(* Title: HOL/Nominal/nominal_fresh_fun.ML
Authors: Stefan Berghofer and Julien Narboux, TU Muenchen
Provides a tactic to generate fresh names and
a tactic to analyse instances of the fresh_fun.
*)
(* First some functions that should be in the library *)
(* A tactical which applies a list of int -> tactic to the *)
(* corresponding subgoals present after the application of *)
(* another tactic. *)
(* *)
(* T THENL [A,B,C] is equivalent to T THEN (C 3 THEN B 2 THEN A 1) *)
infix 1 THENL
fun tac THENL tacs =
tac THEN
(EVERY (map (fn (tac,i) => tac i) (rev tacs ~~ (length tacs downto 1))))
(* A tactic which only succeeds when the argument *)
(* tactic solves completely the specified subgoal *)
fun SOLVEI t = t THEN_ALL_NEW (fn i => no_tac);
(* A version of TRY for int -> tactic *)
fun TRY' tac i = TRY (tac i);
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 (RuleInsts.make_elim_preserve th);
fun get_dyn_thm thy name atom_name =
PureThy.get_thm thy name handle ERROR _ =>
error ("The atom type "^atom_name^" is not defined.");
(* End of function waiting to be in the library :o) *)
(* 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 = Long_Name.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 = Sign.of_sort 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)))
(OldTerm.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) handle _ => HOLogic.unit ; (* FIXME avoid handle _ *)
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 (OldTerm.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 innermost 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
(* Two substitution tactics which looks for the innermost occurence in
one assumption or in the conclusion *)
val search_fun = curry (Seq.flat o (uncurry EqSubst.searchf_bt_unify_valid));
val search_fun_asm = EqSubst.skip_first_asm_occs_search EqSubst.searchf_bt_unify_valid;
fun subst_inner_tac ctx = EqSubst.eqsubst_tac' ctx search_fun;
fun subst_inner_asm_tac_aux i ctx = EqSubst.eqsubst_asm_tac' ctx search_fun_asm i;
(* A tactic to substitute in the first assumption
which contains an occurence. *)
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;
fun fresh_fun_tac no_asm 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 "abs_fresh";
val fresh_perm_app = PureThy.get_thms thy "fresh_perm_app";
val ss' = ss addsimps fresh_prod::abs_fresh;
val ss'' = ss' addsimps fresh_perm_app;
val x = hd (tl (OldTerm.term_vars (prop_of exI)));
val goal = 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 = Long_Name.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;
fun inst_fresh vars params i st =
let val vars' = OldTerm.term_vars (prop_of st);
val thy = theory_of_thm st;
in case vars' \\ vars of
[x] => Seq.single (Thm.instantiate ([],[(cterm_of thy x,cterm_of thy (list_abs (params,Bound 0)))]) st)
| _ => error "fresh_fun_simp: Too many variables, please report."
end
in
((fn st =>
let
val vars = OldTerm.term_vars (prop_of st);
val params = Logic.strip_params (nth (prems_of st) (i-1))
(* The tactics which solve the subgoals generated
by the conditionnal rewrite rule. *)
val post_rewrite_tacs =
[rtac pt_name_inst,
rtac at_name_inst,
TRY' (SOLVEI (NominalPermeq.finite_guess_tac ss'')),
inst_fresh vars params THEN'
(TRY' (SOLVEI (NominalPermeq.fresh_guess_tac ss''))) THEN'
(TRY' (SOLVEI (asm_full_simp_tac ss'')))]
in
((if no_asm then no_tac else
(subst_inner_asm_tac ctx fresh_fun_app' i THENL post_rewrite_tacs))
ORELSE
(subst_inner_tac ctx fresh_fun_app' i THENL post_rewrite_tacs)) st
end)) thm
end
end
(* syntax for options, given "(no_asm)" will give back true, without
gives back false *)
val options_syntax =
(Args.parens (Args.$$$ "no_asm") >> (K true)) ||
(Scan.succeed false);
val setup_generate_fresh =
Method.goal_args_ctxt' Args.tyname (fn ctxt => generate_fresh_tac)
val setup_fresh_fun_simp =
Method.simple_args options_syntax
(fn b => fn _ => Method.SIMPLE_METHOD (fresh_fun_tac b 1))