# HG changeset patch
# User haftmann
# Date 1409469042 -7200
# Node ID e7ebe555428137d03a2dd3e6cabb31c0668ec942
# Parent  f54a8a4134d32aa4baff4fad08a25566f637d452
separated listsum material

diff -r f54a8a4134d3 -r e7ebe5554281 src/Doc/Main/Main_Doc.thy
--- a/src/Doc/Main/Main_Doc.thy	Sun Aug 31 09:10:41 2014 +0200
+++ b/src/Doc/Main/Main_Doc.thy	Sun Aug 31 09:10:42 2014 +0200
@@ -517,7 +517,7 @@
 @{const List.listrel1} & @{term_type_only List.listrel1 "('a*'a)set\<Rightarrow>('a list * 'a list)set"}\\
 @{const List.lists} & @{term_type_only List.lists "'a set\<Rightarrow>'a list set"}\\
 @{const List.listset} & @{term_type_only List.listset "'a set list \<Rightarrow> 'a list set"}\\
-@{const List.listsum} & @{typeof List.listsum}\\
+@{const Groups_List.listsum} & @{typeof Groups_List.listsum}\\
 @{const List.list_all2} & @{typeof List.list_all2}\\
 @{const List.list_update} & @{typeof List.list_update}\\
 @{const List.map} & @{typeof List.map}\\
diff -r f54a8a4134d3 -r e7ebe5554281 src/HOL/Enum.thy
--- a/src/HOL/Enum.thy	Sun Aug 31 09:10:41 2014 +0200
+++ b/src/HOL/Enum.thy	Sun Aug 31 09:10:42 2014 +0200
@@ -3,7 +3,7 @@
 header {* Finite types as explicit enumerations *}
 
 theory Enum
-imports Map
+imports Map Groups_List
 begin
 
 subsection {* Class @{text enum} *}
diff -r f54a8a4134d3 -r e7ebe5554281 src/HOL/Groups_List.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Groups_List.thy	Sun Aug 31 09:10:42 2014 +0200
@@ -0,0 +1,212 @@
+
+(* Author: Tobias Nipkow, TU Muenchen *)
+
+header {* Summation over lists *}
+
+theory Groups_List
+imports List
+begin
+
+definition (in monoid_add) listsum :: "'a list \<Rightarrow> 'a" where
+"listsum xs = foldr plus xs 0"
+
+subsubsection {* List summation: @{const listsum} and @{text"\<Sum>"}*}
+
+lemma (in monoid_add) listsum_simps [simp]:
+  "listsum [] = 0"
+  "listsum (x # xs) = x + listsum xs"
+  by (simp_all add: listsum_def)
+
+lemma (in monoid_add) listsum_append [simp]:
+  "listsum (xs @ ys) = listsum xs + listsum ys"
+  by (induct xs) (simp_all add: add.assoc)
+
+lemma (in comm_monoid_add) listsum_rev [simp]:
+  "listsum (rev xs) = listsum xs"
+  by (simp add: listsum_def foldr_fold fold_rev fun_eq_iff add_ac)
+
+lemma (in monoid_add) fold_plus_listsum_rev:
+  "fold plus xs = plus (listsum (rev xs))"
+proof
+  fix x
+  have "fold plus xs x = fold plus xs (x + 0)" by simp
+  also have "\<dots> = fold plus (x # xs) 0" by simp
+  also have "\<dots> = foldr plus (rev xs @ [x]) 0" by (simp add: foldr_conv_fold)
+  also have "\<dots> = listsum (rev xs @ [x])" by (simp add: listsum_def)
+  also have "\<dots> = listsum (rev xs) + listsum [x]" by simp
+  finally show "fold plus xs x = listsum (rev xs) + x" by simp
+qed
+
+text{* Some syntactic sugar for summing a function over a list: *}
+
+syntax
+  "_listsum" :: "pttrn => 'a list => 'b => 'b"    ("(3SUM _<-_. _)" [0, 51, 10] 10)
+syntax (xsymbols)
+  "_listsum" :: "pttrn => 'a list => 'b => 'b"    ("(3\<Sum>_\<leftarrow>_. _)" [0, 51, 10] 10)
+syntax (HTML output)
+  "_listsum" :: "pttrn => 'a list => 'b => 'b"    ("(3\<Sum>_\<leftarrow>_. _)" [0, 51, 10] 10)
+
+translations -- {* Beware of argument permutation! *}
+  "SUM x<-xs. b" == "CONST listsum (CONST map (%x. b) xs)"
+  "\<Sum>x\<leftarrow>xs. b" == "CONST listsum (CONST map (%x. b) xs)"
+
+lemma (in comm_monoid_add) listsum_map_remove1:
+  "x \<in> set xs \<Longrightarrow> listsum (map f xs) = f x + listsum (map f (remove1 x xs))"
+  by (induct xs) (auto simp add: ac_simps)
+
+lemma (in monoid_add) size_list_conv_listsum:
+  "size_list f xs = listsum (map f xs) + size xs"
+  by (induct xs) auto
+
+lemma (in monoid_add) length_concat:
+  "length (concat xss) = listsum (map length xss)"
+  by (induct xss) simp_all
+
+lemma (in monoid_add) length_product_lists:
+  "length (product_lists xss) = foldr op * (map length xss) 1"
+proof (induct xss)
+  case (Cons xs xss) then show ?case by (induct xs) (auto simp: length_concat o_def)
+qed simp
+
+lemma (in monoid_add) listsum_map_filter:
+  assumes "\<And>x. x \<in> set xs \<Longrightarrow> \<not> P x \<Longrightarrow> f x = 0"
+  shows "listsum (map f (filter P xs)) = listsum (map f xs)"
+  using assms by (induct xs) auto
+
+lemma (in comm_monoid_add) distinct_listsum_conv_Setsum:
+  "distinct xs \<Longrightarrow> listsum xs = Setsum (set xs)"
+  by (induct xs) simp_all
+
+lemma listsum_eq_0_nat_iff_nat [simp]:
+  "listsum ns = (0::nat) \<longleftrightarrow> (\<forall>n \<in> set ns. n = 0)"
+  by (induct ns) simp_all
+
+lemma member_le_listsum_nat:
+  "(n :: nat) \<in> set ns \<Longrightarrow> n \<le> listsum ns"
+  by (induct ns) auto
+
+lemma elem_le_listsum_nat:
+  "k < size ns \<Longrightarrow> ns ! k \<le> listsum (ns::nat list)"
+  by (rule member_le_listsum_nat) simp
+
+lemma listsum_update_nat:
+  "k < size ns \<Longrightarrow> listsum (ns[k := (n::nat)]) = listsum ns + n - ns ! k"
+apply(induct ns arbitrary:k)
+ apply (auto split:nat.split)
+apply(drule elem_le_listsum_nat)
+apply arith
+done
+
+lemma (in monoid_add) listsum_triv:
+  "(\<Sum>x\<leftarrow>xs. r) = of_nat (length xs) * r"
+  by (induct xs) (simp_all add: distrib_right)
+
+lemma (in monoid_add) listsum_0 [simp]:
+  "(\<Sum>x\<leftarrow>xs. 0) = 0"
+  by (induct xs) (simp_all add: distrib_right)
+
+text{* For non-Abelian groups @{text xs} needs to be reversed on one side: *}
+lemma (in ab_group_add) uminus_listsum_map:
+  "- listsum (map f xs) = listsum (map (uminus \<circ> f) xs)"
+  by (induct xs) simp_all
+
+lemma (in comm_monoid_add) listsum_addf:
+  "(\<Sum>x\<leftarrow>xs. f x + g x) = listsum (map f xs) + listsum (map g xs)"
+  by (induct xs) (simp_all add: algebra_simps)
+
+lemma (in ab_group_add) listsum_subtractf:
+  "(\<Sum>x\<leftarrow>xs. f x - g x) = listsum (map f xs) - listsum (map g xs)"
+  by (induct xs) (simp_all add: algebra_simps)
+
+lemma (in semiring_0) listsum_const_mult:
+  "(\<Sum>x\<leftarrow>xs. c * f x) = c * (\<Sum>x\<leftarrow>xs. f x)"
+  by (induct xs) (simp_all add: algebra_simps)
+
+lemma (in semiring_0) listsum_mult_const:
+  "(\<Sum>x\<leftarrow>xs. f x * c) = (\<Sum>x\<leftarrow>xs. f x) * c"
+  by (induct xs) (simp_all add: algebra_simps)
+
+lemma (in ordered_ab_group_add_abs) listsum_abs:
+  "\<bar>listsum xs\<bar> \<le> listsum (map abs xs)"
+  by (induct xs) (simp_all add: order_trans [OF abs_triangle_ineq])
+
+lemma listsum_mono:
+  fixes f g :: "'a \<Rightarrow> 'b::{monoid_add, ordered_ab_semigroup_add}"
+  shows "(\<And>x. x \<in> set xs \<Longrightarrow> f x \<le> g x) \<Longrightarrow> (\<Sum>x\<leftarrow>xs. f x) \<le> (\<Sum>x\<leftarrow>xs. g x)"
+  by (induct xs) (simp, simp add: add_mono)
+
+lemma (in monoid_add) listsum_distinct_conv_setsum_set:
+  "distinct xs \<Longrightarrow> listsum (map f xs) = setsum f (set xs)"
+  by (induct xs) simp_all
+
+lemma (in monoid_add) interv_listsum_conv_setsum_set_nat:
+  "listsum (map f [m..<n]) = setsum f (set [m..<n])"
+  by (simp add: listsum_distinct_conv_setsum_set)
+
+lemma (in monoid_add) interv_listsum_conv_setsum_set_int:
+  "listsum (map f [k..l]) = setsum f (set [k..l])"
+  by (simp add: listsum_distinct_conv_setsum_set)
+
+text {* General equivalence between @{const listsum} and @{const setsum} *}
+lemma (in monoid_add) listsum_setsum_nth:
+  "listsum xs = (\<Sum> i = 0 ..< length xs. xs ! i)"
+  using interv_listsum_conv_setsum_set_nat [of "op ! xs" 0 "length xs"] by (simp add: map_nth)
+
+
+subsection {* Further facts about @{const List.n_lists} *}
+
+lemma length_n_lists: "length (List.n_lists n xs) = length xs ^ n"
+  by (induct n) (auto simp add: comp_def length_concat listsum_triv)
+
+lemma distinct_n_lists:
+  assumes "distinct xs"
+  shows "distinct (List.n_lists n xs)"
+proof (rule card_distinct)
+  from assms have card_length: "card (set xs) = length xs" by (rule distinct_card)
+  have "card (set (List.n_lists n xs)) = card (set xs) ^ n"
+  proof (induct n)
+    case 0 then show ?case by simp
+  next
+    case (Suc n)
+    moreover have "card (\<Union>ys\<in>set (List.n_lists n xs). (\<lambda>y. y # ys) ` set xs)
+      = (\<Sum>ys\<in>set (List.n_lists n xs). card ((\<lambda>y. y # ys) ` set xs))"
+      by (rule card_UN_disjoint) auto
+    moreover have "\<And>ys. card ((\<lambda>y. y # ys) ` set xs) = card (set xs)"
+      by (rule card_image) (simp add: inj_on_def)
+    ultimately show ?case by auto
+  qed
+  also have "\<dots> = length xs ^ n" by (simp add: card_length)
+  finally show "card (set (List.n_lists n xs)) = length (List.n_lists n xs)"
+    by (simp add: length_n_lists)
+qed
+
+
+subsection {* Tools setup *}
+
+lemma setsum_set_upto_conv_listsum_int [code_unfold]:
+  "setsum f (set [i..j::int]) = listsum (map f [i..j])"
+  by (simp add: interv_listsum_conv_setsum_set_int)
+
+lemma setsum_set_upt_conv_listsum_nat [code_unfold]:
+  "setsum f (set [m..<n]) = listsum (map f [m..<n])"
+  by (simp add: interv_listsum_conv_setsum_set_nat)
+
+lemma setsum_code [code]:
+  "setsum f (set xs) = listsum (map f (remdups xs))"
+  by (simp add: listsum_distinct_conv_setsum_set)
+
+context
+begin
+
+interpretation lifting_syntax .
+
+lemma listsum_transfer[transfer_rule]:
+  assumes [transfer_rule]: "A 0 0"
+  assumes [transfer_rule]: "(A ===> A ===> A) op + op +"
+  shows "(list_all2 A ===> A) listsum listsum"
+  unfolding listsum_def[abs_def]
+  by transfer_prover
+
+end
+
+end
\ No newline at end of file
diff -r f54a8a4134d3 -r e7ebe5554281 src/HOL/List.thy
--- a/src/HOL/List.thy	Sun Aug 31 09:10:41 2014 +0200
+++ b/src/HOL/List.thy	Sun Aug 31 09:10:42 2014 +0200
@@ -105,9 +105,6 @@
 "concat [] = []" |
 "concat (x # xs) = x @ concat xs"
 
-definition (in monoid_add) listsum :: "'a list \<Rightarrow> 'a" where
-"listsum xs = foldr plus xs 0"
-
 primrec drop:: "nat \<Rightarrow> 'a list \<Rightarrow> 'a list" where
 drop_Nil: "drop n [] = []" |
 drop_Cons: "drop n (x # xs) = (case n of 0 \<Rightarrow> x # xs | Suc m \<Rightarrow> drop m xs)"
@@ -313,8 +310,7 @@
 @{lemma "rotate1 [a,b,c,d] = [b,c,d,a]" by simp}\\
 @{lemma "rotate 3 [a,b,c,d] = [d,a,b,c]" by (simp add:rotate_def eval_nat_numeral)}\\
 @{lemma "replicate 4 a = [a,a,a,a]" by (simp add:eval_nat_numeral)}\\
-@{lemma "[2..<5] = [2,3,4]" by (simp add:eval_nat_numeral)}\\
-@{lemma "listsum [1,2,3::nat] = 6" by (simp add: listsum_def)}
+@{lemma "[2..<5] = [2,3,4]" by (simp add:eval_nat_numeral)}
 \end{tabular}}
 \caption{Characteristic examples}
 \label{fig:Characteristic}
@@ -3490,149 +3486,6 @@
       auto simp add: injD[OF assms])
 
 
-subsubsection {* List summation: @{const listsum} and @{text"\<Sum>"}*}
-
-lemma (in monoid_add) listsum_simps [simp]:
-  "listsum [] = 0"
-  "listsum (x # xs) = x + listsum xs"
-  by (simp_all add: listsum_def)
-
-lemma (in monoid_add) listsum_append [simp]:
-  "listsum (xs @ ys) = listsum xs + listsum ys"
-  by (induct xs) (simp_all add: add.assoc)
-
-lemma (in comm_monoid_add) listsum_rev [simp]:
-  "listsum (rev xs) = listsum xs"
-  by (simp add: listsum_def foldr_fold fold_rev fun_eq_iff ac_simps)
-
-lemma (in monoid_add) fold_plus_listsum_rev:
-  "fold plus xs = plus (listsum (rev xs))"
-proof
-  fix x
-  have "fold plus xs x = fold plus xs (x + 0)" by simp
-  also have "\<dots> = fold plus (x # xs) 0" by simp
-  also have "\<dots> = foldr plus (rev xs @ [x]) 0" by (simp add: foldr_conv_fold)
-  also have "\<dots> = listsum (rev xs @ [x])" by (simp add: listsum_def)
-  also have "\<dots> = listsum (rev xs) + listsum [x]" by simp
-  finally show "fold plus xs x = listsum (rev xs) + x" by simp
-qed
-
-text{* Some syntactic sugar for summing a function over a list: *}
-
-syntax
-  "_listsum" :: "pttrn => 'a list => 'b => 'b"    ("(3SUM _<-_. _)" [0, 51, 10] 10)
-syntax (xsymbols)
-  "_listsum" :: "pttrn => 'a list => 'b => 'b"    ("(3\<Sum>_\<leftarrow>_. _)" [0, 51, 10] 10)
-syntax (HTML output)
-  "_listsum" :: "pttrn => 'a list => 'b => 'b"    ("(3\<Sum>_\<leftarrow>_. _)" [0, 51, 10] 10)
-
-translations -- {* Beware of argument permutation! *}
-  "SUM x<-xs. b" == "CONST listsum (CONST map (%x. b) xs)"
-  "\<Sum>x\<leftarrow>xs. b" == "CONST listsum (CONST map (%x. b) xs)"
-
-lemma (in comm_monoid_add) listsum_map_remove1:
-  "x \<in> set xs \<Longrightarrow> listsum (map f xs) = f x + listsum (map f (remove1 x xs))"
-  by (induct xs) (auto simp add: ac_simps)
-
-lemma (in monoid_add) size_list_conv_listsum:
-  "size_list f xs = listsum (map f xs) + size xs"
-  by (induct xs) auto
-
-lemma (in monoid_add) length_concat:
-  "length (concat xss) = listsum (map length xss)"
-  by (induct xss) simp_all
-
-lemma (in monoid_add) length_product_lists:
-  "length (product_lists xss) = foldr op * (map length xss) 1"
-proof (induct xss)
-  case (Cons xs xss) then show ?case by (induct xs) (auto simp: length_concat o_def)
-qed simp
-
-lemma (in monoid_add) listsum_map_filter:
-  assumes "\<And>x. x \<in> set xs \<Longrightarrow> \<not> P x \<Longrightarrow> f x = 0"
-  shows "listsum (map f (filter P xs)) = listsum (map f xs)"
-  using assms by (induct xs) auto
-
-lemma (in comm_monoid_add) distinct_listsum_conv_Setsum:
-  "distinct xs \<Longrightarrow> listsum xs = Setsum (set xs)"
-  by (induct xs) simp_all
-
-lemma listsum_eq_0_nat_iff_nat [simp]:
-  "listsum ns = (0::nat) \<longleftrightarrow> (\<forall>n \<in> set ns. n = 0)"
-  by (induct ns) simp_all
-
-lemma member_le_listsum_nat:
-  "(n :: nat) \<in> set ns \<Longrightarrow> n \<le> listsum ns"
-  by (induct ns) auto
-
-lemma elem_le_listsum_nat:
-  "k < size ns \<Longrightarrow> ns ! k \<le> listsum (ns::nat list)"
-  by (rule member_le_listsum_nat) simp
-
-lemma listsum_update_nat:
-  "k < size ns \<Longrightarrow> listsum (ns[k := (n::nat)]) = listsum ns + n - ns ! k"
-apply(induct ns arbitrary:k)
- apply (auto split:nat.split)
-apply(drule elem_le_listsum_nat)
-apply arith
-done
-
-lemma (in monoid_add) listsum_triv:
-  "(\<Sum>x\<leftarrow>xs. r) = of_nat (length xs) * r"
-  by (induct xs) (simp_all add: distrib_right)
-
-lemma (in monoid_add) listsum_0 [simp]:
-  "(\<Sum>x\<leftarrow>xs. 0) = 0"
-  by (induct xs) (simp_all add: distrib_right)
-
-text{* For non-Abelian groups @{text xs} needs to be reversed on one side: *}
-lemma (in ab_group_add) uminus_listsum_map:
-  "- listsum (map f xs) = listsum (map (uminus \<circ> f) xs)"
-  by (induct xs) simp_all
-
-lemma (in comm_monoid_add) listsum_addf:
-  "(\<Sum>x\<leftarrow>xs. f x + g x) = listsum (map f xs) + listsum (map g xs)"
-  by (induct xs) (simp_all add: algebra_simps)
-
-lemma (in ab_group_add) listsum_subtractf:
-  "(\<Sum>x\<leftarrow>xs. f x - g x) = listsum (map f xs) - listsum (map g xs)"
-  by (induct xs) (simp_all add: algebra_simps)
-
-lemma (in semiring_0) listsum_const_mult:
-  "(\<Sum>x\<leftarrow>xs. c * f x) = c * (\<Sum>x\<leftarrow>xs. f x)"
-  by (induct xs) (simp_all add: algebra_simps)
-
-lemma (in semiring_0) listsum_mult_const:
-  "(\<Sum>x\<leftarrow>xs. f x * c) = (\<Sum>x\<leftarrow>xs. f x) * c"
-  by (induct xs) (simp_all add: algebra_simps)
-
-lemma (in ordered_ab_group_add_abs) listsum_abs:
-  "\<bar>listsum xs\<bar> \<le> listsum (map abs xs)"
-  by (induct xs) (simp_all add: order_trans [OF abs_triangle_ineq])
-
-lemma listsum_mono:
-  fixes f g :: "'a \<Rightarrow> 'b::{monoid_add, ordered_ab_semigroup_add}"
-  shows "(\<And>x. x \<in> set xs \<Longrightarrow> f x \<le> g x) \<Longrightarrow> (\<Sum>x\<leftarrow>xs. f x) \<le> (\<Sum>x\<leftarrow>xs. g x)"
-  by (induct xs) (simp, simp add: add_mono)
-
-lemma (in monoid_add) listsum_distinct_conv_setsum_set:
-  "distinct xs \<Longrightarrow> listsum (map f xs) = setsum f (set xs)"
-  by (induct xs) simp_all
-
-lemma (in monoid_add) interv_listsum_conv_setsum_set_nat:
-  "listsum (map f [m..<n]) = setsum f (set [m..<n])"
-  by (simp add: listsum_distinct_conv_setsum_set)
-
-lemma (in monoid_add) interv_listsum_conv_setsum_set_int:
-  "listsum (map f [k..l]) = setsum f (set [k..l])"
-  by (simp add: listsum_distinct_conv_setsum_set)
-
-text {* General equivalence between @{const listsum} and @{const setsum} *}
-lemma (in monoid_add) listsum_setsum_nth:
-  "listsum xs = (\<Sum> i = 0 ..< length xs. xs ! i)"
-  using interv_listsum_conv_setsum_set_nat [of "op ! xs" 0 "length xs"] by (simp add: map_nth)
-
-
 subsubsection {* @{const insert} *}
 
 lemma in_set_insert [simp]:
@@ -4314,9 +4167,6 @@
 lemma n_lists_Nil [simp]: "List.n_lists n [] = (if n = 0 then [[]] else [])"
   by (induct n) simp_all
 
-lemma length_n_lists: "length (List.n_lists n xs) = length xs ^ n"
-  by (induct n) (auto simp add: length_concat o_def listsum_triv)
-
 lemma length_n_lists_elem: "ys \<in> set (List.n_lists n xs) \<Longrightarrow> length ys = n"
   by (induct n arbitrary: ys) auto
 
@@ -4335,28 +4185,6 @@
   qed
 qed
 
-lemma distinct_n_lists:
-  assumes "distinct xs"
-  shows "distinct (List.n_lists n xs)"
-proof (rule card_distinct)
-  from assms have card_length: "card (set xs) = length xs" by (rule distinct_card)
-  have "card (set (List.n_lists n xs)) = card (set xs) ^ n"
-  proof (induct n)
-    case 0 then show ?case by simp
-  next
-    case (Suc n)
-    moreover have "card (\<Union>ys\<in>set (List.n_lists n xs). (\<lambda>y. y # ys) ` set xs)
-      = (\<Sum>ys\<in>set (List.n_lists n xs). card ((\<lambda>y. y # ys) ` set xs))"
-      by (rule card_UN_disjoint) auto
-    moreover have "\<And>ys. card ((\<lambda>y. y # ys) ` set xs) = card (set xs)"
-      by (rule card_image) (simp add: inj_on_def)
-    ultimately show ?case by auto
-  qed
-  also have "\<dots> = length xs ^ n" by (simp add: card_length)
-  finally show "card (set (List.n_lists n xs)) = length (List.n_lists n xs)"
-    by (simp add: length_n_lists)
-qed
-
 
 subsubsection {* @{const splice} *}
 
@@ -6264,10 +6092,6 @@
   "(\<exists>m\<le>n\<Colon>nat. P m) \<longleftrightarrow> (\<exists>m \<in> {0..n}. P m)"
   by auto
 
-lemma setsum_set_upt_conv_listsum_nat [code_unfold]:
-  "setsum f (set [m..<n]) = listsum (map f [m..<n])"
-  by (simp add: interv_listsum_conv_setsum_set_nat)
-
 text{* Bounded @{text LEAST} operator: *}
 
 definition "Bleast S P = (LEAST x. x \<in> S \<and> P x)"
@@ -6315,10 +6139,6 @@
 
 lemmas atLeastAtMost_upto [code_unfold] = set_upto [symmetric]
 
-lemma setsum_set_upto_conv_listsum_int [code_unfold]:
-  "setsum f (set [i..j::int]) = listsum (map f [i..j])"
-  by (simp add: interv_listsum_conv_setsum_set_int)
-
 
 subsubsection {* Optimizing by rewriting *}
 
@@ -6629,10 +6449,6 @@
   "Pow (set (x # xs)) = (let A = Pow (set xs) in A \<union> insert x ` A)"
   by (simp_all add: Pow_insert Let_def)
 
-lemma setsum_code [code]:
-  "setsum f (set xs) = listsum (map f (remdups xs))"
-by (simp add: listsum_distinct_conv_setsum_set)
-
 definition map_project :: "('a \<Rightarrow> 'b option) \<Rightarrow> 'a set \<Rightarrow> 'b set" where
   "map_project f A = {b. \<exists> a \<in> A. f a = Some b}"
 
@@ -6883,13 +6699,6 @@
   apply (erule_tac xs=x in list_all2_induct, simp, simp add: rel_fun_def)
   done
 
-lemma listsum_transfer[transfer_rule]:
-  assumes [transfer_rule]: "A 0 0"
-  assumes [transfer_rule]: "(A ===> A ===> A) op + op +"
-  shows "(list_all2 A ===> A) listsum listsum"
-  unfolding listsum_def[abs_def]
-  by transfer_prover
-
 lemma rtrancl_parametric [transfer_rule]:
   assumes [transfer_rule]: "bi_unique A" "bi_total A"
   shows "(rel_set (rel_prod A A) ===> rel_set (rel_prod A A)) rtrancl rtrancl"
diff -r f54a8a4134d3 -r e7ebe5554281 src/HOL/Random.thy
--- a/src/HOL/Random.thy	Sun Aug 31 09:10:41 2014 +0200
+++ b/src/HOL/Random.thy	Sun Aug 31 09:10:42 2014 +0200
@@ -4,7 +4,7 @@
 header {* A HOL random engine *}
 
 theory Random
-imports List
+imports List Groups_List
 begin
 
 notation fcomp (infixl "\<circ>>" 60)