pt_"^atom_basename^"_inst") atom_basename;
   147     val at_name_inst = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
   148     fun inst_fresh vars params i st =
   149    let val vars' = OldTerm.term_vars (prop_of st);
   150        val thy = theory_of_thm st;
   151    in case subtract (op =) vars vars' of
   152      [x] => Seq.single (Thm.instantiate ([],[(cterm_of thy x,cterm_of thy (list_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 = OldTerm.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 ss''),
   166            inst_fresh vars params THEN'
   167            (TRY o SOLVED' (NominalPermeq.fresh_guess_tac ss'')) THEN'
   168            (TRY o SOLVED' (asm_full_simp_tac ss''))]
   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)) thm
   175 
   176   end
   177   end
   178 
   179 (* syntax for options, given "(no_asm)" will give back true, without
   180    gives back false *)
   181 val options_syntax =
   182     (Args.parens (Args.$$$ "no_asm") >> (K true)) ||
   183      (Scan.succeed false);
   184 
   185 fun setup_generate_fresh x =
   186   (Args.goal_spec -- Args.type_name true >>
   187     (fn (quant, s) => K (SIMPLE_METHOD'' quant (generate_fresh_tac s)))) x;
   188 
   189 fun setup_fresh_fun_simp x =
   190   (Scan.lift options_syntax >> (fn b => K (SIMPLE_METHOD' (fresh_fun_tac b)))) x;
   191