src/HOL/Library/bnf_axiomatization.ML
author blanchet
Wed Sep 24 15:45:55 2014 +0200 (2014-09-24)
changeset 58425 246985c6b20b
parent 58189 9d714be4f028
child 58659 6c9821c32dd5
permissions -rw-r--r--
simpler proof
     1 (*  Title:      HOL/Library/bnf_axiomatization.ML
     2     Author:     Dmitriy Traytel, TU Muenchen
     3     Copyright   2013
     4 
     5 Axiomatic declaration of bounded natural functors.
     6 *)
     7 
     8 signature BNF_AXIOMATIZATION =
     9 sig
    10   val bnf_axiomatization: (string -> bool) -> (binding option * (typ * sort)) list -> binding ->
    11     mixfix -> binding -> binding -> typ list -> local_theory -> BNF_Def.bnf * local_theory
    12 end
    13 
    14 structure BNF_Axiomatization : BNF_AXIOMATIZATION =
    15 struct
    16 
    17 open BNF_Util
    18 open BNF_Def
    19 
    20 fun prepare_decl prepare_constraint prepare_typ plugins raw_vars b mx user_mapb user_relb user_witTs
    21   lthy =
    22   let
    23    fun prepare_type_arg (set_opt, (ty, c)) =
    24       let val s = fst (dest_TFree (prepare_typ lthy ty)) in
    25         (set_opt, (s, prepare_constraint lthy c))
    26       end;
    27     val ((user_setbs, vars), raw_vars') =
    28       map prepare_type_arg raw_vars
    29       |> `split_list
    30       |>> apfst (map_filter I);
    31     val deads = map_filter (fn (NONE, x) => SOME x | _ => NONE) raw_vars';
    32 
    33     fun mk_b name user_b =
    34       (if Binding.is_empty user_b then Binding.prefix_name (name ^ "_") b else user_b)
    35       |> Binding.qualify false (Binding.name_of b);
    36     val (Tname, lthy) = Typedecl.basic_typedecl (b, length vars, mx) lthy;
    37     val (bd_type_Tname, lthy) =
    38       Typedecl.basic_typedecl (mk_b "bd_type" Binding.empty, length deads, NoSyn) lthy;
    39     val T = Type (Tname, map TFree vars);
    40     val bd_type_T = Type (bd_type_Tname, map TFree deads);
    41     val lives = map TFree (filter_out (member (op =) deads) vars);
    42     val live = length lives;
    43     val _ = "Trying to declare a BNF with no live variables" |> null lives ? error;
    44     val (lives', _) = BNF_Util.mk_TFrees (length lives)
    45       (fold Variable.declare_typ (map TFree vars) lthy);
    46     val T' = Term.typ_subst_atomic (lives ~~ lives') T;
    47     val mapT = map2 (curry op -->) lives lives' ---> T --> T';
    48     val setTs = map (fn U => T --> HOLogic.mk_setT U) lives;
    49     val bdT = BNF_Util.mk_relT (bd_type_T, bd_type_T);
    50     val mapb = mk_b mapN user_mapb;
    51     val bdb = mk_b "bd" Binding.empty;
    52     val setbs = map2 (fn b => fn i => mk_b (mk_setN i) b) user_setbs
    53       (if live = 1 then [0] else 1 upto live);
    54 
    55     val witTs = map (prepare_typ lthy) user_witTs;
    56     val nwits = length witTs;
    57     val witbs = map (fn i => mk_b (mk_witN i) Binding.empty)
    58       (if nwits = 1 then [0] else 1 upto nwits);
    59 
    60     val lthy = Local_Theory.background_theory
    61       (Sign.add_consts ((mapb, mapT, NoSyn) :: (bdb, bdT, NoSyn) ::
    62         map2 (fn b => fn T => (b, T, NoSyn)) setbs setTs @
    63         map2 (fn b => fn T => (b, T, NoSyn)) witbs witTs))
    64       lthy;
    65     val Fmap = Const (Local_Theory.full_name lthy mapb, mapT);
    66     val Fsets = map2 (fn setb => fn setT =>
    67       Const (Local_Theory.full_name lthy setb, setT)) setbs setTs;
    68     val Fbd = Const (Local_Theory.full_name lthy bdb, bdT);
    69     val Fwits = map2 (fn witb => fn witT =>
    70       Const (Local_Theory.full_name lthy witb, witT)) witbs witTs;
    71     val (key, goals, (triv_tac_opt, wit_goalss), after_qed, lthy, _) =
    72       prepare_def Do_Inline (user_policy Note_Some) false I (K I) (K I) (SOME (map TFree deads))
    73       user_mapb user_relb user_setbs ((((((Binding.empty, T), Fmap), Fsets), Fbd), Fwits), NONE)
    74       lthy;
    75 
    76     fun mk_wits_tac ctxt set_maps = TRYALL Goal.conjunction_tac THEN the triv_tac_opt ctxt set_maps;
    77     val wit_goals = map Logic.mk_conjunction_balanced wit_goalss;
    78     val all_goalss = map single goals @ (if nwits > 0 then wit_goalss else []);
    79 
    80     val (((_, [raw_thms])), (lthy_old, lthy)) = Local_Theory.background_theory_result
    81       (Specification.axiomatization [] [((mk_b "axioms" Binding.empty, []), flat all_goalss)]) lthy
    82       ||> `Local_Theory.restore;
    83 
    84     fun mk_wit_thms set_maps =
    85       Goal.prove_sorry lthy [] [] (Logic.mk_conjunction_balanced wit_goals)
    86         (fn {context = ctxt, prems = _} => mk_wits_tac ctxt set_maps)
    87       |> Conjunction.elim_balanced (length wit_goals)
    88       |> map2 (Conjunction.elim_balanced o length) wit_goalss
    89       |> map (map (Thm.close_derivation o Thm.forall_elim_vars 0));
    90     val phi = Proof_Context.export_morphism lthy_old lthy;
    91     val thms = unflat all_goalss (Morphism.fact phi raw_thms);
    92 
    93     val (bnf, lthy') = after_qed mk_wit_thms thms lthy
    94   in
    95     (bnf, register_bnf plugins key bnf lthy')
    96   end;
    97 
    98 val bnf_axiomatization = prepare_decl (K I) (K I);
    99 
   100 fun read_constraint _ NONE = @{sort type}
   101   | read_constraint ctxt (SOME s) = Syntax.read_sort ctxt s;
   102 
   103 val bnf_axiomatization_cmd = prepare_decl read_constraint Syntax.read_typ;
   104 
   105 val parse_witTs =
   106   @{keyword "["} |-- (Parse.short_ident --| @{keyword ":"} -- Scan.repeat Parse.typ
   107     >> (fn ("wits", Ts) => Ts
   108          | (s, _) => error ("Unknown label " ^ quote s ^ " (expected \"wits\")"))) --|
   109   @{keyword "]"} || Scan.succeed [];
   110 
   111 val parse_bnf_axiomatization_options =
   112   Scan.optional (@{keyword "("} |-- parse_plugins --| @{keyword ")"}) (K true);
   113 
   114 val parse_bnf_axiomatization =
   115   parse_bnf_axiomatization_options -- parse_type_args_named_constrained -- Parse.binding --
   116   parse_witTs -- Parse.opt_mixfix -- parse_map_rel_bindings;
   117 
   118 val _ =
   119   Outer_Syntax.local_theory @{command_spec "bnf_axiomatization"} "bnf declaration"
   120     (parse_bnf_axiomatization >> 
   121       (fn (((((plugins, bsTs), b), witTs), mx), (mapb, relb)) =>
   122          bnf_axiomatization_cmd plugins bsTs b mx mapb relb witTs #> snd));
   123 
   124 end;