isabelle: changeset 29542:d20f453eb4a3

--- a/doc-src/IsarAdvanced/Classes/Thy/Classes.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/doc-src/IsarAdvanced/Classes/Thy/Classes.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -368,14 +368,14 @@
 text {*
   \noindent The connection to the type system is done by means
   of a primitive axclass
-*}
+*} setup %invisible {* Sign.add_path "foo" *}
 
 axclass %quote idem < type
-  idem: "f (f x) = f x"
+  idem: "f (f x) = f x" setup %invisible {* Sign.parent_path *}
 
 text {* \noindent together with a corresponding interpretation: *}
 
-interpretation %quote idem_class':    (* FIXME proper prefix? *)
+interpretation %quote idem_class:
   idem "f \<Colon> (\<alpha>\<Colon>idem) \<Rightarrow> \<alpha>"
 proof qed (rule idem)
 
@@ -459,7 +459,7 @@
   of monoids for lists:
 *}
 
-class_interpretation %quote list_monoid: monoid [append "[]"]
+interpretation %quote list_monoid!: monoid append "[]"
   proof qed auto
 
 text {*
@@ -474,10 +474,10 @@
   "replicate 0 _ = []"
   | "replicate (Suc n) xs = xs @ replicate n xs"
 
-class_interpretation %quote list_monoid: monoid [append "[]"] where
+interpretation %quote list_monoid!: monoid append "[]" where
   "monoid.pow_nat append [] = replicate"
 proof -
-  class_interpret monoid [append "[]"] ..
+  interpret monoid append "[]" ..
   show "monoid.pow_nat append [] = replicate"
   proof
     fix n

--- a/doc-src/IsarAdvanced/Classes/Thy/document/Classes.tex	Thu Jan 15 14:33:38 2009 -0800
+++ b/doc-src/IsarAdvanced/Classes/Thy/document/Classes.tex	Fri Jan 16 13:07:44 2009 -0800
@@ -655,7 +655,23 @@
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
+\isadeliminvisible
+\ %
+\endisadeliminvisible
+%
+\isataginvisible
+\isacommand{setup}\isamarkupfalse%
+\ {\isacharverbatimopen}\ Sign{\isachardot}add{\isacharunderscore}path\ {\isachardoublequote}foo{\isachardoublequote}\ {\isacharverbatimclose}%
+\endisataginvisible
+{\isafoldinvisible}%
+%
+\isadeliminvisible
+%
+\endisadeliminvisible
+\isanewline
+%
 \isadelimquote
+\isanewline
 %
 \endisadelimquote
 %
@@ -670,6 +686,20 @@
 %
 \endisadelimquote
 %
+\isadeliminvisible
+\ %
+\endisadeliminvisible
+%
+\isataginvisible
+\isacommand{setup}\isamarkupfalse%
+\ {\isacharverbatimopen}\ Sign{\isachardot}parent{\isacharunderscore}path\ {\isacharverbatimclose}%
+\endisataginvisible
+{\isafoldinvisible}%
+%
+\isadeliminvisible
+%
+\endisadeliminvisible
+%
 \begin{isamarkuptext}%
 \noindent together with a corresponding interpretation:%
 \end{isamarkuptext}%
@@ -681,7 +711,7 @@
 %
 \isatagquote
 \isacommand{interpretation}\isamarkupfalse%
-\ idem{\isacharunderscore}class{\isacharprime}{\isacharcolon}\ \ \ \ \isanewline
+\ idem{\isacharunderscore}class{\isacharcolon}\isanewline
 \ \ idem\ {\isachardoublequoteopen}f\ {\isasymColon}\ {\isacharparenleft}{\isasymalpha}{\isasymColon}idem{\isacharparenright}\ {\isasymRightarrow}\ {\isasymalpha}{\isachardoublequoteclose}\isanewline
 \isacommand{proof}\isamarkupfalse%
 \ \isacommand{qed}\isamarkupfalse%
@@ -843,8 +873,8 @@
 \endisadelimquote
 %
 \isatagquote
-\isacommand{class{\isacharunderscore}interpretation}\isamarkupfalse%
-\ list{\isacharunderscore}monoid{\isacharcolon}\ monoid\ {\isacharbrackleft}append\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}{\isacharbrackright}\isanewline
+\isacommand{interpretation}\isamarkupfalse%
+\ list{\isacharunderscore}monoid{\isacharbang}{\isacharcolon}\ monoid\ append\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
 \ \ \isacommand{proof}\isamarkupfalse%
 \ \isacommand{qed}\isamarkupfalse%
 \ auto%
@@ -874,13 +904,13 @@
 \ \ {\isachardoublequoteopen}replicate\ {\isadigit{0}}\ {\isacharunderscore}\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
 \ \ {\isacharbar}\ {\isachardoublequoteopen}replicate\ {\isacharparenleft}Suc\ n{\isacharparenright}\ xs\ {\isacharequal}\ xs\ {\isacharat}\ replicate\ n\ xs{\isachardoublequoteclose}\isanewline
 \isanewline
-\isacommand{class{\isacharunderscore}interpretation}\isamarkupfalse%
-\ list{\isacharunderscore}monoid{\isacharcolon}\ monoid\ {\isacharbrackleft}append\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}{\isacharbrackright}\ \isakeyword{where}\isanewline
+\isacommand{interpretation}\isamarkupfalse%
+\ list{\isacharunderscore}monoid{\isacharbang}{\isacharcolon}\ monoid\ append\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
 \ \ {\isachardoublequoteopen}monoid{\isachardot}pow{\isacharunderscore}nat\ append\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ replicate{\isachardoublequoteclose}\isanewline
 \isacommand{proof}\isamarkupfalse%
 \ {\isacharminus}\isanewline
-\ \ \isacommand{class{\isacharunderscore}interpret}\isamarkupfalse%
-\ monoid\ {\isacharbrackleft}append\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}{\isacharbrackright}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ \ \isacommand{interpret}\isamarkupfalse%
+\ monoid\ append\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
 \isanewline
 \ \ \isacommand{show}\isamarkupfalse%
 \ {\isachardoublequoteopen}monoid{\isachardot}pow{\isacharunderscore}nat\ append\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ replicate{\isachardoublequoteclose}\isanewline

--- a/doc-src/IsarAdvanced/Codegen/Thy/Setup.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/doc-src/IsarAdvanced/Codegen/Thy/Setup.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -4,7 +4,7 @@
 begin
 
 ML {* no_document use_thys
-  ["Efficient_Nat", "Code_Char_chr", "Product_ord", "Imperative_HOL",
+  ["Efficient_Nat", "Code_Char_chr", "Product_ord", "~~/src/HOL/Imperative_HOL/Imperative_HOL",
    "~~/src/HOL/ex/ReflectedFerrack"] *}
 
 ML_val {* Code_Target.code_width := 74 *}

--- a/src/FOL/ex/LocaleTest.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/FOL/ex/LocaleTest.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -8,9 +8,6 @@
 imports FOL
 begin
 
-ML_val {* set Toplevel.debug *}
-
-
 typedecl int arities int :: "term"
 consts plus :: "int => int => int" (infixl "+" 60)
   zero :: int ("0")
@@ -483,6 +480,4 @@
   thm local_free.lone [where ?zero = 0]
 qed
 
-ML_val {* reset Toplevel.debug *}
-
 end

--- a/src/HOL/Dense_Linear_Order.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/Dense_Linear_Order.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -301,7 +301,7 @@
 
 text {* Linear order without upper bounds *}
 
-class_locale linorder_stupid_syntax = linorder
+locale linorder_stupid_syntax = linorder
 begin
 notation
   less_eq  ("op \<sqsubseteq>") and
@@ -311,7 +311,7 @@
 
 end
 
-class_locale linorder_no_ub = linorder_stupid_syntax +
+locale linorder_no_ub = linorder_stupid_syntax +
   assumes gt_ex: "\<exists>y. less x y"
 begin
 lemma ge_ex: "\<exists>y. x \<sqsubseteq> y" using gt_ex by auto
@@ -360,7 +360,7 @@
 
 text {* Linear order without upper bounds *}
 
-class_locale linorder_no_lb = linorder_stupid_syntax +
+locale linorder_no_lb = linorder_stupid_syntax +
   assumes lt_ex: "\<exists>y. less y x"
 begin
 lemma le_ex: "\<exists>y. y \<sqsubseteq> x" using lt_ex by auto
@@ -407,12 +407,12 @@
 end
 
 
-class_locale constr_dense_linear_order = linorder_no_lb + linorder_no_ub +
+locale constr_dense_linear_order = linorder_no_lb + linorder_no_ub +
   fixes between
   assumes between_less: "less x y \<Longrightarrow> less x (between x y) \<and> less (between x y) y"
      and  between_same: "between x x = x"
 
-class_interpretation  constr_dense_linear_order < dense_linear_order 
+sublocale  constr_dense_linear_order < dense_linear_order 
   apply unfold_locales
   using gt_ex lt_ex between_less
     by (auto, rule_tac x="between x y" in exI, simp)
@@ -635,9 +635,9 @@
   using eq_diff_eq[where a= x and b=t and c=0] by simp
 
 
-class_interpretation class_ordered_field_dense_linear_order: constr_dense_linear_order
- ["op <=" "op <"
-   "\<lambda> x y. 1/2 * ((x::'a::{ordered_field,recpower,number_ring}) + y)"]
+interpretation class_ordered_field_dense_linear_order!: constr_dense_linear_order
+ "op <=" "op <"
+   "\<lambda> x y. 1/2 * ((x::'a::{ordered_field,recpower,number_ring}) + y)"
 proof (unfold_locales, dlo, dlo, auto)
   fix x y::'a assume lt: "x < y"
   from  less_half_sum[OF lt] show "x < (x + y) /2" by simp

--- a/src/HOL/Divides.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/Divides.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -20,7 +20,7 @@
 
 subsection {* Abstract division in commutative semirings. *}
 
-class semiring_div = comm_semiring_1_cancel + div + 
+class semiring_div = comm_semiring_1_cancel + div +
   assumes mod_div_equality: "a div b * b + a mod b = a"
     and div_by_0 [simp]: "a div 0 = 0"
     and div_0 [simp]: "0 div a = 0"
@@ -800,7 +800,7 @@
 
 text {* @{term "op dvd"} is a partial order *}
 
-class_interpretation dvd: order ["op dvd" "\<lambda>n m \<Colon> nat. n dvd m \<and> \<not> m dvd n"]
+interpretation dvd!: order "op dvd" "\<lambda>n m \<Colon> nat. n dvd m \<and> \<not> m dvd n"
   proof qed (auto intro: dvd_refl dvd_trans dvd_anti_sym)
 
 lemma dvd_diff: "[| k dvd m; k dvd n |] ==> k dvd (m-n :: nat)"

--- a/src/HOL/Finite_Set.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/Finite_Set.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -873,7 +873,7 @@
 
 subsection {* Generalized summation over a set *}
 
-class_interpretation comm_monoid_add: comm_monoid_mult ["0::'a::comm_monoid_add" "op +"]
+interpretation comm_monoid_add!: comm_monoid_mult "0::'a::comm_monoid_add" "op +"
   proof qed (auto intro: add_assoc add_commute)
 
 definition setsum :: "('a => 'b) => 'a set => 'b::comm_monoid_add"
@@ -1760,7 +1760,7 @@
 proof (induct rule: finite_induct)
   case empty then show ?case by simp
 next
-  class_interpret ab_semigroup_mult ["op Un"]
+  interpret ab_semigroup_mult "op Un"
     proof qed auto
   case insert 
   then show ?case by simp
@@ -2198,7 +2198,7 @@
   assumes "finite A" "A \<noteq> {}"
   shows "x \<le> fold1 inf A \<longleftrightarrow> (\<forall>a\<in>A. x \<le> a)"
 proof -
-  class_interpret ab_semigroup_idem_mult [inf]
+  interpret ab_semigroup_idem_mult inf
     by (rule ab_semigroup_idem_mult_inf)
   show ?thesis using assms by (induct rule: finite_ne_induct) simp_all
 qed
@@ -2213,7 +2213,7 @@
   proof (induct rule: finite_ne_induct)
     case singleton thus ?case by simp
   next
-    class_interpret ab_semigroup_idem_mult [inf]
+    interpret ab_semigroup_idem_mult inf
       by (rule ab_semigroup_idem_mult_inf)
     case (insert x F)
     from insert(5) have "a = x \<or> a \<in> F" by simp
@@ -2288,7 +2288,7 @@
     and "A \<noteq> {}"
   shows "sup x (\<Sqinter>\<^bsub>fin\<^esub>A) = \<Sqinter>\<^bsub>fin\<^esub>{sup x a|a. a \<in> A}"
 proof -
-  class_interpret ab_semigroup_idem_mult [inf]
+  interpret ab_semigroup_idem_mult inf
     by (rule ab_semigroup_idem_mult_inf)
   from assms show ?thesis
     by (simp add: Inf_fin_def image_def
@@ -2303,7 +2303,7 @@
   case singleton thus ?case
     by (simp add: sup_Inf1_distrib [OF B] fold1_singleton_def [OF Inf_fin_def])
 next
-  class_interpret ab_semigroup_idem_mult [inf]
+  interpret ab_semigroup_idem_mult inf
     by (rule ab_semigroup_idem_mult_inf)
   case (insert x A)
   have finB: "finite {sup x b |b. b \<in> B}"
@@ -2333,7 +2333,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "inf x (\<Squnion>\<^bsub>fin\<^esub>A) = \<Squnion>\<^bsub>fin\<^esub>{inf x a|a. a \<in> A}"
 proof -
-  class_interpret ab_semigroup_idem_mult [sup]
+  interpret ab_semigroup_idem_mult sup
     by (rule ab_semigroup_idem_mult_sup)
   from assms show ?thesis
     by (simp add: Sup_fin_def image_def hom_fold1_commute [where h="inf x", OF inf_sup_distrib1])
@@ -2357,7 +2357,7 @@
     thus ?thesis by(simp add: insert(1) B(1))
   qed
   have ne: "{inf a b |a b. a \<in> A \<and> b \<in> B} \<noteq> {}" using insert B by blast
-  class_interpret ab_semigroup_idem_mult [sup]
+  interpret ab_semigroup_idem_mult sup
     by (rule ab_semigroup_idem_mult_sup)
   have "inf (\<Squnion>\<^bsub>fin\<^esub>(insert x A)) (\<Squnion>\<^bsub>fin\<^esub>B) = inf (sup x (\<Squnion>\<^bsub>fin\<^esub>A)) (\<Squnion>\<^bsub>fin\<^esub>B)"
     using insert by (simp add: fold1_insert_idem_def [OF Sup_fin_def])
@@ -2386,7 +2386,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "\<Sqinter>\<^bsub>fin\<^esub>A = Inf A"
 proof -
-  class_interpret ab_semigroup_idem_mult [inf]
+    interpret ab_semigroup_idem_mult inf
     by (rule ab_semigroup_idem_mult_inf)
   from assms show ?thesis
   unfolding Inf_fin_def by (induct A set: finite)
@@ -2397,7 +2397,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "\<Squnion>\<^bsub>fin\<^esub>A = Sup A"
 proof -
-  class_interpret ab_semigroup_idem_mult [sup]
+  interpret ab_semigroup_idem_mult sup
     by (rule ab_semigroup_idem_mult_sup)
   from assms show ?thesis
   unfolding Sup_fin_def by (induct A set: finite)
@@ -2446,7 +2446,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "x < fold1 min A \<longleftrightarrow> (\<forall>a\<in>A. x < a)"
 proof -
-  class_interpret ab_semigroup_idem_mult [min]
+  interpret ab_semigroup_idem_mult min
     by (rule ab_semigroup_idem_mult_min)
   from assms show ?thesis
   by (induct rule: finite_ne_induct)
@@ -2457,7 +2457,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "fold1 min A \<le> x \<longleftrightarrow> (\<exists>a\<in>A. a \<le> x)"
 proof -
-  class_interpret ab_semigroup_idem_mult [min]
+  interpret ab_semigroup_idem_mult min
     by (rule ab_semigroup_idem_mult_min)
   from assms show ?thesis
   by (induct rule: finite_ne_induct)
@@ -2468,7 +2468,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "fold1 min A < x \<longleftrightarrow> (\<exists>a\<in>A. a < x)"
 proof -
-  class_interpret ab_semigroup_idem_mult [min]
+  interpret ab_semigroup_idem_mult min
     by (rule ab_semigroup_idem_mult_min)
   from assms show ?thesis
   by (induct rule: finite_ne_induct)
@@ -2481,7 +2481,7 @@
 proof cases
   assume "A = B" thus ?thesis by simp
 next
-  class_interpret ab_semigroup_idem_mult [min]
+  interpret ab_semigroup_idem_mult min
     by (rule ab_semigroup_idem_mult_min)
   assume "A \<noteq> B"
   have B: "B = A \<union> (B-A)" using `A \<subseteq> B` by blast
@@ -2515,7 +2515,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "Min (insert x A) = min x (Min A)"
 proof -
-  class_interpret ab_semigroup_idem_mult [min]
+  interpret ab_semigroup_idem_mult min
     by (rule ab_semigroup_idem_mult_min)
   from assms show ?thesis by (rule fold1_insert_idem_def [OF Min_def])
 qed
@@ -2524,7 +2524,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "Max (insert x A) = max x (Max A)"
 proof -
-  class_interpret ab_semigroup_idem_mult [max]
+  interpret ab_semigroup_idem_mult max
     by (rule ab_semigroup_idem_mult_max)
   from assms show ?thesis by (rule fold1_insert_idem_def [OF Max_def])
 qed
@@ -2533,7 +2533,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "Min A \<in> A"
 proof -
-  class_interpret ab_semigroup_idem_mult [min]
+  interpret ab_semigroup_idem_mult min
     by (rule ab_semigroup_idem_mult_min)
   from assms fold1_in show ?thesis by (fastsimp simp: Min_def min_def)
 qed
@@ -2542,7 +2542,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "Max A \<in> A"
 proof -
-  class_interpret ab_semigroup_idem_mult [max]
+  interpret ab_semigroup_idem_mult max
     by (rule ab_semigroup_idem_mult_max)
   from assms fold1_in [of A] show ?thesis by (fastsimp simp: Max_def max_def)
 qed
@@ -2551,7 +2551,7 @@
   assumes "finite A" and "A \<noteq> {}" and "finite B" and "B \<noteq> {}"
   shows "Min (A \<union> B) = min (Min A) (Min B)"
 proof -
-  class_interpret ab_semigroup_idem_mult [min]
+  interpret ab_semigroup_idem_mult min
     by (rule ab_semigroup_idem_mult_min)
   from assms show ?thesis
     by (simp add: Min_def fold1_Un2)
@@ -2561,7 +2561,7 @@
   assumes "finite A" and "A \<noteq> {}" and "finite B" and "B \<noteq> {}"
   shows "Max (A \<union> B) = max (Max A) (Max B)"
 proof -
-  class_interpret ab_semigroup_idem_mult [max]
+  interpret ab_semigroup_idem_mult max
     by (rule ab_semigroup_idem_mult_max)
   from assms show ?thesis
     by (simp add: Max_def fold1_Un2)
@@ -2572,7 +2572,7 @@
     and "finite N" and "N \<noteq> {}"
   shows "h (Min N) = Min (h ` N)"
 proof -
-  class_interpret ab_semigroup_idem_mult [min]
+  interpret ab_semigroup_idem_mult min
     by (rule ab_semigroup_idem_mult_min)
   from assms show ?thesis
     by (simp add: Min_def hom_fold1_commute)
@@ -2583,7 +2583,7 @@
     and "finite N" and "N \<noteq> {}"
   shows "h (Max N) = Max (h ` N)"
 proof -
-  class_interpret ab_semigroup_idem_mult [max]
+  interpret ab_semigroup_idem_mult max
     by (rule ab_semigroup_idem_mult_max)
   from assms show ?thesis
     by (simp add: Max_def hom_fold1_commute [of h])
@@ -2593,7 +2593,7 @@
   assumes "finite A" and "x \<in> A"
   shows "Min A \<le> x"
 proof -
-  class_interpret lower_semilattice ["op \<le>" "op <" min]
+  interpret lower_semilattice "op \<le>" "op <" min
     by (rule min_lattice)
   from assms show ?thesis by (simp add: Min_def fold1_belowI)
 qed
@@ -2602,7 +2602,7 @@
   assumes "finite A" and "x \<in> A"
   shows "x \<le> Max A"
 proof -
-  invoke lower_semilattice ["op \<ge>" "op >" max]
+  interpret lower_semilattice "op \<ge>" "op >" max
     by (rule max_lattice)
   from assms show ?thesis by (simp add: Max_def fold1_belowI)
 qed
@@ -2611,7 +2611,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "x \<le> Min A \<longleftrightarrow> (\<forall>a\<in>A. x \<le> a)"
 proof -
-  class_interpret lower_semilattice ["op \<le>" "op <" min]
+  interpret lower_semilattice "op \<le>" "op <" min
     by (rule min_lattice)
   from assms show ?thesis by (simp add: Min_def below_fold1_iff)
 qed
@@ -2620,7 +2620,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "Max A \<le> x \<longleftrightarrow> (\<forall>a\<in>A. a \<le> x)"
 proof -
-  invoke lower_semilattice ["op \<ge>" "op >" max]
+  interpret lower_semilattice "op \<ge>" "op >" max
     by (rule max_lattice)
   from assms show ?thesis by (simp add: Max_def below_fold1_iff)
 qed
@@ -2629,7 +2629,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "x < Min A \<longleftrightarrow> (\<forall>a\<in>A. x < a)"
 proof -
-  class_interpret lower_semilattice ["op \<le>" "op <" min]
+  interpret lower_semilattice "op \<le>" "op <" min
     by (rule min_lattice)
   from assms show ?thesis by (simp add: Min_def strict_below_fold1_iff)
 qed
@@ -2639,7 +2639,7 @@
   shows "Max A < x \<longleftrightarrow> (\<forall>a\<in>A. a < x)"
 proof -
   note Max = Max_def
-  class_interpret linorder ["op \<ge>" "op >"]
+  interpret linorder "op \<ge>" "op >"
     by (rule dual_linorder)
   from assms show ?thesis
     by (simp add: Max strict_below_fold1_iff [folded dual_max])
@@ -2649,7 +2649,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "Min A \<le> x \<longleftrightarrow> (\<exists>a\<in>A. a \<le> x)"
 proof -
-  class_interpret lower_semilattice ["op \<le>" "op <" min]
+  interpret lower_semilattice "op \<le>" "op <" min
     by (rule min_lattice)
   from assms show ?thesis
     by (simp add: Min_def fold1_below_iff)
@@ -2660,7 +2660,7 @@
   shows "x \<le> Max A \<longleftrightarrow> (\<exists>a\<in>A. x \<le> a)"
 proof -
   note Max = Max_def
-  class_interpret linorder ["op \<ge>" "op >"]
+  interpret linorder "op \<ge>" "op >"
     by (rule dual_linorder)
   from assms show ?thesis
     by (simp add: Max fold1_below_iff [folded dual_max])
@@ -2670,7 +2670,7 @@
   assumes "finite A" and "A \<noteq> {}"
   shows "Min A < x \<longleftrightarrow> (\<exists>a\<in>A. a < x)"
 proof -
-  class_interpret lower_semilattice ["op \<le>" "op <" min]
+  interpret lower_semilattice "op \<le>" "op <" min
     by (rule min_lattice)
   from assms show ?thesis
     by (simp add: Min_def fold1_strict_below_iff)
@@ -2681,7 +2681,7 @@
   shows "x < Max A \<longleftrightarrow> (\<exists>a\<in>A. x < a)"
 proof -
   note Max = Max_def
-  class_interpret linorder ["op \<ge>" "op >"]
+  interpret linorder "op \<ge>" "op >"
     by (rule dual_linorder)
   from assms show ?thesis
     by (simp add: Max fold1_strict_below_iff [folded dual_max])
@@ -2691,7 +2691,7 @@
   assumes "M \<subseteq> N" and "M \<noteq> {}" and "finite N"
   shows "Min N \<le> Min M"
 proof -
-  class_interpret distrib_lattice ["op \<le>" "op <" min max]
+  interpret distrib_lattice "op \<le>" "op <" min max
     by (rule distrib_lattice_min_max)
   from assms show ?thesis by (simp add: Min_def fold1_antimono)
 qed
@@ -2701,7 +2701,7 @@
   shows "Max M \<le> Max N"
 proof -
   note Max = Max_def
-  class_interpret linorder ["op \<ge>" "op >"]
+  interpret linorder "op \<ge>" "op >"
     by (rule dual_linorder)
   from assms show ?thesis
     by (simp add: Max fold1_antimono [folded dual_max])

--- a/src/HOL/HOL.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/HOL.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -35,7 +35,7 @@
   "~~/src/Tools/code/code_ml.ML"
   "~~/src/Tools/code/code_haskell.ML"
   "~~/src/Tools/nbe.ML"
-  ("~~/src/HOL/Tools/recfun_codegen.ML")
+  ("Tools/recfun_codegen.ML")
 begin
 
 subsection {* Primitive logic *}
@@ -1690,7 +1690,7 @@
 
 text {* Module setup *}
 
-use "~~/src/HOL/Tools/recfun_codegen.ML"
+use "Tools/recfun_codegen.ML"
 
 setup {*
   Code_ML.setup

--- a/src/HOL/IsaMakefile	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/IsaMakefile	Fri Jan 16 13:07:44 2009 -0800
@@ -6,7 +6,7 @@
 
 default: HOL
 generate: HOL-Generate-HOL HOL-Generate-HOLLight
-images: HOL-Plain HOL-Main HOL HOL-Algebra HOL-Nominal HOL-NSA HOL-Word TLA HOL4
+images: HOL HOL-Base HOL-Plain HOL-Main HOL-Algebra HOL-Nominal HOL-NSA HOL-Word TLA HOL4
 
 #Note: keep targets sorted (except for HOL-Library and HOL-ex)
 test: \
@@ -66,6 +66,8 @@
 
 HOL: Pure $(OUT)/HOL
 
+HOL-Base: Pure $(OUT)/HOL-Base
+
 HOL-Plain: Pure $(OUT)/HOL-Plain
 
 HOL-Main: Pure $(OUT)/HOL-Main
@@ -75,15 +77,50 @@
 
 $(OUT)/Pure: Pure
 
-PLAIN_DEPENDENCIES = $(OUT)/Pure \
+BASE_DEPENDENCIES = $(OUT)/Pure \
   Code_Setup.thy \
+  HOL.thy \
+  Tools/hologic.ML \
+  Tools/recfun_codegen.ML \
+  Tools/simpdata.ML \
+  $(SRC)/Tools/atomize_elim.ML \
+  $(SRC)/Tools/code/code_funcgr.ML \
+  $(SRC)/Tools/code/code_funcgr.ML \
+  $(SRC)/Tools/code/code_name.ML \
+  $(SRC)/Tools/code/code_printer.ML \
+  $(SRC)/Tools/code/code_target.ML \
+  $(SRC)/Tools/code/code_ml.ML \
+  $(SRC)/Tools/code/code_haskell.ML \
+  $(SRC)/Tools/code/code_thingol.ML \
+  $(SRC)/Tools/induct.ML \
+  $(SRC)/Tools/induct_tacs.ML \
+  $(SRC)/Tools/IsaPlanner/isand.ML \
+  $(SRC)/Tools/IsaPlanner/rw_inst.ML \
+  $(SRC)/Tools/IsaPlanner/rw_tools.ML \
+  $(SRC)/Tools/IsaPlanner/zipper.ML \
+  $(SRC)/Tools/nbe.ML \
+  $(SRC)/Tools/random_word.ML \
+  $(SRC)/Tools/value.ML \
+  $(SRC)/Provers/blast.ML \
+  $(SRC)/Provers/clasimp.ML \
+  $(SRC)/Provers/classical.ML \
+  $(SRC)/Provers/coherent.ML \
+  $(SRC)/Provers/eqsubst.ML \
+  $(SRC)/Provers/hypsubst.ML \
+  $(SRC)/Provers/project_rule.ML \
+  $(SRC)/Provers/quantifier1.ML \
+  $(SRC)/Provers/splitter.ML \
+
+$(OUT)/HOL-Base: base.ML $(BASE_DEPENDENCIES)
+	@$(ISABELLE_TOOL) usedir -b -f base.ML -g true $(OUT)/Pure HOL-Base
+
+PLAIN_DEPENDENCIES = $(BASE_DEPENDENCIES)\
   Datatype.thy \
   Divides.thy \
   Extraction.thy \
   Finite_Set.thy \
   Fun.thy \
   FunDef.thy \
-  HOL.thy \
   Inductive.thy \
   Lattices.thy \
   Nat.thy \
@@ -131,7 +168,6 @@
   Tools/function_package/size.ML \
   Tools/function_package/sum_tree.ML \
   Tools/function_package/termination.ML \
-  Tools/hologic.ML \
   Tools/inductive_codegen.ML \
   Tools/inductive_package.ML \
   Tools/inductive_realizer.ML \
@@ -140,14 +176,12 @@
   Tools/old_primrec_package.ML \
   Tools/primrec_package.ML \
   Tools/prop_logic.ML \
-  Tools/recfun_codegen.ML \
   Tools/record_package.ML \
   Tools/refute.ML \
   Tools/refute_isar.ML \
   Tools/rewrite_hol_proof.ML \
   Tools/sat_funcs.ML \
   Tools/sat_solver.ML \
-  Tools/simpdata.ML \
   Tools/split_rule.ML \
   Tools/typecopy_package.ML \
   Tools/typedef_codegen.ML \
@@ -159,35 +193,8 @@
   $(SRC)/Provers/Arith/cancel_div_mod.ML \
   $(SRC)/Provers/Arith/cancel_sums.ML \
   $(SRC)/Provers/Arith/fast_lin_arith.ML \
-  $(SRC)/Provers/blast.ML \
-  $(SRC)/Provers/clasimp.ML \
-  $(SRC)/Provers/classical.ML \
-  $(SRC)/Provers/coherent.ML \
-  $(SRC)/Provers/eqsubst.ML \
-  $(SRC)/Provers/hypsubst.ML \
   $(SRC)/Provers/order.ML \
-  $(SRC)/Provers/project_rule.ML \
-  $(SRC)/Provers/quantifier1.ML \
-  $(SRC)/Provers/splitter.ML \
   $(SRC)/Provers/trancl.ML \
-  $(SRC)/Tools/IsaPlanner/isand.ML \
-  $(SRC)/Tools/IsaPlanner/rw_inst.ML \
-  $(SRC)/Tools/IsaPlanner/rw_tools.ML \
-  $(SRC)/Tools/IsaPlanner/zipper.ML \
-  $(SRC)/Tools/atomize_elim.ML \
-  $(SRC)/Tools/code/code_funcgr.ML \
-  $(SRC)/Tools/code/code_funcgr.ML \
-  $(SRC)/Tools/code/code_name.ML \
-  $(SRC)/Tools/code/code_printer.ML \
-  $(SRC)/Tools/code/code_target.ML \
-  $(SRC)/Tools/code/code_ml.ML \
-  $(SRC)/Tools/code/code_haskell.ML \
-  $(SRC)/Tools/code/code_thingol.ML \
-  $(SRC)/Tools/induct.ML \
-  $(SRC)/Tools/induct_tacs.ML \
-  $(SRC)/Tools/value.ML \
-  $(SRC)/Tools/nbe.ML \
-  $(SRC)/Tools/random_word.ML \
   $(SRC)/Tools/rat.ML
 
 $(OUT)/HOL-Plain: plain.ML $(PLAIN_DEPENDENCIES)
@@ -280,7 +287,6 @@
   GCD.thy \
   Order_Relation.thy \
   Parity.thy \
-  Univ_Poly.thy \
   Lubs.thy \
   Polynomial.thy \
   PReal.thy \
@@ -327,7 +333,7 @@
   Library/Code_Char_chr.thy Library/Code_Integer.thy			\
   Library/Numeral_Type.thy			\
   Library/Boolean_Algebra.thy Library/Countable.thy	\
-  Library/RBT.thy		\
+  Library/RBT.thy	Library/Univ_Poly.thy	\
   Library/Enum.thy Library/Float.thy $(SRC)/Tools/float.ML $(SRC)/HOL/Tools/float_arith.ML
 	@cd Library; $(ISABELLE_TOOL) usedir $(OUT)/HOL Library

--- a/src/HOL/Lattices.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/Lattices.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -300,8 +300,7 @@
   by auto
 qed (auto simp add: min_def max_def not_le less_imp_le)
 
-class_interpretation min_max:
-  distrib_lattice ["op \<le> \<Colon> 'a\<Colon>linorder \<Rightarrow> 'a \<Rightarrow> bool" "op <" min max]
+interpretation min_max!: distrib_lattice "op \<le> :: 'a::linorder \<Rightarrow> 'a \<Rightarrow> bool" "op <" min max
   by (rule distrib_lattice_min_max)
 
 lemma inf_min: "inf = (min \<Colon> 'a\<Colon>{lower_semilattice, linorder} \<Rightarrow> 'a \<Rightarrow> 'a)"

--- a/src/HOL/Library/Countable.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/Library/Countable.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -1,5 +1,4 @@
 (*  Title:      HOL/Library/Countable.thy
-    ID:         $Id$
     Author:     Alexander Krauss, TU Muenchen
 *)

--- a/src/HOL/Library/Library.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/Library/Library.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -1,4 +1,3 @@
-(* $Id$ *)
 (*<*)
 theory Library
 imports
@@ -38,6 +37,7 @@
   Ramsey
   RBT
   State_Monad
+  Univ_Poly
   While_Combinator
   Word
   Zorn

--- a/src/HOL/Library/Multiset.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/Library/Multiset.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -1,5 +1,4 @@
 (*  Title:      HOL/Library/Multiset.thy
-    ID:         $Id$
     Author:     Tobias Nipkow, Markus Wenzel, Lawrence C Paulson, Norbert Voelker
 *)
 
@@ -1080,16 +1079,16 @@
 apply simp
 done
 
-class_interpretation mset_order: order ["op \<le>#" "op <#"]
+interpretation mset_order!: order "op \<le>#" "op <#"
 proof qed (auto intro: order.intro mset_le_refl mset_le_antisym
   mset_le_trans simp: mset_less_def)
 
-class_interpretation mset_order_cancel_semigroup:
-  pordered_cancel_ab_semigroup_add ["op +" "op \<le>#" "op <#"]
+interpretation mset_order_cancel_semigroup!:
+  pordered_cancel_ab_semigroup_add "op +" "op \<le>#" "op <#"
 proof qed (erule mset_le_mono_add [OF mset_le_refl])
 
-class_interpretation mset_order_semigroup_cancel:
-  pordered_ab_semigroup_add_imp_le ["op +" "op \<le>#" "op <#"]
+interpretation mset_order_semigroup_cancel!:
+  pordered_ab_semigroup_add_imp_le "op +" "op \<le>#" "op <#"
 proof qed simp
 
 
@@ -1156,7 +1155,7 @@
   then show ?case using T by simp
 qed
 
-lemmas mset_less_trans = mset_order.less_eq_less.less_trans
+lemmas mset_less_trans = mset_order.less_trans
 
 lemma mset_less_diff_self: "c \<in># B \<Longrightarrow> B - {#c#} \<subset># B"
 by (auto simp: mset_le_def mset_less_def multi_drop_mem_not_eq)

--- a/src/HOL/Library/SetsAndFunctions.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/Library/SetsAndFunctions.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -107,26 +107,26 @@
   apply simp
   done
 
-class_interpretation set_semigroup_add: semigroup_add ["op \<oplus> :: ('a::semigroup_add) set => 'a set => 'a set"]
+interpretation set_semigroup_add!: semigroup_add "op \<oplus> :: ('a::semigroup_add) set => 'a set => 'a set"
   apply default
   apply (unfold set_plus_def)
   apply (force simp add: add_assoc)
   done
 
-class_interpretation set_semigroup_mult: semigroup_mult ["op \<otimes> :: ('a::semigroup_mult) set => 'a set => 'a set"]
+interpretation set_semigroup_mult!: semigroup_mult "op \<otimes> :: ('a::semigroup_mult) set => 'a set => 'a set"
   apply default
   apply (unfold set_times_def)
   apply (force simp add: mult_assoc)
   done
 
-class_interpretation set_comm_monoid_add: comm_monoid_add ["{0}" "op \<oplus> :: ('a::comm_monoid_add) set => 'a set => 'a set"]
+interpretation set_comm_monoid_add!: comm_monoid_add "{0}" "op \<oplus> :: ('a::comm_monoid_add) set => 'a set => 'a set"
   apply default
    apply (unfold set_plus_def)
    apply (force simp add: add_ac)
   apply force
   done
 
-class_interpretation set_comm_monoid_mult: comm_monoid_mult ["{1}" "op \<otimes> :: ('a::comm_monoid_mult) set => 'a set => 'a set"]
+interpretation set_comm_monoid_mult!: comm_monoid_mult "{1}" "op \<otimes> :: ('a::comm_monoid_mult) set => 'a set => 'a set"
   apply default
    apply (unfold set_times_def)
    apply (force simp add: mult_ac)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/Univ_Poly.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -0,0 +1,1050 @@
+(*  Title:       Univ_Poly.thy
+    Author:      Amine Chaieb
+*)
+
+header {* Univariate Polynomials *}
+
+theory Univ_Poly
+imports Plain List
+begin
+
+text{* Application of polynomial as a function. *}
+
+primrec (in semiring_0) poly :: "'a list => 'a  => 'a" where
+  poly_Nil:  "poly [] x = 0"
+| poly_Cons: "poly (h#t) x = h + x * poly t x"
+
+
+subsection{*Arithmetic Operations on Polynomials*}
+
+text{*addition*}
+
+primrec (in semiring_0) padd :: "'a list \<Rightarrow> 'a list \<Rightarrow> 'a list"  (infixl "+++" 65) 
+where
+  padd_Nil:  "[] +++ l2 = l2"
+| padd_Cons: "(h#t) +++ l2 = (if l2 = [] then h#t
+                            else (h + hd l2)#(t +++ tl l2))"
+
+text{*Multiplication by a constant*}
+primrec (in semiring_0) cmult :: "'a \<Rightarrow> 'a list \<Rightarrow> 'a list"  (infixl "%*" 70) where
+   cmult_Nil:  "c %* [] = []"
+|  cmult_Cons: "c %* (h#t) = (c * h)#(c %* t)"
+
+text{*Multiplication by a polynomial*}
+primrec (in semiring_0) pmult :: "'a list \<Rightarrow> 'a list \<Rightarrow> 'a list"  (infixl "***" 70)
+where
+   pmult_Nil:  "[] *** l2 = []"
+|  pmult_Cons: "(h#t) *** l2 = (if t = [] then h %* l2
+                              else (h %* l2) +++ ((0) # (t *** l2)))"
+
+text{*Repeated multiplication by a polynomial*}
+primrec (in semiring_0) mulexp :: "nat \<Rightarrow> 'a list \<Rightarrow> 'a  list \<Rightarrow> 'a list" where
+   mulexp_zero:  "mulexp 0 p q = q"
+|  mulexp_Suc:   "mulexp (Suc n) p q = p *** mulexp n p q"
+
+text{*Exponential*}
+primrec (in semiring_1) pexp :: "'a list \<Rightarrow> nat \<Rightarrow> 'a list"  (infixl "%^" 80) where
+   pexp_0:   "p %^ 0 = [1]"
+|  pexp_Suc: "p %^ (Suc n) = p *** (p %^ n)"
+
+text{*Quotient related value of dividing a polynomial by x + a*}
+(* Useful for divisor properties in inductive proofs *)
+primrec (in field) "pquot" :: "'a list \<Rightarrow> 'a \<Rightarrow> 'a list" where
+   pquot_Nil:  "pquot [] a= []"
+|  pquot_Cons: "pquot (h#t) a = (if t = [] then [h]
+                   else (inverse(a) * (h - hd( pquot t a)))#(pquot t a))"
+
+text{*normalization of polynomials (remove extra 0 coeff)*}
+primrec (in semiring_0) pnormalize :: "'a list \<Rightarrow> 'a list" where
+  pnormalize_Nil:  "pnormalize [] = []"
+| pnormalize_Cons: "pnormalize (h#p) = (if ( (pnormalize p) = [])
+                                     then (if (h = 0) then [] else [h])
+                                     else (h#(pnormalize p)))"
+
+definition (in semiring_0) "pnormal p = ((pnormalize p = p) \<and> p \<noteq> [])"
+definition (in semiring_0) "nonconstant p = (pnormal p \<and> (\<forall>x. p \<noteq> [x]))"
+text{*Other definitions*}
+
+definition (in ring_1)
+  poly_minus :: "'a list => 'a list" ("-- _" [80] 80) where
+  "-- p = (- 1) %* p"
+
+definition (in semiring_0)
+  divides :: "'a list \<Rightarrow> 'a list \<Rightarrow> bool"  (infixl "divides" 70) where
+  [code del]: "p1 divides p2 = (\<exists>q. poly p2 = poly(p1 *** q))"
+
+    --{*order of a polynomial*}
+definition (in ring_1) order :: "'a => 'a list => nat" where
+  "order a p = (SOME n. ([-a, 1] %^ n) divides p &
+                      ~ (([-a, 1] %^ (Suc n)) divides p))"
+
+     --{*degree of a polynomial*}
+definition (in semiring_0) degree :: "'a list => nat" where 
+  "degree p = length (pnormalize p) - 1"
+
+     --{*squarefree polynomials --- NB with respect to real roots only.*}
+definition (in ring_1)
+  rsquarefree :: "'a list => bool" where
+  "rsquarefree p = (poly p \<noteq> poly [] &
+                     (\<forall>a. (order a p = 0) | (order a p = 1)))"
+
+context semiring_0
+begin
+
+lemma padd_Nil2[simp]: "p +++ [] = p"
+by (induct p) auto
+
+lemma padd_Cons_Cons: "(h1 # p1) +++ (h2 # p2) = (h1 + h2) # (p1 +++ p2)"
+by auto
+
+lemma pminus_Nil[simp]: "-- [] = []"
+by (simp add: poly_minus_def)
+
+lemma pmult_singleton: "[h1] *** p1 = h1 %* p1" by simp
+end
+
+lemma (in semiring_1) poly_ident_mult[simp]: "1 %* t = t" by (induct "t", auto)
+
+lemma (in semiring_0) poly_simple_add_Cons[simp]: "[a] +++ ((0)#t) = (a#t)"
+by simp
+
+text{*Handy general properties*}
+
+lemma (in comm_semiring_0) padd_commut: "b +++ a = a +++ b"
+proof(induct b arbitrary: a)
+  case Nil thus ?case by auto
+next
+  case (Cons b bs a) thus ?case by (cases a, simp_all add: add_commute)
+qed
+
+lemma (in comm_semiring_0) padd_assoc: "\<forall>b c. (a +++ b) +++ c = a +++ (b +++ c)"
+apply (induct a arbitrary: b c)
+apply (simp, clarify)
+apply (case_tac b, simp_all add: add_ac)
+done
+
+lemma (in semiring_0) poly_cmult_distr: "a %* ( p +++ q) = (a %* p +++ a %* q)"
+apply (induct p arbitrary: q,simp)
+apply (case_tac q, simp_all add: right_distrib)
+done
+
+lemma (in ring_1) pmult_by_x[simp]: "[0, 1] *** t = ((0)#t)"
+apply (induct "t", simp)
+apply (auto simp add: mult_zero_left poly_ident_mult padd_commut)
+apply (case_tac t, auto)
+done
+
+text{*properties of evaluation of polynomials.*}
+
+lemma (in semiring_0) poly_add: "poly (p1 +++ p2) x = poly p1 x + poly p2 x"
+proof(induct p1 arbitrary: p2)
+  case Nil thus ?case by simp
+next
+  case (Cons a as p2) thus ?case 
+    by (cases p2, simp_all  add: add_ac right_distrib)
+qed
+
+lemma (in comm_semiring_0) poly_cmult: "poly (c %* p) x = c * poly p x"
+apply (induct "p") 
+apply (case_tac [2] "x=zero")
+apply (auto simp add: right_distrib mult_ac)
+done
+
+lemma (in comm_semiring_0) poly_cmult_map: "poly (map (op * c) p) x = c*poly p x"
+  by (induct p, auto simp add: right_distrib mult_ac)
+
+lemma (in comm_ring_1) poly_minus: "poly (-- p) x = - (poly p x)"
+apply (simp add: poly_minus_def)
+apply (auto simp add: poly_cmult minus_mult_left[symmetric])
+done
+
+lemma (in comm_semiring_0) poly_mult: "poly (p1 *** p2) x = poly p1 x * poly p2 x"
+proof(induct p1 arbitrary: p2)
+  case Nil thus ?case by simp
+next
+  case (Cons a as p2)
+  thus ?case by (cases as, 
+    simp_all add: poly_cmult poly_add left_distrib right_distrib mult_ac)
+qed
+
+class recpower_semiring = semiring + recpower
+class recpower_semiring_1 = semiring_1 + recpower
+class recpower_semiring_0 = semiring_0 + recpower
+class recpower_ring = ring + recpower
+class recpower_ring_1 = ring_1 + recpower
+subclass (in recpower_ring_1) recpower_ring ..
+class recpower_comm_semiring_1 = recpower + comm_semiring_1
+class recpower_comm_ring_1 = recpower + comm_ring_1
+subclass (in recpower_comm_ring_1) recpower_comm_semiring_1 ..
+class recpower_idom = recpower + idom
+subclass (in recpower_idom) recpower_comm_ring_1 ..
+class idom_char_0 = idom + ring_char_0
+class recpower_idom_char_0 = recpower + idom_char_0
+subclass (in recpower_idom_char_0) recpower_idom ..
+
+lemma (in recpower_comm_ring_1) poly_exp: "poly (p %^ n) x = (poly p x) ^ n"
+apply (induct "n")
+apply (auto simp add: poly_cmult poly_mult power_Suc)
+done
+
+text{*More Polynomial Evaluation Lemmas*}
+
+lemma  (in semiring_0) poly_add_rzero[simp]: "poly (a +++ []) x = poly a x"
+by simp
+
+lemma (in comm_semiring_0) poly_mult_assoc: "poly ((a *** b) *** c) x = poly (a *** (b *** c)) x"
+  by (simp add: poly_mult mult_assoc)
+
+lemma (in semiring_0) poly_mult_Nil2[simp]: "poly (p *** []) x = 0"
+by (induct "p", auto)
+
+lemma (in comm_semiring_1) poly_exp_add: "poly (p %^ (n + d)) x = poly( p %^ n *** p %^ d) x"
+apply (induct "n")
+apply (auto simp add: poly_mult mult_assoc)
+done
+
+subsection{*Key Property: if @{term "f(a) = 0"} then @{term "(x - a)"} divides
+ @{term "p(x)"} *}
+
+lemma (in comm_ring_1) lemma_poly_linear_rem: "\<forall>h. \<exists>q r. h#t = [r] +++ [-a, 1] *** q"
+proof(induct t)
+  case Nil
+  {fix h have "[h] = [h] +++ [- a, 1] *** []" by simp}
+  thus ?case by blast
+next
+  case (Cons  x xs)
+  {fix h 
+    from Cons.hyps[rule_format, of x] 
+    obtain q r where qr: "x#xs = [r] +++ [- a, 1] *** q" by blast
+    have "h#x#xs = [a*r + h] +++ [-a, 1] *** (r#q)" 
+      using qr by(cases q, simp_all add: ring_simps diff_def[symmetric] 
+	minus_mult_left[symmetric] right_minus)
+    hence "\<exists>q r. h#x#xs = [r] +++ [-a, 1] *** q" by blast}
+  thus ?case by blast
+qed
+
+lemma (in comm_ring_1) poly_linear_rem: "\<exists>q r. h#t = [r] +++ [-a, 1] *** q"
+by (cut_tac t = t and a = a in lemma_poly_linear_rem, auto)
+
+
+lemma (in comm_ring_1) poly_linear_divides: "(poly p a = 0) = ((p = []) | (\<exists>q. p = [-a, 1] *** q))"
+proof-
+  {assume p: "p = []" hence ?thesis by simp}
+  moreover
+  {fix x xs assume p: "p = x#xs"
+    {fix q assume "p = [-a, 1] *** q" hence "poly p a = 0" 
+	by (simp add: poly_add poly_cmult minus_mult_left[symmetric])}
+    moreover
+    {assume p0: "poly p a = 0"
+      from poly_linear_rem[of x xs a] obtain q r 
+      where qr: "x#xs = [r] +++ [- a, 1] *** q" by blast
+      have "r = 0" using p0 by (simp only: p qr poly_mult poly_add) simp
+      hence "\<exists>q. p = [- a, 1] *** q" using p qr  apply - apply (rule exI[where x=q])apply auto apply (cases q) apply auto done}
+    ultimately have ?thesis using p by blast}
+  ultimately show ?thesis by (cases p, auto)
+qed
+
+lemma (in semiring_0) lemma_poly_length_mult[simp]: "\<forall>h k a. length (k %* p +++  (h # (a %* p))) = Suc (length p)"
+by (induct "p", auto)
+
+lemma (in semiring_0) lemma_poly_length_mult2[simp]: "\<forall>h k. length (k %* p +++  (h # p)) = Suc (length p)"
+by (induct "p", auto)
+
+lemma (in ring_1) poly_length_mult[simp]: "length([-a,1] *** q) = Suc (length q)"
+by auto
+
+subsection{*Polynomial length*}
+
+lemma (in semiring_0) poly_cmult_length[simp]: "length (a %* p) = length p"
+by (induct "p", auto)
+
+lemma (in semiring_0) poly_add_length: "length (p1 +++ p2) = max (length p1) (length p2)"
+apply (induct p1 arbitrary: p2, simp_all)
+apply arith
+done
+
+lemma (in semiring_0) poly_root_mult_length[simp]: "length([a,b] *** p) = Suc (length p)"
+by (simp add: poly_add_length)
+
+lemma (in idom) poly_mult_not_eq_poly_Nil[simp]: 
+ "poly (p *** q) x \<noteq> poly [] x \<longleftrightarrow> poly p x \<noteq> poly [] x \<and> poly q x \<noteq> poly [] x"
+by (auto simp add: poly_mult)
+
+lemma (in idom) poly_mult_eq_zero_disj: "poly (p *** q) x = 0 \<longleftrightarrow> poly p x = 0 \<or> poly q x = 0"
+by (auto simp add: poly_mult)
+
+text{*Normalisation Properties*}
+
+lemma (in semiring_0) poly_normalized_nil: "(pnormalize p = []) --> (poly p x = 0)"
+by (induct "p", auto)
+
+text{*A nontrivial polynomial of degree n has no more than n roots*}
+lemma (in idom) poly_roots_index_lemma:
+   assumes p: "poly p x \<noteq> poly [] x" and n: "length p = n" 
+  shows "\<exists>i. \<forall>x. poly p x = 0 \<longrightarrow> (\<exists>m\<le>n. x = i m)"
+  using p n
+proof(induct n arbitrary: p x)
+  case 0 thus ?case by simp 
+next
+  case (Suc n p x)
+  {assume C: "\<And>i. \<exists>x. poly p x = 0 \<and> (\<forall>m\<le>Suc n. x \<noteq> i m)"
+    from Suc.prems have p0: "poly p x \<noteq> 0" "p\<noteq> []" by auto
+    from p0(1)[unfolded poly_linear_divides[of p x]] 
+    have "\<forall>q. p \<noteq> [- x, 1] *** q" by blast
+    from C obtain a where a: "poly p a = 0" by blast
+    from a[unfolded poly_linear_divides[of p a]] p0(2) 
+    obtain q where q: "p = [-a, 1] *** q" by blast
+    have lg: "length q = n" using q Suc.prems(2) by simp
+    from q p0 have qx: "poly q x \<noteq> poly [] x" 
+      by (auto simp add: poly_mult poly_add poly_cmult)
+    from Suc.hyps[OF qx lg] obtain i where 
+      i: "\<forall>x. poly q x = 0 \<longrightarrow> (\<exists>m\<le>n. x = i m)" by blast
+    let ?i = "\<lambda>m. if m = Suc n then a else i m"
+    from C[of ?i] obtain y where y: "poly p y = 0" "\<forall>m\<le> Suc n. y \<noteq> ?i m" 
+      by blast
+    from y have "y = a \<or> poly q y = 0" 
+      by (simp only: q poly_mult_eq_zero_disj poly_add) (simp add: ring_simps)
+    with i[rule_format, of y] y(1) y(2) have False apply auto 
+      apply (erule_tac x="m" in allE)
+      apply auto
+      done}
+  thus ?case by blast
+qed
+
+
+lemma (in idom) poly_roots_index_length: "poly p x \<noteq> poly [] x ==>
+      \<exists>i. \<forall>x. (poly p x = 0) --> (\<exists>n. n \<le> length p & x = i n)"
+by (blast intro: poly_roots_index_lemma)
+
+lemma (in idom) poly_roots_finite_lemma1: "poly p x \<noteq> poly [] x ==>
+      \<exists>N i. \<forall>x. (poly p x = 0) --> (\<exists>n. (n::nat) < N & x = i n)"
+apply (drule poly_roots_index_length, safe)
+apply (rule_tac x = "Suc (length p)" in exI)
+apply (rule_tac x = i in exI) 
+apply (simp add: less_Suc_eq_le)
+done
+
+
+lemma (in idom) idom_finite_lemma:
+  assumes P: "\<forall>x. P x --> (\<exists>n. n < length j & x = j!n)"
+  shows "finite {x. P x}"
+proof-
+  let ?M = "{x. P x}"
+  let ?N = "set j"
+  have "?M \<subseteq> ?N" using P by auto
+  thus ?thesis using finite_subset by auto
+qed
+
+
+lemma (in idom) poly_roots_finite_lemma2: "poly p x \<noteq> poly [] x ==>
+      \<exists>i. \<forall>x. (poly p x = 0) --> x \<in> set i"
+apply (drule poly_roots_index_length, safe)
+apply (rule_tac x="map (\<lambda>n. i n) [0 ..< Suc (length p)]" in exI)
+apply (auto simp add: image_iff)
+apply (erule_tac x="x" in allE, clarsimp)
+by (case_tac "n=length p", auto simp add: order_le_less)
+
+lemma UNIV_nat_infinite: "\<not> finite (UNIV :: nat set)"
+  unfolding finite_conv_nat_seg_image
+proof(auto simp add: expand_set_eq image_iff)
+  fix n::nat and f:: "nat \<Rightarrow> nat"
+  let ?N = "{i. i < n}"
+  let ?fN = "f ` ?N"
+  let ?y = "Max ?fN + 1"
+  from nat_seg_image_imp_finite[of "?fN" "f" n] 
+  have thfN: "finite ?fN" by simp
+  {assume "n =0" hence "\<exists>x. \<forall>xa<n. x \<noteq> f xa" by auto}
+  moreover
+  {assume nz: "n \<noteq> 0"
+    hence thne: "?fN \<noteq> {}" by (auto simp add: neq0_conv)
+    have "\<forall>x\<in> ?fN. Max ?fN \<ge> x" using nz Max_ge_iff[OF thfN thne] by auto
+    hence "\<forall>x\<in> ?fN. ?y > x" by auto
+    hence "?y \<notin> ?fN" by auto
+    hence "\<exists>x. \<forall>xa<n. x \<noteq> f xa" by auto }
+  ultimately show "\<exists>x. \<forall>xa<n. x \<noteq> f xa" by blast
+qed
+
+lemma (in ring_char_0) UNIV_ring_char_0_infinte: 
+  "\<not> (finite (UNIV:: 'a set))" 
+proof
+  assume F: "finite (UNIV :: 'a set)"
+  have "finite (UNIV :: nat set)"
+  proof (rule finite_imageD)
+    have "of_nat ` UNIV \<subseteq> UNIV" by simp
+    then show "finite (of_nat ` UNIV :: 'a set)" using F by (rule finite_subset)
+    show "inj (of_nat :: nat \<Rightarrow> 'a)" by (simp add: inj_on_def)
+  qed
+  with UNIV_nat_infinite show False ..
+qed
+
+lemma (in idom_char_0) poly_roots_finite: "(poly p \<noteq> poly []) = 
+  finite {x. poly p x = 0}"
+proof
+  assume H: "poly p \<noteq> poly []"
+  show "finite {x. poly p x = (0::'a)}"
+    using H
+    apply -
+    apply (erule contrapos_np, rule ext)
+    apply (rule ccontr)
+    apply (clarify dest!: poly_roots_finite_lemma2)
+    using finite_subset
+  proof-
+    fix x i
+    assume F: "\<not> finite {x. poly p x = (0\<Colon>'a)}" 
+      and P: "\<forall>x. poly p x = (0\<Colon>'a) \<longrightarrow> x \<in> set i"
+    let ?M= "{x. poly p x = (0\<Colon>'a)}"
+    from P have "?M \<subseteq> set i" by auto
+    with finite_subset F show False by auto
+  qed
+next
+  assume F: "finite {x. poly p x = (0\<Colon>'a)}"
+  show "poly p \<noteq> poly []" using F UNIV_ring_char_0_infinte by auto  
+qed
+
+text{*Entirety and Cancellation for polynomials*}
+
+lemma (in idom_char_0) poly_entire_lemma2: 
+  assumes p0: "poly p \<noteq> poly []" and q0: "poly q \<noteq> poly []"
+  shows "poly (p***q) \<noteq> poly []"
+proof-
+  let ?S = "\<lambda>p. {x. poly p x = 0}"
+  have "?S (p *** q) = ?S p \<union> ?S q" by (auto simp add: poly_mult)
+  with p0 q0 show ?thesis  unfolding poly_roots_finite by auto
+qed
+
+lemma (in idom_char_0) poly_entire: 
+  "poly (p *** q) = poly [] \<longleftrightarrow> poly p = poly [] \<or> poly q = poly []"
+using poly_entire_lemma2[of p q] 
+by auto (rule ext, simp add: poly_mult)+
+
+lemma (in idom_char_0) poly_entire_neg: "(poly (p *** q) \<noteq> poly []) = ((poly p \<noteq> poly []) & (poly q \<noteq> poly []))"
+by (simp add: poly_entire)
+
+lemma fun_eq: " (f = g) = (\<forall>x. f x = g x)"
+by (auto intro!: ext)
+
+lemma (in comm_ring_1) poly_add_minus_zero_iff: "(poly (p +++ -- q) = poly []) = (poly p = poly q)"
+by (auto simp add: ring_simps poly_add poly_minus_def fun_eq poly_cmult minus_mult_left[symmetric])
+
+lemma (in comm_ring_1) poly_add_minus_mult_eq: "poly (p *** q +++ --(p *** r)) = poly (p *** (q +++ -- r))"
+by (auto simp add: poly_add poly_minus_def fun_eq poly_mult poly_cmult right_distrib minus_mult_left[symmetric] minus_mult_right[symmetric])
+
+subclass (in idom_char_0) comm_ring_1 ..
+lemma (in idom_char_0) poly_mult_left_cancel: "(poly (p *** q) = poly (p *** r)) = (poly p = poly [] | poly q = poly r)"
+proof-
+  have "poly (p *** q) = poly (p *** r) \<longleftrightarrow> poly (p *** q +++ -- (p *** r)) = poly []" by (simp only: poly_add_minus_zero_iff)
+  also have "\<dots> \<longleftrightarrow> poly p = poly [] | poly q = poly r"
+    by (auto intro: ext simp add: poly_add_minus_mult_eq poly_entire poly_add_minus_zero_iff)
+  finally show ?thesis .
+qed
+
+lemma (in recpower_idom) poly_exp_eq_zero[simp]:
+     "(poly (p %^ n) = poly []) = (poly p = poly [] & n \<noteq> 0)"
+apply (simp only: fun_eq add: all_simps [symmetric]) 
+apply (rule arg_cong [where f = All]) 
+apply (rule ext)
+apply (induct n)
+apply (auto simp add: poly_exp poly_mult)
+done
+
+lemma (in semiring_1) one_neq_zero[simp]: "1 \<noteq> 0" using zero_neq_one by blast
+lemma (in comm_ring_1) poly_prime_eq_zero[simp]: "poly [a,1] \<noteq> poly []"
+apply (simp add: fun_eq)
+apply (rule_tac x = "minus one a" in exI)
+apply (unfold diff_minus)
+apply (subst add_commute)
+apply (subst add_assoc)
+apply simp
+done 
+
+lemma (in recpower_idom) poly_exp_prime_eq_zero: "(poly ([a, 1] %^ n) \<noteq> poly [])"
+by auto
+
+text{*A more constructive notion of polynomials being trivial*}
+
+lemma (in idom_char_0) poly_zero_lemma': "poly (h # t) = poly [] ==> h = 0 & poly t = poly []"
+apply(simp add: fun_eq)
+apply (case_tac "h = zero")
+apply (drule_tac [2] x = zero in spec, auto) 
+apply (cases "poly t = poly []", simp) 
+proof-
+  fix x
+  assume H: "\<forall>x. x = (0\<Colon>'a) \<or> poly t x = (0\<Colon>'a)"  and pnz: "poly t \<noteq> poly []"
+  let ?S = "{x. poly t x = 0}"
+  from H have "\<forall>x. x \<noteq>0 \<longrightarrow> poly t x = 0" by blast
+  hence th: "?S \<supseteq> UNIV - {0}" by auto
+  from poly_roots_finite pnz have th': "finite ?S" by blast
+  from finite_subset[OF th th'] UNIV_ring_char_0_infinte
+  show "poly t x = (0\<Colon>'a)" by simp
+  qed
+
+lemma (in idom_char_0) poly_zero: "(poly p = poly []) = list_all (%c. c = 0) p"
+apply (induct "p", simp)
+apply (rule iffI)
+apply (drule poly_zero_lemma', auto)
+done
+
+lemma (in idom_char_0) poly_0: "list_all (\<lambda>c. c = 0) p \<Longrightarrow> poly p x = 0"
+  unfolding poly_zero[symmetric] by simp
+
+
+
+text{*Basics of divisibility.*}
+
+lemma (in idom) poly_primes: "([a, 1] divides (p *** q)) = ([a, 1] divides p | [a, 1] divides q)"
+apply (auto simp add: divides_def fun_eq poly_mult poly_add poly_cmult left_distrib [symmetric])
+apply (drule_tac x = "uminus a" in spec)
+apply (simp add: poly_linear_divides poly_add poly_cmult left_distrib [symmetric])
+apply (cases "p = []")
+apply (rule exI[where x="[]"])
+apply simp
+apply (cases "q = []")
+apply (erule allE[where x="[]"], simp)
+
+apply clarsimp
+apply (cases "\<exists>q\<Colon>'a list. p = a %* q +++ ((0\<Colon>'a) # q)")
+apply (clarsimp simp add: poly_add poly_cmult)
+apply (rule_tac x="qa" in exI)
+apply (simp add: left_distrib [symmetric])
+apply clarsimp
+
+apply (auto simp add: right_minus poly_linear_divides poly_add poly_cmult left_distrib [symmetric])
+apply (rule_tac x = "pmult qa q" in exI)
+apply (rule_tac [2] x = "pmult p qa" in exI)
+apply (auto simp add: poly_add poly_mult poly_cmult mult_ac)
+done
+
+lemma (in comm_semiring_1) poly_divides_refl[simp]: "p divides p"
+apply (simp add: divides_def)
+apply (rule_tac x = "[one]" in exI)
+apply (auto simp add: poly_mult fun_eq)
+done
+
+lemma (in comm_semiring_1) poly_divides_trans: "[| p divides q; q divides r |] ==> p divides r"
+apply (simp add: divides_def, safe)
+apply (rule_tac x = "pmult qa qaa" in exI)
+apply (auto simp add: poly_mult fun_eq mult_assoc)
+done
+
+
+lemma (in recpower_comm_semiring_1) poly_divides_exp: "m \<le> n ==> (p %^ m) divides (p %^ n)"
+apply (auto simp add: le_iff_add)
+apply (induct_tac k)
+apply (rule_tac [2] poly_divides_trans)
+apply (auto simp add: divides_def)
+apply (rule_tac x = p in exI)
+apply (auto simp add: poly_mult fun_eq mult_ac)
+done
+
+lemma (in recpower_comm_semiring_1) poly_exp_divides: "[| (p %^ n) divides q;  m\<le>n |] ==> (p %^ m) divides q"
+by (blast intro: poly_divides_exp poly_divides_trans)
+
+lemma (in comm_semiring_0) poly_divides_add:
+   "[| p divides q; p divides r |] ==> p divides (q +++ r)"
+apply (simp add: divides_def, auto)
+apply (rule_tac x = "padd qa qaa" in exI)
+apply (auto simp add: poly_add fun_eq poly_mult right_distrib)
+done
+
+lemma (in comm_ring_1) poly_divides_diff:
+   "[| p divides q; p divides (q +++ r) |] ==> p divides r"
+apply (simp add: divides_def, auto)
+apply (rule_tac x = "padd qaa (poly_minus qa)" in exI)
+apply (auto simp add: poly_add fun_eq poly_mult poly_minus right_diff_distrib compare_rls add_ac)
+done
+
+lemma (in comm_ring_1) poly_divides_diff2: "[| p divides r; p divides (q +++ r) |] ==> p divides q"
+apply (erule poly_divides_diff)
+apply (auto simp add: poly_add fun_eq poly_mult divides_def add_ac)
+done
+
+lemma (in semiring_0) poly_divides_zero: "poly p = poly [] ==> q divides p"
+apply (simp add: divides_def)
+apply (rule exI[where x="[]"])
+apply (auto simp add: fun_eq poly_mult)
+done
+
+lemma (in semiring_0) poly_divides_zero2[simp]: "q divides []"
+apply (simp add: divides_def)
+apply (rule_tac x = "[]" in exI)
+apply (auto simp add: fun_eq)
+done
+
+text{*At last, we can consider the order of a root.*}
+
+lemma (in idom_char_0)  poly_order_exists_lemma:
+  assumes lp: "length p = d" and p: "poly p \<noteq> poly []"
+  shows "\<exists>n q. p = mulexp n [-a, 1] q \<and> poly q a \<noteq> 0"
+using lp p
+proof(induct d arbitrary: p)
+  case 0 thus ?case by simp
+next
+  case (Suc n p)
+  {assume p0: "poly p a = 0"
+    from Suc.prems have h: "length p = Suc n" "poly p \<noteq> poly []" by auto
+    hence pN: "p \<noteq> []" by auto
+    from p0[unfolded poly_linear_divides] pN  obtain q where 
+      q: "p = [-a, 1] *** q" by blast
+    from q h p0 have qh: "length q = n" "poly q \<noteq> poly []" 
+      apply -
+      apply simp
+      apply (simp only: fun_eq)
+      apply (rule ccontr)
+      apply (simp add: fun_eq poly_add poly_cmult minus_mult_left[symmetric])
+      done
+    from Suc.hyps[OF qh] obtain m r where 
+      mr: "q = mulexp m [-a,1] r" "poly r a \<noteq> 0" by blast    
+    from mr q have "p = mulexp (Suc m) [-a,1] r \<and> poly r a \<noteq> 0" by simp
+    hence ?case by blast}
+  moreover
+  {assume p0: "poly p a \<noteq> 0"
+    hence ?case using Suc.prems apply simp by (rule exI[where x="0::nat"], simp)}
+  ultimately show ?case by blast
+qed
+
+
+lemma (in recpower_comm_semiring_1) poly_mulexp: "poly (mulexp n p q) x = (poly p x) ^ n * poly q x"
+by(induct n, auto simp add: poly_mult power_Suc mult_ac)
+
+lemma (in comm_semiring_1) divides_left_mult:
+  assumes d:"(p***q) divides r" shows "p divides r \<and> q divides r"
+proof-
+  from d obtain t where r:"poly r = poly (p***q *** t)"
+    unfolding divides_def by blast
+  hence "poly r = poly (p *** (q *** t))"
+    "poly r = poly (q *** (p***t))" by(auto simp add: fun_eq poly_mult mult_ac)
+  thus ?thesis unfolding divides_def by blast
+qed
+
+
+
+(* FIXME: Tidy up *)
+
+lemma (in recpower_semiring_1) 
+  zero_power_iff: "0 ^ n = (if n = 0 then 1 else 0)"
+  by (induct n, simp_all add: power_Suc)
+
+lemma (in recpower_idom_char_0) poly_order_exists:
+  assumes lp: "length p = d" and p0: "poly p \<noteq> poly []"
+  shows "\<exists>n. ([-a, 1] %^ n) divides p & ~(([-a, 1] %^ (Suc n)) divides p)"
+proof-
+let ?poly = poly
+let ?mulexp = mulexp
+let ?pexp = pexp
+from lp p0
+show ?thesis
+apply -
+apply (drule poly_order_exists_lemma [where a=a], assumption, clarify)  
+apply (rule_tac x = n in exI, safe)
+apply (unfold divides_def)
+apply (rule_tac x = q in exI)
+apply (induct_tac "n", simp)
+apply (simp (no_asm_simp) add: poly_add poly_cmult poly_mult right_distrib mult_ac)
+apply safe
+apply (subgoal_tac "?poly (?mulexp n [uminus a, one] q) \<noteq> ?poly (pmult (?pexp [uminus a, one] (Suc n)) qa)") 
+apply simp 
+apply (induct_tac "n")
+apply (simp del: pmult_Cons pexp_Suc)
+apply (erule_tac Q = "?poly q a = zero" in contrapos_np)
+apply (simp add: poly_add poly_cmult minus_mult_left[symmetric])
+apply (rule pexp_Suc [THEN ssubst])
+apply (rule ccontr)
+apply (simp add: poly_mult_left_cancel poly_mult_assoc del: pmult_Cons pexp_Suc)
+done
+qed
+
+
+lemma (in semiring_1) poly_one_divides[simp]: "[1] divides p"
+by (simp add: divides_def, auto)
+
+lemma (in recpower_idom_char_0) poly_order: "poly p \<noteq> poly []
+      ==> EX! n. ([-a, 1] %^ n) divides p &
+                 ~(([-a, 1] %^ (Suc n)) divides p)"
+apply (auto intro: poly_order_exists simp add: less_linear simp del: pmult_Cons pexp_Suc)
+apply (cut_tac x = y and y = n in less_linear)
+apply (drule_tac m = n in poly_exp_divides)
+apply (auto dest: Suc_le_eq [THEN iffD2, THEN [2] poly_exp_divides]
+            simp del: pmult_Cons pexp_Suc)
+done
+
+text{*Order*}
+
+lemma some1_equalityD: "[| n = (@n. P n); EX! n. P n |] ==> P n"
+by (blast intro: someI2)
+
+lemma (in recpower_idom_char_0) order:
+      "(([-a, 1] %^ n) divides p &
+        ~(([-a, 1] %^ (Suc n)) divides p)) =
+        ((n = order a p) & ~(poly p = poly []))"
+apply (unfold order_def)
+apply (rule iffI)
+apply (blast dest: poly_divides_zero intro!: some1_equality [symmetric] poly_order)
+apply (blast intro!: poly_order [THEN [2] some1_equalityD])
+done
+
+lemma (in recpower_idom_char_0) order2: "[| poly p \<noteq> poly [] |]
+      ==> ([-a, 1] %^ (order a p)) divides p &
+              ~(([-a, 1] %^ (Suc(order a p))) divides p)"
+by (simp add: order del: pexp_Suc)
+
+lemma (in recpower_idom_char_0) order_unique: "[| poly p \<noteq> poly []; ([-a, 1] %^ n) divides p;
+         ~(([-a, 1] %^ (Suc n)) divides p)
+      |] ==> (n = order a p)"
+by (insert order [of a n p], auto) 
+
+lemma (in recpower_idom_char_0) order_unique_lemma: "(poly p \<noteq> poly [] & ([-a, 1] %^ n) divides p &
+         ~(([-a, 1] %^ (Suc n)) divides p))
+      ==> (n = order a p)"
+by (blast intro: order_unique)
+
+lemma (in ring_1) order_poly: "poly p = poly q ==> order a p = order a q"
+by (auto simp add: fun_eq divides_def poly_mult order_def)
+
+lemma (in semiring_1) pexp_one[simp]: "p %^ (Suc 0) = p"
+apply (induct "p")
+apply (auto simp add: numeral_1_eq_1)
+done
+
+lemma (in comm_ring_1) lemma_order_root:
+     " 0 < n & [- a, 1] %^ n divides p & ~ [- a, 1] %^ (Suc n) divides p
+             \<Longrightarrow> poly p a = 0"
+apply (induct n arbitrary: a p, blast)
+apply (auto simp add: divides_def poly_mult simp del: pmult_Cons)
+done
+
+lemma (in recpower_idom_char_0) order_root: "(poly p a = 0) = ((poly p = poly []) | order a p \<noteq> 0)"
+proof-
+  let ?poly = poly
+  show ?thesis 
+apply (case_tac "?poly p = ?poly []", auto)
+apply (simp add: poly_linear_divides del: pmult_Cons, safe)
+apply (drule_tac [!] a = a in order2)
+apply (rule ccontr)
+apply (simp add: divides_def poly_mult fun_eq del: pmult_Cons, blast)
+using neq0_conv
+apply (blast intro: lemma_order_root)
+done
+qed
+
+lemma (in recpower_idom_char_0) order_divides: "(([-a, 1] %^ n) divides p) = ((poly p = poly []) | n \<le> order a p)"
+proof-
+  let ?poly = poly
+  show ?thesis 
+apply (case_tac "?poly p = ?poly []", auto)
+apply (simp add: divides_def fun_eq poly_mult)
+apply (rule_tac x = "[]" in exI)
+apply (auto dest!: order2 [where a=a]
+	    intro: poly_exp_divides simp del: pexp_Suc)
+done
+qed
+
+lemma (in recpower_idom_char_0) order_decomp:
+     "poly p \<noteq> poly []
+      ==> \<exists>q. (poly p = poly (([-a, 1] %^ (order a p)) *** q)) &
+                ~([-a, 1] divides q)"
+apply (unfold divides_def)
+apply (drule order2 [where a = a])
+apply (simp add: divides_def del: pexp_Suc pmult_Cons, safe)
+apply (rule_tac x = q in exI, safe)
+apply (drule_tac x = qa in spec)
+apply (auto simp add: poly_mult fun_eq poly_exp mult_ac simp del: pmult_Cons)
+done
+
+text{*Important composition properties of orders.*}
+lemma order_mult: "poly (p *** q) \<noteq> poly []
+      ==> order a (p *** q) = order a p + order (a::'a::{recpower_idom_char_0}) q"
+apply (cut_tac a = a and p = "p *** q" and n = "order a p + order a q" in order)
+apply (auto simp add: poly_entire simp del: pmult_Cons)
+apply (drule_tac a = a in order2)+
+apply safe
+apply (simp add: divides_def fun_eq poly_exp_add poly_mult del: pmult_Cons, safe)
+apply (rule_tac x = "qa *** qaa" in exI)
+apply (simp add: poly_mult mult_ac del: pmult_Cons)
+apply (drule_tac a = a in order_decomp)+
+apply safe
+apply (subgoal_tac "[-a,1] divides (qa *** qaa) ")
+apply (simp add: poly_primes del: pmult_Cons)
+apply (auto simp add: divides_def simp del: pmult_Cons)
+apply (rule_tac x = qb in exI)
+apply (subgoal_tac "poly ([-a, 1] %^ (order a p) *** (qa *** qaa)) = poly ([-a, 1] %^ (order a p) *** ([-a, 1] *** qb))")
+apply (drule poly_mult_left_cancel [THEN iffD1], force)
+apply (subgoal_tac "poly ([-a, 1] %^ (order a q) *** ([-a, 1] %^ (order a p) *** (qa *** qaa))) = poly ([-a, 1] %^ (order a q) *** ([-a, 1] %^ (order a p) *** ([-a, 1] *** qb))) ")
+apply (drule poly_mult_left_cancel [THEN iffD1], force)
+apply (simp add: fun_eq poly_exp_add poly_mult mult_ac del: pmult_Cons)
+done
+
+lemma (in recpower_idom_char_0) order_mult: 
+  assumes pq0: "poly (p *** q) \<noteq> poly []"
+  shows "order a (p *** q) = order a p + order a q"
+proof-
+  let ?order = order
+  let ?divides = "op divides"
+  let ?poly = poly
+from pq0 
+show ?thesis
+apply (cut_tac a = a and p = "pmult p q" and n = "?order a p + ?order a q" in order)
+apply (auto simp add: poly_entire simp del: pmult_Cons)
+apply (drule_tac a = a in order2)+
+apply safe
+apply (simp add: divides_def fun_eq poly_exp_add poly_mult del: pmult_Cons, safe)
+apply (rule_tac x = "pmult qa qaa" in exI)
+apply (simp add: poly_mult mult_ac del: pmult_Cons)
+apply (drule_tac a = a in order_decomp)+
+apply safe
+apply (subgoal_tac "?divides [uminus a,one ] (pmult qa qaa) ")
+apply (simp add: poly_primes del: pmult_Cons)
+apply (auto simp add: divides_def simp del: pmult_Cons)
+apply (rule_tac x = qb in exI)
+apply (subgoal_tac "?poly (pmult (pexp [uminus a, one] (?order a p)) (pmult qa qaa)) = ?poly (pmult (pexp [uminus a, one] (?order a p)) (pmult [uminus a, one] qb))")
+apply (drule poly_mult_left_cancel [THEN iffD1], force)
+apply (subgoal_tac "?poly (pmult (pexp [uminus a, one ] (order a q)) (pmult (pexp [uminus a, one] (order a p)) (pmult qa qaa))) = ?poly (pmult (pexp [uminus a, one] (order a q)) (pmult (pexp [uminus a, one] (order a p)) (pmult [uminus a, one] qb))) ")
+apply (drule poly_mult_left_cancel [THEN iffD1], force)
+apply (simp add: fun_eq poly_exp_add poly_mult mult_ac del: pmult_Cons)
+done
+qed
+
+lemma (in recpower_idom_char_0) order_root2: "poly p \<noteq> poly [] ==> (poly p a = 0) = (order a p \<noteq> 0)"
+by (rule order_root [THEN ssubst], auto)
+
+lemma (in semiring_1) pmult_one[simp]: "[1] *** p = p" by auto
+
+lemma (in semiring_0) poly_Nil_zero: "poly [] = poly [0]"
+by (simp add: fun_eq)
+
+lemma (in recpower_idom_char_0) rsquarefree_decomp:
+     "[| rsquarefree p; poly p a = 0 |]
+      ==> \<exists>q. (poly p = poly ([-a, 1] *** q)) & poly q a \<noteq> 0"
+apply (simp add: rsquarefree_def, safe)
+apply (frule_tac a = a in order_decomp)
+apply (drule_tac x = a in spec)
+apply (drule_tac a = a in order_root2 [symmetric])
+apply (auto simp del: pmult_Cons)
+apply (rule_tac x = q in exI, safe)
+apply (simp add: poly_mult fun_eq)
+apply (drule_tac p1 = q in poly_linear_divides [THEN iffD1])
+apply (simp add: divides_def del: pmult_Cons, safe)
+apply (drule_tac x = "[]" in spec)
+apply (auto simp add: fun_eq)
+done
+
+
+text{*Normalization of a polynomial.*}
+
+lemma (in semiring_0) poly_normalize[simp]: "poly (pnormalize p) = poly p"
+apply (induct "p")
+apply (auto simp add: fun_eq)
+done
+
+text{*The degree of a polynomial.*}
+
+lemma (in semiring_0) lemma_degree_zero:
+     "list_all (%c. c = 0) p \<longleftrightarrow>  pnormalize p = []"
+by (induct "p", auto)
+
+lemma (in idom_char_0) degree_zero: 
+  assumes pN: "poly p = poly []" shows"degree p = 0"
+proof-
+  let ?pn = pnormalize
+  from pN
+  show ?thesis 
+    apply (simp add: degree_def)
+    apply (case_tac "?pn p = []")
+    apply (auto simp add: poly_zero lemma_degree_zero )
+    done
+qed
+
+lemma (in semiring_0) pnormalize_sing: "(pnormalize [x] = [x]) \<longleftrightarrow> x \<noteq> 0" by simp
+lemma (in semiring_0) pnormalize_pair: "y \<noteq> 0 \<longleftrightarrow> (pnormalize [x, y] = [x, y])" by simp
+lemma (in semiring_0) pnormal_cons: "pnormal p \<Longrightarrow> pnormal (c#p)" 
+  unfolding pnormal_def by simp
+lemma (in semiring_0) pnormal_tail: "p\<noteq>[] \<Longrightarrow> pnormal (c#p) \<Longrightarrow> pnormal p"
+  unfolding pnormal_def 
+  apply (cases "pnormalize p = []", auto)
+  by (cases "c = 0", auto)
+
+
+lemma (in semiring_0) pnormal_last_nonzero: "pnormal p ==> last p \<noteq> 0"
+proof(induct p)
+  case Nil thus ?case by (simp add: pnormal_def)
+next 
+  case (Cons a as) thus ?case
+    apply (simp add: pnormal_def)
+    apply (cases "pnormalize as = []", simp_all)
+    apply (cases "as = []", simp_all)
+    apply (cases "a=0", simp_all)
+    apply (cases "a=0", simp_all)
+    done
+qed
+
+lemma (in semiring_0) pnormal_length: "pnormal p \<Longrightarrow> 0 < length p"
+  unfolding pnormal_def length_greater_0_conv by blast
+
+lemma (in semiring_0) pnormal_last_length: "\<lbrakk>0 < length p ; last p \<noteq> 0\<rbrakk> \<Longrightarrow> pnormal p"
+  apply (induct p, auto)
+  apply (case_tac "p = []", auto)
+  apply (simp add: pnormal_def)
+  by (rule pnormal_cons, auto)
+
+lemma (in semiring_0) pnormal_id: "pnormal p \<longleftrightarrow> (0 < length p \<and> last p \<noteq> 0)"
+  using pnormal_last_length pnormal_length pnormal_last_nonzero by blast
+
+lemma (in idom_char_0) poly_Cons_eq: "poly (c#cs) = poly (d#ds) \<longleftrightarrow> c=d \<and> poly cs = poly ds" (is "?lhs \<longleftrightarrow> ?rhs")
+proof
+  assume eq: ?lhs
+  hence "\<And>x. poly ((c#cs) +++ -- (d#ds)) x = 0"
+    by (simp only: poly_minus poly_add ring_simps) simp
+  hence "poly ((c#cs) +++ -- (d#ds)) = poly []" by - (rule ext, simp) 
+  hence "c = d \<and> list_all (\<lambda>x. x=0) ((cs +++ -- ds))"
+    unfolding poly_zero by (simp add: poly_minus_def ring_simps minus_mult_left[symmetric])
+  hence "c = d \<and> (\<forall>x. poly (cs +++ -- ds) x = 0)"
+    unfolding poly_zero[symmetric] by simp 
+  thus ?rhs  apply (simp add: poly_minus poly_add ring_simps) apply (rule ext, simp) done
+next
+  assume ?rhs then show ?lhs  by -  (rule ext,simp)
+qed
+  
+lemma (in idom_char_0) pnormalize_unique: "poly p = poly q \<Longrightarrow> pnormalize p = pnormalize q"
+proof(induct q arbitrary: p)
+  case Nil thus ?case by (simp only: poly_zero lemma_degree_zero) simp
+next
+  case (Cons c cs p)
+  thus ?case
+  proof(induct p)
+    case Nil
+    hence "poly [] = poly (c#cs)" by blast
+    then have "poly (c#cs) = poly [] " by simp 
+    thus ?case by (simp only: poly_zero lemma_degree_zero) simp
+  next
+    case (Cons d ds)
+    hence eq: "poly (d # ds) = poly (c # cs)" by blast
+    hence eq': "\<And>x. poly (d # ds) x = poly (c # cs) x" by simp
+    hence "poly (d # ds) 0 = poly (c # cs) 0" by blast
+    hence dc: "d = c" by auto
+    with eq have "poly ds = poly cs"
+      unfolding  poly_Cons_eq by simp
+    with Cons.prems have "pnormalize ds = pnormalize cs" by blast
+    with dc show ?case by simp
+  qed
+qed
+
+lemma (in idom_char_0) degree_unique: assumes pq: "poly p = poly q"
+  shows "degree p = degree q"
+using pnormalize_unique[OF pq] unfolding degree_def by simp
+
+lemma (in semiring_0) pnormalize_length: "length (pnormalize p) \<le> length p" by (induct p, auto)
+
+lemma (in semiring_0) last_linear_mul_lemma: 
+  "last ((a %* p) +++ (x#(b %* p))) = (if p=[] then x else b*last p)"
+
+apply (induct p arbitrary: a x b, auto)
+apply (subgoal_tac "padd (cmult aa p) (times b a # cmult b p) \<noteq> []", simp)
+apply (induct_tac p, auto)
+done
+
+lemma (in semiring_1) last_linear_mul: assumes p:"p\<noteq>[]" shows "last ([a,1] *** p) = last p"
+proof-
+  from p obtain c cs where cs: "p = c#cs" by (cases p, auto)
+  from cs have eq:"[a,1] *** p = (a %* (c#cs)) +++ (0#(1 %* (c#cs)))"
+    by (simp add: poly_cmult_distr)
+  show ?thesis using cs
+    unfolding eq last_linear_mul_lemma by simp
+qed
+
+lemma (in semiring_0) pnormalize_eq: "last p \<noteq> 0 \<Longrightarrow> pnormalize p = p"
+  apply (induct p, auto)
+  apply (case_tac p, auto)+
+  done
+
+lemma (in semiring_0) last_pnormalize: "pnormalize p \<noteq> [] \<Longrightarrow> last (pnormalize p) \<noteq> 0"
+  by (induct p, auto)
+
+lemma (in semiring_0) pnormal_degree: "last p \<noteq> 0 \<Longrightarrow> degree p = length p - 1"
+  using pnormalize_eq[of p] unfolding degree_def by simp
+
+lemma (in semiring_0) poly_Nil_ext: "poly [] = (\<lambda>x. 0)" by (rule ext) simp
+
+lemma (in idom_char_0) linear_mul_degree: assumes p: "poly p \<noteq> poly []"
+  shows "degree ([a,1] *** p) = degree p + 1"
+proof-
+  from p have pnz: "pnormalize p \<noteq> []"
+    unfolding poly_zero lemma_degree_zero .
+  
+  from last_linear_mul[OF pnz, of a] last_pnormalize[OF pnz]
+  have l0: "last ([a, 1] *** pnormalize p) \<noteq> 0" by simp
+  from last_pnormalize[OF pnz] last_linear_mul[OF pnz, of a]
+    pnormal_degree[OF l0] pnormal_degree[OF last_pnormalize[OF pnz]] pnz
+ 
+
+  have th: "degree ([a,1] *** pnormalize p) = degree (pnormalize p) + 1" 
+    by (auto simp add: poly_length_mult)
+
+  have eqs: "poly ([a,1] *** pnormalize p) = poly ([a,1] *** p)"
+    by (rule ext) (simp add: poly_mult poly_add poly_cmult)
+  from degree_unique[OF eqs] th
+  show ?thesis by (simp add: degree_unique[OF poly_normalize])
+qed
+
+lemma (in idom_char_0) linear_pow_mul_degree:
+  "degree([a,1] %^n *** p) = (if poly p = poly [] then 0 else degree p + n)"
+proof(induct n arbitrary: a p)
+  case (0 a p)
+  {assume p: "poly p = poly []"
+    hence ?case using degree_unique[OF p] by (simp add: degree_def)}
+  moreover
+  {assume p: "poly p \<noteq> poly []" hence ?case by (auto simp add: poly_Nil_ext) }
+  ultimately show ?case by blast
+next
+  case (Suc n a p)
+  have eq: "poly ([a,1] %^(Suc n) *** p) = poly ([a,1] %^ n *** ([a,1] *** p))"
+    apply (rule ext, simp add: poly_mult poly_add poly_cmult)
+    by (simp add: mult_ac add_ac right_distrib)
+  note deq = degree_unique[OF eq]
+  {assume p: "poly p = poly []"
+    with eq have eq': "poly ([a,1] %^(Suc n) *** p) = poly []" 
+      by - (rule ext,simp add: poly_mult poly_cmult poly_add)
+    from degree_unique[OF eq'] p have ?case by (simp add: degree_def)}
+  moreover
+  {assume p: "poly p \<noteq> poly []"
+    from p have ap: "poly ([a,1] *** p) \<noteq> poly []"
+      using poly_mult_not_eq_poly_Nil unfolding poly_entire by auto 
+    have eq: "poly ([a,1] %^(Suc n) *** p) = poly ([a,1]%^n *** ([a,1] *** p))"
+     by (rule ext, simp add: poly_mult poly_add poly_exp poly_cmult mult_ac add_ac right_distrib)
+   from ap have ap': "(poly ([a,1] *** p) = poly []) = False" by blast
+   have  th0: "degree ([a,1]%^n *** ([a,1] *** p)) = degree ([a,1] *** p) + n"
+     apply (simp only: Suc.hyps[of a "pmult [a,one] p"] ap')
+     by simp
+    
+   from degree_unique[OF eq] ap p th0 linear_mul_degree[OF p, of a]
+   have ?case by (auto simp del: poly.simps)}
+  ultimately show ?case by blast
+qed
+
+lemma (in recpower_idom_char_0) order_degree: 
+  assumes p0: "poly p \<noteq> poly []"
+  shows "order a p \<le> degree p"
+proof-
+  from order2[OF p0, unfolded divides_def]
+  obtain q where q: "poly p = poly ([- a, 1]%^ (order a p) *** q)" by blast
+  {assume "poly q = poly []"
+    with q p0 have False by (simp add: poly_mult poly_entire)}
+  with degree_unique[OF q, unfolded linear_pow_mul_degree] 
+  show ?thesis by auto
+qed
+
+text{*Tidier versions of finiteness of roots.*}
+
+lemma (in idom_char_0) poly_roots_finite_set: "poly p \<noteq> poly [] ==> finite {x. poly p x = 0}"
+unfolding poly_roots_finite .
+
+text{*bound for polynomial.*}
+
+lemma poly_mono: "abs(x) \<le> k ==> abs(poly p (x::'a::{ordered_idom})) \<le> poly (map abs p) k"
+apply (induct "p", auto)
+apply (rule_tac y = "abs a + abs (x * poly p x)" in order_trans)
+apply (rule abs_triangle_ineq)
+apply (auto intro!: mult_mono simp add: abs_mult)
+done
+
+lemma (in semiring_0) poly_Sing: "poly [c] x = c" by simp
+
+end

--- a/src/HOL/List.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/List.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -547,9 +547,9 @@
 lemma append_Nil2 [simp]: "xs @ [] = xs"
 by (induct xs) auto
 
-class_interpretation semigroup_append: semigroup_add ["op @"]
+interpretation semigroup_append!: semigroup_add "op @"
   proof qed simp
-class_interpretation monoid_append: monoid_add ["[]" "op @"]
+interpretation monoid_append!: monoid_add "[]" "op @"
   proof qed simp+
 
 lemma append_is_Nil_conv [iff]: "(xs @ ys = []) = (xs = [] \<and> ys = [])"

--- a/src/HOL/MetisExamples/BT.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/MetisExamples/BT.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -84,7 +84,7 @@
 lemma depth_reflect: "depth (reflect t) = depth t"
   apply (induct t)
   apply (metis depth.simps(1) reflect.simps(1))
-  apply (metis depth.simps(2) min_max.less_eq_less_sup.sup_commute reflect.simps(2))
+  apply (metis depth.simps(2) min_max.sup_commute reflect.simps(2))
   done
 
 text {*

--- a/src/HOL/MetisExamples/BigO.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/MetisExamples/BigO.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -1,5 +1,4 @@
 (*  Title:      HOL/MetisExamples/BigO.thy
-    ID:         $Id$
     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
 
 Testing the metis method
@@ -13,9 +12,7 @@
 
 subsection {* Definitions *}
 
-constdefs 
-
-  bigo :: "('a => 'b::ordered_idom) => ('a => 'b) set"    ("(1O'(_'))")
+definition bigo :: "('a => 'b::ordered_idom) => ('a => 'b) set"    ("(1O'(_'))") where
   "O(f::('a => 'b)) ==   {h. EX c. ALL x. abs (h x) <= c * abs (f x)}"
 
 ML_command{*AtpWrapper.problem_name := "BigO__bigo_pos_const"*}
@@ -362,7 +359,7 @@
   apply (rule add_mono)
 ML_command{*AtpWrapper.problem_name := "BigO__bigo_plus_eq_simpler"*} 
 (*Found by SPASS; SLOW*)
-apply (metis le_maxI2 linorder_linear linorder_not_le min_max.less_eq_less_sup.sup_absorb1 mult_le_cancel_right order_trans)
+apply (metis le_maxI2 linorder_linear linorder_not_le min_max.sup_absorb1 mult_le_cancel_right order_trans)
 apply (metis le_maxI2 linorder_not_le mult_le_cancel_right order_trans)
 done
 
@@ -1164,7 +1161,7 @@
 (*sledgehammer*);  
   apply (case_tac "0 <= k x - g x")
   prefer 2 (*re-order subgoals because I don't know what to put after a structured proof*)
-   apply (metis abs_ge_zero abs_minus_commute linorder_linear min_max.less_eq_less_sup.sup_absorb1 min_max.less_eq_less_sup.sup_commute)
+   apply (metis abs_ge_zero abs_minus_commute linorder_linear min_max.sup_absorb1 min_max.sup_commute)
 proof (neg_clausify)
 fix x
 assume 0: "\<And>A. k A \<le> f A"
@@ -1174,16 +1171,16 @@
 have 3: "\<not> k x - g x < (0\<Colon>'b)"
   by (metis 2 linorder_not_less)
 have 4: "\<And>X1 X2. min X1 (k X2) \<le> f X2"
-  by (metis min_max.less_eq_less_inf.inf_le2 min_max.less_eq_less_inf.le_inf_iff min_max.less_eq_less_inf.le_iff_inf 0)
+  by (metis min_max.inf_le2 min_max.le_inf_iff min_max.le_iff_inf 0)
 have 5: "\<bar>g x - f x\<bar> = f x - g x"
-  by (metis abs_minus_commute combine_common_factor mult_zero_right minus_add_cancel minus_zero abs_if diff_less_eq min_max.less_eq_less_inf.inf_commute 4 linorder_not_le min_max.less_eq_less_inf.le_iff_inf 3 diff_less_0_iff_less linorder_not_less)
+  by (metis abs_minus_commute combine_common_factor mult_zero_right minus_add_cancel minus_zero abs_if diff_less_eq min_max.inf_commute 4 linorder_not_le min_max.le_iff_inf 3 diff_less_0_iff_less linorder_not_less)
 have 6: "max (0\<Colon>'b) (k x - g x) = k x - g x"
-  by (metis min_max.less_eq_less_sup.le_iff_sup 2)
+  by (metis min_max.le_iff_sup 2)
 assume 7: "\<not> max (k x - g x) (0\<Colon>'b) \<le> \<bar>f x - g x\<bar>"
 have 8: "\<not> k x - g x \<le> f x - g x"
-  by (metis 5 abs_minus_commute 7 min_max.less_eq_less_sup.sup_commute 6)
+  by (metis 5 abs_minus_commute 7 min_max.sup_commute 6)
 show "False"
-  by (metis min_max.less_eq_less_sup.sup_commute min_max.less_eq_less_inf.inf_commute min_max.less_eq_less_inf_sup.sup_inf_absorb min_max.less_eq_less_inf.le_iff_inf 0 max_diff_distrib_left 1 linorder_not_le 8)
+  by (metis min_max.sup_commute min_max.inf_commute min_max.sup_inf_absorb min_max.le_iff_inf 0 max_diff_distrib_left 1 linorder_not_le 8)
 qed
 
 ML_command{*AtpWrapper.problem_name := "BigO__bigo_lesso3"*}
@@ -1206,7 +1203,7 @@
 ML_command{*AtpWrapper.problem_name := "BigO__bigo_lesso3_simpler"*}
 apply (metis diff_less_0_iff_less linorder_not_le not_leE uminus_add_conv_diff xt1(12) xt1(6))
 apply (metis add_minus_cancel diff_le_eq le_diff_eq uminus_add_conv_diff)
-apply (metis abs_ge_zero linorder_linear min_max.less_eq_less_sup.sup_absorb1 min_max.less_eq_less_sup.sup_commute)
+apply (metis abs_ge_zero linorder_linear min_max.sup_absorb1 min_max.sup_commute)
 done
 
 lemma bigo_lesso4: "f <o g =o O(k::'a=>'b::ordered_field) ==>

--- a/src/HOL/Statespace/StateSpaceEx.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/Statespace/StateSpaceEx.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -41,7 +41,7 @@
 projection~/ injection functions that convert from abstract values to
 @{typ "nat"} and @{text "bool"}. The logical content of the locale is: *}
 
-class_locale vars' =
+locale vars' =
   fixes n::'name and b::'name
   assumes "distinct [n, b]"

--- a/src/HOL/Univ_Poly.thy	Thu Jan 15 14:33:38 2009 -0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,1050 +0,0 @@
-(*  Title:       Univ_Poly.thy
-    Author:      Amine Chaieb
-*)
-
-header {* Univariate Polynomials *}
-
-theory Univ_Poly
-imports Plain List
-begin
-
-text{* Application of polynomial as a function. *}
-
-primrec (in semiring_0) poly :: "'a list => 'a  => 'a" where
-  poly_Nil:  "poly [] x = 0"
-| poly_Cons: "poly (h#t) x = h + x * poly t x"
-
-
-subsection{*Arithmetic Operations on Polynomials*}
-
-text{*addition*}
-
-primrec (in semiring_0) padd :: "'a list \<Rightarrow> 'a list \<Rightarrow> 'a list"  (infixl "+++" 65) 
-where
-  padd_Nil:  "[] +++ l2 = l2"
-| padd_Cons: "(h#t) +++ l2 = (if l2 = [] then h#t
-                            else (h + hd l2)#(t +++ tl l2))"
-
-text{*Multiplication by a constant*}
-primrec (in semiring_0) cmult :: "'a \<Rightarrow> 'a list \<Rightarrow> 'a list"  (infixl "%*" 70) where
-   cmult_Nil:  "c %* [] = []"
-|  cmult_Cons: "c %* (h#t) = (c * h)#(c %* t)"
-
-text{*Multiplication by a polynomial*}
-primrec (in semiring_0) pmult :: "'a list \<Rightarrow> 'a list \<Rightarrow> 'a list"  (infixl "***" 70)
-where
-   pmult_Nil:  "[] *** l2 = []"
-|  pmult_Cons: "(h#t) *** l2 = (if t = [] then h %* l2
-                              else (h %* l2) +++ ((0) # (t *** l2)))"
-
-text{*Repeated multiplication by a polynomial*}
-primrec (in semiring_0) mulexp :: "nat \<Rightarrow> 'a list \<Rightarrow> 'a  list \<Rightarrow> 'a list" where
-   mulexp_zero:  "mulexp 0 p q = q"
-|  mulexp_Suc:   "mulexp (Suc n) p q = p *** mulexp n p q"
-
-text{*Exponential*}
-primrec (in semiring_1) pexp :: "'a list \<Rightarrow> nat \<Rightarrow> 'a list"  (infixl "%^" 80) where
-   pexp_0:   "p %^ 0 = [1]"
-|  pexp_Suc: "p %^ (Suc n) = p *** (p %^ n)"
-
-text{*Quotient related value of dividing a polynomial by x + a*}
-(* Useful for divisor properties in inductive proofs *)
-primrec (in field) "pquot" :: "'a list \<Rightarrow> 'a \<Rightarrow> 'a list" where
-   pquot_Nil:  "pquot [] a= []"
-|  pquot_Cons: "pquot (h#t) a = (if t = [] then [h]
-                   else (inverse(a) * (h - hd( pquot t a)))#(pquot t a))"
-
-text{*normalization of polynomials (remove extra 0 coeff)*}
-primrec (in semiring_0) pnormalize :: "'a list \<Rightarrow> 'a list" where
-  pnormalize_Nil:  "pnormalize [] = []"
-| pnormalize_Cons: "pnormalize (h#p) = (if ( (pnormalize p) = [])
-                                     then (if (h = 0) then [] else [h])
-                                     else (h#(pnormalize p)))"
-
-definition (in semiring_0) "pnormal p = ((pnormalize p = p) \<and> p \<noteq> [])"
-definition (in semiring_0) "nonconstant p = (pnormal p \<and> (\<forall>x. p \<noteq> [x]))"
-text{*Other definitions*}
-
-definition (in ring_1)
-  poly_minus :: "'a list => 'a list" ("-- _" [80] 80) where
-  "-- p = (- 1) %* p"
-
-definition (in semiring_0)
-  divides :: "'a list \<Rightarrow> 'a list \<Rightarrow> bool"  (infixl "divides" 70) where
-  [code del]: "p1 divides p2 = (\<exists>q. poly p2 = poly(p1 *** q))"
-
-    --{*order of a polynomial*}
-definition (in ring_1) order :: "'a => 'a list => nat" where
-  "order a p = (SOME n. ([-a, 1] %^ n) divides p &
-                      ~ (([-a, 1] %^ (Suc n)) divides p))"
-
-     --{*degree of a polynomial*}
-definition (in semiring_0) degree :: "'a list => nat" where 
-  "degree p = length (pnormalize p) - 1"
-
-     --{*squarefree polynomials --- NB with respect to real roots only.*}
-definition (in ring_1)
-  rsquarefree :: "'a list => bool" where
-  "rsquarefree p = (poly p \<noteq> poly [] &
-                     (\<forall>a. (order a p = 0) | (order a p = 1)))"
-
-context semiring_0
-begin
-
-lemma padd_Nil2[simp]: "p +++ [] = p"
-by (induct p) auto
-
-lemma padd_Cons_Cons: "(h1 # p1) +++ (h2 # p2) = (h1 + h2) # (p1 +++ p2)"
-by auto
-
-lemma pminus_Nil[simp]: "-- [] = []"
-by (simp add: poly_minus_def)
-
-lemma pmult_singleton: "[h1] *** p1 = h1 %* p1" by simp
-end
-
-lemma (in semiring_1) poly_ident_mult[simp]: "1 %* t = t" by (induct "t", auto)
-
-lemma (in semiring_0) poly_simple_add_Cons[simp]: "[a] +++ ((0)#t) = (a#t)"
-by simp
-
-text{*Handy general properties*}
-
-lemma (in comm_semiring_0) padd_commut: "b +++ a = a +++ b"
-proof(induct b arbitrary: a)
-  case Nil thus ?case by auto
-next
-  case (Cons b bs a) thus ?case by (cases a, simp_all add: add_commute)
-qed
-
-lemma (in comm_semiring_0) padd_assoc: "\<forall>b c. (a +++ b) +++ c = a +++ (b +++ c)"
-apply (induct a arbitrary: b c)
-apply (simp, clarify)
-apply (case_tac b, simp_all add: add_ac)
-done
-
-lemma (in semiring_0) poly_cmult_distr: "a %* ( p +++ q) = (a %* p +++ a %* q)"
-apply (induct p arbitrary: q,simp)
-apply (case_tac q, simp_all add: right_distrib)
-done
-
-lemma (in ring_1) pmult_by_x[simp]: "[0, 1] *** t = ((0)#t)"
-apply (induct "t", simp)
-apply (auto simp add: mult_zero_left poly_ident_mult padd_commut)
-apply (case_tac t, auto)
-done
-
-text{*properties of evaluation of polynomials.*}
-
-lemma (in semiring_0) poly_add: "poly (p1 +++ p2) x = poly p1 x + poly p2 x"
-proof(induct p1 arbitrary: p2)
-  case Nil thus ?case by simp
-next
-  case (Cons a as p2) thus ?case 
-    by (cases p2, simp_all  add: add_ac right_distrib)
-qed
-
-lemma (in comm_semiring_0) poly_cmult: "poly (c %* p) x = c * poly p x"
-apply (induct "p") 
-apply (case_tac [2] "x=zero")
-apply (auto simp add: right_distrib mult_ac)
-done
-
-lemma (in comm_semiring_0) poly_cmult_map: "poly (map (op * c) p) x = c*poly p x"
-  by (induct p, auto simp add: right_distrib mult_ac)
-
-lemma (in comm_ring_1) poly_minus: "poly (-- p) x = - (poly p x)"
-apply (simp add: poly_minus_def)
-apply (auto simp add: poly_cmult minus_mult_left[symmetric])
-done
-
-lemma (in comm_semiring_0) poly_mult: "poly (p1 *** p2) x = poly p1 x * poly p2 x"
-proof(induct p1 arbitrary: p2)
-  case Nil thus ?case by simp
-next
-  case (Cons a as p2)
-  thus ?case by (cases as, 
-    simp_all add: poly_cmult poly_add left_distrib right_distrib mult_ac)
-qed
-
-class recpower_semiring = semiring + recpower
-class recpower_semiring_1 = semiring_1 + recpower
-class recpower_semiring_0 = semiring_0 + recpower
-class recpower_ring = ring + recpower
-class recpower_ring_1 = ring_1 + recpower
-subclass (in recpower_ring_1) recpower_ring ..
-class recpower_comm_semiring_1 = recpower + comm_semiring_1
-class recpower_comm_ring_1 = recpower + comm_ring_1
-subclass (in recpower_comm_ring_1) recpower_comm_semiring_1 ..
-class recpower_idom = recpower + idom
-subclass (in recpower_idom) recpower_comm_ring_1 ..
-class idom_char_0 = idom + ring_char_0
-class recpower_idom_char_0 = recpower + idom_char_0
-subclass (in recpower_idom_char_0) recpower_idom ..
-
-lemma (in recpower_comm_ring_1) poly_exp: "poly (p %^ n) x = (poly p x) ^ n"
-apply (induct "n")
-apply (auto simp add: poly_cmult poly_mult power_Suc)
-done
-
-text{*More Polynomial Evaluation Lemmas*}
-
-lemma  (in semiring_0) poly_add_rzero[simp]: "poly (a +++ []) x = poly a x"
-by simp
-
-lemma (in comm_semiring_0) poly_mult_assoc: "poly ((a *** b) *** c) x = poly (a *** (b *** c)) x"
-  by (simp add: poly_mult mult_assoc)
-
-lemma (in semiring_0) poly_mult_Nil2[simp]: "poly (p *** []) x = 0"
-by (induct "p", auto)
-
-lemma (in comm_semiring_1) poly_exp_add: "poly (p %^ (n + d)) x = poly( p %^ n *** p %^ d) x"
-apply (induct "n")
-apply (auto simp add: poly_mult mult_assoc)
-done
-
-subsection{*Key Property: if @{term "f(a) = 0"} then @{term "(x - a)"} divides
- @{term "p(x)"} *}
-
-lemma (in comm_ring_1) lemma_poly_linear_rem: "\<forall>h. \<exists>q r. h#t = [r] +++ [-a, 1] *** q"
-proof(induct t)
-  case Nil
-  {fix h have "[h] = [h] +++ [- a, 1] *** []" by simp}
-  thus ?case by blast
-next
-  case (Cons  x xs)
-  {fix h 
-    from Cons.hyps[rule_format, of x] 
-    obtain q r where qr: "x#xs = [r] +++ [- a, 1] *** q" by blast
-    have "h#x#xs = [a*r + h] +++ [-a, 1] *** (r#q)" 
-      using qr by(cases q, simp_all add: ring_simps diff_def[symmetric] 
-	minus_mult_left[symmetric] right_minus)
-    hence "\<exists>q r. h#x#xs = [r] +++ [-a, 1] *** q" by blast}
-  thus ?case by blast
-qed
-
-lemma (in comm_ring_1) poly_linear_rem: "\<exists>q r. h#t = [r] +++ [-a, 1] *** q"
-by (cut_tac t = t and a = a in lemma_poly_linear_rem, auto)
-
-
-lemma (in comm_ring_1) poly_linear_divides: "(poly p a = 0) = ((p = []) | (\<exists>q. p = [-a, 1] *** q))"
-proof-
-  {assume p: "p = []" hence ?thesis by simp}
-  moreover
-  {fix x xs assume p: "p = x#xs"
-    {fix q assume "p = [-a, 1] *** q" hence "poly p a = 0" 
-	by (simp add: poly_add poly_cmult minus_mult_left[symmetric])}
-    moreover
-    {assume p0: "poly p a = 0"
-      from poly_linear_rem[of x xs a] obtain q r 
-      where qr: "x#xs = [r] +++ [- a, 1] *** q" by blast
-      have "r = 0" using p0 by (simp only: p qr poly_mult poly_add) simp
-      hence "\<exists>q. p = [- a, 1] *** q" using p qr  apply - apply (rule exI[where x=q])apply auto apply (cases q) apply auto done}
-    ultimately have ?thesis using p by blast}
-  ultimately show ?thesis by (cases p, auto)
-qed
-
-lemma (in semiring_0) lemma_poly_length_mult[simp]: "\<forall>h k a. length (k %* p +++  (h # (a %* p))) = Suc (length p)"
-by (induct "p", auto)
-
-lemma (in semiring_0) lemma_poly_length_mult2[simp]: "\<forall>h k. length (k %* p +++  (h # p)) = Suc (length p)"
-by (induct "p", auto)
-
-lemma (in ring_1) poly_length_mult[simp]: "length([-a,1] *** q) = Suc (length q)"
-by auto
-
-subsection{*Polynomial length*}
-
-lemma (in semiring_0) poly_cmult_length[simp]: "length (a %* p) = length p"
-by (induct "p", auto)
-
-lemma (in semiring_0) poly_add_length: "length (p1 +++ p2) = max (length p1) (length p2)"
-apply (induct p1 arbitrary: p2, simp_all)
-apply arith
-done
-
-lemma (in semiring_0) poly_root_mult_length[simp]: "length([a,b] *** p) = Suc (length p)"
-by (simp add: poly_add_length)
-
-lemma (in idom) poly_mult_not_eq_poly_Nil[simp]: 
- "poly (p *** q) x \<noteq> poly [] x \<longleftrightarrow> poly p x \<noteq> poly [] x \<and> poly q x \<noteq> poly [] x"
-by (auto simp add: poly_mult)
-
-lemma (in idom) poly_mult_eq_zero_disj: "poly (p *** q) x = 0 \<longleftrightarrow> poly p x = 0 \<or> poly q x = 0"
-by (auto simp add: poly_mult)
-
-text{*Normalisation Properties*}
-
-lemma (in semiring_0) poly_normalized_nil: "(pnormalize p = []) --> (poly p x = 0)"
-by (induct "p", auto)
-
-text{*A nontrivial polynomial of degree n has no more than n roots*}
-lemma (in idom) poly_roots_index_lemma:
-   assumes p: "poly p x \<noteq> poly [] x" and n: "length p = n" 
-  shows "\<exists>i. \<forall>x. poly p x = 0 \<longrightarrow> (\<exists>m\<le>n. x = i m)"
-  using p n
-proof(induct n arbitrary: p x)
-  case 0 thus ?case by simp 
-next
-  case (Suc n p x)
-  {assume C: "\<And>i. \<exists>x. poly p x = 0 \<and> (\<forall>m\<le>Suc n. x \<noteq> i m)"
-    from Suc.prems have p0: "poly p x \<noteq> 0" "p\<noteq> []" by auto
-    from p0(1)[unfolded poly_linear_divides[of p x]] 
-    have "\<forall>q. p \<noteq> [- x, 1] *** q" by blast
-    from C obtain a where a: "poly p a = 0" by blast
-    from a[unfolded poly_linear_divides[of p a]] p0(2) 
-    obtain q where q: "p = [-a, 1] *** q" by blast
-    have lg: "length q = n" using q Suc.prems(2) by simp
-    from q p0 have qx: "poly q x \<noteq> poly [] x" 
-      by (auto simp add: poly_mult poly_add poly_cmult)
-    from Suc.hyps[OF qx lg] obtain i where 
-      i: "\<forall>x. poly q x = 0 \<longrightarrow> (\<exists>m\<le>n. x = i m)" by blast
-    let ?i = "\<lambda>m. if m = Suc n then a else i m"
-    from C[of ?i] obtain y where y: "poly p y = 0" "\<forall>m\<le> Suc n. y \<noteq> ?i m" 
-      by blast
-    from y have "y = a \<or> poly q y = 0" 
-      by (simp only: q poly_mult_eq_zero_disj poly_add) (simp add: ring_simps)
-    with i[rule_format, of y] y(1) y(2) have False apply auto 
-      apply (erule_tac x="m" in allE)
-      apply auto
-      done}
-  thus ?case by blast
-qed
-
-
-lemma (in idom) poly_roots_index_length: "poly p x \<noteq> poly [] x ==>
-      \<exists>i. \<forall>x. (poly p x = 0) --> (\<exists>n. n \<le> length p & x = i n)"
-by (blast intro: poly_roots_index_lemma)
-
-lemma (in idom) poly_roots_finite_lemma1: "poly p x \<noteq> poly [] x ==>
-      \<exists>N i. \<forall>x. (poly p x = 0) --> (\<exists>n. (n::nat) < N & x = i n)"
-apply (drule poly_roots_index_length, safe)
-apply (rule_tac x = "Suc (length p)" in exI)
-apply (rule_tac x = i in exI) 
-apply (simp add: less_Suc_eq_le)
-done
-
-
-lemma (in idom) idom_finite_lemma:
-  assumes P: "\<forall>x. P x --> (\<exists>n. n < length j & x = j!n)"
-  shows "finite {x. P x}"
-proof-
-  let ?M = "{x. P x}"
-  let ?N = "set j"
-  have "?M \<subseteq> ?N" using P by auto
-  thus ?thesis using finite_subset by auto
-qed
-
-
-lemma (in idom) poly_roots_finite_lemma2: "poly p x \<noteq> poly [] x ==>
-      \<exists>i. \<forall>x. (poly p x = 0) --> x \<in> set i"
-apply (drule poly_roots_index_length, safe)
-apply (rule_tac x="map (\<lambda>n. i n) [0 ..< Suc (length p)]" in exI)
-apply (auto simp add: image_iff)
-apply (erule_tac x="x" in allE, clarsimp)
-by (case_tac "n=length p", auto simp add: order_le_less)
-
-lemma UNIV_nat_infinite: "\<not> finite (UNIV :: nat set)"
-  unfolding finite_conv_nat_seg_image
-proof(auto simp add: expand_set_eq image_iff)
-  fix n::nat and f:: "nat \<Rightarrow> nat"
-  let ?N = "{i. i < n}"
-  let ?fN = "f ` ?N"
-  let ?y = "Max ?fN + 1"
-  from nat_seg_image_imp_finite[of "?fN" "f" n] 
-  have thfN: "finite ?fN" by simp
-  {assume "n =0" hence "\<exists>x. \<forall>xa<n. x \<noteq> f xa" by auto}
-  moreover
-  {assume nz: "n \<noteq> 0"
-    hence thne: "?fN \<noteq> {}" by (auto simp add: neq0_conv)
-    have "\<forall>x\<in> ?fN. Max ?fN \<ge> x" using nz Max_ge_iff[OF thfN thne] by auto
-    hence "\<forall>x\<in> ?fN. ?y > x" by auto
-    hence "?y \<notin> ?fN" by auto
-    hence "\<exists>x. \<forall>xa<n. x \<noteq> f xa" by auto }
-  ultimately show "\<exists>x. \<forall>xa<n. x \<noteq> f xa" by blast
-qed
-
-lemma (in ring_char_0) UNIV_ring_char_0_infinte: 
-  "\<not> (finite (UNIV:: 'a set))" 
-proof
-  assume F: "finite (UNIV :: 'a set)"
-  have "finite (UNIV :: nat set)"
-  proof (rule finite_imageD)
-    have "of_nat ` UNIV \<subseteq> UNIV" by simp
-    then show "finite (of_nat ` UNIV :: 'a set)" using F by (rule finite_subset)
-    show "inj (of_nat :: nat \<Rightarrow> 'a)" by (simp add: inj_on_def)
-  qed
-  with UNIV_nat_infinite show False ..
-qed
-
-lemma (in idom_char_0) poly_roots_finite: "(poly p \<noteq> poly []) = 
-  finite {x. poly p x = 0}"
-proof
-  assume H: "poly p \<noteq> poly []"
-  show "finite {x. poly p x = (0::'a)}"
-    using H
-    apply -
-    apply (erule contrapos_np, rule ext)
-    apply (rule ccontr)
-    apply (clarify dest!: poly_roots_finite_lemma2)
-    using finite_subset
-  proof-
-    fix x i
-    assume F: "\<not> finite {x. poly p x = (0\<Colon>'a)}" 
-      and P: "\<forall>x. poly p x = (0\<Colon>'a) \<longrightarrow> x \<in> set i"
-    let ?M= "{x. poly p x = (0\<Colon>'a)}"
-    from P have "?M \<subseteq> set i" by auto
-    with finite_subset F show False by auto
-  qed
-next
-  assume F: "finite {x. poly p x = (0\<Colon>'a)}"
-  show "poly p \<noteq> poly []" using F UNIV_ring_char_0_infinte by auto  
-qed
-
-text{*Entirety and Cancellation for polynomials*}
-
-lemma (in idom_char_0) poly_entire_lemma2: 
-  assumes p0: "poly p \<noteq> poly []" and q0: "poly q \<noteq> poly []"
-  shows "poly (p***q) \<noteq> poly []"
-proof-
-  let ?S = "\<lambda>p. {x. poly p x = 0}"
-  have "?S (p *** q) = ?S p \<union> ?S q" by (auto simp add: poly_mult)
-  with p0 q0 show ?thesis  unfolding poly_roots_finite by auto
-qed
-
-lemma (in idom_char_0) poly_entire: 
-  "poly (p *** q) = poly [] \<longleftrightarrow> poly p = poly [] \<or> poly q = poly []"
-using poly_entire_lemma2[of p q] 
-by auto (rule ext, simp add: poly_mult)+
-
-lemma (in idom_char_0) poly_entire_neg: "(poly (p *** q) \<noteq> poly []) = ((poly p \<noteq> poly []) & (poly q \<noteq> poly []))"
-by (simp add: poly_entire)
-
-lemma fun_eq: " (f = g) = (\<forall>x. f x = g x)"
-by (auto intro!: ext)
-
-lemma (in comm_ring_1) poly_add_minus_zero_iff: "(poly (p +++ -- q) = poly []) = (poly p = poly q)"
-by (auto simp add: ring_simps poly_add poly_minus_def fun_eq poly_cmult minus_mult_left[symmetric])
-
-lemma (in comm_ring_1) poly_add_minus_mult_eq: "poly (p *** q +++ --(p *** r)) = poly (p *** (q +++ -- r))"
-by (auto simp add: poly_add poly_minus_def fun_eq poly_mult poly_cmult right_distrib minus_mult_left[symmetric] minus_mult_right[symmetric])
-
-subclass (in idom_char_0) comm_ring_1 ..
-lemma (in idom_char_0) poly_mult_left_cancel: "(poly (p *** q) = poly (p *** r)) = (poly p = poly [] | poly q = poly r)"
-proof-
-  have "poly (p *** q) = poly (p *** r) \<longleftrightarrow> poly (p *** q +++ -- (p *** r)) = poly []" by (simp only: poly_add_minus_zero_iff)
-  also have "\<dots> \<longleftrightarrow> poly p = poly [] | poly q = poly r"
-    by (auto intro: ext simp add: poly_add_minus_mult_eq poly_entire poly_add_minus_zero_iff)
-  finally show ?thesis .
-qed
-
-lemma (in recpower_idom) poly_exp_eq_zero[simp]:
-     "(poly (p %^ n) = poly []) = (poly p = poly [] & n \<noteq> 0)"
-apply (simp only: fun_eq add: all_simps [symmetric]) 
-apply (rule arg_cong [where f = All]) 
-apply (rule ext)
-apply (induct n)
-apply (auto simp add: poly_exp poly_mult)
-done
-
-lemma (in semiring_1) one_neq_zero[simp]: "1 \<noteq> 0" using zero_neq_one by blast
-lemma (in comm_ring_1) poly_prime_eq_zero[simp]: "poly [a,1] \<noteq> poly []"
-apply (simp add: fun_eq)
-apply (rule_tac x = "minus one a" in exI)
-apply (unfold diff_minus)
-apply (subst add_commute)
-apply (subst add_assoc)
-apply simp
-done 
-
-lemma (in recpower_idom) poly_exp_prime_eq_zero: "(poly ([a, 1] %^ n) \<noteq> poly [])"
-by auto
-
-text{*A more constructive notion of polynomials being trivial*}
-
-lemma (in idom_char_0) poly_zero_lemma': "poly (h # t) = poly [] ==> h = 0 & poly t = poly []"
-apply(simp add: fun_eq)
-apply (case_tac "h = zero")
-apply (drule_tac [2] x = zero in spec, auto) 
-apply (cases "poly t = poly []", simp) 
-proof-
-  fix x
-  assume H: "\<forall>x. x = (0\<Colon>'a) \<or> poly t x = (0\<Colon>'a)"  and pnz: "poly t \<noteq> poly []"
-  let ?S = "{x. poly t x = 0}"
-  from H have "\<forall>x. x \<noteq>0 \<longrightarrow> poly t x = 0" by blast
-  hence th: "?S \<supseteq> UNIV - {0}" by auto
-  from poly_roots_finite pnz have th': "finite ?S" by blast
-  from finite_subset[OF th th'] UNIV_ring_char_0_infinte
-  show "poly t x = (0\<Colon>'a)" by simp
-  qed
-
-lemma (in idom_char_0) poly_zero: "(poly p = poly []) = list_all (%c. c = 0) p"
-apply (induct "p", simp)
-apply (rule iffI)
-apply (drule poly_zero_lemma', auto)
-done
-
-lemma (in idom_char_0) poly_0: "list_all (\<lambda>c. c = 0) p \<Longrightarrow> poly p x = 0"
-  unfolding poly_zero[symmetric] by simp
-
-
-
-text{*Basics of divisibility.*}
-
-lemma (in idom) poly_primes: "([a, 1] divides (p *** q)) = ([a, 1] divides p | [a, 1] divides q)"
-apply (auto simp add: divides_def fun_eq poly_mult poly_add poly_cmult left_distrib [symmetric])
-apply (drule_tac x = "uminus a" in spec)
-apply (simp add: poly_linear_divides poly_add poly_cmult left_distrib [symmetric])
-apply (cases "p = []")
-apply (rule exI[where x="[]"])
-apply simp
-apply (cases "q = []")
-apply (erule allE[where x="[]"], simp)
-
-apply clarsimp
-apply (cases "\<exists>q\<Colon>'a list. p = a %* q +++ ((0\<Colon>'a) # q)")
-apply (clarsimp simp add: poly_add poly_cmult)
-apply (rule_tac x="qa" in exI)
-apply (simp add: left_distrib [symmetric])
-apply clarsimp
-
-apply (auto simp add: right_minus poly_linear_divides poly_add poly_cmult left_distrib [symmetric])
-apply (rule_tac x = "pmult qa q" in exI)
-apply (rule_tac [2] x = "pmult p qa" in exI)
-apply (auto simp add: poly_add poly_mult poly_cmult mult_ac)
-done
-
-lemma (in comm_semiring_1) poly_divides_refl[simp]: "p divides p"
-apply (simp add: divides_def)
-apply (rule_tac x = "[one]" in exI)
-apply (auto simp add: poly_mult fun_eq)
-done
-
-lemma (in comm_semiring_1) poly_divides_trans: "[| p divides q; q divides r |] ==> p divides r"
-apply (simp add: divides_def, safe)
-apply (rule_tac x = "pmult qa qaa" in exI)
-apply (auto simp add: poly_mult fun_eq mult_assoc)
-done
-
-
-lemma (in recpower_comm_semiring_1) poly_divides_exp: "m \<le> n ==> (p %^ m) divides (p %^ n)"
-apply (auto simp add: le_iff_add)
-apply (induct_tac k)
-apply (rule_tac [2] poly_divides_trans)
-apply (auto simp add: divides_def)
-apply (rule_tac x = p in exI)
-apply (auto simp add: poly_mult fun_eq mult_ac)
-done
-
-lemma (in recpower_comm_semiring_1) poly_exp_divides: "[| (p %^ n) divides q;  m\<le>n |] ==> (p %^ m) divides q"
-by (blast intro: poly_divides_exp poly_divides_trans)
-
-lemma (in comm_semiring_0) poly_divides_add:
-   "[| p divides q; p divides r |] ==> p divides (q +++ r)"
-apply (simp add: divides_def, auto)
-apply (rule_tac x = "padd qa qaa" in exI)
-apply (auto simp add: poly_add fun_eq poly_mult right_distrib)
-done
-
-lemma (in comm_ring_1) poly_divides_diff:
-   "[| p divides q; p divides (q +++ r) |] ==> p divides r"
-apply (simp add: divides_def, auto)
-apply (rule_tac x = "padd qaa (poly_minus qa)" in exI)
-apply (auto simp add: poly_add fun_eq poly_mult poly_minus right_diff_distrib compare_rls add_ac)
-done
-
-lemma (in comm_ring_1) poly_divides_diff2: "[| p divides r; p divides (q +++ r) |] ==> p divides q"
-apply (erule poly_divides_diff)
-apply (auto simp add: poly_add fun_eq poly_mult divides_def add_ac)
-done
-
-lemma (in semiring_0) poly_divides_zero: "poly p = poly [] ==> q divides p"
-apply (simp add: divides_def)
-apply (rule exI[where x="[]"])
-apply (auto simp add: fun_eq poly_mult)
-done
-
-lemma (in semiring_0) poly_divides_zero2[simp]: "q divides []"
-apply (simp add: divides_def)
-apply (rule_tac x = "[]" in exI)
-apply (auto simp add: fun_eq)
-done
-
-text{*At last, we can consider the order of a root.*}
-
-lemma (in idom_char_0)  poly_order_exists_lemma:
-  assumes lp: "length p = d" and p: "poly p \<noteq> poly []"
-  shows "\<exists>n q. p = mulexp n [-a, 1] q \<and> poly q a \<noteq> 0"
-using lp p
-proof(induct d arbitrary: p)
-  case 0 thus ?case by simp
-next
-  case (Suc n p)
-  {assume p0: "poly p a = 0"
-    from Suc.prems have h: "length p = Suc n" "poly p \<noteq> poly []" by auto
-    hence pN: "p \<noteq> []" by auto
-    from p0[unfolded poly_linear_divides] pN  obtain q where 
-      q: "p = [-a, 1] *** q" by blast
-    from q h p0 have qh: "length q = n" "poly q \<noteq> poly []" 
-      apply -
-      apply simp
-      apply (simp only: fun_eq)
-      apply (rule ccontr)
-      apply (simp add: fun_eq poly_add poly_cmult minus_mult_left[symmetric])
-      done
-    from Suc.hyps[OF qh] obtain m r where 
-      mr: "q = mulexp m [-a,1] r" "poly r a \<noteq> 0" by blast    
-    from mr q have "p = mulexp (Suc m) [-a,1] r \<and> poly r a \<noteq> 0" by simp
-    hence ?case by blast}
-  moreover
-  {assume p0: "poly p a \<noteq> 0"
-    hence ?case using Suc.prems apply simp by (rule exI[where x="0::nat"], simp)}
-  ultimately show ?case by blast
-qed
-
-
-lemma (in recpower_comm_semiring_1) poly_mulexp: "poly (mulexp n p q) x = (poly p x) ^ n * poly q x"
-by(induct n, auto simp add: poly_mult power_Suc mult_ac)
-
-lemma (in comm_semiring_1) divides_left_mult:
-  assumes d:"(p***q) divides r" shows "p divides r \<and> q divides r"
-proof-
-  from d obtain t where r:"poly r = poly (p***q *** t)"
-    unfolding divides_def by blast
-  hence "poly r = poly (p *** (q *** t))"
-    "poly r = poly (q *** (p***t))" by(auto simp add: fun_eq poly_mult mult_ac)
-  thus ?thesis unfolding divides_def by blast
-qed
-
-
-
-(* FIXME: Tidy up *)
-
-lemma (in recpower_semiring_1) 
-  zero_power_iff: "0 ^ n = (if n = 0 then 1 else 0)"
-  by (induct n, simp_all add: power_Suc)
-
-lemma (in recpower_idom_char_0) poly_order_exists:
-  assumes lp: "length p = d" and p0: "poly p \<noteq> poly []"
-  shows "\<exists>n. ([-a, 1] %^ n) divides p & ~(([-a, 1] %^ (Suc n)) divides p)"
-proof-
-let ?poly = poly
-let ?mulexp = mulexp
-let ?pexp = pexp
-from lp p0
-show ?thesis
-apply -
-apply (drule poly_order_exists_lemma [where a=a], assumption, clarify)  
-apply (rule_tac x = n in exI, safe)
-apply (unfold divides_def)
-apply (rule_tac x = q in exI)
-apply (induct_tac "n", simp)
-apply (simp (no_asm_simp) add: poly_add poly_cmult poly_mult right_distrib mult_ac)
-apply safe
-apply (subgoal_tac "?poly (?mulexp n [uminus a, one] q) \<noteq> ?poly (pmult (?pexp [uminus a, one] (Suc n)) qa)") 
-apply simp 
-apply (induct_tac "n")
-apply (simp del: pmult_Cons pexp_Suc)
-apply (erule_tac Q = "?poly q a = zero" in contrapos_np)
-apply (simp add: poly_add poly_cmult minus_mult_left[symmetric])
-apply (rule pexp_Suc [THEN ssubst])
-apply (rule ccontr)
-apply (simp add: poly_mult_left_cancel poly_mult_assoc del: pmult_Cons pexp_Suc)
-done
-qed
-
-
-lemma (in semiring_1) poly_one_divides[simp]: "[1] divides p"
-by (simp add: divides_def, auto)
-
-lemma (in recpower_idom_char_0) poly_order: "poly p \<noteq> poly []
-      ==> EX! n. ([-a, 1] %^ n) divides p &
-                 ~(([-a, 1] %^ (Suc n)) divides p)"
-apply (auto intro: poly_order_exists simp add: less_linear simp del: pmult_Cons pexp_Suc)
-apply (cut_tac x = y and y = n in less_linear)
-apply (drule_tac m = n in poly_exp_divides)
-apply (auto dest: Suc_le_eq [THEN iffD2, THEN [2] poly_exp_divides]
-            simp del: pmult_Cons pexp_Suc)
-done
-
-text{*Order*}
-
-lemma some1_equalityD: "[| n = (@n. P n); EX! n. P n |] ==> P n"
-by (blast intro: someI2)
-
-lemma (in recpower_idom_char_0) order:
-      "(([-a, 1] %^ n) divides p &
-        ~(([-a, 1] %^ (Suc n)) divides p)) =
-        ((n = order a p) & ~(poly p = poly []))"
-apply (unfold order_def)
-apply (rule iffI)
-apply (blast dest: poly_divides_zero intro!: some1_equality [symmetric] poly_order)
-apply (blast intro!: poly_order [THEN [2] some1_equalityD])
-done
-
-lemma (in recpower_idom_char_0) order2: "[| poly p \<noteq> poly [] |]
-      ==> ([-a, 1] %^ (order a p)) divides p &
-              ~(([-a, 1] %^ (Suc(order a p))) divides p)"
-by (simp add: order del: pexp_Suc)
-
-lemma (in recpower_idom_char_0) order_unique: "[| poly p \<noteq> poly []; ([-a, 1] %^ n) divides p;
-         ~(([-a, 1] %^ (Suc n)) divides p)
-      |] ==> (n = order a p)"
-by (insert order [of a n p], auto) 
-
-lemma (in recpower_idom_char_0) order_unique_lemma: "(poly p \<noteq> poly [] & ([-a, 1] %^ n) divides p &
-         ~(([-a, 1] %^ (Suc n)) divides p))
-      ==> (n = order a p)"
-by (blast intro: order_unique)
-
-lemma (in ring_1) order_poly: "poly p = poly q ==> order a p = order a q"
-by (auto simp add: fun_eq divides_def poly_mult order_def)
-
-lemma (in semiring_1) pexp_one[simp]: "p %^ (Suc 0) = p"
-apply (induct "p")
-apply (auto simp add: numeral_1_eq_1)
-done
-
-lemma (in comm_ring_1) lemma_order_root:
-     " 0 < n & [- a, 1] %^ n divides p & ~ [- a, 1] %^ (Suc n) divides p
-             \<Longrightarrow> poly p a = 0"
-apply (induct n arbitrary: a p, blast)
-apply (auto simp add: divides_def poly_mult simp del: pmult_Cons)
-done
-
-lemma (in recpower_idom_char_0) order_root: "(poly p a = 0) = ((poly p = poly []) | order a p \<noteq> 0)"
-proof-
-  let ?poly = poly
-  show ?thesis 
-apply (case_tac "?poly p = ?poly []", auto)
-apply (simp add: poly_linear_divides del: pmult_Cons, safe)
-apply (drule_tac [!] a = a in order2)
-apply (rule ccontr)
-apply (simp add: divides_def poly_mult fun_eq del: pmult_Cons, blast)
-using neq0_conv
-apply (blast intro: lemma_order_root)
-done
-qed
-
-lemma (in recpower_idom_char_0) order_divides: "(([-a, 1] %^ n) divides p) = ((poly p = poly []) | n \<le> order a p)"
-proof-
-  let ?poly = poly
-  show ?thesis 
-apply (case_tac "?poly p = ?poly []", auto)
-apply (simp add: divides_def fun_eq poly_mult)
-apply (rule_tac x = "[]" in exI)
-apply (auto dest!: order2 [where a=a]
-	    intro: poly_exp_divides simp del: pexp_Suc)
-done
-qed
-
-lemma (in recpower_idom_char_0) order_decomp:
-     "poly p \<noteq> poly []
-      ==> \<exists>q. (poly p = poly (([-a, 1] %^ (order a p)) *** q)) &
-                ~([-a, 1] divides q)"
-apply (unfold divides_def)
-apply (drule order2 [where a = a])
-apply (simp add: divides_def del: pexp_Suc pmult_Cons, safe)
-apply (rule_tac x = q in exI, safe)
-apply (drule_tac x = qa in spec)
-apply (auto simp add: poly_mult fun_eq poly_exp mult_ac simp del: pmult_Cons)
-done
-
-text{*Important composition properties of orders.*}
-lemma order_mult: "poly (p *** q) \<noteq> poly []
-      ==> order a (p *** q) = order a p + order (a::'a::{recpower_idom_char_0}) q"
-apply (cut_tac a = a and p = "p *** q" and n = "order a p + order a q" in order)
-apply (auto simp add: poly_entire simp del: pmult_Cons)
-apply (drule_tac a = a in order2)+
-apply safe
-apply (simp add: divides_def fun_eq poly_exp_add poly_mult del: pmult_Cons, safe)
-apply (rule_tac x = "qa *** qaa" in exI)
-apply (simp add: poly_mult mult_ac del: pmult_Cons)
-apply (drule_tac a = a in order_decomp)+
-apply safe
-apply (subgoal_tac "[-a,1] divides (qa *** qaa) ")
-apply (simp add: poly_primes del: pmult_Cons)
-apply (auto simp add: divides_def simp del: pmult_Cons)
-apply (rule_tac x = qb in exI)
-apply (subgoal_tac "poly ([-a, 1] %^ (order a p) *** (qa *** qaa)) = poly ([-a, 1] %^ (order a p) *** ([-a, 1] *** qb))")
-apply (drule poly_mult_left_cancel [THEN iffD1], force)
-apply (subgoal_tac "poly ([-a, 1] %^ (order a q) *** ([-a, 1] %^ (order a p) *** (qa *** qaa))) = poly ([-a, 1] %^ (order a q) *** ([-a, 1] %^ (order a p) *** ([-a, 1] *** qb))) ")
-apply (drule poly_mult_left_cancel [THEN iffD1], force)
-apply (simp add: fun_eq poly_exp_add poly_mult mult_ac del: pmult_Cons)
-done
-
-lemma (in recpower_idom_char_0) order_mult: 
-  assumes pq0: "poly (p *** q) \<noteq> poly []"
-  shows "order a (p *** q) = order a p + order a q"
-proof-
-  let ?order = order
-  let ?divides = "op divides"
-  let ?poly = poly
-from pq0 
-show ?thesis
-apply (cut_tac a = a and p = "pmult p q" and n = "?order a p + ?order a q" in order)
-apply (auto simp add: poly_entire simp del: pmult_Cons)
-apply (drule_tac a = a in order2)+
-apply safe
-apply (simp add: divides_def fun_eq poly_exp_add poly_mult del: pmult_Cons, safe)
-apply (rule_tac x = "pmult qa qaa" in exI)
-apply (simp add: poly_mult mult_ac del: pmult_Cons)
-apply (drule_tac a = a in order_decomp)+
-apply safe
-apply (subgoal_tac "?divides [uminus a,one ] (pmult qa qaa) ")
-apply (simp add: poly_primes del: pmult_Cons)
-apply (auto simp add: divides_def simp del: pmult_Cons)
-apply (rule_tac x = qb in exI)
-apply (subgoal_tac "?poly (pmult (pexp [uminus a, one] (?order a p)) (pmult qa qaa)) = ?poly (pmult (pexp [uminus a, one] (?order a p)) (pmult [uminus a, one] qb))")
-apply (drule poly_mult_left_cancel [THEN iffD1], force)
-apply (subgoal_tac "?poly (pmult (pexp [uminus a, one ] (order a q)) (pmult (pexp [uminus a, one] (order a p)) (pmult qa qaa))) = ?poly (pmult (pexp [uminus a, one] (order a q)) (pmult (pexp [uminus a, one] (order a p)) (pmult [uminus a, one] qb))) ")
-apply (drule poly_mult_left_cancel [THEN iffD1], force)
-apply (simp add: fun_eq poly_exp_add poly_mult mult_ac del: pmult_Cons)
-done
-qed
-
-lemma (in recpower_idom_char_0) order_root2: "poly p \<noteq> poly [] ==> (poly p a = 0) = (order a p \<noteq> 0)"
-by (rule order_root [THEN ssubst], auto)
-
-lemma (in semiring_1) pmult_one[simp]: "[1] *** p = p" by auto
-
-lemma (in semiring_0) poly_Nil_zero: "poly [] = poly [0]"
-by (simp add: fun_eq)
-
-lemma (in recpower_idom_char_0) rsquarefree_decomp:
-     "[| rsquarefree p; poly p a = 0 |]
-      ==> \<exists>q. (poly p = poly ([-a, 1] *** q)) & poly q a \<noteq> 0"
-apply (simp add: rsquarefree_def, safe)
-apply (frule_tac a = a in order_decomp)
-apply (drule_tac x = a in spec)
-apply (drule_tac a = a in order_root2 [symmetric])
-apply (auto simp del: pmult_Cons)
-apply (rule_tac x = q in exI, safe)
-apply (simp add: poly_mult fun_eq)
-apply (drule_tac p1 = q in poly_linear_divides [THEN iffD1])
-apply (simp add: divides_def del: pmult_Cons, safe)
-apply (drule_tac x = "[]" in spec)
-apply (auto simp add: fun_eq)
-done
-
-
-text{*Normalization of a polynomial.*}
-
-lemma (in semiring_0) poly_normalize[simp]: "poly (pnormalize p) = poly p"
-apply (induct "p")
-apply (auto simp add: fun_eq)
-done
-
-text{*The degree of a polynomial.*}
-
-lemma (in semiring_0) lemma_degree_zero:
-     "list_all (%c. c = 0) p \<longleftrightarrow>  pnormalize p = []"
-by (induct "p", auto)
-
-lemma (in idom_char_0) degree_zero: 
-  assumes pN: "poly p = poly []" shows"degree p = 0"
-proof-
-  let ?pn = pnormalize
-  from pN
-  show ?thesis 
-    apply (simp add: degree_def)
-    apply (case_tac "?pn p = []")
-    apply (auto simp add: poly_zero lemma_degree_zero )
-    done
-qed
-
-lemma (in semiring_0) pnormalize_sing: "(pnormalize [x] = [x]) \<longleftrightarrow> x \<noteq> 0" by simp
-lemma (in semiring_0) pnormalize_pair: "y \<noteq> 0 \<longleftrightarrow> (pnormalize [x, y] = [x, y])" by simp
-lemma (in semiring_0) pnormal_cons: "pnormal p \<Longrightarrow> pnormal (c#p)" 
-  unfolding pnormal_def by simp
-lemma (in semiring_0) pnormal_tail: "p\<noteq>[] \<Longrightarrow> pnormal (c#p) \<Longrightarrow> pnormal p"
-  unfolding pnormal_def 
-  apply (cases "pnormalize p = []", auto)
-  by (cases "c = 0", auto)
-
-
-lemma (in semiring_0) pnormal_last_nonzero: "pnormal p ==> last p \<noteq> 0"
-proof(induct p)
-  case Nil thus ?case by (simp add: pnormal_def)
-next 
-  case (Cons a as) thus ?case
-    apply (simp add: pnormal_def)
-    apply (cases "pnormalize as = []", simp_all)
-    apply (cases "as = []", simp_all)
-    apply (cases "a=0", simp_all)
-    apply (cases "a=0", simp_all)
-    done
-qed
-
-lemma (in semiring_0) pnormal_length: "pnormal p \<Longrightarrow> 0 < length p"
-  unfolding pnormal_def length_greater_0_conv by blast
-
-lemma (in semiring_0) pnormal_last_length: "\<lbrakk>0 < length p ; last p \<noteq> 0\<rbrakk> \<Longrightarrow> pnormal p"
-  apply (induct p, auto)
-  apply (case_tac "p = []", auto)
-  apply (simp add: pnormal_def)
-  by (rule pnormal_cons, auto)
-
-lemma (in semiring_0) pnormal_id: "pnormal p \<longleftrightarrow> (0 < length p \<and> last p \<noteq> 0)"
-  using pnormal_last_length pnormal_length pnormal_last_nonzero by blast
-
-lemma (in idom_char_0) poly_Cons_eq: "poly (c#cs) = poly (d#ds) \<longleftrightarrow> c=d \<and> poly cs = poly ds" (is "?lhs \<longleftrightarrow> ?rhs")
-proof
-  assume eq: ?lhs
-  hence "\<And>x. poly ((c#cs) +++ -- (d#ds)) x = 0"
-    by (simp only: poly_minus poly_add ring_simps) simp
-  hence "poly ((c#cs) +++ -- (d#ds)) = poly []" by - (rule ext, simp) 
-  hence "c = d \<and> list_all (\<lambda>x. x=0) ((cs +++ -- ds))"
-    unfolding poly_zero by (simp add: poly_minus_def ring_simps minus_mult_left[symmetric])
-  hence "c = d \<and> (\<forall>x. poly (cs +++ -- ds) x = 0)"
-    unfolding poly_zero[symmetric] by simp 
-  thus ?rhs  apply (simp add: poly_minus poly_add ring_simps) apply (rule ext, simp) done
-next
-  assume ?rhs then show ?lhs  by -  (rule ext,simp)
-qed
-  
-lemma (in idom_char_0) pnormalize_unique: "poly p = poly q \<Longrightarrow> pnormalize p = pnormalize q"
-proof(induct q arbitrary: p)
-  case Nil thus ?case by (simp only: poly_zero lemma_degree_zero) simp
-next
-  case (Cons c cs p)
-  thus ?case
-  proof(induct p)
-    case Nil
-    hence "poly [] = poly (c#cs)" by blast
-    then have "poly (c#cs) = poly [] " by simp 
-    thus ?case by (simp only: poly_zero lemma_degree_zero) simp
-  next
-    case (Cons d ds)
-    hence eq: "poly (d # ds) = poly (c # cs)" by blast
-    hence eq': "\<And>x. poly (d # ds) x = poly (c # cs) x" by simp
-    hence "poly (d # ds) 0 = poly (c # cs) 0" by blast
-    hence dc: "d = c" by auto
-    with eq have "poly ds = poly cs"
-      unfolding  poly_Cons_eq by simp
-    with Cons.prems have "pnormalize ds = pnormalize cs" by blast
-    with dc show ?case by simp
-  qed
-qed
-
-lemma (in idom_char_0) degree_unique: assumes pq: "poly p = poly q"
-  shows "degree p = degree q"
-using pnormalize_unique[OF pq] unfolding degree_def by simp
-
-lemma (in semiring_0) pnormalize_length: "length (pnormalize p) \<le> length p" by (induct p, auto)
-
-lemma (in semiring_0) last_linear_mul_lemma: 
-  "last ((a %* p) +++ (x#(b %* p))) = (if p=[] then x else b*last p)"
-
-apply (induct p arbitrary: a x b, auto)
-apply (subgoal_tac "padd (cmult aa p) (times b a # cmult b p) \<noteq> []", simp)
-apply (induct_tac p, auto)
-done
-
-lemma (in semiring_1) last_linear_mul: assumes p:"p\<noteq>[]" shows "last ([a,1] *** p) = last p"
-proof-
-  from p obtain c cs where cs: "p = c#cs" by (cases p, auto)
-  from cs have eq:"[a,1] *** p = (a %* (c#cs)) +++ (0#(1 %* (c#cs)))"
-    by (simp add: poly_cmult_distr)
-  show ?thesis using cs
-    unfolding eq last_linear_mul_lemma by simp
-qed
-
-lemma (in semiring_0) pnormalize_eq: "last p \<noteq> 0 \<Longrightarrow> pnormalize p = p"
-  apply (induct p, auto)
-  apply (case_tac p, auto)+
-  done
-
-lemma (in semiring_0) last_pnormalize: "pnormalize p \<noteq> [] \<Longrightarrow> last (pnormalize p) \<noteq> 0"
-  by (induct p, auto)
-
-lemma (in semiring_0) pnormal_degree: "last p \<noteq> 0 \<Longrightarrow> degree p = length p - 1"
-  using pnormalize_eq[of p] unfolding degree_def by simp
-
-lemma (in semiring_0) poly_Nil_ext: "poly [] = (\<lambda>x. 0)" by (rule ext) simp
-
-lemma (in idom_char_0) linear_mul_degree: assumes p: "poly p \<noteq> poly []"
-  shows "degree ([a,1] *** p) = degree p + 1"
-proof-
-  from p have pnz: "pnormalize p \<noteq> []"
-    unfolding poly_zero lemma_degree_zero .
-  
-  from last_linear_mul[OF pnz, of a] last_pnormalize[OF pnz]
-  have l0: "last ([a, 1] *** pnormalize p) \<noteq> 0" by simp
-  from last_pnormalize[OF pnz] last_linear_mul[OF pnz, of a]
-    pnormal_degree[OF l0] pnormal_degree[OF last_pnormalize[OF pnz]] pnz
- 
-
-  have th: "degree ([a,1] *** pnormalize p) = degree (pnormalize p) + 1" 
-    by (auto simp add: poly_length_mult)
-
-  have eqs: "poly ([a,1] *** pnormalize p) = poly ([a,1] *** p)"
-    by (rule ext) (simp add: poly_mult poly_add poly_cmult)
-  from degree_unique[OF eqs] th
-  show ?thesis by (simp add: degree_unique[OF poly_normalize])
-qed
-
-lemma (in idom_char_0) linear_pow_mul_degree:
-  "degree([a,1] %^n *** p) = (if poly p = poly [] then 0 else degree p + n)"
-proof(induct n arbitrary: a p)
-  case (0 a p)
-  {assume p: "poly p = poly []"
-    hence ?case using degree_unique[OF p] by (simp add: degree_def)}
-  moreover
-  {assume p: "poly p \<noteq> poly []" hence ?case by (auto simp add: poly_Nil_ext) }
-  ultimately show ?case by blast
-next
-  case (Suc n a p)
-  have eq: "poly ([a,1] %^(Suc n) *** p) = poly ([a,1] %^ n *** ([a,1] *** p))"
-    apply (rule ext, simp add: poly_mult poly_add poly_cmult)
-    by (simp add: mult_ac add_ac right_distrib)
-  note deq = degree_unique[OF eq]
-  {assume p: "poly p = poly []"
-    with eq have eq': "poly ([a,1] %^(Suc n) *** p) = poly []" 
-      by - (rule ext,simp add: poly_mult poly_cmult poly_add)
-    from degree_unique[OF eq'] p have ?case by (simp add: degree_def)}
-  moreover
-  {assume p: "poly p \<noteq> poly []"
-    from p have ap: "poly ([a,1] *** p) \<noteq> poly []"
-      using poly_mult_not_eq_poly_Nil unfolding poly_entire by auto 
-    have eq: "poly ([a,1] %^(Suc n) *** p) = poly ([a,1]%^n *** ([a,1] *** p))"
-     by (rule ext, simp add: poly_mult poly_add poly_exp poly_cmult mult_ac add_ac right_distrib)
-   from ap have ap': "(poly ([a,1] *** p) = poly []) = False" by blast
-   have  th0: "degree ([a,1]%^n *** ([a,1] *** p)) = degree ([a,1] *** p) + n"
-     apply (simp only: Suc.hyps[of a "pmult [a,one] p"] ap')
-     by simp
-    
-   from degree_unique[OF eq] ap p th0 linear_mul_degree[OF p, of a]
-   have ?case by (auto simp del: poly.simps)}
-  ultimately show ?case by blast
-qed
-
-lemma (in recpower_idom_char_0) order_degree: 
-  assumes p0: "poly p \<noteq> poly []"
-  shows "order a p \<le> degree p"
-proof-
-  from order2[OF p0, unfolded divides_def]
-  obtain q where q: "poly p = poly ([- a, 1]%^ (order a p) *** q)" by blast
-  {assume "poly q = poly []"
-    with q p0 have False by (simp add: poly_mult poly_entire)}
-  with degree_unique[OF q, unfolded linear_pow_mul_degree] 
-  show ?thesis by auto
-qed
-
-text{*Tidier versions of finiteness of roots.*}
-
-lemma (in idom_char_0) poly_roots_finite_set: "poly p \<noteq> poly [] ==> finite {x. poly p x = 0}"
-unfolding poly_roots_finite .
-
-text{*bound for polynomial.*}
-
-lemma poly_mono: "abs(x) \<le> k ==> abs(poly p (x::'a::{ordered_idom})) \<le> poly (map abs p) k"
-apply (induct "p", auto)
-apply (rule_tac y = "abs a + abs (x * poly p x)" in order_trans)
-apply (rule abs_triangle_ineq)
-apply (auto intro!: mult_mono simp add: abs_mult)
-done
-
-lemma (in semiring_0) poly_Sing: "poly [c] x = c" by simp
-
-end

--- a/src/HOL/Word/WordArith.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOL/Word/WordArith.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -22,7 +22,7 @@
 proof
 qed (unfold word_sle_def word_sless_def, auto)
 
-class_interpretation signed: linorder ["word_sle" "word_sless"] 
+interpretation signed!: linorder "word_sle" "word_sless"
   by (rule signed_linorder)
 
 lemmas word_arith_wis =

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/base.ML	Fri Jan 16 13:07:44 2009 -0800
@@ -0,0 +1,2 @@
+(*side-entry for HOL-Base*)
+use_thy "Code_Setup";

--- a/src/HOLCF/CompactBasis.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOLCF/CompactBasis.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -244,7 +244,7 @@
   assumes "ab_semigroup_idem_mult f"
   shows "fold_pd g f (PDPlus t u) = f (fold_pd g f t) (fold_pd g f u)"
 proof -
-  class_interpret ab_semigroup_idem_mult [f] by fact
+  interpret ab_semigroup_idem_mult f by fact
   show ?thesis unfolding fold_pd_def Rep_PDPlus by (simp add: image_Un fold1_Un2)
 qed

--- a/src/HOLCF/ConvexPD.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOLCF/ConvexPD.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -296,9 +296,8 @@
 apply (simp add: PDPlus_absorb)
 done
 
-class_interpretation aci_convex_plus: ab_semigroup_idem_mult ["op +\<natural>"]
-  by unfold_locales
-    (rule convex_plus_assoc convex_plus_commute convex_plus_absorb)+
+interpretation aci_convex_plus!: ab_semigroup_idem_mult "op +\<natural>"
+  proof qed (rule convex_plus_assoc convex_plus_commute convex_plus_absorb)+
 
 lemma convex_plus_left_commute: "xs +\<natural> (ys +\<natural> zs) = ys +\<natural> (xs +\<natural> zs)"
 by (rule aci_convex_plus.mult_left_commute)

--- a/src/HOLCF/HOLCF.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOLCF/HOLCF.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -17,7 +17,6 @@
   "Tools/domain/domain_theorems.ML"
   "Tools/domain/domain_extender.ML"
   "Tools/adm_tac.ML"
-
 begin
 
 defaultsort pcpo

--- a/src/HOLCF/LowerPD.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOLCF/LowerPD.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -250,9 +250,8 @@
 apply (simp add: PDPlus_absorb)
 done
 
-class_interpretation aci_lower_plus: ab_semigroup_idem_mult ["op +\<flat>"]
-  by unfold_locales
-    (rule lower_plus_assoc lower_plus_commute lower_plus_absorb)+
+interpretation aci_lower_plus!: ab_semigroup_idem_mult "op +\<flat>"
+  proof qed (rule lower_plus_assoc lower_plus_commute lower_plus_absorb)+
 
 lemma lower_plus_left_commute: "xs +\<flat> (ys +\<flat> zs) = ys +\<flat> (xs +\<flat> zs)"
 by (rule aci_lower_plus.mult_left_commute)

--- a/src/HOLCF/UpperPD.thy	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/HOLCF/UpperPD.thy	Fri Jan 16 13:07:44 2009 -0800
@@ -248,9 +248,8 @@
 apply (simp add: PDPlus_absorb)
 done
 
-class_interpretation aci_upper_plus: ab_semigroup_idem_mult ["op +\<sharp>"]
-  by unfold_locales
-    (rule upper_plus_assoc upper_plus_commute upper_plus_absorb)+
+interpretation aci_upper_plus!: ab_semigroup_idem_mult "op +\<sharp>"
+  proof qed (rule upper_plus_assoc upper_plus_commute upper_plus_absorb)+
 
 lemma upper_plus_left_commute: "xs +\<sharp> (ys +\<sharp> zs) = ys +\<sharp> (xs +\<sharp> zs)"
 by (rule aci_upper_plus.mult_left_commute)

--- a/src/Pure/Isar/class.ML	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/Pure/Isar/class.ML	Fri Jan 16 13:07:44 2009 -0800
@@ -27,9 +27,9 @@
 (** rule calculation **)
 
 fun calculate_axiom thy sups base_sort assm_axiom param_map class =
-  case Old_Locale.intros thy class
-   of (_, []) => assm_axiom
-    | (_, [intro]) =>
+  case Locale.intros_of thy class
+   of (_, NONE) => assm_axiom
+    | (_, SOME intro) =>
       let
         fun instantiate thy sort = Thm.instantiate ([pairself (Thm.ctyp_of thy o TVar o pair (Name.aT, 0))
           (base_sort, sort)], map (fn (v, (c, ty)) => pairself (Thm.cterm_of thy)
@@ -45,23 +45,22 @@
         |> SOME
       end;
 
-fun raw_morphism thy class param_map some_axiom =
+fun raw_morphism thy class sups param_map some_axiom =
   let
     val ctxt = ProofContext.init thy;
-    val some_wit = case some_axiom
-     of SOME axiom => SOME (Element.prove_witness ctxt
-          (Logic.unvarify (Thm.prop_of axiom))
-            (ALLGOALS (ProofContext.fact_tac [axiom])))
-      | NONE => NONE;
-    val instT = Symtab.empty |> Symtab.update ("'a", TFree ("'a", [class]));
-    val inst = Symtab.make ((map o apsnd) Const param_map);
-  in case some_wit
-   of SOME wit => Element.inst_morphism thy (instT, inst)
-        $> Morphism.binding_morphism (Binding.add_prefix false (class_prefix class))
-        $> Element.satisfy_morphism [wit]
-    | NONE => Element.inst_morphism thy (instT, inst)
-        $> Morphism.binding_morphism (Binding.add_prefix false (class_prefix class))
-  end;
+    val (([props], [(_, morph1)], export_morph), _) = ctxt
+      |> Expression.cert_goal_expression ([(class, (("", false),
+           Expression.Named ((map o apsnd) Const param_map)))], []);
+    val morph2 = morph1
+      $> Morphism.binding_morphism (Binding.add_prefix false (class_prefix class));
+    val morph3 = case props
+     of [prop] => morph2
+          $> Element.satisfy_morphism [(Element.prove_witness ctxt prop
+               (ALLGOALS (ProofContext.fact_tac (the_list some_axiom))))]
+        | [] => morph2;
+    (*FIXME generic amend operation for classes*)
+    val morph4 = morph3 $> eq_morph thy (these_defs thy sups);
+  in (morph4, export_morph) end;
 
 fun calculate_rules thy morph sups base_sort param_map axiom class =
   let
@@ -70,19 +69,18 @@
         (Var ((v, 0), map_atyps (fn _ => TVar ((Name.aT, 0), sort)) ty),
           Const (c, map_atyps (fn _ => TVar ((Name.aT, 0), sort)) ty))) param_map);
     val defs = these_defs thy sups;
-    val assm_intro = Old_Locale.intros thy class
+    val assm_intro = Locale.intros_of thy class
       |> fst
-      |> map (instantiate thy base_sort)
-      |> map (MetaSimplifier.rewrite_rule defs)
-      |> map Thm.close_derivation
-      |> try the_single;
+      |> Option.map (instantiate thy base_sort)
+      |> Option.map (MetaSimplifier.rewrite_rule defs)
+      |> Option.map Thm.close_derivation;
     val fixate = Thm.instantiate
       (map (pairself (Thm.ctyp_of thy)) [(TVar ((Name.aT, 0), []), TFree (Name.aT, base_sort)),
         (TVar ((Name.aT, 0), base_sort), TFree (Name.aT, base_sort))], [])
     val of_class_sups = if null sups
       then map (fixate o Thm.class_triv thy) base_sort
       else map (fixate o snd o rules thy) sups;
-    val locale_dests = map Drule.standard' (Old_Locale.dests thy class);
+    val locale_dests = map Drule.standard' (Locale.axioms_of thy class);
     val num_trivs = case length locale_dests
      of 0 => if is_none axiom then 0 else 1
       | n => n;
@@ -110,55 +108,54 @@
 
 local
 
-fun gen_class_spec prep_class process_expr thy raw_supclasses raw_elems =
+fun gen_class_spec prep_class process_decl thy raw_supclasses raw_elems =
   let
     val supclasses = map (prep_class thy) raw_supclasses;
     val supsort = Sign.minimize_sort thy supclasses;
     val sups = filter (is_class thy) supsort;
-    val supparam_names = map fst (these_params thy sups);
+    val base_sort = if null sups then supsort else
+      foldr1 (Sorts.inter_sort (Sign.classes_of thy))
+        (map (base_sort thy) sups);
+    val supparams = (map o apsnd) (snd o snd) (these_params thy sups);
+    val supparam_names = map fst supparams;
     val _ = if has_duplicates (op =) supparam_names
       then error ("Duplicate parameter(s) in superclasses: "
         ^ (commas o map quote o duplicates (op =)) supparam_names)
       else ();
-    val base_sort = if null sups then supsort else
-      foldr1 (Sorts.inter_sort (Sign.classes_of thy))
-        (map (base_sort thy) sups);
-    val suplocales = map Old_Locale.Locale sups;
-    val supexpr = Old_Locale.Merge suplocales;
-    val supparams = (map fst o Old_Locale.parameters_of_expr thy) supexpr;
-    val mergeexpr = Old_Locale.Merge suplocales;
+
+    val supexpr = (map (fn sup => (sup, (("", false), Expression.Positional [])))
+      sups, []);
     val constrain = Element.Constrains ((map o apsnd o map_atyps)
       (K (TFree (Name.aT, base_sort))) supparams);
+      (*FIXME perhaps better: control type variable by explicit
+      parameter instantiation of import expression*)
+    val begin_ctxt = begin sups base_sort
+      #> fold (Variable.declare_constraints o Free) ((map o apsnd o map_atyps)
+          (K (TFree (Name.aT, base_sort))) supparams) (*FIXME
+            should constraints be issued in begin?*)
+    val ((_, _, syntax_elems), _) = ProofContext.init thy
+      |> begin_ctxt
+      |> process_decl supexpr raw_elems;
     fun fork_syn (Element.Fixes xs) =
           fold_map (fn (c, ty, syn) => cons (Binding.base_name c, syn) #> pair (c, ty, NoSyn)) xs
           #>> Element.Fixes
       | fork_syn x = pair x;
-    fun fork_syntax elems =
-      let
-        val (elems', global_syntax) = fold_map fork_syn elems [];
-      in (constrain :: elems', global_syntax) end;
-    val (elems, global_syntax) =
-      ProofContext.init thy
-      |> Old_Locale.cert_expr supexpr [constrain]
-      |> snd
-      |> begin sups base_sort
-      |> process_expr Old_Locale.empty raw_elems
-      |> fst
-      |> fork_syntax
-  in (((sups, supparams), (supsort, base_sort, mergeexpr)), (elems, global_syntax)) end;
+    val (elems, global_syntax) = fold_map fork_syn syntax_elems [];
+  in (((sups, supparam_names), (supsort, base_sort, supexpr)), (constrain :: elems, global_syntax)) end;
 
-val read_class_spec = gen_class_spec Sign.intern_class Old_Locale.read_expr;
-val check_class_spec = gen_class_spec (K I) Old_Locale.cert_expr;
+val cert_class_spec = gen_class_spec (K I) Expression.cert_declaration;
+val read_class_spec = gen_class_spec Sign.intern_class Expression.cert_read_declaration;
 
 fun add_consts bname class base_sort sups supparams global_syntax thy =
   let
-    val supconsts = map fst supparams
+    val supconsts = supparams
       |> AList.make (snd o the o AList.lookup (op =) (these_params thy sups))
       |> (map o apsnd o apsnd o map_atyps o K o TFree) (Name.aT, [class]);
-    val all_params = map fst (Old_Locale.parameters_of thy class);
+    val all_params = Locale.params_of thy class;
     val raw_params = (snd o chop (length supparams)) all_params;
-    fun add_const (v, raw_ty) thy =
+    fun add_const (b, SOME raw_ty, _) thy =
       let
+        val v = Binding.base_name b;
         val c = Sign.full_bname thy v;
         val ty = map_atyps (K (TFree (Name.aT, base_sort))) raw_ty;
         val ty0 = Type.strip_sorts ty;
@@ -183,9 +180,9 @@
     fun globalize param_map = map_aterms
       (fn Free (v, ty) => Const ((fst o the o AList.lookup (op =) param_map) v, ty)
         | t => t);
-    val raw_pred = Old_Locale.intros thy class
+    val raw_pred = Locale.intros_of thy class
       |> fst
-      |> map (Logic.unvarify o Logic.strip_imp_concl o Thm.prop_of);
+      |> Option.map (Logic.unvarify o Logic.strip_imp_concl o Thm.prop_of);
     fun get_axiom thy = case (#axioms o AxClass.get_info thy) class
      of [] => NONE
       | [thm] => SOME thm;
@@ -194,7 +191,8 @@
     |> add_consts bname class base_sort sups supparams global_syntax
     |-> (fn (param_map, params) => AxClass.define_class (bname, supsort)
           (map (fst o snd) params)
-          [((Binding.name (bname ^ "_" ^ AxClass.axiomsN), []), map (globalize param_map) raw_pred)]
+          [(((*Binding.name (bname ^ "_" ^ AxClass.axiomsN*) Binding.empty, []),
+            Option.map (globalize param_map) raw_pred |> the_list)]
     #> snd
     #> `get_axiom
     #-> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params
@@ -204,35 +202,42 @@
 fun gen_class prep_spec bname raw_supclasses raw_elems thy =
   let
     val class = Sign.full_bname thy bname;
-    val (((sups, supparams), (supsort, base_sort, mergeexpr)), (elems, global_syntax)) =
+    val (((sups, supparams), (supsort, base_sort, supexpr)), (elems, global_syntax)) =
       prep_spec thy raw_supclasses raw_elems;
-    val supconsts = map (apsnd fst o snd) (these_params thy sups);
+    (*val export_morph = (*FIXME how canonical is this?*)
+      Morphism.morphism { binding = I, var = I,
+        typ = Logic.varifyT,
+        term = (*map_types Logic.varifyT*) I,
+        fact = map Thm.varifyT
+      } $> Morphism.morphism { binding = I, var = I,
+        typ = Logic.type_map TermSubst.zero_var_indexes,
+        term = TermSubst.zero_var_indexes,
+        fact = Drule.zero_var_indexes_list o map Thm.strip_shyps
+      };*)
   in
     thy
-    |> Old_Locale.add_locale "" bname mergeexpr elems
-    |> snd
-    |> ProofContext.theory_of
+    |> Expression.add_locale bname "" supexpr elems
+    |> snd |> LocalTheory.exit_global
     |> adjungate_axclass bname class base_sort sups supsort supparams global_syntax
     |-> (fn (inst, param_map, params, assm_axiom) =>
-        `(fn thy => calculate_axiom thy sups base_sort assm_axiom param_map class)
+       `(fn thy => calculate_axiom thy sups base_sort assm_axiom param_map class)
     #-> (fn axiom =>
-        prove_class_interpretation class inst
-          (supconsts @ map (pair class o fst o snd) params) (the_list axiom) []
-    #> `(fn thy => raw_morphism thy class param_map axiom)
-    #-> (fn morph =>
-        `(fn thy => calculate_rules thy morph sups base_sort param_map axiom class)
+       `(fn thy => raw_morphism thy class sups param_map axiom)
+    #-> (fn (morph, export_morph) => Locale.add_registration (class, (morph, export_morph))
+    #>  Locale.activate_global_facts (class, morph $> export_morph)
+    #> `(fn thy => calculate_rules thy morph sups base_sort param_map axiom class)
     #-> (fn (assm_intro, of_class) =>
         register class sups params base_sort inst
           morph axiom assm_intro of_class
-    #> fold (note_assm_intro class) (the_list assm_intro)))))
+    (*#> fold (note_assm_intro class) (the_list assm_intro*)))))
     |> TheoryTarget.init (SOME class)
     |> pair class
   end;
 
 in
 
+val class = gen_class cert_class_spec;
 val class_cmd = gen_class read_class_spec;
-val class = gen_class check_class_spec;
 
 end; (*local*)
 
@@ -241,6 +246,12 @@
 
 local
 
+fun prove_sublocale tac (sub, expr) =
+  Expression.sublocale sub expr
+  #> Proof.global_terminal_proof
+      (Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)
+  #> ProofContext.theory_of;
+
 fun gen_subclass prep_class do_proof raw_sup lthy =
   let
     val thy = ProofContext.theory_of lthy;
@@ -258,16 +269,18 @@
     val _ = if null err_params then [] else
       error ("Class " ^ Syntax.string_of_sort lthy [sub] ^ " lacks parameter(s) " ^
         commas_quote err_params ^ " of " ^ Syntax.string_of_sort lthy [sup]);
-    val sublocale_prop =
-      Old_Locale.global_asms_of thy sup
-      |> maps snd
-      |> try the_single
-      |> Option.map (ObjectLogic.ensure_propT thy);
+
+    val expr = ([(sup, (("", false), Expression.Positional []))], []);
+    val (([props], _, _), goal_ctxt) =
+      Expression.cert_goal_expression expr lthy;
+    val some_prop = try the_single props; (*FIXME*)
     fun after_qed some_thm =
-      LocalTheory.theory (prove_subclass_relation (sub, sup) some_thm)
+      LocalTheory.theory (register_subclass (sub, sup) some_thm)
+      #> is_some some_thm ? LocalTheory.theory
+        (prove_sublocale (ALLGOALS (ProofContext.fact_tac (the_list some_thm))) (sub, expr))
       #> (TheoryTarget.init (SOME sub) o ProofContext.theory_of);
   in
-    do_proof after_qed sublocale_prop lthy
+    do_proof after_qed some_prop lthy
   end;
 
 fun user_proof after_qed NONE =

--- a/src/Pure/Isar/class_target.ML	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/Pure/Isar/class_target.ML	Fri Jan 16 13:07:44 2009 -0800
@@ -10,6 +10,8 @@
   val register: class -> class list -> ((string * typ) * (string * typ)) list
     -> sort -> term list -> morphism
     -> thm option -> thm option -> thm -> theory -> theory
+  val register_subclass: class * class -> thm option
+    -> theory -> theory
 
   val begin: class list -> sort -> Proof.context -> Proof.context
   val init: class -> theory -> Proof.context
@@ -21,14 +23,12 @@
 
   val intro_classes_tac: thm list -> tactic
   val default_intro_tac: Proof.context -> thm list -> tactic
-  val prove_class_interpretation: class -> term list -> (class * string) list
-    -> thm list -> thm list -> theory -> theory
-  val prove_subclass_relation: class * class -> thm option -> theory -> theory
 
   val class_prefix: string -> string
   val is_class: theory -> class -> bool
   val these_params: theory -> sort -> (string * (class * (string * typ))) list
   val these_defs: theory -> sort -> thm list
+  val eq_morph: theory -> thm list -> morphism
   val base_sort: theory -> class -> sort
   val rules: theory -> class -> thm option * thm
   val print_classes: theory -> unit
@@ -64,36 +64,6 @@
 structure Class_Target : CLASS_TARGET =
 struct
 
-(*temporary adaption code to mediate between old and new locale code*)
-
-structure Locale_Layer =
-struct
-
-val init = Old_Locale.init;
-val parameters_of = Old_Locale.parameters_of;
-val intros = Old_Locale.intros;
-val dests = Old_Locale.dests;
-val get_interpret_morph = Old_Locale.get_interpret_morph;
-val Locale = Old_Locale.Locale;
-val extern = Old_Locale.extern;
-val intro_locales_tac = Old_Locale.intro_locales_tac;
-
-fun prove_interpretation tac prfx_atts expr inst =
-  Old_Locale.interpretation I prfx_atts expr inst
-  ##> Proof.global_terminal_proof
-      (Method.Basic (fn ctxt => Method.SIMPLE_METHOD (tac ctxt), Position.none), NONE)
-  ##> ProofContext.theory_of;
-
-fun prove_interpretation_in tac after_qed (name, expr) =
-  Old_Locale.interpretation_in_locale
-      (ProofContext.theory after_qed) (name, expr)
-  #> Proof.global_terminal_proof
-      (Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)
-  #> ProofContext.theory_of;
-
-end;
-
-
 (** primitive axclass and instance commands **)
 
 fun axclass_cmd (class, raw_superclasses) raw_specs thy =
@@ -201,6 +171,8 @@
 
 val ancestry = Graph.all_succs o ClassData.get;
 
+val heritage = Graph.all_preds o ClassData.get;
+
 fun the_inst thy = #inst o the_class_data thy;
 
 fun these_params thy =
@@ -235,14 +207,14 @@
 fun class_binding_morph class =
   Binding.map_prefix (K (Binding.add_prefix false (class_prefix class)));
 
+fun eq_morph thy thms = (*FIXME how general is this?*)
+  Morphism.term_morphism (MetaSimplifier.rewrite_term thy thms [])
+  $> Morphism.thm_morphism (MetaSimplifier.rewrite_rule thms);
+
 fun morphism thy class =
   let
     val { base_morph, defs, ... } = the_class_data thy class;
-  in
-    base_morph 
-    $> Morphism.term_morphism (MetaSimplifier.rewrite_term thy defs [])
-    $> Morphism.thm_morphism (MetaSimplifier.rewrite_rule defs)
-  end;
+  in base_morph $> eq_morph thy defs end;
 
 fun print_classes thy =
   let
@@ -265,7 +237,7 @@
       (SOME o Pretty.block) [Pretty.str "supersort: ",
         (Syntax.pretty_sort ctxt o Sign.minimize_sort thy o Sign.super_classes thy) class],
       if is_class thy class then (SOME o Pretty.str)
-        ("locale: " ^ Locale_Layer.extern thy class) else NONE,
+        ("locale: " ^ Locale.extern thy class) else NONE,
       ((fn [] => NONE | ps => (SOME o Pretty.block o Pretty.fbreaks)
           (Pretty.str "parameters:" :: ps)) o map mk_param
         o these o Option.map #params o try (AxClass.get_info thy)) class,
@@ -312,39 +284,26 @@
 
 (** tactics and methods **)
 
-fun prove_class_interpretation class inst consts hyp_facts def_facts thy =
-  let
-    val constraints = map (fn (class, c) => map_atyps (K (TFree (Name.aT,
-      [class]))) (Sign.the_const_type thy c)) consts;
-    val no_constraints = map (map_atyps (K (TFree (Name.aT, [])))) constraints;
-    fun add_constraint c T = Sign.add_const_constraint (c, SOME T);
-    fun tac ctxt = ALLGOALS (ProofContext.fact_tac (hyp_facts @ def_facts)
-      ORELSE' (fn n => SELECT_GOAL (Locale_Layer.intro_locales_tac false ctxt []) n));
-    val prfx = class_prefix class;
-  in
-    thy
-    |> fold2 add_constraint (map snd consts) no_constraints
-    |> Locale_Layer.prove_interpretation tac (class_binding_morph class) (Locale_Layer.Locale class)
-          (map SOME inst, map (pair (Attrib.empty_binding) o Thm.prop_of) def_facts)
-    |> snd
-    |> fold2 add_constraint (map snd consts) constraints
-  end;
-
-fun prove_subclass_relation (sub, sup) some_thm thy =
+fun register_subclass (sub, sup) thms thy =
   let
     val of_class = (snd o rules thy) sup;
-    val intro = case some_thm
+    val intro = case thms
      of SOME thm => Drule.standard' (of_class OF [Drule.standard' thm])
       | NONE => Thm.instantiate ([pairself (Thm.ctyp_of thy o TVar o pair (Name.aT, 0))
           ([], [sub])], []) of_class;
     val classrel = (intro OF (the_list o fst o rules thy) sub)
       |> Thm.close_derivation;
+    (*FIXME generic amend operation for classes*)
+    val amendments = map (fn class => (class, morphism thy class))
+      (heritage thy [sub]);
+    val diff_sort = Sign.complete_sort thy [sup]
+      |> subtract (op =) (Sign.complete_sort thy [sub]);
+    val defs_morph = eq_morph thy (these_defs thy diff_sort);
   in
     thy
     |> AxClass.add_classrel classrel
-    |> Locale_Layer.prove_interpretation_in (ALLGOALS (ProofContext.fact_tac (the_list some_thm)))
-         I (sub, Locale_Layer.Locale sup)
     |> ClassData.map (Graph.add_edge (sub, sup))
+    |> fold (Locale.amend_registration defs_morph) amendments
   end;
 
 fun intro_classes_tac facts st =
@@ -428,7 +387,7 @@
 
 fun init class thy =
   thy
-  |> Locale_Layer.init class
+  |> Locale.init class
   |> begin [class] (base_sort thy class);
 
 
@@ -441,12 +400,18 @@
     val morph = morphism thy' class;
     val inst = the_inst thy' class;
     val params = map (apsnd fst o snd) (these_params thy' [class]);
+    val amendments = map (fn class => (class, morphism thy' class))
+      (heritage thy' [class]);
 
     val c' = Sign.full_bname thy' c;
     val dict' = Morphism.term morph dict;
     val ty' = Term.fastype_of dict';
     val ty'' = Type.strip_sorts ty';
     val def_eq = Logic.mk_equals (Const (c', ty'), dict');
+    (*FIXME a mess*)
+    fun amend def def' (class, morph) thy =
+      Locale.amend_registration (eq_morph thy [Thm.varifyT def])
+        (class, morph) thy;
     fun get_axiom thy = ((Thm.varifyT o Thm.axiom thy) c', thy);
   in
     thy'
@@ -454,9 +419,9 @@
     |> Thm.add_def false false (c, def_eq)
     |>> Thm.symmetric
     ||>> get_axiom
-    |-> (fn (def, def') => prove_class_interpretation class inst params [] [def]
-      #> register_operation class (c', (dict', SOME (Thm.symmetric def')))
-      #> PureThy.store_thm (c ^ "_raw", def')
+    |-> (fn (def, def') => register_operation class (c', (dict', SOME (Thm.symmetric def')))
+      #> fold (amend def def') amendments
+      #> PureThy.store_thm (c ^ "_raw", def') (*FIXME name*)
       #> snd)
     |> Sign.restore_naming thy
     |> Sign.add_const_constraint (c', SOME ty')

--- a/src/Pure/Isar/expression.ML	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/Pure/Isar/expression.ML	Fri Jan 16 13:07:44 2009 -0800
@@ -6,37 +6,47 @@
 
 signature EXPRESSION =
 sig
-  datatype 'term map = Positional of 'term option list | Named of (string * 'term) list;
-  type 'term expr = (string * ((string * bool) * 'term map)) list;
-  type expression_i = term expr * (Binding.T * typ option * mixfix) list;
-  type expression = string expr * (Binding.T * string option * mixfix) list;
+  (* Locale expressions *)
+  datatype 'term map = Positional of 'term option list | Named of (string * 'term) list
+  type 'term expr = (string * ((string * bool) * 'term map)) list
+  type expression_i = term expr * (Binding.T * typ option * mixfix) list
+  type expression = string expr * (Binding.T * string option * mixfix) list
 
   (* Processing of context statements *)
   val cert_statement: Element.context_i list -> (term * term list) list list ->
-    Proof.context -> (term * term list) list list * Proof.context;
+    Proof.context -> (term * term list) list list * Proof.context
   val read_statement: Element.context list -> (string * string list) list list ->
-    Proof.context ->  (term * term list) list list * Proof.context;
+    Proof.context -> (term * term list) list list * Proof.context
 
   (* Declaring locales *)
+  val cert_declaration: expression_i -> Element.context_i list -> Proof.context ->
+    ((Binding.T * typ option * mixfix) list * (string * morphism) list
+      * Element.context_i list) * ((string * typ) list * Proof.context)
+  val cert_read_declaration: expression_i -> Element.context list -> Proof.context ->
+    ((Binding.T * typ option * mixfix) list * (string * morphism) list
+      * Element.context_i list) * ((string * typ) list * Proof.context)
+      (*FIXME*)
+  val read_declaration: expression -> Element.context list -> Proof.context ->
+    ((Binding.T * typ option * mixfix) list * (string * morphism) list
+      * Element.context_i list) * ((string * typ) list * Proof.context)
   val add_locale: bstring -> bstring -> expression_i -> Element.context_i list ->
-    theory -> string * local_theory;
+    theory -> string * local_theory
   val add_locale_cmd: bstring -> bstring -> expression -> Element.context list ->
-    theory -> string * local_theory;
+    theory -> string * local_theory
 
   (* Interpretation *)
   val cert_goal_expression: expression_i -> Proof.context ->
-    (term list list * (string * morphism) list * morphism) * Proof.context;
+    (term list list * (string * morphism) list * morphism) * Proof.context
   val read_goal_expression: expression -> Proof.context ->
-    (term list list * (string * morphism) list * morphism) * Proof.context;
-
-  val sublocale: string -> expression_i -> theory -> Proof.state;
-  val sublocale_cmd: string -> expression -> theory -> Proof.state;
+    (term list list * (string * morphism) list * morphism) * Proof.context
+  val sublocale: string -> expression_i -> theory -> Proof.state
+  val sublocale_cmd: string -> expression -> theory -> Proof.state
   val interpretation: expression_i -> (Attrib.binding * term) list ->
-    theory -> Proof.state;
+    theory -> Proof.state
   val interpretation_cmd: expression -> (Attrib.binding * string) list ->
-    theory -> Proof.state;
-  val interpret: expression_i -> bool -> Proof.state -> Proof.state;
-  val interpret_cmd: expression -> bool -> Proof.state -> Proof.state;
+    theory -> Proof.state
+  val interpret: expression_i -> bool -> Proof.state -> Proof.state
+  val interpret_cmd: expression -> bool -> Proof.state -> Proof.state
 end;
 
 
@@ -140,14 +150,14 @@
 
 local
 
-fun prep_inst parse_term parms (Positional insts) ctxt =
+fun prep_inst parse_term ctxt parms (Positional insts) =
       (insts ~~ parms) |> map (fn
-        (NONE, p) => Syntax.parse_term ctxt p |
+        (NONE, p) => Free (p, the (Variable.default_type ctxt p)) |
         (SOME t, _) => parse_term ctxt t)
-  | prep_inst parse_term parms (Named insts) ctxt =
+  | prep_inst parse_term ctxt parms (Named insts) =
       parms |> map (fn p => case AList.lookup (op =) insts p of
         SOME t => parse_term ctxt t |
-        NONE => Syntax.parse_term ctxt p);
+        NONE => Free (p, the (Variable.default_type ctxt p)));
 
 in
 
@@ -315,7 +325,7 @@
   let
     val thy = ProofContext.theory_of ctxt;
     val (parm_names, parm_types) = Locale.params_of thy loc |>
-      map (fn (b, SOME T, _) => (Binding.base_name b, T)) |> split_list;
+      map_split (fn (b, SOME T, _) => (Binding.base_name b, T));
     val (morph, _) = inst_morph (parm_names, parm_types) (prfx, inst) ctxt;
   in (loc, morph) end;
 
@@ -337,7 +347,7 @@
 
 local
 
-fun prep_full_context_statement parse_typ parse_prop parse_inst prep_vars prep_expr
+fun prep_full_context_statement parse_typ parse_prop prep_vars_elem parse_inst prep_vars_inst prep_expr
     strict do_close raw_import raw_elems raw_concl ctxt1 =
   let
     val thy = ProofContext.theory_of ctxt1;
@@ -347,8 +357,9 @@
     fun prep_inst (loc, (prfx, inst)) (i, insts, ctxt) =
       let
         val (parm_names, parm_types) = Locale.params_of thy loc |>
-          map (fn (b, SOME T, _) => (Binding.base_name b, T)) |> split_list;
-        val inst' = parse_inst parm_names inst ctxt;
+          map_split (fn (b, SOME T, _) => (Binding.base_name b, T))
+            (*FIXME return value of Locale.params_of has strange type*)
+        val inst' = parse_inst ctxt parm_names inst;
         val parm_types' = map (TypeInfer.paramify_vars o
           Term.map_type_tvar (fn ((x, _), S) => TVar ((x, i), S)) o Logic.varifyT) parm_types;
         val inst'' = map2 TypeInfer.constrain parm_types' inst';
@@ -359,43 +370,47 @@
         val ctxt'' = Locale.activate_declarations thy (loc, morph) ctxt;
       in (i+1, insts', ctxt'') end;
   
-    fun prep_elem raw_elem (insts, elems, ctxt) =
+    fun prep_elem insts raw_elem (elems, ctxt) =
       let
-        val ctxt' = declare_elem prep_vars raw_elem ctxt;
+        val ctxt' = declare_elem prep_vars_elem raw_elem ctxt;
         val elems' = elems @ [parse_elem parse_typ parse_prop ctxt' raw_elem];
         val (_, _, _, ctxt'') = check_autofix insts elems' [] ctxt';
-      in (insts, elems', ctxt') end;
+      in (elems', ctxt') end;
 
     fun prep_concl raw_concl (insts, elems, ctxt) =
       let
         val concl = parse_concl parse_prop ctxt raw_concl;
       in check_autofix insts elems concl ctxt end;
 
-    val fors = prep_vars fixed ctxt1 |> fst;
+    val fors = prep_vars_inst fixed ctxt1 |> fst;
     val ctxt2 = ctxt1 |> ProofContext.add_fixes_i fors |> snd;
     val (_, insts', ctxt3) = fold prep_inst raw_insts (0, [], ctxt2);
-    val (_, elems'', ctxt4) = fold prep_elem raw_elems (insts', [], ctxt3);
-    val (insts, elems, concl, ctxt5) =
-      prep_concl raw_concl (insts', elems'', ctxt4);
+    val (elems, ctxt4) = fold (prep_elem insts') raw_elems ([], ctxt3);
+    val (insts, elems', concl, ctxt5) =
+      prep_concl raw_concl (insts', elems, ctxt4);
 
     (* Retrieve parameter types *)
-    val xs = fold (fn Fixes fixes => (fn ps => ps @ map (Binding.base_name o #1) fixes) |
-      _ => fn ps => ps) (Fixes fors :: elems) [];
+    val xs = fold (fn Fixes fixes => (fn ps => ps @ map (Binding.base_name o #1) fixes)
+      | _ => fn ps => ps) (Fixes fors :: elems') [];
     val (Ts, ctxt6) = fold_map ProofContext.inferred_param xs ctxt5; 
     val parms = xs ~~ Ts;  (* params from expression and elements *)
 
     val Fixes fors' = finish_primitive parms I (Fixes fors);
-    val (deps, elems') = finish ctxt6 parms do_close insts elems;
+    val (deps, elems'') = finish ctxt6 parms do_close insts elems';
 
-  in ((fors', deps, elems', concl), (parms, ctxt6)) end
+  in ((fors', deps, elems'', concl), (parms, ctxt6)) end
 
 in
 
+fun cert_full_context_statement x =
+  prep_full_context_statement (K I) (K I) ProofContext.cert_vars
+  make_inst ProofContext.cert_vars (K I) x;
+fun cert_read_full_context_statement x =
+  prep_full_context_statement Syntax.parse_typ Syntax.parse_prop ProofContext.read_vars
+  make_inst ProofContext.cert_vars (K I) x;
 fun read_full_context_statement x =
-  prep_full_context_statement Syntax.parse_typ Syntax.parse_prop parse_inst
-  ProofContext.read_vars intern x;
-fun cert_full_context_statement x =
-  prep_full_context_statement (K I) (K I) make_inst ProofContext.cert_vars (K I) x;
+  prep_full_context_statement Syntax.parse_typ Syntax.parse_prop ProofContext.read_vars
+  parse_inst ProofContext.read_vars intern x;
 
 end;
 
@@ -407,14 +422,16 @@
 fun prep_statement prep activate raw_elems raw_concl context =
   let
      val ((_, _, elems, concl), _) =
-       prep true false ([], []) raw_elems raw_concl context ;
-     val (_, context') = activate elems (ProofContext.set_stmt true context);
+       prep true false ([], []) raw_elems raw_concl context;
+     val (_, context') = context |>
+       ProofContext.set_stmt true |>
+       activate elems;
   in (concl, context') end;
 
 in
 
+fun cert_statement x = prep_statement cert_full_context_statement Element.activate_i x;
 fun read_statement x = prep_statement read_full_context_statement Element.activate x;
-fun cert_statement x = prep_statement cert_full_context_statement Element.activate_i x;
 
 end;
 
@@ -431,13 +448,16 @@
     val context' = context |>
       ProofContext.add_fixes_i fixed |> snd |>
       fold Locale.activate_local_facts deps;
-    val (elems', _) = activate elems (ProofContext.set_stmt true context');
+    val (elems', _) = context' |>
+      ProofContext.set_stmt true |>
+      activate elems;
   in ((fixed, deps, elems'), (parms, ctxt')) end;
 
 in
 
+fun cert_declaration x = prep_declaration cert_full_context_statement Element.activate_i x;
+fun cert_read_declaration x = prep_declaration cert_read_full_context_statement Element.activate x;
 fun read_declaration x = prep_declaration read_full_context_statement Element.activate x;
-fun cert_declaration x = prep_declaration cert_full_context_statement Element.activate_i x;
 
 end;
 
@@ -476,8 +496,8 @@
     
 in
 
+fun cert_goal_expression x = prep_goal_expression cert_full_context_statement x;
 fun read_goal_expression x = prep_goal_expression read_full_context_statement x;
-fun cert_goal_expression x = prep_goal_expression cert_full_context_statement x;
 
 end;
 
@@ -758,8 +778,8 @@
 
 in
 
+val add_locale = gen_add_locale cert_declaration;
 val add_locale_cmd = gen_add_locale read_declaration;
-val add_locale = gen_add_locale cert_declaration;
 
 end;
 
@@ -804,8 +824,8 @@
 
 in
 
+fun sublocale x = gen_sublocale cert_goal_expression (K I) x;
 fun sublocale_cmd x = gen_sublocale read_goal_expression Locale.intern x;
-fun sublocale x = gen_sublocale cert_goal_expression (K I) x;
 
 end;
 
@@ -873,9 +893,9 @@
 
 in
 
+fun interpretation x = gen_interpretation cert_goal_expression (K I) (K I) x;
 fun interpretation_cmd x = gen_interpretation read_goal_expression
   Syntax.parse_prop Attrib.intern_src x;
-fun interpretation x = gen_interpretation cert_goal_expression (K I) (K I) x;
 
 end;
 
@@ -910,8 +930,8 @@
 
 in
 
+fun interpret x = gen_interpret cert_goal_expression x;
 fun interpret_cmd x = gen_interpret read_goal_expression x;
-fun interpret x = gen_interpret cert_goal_expression x;
 
 end;

--- a/src/Pure/Isar/isar_document.ML	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/Pure/Isar/isar_document.ML	Fri Jan 16 13:07:44 2009 -0800
@@ -24,7 +24,7 @@
 type command_id = string;
 type document_id = string;
 
-fun new_id () = "isabelle:" ^ serial_string ();
+fun make_id () = "isabelle:" ^ serial_string ();
 
 fun err_dup kind id = error ("Duplicate " ^ kind ^ ": " ^ quote id);
 fun err_undef kind id = error ("Unknown " ^ kind ^ ": " ^ quote id);
@@ -53,7 +53,6 @@
 fun set_entry_state (id, state_id) = put_entry_state id (SOME state_id);
 
 
-
 (* document *)
 
 datatype document = Document of
@@ -71,19 +70,21 @@
 
 (* iterate entries *)
 
-fun fold_entries opt_id f (Document {start, entries, ...}) =
+fun fold_entries id0 f (Document {entries, ...}) =
   let
     fun apply NONE x = x
-      | apply (SOME id) x = apply (#next (the_entry entries id)) (f id x);
-  in if is_some opt_id then apply opt_id else apply (SOME start) end;
+      | apply (SOME id) x =
+          let val entry = the_entry entries id
+          in apply (#next entry) (f (id, entry) x) end;
+  in if Symtab.defined entries id0 then apply (SOME id0) else I end;
 
-fun find_entries P (Document {start, entries, ...}) =
+fun first_entry P (Document {start, entries, ...}) =
   let
-    fun find _ NONE = NONE
-      | find prev (SOME id) =
-          if P id then SOME (prev, id)
-          else find (SOME id) (#next (the_entry entries id));
-  in find NONE (SOME start) end;
+    fun first _ NONE = NONE
+      | first prev (SOME id) =
+          let val entry = the_entry entries id
+          in if P (id, entry) then SOME (prev, id, entry) else first (SOME id) (#next entry) end;
+  in first NONE (SOME start) end;
 
 
 (* modify entries *)
@@ -133,16 +134,24 @@
 end;
 
 
-fun define_state (id: state_id) state =
-  change_states (Symtab.update_new (id, state))
+(* state *)
+
+val empty_state = Future.value (SOME Toplevel.toplevel);
+
+fun define_state (id: state_id) =
+  change_states (Symtab.update_new (id, empty_state))
     handle Symtab.DUP dup => err_dup "state" dup;
 
+fun put_state (id: state_id) state = change_states (Symtab.update (id, state));
+
 fun the_state (id: state_id) =
   (case Symtab.lookup (get_states ()) id of
     NONE => err_undef "state" id
   | SOME state => state);
 
 
+(* command *)
+
 fun define_command id tr =
   change_commands (Symtab.update_new (id, Toplevel.put_id id tr))
     handle Symtab.DUP dup => err_dup "command" dup;
@@ -153,6 +162,8 @@
   | SOME tr => tr);
 
 
+(* document *)
+
 fun define_document (id: document_id) document =
   change_documents (Symtab.update_new (id, document))
     handle Symtab.DUP dup => err_dup "document" dup;
@@ -160,60 +171,64 @@
 fun the_document (id: document_id) =
   (case Symtab.lookup (get_documents ()) id of
     NONE => err_undef "document" id
-  | SOME (Document doc) => doc);
+  | SOME document => document);
+
 
 
+(** main operations **)
+
 (* begin/end document *)
 
 fun begin_document (id: document_id) path =
   let
     val (dir, name) = ThyLoad.split_thy_path path;
     val _ = define_command id Toplevel.empty;
-    val _ = define_state id (Future.value (SOME Toplevel.toplevel));
+    val _ = define_state id;
     val entries = Symtab.make [(id, make_entry NONE (SOME id))];
     val _ = define_document id (make_document dir name id entries);
   in () end;
 
-fun end_document (id: document_id) = error "FIXME";
+fun end_document (id: document_id) =
+  let
+    val document as Document {name, ...} = the_document id;
+    val end_state =
+      the_state (the (#state (#3 (the
+        (first_entry (fn (_, {next, ...}) => is_none next) document)))));
+    val _ =
+      Future.fork_deps [end_state] (fn () =>
+        (case Future.join end_state of
+          SOME st =>
+           (Toplevel.run_command name (Toplevel.put_id id (Toplevel.commit_exit Position.none)) st;
+            ThyInfo.touch_child_thys name;
+            ThyInfo.register_thy name)
+        | NONE => error ("Failed to finish theory " ^ quote name)));
+  in () end;
 
 
 (* document editing *)
 
-fun update_state tr state = Future.fork_deps [state] (fn () =>
-  (case Future.join state of NONE => NONE | SOME st => Toplevel.run_command tr st));
-
-fun update_states old_document new_document =
-  let
-    val Document {entries = old_entries, ...} = old_document;
-    val Document {entries = new_entries, ...} = new_document;
+local
 
-    fun is_changed id =
-      (case try (the_entry new_entries) id of
-        SOME {state = SOME _, ...} => false
-      | _ => true);
-
-    fun cancel_state id () =
-      (case the_entry old_entries id of
-        {state = SOME state_id, ...} => Future.cancel (the_state state_id)
-      | _ => ());
+fun is_changed entries' (id, {next = _, state}) =
+  (case try (the_entry entries') id of
+    NONE => true
+  | SOME {next = _, state = state'} => state' <> state);
 
-    fun new_state id (state_id, updates) =
+fun new_state name (id, _) (state_id, updates) =
+  let
+    val state_id' = make_id ();
+    val _ = define_state state_id';
+    val tr = Toplevel.put_id state_id' (the_command id);
+    fun make_state' () =
       let
-        val state_id' = new_id ();
-        val state' = update_state (the_command id) (the_state state_id);
-        val _ = define_state state_id' state';
-      in (state_id', (id, state_id') :: updates) end;
-  in
-    (case find_entries is_changed old_document of
-      NONE => ([], new_document)
-    | SOME (prev, id) =>
-        let
-          val _ = fold_entries (SOME id) cancel_state old_document ();
-          val prev_state_id = the (#state (the_entry new_entries (the prev)));
-          val (_, updates) = fold_entries (SOME id) new_state new_document (prev_state_id, []);
-          val new_document' = new_document |> map_entries (fold set_entry_state updates);
-        in (updates, new_document') end)
-  end;
+        val state = the_state state_id;
+        val state' =
+          Future.fork_deps [state] (fn () =>
+            (case Future.join state of
+              NONE => NONE
+            | SOME st => Toplevel.run_command name tr st));
+      in put_state state_id' state' end;
+  in (state_id', ((id, state_id'), make_state') :: updates) end;
 
 fun report_updates _ [] = ()
   | report_updates (document_id: document_id) updates =
@@ -221,17 +236,39 @@
       |> Markup.markup (Markup.edits document_id)
       |> Output.status;
 
-fun edit_document (id: document_id) (id': document_id) edits =
+in
+
+fun edit_document (old_id: document_id) (new_id: document_id) edits =
   let
-    val document = Document (the_document id);
-    val (updates, document') =
-      document
-      |> fold (fn (id, SOME id2) => insert_after id id2 | (id, NONE) => delete_after id) edits
-      |> update_states document;
-    val _ = define_document id' document';
-    val _ = report_updates id' updates;
+    val old_document as Document {name, entries = old_entries, ...} = the_document old_id;
+    val new_document as Document {entries = new_entries, ...} = old_document
+      |> fold (fn (id, SOME id2) => insert_after id id2 | (id, NONE) => delete_after id) edits;
+
+    fun cancel_old id = fold_entries id
+      (fn (_, {state = SOME state_id, ...}) => K (Future.cancel (the_state state_id)) | _ => K ())
+      old_document ();
+
+    val (updates, new_document') =
+      (case first_entry (is_changed old_entries) new_document of
+        NONE =>
+          (case first_entry (is_changed new_entries) old_document of
+            NONE => ([], new_document)
+          | SOME (_, id, _) => (cancel_old id; ([], new_document)))
+      | SOME (prev, id, _) =>
+          let
+            val _ = cancel_old id;
+            val prev_state_id = the (#state (the_entry new_entries (the prev)));
+            val (_, updates) = fold_entries id (new_state name) new_document (prev_state_id, []);
+            val new_document' = new_document |> map_entries (fold (set_entry_state o #1) updates);
+          in (rev updates, new_document') end);
+
+    val _ = define_document new_id new_document';
+    val _ = report_updates new_id (map #1 updates);
+    val _ = List.app (fn (_, run) => run ()) updates;
   in () end;
 
+end;
+
 
 
 (** concrete syntax **)

--- a/src/Pure/Isar/locale.ML	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/Pure/Isar/locale.ML	Fri Jan 16 13:07:44 2009 -0800
@@ -58,7 +58,7 @@
   val add_type_syntax: string -> declaration -> Proof.context -> Proof.context
   val add_term_syntax: string -> declaration -> Proof.context -> Proof.context
   val add_declaration: string -> declaration -> Proof.context -> Proof.context
-  val add_dependency: string -> (string * Morphism.morphism) -> theory -> theory
+  val add_dependency: string -> string * Morphism.morphism -> theory -> theory
 
   (* Activation *)
   val activate_declarations: theory -> string * Morphism.morphism ->
@@ -74,9 +74,9 @@
   val intro_locales_tac: bool -> Proof.context -> thm list -> tactic
 
   (* Registrations *)
-  val add_registration: (string * (Morphism.morphism * Morphism.morphism)) ->
+  val add_registration: string * (Morphism.morphism * Morphism.morphism) ->
     theory -> theory
-  val amend_registration: Morphism.morphism -> (string * Morphism.morphism) ->
+  val amend_registration: Morphism.morphism -> string * Morphism.morphism ->
     theory -> theory
   val get_registrations: theory -> (string * Morphism.morphism) list
 
@@ -356,23 +356,20 @@
 in
 
 fun activate_declarations thy dep ctxt =
-  roundup thy activate_decls dep (get_local_idents ctxt, ctxt) |> uncurry put_local_idents;
+  roundup thy activate_decls dep (get_local_idents ctxt, ctxt) |-> put_local_idents;
 
 fun activate_global_facts dep thy =
   roundup thy (activate_notes init_global_elem Element.transfer_morphism)
-    dep (get_global_idents thy, thy) |>
-  uncurry put_global_idents;
+    dep (get_global_idents thy, thy) |-> put_global_idents;
 
 fun activate_local_facts dep ctxt =
   roundup (ProofContext.theory_of ctxt)
   (activate_notes init_local_elem (Element.transfer_morphism o ProofContext.theory_of)) dep
-    (get_local_idents ctxt, ctxt) |>
-  uncurry put_local_idents;
+    (get_local_idents ctxt, ctxt) |-> put_local_idents;
 
 fun init name thy =
   activate_all name thy init_local_elem (Element.transfer_morphism o ProofContext.theory_of)
-    (empty, ProofContext.init thy) |>
-  uncurry put_local_idents;
+    (empty, ProofContext.init thy) |-> put_local_idents;
 
 fun print_locale thy show_facts name =
   let
@@ -408,8 +405,8 @@
 fun add_registration (name, (base_morph, export)) thy =
   roundup thy (fn _ => fn (name', morph') =>
     (RegistrationsData.map o cons) ((name', (morph', export)), stamp ()))
-    (name, base_morph) (get_global_idents thy, thy) |>
-    snd (* FIXME ?? uncurry put_global_idents *);
+    (name, base_morph) (get_global_idents thy, thy) |> snd
+    (* FIXME |-> put_global_idents ?*);
 
 fun amend_registration morph (name, base_morph) thy =
   let
@@ -428,6 +425,7 @@
   end;
 
 
+
 (*** Storing results ***)
 
 (* Theorems *)

--- a/src/Pure/Isar/toplevel.ML	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/Pure/Isar/toplevel.ML	Fri Jan 16 13:07:44 2009 -0800
@@ -96,7 +96,7 @@
   val transition: bool -> transition -> state -> (state * (exn * string) option) option
   val commit_exit: Position.T -> transition
   val command: transition -> state -> state
-  val run_command: transition -> state -> state option
+  val run_command: string -> transition -> state -> state option
   val excursion: (transition * transition list) list -> (transition * state) list lazy
 end;
 
@@ -698,11 +698,17 @@
   let val st' = command tr st
   in (st', st') end;
 
-fun run_command tr st =
-  (case transition true tr st of
-    SOME (st', NONE) => (status tr Markup.finished; SOME st')
-  | SOME (_, SOME exn_info) => (error_msg tr exn_info; status tr Markup.failed; NONE)
-  | NONE => (error_msg tr (TERMINATE, at_command tr); status tr Markup.failed; NONE));
+fun run_command thy_name tr st =
+  (case
+      (case init_of tr of
+        SOME name => Exn.capture (fn () => ThyLoad.check_name thy_name name) ()
+      | NONE => Exn.Result ()) of
+    Exn.Result () =>
+      (case transition true tr st of
+        SOME (st', NONE) => (status tr Markup.finished; SOME st')
+      | SOME (_, SOME exn_info) => (error_msg tr exn_info; status tr Markup.failed; NONE)
+      | NONE => (error_msg tr (TERMINATE, at_command tr); status tr Markup.failed; NONE))
+  | Exn.Exn exn => (error_msg tr (exn, at_command tr); status tr Markup.failed; NONE));
 
 
 (* excursion of units, consisting of commands with proof *)

--- a/src/Pure/Thy/thy_load.ML	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/Pure/Thy/thy_load.ML	Fri Jan 16 13:07:44 2009 -0800
@@ -25,6 +25,7 @@
   val check_file: Path.T -> Path.T -> (Path.T * File.ident) option
   val check_ml: Path.T -> Path.T -> (Path.T * File.ident) option
   val check_thy: Path.T -> string -> Path.T * File.ident
+  val check_name: string -> string -> unit
   val deps_thy: Path.T -> string ->
    {master: Path.T * File.ident, text: string list, imports: string list, uses: Path.T list}
   val load_ml: Path.T -> Path.T -> Path.T * File.ident
@@ -95,6 +96,11 @@
     | SOME thy_id => thy_id)
   end;
 
+fun check_name name name' =
+  if name = name' then ()
+  else error ("Filename " ^ quote (Path.implode (thy_path name)) ^
+    " does not agree with theory name " ^ quote name');
+
 
 (* theory deps *)
 
@@ -104,9 +110,7 @@
     val text = explode (File.read path);
     val (name', imports, uses) =
       ThyHeader.read (Path.position path) (Source.of_list_limited 8000 text);
-    val _ = name = name' orelse
-      error ("Filename " ^ quote (Path.implode (Path.base path)) ^
-        " does not agree with theory name " ^ quote name');
+    val _ = check_name name name';
     val uses = map (Path.explode o #1) uses;
   in {master = master, text = text, imports = imports, uses = uses} end;

--- a/src/Pure/Tools/isabelle_process.scala	Thu Jan 15 14:33:38 2009 -0800
+++ b/src/Pure/Tools/isabelle_process.scala	Fri Jan 16 13:07:44 2009 -0800
@@ -67,7 +67,8 @@
 
   class Result(val kind: Kind.Value, val props: Properties, val result: String) {
     override def toString = {
-      val res = XML.content(YXML.parse_failsafe(result)).mkString
+      val tree = YXML.parse_failsafe(result)
+      val res = if (kind == Kind.STATUS) tree.toString else XML.content(tree).mkString
       if (props == null) kind.toString + " [[" + res + "]]"
       else kind.toString + " " + props.toString + " [[" + res + "]]"
     }

author	huffman
	Fri, 16 Jan 2009 13:07:44 -0800
changeset 29542	d20f453eb4a3
parent 29541	35c2654a95da (current diff)
parent 29520	7402322256b0 (diff)
child 29543	64cc846d4a63

src/HOL/Univ_Poly.thy		file \| annotate \| diff \| comparison \| revisions
src/HOLCF/HOLCF.thy		file \| annotate \| diff \| comparison \| revisions