src/HOL/Nominal/nominal_fresh_fun.ML
author narboux
Fri Apr 20 14:30:35 2007 +0200 (2007-04-20)
changeset 22753 49d7818e6161
parent 22729 69ef734825c5
child 22774 8c64803fae48
permissions -rw-r--r--
modify fresh_fun_simp to ease debugging
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(*  Title:      HOL/Nominal/nominal_fresh_fun.ML
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    ID:         $Id$
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    Authors:    Stefan Berghofer, Julien Narboux, TU Muenchen
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A tactic to generate fresh names.
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A tactic to get rid of the fresh_fun.
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*)
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(* First some functions that could be
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 in the library *)
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(* A tactical which implements Coq's T;[a,b,c] *)
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infix 1 THENL
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fun THENL (tac,tacs) =
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 tac THEN
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  (EVERY (map  (fn (tac,i) => tac i) (rev tacs ~~ (length tacs downto 1))))
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fun gen_res_inst_tac_term instf tyinst tinst elim th i st =
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  let
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    val thy = theory_of_thm st;
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    val cgoal = nth (cprems_of st) (i - 1);
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    val {maxidx, ...} = rep_cterm cgoal;
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    val j = maxidx + 1;
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    val tyinst' = map (apfst (Logic.incr_tvar j)) tyinst;
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    val ps = Logic.strip_params (term_of cgoal);
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    val Ts = map snd ps;
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    val tinst' = map (fn (t, u) =>
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      (head_of (Logic.incr_indexes (Ts, j) t),
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       list_abs (ps, u))) tinst;
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    val th' = instf
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      (map (pairself (ctyp_of thy)) tyinst')
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      (map (pairself (cterm_of thy)) tinst')
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      (Thm.lift_rule cgoal th)
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  in
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    compose_tac (elim, th', nprems_of th) i st
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  end handle Subscript => Seq.empty;
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val res_inst_tac_term = 
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  gen_res_inst_tac_term (curry Thm.instantiate);
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val res_inst_tac_term' = 
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  gen_res_inst_tac_term (K Drule.cterm_instantiate) [];
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fun cut_inst_tac_term' tinst th =
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  res_inst_tac_term' tinst false (Tactic.make_elim_preserve th);
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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."); 
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(* End of function waiting to be
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 in the library *)
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(* The theorems needed that are known at
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compile time. *)
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val at_exists_fresh' = thm "at_exists_fresh'";
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val fresh_fun_app = thm "fresh_fun_app";
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val fresh_prod = thm "fresh_prod";
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(* A tactic to generate a name fresh for 
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all the free variables and parameters of the goal *)
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fun generate_fresh_tac atom_name i thm =
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 let 
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   val thy = theory_of_thm thm;
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(* the parsing function returns a qualified name, we get back the base name *)
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   val atom_basename = Sign.base_name atom_name;
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   val goal = List.nth(prems_of thm, i-1);
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   val ps = Logic.strip_params goal;
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   val Ts = rev (map snd ps);
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   fun is_of_fs_name T = Type.of_sort (Sign.tsig_of thy)
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     (T, Sign.intern_sort thy ["fs_"^atom_basename]); 
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(* rebuild de bruijn indices *)
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   val bvs = map_index (Bound o fst) ps;
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(* select variables of the right class *)
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   val vs = filter (fn t => is_of_fs_name (fastype_of1 (Ts, t)))
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     (term_frees goal @ bvs);
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(* build the tuple *)
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   val s = Library.foldr1 (fn (v, s) =>
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     HOLogic.pair_const (fastype_of1 (Ts, v)) (fastype_of1 (Ts, s)) $ v $ s)
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       vs;
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   val fs_name_thm = get_dyn_thm thy ("fs_"^atom_basename^"1") atom_basename;
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   val at_name_inst_thm = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
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   val exists_fresh' = at_name_inst_thm RS at_exists_fresh';
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(* find the variable we want to instantiate *)
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   val x = hd (term_vars (prop_of exists_fresh'));
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 in 
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   (cut_inst_tac_term' [(x,s)] exists_fresh' 1 THEN
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   rtac fs_name_thm 1 THEN
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   etac exE 1) thm
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  handle Empty  => all_tac thm (* if we collected no variables then we do nothing *)
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  end;
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fun get_inner_fresh_fun (Bound j) = NONE
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  | get_inner_fresh_fun (v as Free _) = NONE 
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  | get_inner_fresh_fun (v as Var _)  = NONE
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  | get_inner_fresh_fun (Const _) = NONE
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  | get_inner_fresh_fun (Abs (_, _, t)) = get_inner_fresh_fun t 
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  | get_inner_fresh_fun (Const ("Nominal.fresh_fun",Type("fun",[Type ("fun",[Type (T,_),_]),_])) $ u) = SOME T 
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  | get_inner_fresh_fun (t $ u) = 
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     let val a = get_inner_fresh_fun u in
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     if a = NONE then get_inner_fresh_fun t else a 
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     end;
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(* This tactic generates a fresh name 
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of the atom type given by the inner most fresh_fun *)
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fun generate_fresh_fun_tac i thm =
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  let
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    val goal = List.nth(prems_of thm, i-1);
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    val atom_name_opt = get_inner_fresh_fun goal;
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  in
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  case atom_name_opt of 
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    NONE => all_tac thm
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  | SOME atom_name  => generate_fresh_tac atom_name i thm               
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  end
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(* A substitution tactic, FIXME : change the search function to get the inner occurence of fresh_fun (bottom -> up search ) *)
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fun subst_outer_tac ctx = EqSubst.eqsubst_tac' ctx (curry (Seq.flat o (uncurry EqSubst.searchf_lr_unify_valid)));
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fun fresh_fun_tac i thm = 
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  (* Find the variable we instantiate *)
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  let
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    val thy = theory_of_thm thm;
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    val ctx = Context.init_proof thy;
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    val ss = simpset_of thy;
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    val abs_fresh = PureThy.get_thms thy (Name "abs_fresh");
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    val ss' = ss addsimps fresh_prod::abs_fresh;
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    val x = hd (tl (term_vars (prop_of exI)));
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    val goal = List.nth(prems_of thm, i-1);
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    val atom_name_opt = get_inner_fresh_fun goal;
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    val n = List.length (Logic.strip_params goal);
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    (* Here we rely on the fact that the variable introduced by generate_fresh_tac is the last one in the list, the inner one *)
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  in
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  case atom_name_opt of 
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    NONE => all_tac thm
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  | SOME atom_name  =>    
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  let 
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    val atom_basename = Sign.base_name atom_name;
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    val pt_name_inst = get_dyn_thm thy ("pt_"^atom_basename^"_inst") atom_basename;
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    val at_name_inst = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
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    fun tac_a i = 
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      res_inst_tac_term' [(x,Bound n)] false exI i THEN
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      asm_full_simp_tac ss' i                      THEN 
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      NominalPermeq.fresh_guess_tac HOL_ss i;
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  in
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  (generate_fresh_tac atom_name i      THEN 
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   subst_outer_tac ctx fresh_fun_app i THENL 
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   [rtac pt_name_inst,
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    rtac at_name_inst, 
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    (fn i => TRY (NominalPermeq.finite_guess_tac HOL_ss i)),   
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    tac_a, 
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    (fn i => TRY (NominalPermeq.fresh_guess_tac  HOL_ss i)),
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    (fn i => auto_tac (HOL_cs, HOL_ss)) 
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]) thm 
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  end
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  end
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val setup_generate_fresh =
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  Method.goal_args_ctxt' Args.tyname (fn ctxt => generate_fresh_tac) 
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val setup_fresh_fun_simp =
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  Method.no_args (Method.SIMPLE_METHOD (fresh_fun_tac 1))