(* Title: HOL/Tools/function_package/size.ML
ID: $Id$
Author: Stefan Berghofer, Florian Haftmann, TU Muenchen
Size functions for datatypes.
*)
signature SIZE =
sig
val size_thms: theory -> string -> thm list
val setup: theory -> theory
end;
structure Size: SIZE =
struct
open DatatypeAux;
structure SizeData = TheoryDataFun
(
type T = thm list Symtab.table;
val empty = Symtab.empty;
val copy = I
val extend = I
fun merge _ = Symtab.merge (K true);
);
fun add_axioms label ts atts thy =
thy
|> PureThy.add_axiomss_i [((label, ts), atts)];
val Const (size_name, _) = HOLogic.size_const dummyT;
val size_name_base = NameSpace.base size_name;
val size_suffix = "_" ^ size_name_base;
fun instance_size_class tyco thy =
let
val n = Sign.arity_number thy tyco;
in
thy
|> Class.prove_instance (Class.intro_classes_tac [])
[(tyco, replicate n HOLogic.typeS, [HOLogic.class_size])] []
|> snd
end
fun plus (t1, t2) = Const ("HOL.plus_class.plus",
HOLogic.natT --> HOLogic.natT --> HOLogic.natT) $ t1 $ t2;
fun indexify_names names =
let
fun index (x :: xs) tab =
(case AList.lookup (op =) tab x of
NONE => if member (op =) xs x then (x ^ "1") :: index xs ((x, 2) :: tab) else x :: index xs tab
| SOME i => (x ^ string_of_int i) :: index xs ((x, i + 1) :: tab))
| index [] _ = [];
in index names [] end;
fun make_size head_len descr' sorts recTs thy =
let
val size_names = replicate head_len size_name @
map (Sign.intern_const thy) (indexify_names
(map (fn T => name_of_typ T ^ size_suffix) (Library.drop (head_len, recTs))));
val size_consts = map2 (fn s => fn T => Const (s, T --> HOLogic.natT))
size_names recTs;
fun make_tnames Ts =
let
fun type_name (TFree (name, _)) = implode (tl (explode name))
| type_name (Type (name, _)) =
let val name' = Sign.base_name name
in if Syntax.is_identifier name' then name' else "x" end;
in indexify_names (map type_name Ts) end;
fun make_size_eqn size_const T (cname, cargs) =
let
val recs = filter is_rec_type cargs;
val Ts = map (typ_of_dtyp descr' sorts) cargs;
val recTs = map (typ_of_dtyp descr' sorts) recs;
val tnames = make_tnames Ts;
val rec_tnames = map fst (filter (is_rec_type o snd) (tnames ~~ cargs));
val ts = map2 (fn (r, s) => fn T => nth size_consts (dest_DtRec r) $
Free (s, T)) (recs ~~ rec_tnames) recTs;
val t = if null ts then HOLogic.zero else
Library.foldl plus (hd ts, tl ts @ [HOLogic.Suc_zero]);
in
HOLogic.mk_Trueprop (HOLogic.mk_eq (size_const $
list_comb (Const (cname, Ts ---> T), map2 (curry Free) tnames Ts), t))
end
in
maps (fn (((_, (_, _, constrs)), size_const), T) =>
map (make_size_eqn size_const T) constrs) (descr' ~~ size_consts ~~ recTs)
end;
fun prove_size_thms (info : datatype_info) head_len thy =
let
val descr' = #descr info;
val sorts = #sorts info;
val reccomb_names = #rec_names info;
val primrec_thms = #rec_rewrites info;
val recTs = get_rec_types descr' sorts;
val size_names = replicate head_len size_name @
map (Sign.full_name thy) (DatatypeProp.indexify_names
(map (fn T => name_of_typ T ^ size_suffix) (Library.drop (head_len, recTs))));
val def_names = map (fn s => s ^ "_def") (DatatypeProp.indexify_names
(map (fn T => name_of_typ T ^ size_suffix) recTs));
fun make_sizefun (_, cargs) =
let
val Ts = map (typ_of_dtyp descr' sorts) cargs;
val k = length (filter is_rec_type cargs);
val ts = map Bound (k - 1 downto 0);
val t = if null ts then HOLogic.zero else
Library.foldl plus (hd ts, tl ts @ [HOLogic.Suc_zero]);
in
foldr (fn (T, t') => Abs ("x", T, t')) t (Ts @ replicate k HOLogic.natT)
end;
val fs = maps (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr';
val fTs = map fastype_of fs;
val (size_def_thms, thy') =
thy
|> Sign.add_consts_i (map (fn (s, T) =>
(Sign.base_name s, T --> HOLogic.natT, NoSyn))
(Library.drop (head_len, size_names ~~ recTs)))
|> fold (fn (_, (name, _, _)) => instance_size_class name) descr'
|> PureThy.add_defs_i true (map (Thm.no_attributes o (fn (((s, T), def_name), rec_name) =>
(def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT),
list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs)))))
(size_names ~~ recTs ~~ def_names ~~ reccomb_names));
val rewrites = size_def_thms @ map mk_meta_eq primrec_thms;
val size_thms = map (fn t => Goal.prove_global thy' [] [] t
(fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1]))
(make_size head_len descr' sorts recTs thy')
in
thy'
|> PureThy.add_thmss [((size_name_base, size_thms), [])]
|>> flat
end;
fun axiomatize_size_thms (info : datatype_info) head_len thy =
let
val descr' = #descr info;
val sorts = #sorts info;
val recTs = get_rec_types descr' sorts;
val used = map fst (fold Term.add_tfreesT recTs []);
val size_names = DatatypeProp.indexify_names
(map (fn T => name_of_typ T ^ size_suffix) (Library.drop (head_len, recTs)));
val thy' = thy |> fold (fn (s, T) =>
snd o Theory.specify_const [] (Sign.base_name s, T --> HOLogic.natT, NoSyn) [])
(size_names ~~ Library.drop (head_len, recTs))
val size_axs = make_size head_len descr' sorts recTs thy';
in
thy'
|> add_axioms size_name_base size_axs []
||> fold (fn (_, (name, _, _)) => instance_size_class name) descr'
|>> flat
end;
fun add_size_thms (name :: _) thy =
let
val info = DatatypePackage.the_datatype thy name;
val descr' = #descr info;
val head_len = #head_len info;
val typnames = map (#1 o snd) (curry Library.take head_len descr');
val prefix = space_implode "_" (map NameSpace.base typnames);
val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists (fn dt =>
is_rec_type dt andalso not (null (fst (strip_dtyp dt)))) cargs) constrs)
(#descr info)
in if no_size then thy
else
thy
|> Sign.add_path prefix
|> (if ! quick_and_dirty
then axiomatize_size_thms info head_len
else prove_size_thms info head_len)
||> Sign.parent_path
|-> (fn thms => PureThy.add_thmss [(("", thms),
[Simplifier.simp_add, Thm.declaration_attribute
(fn thm => Context.mapping (Code.add_default_func thm) I)])])
|-> (fn thms => SizeData.map (fold (fn typname => Symtab.update_new
(typname, flat thms)) typnames))
end;
fun size_thms thy = the o Symtab.lookup (SizeData.get thy);
val setup = DatatypePackage.interpretation add_size_thms;
end;