--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/BNF/bnf_axiomatization.ML Tue Mar 22 12:39:37 2016 +0100
@@ -0,0 +1,128 @@
+(* Title: HOL/Tools/BNF/bnf_axiomatization.ML
+ Author: Dmitriy Traytel, TU Muenchen
+ Copyright 2013
+
+Axiomatic declaration of bounded natural functors.
+*)
+
+signature BNF_AXIOMATIZATION =
+sig
+ val bnf_axiomatization: (string -> bool) -> (binding option * (typ * sort)) list -> binding ->
+ mixfix -> binding -> binding -> binding -> typ list -> local_theory ->
+ BNF_Def.bnf * local_theory
+end
+
+structure BNF_Axiomatization : BNF_AXIOMATIZATION =
+struct
+
+open BNF_Util
+open BNF_Def
+
+fun prepare_decl prepare_plugins prepare_constraint prepare_typ
+ raw_plugins raw_vars b mx user_mapb user_relb user_predb user_witTs lthy =
+ let
+ val plugins = prepare_plugins lthy raw_plugins;
+
+ fun prepare_type_arg (set_opt, (ty, c)) =
+ let val s = fst (dest_TFree (prepare_typ lthy ty)) in
+ (set_opt, (s, prepare_constraint lthy c))
+ end;
+ val ((user_setbs, vars), raw_vars') =
+ map prepare_type_arg raw_vars
+ |> `split_list
+ |>> apfst (map_filter I);
+ val deads = map_filter (fn (NONE, x) => SOME x | _ => NONE) raw_vars';
+
+ fun mk_b name user_b =
+ (if Binding.is_empty user_b then Binding.prefix_name (name ^ "_") b else user_b)
+ |> Binding.qualify false (Binding.name_of b);
+ val (Tname, lthy) = Typedecl.basic_typedecl {final = true} (b, length vars, mx) lthy;
+ val (bd_type_Tname, lthy) = lthy
+ |> Typedecl.basic_typedecl {final = true} (mk_b "bd_type" Binding.empty, length deads, NoSyn);
+ val T = Type (Tname, map TFree vars);
+ val bd_type_T = Type (bd_type_Tname, map TFree deads);
+ val lives = map TFree (filter_out (member (op =) deads) vars);
+ val live = length lives;
+ val _ = "Trying to declare a BNF with no live variables" |> null lives ? error;
+ val (lives', _) = BNF_Util.mk_TFrees (length lives)
+ (fold Variable.declare_typ (map TFree vars) lthy);
+ val T' = Term.typ_subst_atomic (lives ~~ lives') T;
+ val mapT = map2 (curry op -->) lives lives' ---> T --> T';
+ val setTs = map (fn U => T --> HOLogic.mk_setT U) lives;
+ val bdT = BNF_Util.mk_relT (bd_type_T, bd_type_T);
+ val mapb = mk_b mapN user_mapb;
+ val bdb = mk_b "bd" Binding.empty;
+ val setbs = map2 (fn b => fn i => mk_b (mk_setN i) b) user_setbs
+ (if live = 1 then [0] else 1 upto live);
+
+ val witTs = map (prepare_typ lthy) user_witTs;
+ val nwits = length witTs;
+ val witbs = map (fn i => mk_b (mk_witN i) Binding.empty)
+ (if nwits = 1 then [0] else 1 upto nwits);
+
+ val lthy = Local_Theory.background_theory
+ (Sign.add_consts ((mapb, mapT, NoSyn) :: (bdb, bdT, NoSyn) ::
+ map2 (fn b => fn T => (b, T, NoSyn)) setbs setTs @
+ map2 (fn b => fn T => (b, T, NoSyn)) witbs witTs))
+ lthy;
+ val Fmap = Const (Local_Theory.full_name lthy mapb, mapT);
+ val Fsets = map2 (fn setb => fn setT =>
+ Const (Local_Theory.full_name lthy setb, setT)) setbs setTs;
+ val Fbd = Const (Local_Theory.full_name lthy bdb, bdT);
+ val Fwits = map2 (fn witb => fn witT =>
+ Const (Local_Theory.full_name lthy witb, witT)) witbs witTs;
+ val (key, goals, (triv_tac_opt, wit_goalss), after_qed, lthy, _) =
+ prepare_def Do_Inline (user_policy Note_Some) false I (K I) (K I) (SOME (map TFree deads))
+ user_mapb user_relb user_predb user_setbs
+ (((((((Binding.empty, T), Fmap), Fsets), Fbd), Fwits), NONE), NONE)
+ lthy;
+
+ fun mk_wits_tac ctxt set_maps = TRYALL Goal.conjunction_tac THEN the triv_tac_opt ctxt set_maps;
+ val wit_goals = map Logic.mk_conjunction_balanced wit_goalss;
+ val all_goalss = map single goals @ (if nwits > 0 then wit_goalss else []);
+
+ val (((_, [raw_thms])), lthy) = Local_Theory.background_theory_result
+ (Specification.axiomatization [] [((mk_b "axioms" Binding.empty, []), flat all_goalss)]) lthy;
+
+ fun mk_wit_thms set_maps =
+ Goal.prove_sorry lthy [] [] (Logic.mk_conjunction_balanced wit_goals)
+ (fn {context = ctxt, prems = _} => mk_wits_tac ctxt set_maps)
+ |> Thm.close_derivation
+ |> Conjunction.elim_balanced (length wit_goals)
+ |> map2 (Conjunction.elim_balanced o length) wit_goalss
+ |> (map o map) (Thm.forall_elim_vars 0);
+ val phi = Local_Theory.target_morphism lthy;
+ val thms = unflat all_goalss (Morphism.fact phi raw_thms);
+
+ val (bnf, lthy') = after_qed mk_wit_thms thms lthy
+ in
+ (bnf, register_bnf plugins key bnf lthy')
+ end;
+
+val bnf_axiomatization = prepare_decl (K I) (K I) (K I);
+
+fun read_constraint _ NONE = @{sort type}
+ | read_constraint ctxt (SOME s) = Syntax.read_sort ctxt s;
+
+val bnf_axiomatization_cmd = prepare_decl Plugin_Name.make_filter read_constraint Syntax.read_typ;
+
+val parse_witTs =
+ @{keyword "["} |-- (Parse.name --| @{keyword ":"} -- Scan.repeat Parse.typ
+ >> (fn ("wits", Ts) => Ts
+ | (s, _) => error ("Unknown label " ^ quote s ^ " (expected \"wits\")"))) --|
+ @{keyword "]"} || Scan.succeed [];
+
+val parse_bnf_axiomatization_options =
+ Scan.optional (@{keyword "("} |-- Plugin_Name.parse_filter --| @{keyword ")"}) (K (K true));
+
+val parse_bnf_axiomatization =
+ parse_bnf_axiomatization_options -- parse_type_args_named_constrained -- Parse.binding --
+ parse_witTs -- Parse.opt_mixfix -- parse_map_rel_pred_bindings;
+
+val _ =
+ Outer_Syntax.local_theory @{command_keyword bnf_axiomatization} "bnf declaration"
+ (parse_bnf_axiomatization >>
+ (fn (((((plugins, bsTs), b), witTs), mx), (mapb, relb, predb)) =>
+ bnf_axiomatization_cmd plugins bsTs b mx mapb relb predb witTs #> snd));
+
+end;