add new theory Product_plus.thy to Library

--- a/src/HOL/IsaMakefile	Fri Feb 20 14:49:39 2009 +0100
+++ b/src/HOL/IsaMakefile	Fri Feb 20 07:41:41 2009 -0800
@@ -339,6 +339,7 @@
   Library/Random.thy	Library/Quickcheck.thy	\
   Library/Poly_Deriv.thy \
   Library/Polynomial.thy \
+  Library/Product_plus.thy \
   Library/Enum.thy Library/Float.thy $(SRC)/Tools/float.ML $(SRC)/HOL/Tools/float_arith.ML \
   Library/reify_data.ML Library/reflection.ML
 	@cd Library; $(ISABELLE_TOOL) usedir $(OUT)/HOL Library

--- a/src/HOL/Library/Library.thy	Fri Feb 20 14:49:39 2009 +0100
+++ b/src/HOL/Library/Library.thy	Fri Feb 20 07:41:41 2009 -0800
@@ -41,6 +41,7 @@
   Poly_Deriv
   Polynomial
   Primes
+  Product_plus
   Quickcheck
   Quicksort
   Quotient

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/Product_plus.thy	Fri Feb 20 07:41:41 2009 -0800
@@ -0,0 +1,115 @@
+(*  Title:      HOL/Library/Product_plus.thy
+    Author:     Brian Huffman
+*)
+
+header {* Additive group operations on product types *}
+
+theory Product_plus
+imports Main
+begin
+
+subsection {* Operations *}
+
+instantiation "*" :: (zero, zero) zero
+begin
+
+definition zero_prod_def: "0 = (0, 0)"
+
+instance ..
+end
+
+instantiation "*" :: (plus, plus) plus
+begin
+
+definition plus_prod_def:
+  "x + y = (fst x + fst y, snd x + snd y)"
+
+instance ..
+end
+
+instantiation "*" :: (minus, minus) minus
+begin
+
+definition minus_prod_def:
+  "x - y = (fst x - fst y, snd x - snd y)"
+
+instance ..
+end
+
+instantiation "*" :: (uminus, uminus) uminus
+begin
+
+definition uminus_prod_def:
+  "- x = (- fst x, - snd x)"
+
+instance ..
+end
+
+lemma fst_zero [simp]: "fst 0 = 0"
+  unfolding zero_prod_def by simp
+
+lemma snd_zero [simp]: "snd 0 = 0"
+  unfolding zero_prod_def by simp
+
+lemma fst_add [simp]: "fst (x + y) = fst x + fst y"
+  unfolding plus_prod_def by simp
+
+lemma snd_add [simp]: "snd (x + y) = snd x + snd y"
+  unfolding plus_prod_def by simp
+
+lemma fst_diff [simp]: "fst (x - y) = fst x - fst y"
+  unfolding minus_prod_def by simp
+
+lemma snd_diff [simp]: "snd (x - y) = snd x - snd y"
+  unfolding minus_prod_def by simp
+
+lemma fst_uminus [simp]: "fst (- x) = - fst x"
+  unfolding uminus_prod_def by simp
+
+lemma snd_uminus [simp]: "snd (- x) = - snd x"
+  unfolding uminus_prod_def by simp
+
+lemma add_Pair [simp]: "(a, b) + (c, d) = (a + c, b + d)"
+  unfolding plus_prod_def by simp
+
+lemma diff_Pair [simp]: "(a, b) - (c, d) = (a - c, b - d)"
+  unfolding minus_prod_def by simp
+
+lemma uminus_Pair [simp, code]: "- (a, b) = (- a, - b)"
+  unfolding uminus_prod_def by simp
+
+lemmas expand_prod_eq = Pair_fst_snd_eq
+
+
+subsection {* Class instances *}
+
+instance "*" :: (semigroup_add, semigroup_add) semigroup_add
+  by default (simp add: expand_prod_eq add_assoc)
+
+instance "*" :: (ab_semigroup_add, ab_semigroup_add) ab_semigroup_add
+  by default (simp add: expand_prod_eq add_commute)
+
+instance "*" :: (monoid_add, monoid_add) monoid_add
+  by default (simp_all add: expand_prod_eq)
+
+instance "*" :: (comm_monoid_add, comm_monoid_add) comm_monoid_add
+  by default (simp add: expand_prod_eq)
+
+instance "*" ::
+  (cancel_semigroup_add, cancel_semigroup_add) cancel_semigroup_add
+    by default (simp_all add: expand_prod_eq)
+
+instance "*" ::
+  (cancel_ab_semigroup_add, cancel_ab_semigroup_add) cancel_ab_semigroup_add
+    by default (simp add: expand_prod_eq)
+
+instance "*" ::
+  (cancel_comm_monoid_add, cancel_comm_monoid_add) cancel_comm_monoid_add ..
+
+instance "*" :: (group_add, group_add) group_add
+  by default (simp_all add: expand_prod_eq diff_minus)
+
+instance "*" :: (ab_group_add, ab_group_add) ab_group_add
+  by default (simp_all add: expand_prod_eq)
+
+end