src/HOL/Nominal/nominal_fresh_fun.ML

add a tactic to generate fresh names

(*  Title:      HOL/Nominal/nominal_fresh_fun.ML
    ID:         $Id$
    Authors:    Stefan Berghofer, Julien Narboux, TU Muenchen

A tactic to generate fresh names.
A tactic to get rid of the fresh_fun.
*)

(* First some functions that could be
 in the library *)

fun gen_res_inst_tac_term instf tyinst tinst elim th i st =
  let
    val thy = theory_of_thm st;
    val cgoal = nth (cprems_of st) (i - 1);
    val {maxidx, ...} = rep_cterm cgoal;
    val j = maxidx + 1;
    val tyinst' = map (apfst (Logic.incr_tvar j)) tyinst;
    val ps = Logic.strip_params (term_of cgoal);
    val Ts = map snd ps;
    val tinst' = map (fn (t, u) =>
      (head_of (Logic.incr_indexes (Ts, j) t),
       list_abs (ps, u))) tinst;
    val th' = instf
      (map (pairself (ctyp_of thy)) tyinst')
      (map (pairself (cterm_of thy)) tinst')
      (Thm.lift_rule cgoal th)
  in
    compose_tac (elim, th', nprems_of th) i st
  end handle Subscript => Seq.empty;

val res_inst_tac_term = 
  gen_res_inst_tac_term (curry Thm.instantiate);

val res_inst_tac_term' = 
  gen_res_inst_tac_term (K Drule.cterm_instantiate) [];

fun cut_inst_tac_term' tinst th =
  res_inst_tac_term' tinst false (Tactic.make_elim_preserve th);

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."); 

(* End of function waiting to be
 in the library *)

(* The theorems needed that are known at
compile time. *)

val at_exists_fresh' = thm "at_exists_fresh'";
val fresh_fun_app = thm "fresh_fun_app";
val fresh_prod = thm "fresh_prod";

(* A tactic to generate a name fresh for 
all the free variables and parameters of the goal *)

fun generate_fresh_tac atom_name i thm =
 let 
   val thy = theory_of_thm thm;
(* the parsing function returns a qualified name, we get back the base name *)
   val atom_basename = Sign.base_name atom_name;
   val goal = List.nth(prems_of thm, i-1);
   val ps = Logic.strip_params goal;
   val Ts = rev (map snd ps);
   fun is_of_fs_name T = Type.of_sort (Sign.tsig_of thy)
     (T, Sign.intern_sort thy ["fs_"^atom_basename]); 
(* rebuild de bruijn indices *)
   val bvs = map_index (Bound o fst) ps;
(* select variables of the right class *)
   val vs = filter (fn t => is_of_fs_name (fastype_of1 (Ts, t)))
     (term_frees goal @ bvs);
(* build the tuple *)
   val s = Library.foldr1 (fn (v, s) =>
     HOLogic.pair_const (fastype_of1 (Ts, v)) (fastype_of1 (Ts, s)) $ v $ s)
       vs;
   val fs_name_thm = get_dyn_thm thy ("fs_"^atom_basename^"1") atom_basename;
   val at_name_inst_thm = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
   val exists_fresh' = at_name_inst_thm RS at_exists_fresh';
(* find the variable we want to instantiate *)
   val x = hd (term_vars (prop_of exists_fresh'));
 in 
   (cut_inst_tac_term' [(x,s)] exists_fresh' 1 THEN
   rtac fs_name_thm 1 THEN
   etac exE 1) thm
  handle Empty  => all_tac thm (* if we collected no variables then we do nothing *)
  end;

fun get_inner_fresh_fun (Bound j) = NONE
  | get_inner_fresh_fun (v as Free _) = NONE 
  | get_inner_fresh_fun (v as Var _)  = NONE
  | get_inner_fresh_fun (Const _) = NONE
  | get_inner_fresh_fun (Abs (_, _, t)) = get_inner_fresh_fun t 
  | get_inner_fresh_fun (Const ("Nominal.fresh_fun",Type("fun",[Type ("fun",[Type (T,_),_]),_])) $ u) = SOME T 
  | get_inner_fresh_fun (t $ u) = 
     let val a = get_inner_fresh_fun u in
     if a = NONE then get_inner_fresh_fun t else a 
     end;

(* This tactic generates a fresh name 
of the atom type given by the inner most fresh_fun *)

fun generate_fresh_fun_tac i thm =
  let
    val goal = List.nth(prems_of thm, i-1);
    val atom_name_opt = get_inner_fresh_fun goal;
  in
  case atom_name_opt of 
    NONE => all_tac thm
  | SOME atom_name  => generate_fresh_tac atom_name i thm               
  end

(* A substitution tactic, FIXME : change the search function to get the inner occurence of fresh_fun (bottom -> up search ) *)

fun subst_outer_tac ctx = EqSubst.eqsubst_tac' ctx (curry (Seq.flat o (uncurry EqSubst.searchf_lr_unify_valid)));

fun fresh_fun_tac i thm = 
  (* Find the variable we instantiate *)
  let
    val thy = theory_of_thm thm;
    val ctx = Context.init_proof thy;
    val ss = simpset_of thy;
    val abs_fresh = PureThy.get_thms thy (Name "abs_fresh");
    val ss' = ss addsimps fresh_prod::abs_fresh;
    val x = hd (tl (term_vars (prop_of exI)));
    val goal = List.nth(prems_of thm, i-1);
    val atom_name_opt = get_inner_fresh_fun goal;
    val n = List.length (Logic.strip_params goal);
    (* Here we rely on the fact that the variable introduced by generate_fresh_tac is the last one in the list, the inner one *)
  in
  case atom_name_opt of 
    NONE => all_tac thm
  | SOME atom_name  =>    
  let 
    val atom_basename = Sign.base_name atom_name;
    val pt_name_inst = get_dyn_thm thy ("pt_"^atom_basename^"_inst") atom_basename;
    val at_name_inst = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
  in
  (generate_fresh_tac atom_name i               THEN
   subst_outer_tac ctx fresh_fun_app i          THEN
   rtac pt_name_inst i                          THEN
   rtac at_name_inst i                          THEN
   NominalPermeq.finite_guess_tac HOL_ss i      THEN
   auto_tac (HOL_cs , HOL_ss)                   THEN
   NominalPermeq.fresh_guess_tac HOL_ss (i+1)   THEN
   res_inst_tac_term' [(x,Bound n)] false exI i THEN
   asm_full_simp_tac ss' i                      THEN
   NominalPermeq.fresh_guess_tac HOL_ss i) thm 
  end
  end

val setup_generate_fresh =
  Method.goal_args_ctxt' Args.tyname (fn ctxt => generate_fresh_tac) 

val setup_fresh_fun_simp =
  Method.no_args (Method.SIMPLE_METHOD (fresh_fun_tac 1))