src/HOL/Tools/function_package/size.ML
author wenzelm
Sun Mar 08 17:26:14 2009 +0100 (2009-03-08)
changeset 30364 577edc39b501
parent 30345 76fd85bbf139
child 31668 a616e56a5ec8
permissions -rw-r--r--
moved basic algebra of long names from structure NameSpace to Long_Name;
     1 (*  Title:      HOL/Tools/function_package/size.ML
     2     Author:     Stefan Berghofer, Florian Haftmann & Alexander Krauss, TU Muenchen
     3 
     4 Size functions for datatypes.
     5 *)
     6 
     7 signature SIZE =
     8 sig
     9   val size_thms: theory -> string -> thm list
    10   val setup: theory -> theory
    11 end;
    12 
    13 structure Size: SIZE =
    14 struct
    15 
    16 open DatatypeAux;
    17 
    18 structure SizeData = TheoryDataFun
    19 (
    20   type T = (string * thm list) Symtab.table;
    21   val empty = Symtab.empty;
    22   val copy = I
    23   val extend = I
    24   fun merge _ = Symtab.merge (K true);
    25 );
    26 
    27 val lookup_size = SizeData.get #> Symtab.lookup;
    28 
    29 fun plus (t1, t2) = Const ("HOL.plus_class.plus",
    30   HOLogic.natT --> HOLogic.natT --> HOLogic.natT) $ t1 $ t2;
    31 
    32 fun size_of_type f g h (T as Type (s, Ts)) =
    33       (case f s of
    34          SOME t => SOME t
    35        | NONE => (case g s of
    36            SOME size_name =>
    37              SOME (list_comb (Const (size_name,
    38                map (fn U => U --> HOLogic.natT) Ts @ [T] ---> HOLogic.natT),
    39                  map (size_of_type' f g h) Ts))
    40          | NONE => NONE))
    41   | size_of_type f g h (TFree (s, _)) = h s
    42 and size_of_type' f g h T = (case size_of_type f g h T of
    43       NONE => Abs ("x", T, HOLogic.zero)
    44     | SOME t => t);
    45 
    46 fun is_poly thy (DtType (name, dts)) =
    47       (case DatatypePackage.get_datatype thy name of
    48          NONE => false
    49        | SOME _ => exists (is_poly thy) dts)
    50   | is_poly _ _ = true;
    51 
    52 fun constrs_of thy name =
    53   let
    54     val {descr, index, ...} = DatatypePackage.the_datatype thy name
    55     val SOME (_, _, constrs) = AList.lookup op = descr index
    56   in constrs end;
    57 
    58 val app = curry (list_comb o swap);
    59 
    60 fun prove_size_thms (info : datatype_info) new_type_names thy =
    61   let
    62     val {descr, alt_names, sorts, rec_names, rec_rewrites, induction, ...} = info;
    63     val l = length new_type_names;
    64     val alt_names' = (case alt_names of
    65       NONE => replicate l NONE | SOME names => map SOME names);
    66     val descr' = List.take (descr, l);
    67     val (rec_names1, rec_names2) = chop l rec_names;
    68     val recTs = get_rec_types descr sorts;
    69     val (recTs1, recTs2) = chop l recTs;
    70     val (_, (_, paramdts, _)) :: _ = descr;
    71     val paramTs = map (typ_of_dtyp descr sorts) paramdts;
    72     val ((param_size_fs, param_size_fTs), f_names) = paramTs |>
    73       map (fn T as TFree (s, _) =>
    74         let
    75           val name = "f" ^ implode (tl (explode s));
    76           val U = T --> HOLogic.natT
    77         in
    78           (((s, Free (name, U)), U), name)
    79         end) |> split_list |>> split_list;
    80     val param_size = AList.lookup op = param_size_fs;
    81 
    82     val extra_rewrites = descr |> map (#1 o snd) |> distinct op = |>
    83       map_filter (Option.map snd o lookup_size thy) |> flat;
    84     val extra_size = Option.map fst o lookup_size thy;
    85 
    86     val (((size_names, size_fns), def_names), def_names') =
    87       recTs1 ~~ alt_names' |>
    88       map (fn (T as Type (s, _), optname) =>
    89         let
    90           val s' = the_default (Long_Name.base_name s) optname ^ "_size";
    91           val s'' = Sign.full_bname thy s'
    92         in
    93           (s'',
    94            (list_comb (Const (s'', param_size_fTs @ [T] ---> HOLogic.natT),
    95               map snd param_size_fs),
    96             (s' ^ "_def", s' ^ "_overloaded_def")))
    97         end) |> split_list ||>> split_list ||>> split_list;
    98     val overloaded_size_fns = map HOLogic.size_const recTs1;
    99 
   100     (* instantiation for primrec combinator *)
   101     fun size_of_constr b size_ofp ((_, cargs), (_, cargs')) =
   102       let
   103         val Ts = map (typ_of_dtyp descr sorts) cargs;
   104         val k = length (filter is_rec_type cargs);
   105         val (ts, _, _) = fold_rev (fn ((dt, dt'), T) => fn (us, i, j) =>
   106           if is_rec_type dt then (Bound i :: us, i + 1, j + 1)
   107           else
   108             (if b andalso is_poly thy dt' then
   109                case size_of_type (K NONE) extra_size size_ofp T of
   110                  NONE => us | SOME sz => sz $ Bound j :: us
   111              else us, i, j + 1))
   112               (cargs ~~ cargs' ~~ Ts) ([], 0, k);
   113         val t =
   114           if null ts andalso (not b orelse not (exists (is_poly thy) cargs'))
   115           then HOLogic.zero
   116           else foldl1 plus (ts @ [HOLogic.Suc_zero])
   117       in
   118         List.foldr (fn (T, t') => Abs ("x", T, t')) t (Ts @ replicate k HOLogic.natT)
   119       end;
   120 
   121     val fs = maps (fn (_, (name, _, constrs)) =>
   122       map (size_of_constr true param_size) (constrs ~~ constrs_of thy name)) descr;
   123     val fs' = maps (fn (n, (name, _, constrs)) =>
   124       map (size_of_constr (l <= n) (K NONE)) (constrs ~~ constrs_of thy name)) descr;
   125     val fTs = map fastype_of fs;
   126 
   127     val (rec_combs1, rec_combs2) = chop l (map (fn (T, rec_name) =>
   128       Const (rec_name, fTs @ [T] ---> HOLogic.natT))
   129         (recTs ~~ rec_names));
   130 
   131     fun define_overloaded (def_name, eq) lthy =
   132       let
   133         val (Free (c, _), rhs) = (Logic.dest_equals o Syntax.check_term lthy) eq;
   134         val ((_, (_, thm)), lthy') = lthy |> LocalTheory.define Thm.definitionK
   135           ((Binding.name c, NoSyn), ((Binding.name def_name, []), rhs));
   136         val ctxt_thy = ProofContext.init (ProofContext.theory_of lthy');
   137         val thm' = singleton (ProofContext.export lthy' ctxt_thy) thm;
   138       in (thm', lthy') end;
   139 
   140     val ((size_def_thms, size_def_thms'), thy') =
   141       thy
   142       |> Sign.add_consts_i (map (fn (s, T) =>
   143            (Binding.name (Long_Name.base_name s), param_size_fTs @ [T] ---> HOLogic.natT, NoSyn))
   144            (size_names ~~ recTs1))
   145       |> PureThy.add_defs false
   146         (map (Thm.no_attributes o apsnd (Logic.mk_equals o apsnd (app fs)))
   147            (map Binding.name def_names ~~ (size_fns ~~ rec_combs1)))
   148       ||> TheoryTarget.instantiation
   149            (map (#1 o snd) descr', map dest_TFree paramTs, [HOLogic.class_size])
   150       ||>> fold_map define_overloaded
   151         (def_names' ~~ map Logic.mk_equals (overloaded_size_fns ~~ map (app fs') rec_combs1))
   152       ||> Class.prove_instantiation_instance (K (Class.intro_classes_tac []))
   153       ||> LocalTheory.exit_global;
   154 
   155     val ctxt = ProofContext.init thy';
   156 
   157     val simpset1 = HOL_basic_ss addsimps @{thm add_0} :: @{thm add_0_right} ::
   158       size_def_thms @ size_def_thms' @ rec_rewrites @ extra_rewrites;
   159     val xs = map (fn i => "x" ^ string_of_int i) (1 upto length recTs2);
   160 
   161     fun mk_unfolded_size_eq tab size_ofp fs (p as (x, T), r) =
   162       HOLogic.mk_eq (app fs r $ Free p,
   163         the (size_of_type tab extra_size size_ofp T) $ Free p);
   164 
   165     fun prove_unfolded_size_eqs size_ofp fs =
   166       if null recTs2 then []
   167       else split_conj_thm (SkipProof.prove ctxt xs []
   168         (HOLogic.mk_Trueprop (mk_conj (replicate l HOLogic.true_const @
   169            map (mk_unfolded_size_eq (AList.lookup op =
   170                (new_type_names ~~ map (app fs) rec_combs1)) size_ofp fs)
   171              (xs ~~ recTs2 ~~ rec_combs2))))
   172         (fn _ => (indtac induction xs THEN_ALL_NEW asm_simp_tac simpset1) 1));
   173 
   174     val unfolded_size_eqs1 = prove_unfolded_size_eqs param_size fs;
   175     val unfolded_size_eqs2 = prove_unfolded_size_eqs (K NONE) fs';
   176 
   177     (* characteristic equations for size functions *)
   178     fun gen_mk_size_eq p size_of size_ofp size_const T (cname, cargs) =
   179       let
   180         val Ts = map (typ_of_dtyp descr sorts) cargs;
   181         val tnames = Name.variant_list f_names (DatatypeProp.make_tnames Ts);
   182         val ts = map_filter (fn (sT as (s, T), dt) =>
   183           Option.map (fn sz => sz $ Free sT)
   184             (if p dt then size_of_type size_of extra_size size_ofp T
   185              else NONE)) (tnames ~~ Ts ~~ cargs)
   186       in
   187         HOLogic.mk_Trueprop (HOLogic.mk_eq
   188           (size_const $ list_comb (Const (cname, Ts ---> T),
   189              map2 (curry Free) tnames Ts),
   190            if null ts then HOLogic.zero
   191            else foldl1 plus (ts @ [HOLogic.Suc_zero])))
   192       end;
   193 
   194     val simpset2 = HOL_basic_ss addsimps
   195       rec_rewrites @ size_def_thms @ unfolded_size_eqs1;
   196     val simpset3 = HOL_basic_ss addsimps
   197       rec_rewrites @ size_def_thms' @ unfolded_size_eqs2;
   198 
   199     fun prove_size_eqs p size_fns size_ofp simpset =
   200       maps (fn (((_, (_, _, constrs)), size_const), T) =>
   201         map (fn constr => standard (SkipProof.prove ctxt [] []
   202           (gen_mk_size_eq p (AList.lookup op = (new_type_names ~~ size_fns))
   203              size_ofp size_const T constr)
   204           (fn _ => simp_tac simpset 1))) constrs)
   205         (descr' ~~ size_fns ~~ recTs1);
   206 
   207     val size_eqns = prove_size_eqs (is_poly thy') size_fns param_size simpset2 @
   208       prove_size_eqs is_rec_type overloaded_size_fns (K NONE) simpset3;
   209 
   210     val ([size_thms], thy'') =  PureThy.add_thmss
   211       [((Binding.name "size", size_eqns),
   212         [Simplifier.simp_add, Nitpick_Const_Simp_Thms.add,
   213          Thm.declaration_attribute
   214              (fn thm => Context.mapping (Code.add_default_eqn thm) I)])] thy'
   215 
   216   in
   217     SizeData.map (fold (Symtab.update_new o apsnd (rpair size_thms))
   218       (new_type_names ~~ size_names)) thy''
   219   end;
   220 
   221 fun add_size_thms (new_type_names as name :: _) thy =
   222   let
   223     val info as {descr, alt_names, ...} = DatatypePackage.the_datatype thy name;
   224     val prefix = Long_Name.map_base_name (K (space_implode "_"
   225       (the_default (map Long_Name.base_name new_type_names) alt_names))) name;
   226     val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists (fn dt =>
   227       is_rec_type dt andalso not (null (fst (strip_dtyp dt)))) cargs) constrs) descr
   228   in if no_size then thy
   229     else
   230       thy
   231       |> Sign.root_path
   232       |> Sign.add_path prefix
   233       |> Theory.checkpoint
   234       |> prove_size_thms info new_type_names
   235       |> Sign.restore_naming thy
   236   end;
   237 
   238 val size_thms = snd oo (the oo lookup_size);
   239 
   240 val setup = DatatypePackage.interpretation add_size_thms;
   241 
   242 end;