--- a/src/HOL/Tools/function_package/size.ML Mon Dec 17 18:32:56 2007 +0100
+++ b/src/HOL/Tools/function_package/size.ML Mon Dec 17 18:37:49 2007 +0100
@@ -18,20 +18,14 @@
structure SizeData = TheoryDataFun
(
- type T = thm list Symtab.table;
+ type T = (string * 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;
+val lookup_size = SizeData.get #> Symtab.lookup;
fun instance_size_class tyco thy =
thy
@@ -44,143 +38,198 @@
fun plus (t1, t2) = Const ("HOL.plus_class.plus",
HOLogic.natT --> HOLogic.natT --> HOLogic.natT) $ t1 $ t2;
-fun make_size head_len descr' sorts recTs thy =
+fun size_of_type f g h (T as Type (s, Ts)) =
+ (case f s of
+ SOME t => SOME t
+ | NONE => (case g s of
+ SOME size_name =>
+ SOME (list_comb (Const (size_name,
+ map (fn U => U --> HOLogic.natT) Ts @ [T] ---> HOLogic.natT),
+ map (size_of_type' f g h) Ts))
+ | NONE => NONE))
+ | size_of_type f g h (TFree (s, _)) = h s
+and size_of_type' f g h T = (case size_of_type f g h T of
+ NONE => Abs ("x", T, HOLogic.zero)
+ | SOME t => t);
+
+fun is_poly thy (DtType (name, dts)) =
+ (case DatatypePackage.get_datatype thy name of
+ NONE => false
+ | SOME _ => exists (is_poly thy) dts)
+ | is_poly _ _ = true;
+
+fun constrs_of thy name =
let
- val size_names = replicate head_len size_name @
- map (Sign.intern_const thy) (DatatypeProp.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;
+ val {descr, index, ...} = DatatypePackage.the_datatype thy name
+ val SOME (_, _, constrs) = AList.lookup op = descr index
+ in constrs end;
+
+val app = curry (list_comb o swap);
- 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 DatatypeProp.indexify_names (map type_name Ts) end;
+fun prove_size_thms (info : datatype_info) new_type_names thy =
+ let
+ val {descr, alt_names, sorts, rec_names, rec_rewrites, induction, ...} = info;
+ val l = length new_type_names;
+ val alt_names' = (case alt_names of
+ NONE => replicate l NONE | SOME names => map SOME names);
+ val descr' = List.take (descr, l);
+ val (rec_names1, rec_names2) = chop l rec_names;
+ val recTs = get_rec_types descr sorts;
+ val (recTs1, recTs2) = chop l recTs;
+ val (_, (_, paramdts, _)) :: _ = descr;
+ val paramTs = map (typ_of_dtyp descr sorts) paramdts;
+ val ((param_size_fs, param_size_fTs), f_names) = paramTs |>
+ map (fn T as TFree (s, _) =>
+ let
+ val name = "f" ^ implode (tl (explode s));
+ val U = T --> HOLogic.natT
+ in
+ (((s, Free (name, U)), U), name)
+ end) |> split_list |>> split_list;
+ val param_size = AList.lookup op = param_size_fs;
- fun make_size_eqn size_const T (cname, cargs) =
+ val extra_rewrites = descr |> map (#1 o snd) |> distinct op = |>
+ List.mapPartial (Option.map snd o lookup_size thy) |> flat;
+ val extra_size = Option.map fst o lookup_size thy;
+
+ val (((size_names, size_fns), def_names), def_names') =
+ recTs1 ~~ alt_names' |>
+ map (fn (T as Type (s, _), optname) =>
+ let
+ val s' = the_default (Sign.base_name s) optname ^ "_size";
+ val s'' = Sign.full_name thy s'
+ in
+ (s'',
+ (list_comb (Const (s'', param_size_fTs @ [T] ---> HOLogic.natT),
+ map snd param_size_fs),
+ (s' ^ "_def", s' ^ "_overloaded_def")))
+ end) |> split_list ||>> split_list ||>> split_list;
+ val overloaded_size_fns = map HOLogic.size_const recTs1;
+
+ (* instantiation for primrec combinator *)
+ fun size_of_constr b size_ofp ((_, cargs), (_, 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 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]);
-
+ val (ts, _, _) = fold_rev (fn ((dt, dt'), T) => fn (us, i, j) =>
+ if is_rec_type dt then (Bound i :: us, i + 1, j + 1)
+ else
+ (if b andalso is_poly thy dt' then
+ case size_of_type (K NONE) extra_size size_ofp T of
+ NONE => us | SOME sz => sz $ Bound j :: us
+ else us, i, j + 1))
+ (cargs ~~ cargs' ~~ Ts) ([], 0, k);
+ val t =
+ if null ts andalso (not b orelse not (exists (is_poly thy) cargs'))
+ then HOLogic.zero
+ else foldl1 plus (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 fs = maps (fn (_, (name, _, constrs)) =>
+ map (size_of_constr true param_size) (constrs ~~ constrs_of thy name)) descr;
+ val fs' = maps (fn (n, (name, _, constrs)) =>
+ map (size_of_constr (l <= n) (K NONE)) (constrs ~~ constrs_of thy name)) descr;
val fTs = map fastype_of fs;
- val (size_def_thms, thy') =
+ val (rec_combs1, rec_combs2) = chop l (map (fn (T, rec_name) =>
+ Const (rec_name, fTs @ [T] ---> HOLogic.natT))
+ (recTs ~~ rec_names));
+
+ val ((size_def_thms, 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)))
+ (Sign.base_name s, param_size_fTs @ [T] ---> HOLogic.natT, NoSyn))
+ (size_names ~~ recTs1))
|> 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));
+ |> PureThy.add_defs_i false
+ (map (Thm.no_attributes o apsnd (Logic.mk_equals o apsnd (app fs)))
+ (def_names ~~ (size_fns ~~ rec_combs1)))
+ ||>> PureThy.add_defs_i true
+ (map (Thm.no_attributes o apsnd (Logic.mk_equals o apsnd (app fs')))
+ (def_names' ~~ (overloaded_size_fns ~~ rec_combs1)));
+
+ val ctxt = ProofContext.init thy';
+
+ val simpset1 = HOL_basic_ss addsimps @{thm add_0} :: @{thm add_0_right} ::
+ size_def_thms @ size_def_thms' @ rec_rewrites @ extra_rewrites;
+ val xs = map (fn i => "x" ^ string_of_int i) (1 upto length recTs2);
+
+ fun mk_unfolded_size_eq tab size_ofp fs (p as (x, T), r) =
+ HOLogic.mk_eq (app fs r $ Free p,
+ the (size_of_type tab extra_size size_ofp T) $ Free p);
+
+ fun prove_unfolded_size_eqs size_ofp fs =
+ if null recTs2 then []
+ else map standard (split_conj_thm (SkipProof.prove ctxt [] []
+ (HOLogic.mk_Trueprop (mk_conj (replicate l HOLogic.true_const @
+ map (mk_unfolded_size_eq (AList.lookup op =
+ (new_type_names ~~ map (app fs) rec_combs1)) size_ofp fs)
+ (xs ~~ recTs2 ~~ rec_combs2))))
+ (fn _ => (indtac induction xs THEN_ALL_NEW asm_simp_tac simpset1) 1)));
+
+ val unfolded_size_eqs = prove_unfolded_size_eqs param_size fs @
+ prove_unfolded_size_eqs (K NONE) fs';
- val rewrites = size_def_thms @ map mk_meta_eq primrec_thms;
+ (* characteristic equations for size functions *)
+ fun gen_mk_size_eq p size_of size_ofp size_const T (cname, cargs) =
+ let
+ val Ts = map (typ_of_dtyp descr sorts) cargs;
+ val tnames = Name.variant_list f_names (DatatypeProp.make_tnames Ts);
+ val ts = List.mapPartial (fn (sT as (s, T), dt) =>
+ Option.map (fn sz => sz $ Free sT)
+ (if p dt then size_of_type size_of extra_size size_ofp T
+ else NONE)) (tnames ~~ Ts ~~ cargs)
+ in
+ HOLogic.mk_Trueprop (HOLogic.mk_eq
+ (size_const $ list_comb (Const (cname, Ts ---> T),
+ map2 (curry Free) tnames Ts),
+ if null ts then HOLogic.zero
+ else foldl1 plus (ts @ [HOLogic.Suc_zero])))
+ end;
- 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')
+ val simpset2 = HOL_basic_ss addsimps
+ size_def_thms @ size_def_thms' @ rec_rewrites @ unfolded_size_eqs;
+
+ fun prove_size_eqs p size_fns size_ofp =
+ maps (fn (((_, (_, _, constrs)), size_const), T) =>
+ map (fn constr => standard (SkipProof.prove ctxt [] []
+ (gen_mk_size_eq p (AList.lookup op = (new_type_names ~~ size_fns))
+ size_ofp size_const T constr)
+ (fn _ => simp_tac simpset2 1))) constrs)
+ (descr' ~~ size_fns ~~ recTs1);
+
+ val size_eqns = prove_size_eqs (is_poly thy') size_fns param_size @
+ prove_size_eqs is_rec_type overloaded_size_fns (K NONE);
+
+ val ([size_thms], thy'') = PureThy.add_thmss
+ [(("size", size_eqns),
+ [Simplifier.simp_add, Thm.declaration_attribute
+ (fn thm => Context.mapping (Code.add_default_func thm) I)])] thy'
in
- thy'
- |> PureThy.add_thmss [((size_name_base, size_thms), [])]
- |>> flat
+ SizeData.map (fold (Symtab.update_new o apsnd (rpair size_thms))
+ (new_type_names ~~ size_names)) thy''
end;
-fun axiomatize_size_thms (info : datatype_info) head_len thy =
+fun add_size_thms (new_type_names as name :: _) 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 info as {descr, ...} = DatatypePackage.the_datatype thy name;
+ val prefix = NameSpace.map_base
+ (K (space_implode "_" (map Sign.base_name new_type_names))) name;
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)
+ is_rec_type dt andalso not (null (fst (strip_dtyp dt)))) cargs) constrs) descr
in if no_size then thy
else
thy
+ |> Sign.root_path
|> 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))
+ |> prove_size_thms info new_type_names
+ |> Sign.restore_naming thy
end;
-fun size_thms thy = the o Symtab.lookup (SizeData.get thy);
+val size_thms = snd oo (the oo lookup_size);
val setup = DatatypePackage.interpretation add_size_thms;