# HG changeset patch
# User huffman
# Date 1323844710 -3600
# Node ID c7a73fb9be68d62e9c9bfedd19bf9c8638739a52
# Parent  caa99836aed8df51531edd8ed9379d0106612bcd# Parent  3fd2cd187299334a19d5119fc5916e916c1a02db
merged

diff -r caa99836aed8 -r c7a73fb9be68 NEWS
--- a/NEWS	Tue Dec 13 18:33:04 2011 +0100
+++ b/NEWS	Wed Dec 14 07:38:30 2011 +0100
@@ -53,6 +53,8 @@
 
 *** HOL ***
 
+* 'datatype' specifications allow explicit sort constraints.
+
 * Theory HOL/Library/Diagonalize has been removed. INCOMPATIBILITY, use
 theory HOL/Library/Nat_Bijection instead.
 
diff -r caa99836aed8 -r c7a73fb9be68 doc-src/IsarRef/Thy/HOL_Specific.thy
--- a/doc-src/IsarRef/Thy/HOL_Specific.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/doc-src/IsarRef/Thy/HOL_Specific.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -693,7 +693,7 @@
     @@{command (HOL) rep_datatype} ('(' (@{syntax name} +) ')')? (@{syntax term} +)
     ;
 
-    spec: @{syntax typespec} @{syntax mixfix}? '=' (cons + '|')
+    spec: @{syntax typespec_sorts} @{syntax mixfix}? '=' (cons + '|')
     ;
     cons: @{syntax name} (@{syntax type} * ) @{syntax mixfix}?
   "}
diff -r caa99836aed8 -r c7a73fb9be68 doc-src/IsarRef/Thy/document/HOL_Specific.tex
--- a/doc-src/IsarRef/Thy/document/HOL_Specific.tex	Tue Dec 13 18:33:04 2011 +0100
+++ b/doc-src/IsarRef/Thy/document/HOL_Specific.tex	Wed Dec 14 07:38:30 2011 +0100
@@ -1036,7 +1036,7 @@
 \rail@endplus
 \rail@end
 \rail@begin{2}{\isa{spec}}
-\rail@nont{\hyperlink{syntax.typespec}{\mbox{\isa{typespec}}}}[]
+\rail@nont{\hyperlink{syntax.typespec-sorts}{\mbox{\isa{typespec{\isaliteral{5F}{\isacharunderscore}}sorts}}}}[]
 \rail@bar
 \rail@nextbar{1}
 \rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[]
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Hoare_Parallel/Gar_Coll.thy
--- a/src/HOL/Hoare_Parallel/Gar_Coll.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Hoare_Parallel/Gar_Coll.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -379,19 +379,18 @@
 
 subsubsection {* Appending garbage nodes to the free list *}
 
-consts Append_to_free :: "nat \<times> edges \<Rightarrow> edges"
-
-axioms
-  Append_to_free0: "length (Append_to_free (i, e)) = length e"
+axiomatization Append_to_free :: "nat \<times> edges \<Rightarrow> edges"
+where
+  Append_to_free0: "length (Append_to_free (i, e)) = length e" and
   Append_to_free1: "Proper_Edges (m, e) 
-                   \<Longrightarrow> Proper_Edges (m, Append_to_free(i, e))"
+                   \<Longrightarrow> Proper_Edges (m, Append_to_free(i, e))" and
   Append_to_free2: "i \<notin> Reach e 
      \<Longrightarrow> n \<in> Reach (Append_to_free(i, e)) = ( n = i \<or> n \<in> Reach e)"
 
 definition AppendInv :: "gar_coll_state \<Rightarrow> nat \<Rightarrow> bool" where
   "AppendInv \<equiv> \<guillemotleft>\<lambda>ind. \<forall>i<length \<acute>M. ind\<le>i \<longrightarrow> i\<in>Reach \<acute>E \<longrightarrow> \<acute>M!i=Black\<guillemotright>"
 
-definition Append :: " gar_coll_state ann_com" where
+definition Append :: "gar_coll_state ann_com" where
    "Append \<equiv>
   .{\<acute>Proper \<and> Roots\<subseteq>Blacks \<acute>M \<and> \<acute>Safe}.
   \<acute>ind:=0;;
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Hoare_Parallel/Mul_Gar_Coll.thy
--- a/src/HOL/Hoare_Parallel/Mul_Gar_Coll.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Hoare_Parallel/Mul_Gar_Coll.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -380,13 +380,12 @@
 
 subsubsection {* Appending garbage nodes to the free list *}
 
-consts  Append_to_free :: "nat \<times> edges \<Rightarrow> edges"
-
-axioms
-  Append_to_free0: "length (Append_to_free (i, e)) = length e"
-  Append_to_free1: "Proper_Edges (m, e) 
-                    \<Longrightarrow> Proper_Edges (m, Append_to_free(i, e))"
-  Append_to_free2: "i \<notin> Reach e 
+axiomatization Append_to_free :: "nat \<times> edges \<Rightarrow> edges"
+where
+  Append_to_free0: "length (Append_to_free (i, e)) = length e" and
+  Append_to_free1: "Proper_Edges (m, e)
+                    \<Longrightarrow> Proper_Edges (m, Append_to_free(i, e))" and
+  Append_to_free2: "i \<notin> Reach e
            \<Longrightarrow> n \<in> Reach (Append_to_free(i, e)) = ( n = i \<or> n \<in> Reach e)"
 
 definition Mul_AppendInv :: "mul_gar_coll_state \<Rightarrow> nat \<Rightarrow> bool" where
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/IMP/VC.thy
--- a/src/HOL/IMP/VC.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/IMP/VC.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -7,16 +7,17 @@
 text{* Annotated commands: commands where loops are annotated with
 invariants. *}
 
-datatype acom = Askip
-              | Aassign vname aexp
-              | Asemi   acom acom
-              | Aif     bexp acom acom
-              | Awhile  assn bexp acom
+datatype acom =
+  ASKIP |
+  Aassign vname aexp     ("(_ ::= _)" [1000, 61] 61) |
+  Asemi   acom acom      ("_;/ _"  [60, 61] 60) |
+  Aif bexp acom acom     ("(IF _/ THEN _/ ELSE _)"  [0, 0, 61] 61) |
+  Awhile assn bexp acom  ("({_}/ WHILE _/ DO _)"  [0, 0, 61] 61)
 
 text{* Weakest precondition from annotated commands: *}
 
 fun pre :: "acom \<Rightarrow> assn \<Rightarrow> assn" where
-"pre Askip Q = Q" |
+"pre ASKIP Q = Q" |
 "pre (Aassign x a) Q = (\<lambda>s. Q(s(x := aval a s)))" |
 "pre (Asemi c\<^isub>1 c\<^isub>2) Q = pre c\<^isub>1 (pre c\<^isub>2 Q)" |
 "pre (Aif b c\<^isub>1 c\<^isub>2) Q =
@@ -27,7 +28,7 @@
 text{* Verification condition: *}
 
 fun vc :: "acom \<Rightarrow> assn \<Rightarrow> assn" where
-"vc Askip Q = (\<lambda>s. True)" |
+"vc ASKIP Q = (\<lambda>s. True)" |
 "vc (Aassign x a) Q = (\<lambda>s. True)" |
 "vc (Asemi c\<^isub>1 c\<^isub>2) Q = (\<lambda>s. vc c\<^isub>1 (pre c\<^isub>2 Q) s \<and> vc c\<^isub>2 Q s)" |
 "vc (Aif b c\<^isub>1 c\<^isub>2) Q = (\<lambda>s. vc c\<^isub>1 Q s \<and> vc c\<^isub>2 Q s)" |
@@ -38,17 +39,16 @@
 
 text{* Strip annotations: *}
 
-fun astrip :: "acom \<Rightarrow> com" where
-"astrip Askip = SKIP" |
-"astrip (Aassign x a) = (x::=a)" |
-"astrip (Asemi c\<^isub>1 c\<^isub>2) = (astrip c\<^isub>1; astrip c\<^isub>2)" |
-"astrip (Aif b c\<^isub>1 c\<^isub>2) = (IF b THEN astrip c\<^isub>1 ELSE astrip c\<^isub>2)" |
-"astrip (Awhile I b c) = (WHILE b DO astrip c)"
-
+fun strip :: "acom \<Rightarrow> com" where
+"strip ASKIP = SKIP" |
+"strip (Aassign x a) = (x::=a)" |
+"strip (Asemi c\<^isub>1 c\<^isub>2) = (strip c\<^isub>1; strip c\<^isub>2)" |
+"strip (Aif b c\<^isub>1 c\<^isub>2) = (IF b THEN strip c\<^isub>1 ELSE strip c\<^isub>2)" |
+"strip (Awhile I b c) = (WHILE b DO strip c)"
 
 subsection "Soundness"
 
-lemma vc_sound: "\<forall>s. vc c Q s \<Longrightarrow> \<turnstile> {pre c Q} astrip c {Q}"
+lemma vc_sound: "\<forall>s. vc c Q s \<Longrightarrow> \<turnstile> {pre c Q} strip c {Q}"
 proof(induction c arbitrary: Q)
   case (Awhile I b c)
   show ?case
@@ -56,15 +56,15 @@
     from `\<forall>s. vc (Awhile I b c) Q s`
     have vc: "\<forall>s. vc c I s" and IQ: "\<forall>s. I s \<and> \<not> bval b s \<longrightarrow> Q s" and
          pre: "\<forall>s. I s \<and> bval b s \<longrightarrow> pre c I s" by simp_all
-    have "\<turnstile> {pre c I} astrip c {I}" by(rule Awhile.IH[OF vc])
-    with pre show "\<turnstile> {\<lambda>s. I s \<and> bval b s} astrip c {I}"
+    have "\<turnstile> {pre c I} strip c {I}" by(rule Awhile.IH[OF vc])
+    with pre show "\<turnstile> {\<lambda>s. I s \<and> bval b s} strip c {I}"
       by(rule strengthen_pre)
     show "\<forall>s. I s \<and> \<not>bval b s \<longrightarrow> Q s" by(rule IQ)
   qed
 qed (auto intro: hoare.conseq)
 
 corollary vc_sound':
-  "(\<forall>s. vc c Q s) \<and> (\<forall>s. P s \<longrightarrow> pre c Q s) \<Longrightarrow> \<turnstile> {P} astrip c {Q}"
+  "(\<forall>s. vc c Q s) \<and> (\<forall>s. P s \<longrightarrow> pre c Q s) \<Longrightarrow> \<turnstile> {P} strip c {Q}"
 by (metis strengthen_pre vc_sound)
 
 
@@ -83,12 +83,12 @@
 qed simp_all
 
 lemma vc_complete:
- "\<turnstile> {P}c{Q} \<Longrightarrow> \<exists>c'. astrip c' = c \<and> (\<forall>s. vc c' Q s) \<and> (\<forall>s. P s \<longrightarrow> pre c' Q s)"
+ "\<turnstile> {P}c{Q} \<Longrightarrow> \<exists>c'. strip c' = c \<and> (\<forall>s. vc c' Q s) \<and> (\<forall>s. P s \<longrightarrow> pre c' Q s)"
   (is "_ \<Longrightarrow> \<exists>c'. ?G P c Q c'")
 proof (induction rule: hoare.induct)
   case Skip
   show ?case (is "\<exists>ac. ?C ac")
-  proof show "?C Askip" by simp qed
+  proof show "?C ASKIP" by simp qed
 next
   case (Assign P a x)
   show ?case (is "\<exists>ac. ?C ac")
@@ -125,7 +125,7 @@
 subsection "An Optimization"
 
 fun vcpre :: "acom \<Rightarrow> assn \<Rightarrow> assn \<times> assn" where
-"vcpre Askip Q = (\<lambda>s. True, Q)" |
+"vcpre ASKIP Q = (\<lambda>s. True, Q)" |
 "vcpre (Aassign x a) Q = (\<lambda>s. True, \<lambda>s. Q(s[a/x]))" |
 "vcpre (Asemi c\<^isub>1 c\<^isub>2) Q =
   (let (vc\<^isub>2,wp\<^isub>2) = vcpre c\<^isub>2 Q;
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Import/HOLLightList.thy
--- a/src/HOL/Import/HOLLightList.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Import/HOLLightList.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -326,10 +326,14 @@
 
    The definitions of TL and ZIP are different for empty lists.
  *)
-axioms
+axiomatization where
   DEF_HD: "hd = (SOME HD. \<forall>t h. HD (h # t) = h)"
+
+axiomatization where
   DEF_LAST: "last =
     (SOME LAST. \<forall>h t. LAST (h # t) = (if t = [] then h else LAST t))"
+
+axiomatization where
   DEF_EL: "list_el =
     (SOME EL. (\<forall>l. EL 0 l = hd l) \<and> (\<forall>n l. EL (Suc n) l = EL n (tl l)))"
 
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Library/While_Combinator.thy
--- a/src/HOL/Library/While_Combinator.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Library/While_Combinator.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -52,16 +52,13 @@
   ultimately show ?thesis unfolding while_option_def by auto 
 qed
 
-lemma while_option_stop:
-assumes "while_option b c s = Some t"
-shows "~ b t"
-proof -
-  from assms have ex: "\<exists>k. ~ b ((c ^^ k) s)"
-  and t: "t = (c ^^ (LEAST k. ~ b ((c ^^ k) s))) s"
-    by (auto simp: while_option_def split: if_splits)
-  from LeastI_ex[OF ex]
-  show "~ b t" unfolding t .
-qed
+lemma while_option_stop2:
+ "while_option b c s = Some t \<Longrightarrow> EX k. t = (c^^k) s \<and> \<not> b t"
+apply(simp add: while_option_def split: if_splits)
+by (metis (lam_lifting) LeastI_ex)
+
+lemma while_option_stop: "while_option b c s = Some t \<Longrightarrow> ~ b t"
+by(metis while_option_stop2)
 
 theorem while_option_rule:
 assumes step: "!!s. P s ==> b s ==> P (c s)"
@@ -145,4 +142,31 @@
   \<Longrightarrow> P s \<Longrightarrow> EX t. while_option b c s = Some t"
 by(blast intro: wf_while_option_Some[OF wf_if_measure, of P b f])
 
+text{* Kleene iteration starting from the empty set and assuming some finite
+bounding set: *}
+
+lemma while_option_finite_subset_Some: fixes C :: "'a set"
+  assumes "mono f" and "!!X. X \<subseteq> C \<Longrightarrow> f X \<subseteq> C" and "finite C"
+  shows "\<exists>P. while_option (\<lambda>A. f A \<noteq> A) f {} = Some P"
+proof(rule measure_while_option_Some[where
+    f= "%A::'a set. card C - card A" and P= "%A. A \<subseteq> C \<and> A \<subseteq> f A" and s= "{}"])
+  fix A assume A: "A \<subseteq> C \<and> A \<subseteq> f A" "f A \<noteq> A"
+  show "(f A \<subseteq> C \<and> f A \<subseteq> f (f A)) \<and> card C - card (f A) < card C - card A"
+    (is "?L \<and> ?R")
+  proof
+    show ?L by(metis A(1) assms(2) monoD[OF `mono f`])
+    show ?R by (metis A assms(2,3) card_seteq diff_less_mono2 equalityI linorder_le_less_linear rev_finite_subset)
+  qed
+qed simp
+
+lemma lfp_the_while_option:
+  assumes "mono f" and "!!X. X \<subseteq> C \<Longrightarrow> f X \<subseteq> C" and "finite C"
+  shows "lfp f = the(while_option (\<lambda>A. f A \<noteq> A) f {})"
+proof-
+  obtain P where "while_option (\<lambda>A. f A \<noteq> A) f {} = Some P"
+    using while_option_finite_subset_Some[OF assms] by blast
+  with while_option_stop2[OF this] lfp_Kleene_iter[OF assms(1)]
+  show ?thesis by auto
+qed
+
 end
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/List.thy
--- a/src/HOL/List.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/List.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -1354,6 +1354,10 @@
 apply (case_tac n, auto)
 done
 
+lemma nth_tl:
+  assumes "n < length (tl x)" shows "tl x ! n = x ! Suc n"
+using assms by (induct x) auto
+
 lemma hd_conv_nth: "xs \<noteq> [] \<Longrightarrow> hd xs = xs!0"
 by(cases xs) simp_all
 
@@ -1545,6 +1549,12 @@
 lemma last_appendR[simp]: "ys \<noteq> [] \<Longrightarrow> last(xs @ ys) = last ys"
 by(simp add:last_append)
 
+lemma last_tl: "xs = [] \<or> tl xs \<noteq> [] \<Longrightarrow>last (tl xs) = last xs"
+by (induct xs) simp_all
+
+lemma butlast_tl: "butlast (tl xs) = tl (butlast xs)"
+by (induct xs) simp_all
+
 lemma hd_rev: "xs \<noteq> [] \<Longrightarrow> hd(rev xs) = last xs"
 by(rule rev_exhaust[of xs]) simp_all
 
@@ -1578,6 +1588,15 @@
 apply (auto split:nat.split)
 done
 
+lemma nth_butlast:
+  assumes "n < length (butlast xs)" shows "butlast xs ! n = xs ! n"
+proof (cases xs)
+  case (Cons y ys)
+  moreover from assms have "butlast xs ! n = (butlast xs @ [last xs]) ! n"
+    by (simp add: nth_append)
+  ultimately show ?thesis using append_butlast_last_id by simp
+qed simp
+
 lemma last_conv_nth: "xs\<noteq>[] \<Longrightarrow> last xs = xs!(length xs - 1)"
 by(induct xs)(auto simp:neq_Nil_conv)
 
@@ -1899,6 +1918,17 @@
 "(!!x. x:set xs ==> P(x)) ==> dropWhile P (xs @ ys) = dropWhile P ys"
 by (induct xs) auto
 
+lemma dropWhile_append3:
+  "\<not> P y \<Longrightarrow>dropWhile P (xs @ y # ys) = dropWhile P xs @ y # ys"
+by (induct xs) auto
+
+lemma dropWhile_last:
+  "x \<in> set xs \<Longrightarrow> \<not> P x \<Longrightarrow> last (dropWhile P xs) = last xs"
+by (auto simp add: dropWhile_append3 in_set_conv_decomp)
+
+lemma set_dropWhileD: "x \<in> set (dropWhile P xs) \<Longrightarrow> x \<in> set xs"
+by (induct xs) (auto split: split_if_asm)
+
 lemma set_takeWhileD: "x : set (takeWhile P xs) ==> x : set xs \<and> P x"
 by (induct xs) (auto split: split_if_asm)
 
@@ -2890,6 +2920,30 @@
 apply (metis Cons_eq_appendI eq_Nil_appendI split_list)
 done
 
+lemma not_distinct_conv_prefix:
+  defines "dec as xs y ys \<equiv> y \<in> set xs \<and> distinct xs \<and> as = xs @ y # ys"
+  shows "\<not>distinct as \<longleftrightarrow> (\<exists>xs y ys. dec as xs y ys)" (is "?L = ?R")
+proof
+  assume "?L" then show "?R"
+  proof (induct "length as" arbitrary: as rule: less_induct)
+    case less
+    obtain xs ys zs y where decomp: "as = (xs @ y # ys) @ y # zs"
+      using not_distinct_decomp[OF less.prems] by auto
+    show ?case
+    proof (cases "distinct (xs @ y # ys)")
+      case True
+      with decomp have "dec as (xs @ y # ys) y zs" by (simp add: dec_def)
+      then show ?thesis by blast
+    next
+      case False
+      with less decomp obtain xs' y' ys' where "dec (xs @ y # ys) xs' y' ys'"
+        by atomize_elim auto
+      with decomp have "dec as xs' y' (ys' @ y # zs)" by (simp add: dec_def)
+      then show ?thesis by blast
+    qed
+  qed
+qed (auto simp: dec_def)
+
 lemma length_remdups_concat:
   "length (remdups (concat xss)) = card (\<Union>xs\<in>set xss. set xs)"
   by (simp add: distinct_card [symmetric])
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/MicroJava/J/Example.thy
--- a/src/HOL/MicroJava/J/Example.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/MicroJava/J/Example.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -39,17 +39,19 @@
 datatype cnam' = Base' | Ext'
 datatype vnam' = vee' | x' | e'
 
-consts
-  cnam' :: "cnam' => cname"
-  vnam' :: "vnam' => vnam"
+text {*
+  @{text cnam'} and @{text vnam'} are intended to be isomorphic 
+  to @{text cnam} and @{text vnam}
+*}
 
--- "@{text cnam'} and @{text vnam'} are intended to be isomorphic 
-    to @{text cnam} and @{text vnam}"
-axioms 
-  inj_cnam':  "(cnam' x = cnam' y) = (x = y)"
-  inj_vnam':  "(vnam' x = vnam' y) = (x = y)"
+axiomatization cnam' :: "cnam' => cname"
+where
+  inj_cnam':  "(cnam' x = cnam' y) = (x = y)" and
+  surj_cnam': "\<exists>m. n = cnam' m"
 
-  surj_cnam': "\<exists>m. n = cnam' m"
+axiomatization vnam' :: "vnam' => vnam"
+where
+  inj_vnam':  "(vnam' x = vnam' y) = (x = y)" and
   surj_vnam': "\<exists>m. n = vnam' m"
 
 declare inj_cnam' [simp] inj_vnam' [simp]
@@ -65,11 +67,11 @@
 abbreviation e :: vname
   where "e == VName (vnam' e')"
 
-axioms
-  Base_not_Object: "Base \<noteq> Object"
-  Ext_not_Object:  "Ext  \<noteq> Object"
-  Base_not_Xcpt:   "Base \<noteq> Xcpt z"
-  Ext_not_Xcpt:    "Ext  \<noteq> Xcpt z"
+axiomatization where
+  Base_not_Object: "Base \<noteq> Object" and
+  Ext_not_Object:  "Ext  \<noteq> Object" and
+  Base_not_Xcpt:   "Base \<noteq> Xcpt z" and
+  Ext_not_Xcpt:    "Ext  \<noteq> Xcpt z" and
   e_not_This:      "e \<noteq> This"  
 
 declare Base_not_Object [simp] Ext_not_Object [simp]
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/MicroJava/J/JListExample.thy
--- a/src/HOL/MicroJava/J/JListExample.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/MicroJava/J/JListExample.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -111,7 +111,9 @@
   "HOL.equal l4_nam l3_nam \<longleftrightarrow> False"
   by(simp_all add: distinct_fields distinct_fields[symmetric] distinct_vars distinct_vars[symmetric] equal_vnam_def)
 
-axioms nat_to_loc'_inject: "nat_to_loc' l = nat_to_loc' l' \<longleftrightarrow> l = l'"
+axiomatization where
+  nat_to_loc'_inject: "nat_to_loc' l = nat_to_loc' l' \<longleftrightarrow> l = l'"
+
 lemma equal_loc'_code [code]:
   "HOL.equal (nat_to_loc' l) (nat_to_loc' l') \<longleftrightarrow> l = l'"
   by(simp add: equal_loc'_def nat_to_loc'_inject)
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/MicroJava/JVM/JVMListExample.thy
--- a/src/HOL/MicroJava/JVM/JVMListExample.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/MicroJava/JVM/JVMListExample.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -13,30 +13,31 @@
   anonymous, we describe distinctness of names in the example by axioms:
 *}
 axiomatization list_nam test_nam :: cnam
-where distinct_classes: "list_nam \<noteq> test_nam"
+  where distinct_classes: "list_nam \<noteq> test_nam"
 
 axiomatization append_name makelist_name :: mname
-where distinct_methods: "append_name \<noteq> makelist_name"
+  where distinct_methods: "append_name \<noteq> makelist_name"
 
 axiomatization val_nam next_nam :: vnam
-where distinct_fields: "val_nam \<noteq> next_nam"
+  where distinct_fields: "val_nam \<noteq> next_nam"
 
-axioms nat_to_loc'_inject: "nat_to_loc' l = nat_to_loc' l' \<longleftrightarrow> l = l'"
+axiomatization
+  where nat_to_loc'_inject: "nat_to_loc' l = nat_to_loc' l' \<longleftrightarrow> l = l'"
 
-definition list_name :: cname where
-  "list_name == Cname list_nam"
+definition list_name :: cname
+  where "list_name = Cname list_nam"
   
-definition test_name :: cname where
-  "test_name == Cname test_nam"
+definition test_name :: cname
+  where "test_name = Cname test_nam"
 
-definition val_name :: vname where
-  "val_name == VName val_nam"
+definition val_name :: vname
+  where "val_name = VName val_nam"
 
-definition next_name :: vname where
-  "next_name == VName next_nam"
+definition next_name :: vname
+  where "next_name = VName next_nam"
 
 definition append_ins :: bytecode where
-  "append_ins == 
+  "append_ins =
        [Load 0,
         Getfield next_name list_name,
         Dup,
@@ -53,14 +54,14 @@
         Return]"
 
 definition list_class :: "jvm_method class" where
-  "list_class ==
+  "list_class =
     (Object,
      [(val_name, PrimT Integer), (next_name, Class list_name)],
      [((append_name, [Class list_name]), PrimT Void,
         (3, 0, append_ins,[(1,2,8,Xcpt NullPointer)]))])"
 
 definition make_list_ins :: bytecode where
-  "make_list_ins ==
+  "make_list_ins =
        [New list_name,
         Dup,
         Store 0,
@@ -86,12 +87,12 @@
         Return]"
 
 definition test_class :: "jvm_method class" where
-  "test_class ==
+  "test_class =
     (Object, [],
      [((makelist_name, []), PrimT Void, (3, 2, make_list_ins,[]))])"
 
 definition E :: jvm_prog where
-  "E == SystemClasses @ [(list_name, list_class), (test_name, test_class)]"
+  "E = SystemClasses @ [(list_name, list_class), (test_name, test_class)]"
 
 code_datatype list_nam test_nam
 lemma equal_cnam_code [code]:
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/NanoJava/AxSem.thy
--- a/src/HOL/NanoJava/AxSem.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/NanoJava/AxSem.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -99,17 +99,18 @@
 
 subsection "Fully polymorphic variants, required for Example only"
 
-axioms
-
+axiomatization where
   Conseq:"[| \<forall>Z. A \<turnstile> {P' Z} c {Q' Z};
              \<forall>s t. (\<forall>Z. P' Z s --> Q' Z t) --> (P s --> Q t) |] ==>
                  A \<turnstile> {P} c {Q }"
 
- eConseq:"[| \<forall>Z. A \<turnstile>\<^sub>e {P' Z} e {Q' Z};
+axiomatization where
+  eConseq:"[| \<forall>Z. A \<turnstile>\<^sub>e {P' Z} e {Q' Z};
              \<forall>s v t. (\<forall>Z. P' Z s --> Q' Z v t) --> (P s --> Q v t) |] ==>
                  A \<turnstile>\<^sub>e {P} e {Q }"
 
- Impl: "\<forall>Z. A\<union> (\<Union>Z. (\<lambda>Cm. (P Z Cm, Impl Cm, Q Z Cm))`Ms) |\<turnstile> 
+axiomatization where
+  Impl: "\<forall>Z. A\<union> (\<Union>Z. (\<lambda>Cm. (P Z Cm, Impl Cm, Q Z Cm))`Ms) |\<turnstile> 
                           (\<lambda>Cm. (P Z Cm, body Cm, Q Z Cm))`Ms ==>
                     A |\<turnstile> (\<lambda>Cm. (P Z Cm, Impl Cm, Q Z Cm))`Ms"
 
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Nat.thy
--- a/src/HOL/Nat.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Nat.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -1261,6 +1261,30 @@
   by (induct n) simp_all
 
 
+subsection {* Kleene iteration *}
+
+lemma Kleene_iter_lpfp: assumes "mono f" and "f p \<le> p" shows "(f^^k) bot \<le> p"
+proof(induction k)
+  case 0 show ?case by simp
+next
+  case Suc
+  from monoD[OF assms(1) Suc] assms(2)
+  show ?case by simp
+qed
+
+lemma lfp_Kleene_iter: assumes "mono f" and "(f^^Suc k) bot = (f^^k) bot"
+shows "lfp f = (f^^k) bot"
+proof(rule antisym)
+  show "lfp f \<le> (f^^k) bot"
+  proof(rule lfp_lowerbound)
+    show "f ((f^^k) bot) \<le> (f^^k) bot" using assms(2) by simp
+  qed
+next
+  show "(f^^k) bot \<le> lfp f"
+    using Kleene_iter_lpfp[OF assms(1)] lfp_unfold[OF assms(1)] by simp
+qed
+
+
 subsection {* Embedding of the Naturals into any @{text semiring_1}: @{term of_nat} *}
 
 context semiring_1
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Nominal/nominal_atoms.ML
--- a/src/HOL/Nominal/nominal_atoms.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Nominal/nominal_atoms.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -99,7 +99,7 @@
     
     val (_,thy1) = 
     fold_map (fn ak => fn thy => 
-          let val dt = ([], Binding.name ak, NoSyn, [(Binding.name ak, [@{typ nat}], NoSyn)])
+          let val dt = ((Binding.name ak, [], NoSyn), [(Binding.name ak, [@{typ nat}], NoSyn)])
               val (dt_names, thy1) = Datatype.add_datatype Datatype.default_config [dt] thy;
             
               val injects = maps (#inject o Datatype.the_info thy1) dt_names;
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Nominal/nominal_datatype.ML
--- a/src/HOL/Nominal/nominal_datatype.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Nominal/nominal_datatype.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -6,9 +6,7 @@
 
 signature NOMINAL_DATATYPE =
 sig
-  val add_nominal_datatype : Datatype.config ->
-    (string list * binding * mixfix * (binding * string list * mixfix) list) list ->
-    theory -> theory
+  val add_nominal_datatype : Datatype.config -> Datatype.spec_cmd list -> theory -> theory
   type descr
   type nominal_datatype_info
   val get_nominal_datatypes : theory -> nominal_datatype_info Symtab.table
@@ -37,18 +35,17 @@
 val Collect_False_empty = @{thm empty_def [THEN sym, THEN eq_reflection]};
 val empty_iff = @{thm empty_iff};
 
-open Datatype_Aux;
 open NominalAtoms;
 
 (** FIXME: Datatype should export this function **)
 
 local
 
-fun dt_recs (DtTFree _) = []
-  | dt_recs (DtType (_, dts)) = maps dt_recs dts
-  | dt_recs (DtRec i) = [i];
+fun dt_recs (Datatype_Aux.DtTFree _) = []
+  | dt_recs (Datatype_Aux.DtType (_, dts)) = maps dt_recs dts
+  | dt_recs (Datatype_Aux.DtRec i) = [i];
 
-fun dt_cases (descr: descr) (_, args, constrs) =
+fun dt_cases (descr: Datatype_Aux.descr) (_, args, constrs) =
   let
     fun the_bname i = Long_Name.base_name (#1 (the (AList.lookup (op =) descr i)));
     val bnames = map the_bname (distinct op = (maps dt_recs args));
@@ -72,7 +69,9 @@
 
 (* theory data *)
 
-type descr = (int * (string * dtyp list * (string * (dtyp list * dtyp) list) list)) list;
+type descr =
+  (int * (string * Datatype_Aux.dtyp list *
+      (string * (Datatype_Aux.dtyp list * Datatype_Aux.dtyp) list) list)) list;
 
 type nominal_datatype_info =
   {index : int,
@@ -186,30 +185,16 @@
 fun fresh_star_const T U =
   Const ("Nominal.fresh_star", HOLogic.mk_setT T --> U --> HOLogic.boolT);
 
-fun gen_add_nominal_datatype prep_typ config dts thy =
+fun gen_add_nominal_datatype prep_specs config dts thy =
   let
-    val new_type_names = map (Binding.name_of o #2) dts;
-
+    val new_type_names = map (fn ((tname, _, _), _) => Binding.name_of tname) dts;
 
-    (* this theory is used just for parsing *)
-
-    val tmp_thy = thy |>
-      Theory.copy |>
-      Sign.add_types_global (map (fn (tvs, tname, mx, _) => (tname, length tvs, mx)) dts);
+    val (dts', _) = prep_specs dts thy;
 
     val atoms = atoms_of thy;
 
-    fun prep_constr (cname, cargs, mx) (constrs, sorts) =
-      let val (cargs', sorts') = fold_map (prep_typ tmp_thy) cargs sorts
-      in (constrs @ [(cname, cargs', mx)], sorts') end
-
-    fun prep_dt_spec (tvs, tname, mx, constrs) (dts, sorts) =
-      let val (constrs', sorts') = fold prep_constr constrs ([], sorts)
-      in (dts @ [(tvs, tname, mx, constrs')], sorts') end
-
-    val (dts', sorts) = fold prep_dt_spec dts ([], []);
-    val tyvars = map (map (fn s =>
-      (s, the (AList.lookup (op =) sorts s))) o #1) dts';
+    val tyvars = map (fn ((_, tvs, _), _) => tvs) dts';
+    val sorts = flat tyvars;
 
     fun inter_sort thy S S' = Sign.inter_sort thy (S, S');
     fun augment_sort_typ thy S =
@@ -219,12 +204,12 @@
       end;
     fun augment_sort thy S = map_types (augment_sort_typ thy S);
 
-    val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts';
-    val constr_syntax = map (fn (tvs, tname, mx, constrs) =>
+    val types_syntax = map (fn ((tname, tvs, mx), constrs) => (tname, mx)) dts';
+    val constr_syntax = map (fn (_, constrs) =>
       map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts';
 
-    val ps = map (fn (_, n, _, _) =>
-      (Sign.full_name tmp_thy n, Sign.full_name tmp_thy (Binding.suffix_name "_Rep" n))) dts;
+    val ps = map (fn ((n, _, _), _) =>
+      (Sign.full_name thy n, Sign.full_name thy (Binding.suffix_name "_Rep" n))) dts;
     val rps = map Library.swap ps;
 
     fun replace_types (Type ("Nominal.ABS", [T, U])) =
@@ -233,8 +218,8 @@
           Type (the_default s (AList.lookup op = ps s), map replace_types Ts)
       | replace_types T = T;
 
-    val dts'' = map (fn (tvs, tname, mx, constrs) =>
-      (tvs, Binding.suffix_name "_Rep" tname, NoSyn,
+    val dts'' = map (fn ((tname, tvs, mx), constrs) =>
+      ((Binding.suffix_name "_Rep" tname, tvs, NoSyn),
         map (fn (cname, cargs, mx) => (Binding.suffix_name "_Rep" cname,
           map replace_types cargs, NoSyn)) constrs)) dts';
 
@@ -243,7 +228,7 @@
     val (full_new_type_names',thy1) = Datatype.add_datatype config dts'' thy;
 
     val {descr, induct, ...} = Datatype.the_info thy1 (hd full_new_type_names');
-    fun nth_dtyp i = typ_of_dtyp descr (DtRec i);
+    fun nth_dtyp i = Datatype_Aux.typ_of_dtyp descr (Datatype_Aux.DtRec i);
 
     val big_name = space_implode "_" new_type_names;
 
@@ -256,7 +241,7 @@
       let val T = nth_dtyp i
       in permT --> T --> T end) descr;
     val perm_names' = Datatype_Prop.indexify_names (map (fn (i, _) =>
-      "perm_" ^ name_of_typ (nth_dtyp i)) descr);
+      "perm_" ^ Datatype_Aux.name_of_typ (nth_dtyp i)) descr);
     val perm_names = replicate (length new_type_names) "Nominal.perm" @
       map (Sign.full_bname thy1) (List.drop (perm_names', length new_type_names));
     val perm_names_types = perm_names ~~ perm_types;
@@ -266,16 +251,16 @@
       let val T = nth_dtyp i
       in map (fn (cname, dts) =>
         let
-          val Ts = map (typ_of_dtyp descr) dts;
+          val Ts = map (Datatype_Aux.typ_of_dtyp descr) dts;
           val names = Name.variant_list ["pi"] (Datatype_Prop.make_tnames Ts);
           val args = map Free (names ~~ Ts);
           val c = Const (cname, Ts ---> T);
           fun perm_arg (dt, x) =
             let val T = type_of x
-            in if is_rec_type dt then
+            in if Datatype_Aux.is_rec_type dt then
                 let val Us = binder_types T
                 in list_abs (map (pair "x") Us,
-                  Free (nth perm_names_types' (body_index dt)) $ pi $
+                  Free (nth perm_names_types' (Datatype_Aux.body_index dt)) $ pi $
                     list_comb (x, map (fn (i, U) =>
                       Const ("Nominal.perm", permT --> U --> U) $
                         (Const ("List.rev", permT --> permT) $ pi) $
@@ -309,7 +294,7 @@
 
     val unfolded_perm_eq_thms =
       if length descr = length new_type_names then []
-      else map Drule.export_without_context (List.drop (split_conj_thm
+      else map Drule.export_without_context (List.drop (Datatype_Aux.split_conj_thm
         (Goal.prove_global thy2 [] []
           (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
             (map (fn (c as (s, T), x) =>
@@ -329,7 +314,7 @@
 
     val perm_empty_thms = maps (fn a =>
       let val permT = mk_permT (Type (a, []))
-      in map Drule.export_without_context (List.take (split_conj_thm
+      in map Drule.export_without_context (List.take (Datatype_Aux.split_conj_thm
         (Goal.prove_global thy2 [] []
           (augment_sort thy2 [pt_class_of thy2 a]
             (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
@@ -361,7 +346,7 @@
         val pt_inst = pt_inst_of thy2 a;
         val pt2' = pt_inst RS pt2;
         val pt2_ax = Global_Theory.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "2") a);
-      in List.take (map Drule.export_without_context (split_conj_thm
+      in List.take (map Drule.export_without_context (Datatype_Aux.split_conj_thm
         (Goal.prove_global thy2 [] []
            (augment_sort thy2 [pt_class_of thy2 a]
              (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
@@ -396,7 +381,7 @@
         val pt3' = pt_inst RS pt3;
         val pt3_rev' = at_inst RS (pt_inst RS pt3_rev);
         val pt3_ax = Global_Theory.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "3") a);
-      in List.take (map Drule.export_without_context (split_conj_thm
+      in List.take (map Drule.export_without_context (Datatype_Aux.split_conj_thm
         (Goal.prove_global thy2 [] []
           (augment_sort thy2 [pt_class_of thy2 a] (Logic.mk_implies
              (HOLogic.mk_Trueprop (Const ("Nominal.prm_eq",
@@ -447,7 +432,7 @@
                 at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym]
             end))
         val sort = Sign.minimize_sort thy (Sign.certify_sort thy (cp_class :: pt_class));
-        val thms = split_conj_thm (Goal.prove_global thy [] []
+        val thms = Datatype_Aux.split_conj_thm (Goal.prove_global thy [] []
           (augment_sort thy sort
             (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
               (map (fn ((s, T), x) =>
@@ -499,24 +484,26 @@
 
     val _ = warning "representing sets";
 
-    val rep_set_names = Datatype_Prop.indexify_names
-      (map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr);
+    val rep_set_names =
+      Datatype_Prop.indexify_names
+        (map (fn (i, _) => Datatype_Aux.name_of_typ (nth_dtyp i) ^ "_set") descr);
     val big_rep_name =
       space_implode "_" (Datatype_Prop.indexify_names (map_filter
         (fn (i, ("Nominal.noption", _, _)) => NONE
-          | (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set";
+          | (i, _) => SOME (Datatype_Aux.name_of_typ (nth_dtyp i))) descr)) ^ "_set";
     val _ = warning ("big_rep_name: " ^ big_rep_name);
 
-    fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) =
+    fun strip_option (dtf as Datatype_Aux.DtType ("fun", [dt, Datatype_Aux.DtRec i])) =
           (case AList.lookup op = descr i of
              SOME ("Nominal.noption", _, [(_, [dt']), _]) =>
                apfst (cons dt) (strip_option dt')
            | _ => ([], dtf))
-      | strip_option (DtType ("fun", [dt, DtType ("Nominal.noption", [dt'])])) =
+      | strip_option (Datatype_Aux.DtType ("fun",
+            [dt, Datatype_Aux.DtType ("Nominal.noption", [dt'])])) =
           apfst (cons dt) (strip_option dt')
       | strip_option dt = ([], dt);
 
-    val dt_atomTs = distinct op = (map (typ_of_dtyp descr)
+    val dt_atomTs = distinct op = (map (Datatype_Aux.typ_of_dtyp descr)
       (maps (fn (_, (_, _, cs)) => maps (maps (fst o strip_option) o snd) cs) descr));
     val dt_atoms = map (fst o dest_Type) dt_atomTs;
 
@@ -525,20 +512,20 @@
         fun mk_prem dt (j, j', prems, ts) =
           let
             val (dts, dt') = strip_option dt;
-            val (dts', dt'') = strip_dtyp dt';
-            val Ts = map (typ_of_dtyp descr) dts;
-            val Us = map (typ_of_dtyp descr) dts';
-            val T = typ_of_dtyp descr dt'';
-            val free = mk_Free "x" (Us ---> T) j;
-            val free' = app_bnds free (length Us);
+            val (dts', dt'') = Datatype_Aux.strip_dtyp dt';
+            val Ts = map (Datatype_Aux.typ_of_dtyp descr) dts;
+            val Us = map (Datatype_Aux.typ_of_dtyp descr) dts';
+            val T = Datatype_Aux.typ_of_dtyp descr dt'';
+            val free = Datatype_Aux.mk_Free "x" (Us ---> T) j;
+            val free' = Datatype_Aux.app_bnds free (length Us);
             fun mk_abs_fun T (i, t) =
               let val U = fastype_of t
               in (i + 1, Const ("Nominal.abs_fun", [T, U, T] --->
-                Type ("Nominal.noption", [U])) $ mk_Free "y" T i $ t)
+                Type ("Nominal.noption", [U])) $ Datatype_Aux.mk_Free "y" T i $ t)
               end
           in (j + 1, j' + length Ts,
             case dt'' of
-                DtRec k => list_all (map (pair "x") Us,
+                Datatype_Aux.DtRec k => list_all (map (pair "x") Us,
                   HOLogic.mk_Trueprop (Free (nth rep_set_names k,
                     T --> HOLogic.boolT) $ free')) :: prems
               | _ => prems,
@@ -584,7 +571,7 @@
       (perm_indnames ~~ descr);
 
     fun mk_perm_closed name = map (fn th => Drule.export_without_context (th RS mp))
-      (List.take (split_conj_thm (Goal.prove_global thy4 [] []
+      (List.take (Datatype_Aux.split_conj_thm (Goal.prove_global thy4 [] []
         (augment_sort thy4
           (pt_class_of thy4 name :: map (cp_class_of thy4 name) (remove (op =) name dt_atoms))
           (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
@@ -717,8 +704,8 @@
       (fn ((i, ("Nominal.noption", _, _)), p) => p
         | ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr;
 
-    fun reindex (DtType (s, dts)) = DtType (s, map reindex dts)
-      | reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i))
+    fun reindex (Datatype_Aux.DtType (s, dts)) = Datatype_Aux.DtType (s, map reindex dts)
+      | reindex (Datatype_Aux.DtRec i) = Datatype_Aux.DtRec (the (AList.lookup op = ty_idxs i))
       | reindex dt = dt;
 
     fun strip_suffix i s = implode (List.take (raw_explode s, size s - i));  (* FIXME Symbol.explode (?) *)
@@ -754,14 +741,14 @@
       map (fn ((cname, cargs), idxs) => (cname, partition_cargs idxs cargs))
         (constrs ~~ idxss)))) (descr'' ~~ ndescr);
 
-    fun nth_dtyp' i = typ_of_dtyp descr'' (DtRec i);
+    fun nth_dtyp' i = Datatype_Aux.typ_of_dtyp descr'' (Datatype_Aux.DtRec i);
 
     val rep_names = map (fn s =>
       Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names;
     val abs_names = map (fn s =>
       Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names;
 
-    val recTs = get_rec_types descr'';
+    val recTs = Datatype_Aux.get_rec_types descr'';
     val newTs' = take (length new_type_names) recTs';
     val newTs = take (length new_type_names) recTs;
 
@@ -772,17 +759,18 @@
       let
         fun constr_arg (dts, dt) (j, l_args, r_args) =
           let
-            val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp descr'' dt) i)
-              (dts ~~ (j upto j + length dts - 1))
-            val x = mk_Free "x" (typ_of_dtyp descr'' dt) (j + length dts)
+            val xs =
+              map (fn (dt, i) => Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) i)
+                (dts ~~ (j upto j + length dts - 1))
+            val x = Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts)
           in
             (j + length dts + 1,
              xs @ x :: l_args,
              fold_rev mk_abs_fun xs
                (case dt of
-                  DtRec k => if k < length new_type_names then
-                      Const (nth rep_names k, typ_of_dtyp descr'' dt -->
-                        typ_of_dtyp descr dt) $ x
+                  Datatype_Aux.DtRec k => if k < length new_type_names then
+                      Const (nth rep_names k, Datatype_Aux.typ_of_dtyp descr'' dt -->
+                        Datatype_Aux.typ_of_dtyp descr dt) $ x
                     else error "nested recursion not (yet) supported"
                 | _ => x) :: r_args)
           end
@@ -900,10 +888,12 @@
 
           fun constr_arg (dts, dt) (j, l_args, r_args) =
             let
-              val Ts = map (typ_of_dtyp descr'') dts;
-              val xs = map (fn (T, i) => mk_Free "x" T i)
-                (Ts ~~ (j upto j + length dts - 1))
-              val x = mk_Free "x" (typ_of_dtyp descr'' dt) (j + length dts)
+              val Ts = map (Datatype_Aux.typ_of_dtyp descr'') dts;
+              val xs =
+                map (fn (T, i) => Datatype_Aux.mk_Free "x" T i)
+                  (Ts ~~ (j upto j + length dts - 1));
+              val x =
+                Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts);
             in
               (j + length dts + 1,
                xs @ x :: l_args,
@@ -950,11 +940,14 @@
 
           fun make_inj (dts, dt) (j, args1, args2, eqs) =
             let
-              val Ts_idx = map (typ_of_dtyp descr'') dts ~~ (j upto j + length dts - 1);
-              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
-              val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx;
-              val x = mk_Free "x" (typ_of_dtyp descr'' dt) (j + length dts);
-              val y = mk_Free "y" (typ_of_dtyp descr'' dt) (j + length dts);
+              val Ts_idx =
+                map (Datatype_Aux.typ_of_dtyp descr'') dts ~~ (j upto j + length dts - 1);
+              val xs = map (fn (T, i) => Datatype_Aux.mk_Free "x" T i) Ts_idx;
+              val ys = map (fn (T, i) => Datatype_Aux.mk_Free "y" T i) Ts_idx;
+              val x =
+                Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts);
+              val y =
+                Datatype_Aux.mk_Free "y" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts);
             in
               (j + length dts + 1,
                xs @ (x :: args1), ys @ (y :: args2),
@@ -993,9 +986,11 @@
 
           fun process_constr (dts, dt) (j, args1, args2) =
             let
-              val Ts_idx = map (typ_of_dtyp descr'') dts ~~ (j upto j + length dts - 1);
-              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
-              val x = mk_Free "x" (typ_of_dtyp descr'' dt) (j + length dts);
+              val Ts_idx =
+                map (Datatype_Aux.typ_of_dtyp descr'') dts ~~ (j upto j + length dts - 1);
+              val xs = map (fn (T, i) => Datatype_Aux.mk_Free "x" T i) Ts_idx;
+              val x =
+                Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts);
             in
               (j + length dts + 1,
                xs @ (x :: args1), fold_rev mk_abs_fun xs x :: args2)
@@ -1034,14 +1029,16 @@
 
     fun mk_indrule_lemma (((i, _), T), U) (prems, concls) =
       let
-        val Rep_t = Const (nth rep_names i, T --> U) $ mk_Free "x" T i;
+        val Rep_t = Const (nth rep_names i, T --> U) $ Datatype_Aux.mk_Free "x" T i;
 
         val Abs_t =  Const (nth abs_names i, U --> T);
 
-      in (prems @ [HOLogic.imp $
+      in
+        (prems @ [HOLogic.imp $
             (Const (nth rep_set_names'' i, U --> HOLogic.boolT) $ Rep_t) $
-              (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
-          concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i])
+              (Datatype_Aux.mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
+         concls @
+           [Datatype_Aux.mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ Datatype_Aux.mk_Free "x" T i])
       end;
 
     val (indrule_lemma_prems, indrule_lemma_concls) =
@@ -1049,8 +1046,8 @@
 
     val indrule_lemma = Goal.prove_global thy8 [] []
       (Logic.mk_implies
-        (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems),
-         HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY
+        (HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_prems),
+         HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_concls))) (fn _ => EVERY
            [REPEAT (etac conjE 1),
             REPEAT (EVERY
               [TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1,
@@ -1090,7 +1087,7 @@
     val finite_supp_thms = map (fn atom =>
       let val atomT = Type (atom, [])
       in map Drule.export_without_context (List.take
-        (split_conj_thm (Goal.prove_global thy8 [] []
+        (Datatype_Aux.split_conj_thm (Goal.prove_global thy8 [] []
            (augment_sort thy8 (fs_class_of thy8 atom :: pt_cp_sort)
              (HOLogic.mk_Trueprop
                (foldr1 HOLogic.mk_conj (map (fn (s, T) =>
@@ -1160,11 +1157,11 @@
 
     fun make_ind_prem fsT f k T ((cname, cargs), idxs) =
       let
-        val recs = filter is_rec_type cargs;
-        val Ts = map (typ_of_dtyp descr'') cargs;
-        val recTs' = map (typ_of_dtyp descr'') recs;
+        val recs = filter Datatype_Aux.is_rec_type cargs;
+        val Ts = map (Datatype_Aux.typ_of_dtyp descr'') cargs;
+        val recTs' = map (Datatype_Aux.typ_of_dtyp descr'') recs;
         val tnames = Name.variant_list pnames (Datatype_Prop.make_tnames Ts);
-        val rec_tnames = map fst (filter (is_rec_type o snd) (tnames ~~ cargs));
+        val rec_tnames = map fst (filter (Datatype_Aux.is_rec_type o snd) (tnames ~~ cargs));
         val frees = tnames ~~ Ts;
         val frees' = partition_cargs idxs frees;
         val z = (singleton (Name.variant_list tnames) "z", fsT);
@@ -1172,9 +1169,12 @@
         fun mk_prem ((dt, s), T) =
           let
             val (Us, U) = strip_type T;
-            val l = length Us
-          in list_all (z :: map (pair "x") Us, HOLogic.mk_Trueprop
-            (make_pred fsT (body_index dt) U $ Bound l $ app_bnds (Free (s, T)) l))
+            val l = length Us;
+          in
+            list_all (z :: map (pair "x") Us,
+              HOLogic.mk_Trueprop
+                (make_pred fsT (Datatype_Aux.body_index dt) U $ Bound l $
+                  Datatype_Aux.app_bnds (Free (s, T)) l))
           end;
 
         val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs');
@@ -1432,7 +1432,7 @@
           (1 upto (length descr''));
     val rec_set_names =  map (Sign.full_bname thy10) rec_set_names';
 
-    val rec_fns = map (uncurry (mk_Free "f"))
+    val rec_fns = map (uncurry (Datatype_Aux.mk_Free "f"))
       (rec_fn_Ts ~~ (1 upto (length rec_fn_Ts)));
     val rec_sets' = map (fn c => list_comb (Free c, rec_fns))
       (rec_set_names' ~~ rec_set_Ts);
@@ -1457,13 +1457,13 @@
     fun make_rec_intr T p rec_set ((cname, cargs), idxs)
         (rec_intr_ts, rec_prems, rec_prems', rec_eq_prems, l) =
       let
-        val Ts = map (typ_of_dtyp descr'') cargs;
+        val Ts = map (Datatype_Aux.typ_of_dtyp descr'') cargs;
         val frees = map (fn i => "x" ^ string_of_int i) (1 upto length Ts) ~~ Ts;
         val frees' = partition_cargs idxs frees;
         val binders = maps fst frees';
         val atomTs = distinct op = (maps (map snd o fst) frees');
         val recs = map_filter
-          (fn ((_, DtRec i), p) => SOME (i, p) | _ => NONE)
+          (fn ((_, Datatype_Aux.DtRec i), p) => SOME (i, p) | _ => NONE)
           (partition_cargs idxs cargs ~~ frees');
         val frees'' = map (fn i => "y" ^ string_of_int i) (1 upto length recs) ~~
           map (fn (i, _) => nth rec_result_Ts i) recs;
@@ -1525,7 +1525,7 @@
       let
         val permT = mk_permT aT;
         val pi = Free ("pi", permT);
-        val rec_fns_pi = map (mk_perm [] pi o uncurry (mk_Free "f"))
+        val rec_fns_pi = map (mk_perm [] pi o uncurry (Datatype_Aux.mk_Free "f"))
           (rec_fn_Ts ~~ (1 upto (length rec_fn_Ts)));
         val rec_sets_pi = map (fn c => list_comb (Const c, rec_fns_pi))
           (rec_set_names ~~ rec_set_Ts);
@@ -1536,7 +1536,7 @@
           in
             (R $ x $ y, R' $ mk_perm [] pi x $ mk_perm [] pi y)
           end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ rec_sets_pi ~~ (1 upto length recTs));
-        val ths = map (fn th => Drule.export_without_context (th RS mp)) (split_conj_thm
+        val ths = map (fn th => Drule.export_without_context (th RS mp)) (Datatype_Aux.split_conj_thm
           (Goal.prove_global thy11 [] []
             (augment_sort thy1 pt_cp_sort
               (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map HOLogic.mk_imp ps))))
@@ -1568,7 +1568,7 @@
           (finite $ (Const ("Nominal.supp", T --> aset) $ f)))
             (rec_fns ~~ rec_fn_Ts)
       in
-        map (fn th => Drule.export_without_context (th RS mp)) (split_conj_thm
+        map (fn th => Drule.export_without_context (th RS mp)) (Datatype_Aux.split_conj_thm
           (Goal.prove_global thy11 []
             (map (augment_sort thy11 fs_cp_sort) fins)
             (augment_sort thy11 fs_cp_sort
@@ -1705,7 +1705,7 @@
         (Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $
            (Const ("Nominal.supp", fsT' --> HOLogic.mk_setT aT) $ rec_ctxt))) dt_atomTs;
 
-    val rec_unique_thms = split_conj_thm (Goal.prove
+    val rec_unique_thms = Datatype_Aux.split_conj_thm (Goal.prove
       (Proof_Context.init_global thy11) (map fst rec_unique_frees)
       (map (augment_sort thy11 fs_cp_sort)
         (flat finite_premss @ finite_ctxt_prems @ rec_prems @ rec_prems'))
@@ -1718,7 +1718,7 @@
              apfst (pair T) (chop k xs)) dt_atomTs prems;
            val (finite_ctxt_ths, ths2) = chop (length dt_atomTs) ths1;
            val (P_ind_ths, fcbs) = chop k ths2;
-           val P_ths = map (fn th => th RS mp) (split_conj_thm
+           val P_ths = map (fn th => th RS mp) (Datatype_Aux.split_conj_thm
              (Goal.prove context
                (map fst (rec_unique_frees'' @ rec_unique_frees')) []
                (augment_sort thy11 fs_cp_sort
@@ -2065,11 +2065,11 @@
     thy13
   end;
 
-val add_nominal_datatype = gen_add_nominal_datatype Datatype.read_typ;
+val add_nominal_datatype = gen_add_nominal_datatype Datatype.read_specs;
 
 val _ =
   Outer_Syntax.command "nominal_datatype" "define inductive datatypes" Keyword.thy_decl
-    (Parse.and_list1 Datatype.parse_decl
+    (Parse.and_list1 Datatype.spec_cmd
       >> (Toplevel.theory o add_nominal_datatype Datatype.default_config));
 
 end
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/SET_Protocol/Public_SET.thy
--- a/src/HOL/SET_Protocol/Public_SET.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/SET_Protocol/Public_SET.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -46,7 +46,7 @@
    done                       
 (*>*)
 
-axioms
+axiomatization where
   (*No private key equals any public key (essential to ensure that private
     keys are private!) *)
   privateKey_neq_publicKey [iff]:
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/SPARK/Tools/spark_vcs.ML
--- a/src/HOL/SPARK/Tools/spark_vcs.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/SPARK/Tools/spark_vcs.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -306,8 +306,7 @@
               in
                 (thy |>
                  Datatype.add_datatype {strict = true, quiet = true}
-                   [([], tyb, NoSyn,
-                     map (fn s => (Binding.name s, [], NoSyn)) els)] |> snd |>
+                   [((tyb, [], NoSyn), map (fn s => (Binding.name s, [], NoSyn)) els)] |> snd |>
                  add_enum_type s tyname,
                  tyname)
               end
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Tools/ATP/atp_problem.ML
--- a/src/HOL/Tools/ATP/atp_problem.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Tools/ATP/atp_problem.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -107,8 +107,7 @@
     (string * string) problem -> (string * string) problem
   val filter_cnf_ueq_problem :
     (string * string) problem -> (string * string) problem
-  val declare_undeclared_syms_in_atp_problem :
-    string -> string -> (string * string) problem -> (string * string) problem
+  val declared_syms_in_problem : (string * ''a) problem -> (string * ''a) list
   val nice_atp_problem :
     bool -> ('a * (string * string) problem_line list) list
     -> ('a * string problem_line list) list
@@ -613,59 +612,11 @@
 
 (** Symbol declarations **)
 
-(* TFF allows implicit declarations of types, function symbols, and predicate
-   symbols (with "$i" as the type of individuals), but some provers (e.g.,
-   SNARK) require explicit declarations. The situation is similar for THF. *)
-fun default_type pred_sym =
-  let
-    fun typ 0 = if pred_sym then bool_atype else individual_atype
-      | typ ary = AFun (individual_atype, typ (ary - 1))
-  in typ end
-
 fun add_declared_syms_in_problem_line (Decl (_, sym, _)) = insert (op =) sym
   | add_declared_syms_in_problem_line _ = I
 fun declared_syms_in_problem problem =
   fold (fold add_declared_syms_in_problem_line o snd) problem []
 
-fun nary_type_constr_type n =
-  funpow n (curry AFun atype_of_types) atype_of_types
-
-fun undeclared_syms_in_problem declared problem =
-  let
-    fun do_sym name ty =
-      if member (op =) declared name then I else AList.default (op =) (name, ty)
-    fun do_type (AType (name as (s, _), tys)) =
-        is_tptp_user_symbol s
-        ? do_sym name (fn _ => nary_type_constr_type (length tys))
-        #> fold do_type tys
-      | do_type (AFun (ty1, ty2)) = do_type ty1 #> do_type ty2
-      | do_type (ATyAbs (_, ty)) = do_type ty
-    fun do_term pred_sym (ATerm (name as (s, _), tms)) =
-        is_tptp_user_symbol s
-        ? do_sym name (fn _ => default_type pred_sym (length tms))
-        #> fold (do_term false) tms
-      | do_term _ (AAbs ((_, ty), tm)) = do_type ty #> do_term false tm
-    fun do_formula (AQuant (_, xs, phi)) =
-        fold do_type (map_filter snd xs) #> do_formula phi
-      | do_formula (AConn (_, phis)) = fold do_formula phis
-      | do_formula (AAtom tm) = do_term true tm
-    fun do_problem_line (Decl (_, _, ty)) = do_type ty
-      | do_problem_line (Formula (_, _, phi, _, _)) = do_formula phi
-  in
-    fold (fold do_problem_line o snd) problem []
-    |> filter_out (is_built_in_tptp_symbol o fst o fst)
-  end
-
-fun declare_undeclared_syms_in_atp_problem prefix heading problem =
-  let
-    fun decl_line (x as (s, _), ty) = Decl (prefix ^ s, x, ty ())
-    val declared = problem |> declared_syms_in_problem
-    val decls =
-      problem |> undeclared_syms_in_problem declared
-              |> sort_wrt (fst o fst)
-              |> map decl_line
-  in (heading, decls) :: problem end
-
 (** Nice names **)
 
 fun empty_name_pool readable_names =
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Tools/ATP/atp_translate.ML
--- a/src/HOL/Tools/ATP/atp_translate.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Tools/ATP/atp_translate.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -1905,7 +1905,8 @@
              AConn (AImplies,
                     [type_class_formula type_enc subclass ty_arg,
                      type_class_formula type_enc superclass ty_arg])
-             |> close_formula_universally,
+             |> mk_aquant AForall
+                          [(tvar_a_name, atype_of_type_vars type_enc)],
              isabelle_info format introN, NONE)
   end
 
@@ -2022,7 +2023,9 @@
     |> is_type_enc_fairly_sound type_enc
        ? (fold (fold add_fact_syms) [conjs, facts]
           #> (case type_enc of
-                Simple_Types (First_Order, Polymorphic, _) => add_TYPE_const ()
+                Simple_Types (First_Order, Polymorphic, _) =>
+                if avoid_first_order_ghost_type_vars then add_TYPE_const ()
+                else I
               | Simple_Types _ => I
               | _ => fold add_undefined_const (var_types ())))
   end
@@ -2281,9 +2284,7 @@
 fun problem_lines_for_sym_decls ctxt format conj_sym_kind mono type_enc
                                 (s, decls) =
   case type_enc of
-    Simple_Types _ =>
-    decls |> rationalize_decls ctxt
-          |> map (decl_line_for_sym ctxt format mono type_enc s)
+    Simple_Types _ => [decl_line_for_sym ctxt format mono type_enc s (hd decls)]
   | Guards (_, level) =>
     let
       val decls = decls |> rationalize_decls ctxt
@@ -2333,6 +2334,58 @@
 val conjsN = "Conjectures"
 val free_typesN = "Type variables"
 
+(* TFF allows implicit declarations of types, function symbols, and predicate
+   symbols (with "$i" as the type of individuals), but some provers (e.g.,
+   SNARK) require explicit declarations. The situation is similar for THF. *)
+
+fun default_type pred_sym s =
+  let
+    val ind =
+      if String.isPrefix type_const_prefix s then atype_of_types
+      else individual_atype
+    fun typ 0 = if pred_sym then bool_atype else ind
+      | typ ary = AFun (ind, typ (ary - 1))
+  in typ end
+
+fun nary_type_constr_type n =
+  funpow n (curry AFun atype_of_types) atype_of_types
+
+fun undeclared_syms_in_problem problem =
+  let
+    val declared = declared_syms_in_problem problem
+    fun do_sym name ty =
+      if member (op =) declared name then I else AList.default (op =) (name, ty)
+    fun do_type (AType (name as (s, _), tys)) =
+        is_tptp_user_symbol s
+        ? do_sym name (fn () => nary_type_constr_type (length tys))
+        #> fold do_type tys
+      | do_type (AFun (ty1, ty2)) = do_type ty1 #> do_type ty2
+      | do_type (ATyAbs (_, ty)) = do_type ty
+    fun do_term pred_sym (ATerm (name as (s, _), tms)) =
+        is_tptp_user_symbol s
+        ? do_sym name (fn _ => default_type pred_sym s (length tms))
+        #> fold (do_term false) tms
+      | do_term _ (AAbs ((_, ty), tm)) = do_type ty #> do_term false tm
+    fun do_formula (AQuant (_, xs, phi)) =
+        fold do_type (map_filter snd xs) #> do_formula phi
+      | do_formula (AConn (_, phis)) = fold do_formula phis
+      | do_formula (AAtom tm) = do_term true tm
+    fun do_problem_line (Decl (_, _, ty)) = do_type ty
+      | do_problem_line (Formula (_, _, phi, _, _)) = do_formula phi
+  in
+    fold (fold do_problem_line o snd) problem []
+    |> filter_out (is_built_in_tptp_symbol o fst o fst)
+  end
+
+fun declare_undeclared_syms_in_atp_problem problem =
+  let
+    val decls =
+      problem
+      |> undeclared_syms_in_problem
+      |> sort_wrt (fst o fst)
+      |> map (fn (x as (s, _), ty) => Decl (type_decl_prefix ^ s, x, ty ()))
+  in (implicit_declsN, decls) :: problem end
+
 val explicit_apply_threshold = 50
 
 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc exporter
@@ -2411,8 +2464,7 @@
           | FOF => I
           | TFF (_, TPTP_Implicit) => I
           | THF (_, TPTP_Implicit, _) => I
-          | _ => declare_undeclared_syms_in_atp_problem type_decl_prefix
-                                                        implicit_declsN)
+          | _ => declare_undeclared_syms_in_atp_problem)
     val (problem, pool) = problem |> nice_atp_problem readable_names
     fun add_sym_ary (s, {min_ary, ...} : sym_info) =
       min_ary > 0 ? Symtab.insert (op =) (s, min_ary)
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Tools/Datatype/datatype.ML
--- a/src/HOL/Tools/Datatype/datatype.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Tools/Datatype/datatype.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -10,13 +10,17 @@
 signature DATATYPE =
 sig
   include DATATYPE_DATA
-  val add_datatype: config ->
-    (string list * binding * mixfix * (binding * typ list * mixfix) list) list ->
-    theory -> string list * theory
-  val add_datatype_cmd:
-    (string list * binding * mixfix * (binding * string list * mixfix) list) list ->
-    theory -> theory
-  val parse_decl: (string list * binding * mixfix * (binding * string list * mixfix) list) parser
+  type spec =
+    (binding * (string * sort) list * mixfix) *
+    (binding * typ list * mixfix) list
+  type spec_cmd =
+    (binding * (string * string option) list * mixfix) *
+    (binding * string list * mixfix) list
+  val read_specs: spec_cmd list -> theory -> spec list * Proof.context
+  val check_specs: spec list -> theory -> spec list * Proof.context
+  val add_datatype: config -> spec list -> theory -> string list * theory
+  val add_datatype_cmd: spec_cmd list -> theory -> theory
+  val spec_cmd: spec_cmd parser
 end;
 
 structure Datatype : DATATYPE =
@@ -670,27 +674,74 @@
 
 (** datatype definition **)
 
-fun gen_add_datatype prep_typ config dts thy =
+(* specifications *)
+
+type spec = (binding * (string * sort) list * mixfix) * (binding * typ list * mixfix) list;
+
+type spec_cmd =
+  (binding * (string * string option) list * mixfix) * (binding * string list * mixfix) list;
+
+local
+
+fun parse_spec ctxt ((b, args, mx), constrs) =
+  ((b, map (apsnd (Typedecl.read_constraint ctxt)) args, mx),
+    constrs |> map (fn (c, Ts, mx') => (c, map (Syntax.parse_typ ctxt) Ts, mx')));
+
+fun check_specs ctxt (specs: spec list) =
+  let
+    fun prep_spec ((tname, args, mx), constrs) tys =
+      let
+        val (args', tys1) = chop (length args) tys;
+        val (constrs', tys3) = (constrs, tys1) |-> fold_map (fn (cname, cargs, mx') => fn tys2 =>
+          let val (cargs', tys3) = chop (length cargs) tys2;
+          in ((cname, cargs', mx'), tys3) end);
+      in (((tname, map dest_TFree args', mx), constrs'), tys3) end;
+
+    val all_tys =
+      specs |> maps (fn ((_, args, _), cs) => map TFree args @ maps #2 cs)
+      |> Syntax.check_typs ctxt;
+
+  in #1 (fold_map prep_spec specs all_tys) end;
+
+fun prep_specs parse raw_specs thy =
+  let
+    val ctxt = thy
+      |> Theory.copy
+      |> Sign.add_types_global (map (fn ((b, args, mx), _) => (b, length args, mx)) raw_specs)
+      |> Proof_Context.init_global
+      |> fold (fn ((_, args, _), _) => fold (fn (a, _) =>
+          Variable.declare_typ (TFree (a, dummyS))) args) raw_specs;
+    val specs = check_specs ctxt (map (parse ctxt) raw_specs);
+  in (specs, ctxt) end;
+
+in
+
+val read_specs = prep_specs parse_spec;
+val check_specs = prep_specs (K I);
+
+end;
+
+
+(* main commands *)
+
+fun gen_add_datatype prep_specs config raw_specs thy =
   let
     val _ = Theory.requires thy "Datatype" "datatype definitions";
 
-    (* this theory is used just for parsing *)
-    val tmp_thy = thy
-      |> Theory.copy
-      |> Sign.add_types_global (map (fn (tvs, tname, mx, _) => (tname, length tvs, mx)) dts);
-    val tmp_ctxt = Proof_Context.init_global tmp_thy;
+    val (dts, spec_ctxt) = prep_specs raw_specs thy;
+    val ((_, tyvars, _), _) :: _ = dts;
+    val string_of_tyvar = Syntax.string_of_typ spec_ctxt o TFree;
 
-    val (tyvars, _, _, _) ::_ = dts;
-    val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
-      let val full_tname = Sign.full_name tmp_thy tname in
+    val (new_dts, types_syntax) = dts |> map (fn ((tname, tvs, mx), _) =>
+      let val full_tname = Sign.full_name thy tname in
         (case duplicates (op =) tvs of
           [] =>
             if eq_set (op =) (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
-            else error ("Mutually recursive datatypes must have same type parameters")
+            else error "Mutually recursive datatypes must have same type parameters"
         | dups =>
             error ("Duplicate parameter(s) for datatype " ^ Binding.print tname ^
-              " : " ^ commas dups))
-      end) dts);
+              " : " ^ commas (map string_of_tyvar dups)))
+      end) |> split_list;
     val dt_names = map fst new_dts;
 
     val _ =
@@ -698,45 +749,37 @@
         [] => ()
       | dups => error ("Duplicate datatypes: " ^ commas_quote dups));
 
-    fun prep_dt_spec (tvs, tname, mx, constrs) (dts', constr_syntax, sorts, i) =
+    fun prep_dt_spec ((tname, tvs, mx), constrs) (dts', constr_syntax, i) =
       let
-        fun prep_constr (cname, cargs, mx') (constrs, constr_syntax', sorts') =
+        fun prep_constr (cname, cargs, mx') (constrs, constr_syntax') =
           let
-            val (cargs', sorts'') = fold_map (prep_typ tmp_thy) cargs sorts';
             val _ =
-              (case subtract (op =) tvs (fold Term.add_tfree_namesT cargs' []) of
+              (case subtract (op =) tvs (fold Term.add_tfreesT cargs []) of
                 [] => ()
-              | vs => error ("Extra type variables on rhs: " ^ commas vs));
-            val c = Sign.full_name_path tmp_thy (Binding.name_of tname) cname;
+              | vs => error ("Extra type variables on rhs: " ^ commas (map string_of_tyvar vs)));
+            val c = Sign.full_name_path thy (Binding.name_of tname) cname;
           in
-            (constrs @ [(c, map (Datatype_Aux.dtyp_of_typ new_dts) cargs')],
-              constr_syntax' @ [(cname, mx')], sorts'')
+            (constrs @ [(c, map (Datatype_Aux.dtyp_of_typ new_dts) cargs)],
+              constr_syntax' @ [(cname, mx')])
           end handle ERROR msg =>
             cat_error msg ("The error above occurred in constructor " ^ Binding.print cname ^
               " of datatype " ^ Binding.print tname);
 
-        val (constrs', constr_syntax', sorts') = fold prep_constr constrs ([], [], sorts);
+        val (constrs', constr_syntax') = fold prep_constr constrs ([], []);
       in
         (case duplicates (op =) (map fst constrs') of
           [] =>
-            (dts' @ [(i, (Sign.full_name tmp_thy tname, tvs, constrs'))],
-              constr_syntax @ [constr_syntax'], sorts', i + 1)
+            (dts' @ [(i, (Sign.full_name thy tname, map Datatype_Aux.DtTFree tvs, constrs'))],
+              constr_syntax @ [constr_syntax'], i + 1)
         | dups =>
             error ("Duplicate constructors " ^ commas_quote dups ^
               " in datatype " ^ Binding.print tname))
       end;
 
-    val (dts0, constr_syntax, sorts', i) = fold prep_dt_spec dts ([], [], [], 0);
-    val tmp_ctxt' = tmp_ctxt |> fold (Variable.declare_typ o TFree) sorts';
-
-    val dts' = dts0 |> map (fn (i, (name, tvs, cs)) =>
-      let
-        val args = tvs |>
-          map (fn a => Datatype_Aux.DtTFree (a, Proof_Context.default_sort tmp_ctxt' (a, ~1)));
-      in (i, (name, args, cs)) end);
+    val (dts', constr_syntax, i) = fold prep_dt_spec dts ([], [], 0);
 
     val dt_info = Datatype_Data.get_all thy;
-    val (descr, _) = Datatype_Aux.unfold_datatypes tmp_ctxt dts' dt_info dts' i;
+    val (descr, _) = Datatype_Aux.unfold_datatypes spec_ctxt dts' dt_info dts' i;
     val _ =
       Datatype_Aux.check_nonempty descr
         handle (exn as Datatype_Aux.Datatype_Empty s) =>
@@ -745,7 +788,7 @@
 
     val _ =
       Datatype_Aux.message config
-        ("Constructing datatype(s) " ^ commas_quote (map (Binding.name_of o #2) dts));
+        ("Constructing datatype(s) " ^ commas_quote (map (Binding.name_of o #1 o #1) dts));
   in
     thy
     |> representation_proofs config dt_info descr types_syntax constr_syntax
@@ -754,20 +797,20 @@
       Datatype_Data.derive_datatype_props config dt_names descr induct inject distinct)
   end;
 
-val add_datatype = gen_add_datatype Datatype_Data.cert_typ;
-val add_datatype_cmd = snd oo gen_add_datatype Datatype_Data.read_typ Datatype_Aux.default_config;
+val add_datatype = gen_add_datatype check_specs;
+val add_datatype_cmd = snd oo gen_add_datatype read_specs Datatype_Aux.default_config;
 
 
-(* concrete syntax *)
+(* outer syntax *)
 
-val parse_decl =
-  Parse.type_args -- Parse.binding -- Parse.opt_mixfix --
+val spec_cmd =
+  Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
   (Parse.$$$ "=" |-- Parse.enum1 "|" (Parse.binding -- Scan.repeat Parse.typ -- Parse.opt_mixfix))
-  >> (fn (((vs, t), mx), cons) => (vs, t, mx, map Parse.triple1 cons));
+  >> (fn (((vs, t), mx), cons) => ((t, vs, mx), map Parse.triple1 cons));
 
 val _ =
   Outer_Syntax.command "datatype" "define inductive datatypes" Keyword.thy_decl
-    (Parse.and_list1 parse_decl >> (Toplevel.theory o add_datatype_cmd));
+    (Parse.and_list1 spec_cmd >> (Toplevel.theory o add_datatype_cmd));
 
 
 open Datatype_Data;
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Tools/Datatype/datatype_aux.ML
--- a/src/HOL/Tools/Datatype/datatype_aux.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Tools/Datatype/datatype_aux.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -57,7 +57,7 @@
   exception Datatype
   exception Datatype_Empty of string
   val name_of_typ : typ -> string
-  val dtyp_of_typ : (string * string list) list -> typ -> dtyp
+  val dtyp_of_typ : (string * (string * sort) list) list -> typ -> dtyp
   val mk_Free : string -> typ -> int -> term
   val is_rec_type : dtyp -> bool
   val typ_of_dtyp : descr -> dtyp -> typ
@@ -242,7 +242,7 @@
       (case AList.lookup (op =) new_dts tname of
         NONE => DtType (tname, map (dtyp_of_typ new_dts) Ts)
       | SOME vs =>
-          if map (try (fst o dest_TFree)) Ts = map SOME vs then
+          if map (try dest_TFree) Ts = map SOME vs then
             DtRec (find_index (curry op = tname o fst) new_dts)
           else error ("Illegal occurrence of recursive type " ^ quote tname));
 
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Tools/Datatype/datatype_data.ML
--- a/src/HOL/Tools/Datatype/datatype_data.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Tools/Datatype/datatype_data.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -28,8 +28,6 @@
   val make_case :  Proof.context -> Datatype_Case.config -> string list -> term ->
     (term * term) list -> term
   val strip_case : Proof.context -> bool -> term -> (term * (term * term) list) option
-  val read_typ: theory -> string -> (string * sort) list -> typ * (string * sort) list
-  val cert_typ: theory -> typ -> (string * sort) list -> typ * (string * sort) list
   val mk_case_names_induct: descr -> attribute
   val setup: theory -> theory
 end;
@@ -171,27 +169,6 @@
 
 (** various auxiliary **)
 
-(* prepare datatype specifications *)
-
-fun read_typ thy str sorts =
-  let
-    val ctxt = Proof_Context.init_global thy
-      |> fold (Variable.declare_typ o TFree) sorts;
-    val T = Syntax.read_typ ctxt str;
-  in (T, Term.add_tfreesT T sorts) end;
-
-fun cert_typ sign raw_T sorts =
-  let
-    val T = Type.no_tvars (Sign.certify_typ sign raw_T)
-      handle TYPE (msg, _, _) => error msg;
-    val sorts' = Term.add_tfreesT T sorts;
-    val _ =
-      (case duplicates (op =) (map fst sorts') of
-        [] => ()
-      | dups => error ("Inconsistent sort constraints for " ^ commas dups));
-  in (T, sorts') end;
-
-
 (* case names *)
 
 local
@@ -427,8 +404,7 @@
         (TFree o (the o AList.lookup (op =) (map fst raw_vs ~~ vs)) o fst o dest_TFree) T);
 
     val cs = map (apsnd (map norm_constr)) raw_cs;
-    val dtyps_of_typ =
-      map (Datatype_Aux.dtyp_of_typ (map (rpair (map fst vs) o fst) cs)) o binder_types;
+    val dtyps_of_typ = map (Datatype_Aux.dtyp_of_typ (map (rpair vs o fst) cs)) o binder_types;
     val dt_names = map fst cs;
 
     fun mk_spec (i, (tyco, constr)) =
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Tools/Quotient/quotient_def.ML
--- a/src/HOL/Tools/Quotient/quotient_def.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Tools/Quotient/quotient_def.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -65,7 +65,7 @@
       | _ => raise Match)
 
     val absrep_trm = Quotient_Term.absrep_fun lthy Quotient_Term.AbsF (fastype_of rhs, lhs_ty) $ rhs
-    val prop = Logic.mk_equals (lhs, Syntax.check_term lthy absrep_trm)
+    val prop = Syntax.check_term lthy (Logic.mk_equals (lhs, absrep_trm))
     val (_, prop') = Local_Defs.cert_def lthy prop
     val (_, newrhs) = Local_Defs.abs_def prop'
 
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Tools/Quotient/quotient_type.ML
--- a/src/HOL/Tools/Quotient/quotient_type.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Tools/Quotient/quotient_type.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -277,6 +277,7 @@
 val quotspec_parser =
   Parse.and_list1
     ((Parse.type_args -- Parse.binding) --
+      (* FIXME Parse.type_args_constrained and standard treatment of sort constraints *)
       Parse.opt_mixfix -- (Parse.$$$ "=" |-- Parse.typ) --
         (Parse.$$$ "/" |-- (partial -- Parse.term))  --
         Scan.option (Parse.$$$ "morphisms" |-- Parse.!!! (Parse.binding -- Parse.binding)))
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Tools/inductive_realizer.ML
--- a/src/HOL/Tools/inductive_realizer.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Tools/inductive_realizer.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -69,8 +69,9 @@
         filter_out (equal Extraction.nullT) (map
           (Logic.unvarifyT_global o Extraction.etype_of thy vs []) (prems_of intr)),
             NoSyn);
-  in (map (fn a => "'" ^ a) vs @ map (fst o fst) iTs, tname, NoSyn,
-    map constr_of_intr intrs)
+  in
+    ((tname, map (rpair dummyS) (map (fn a => "'" ^ a) vs @ map (fst o fst) iTs), NoSyn),
+      map constr_of_intr intrs)
   end;
 
 fun mk_rlz T = Const ("realizes", [T, HOLogic.boolT] ---> HOLogic.boolT);
@@ -233,8 +234,9 @@
       end) concls rec_names)
   end;
 
-fun add_dummy name dname (x as (_, (vs, s, mfx, cs))) =
-  if Binding.eq_name (name, s) then (true, (vs, s, mfx, (dname, [HOLogic.unitT], NoSyn) :: cs))
+fun add_dummy name dname (x as (_, ((s, vs, mx), cs))) =
+  if Binding.eq_name (name, s)
+  then (true, ((s, vs, mx), (dname, [HOLogic.unitT], NoSyn) :: cs))
   else x;
 
 fun add_dummies f [] _ thy =
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/Tools/record.ML
--- a/src/HOL/Tools/record.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/Tools/record.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -49,8 +49,6 @@
   val updateN: string
   val ext_typeN: string
   val extN: string
-  val read_typ: Proof.context -> string -> (string * sort) list -> typ * (string * sort) list
-  val cert_typ: Proof.context -> typ -> (string * sort) list -> typ * (string * sort) list
   val setup: theory -> theory
 end;
 
@@ -1489,24 +1487,6 @@
 
 (** theory extender interface **)
 
-(* prepare arguments *)
-
-fun read_typ ctxt raw_T env =
-  let
-    val ctxt' = fold (Variable.declare_typ o TFree) env ctxt;
-    val T = Syntax.read_typ ctxt' raw_T;
-    val env' = Term.add_tfreesT T env;
-  in (T, env') end;
-
-fun cert_typ ctxt raw_T env =
-  let
-    val thy = Proof_Context.theory_of ctxt;
-    val T = Type.no_tvars (Sign.certify_typ thy raw_T)
-      handle TYPE (msg, _, _) => error msg;
-    val env' = Term.add_tfreesT T env;
-  in (T, env') end;
-
-
 (* attributes *)
 
 fun case_names_fields x = Rule_Cases.case_names ["fields"] x;
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/UNITY/Comp/AllocBase.thy
--- a/src/HOL/UNITY/Comp/AllocBase.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/UNITY/Comp/AllocBase.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -7,12 +7,10 @@
 
 theory AllocBase imports "../UNITY_Main" begin
 
-consts
-  NbT      :: nat       (*Number of tokens in system*)
-  Nclients :: nat       (*Number of clients*)
+consts Nclients :: nat  (*Number of clients*)
 
-axioms
-  NbT_pos:  "0 < NbT"
+axiomatization NbT :: nat  (*Number of tokens in system*)
+  where NbT_pos: "0 < NbT"
 
 (*This function merely sums the elements of a list*)
 primrec tokens :: "nat list => nat" where
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/UNITY/Comp/PriorityAux.thy
--- a/src/HOL/UNITY/Comp/PriorityAux.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/UNITY/Comp/PriorityAux.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -45,7 +45,7 @@
     --{* Our alternative definition *}
   "derive i r q == A i r = {} & (q = reverse i r)"
 
-axioms
+axiomatization where
   finite_vertex_univ:  "finite (UNIV :: vertex set)"
     --{* we assume that the universe of vertices is finite  *}
 
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/UNITY/Simple/Reachability.thy
--- a/src/HOL/UNITY/Simple/Reachability.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/UNITY/Simple/Reachability.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -44,27 +44,27 @@
   "final == (\<Inter>v\<in>V. reachable v <==> {s. (root, v) \<in> REACHABLE}) \<inter> 
             (INTER E (nmsg_eq 0))"
 
-axioms
+axiomatization
+where
+    Graph1: "root \<in> V" and
 
-    Graph1: "root \<in> V"
-
-    Graph2: "(v,w) \<in> E ==> (v \<in> V) & (w \<in> V)"
+    Graph2: "(v,w) \<in> E ==> (v \<in> V) & (w \<in> V)" and
 
-    MA1:  "F \<in> Always (reachable root)"
+    MA1:  "F \<in> Always (reachable root)" and
 
-    MA2:  "v \<in> V ==> F \<in> Always (- reachable v \<union> {s. ((root,v) \<in> REACHABLE)})"
+    MA2:  "v \<in> V ==> F \<in> Always (- reachable v \<union> {s. ((root,v) \<in> REACHABLE)})" and
 
-    MA3:  "[|v \<in> V;w \<in> V|] ==> F \<in> Always (-(nmsg_gt 0 (v,w)) \<union> (reachable v))"
+    MA3:  "[|v \<in> V;w \<in> V|] ==> F \<in> Always (-(nmsg_gt 0 (v,w)) \<union> (reachable v))" and
 
     MA4:  "(v,w) \<in> E ==> 
-           F \<in> Always (-(reachable v) \<union> (nmsg_gt 0 (v,w)) \<union> (reachable w))"
+           F \<in> Always (-(reachable v) \<union> (nmsg_gt 0 (v,w)) \<union> (reachable w))" and
 
     MA5:  "[|v \<in> V; w \<in> V|] 
-           ==> F \<in> Always (nmsg_gte 0 (v,w) \<inter> nmsg_lte (Suc 0) (v,w))"
+           ==> F \<in> Always (nmsg_gte 0 (v,w) \<inter> nmsg_lte (Suc 0) (v,w))" and
 
-    MA6:  "[|v \<in> V|] ==> F \<in> Stable (reachable v)"
+    MA6:  "[|v \<in> V|] ==> F \<in> Stable (reachable v)" and
 
-    MA6b: "[|v \<in> V;w \<in> W|] ==> F \<in> Stable (reachable v \<inter> nmsg_lte k (v,w))"
+    MA6b: "[|v \<in> V;w \<in> W|] ==> F \<in> Stable (reachable v \<inter> nmsg_lte k (v,w))" and
 
     MA7:  "[|v \<in> V;w \<in> V|] ==> F \<in> UNIV LeadsTo nmsg_eq 0 (v,w)"
 
diff -r caa99836aed8 -r c7a73fb9be68 src/HOL/ZF/HOLZF.thy
--- a/src/HOL/ZF/HOLZF.thy	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/HOL/ZF/HOLZF.thy	Wed Dec 14 07:38:30 2011 +0100
@@ -34,13 +34,13 @@
 definition subset :: "ZF \<Rightarrow> ZF \<Rightarrow> bool" where
   "subset A B == ! x. Elem x A \<longrightarrow> Elem x B"
 
-axioms
-  Empty: "Not (Elem x Empty)"
-  Ext: "(x = y) = (! z. Elem z x = Elem z y)"
-  Sum: "Elem z (Sum x) = (? y. Elem z y & Elem y x)"
-  Power: "Elem y (Power x) = (subset y x)"
-  Repl: "Elem b (Repl A f) = (? a. Elem a A & b = f a)"
-  Regularity: "A \<noteq> Empty \<longrightarrow> (? x. Elem x A & (! y. Elem y x \<longrightarrow> Not (Elem y A)))"
+axiomatization where
+  Empty: "Not (Elem x Empty)" and
+  Ext: "(x = y) = (! z. Elem z x = Elem z y)" and
+  Sum: "Elem z (Sum x) = (? y. Elem z y & Elem y x)" and
+  Power: "Elem y (Power x) = (subset y x)" and
+  Repl: "Elem b (Repl A f) = (? a. Elem a A & b = f a)" and
+  Regularity: "A \<noteq> Empty \<longrightarrow> (? x. Elem x A & (! y. Elem y x \<longrightarrow> Not (Elem y A)))" and
   Infinity: "Elem Empty Inf & (! x. Elem x Inf \<longrightarrow> Elem (SucNat x) Inf)"
 
 definition Sep :: "ZF \<Rightarrow> (ZF \<Rightarrow> bool) \<Rightarrow> ZF" where
diff -r caa99836aed8 -r c7a73fb9be68 src/Pure/Isar/isar_syn.ML
--- a/src/Pure/Isar/isar_syn.ML	Tue Dec 13 18:33:04 2011 +0100
+++ b/src/Pure/Isar/isar_syn.ML	Wed Dec 14 07:38:30 2011 +0100
@@ -113,13 +113,11 @@
     (Parse.type_args -- Parse.binding -- Parse.opt_mixfix
       >> (fn ((args, a), mx) => Typedecl.typedecl (a, map (rpair dummyS) args, mx) #> snd));
 
-val type_abbrev =
-  Parse.type_args -- Parse.binding --
-    (Parse.$$$ "=" |-- Parse.!!! (Parse.typ -- Parse.opt_mixfix'));
-
 val _ =
   Outer_Syntax.local_theory "type_synonym" "declare type abbreviation" Keyword.thy_decl
-    (type_abbrev >> (fn ((args, a), (rhs, mx)) => snd o Typedecl.abbrev_cmd (a, args, mx) rhs));
+    (Parse.type_args -- Parse.binding --
+      (Parse.$$$ "=" |-- Parse.!!! (Parse.typ -- Parse.opt_mixfix'))
+      >> (fn ((args, a), (rhs, mx)) => snd o Typedecl.abbrev_cmd (a, args, mx) rhs));
 
 val _ =
   Outer_Syntax.command "nonterminal"