--- a/src/HOL/Algebra/Ideal.thy Sat Sep 03 11:10:38 2011 -0700
+++ b/src/HOL/Algebra/Ideal.thy Sat Sep 03 14:33:45 2011 -0700
@@ -14,25 +14,24 @@
locale ideal = additive_subgroup I R + ring R for I and R (structure) +
assumes I_l_closed: "\<lbrakk>a \<in> I; x \<in> carrier R\<rbrakk> \<Longrightarrow> x \<otimes> a \<in> I"
- and I_r_closed: "\<lbrakk>a \<in> I; x \<in> carrier R\<rbrakk> \<Longrightarrow> a \<otimes> x \<in> I"
+ and I_r_closed: "\<lbrakk>a \<in> I; x \<in> carrier R\<rbrakk> \<Longrightarrow> a \<otimes> x \<in> I"
sublocale ideal \<subseteq> abelian_subgroup I R
-apply (intro abelian_subgroupI3 abelian_group.intro)
- apply (rule ideal.axioms, rule ideal_axioms)
- apply (rule abelian_group.axioms, rule ring.axioms, rule ideal.axioms, rule ideal_axioms)
-apply (rule abelian_group.axioms, rule ring.axioms, rule ideal.axioms, rule ideal_axioms)
-done
+ apply (intro abelian_subgroupI3 abelian_group.intro)
+ apply (rule ideal.axioms, rule ideal_axioms)
+ apply (rule abelian_group.axioms, rule ring.axioms, rule ideal.axioms, rule ideal_axioms)
+ apply (rule abelian_group.axioms, rule ring.axioms, rule ideal.axioms, rule ideal_axioms)
+ done
-lemma (in ideal) is_ideal:
- "ideal I R"
-by (rule ideal_axioms)
+lemma (in ideal) is_ideal: "ideal I R"
+ by (rule ideal_axioms)
lemma idealI:
fixes R (structure)
assumes "ring R"
assumes a_subgroup: "subgroup I \<lparr>carrier = carrier R, mult = add R, one = zero R\<rparr>"
- and I_l_closed: "\<And>a x. \<lbrakk>a \<in> I; x \<in> carrier R\<rbrakk> \<Longrightarrow> x \<otimes> a \<in> I"
- and I_r_closed: "\<And>a x. \<lbrakk>a \<in> I; x \<in> carrier R\<rbrakk> \<Longrightarrow> a \<otimes> x \<in> I"
+ and I_l_closed: "\<And>a x. \<lbrakk>a \<in> I; x \<in> carrier R\<rbrakk> \<Longrightarrow> x \<otimes> a \<in> I"
+ and I_r_closed: "\<And>a x. \<lbrakk>a \<in> I; x \<in> carrier R\<rbrakk> \<Longrightarrow> a \<otimes> x \<in> I"
shows "ideal I R"
proof -
interpret ring R by fact
@@ -47,19 +46,16 @@
subsubsection (in ring) {* Ideals Generated by a Subset of @{term "carrier R"} *}
-definition
- genideal :: "('a, 'b) ring_scheme \<Rightarrow> 'a set \<Rightarrow> 'a set" ("Idl\<index> _" [80] 79)
+definition genideal :: "_ \<Rightarrow> 'a set \<Rightarrow> 'a set" ("Idl\<index> _" [80] 79)
where "genideal R S = Inter {I. ideal I R \<and> S \<subseteq> I}"
-
subsubsection {* Principal Ideals *}
locale principalideal = ideal +
assumes generate: "\<exists>i \<in> carrier R. I = Idl {i}"
-lemma (in principalideal) is_principalideal:
- shows "principalideal I R"
-by (rule principalideal_axioms)
+lemma (in principalideal) is_principalideal: "principalideal I R"
+ by (rule principalideal_axioms)
lemma principalidealI:
fixes R (structure)
@@ -68,7 +64,9 @@
shows "principalideal I R"
proof -
interpret ideal I R by fact
- show ?thesis by (intro principalideal.intro principalideal_axioms.intro) (rule is_ideal, rule generate)
+ show ?thesis
+ by (intro principalideal.intro principalideal_axioms.intro)
+ (rule is_ideal, rule generate)
qed
@@ -76,22 +74,22 @@
locale maximalideal = ideal +
assumes I_notcarr: "carrier R \<noteq> I"
- and I_maximal: "\<lbrakk>ideal J R; I \<subseteq> J; J \<subseteq> carrier R\<rbrakk> \<Longrightarrow> J = I \<or> J = carrier R"
+ and I_maximal: "\<lbrakk>ideal J R; I \<subseteq> J; J \<subseteq> carrier R\<rbrakk> \<Longrightarrow> J = I \<or> J = carrier R"
-lemma (in maximalideal) is_maximalideal:
- shows "maximalideal I R"
-by (rule maximalideal_axioms)
+lemma (in maximalideal) is_maximalideal: "maximalideal I R"
+ by (rule maximalideal_axioms)
lemma maximalidealI:
fixes R
assumes "ideal I R"
assumes I_notcarr: "carrier R \<noteq> I"
- and I_maximal: "\<And>J. \<lbrakk>ideal J R; I \<subseteq> J; J \<subseteq> carrier R\<rbrakk> \<Longrightarrow> J = I \<or> J = carrier R"
+ and I_maximal: "\<And>J. \<lbrakk>ideal J R; I \<subseteq> J; J \<subseteq> carrier R\<rbrakk> \<Longrightarrow> J = I \<or> J = carrier R"
shows "maximalideal I R"
proof -
interpret ideal I R by fact
- show ?thesis by (intro maximalideal.intro maximalideal_axioms.intro)
- (rule is_ideal, rule I_notcarr, rule I_maximal)
+ show ?thesis
+ by (intro maximalideal.intro maximalideal_axioms.intro)
+ (rule is_ideal, rule I_notcarr, rule I_maximal)
qed
@@ -99,24 +97,24 @@
locale primeideal = ideal + cring +
assumes I_notcarr: "carrier R \<noteq> I"
- and I_prime: "\<lbrakk>a \<in> carrier R; b \<in> carrier R; a \<otimes> b \<in> I\<rbrakk> \<Longrightarrow> a \<in> I \<or> b \<in> I"
+ and I_prime: "\<lbrakk>a \<in> carrier R; b \<in> carrier R; a \<otimes> b \<in> I\<rbrakk> \<Longrightarrow> a \<in> I \<or> b \<in> I"
-lemma (in primeideal) is_primeideal:
- shows "primeideal I R"
-by (rule primeideal_axioms)
+lemma (in primeideal) is_primeideal: "primeideal I R"
+ by (rule primeideal_axioms)
lemma primeidealI:
fixes R (structure)
assumes "ideal I R"
assumes "cring R"
assumes I_notcarr: "carrier R \<noteq> I"
- and I_prime: "\<And>a b. \<lbrakk>a \<in> carrier R; b \<in> carrier R; a \<otimes> b \<in> I\<rbrakk> \<Longrightarrow> a \<in> I \<or> b \<in> I"
+ and I_prime: "\<And>a b. \<lbrakk>a \<in> carrier R; b \<in> carrier R; a \<otimes> b \<in> I\<rbrakk> \<Longrightarrow> a \<in> I \<or> b \<in> I"
shows "primeideal I R"
proof -
interpret ideal I R by fact
interpret cring R by fact
- show ?thesis by (intro primeideal.intro primeideal_axioms.intro)
- (rule is_ideal, rule is_cring, rule I_notcarr, rule I_prime)
+ show ?thesis
+ by (intro primeideal.intro primeideal_axioms.intro)
+ (rule is_ideal, rule is_cring, rule I_notcarr, rule I_prime)
qed
lemma primeidealI2:
@@ -124,9 +122,9 @@
assumes "additive_subgroup I R"
assumes "cring R"
assumes I_l_closed: "\<And>a x. \<lbrakk>a \<in> I; x \<in> carrier R\<rbrakk> \<Longrightarrow> x \<otimes> a \<in> I"
- and I_r_closed: "\<And>a x. \<lbrakk>a \<in> I; x \<in> carrier R\<rbrakk> \<Longrightarrow> a \<otimes> x \<in> I"
- and I_notcarr: "carrier R \<noteq> I"
- and I_prime: "\<And>a b. \<lbrakk>a \<in> carrier R; b \<in> carrier R; a \<otimes> b \<in> I\<rbrakk> \<Longrightarrow> a \<in> I \<or> b \<in> I"
+ and I_r_closed: "\<And>a x. \<lbrakk>a \<in> I; x \<in> carrier R\<rbrakk> \<Longrightarrow> a \<otimes> x \<in> I"
+ and I_notcarr: "carrier R \<noteq> I"
+ and I_prime: "\<And>a b. \<lbrakk>a \<in> carrier R; b \<in> carrier R; a \<otimes> b \<in> I\<rbrakk> \<Longrightarrow> a \<in> I \<or> b \<in> I"
shows "primeideal I R"
proof -
interpret additive_subgroup I R by fact
@@ -144,31 +142,27 @@
subsection {* Special Ideals *}
-lemma (in ring) zeroideal:
- shows "ideal {\<zero>} R"
-apply (intro idealI subgroup.intro)
- apply (rule is_ring)
- apply simp+
- apply (fold a_inv_def, simp)
- apply simp+
-done
+lemma (in ring) zeroideal: "ideal {\<zero>} R"
+ apply (intro idealI subgroup.intro)
+ apply (rule is_ring)
+ apply simp+
+ apply (fold a_inv_def, simp)
+ apply simp+
+ done
-lemma (in ring) oneideal:
- shows "ideal (carrier R) R"
+lemma (in ring) oneideal: "ideal (carrier R) R"
by (rule idealI) (auto intro: is_ring add.subgroupI)
-lemma (in "domain") zeroprimeideal:
- shows "primeideal {\<zero>} R"
-apply (intro primeidealI)
- apply (rule zeroideal)
- apply (rule domain.axioms, rule domain_axioms)
- defer 1
- apply (simp add: integral)
+lemma (in "domain") zeroprimeideal: "primeideal {\<zero>} R"
+ apply (intro primeidealI)
+ apply (rule zeroideal)
+ apply (rule domain.axioms, rule domain_axioms)
+ defer 1
+ apply (simp add: integral)
proof (rule ccontr, simp)
assume "carrier R = {\<zero>}"
- from this have "\<one> = \<zero>" by (rule one_zeroI)
- from this and one_not_zero
- show "False" by simp
+ then have "\<one> = \<zero>" by (rule one_zeroI)
+ with one_not_zero show False by simp
qed
@@ -177,22 +171,20 @@
lemma (in ideal) one_imp_carrier:
assumes I_one_closed: "\<one> \<in> I"
shows "I = carrier R"
-apply (rule)
-apply (rule)
-apply (rule a_Hcarr, simp)
+ apply (rule)
+ apply (rule)
+ apply (rule a_Hcarr, simp)
proof
fix x
assume xcarr: "x \<in> carrier R"
- from I_one_closed and this
- have "x \<otimes> \<one> \<in> I" by (intro I_l_closed)
- from this and xcarr
- show "x \<in> I" by simp
+ with I_one_closed have "x \<otimes> \<one> \<in> I" by (intro I_l_closed)
+ with xcarr show "x \<in> I" by simp
qed
lemma (in ideal) Icarr:
assumes iI: "i \<in> I"
shows "i \<in> carrier R"
-using iI by (rule a_Hcarr)
+ using iI by (rule a_Hcarr)
subsection {* Intersection of Ideals *}
@@ -207,17 +199,17 @@
interpret ideal I R by fact
interpret ideal J R by fact
show ?thesis
-apply (intro idealI subgroup.intro)
- apply (rule is_ring)
- apply (force simp add: a_subset)
- apply (simp add: a_inv_def[symmetric])
- apply simp
- apply (simp add: a_inv_def[symmetric])
- apply (clarsimp, rule)
- apply (fast intro: ideal.I_l_closed ideal.intro assms)+
-apply (clarsimp, rule)
- apply (fast intro: ideal.I_r_closed ideal.intro assms)+
-done
+ apply (intro idealI subgroup.intro)
+ apply (rule is_ring)
+ apply (force simp add: a_subset)
+ apply (simp add: a_inv_def[symmetric])
+ apply simp
+ apply (simp add: a_inv_def[symmetric])
+ apply (clarsimp, rule)
+ apply (fast intro: ideal.I_l_closed ideal.intro assms)+
+ apply (clarsimp, rule)
+ apply (fast intro: ideal.I_r_closed ideal.intro assms)+
+ done
qed
text {* The intersection of any Number of Ideals is again
@@ -226,26 +218,25 @@
assumes Sideals: "\<And>I. I \<in> S \<Longrightarrow> ideal I R"
and notempty: "S \<noteq> {}"
shows "ideal (Inter S) R"
-apply (unfold_locales)
-apply (simp_all add: Inter_eq)
- apply rule unfolding mem_Collect_eq defer 1
- apply rule defer 1
- apply rule defer 1
- apply (fold a_inv_def, rule) defer 1
- apply rule defer 1
- apply rule defer 1
+ apply (unfold_locales)
+ apply (simp_all add: Inter_eq)
+ apply rule unfolding mem_Collect_eq defer 1
+ apply rule defer 1
+ apply rule defer 1
+ apply (fold a_inv_def, rule) defer 1
+ apply rule defer 1
+ apply rule defer 1
proof -
fix x y
assume "\<forall>I\<in>S. x \<in> I"
- hence xI: "\<And>I. I \<in> S \<Longrightarrow> x \<in> I" by simp
+ then have xI: "\<And>I. I \<in> S \<Longrightarrow> x \<in> I" by simp
assume "\<forall>I\<in>S. y \<in> I"
- hence yI: "\<And>I. I \<in> S \<Longrightarrow> y \<in> I" by simp
+ then have yI: "\<And>I. I \<in> S \<Longrightarrow> y \<in> I" by simp
fix J
assume JS: "J \<in> S"
interpret ideal J R by (rule Sideals[OF JS])
- from xI[OF JS] and yI[OF JS]
- show "x \<oplus> y \<in> J" by (rule a_closed)
+ from xI[OF JS] and yI[OF JS] show "x \<oplus> y \<in> J" by (rule a_closed)
next
fix J
assume JS: "J \<in> S"
@@ -254,50 +245,47 @@
next
fix x
assume "\<forall>I\<in>S. x \<in> I"
- hence xI: "\<And>I. I \<in> S \<Longrightarrow> x \<in> I" by simp
+ then have xI: "\<And>I. I \<in> S \<Longrightarrow> x \<in> I" by simp
fix J
assume JS: "J \<in> S"
interpret ideal J R by (rule Sideals[OF JS])
- from xI[OF JS]
- show "\<ominus> x \<in> J" by (rule a_inv_closed)
+ from xI[OF JS] show "\<ominus> x \<in> J" by (rule a_inv_closed)
next
fix x y
assume "\<forall>I\<in>S. x \<in> I"
- hence xI: "\<And>I. I \<in> S \<Longrightarrow> x \<in> I" by simp
+ then have xI: "\<And>I. I \<in> S \<Longrightarrow> x \<in> I" by simp
assume ycarr: "y \<in> carrier R"
fix J
assume JS: "J \<in> S"
interpret ideal J R by (rule Sideals[OF JS])
- from xI[OF JS] and ycarr
- show "y \<otimes> x \<in> J" by (rule I_l_closed)
+ from xI[OF JS] and ycarr show "y \<otimes> x \<in> J" by (rule I_l_closed)
next
fix x y
assume "\<forall>I\<in>S. x \<in> I"
- hence xI: "\<And>I. I \<in> S \<Longrightarrow> x \<in> I" by simp
+ then have xI: "\<And>I. I \<in> S \<Longrightarrow> x \<in> I" by simp
assume ycarr: "y \<in> carrier R"
fix J
assume JS: "J \<in> S"
interpret ideal J R by (rule Sideals[OF JS])
- from xI[OF JS] and ycarr
- show "x \<otimes> y \<in> J" by (rule I_r_closed)
+ from xI[OF JS] and ycarr show "x \<otimes> y \<in> J" by (rule I_r_closed)
next
fix x
assume "\<forall>I\<in>S. x \<in> I"
- hence xI: "\<And>I. I \<in> S \<Longrightarrow> x \<in> I" by simp
+ then have xI: "\<And>I. I \<in> S \<Longrightarrow> x \<in> I" by simp
from notempty have "\<exists>I0. I0 \<in> S" by blast
- from this obtain I0 where I0S: "I0 \<in> S" by auto
+ then obtain I0 where I0S: "I0 \<in> S" by auto
interpret ideal I0 R by (rule Sideals[OF I0S])
from xI[OF I0S] have "x \<in> I0" .
- from this and a_subset show "x \<in> carrier R" by fast
+ with a_subset show "x \<in> carrier R" by fast
next
qed
@@ -309,40 +297,41 @@
assumes idealI: "ideal I R"
and idealJ: "ideal J R"
shows "ideal (I <+> J) R"
-apply (rule ideal.intro)
- apply (rule add_additive_subgroups)
- apply (intro ideal.axioms[OF idealI])
- apply (intro ideal.axioms[OF idealJ])
- apply (rule is_ring)
-apply (rule ideal_axioms.intro)
- apply (simp add: set_add_defs, clarsimp) defer 1
- apply (simp add: set_add_defs, clarsimp) defer 1
+ apply (rule ideal.intro)
+ apply (rule add_additive_subgroups)
+ apply (intro ideal.axioms[OF idealI])
+ apply (intro ideal.axioms[OF idealJ])
+ apply (rule is_ring)
+ apply (rule ideal_axioms.intro)
+ apply (simp add: set_add_defs, clarsimp) defer 1
+ apply (simp add: set_add_defs, clarsimp) defer 1
proof -
fix x i j
assume xcarr: "x \<in> carrier R"
- and iI: "i \<in> I"
- and jJ: "j \<in> J"
+ and iI: "i \<in> I"
+ and jJ: "j \<in> J"
from xcarr ideal.Icarr[OF idealI iI] ideal.Icarr[OF idealJ jJ]
- have c: "(i \<oplus> j) \<otimes> x = (i \<otimes> x) \<oplus> (j \<otimes> x)" by algebra
- from xcarr and iI
- have a: "i \<otimes> x \<in> I" by (simp add: ideal.I_r_closed[OF idealI])
- from xcarr and jJ
- have b: "j \<otimes> x \<in> J" by (simp add: ideal.I_r_closed[OF idealJ])
- from a b c
- show "\<exists>ha\<in>I. \<exists>ka\<in>J. (i \<oplus> j) \<otimes> x = ha \<oplus> ka" by fast
+ have c: "(i \<oplus> j) \<otimes> x = (i \<otimes> x) \<oplus> (j \<otimes> x)"
+ by algebra
+ from xcarr and iI have a: "i \<otimes> x \<in> I"
+ by (simp add: ideal.I_r_closed[OF idealI])
+ from xcarr and jJ have b: "j \<otimes> x \<in> J"
+ by (simp add: ideal.I_r_closed[OF idealJ])
+ from a b c show "\<exists>ha\<in>I. \<exists>ka\<in>J. (i \<oplus> j) \<otimes> x = ha \<oplus> ka"
+ by fast
next
fix x i j
assume xcarr: "x \<in> carrier R"
- and iI: "i \<in> I"
- and jJ: "j \<in> J"
+ and iI: "i \<in> I"
+ and jJ: "j \<in> J"
from xcarr ideal.Icarr[OF idealI iI] ideal.Icarr[OF idealJ jJ]
- have c: "x \<otimes> (i \<oplus> j) = (x \<otimes> i) \<oplus> (x \<otimes> j)" by algebra
- from xcarr and iI
- have a: "x \<otimes> i \<in> I" by (simp add: ideal.I_l_closed[OF idealI])
- from xcarr and jJ
- have b: "x \<otimes> j \<in> J" by (simp add: ideal.I_l_closed[OF idealJ])
- from a b c
- show "\<exists>ha\<in>I. \<exists>ka\<in>J. x \<otimes> (i \<oplus> j) = ha \<oplus> ka" by fast
+ have c: "x \<otimes> (i \<oplus> j) = (x \<otimes> i) \<oplus> (x \<otimes> j)" by algebra
+ from xcarr and iI have a: "x \<otimes> i \<in> I"
+ by (simp add: ideal.I_l_closed[OF idealI])
+ from xcarr and jJ have b: "x \<otimes> j \<in> J"
+ by (simp add: ideal.I_l_closed[OF idealJ])
+ from a b c show "\<exists>ha\<in>I. \<exists>ka\<in>J. x \<otimes> (i \<oplus> j) = ha \<oplus> ka"
+ by fast
qed
@@ -361,87 +350,74 @@
lemma (in ring) genideal_self:
assumes "S \<subseteq> carrier R"
shows "S \<subseteq> Idl S"
-unfolding genideal_def
-by fast
+ unfolding genideal_def by fast
lemma (in ring) genideal_self':
assumes carr: "i \<in> carrier R"
shows "i \<in> Idl {i}"
proof -
- from carr
- have "{i} \<subseteq> Idl {i}" by (fast intro!: genideal_self)
- thus "i \<in> Idl {i}" by fast
+ from carr have "{i} \<subseteq> Idl {i}" by (fast intro!: genideal_self)
+ then show "i \<in> Idl {i}" by fast
qed
text {* @{term genideal} generates the minimal ideal *}
lemma (in ring) genideal_minimal:
assumes a: "ideal I R"
- and b: "S \<subseteq> I"
+ and b: "S \<subseteq> I"
shows "Idl S \<subseteq> I"
-unfolding genideal_def
-by (rule, elim InterD, simp add: a b)
+ unfolding genideal_def by rule (elim InterD, simp add: a b)
text {* Generated ideals and subsets *}
lemma (in ring) Idl_subset_ideal:
assumes Iideal: "ideal I R"
- and Hcarr: "H \<subseteq> carrier R"
+ and Hcarr: "H \<subseteq> carrier R"
shows "(Idl H \<subseteq> I) = (H \<subseteq> I)"
proof
assume a: "Idl H \<subseteq> I"
from Hcarr have "H \<subseteq> Idl H" by (rule genideal_self)
- from this and a
- show "H \<subseteq> I" by simp
+ with a show "H \<subseteq> I" by simp
next
fix x
assume HI: "H \<subseteq> I"
-
- from Iideal and HI
- have "I \<in> {I. ideal I R \<and> H \<subseteq> I}" by fast
- from this
- show "Idl H \<subseteq> I"
- unfolding genideal_def
- by fast
+ from Iideal and HI have "I \<in> {I. ideal I R \<and> H \<subseteq> I}" by fast
+ then show "Idl H \<subseteq> I" unfolding genideal_def by fast
qed
lemma (in ring) subset_Idl_subset:
assumes Icarr: "I \<subseteq> carrier R"
- and HI: "H \<subseteq> I"
+ and HI: "H \<subseteq> I"
shows "Idl H \<subseteq> Idl I"
proof -
- from HI and genideal_self[OF Icarr]
- have HIdlI: "H \<subseteq> Idl I" by fast
+ from HI and genideal_self[OF Icarr] have HIdlI: "H \<subseteq> Idl I"
+ by fast
- from Icarr
- have Iideal: "ideal (Idl I) R" by (rule genideal_ideal)
- from HI and Icarr
- have "H \<subseteq> carrier R" by fast
- from Iideal and this
- have "(H \<subseteq> Idl I) = (Idl H \<subseteq> Idl I)"
- by (rule Idl_subset_ideal[symmetric])
+ from Icarr have Iideal: "ideal (Idl I) R"
+ by (rule genideal_ideal)
+ from HI and Icarr have "H \<subseteq> carrier R"
+ by fast
+ with Iideal have "(H \<subseteq> Idl I) = (Idl H \<subseteq> Idl I)"
+ by (rule Idl_subset_ideal[symmetric])
- from HIdlI and this
- show "Idl H \<subseteq> Idl I" by simp
+ with HIdlI show "Idl H \<subseteq> Idl I" by simp
qed
lemma (in ring) Idl_subset_ideal':
assumes acarr: "a \<in> carrier R" and bcarr: "b \<in> carrier R"
shows "(Idl {a} \<subseteq> Idl {b}) = (a \<in> Idl {b})"
-apply (subst Idl_subset_ideal[OF genideal_ideal[of "{b}"], of "{a}"])
- apply (fast intro: bcarr, fast intro: acarr)
-apply fast
-done
+ apply (subst Idl_subset_ideal[OF genideal_ideal[of "{b}"], of "{a}"])
+ apply (fast intro: bcarr, fast intro: acarr)
+ apply fast
+ done
-lemma (in ring) genideal_zero:
- "Idl {\<zero>} = {\<zero>}"
-apply rule
- apply (rule genideal_minimal[OF zeroideal], simp)
-apply (simp add: genideal_self')
-done
+lemma (in ring) genideal_zero: "Idl {\<zero>} = {\<zero>}"
+ apply rule
+ apply (rule genideal_minimal[OF zeroideal], simp)
+ apply (simp add: genideal_self')
+ done
-lemma (in ring) genideal_one:
- "Idl {\<one>} = carrier R"
+lemma (in ring) genideal_one: "Idl {\<one>} = carrier R"
proof -
- interpret ideal "Idl {\<one>}" "R" by (rule genideal_ideal, fast intro: one_closed)
+ interpret ideal "Idl {\<one>}" "R" by (rule genideal_ideal) fast
show "Idl {\<one>} = carrier R"
apply (rule, rule a_subset)
apply (simp add: one_imp_carrier genideal_self')
@@ -451,77 +427,76 @@
text {* Generation of Principal Ideals in Commutative Rings *}
-definition
- cgenideal :: "('a, 'b) monoid_scheme \<Rightarrow> 'a \<Rightarrow> 'a set" ("PIdl\<index> _" [80] 79)
+definition cgenideal :: "_ \<Rightarrow> 'a \<Rightarrow> 'a set" ("PIdl\<index> _" [80] 79)
where "cgenideal R a = {x \<otimes>\<^bsub>R\<^esub> a | x. x \<in> carrier R}"
text {* genhideal (?) really generates an ideal *}
lemma (in cring) cgenideal_ideal:
assumes acarr: "a \<in> carrier R"
shows "ideal (PIdl a) R"
-apply (unfold cgenideal_def)
-apply (rule idealI[OF is_ring])
- apply (rule subgroup.intro)
- apply (simp_all add: monoid_record_simps)
- apply (blast intro: acarr m_closed)
- apply clarsimp defer 1
- defer 1
- apply (fold a_inv_def, clarsimp) defer 1
- apply clarsimp defer 1
- apply clarsimp defer 1
+ apply (unfold cgenideal_def)
+ apply (rule idealI[OF is_ring])
+ apply (rule subgroup.intro)
+ apply simp_all
+ apply (blast intro: acarr)
+ apply clarsimp defer 1
+ defer 1
+ apply (fold a_inv_def, clarsimp) defer 1
+ apply clarsimp defer 1
+ apply clarsimp defer 1
proof -
fix x y
assume xcarr: "x \<in> carrier R"
- and ycarr: "y \<in> carrier R"
+ and ycarr: "y \<in> carrier R"
note carr = acarr xcarr ycarr
- from carr
- have "x \<otimes> a \<oplus> y \<otimes> a = (x \<oplus> y) \<otimes> a" by (simp add: l_distr)
- from this and carr
- show "\<exists>z. x \<otimes> a \<oplus> y \<otimes> a = z \<otimes> a \<and> z \<in> carrier R" by fast
+ from carr have "x \<otimes> a \<oplus> y \<otimes> a = (x \<oplus> y) \<otimes> a"
+ by (simp add: l_distr)
+ with carr show "\<exists>z. x \<otimes> a \<oplus> y \<otimes> a = z \<otimes> a \<and> z \<in> carrier R"
+ by fast
next
from l_null[OF acarr, symmetric] and zero_closed
- show "\<exists>x. \<zero> = x \<otimes> a \<and> x \<in> carrier R" by fast
+ show "\<exists>x. \<zero> = x \<otimes> a \<and> x \<in> carrier R" by fast
next
fix x
assume xcarr: "x \<in> carrier R"
note carr = acarr xcarr
- from carr
- have "\<ominus> (x \<otimes> a) = (\<ominus> x) \<otimes> a" by (simp add: l_minus)
- from this and carr
- show "\<exists>z. \<ominus> (x \<otimes> a) = z \<otimes> a \<and> z \<in> carrier R" by fast
+ from carr have "\<ominus> (x \<otimes> a) = (\<ominus> x) \<otimes> a"
+ by (simp add: l_minus)
+ with carr show "\<exists>z. \<ominus> (x \<otimes> a) = z \<otimes> a \<and> z \<in> carrier R"
+ by fast
next
fix x y
assume xcarr: "x \<in> carrier R"
and ycarr: "y \<in> carrier R"
note carr = acarr xcarr ycarr
- from carr
- have "y \<otimes> a \<otimes> x = (y \<otimes> x) \<otimes> a" by (simp add: m_assoc, simp add: m_comm)
- from this and carr
- show "\<exists>z. y \<otimes> a \<otimes> x = z \<otimes> a \<and> z \<in> carrier R" by fast
+ from carr have "y \<otimes> a \<otimes> x = (y \<otimes> x) \<otimes> a"
+ by (simp add: m_assoc) (simp add: m_comm)
+ with carr show "\<exists>z. y \<otimes> a \<otimes> x = z \<otimes> a \<and> z \<in> carrier R"
+ by fast
next
fix x y
assume xcarr: "x \<in> carrier R"
and ycarr: "y \<in> carrier R"
note carr = acarr xcarr ycarr
- from carr
- have "x \<otimes> (y \<otimes> a) = (x \<otimes> y) \<otimes> a" by (simp add: m_assoc)
- from this and carr
- show "\<exists>z. x \<otimes> (y \<otimes> a) = z \<otimes> a \<and> z \<in> carrier R" by fast
+ from carr have "x \<otimes> (y \<otimes> a) = (x \<otimes> y) \<otimes> a"
+ by (simp add: m_assoc)
+ with carr show "\<exists>z. x \<otimes> (y \<otimes> a) = z \<otimes> a \<and> z \<in> carrier R"
+ by fast
qed
lemma (in ring) cgenideal_self:
assumes icarr: "i \<in> carrier R"
shows "i \<in> PIdl i"
-unfolding cgenideal_def
+ unfolding cgenideal_def
proof simp
- from icarr
- have "i = \<one> \<otimes> i" by simp
- from this and icarr
- show "\<exists>x. i = x \<otimes> i \<and> x \<in> carrier R" by fast
+ from icarr have "i = \<one> \<otimes> i"
+ by simp
+ with icarr show "\<exists>x. i = x \<otimes> i \<and> x \<in> carrier R"
+ by fast
qed
text {* @{const "cgenideal"} is minimal *}
@@ -532,7 +507,8 @@
shows "PIdl a \<subseteq> J"
proof -
interpret ideal J R by fact
- show ?thesis unfolding cgenideal_def
+ show ?thesis
+ unfolding cgenideal_def
apply rule
apply clarify
using aJ
@@ -543,30 +519,28 @@
lemma (in cring) cgenideal_eq_genideal:
assumes icarr: "i \<in> carrier R"
shows "PIdl i = Idl {i}"
-apply rule
- apply (intro cgenideal_minimal)
- apply (rule genideal_ideal, fast intro: icarr)
- apply (rule genideal_self', fast intro: icarr)
-apply (intro genideal_minimal)
- apply (rule cgenideal_ideal [OF icarr])
-apply (simp, rule cgenideal_self [OF icarr])
-done
+ apply rule
+ apply (intro cgenideal_minimal)
+ apply (rule genideal_ideal, fast intro: icarr)
+ apply (rule genideal_self', fast intro: icarr)
+ apply (intro genideal_minimal)
+ apply (rule cgenideal_ideal [OF icarr])
+ apply (simp, rule cgenideal_self [OF icarr])
+ done
-lemma (in cring) cgenideal_eq_rcos:
- "PIdl i = carrier R #> i"
-unfolding cgenideal_def r_coset_def
-by fast
+lemma (in cring) cgenideal_eq_rcos: "PIdl i = carrier R #> i"
+ unfolding cgenideal_def r_coset_def by fast
lemma (in cring) cgenideal_is_principalideal:
assumes icarr: "i \<in> carrier R"
shows "principalideal (PIdl i) R"
-apply (rule principalidealI)
-apply (rule cgenideal_ideal [OF icarr])
+ apply (rule principalidealI)
+ apply (rule cgenideal_ideal [OF icarr])
proof -
- from icarr
- have "PIdl i = Idl {i}" by (rule cgenideal_eq_genideal)
- from icarr and this
- show "\<exists>i'\<in>carrier R. PIdl i = Idl {i'}" by fast
+ from icarr have "PIdl i = Idl {i}"
+ by (rule cgenideal_eq_genideal)
+ with icarr show "\<exists>i'\<in>carrier R. PIdl i = Idl {i'}"
+ by fast
qed
@@ -574,83 +548,79 @@
lemma (in ring) union_genideal:
assumes idealI: "ideal I R"
- and idealJ: "ideal J R"
+ and idealJ: "ideal J R"
shows "Idl (I \<union> J) = I <+> J"
-apply rule
- apply (rule ring.genideal_minimal)
- apply (rule is_ring)
- apply (rule add_ideals[OF idealI idealJ])
- apply (rule)
- apply (simp add: set_add_defs) apply (elim disjE) defer 1 defer 1
- apply (rule) apply (simp add: set_add_defs genideal_def) apply clarsimp defer 1
+ apply rule
+ apply (rule ring.genideal_minimal)
+ apply (rule is_ring)
+ apply (rule add_ideals[OF idealI idealJ])
+ apply (rule)
+ apply (simp add: set_add_defs) apply (elim disjE) defer 1 defer 1
+ apply (rule) apply (simp add: set_add_defs genideal_def) apply clarsimp defer 1
proof -
fix x
assume xI: "x \<in> I"
have ZJ: "\<zero> \<in> J"
- by (intro additive_subgroup.zero_closed, rule ideal.axioms[OF idealJ])
- from ideal.Icarr[OF idealI xI]
- have "x = x \<oplus> \<zero>" by algebra
- from xI and ZJ and this
- show "\<exists>h\<in>I. \<exists>k\<in>J. x = h \<oplus> k" by fast
+ by (intro additive_subgroup.zero_closed) (rule ideal.axioms[OF idealJ])
+ from ideal.Icarr[OF idealI xI] have "x = x \<oplus> \<zero>"
+ by algebra
+ with xI and ZJ show "\<exists>h\<in>I. \<exists>k\<in>J. x = h \<oplus> k"
+ by fast
next
fix x
assume xJ: "x \<in> J"
have ZI: "\<zero> \<in> I"
- by (intro additive_subgroup.zero_closed, rule ideal.axioms[OF idealI])
- from ideal.Icarr[OF idealJ xJ]
- have "x = \<zero> \<oplus> x" by algebra
- from ZI and xJ and this
- show "\<exists>h\<in>I. \<exists>k\<in>J. x = h \<oplus> k" by fast
+ by (intro additive_subgroup.zero_closed, rule ideal.axioms[OF idealI])
+ from ideal.Icarr[OF idealJ xJ] have "x = \<zero> \<oplus> x"
+ by algebra
+ with ZI and xJ show "\<exists>h\<in>I. \<exists>k\<in>J. x = h \<oplus> k"
+ by fast
next
fix i j K
assume iI: "i \<in> I"
- and jJ: "j \<in> J"
- and idealK: "ideal K R"
- and IK: "I \<subseteq> K"
- and JK: "J \<subseteq> K"
- from iI and IK
- have iK: "i \<in> K" by fast
- from jJ and JK
- have jK: "j \<in> K" by fast
- from iK and jK
- show "i \<oplus> j \<in> K" by (intro additive_subgroup.a_closed) (rule ideal.axioms[OF idealK])
+ and jJ: "j \<in> J"
+ and idealK: "ideal K R"
+ and IK: "I \<subseteq> K"
+ and JK: "J \<subseteq> K"
+ from iI and IK have iK: "i \<in> K" by fast
+ from jJ and JK have jK: "j \<in> K" by fast
+ from iK and jK show "i \<oplus> j \<in> K"
+ by (intro additive_subgroup.a_closed) (rule ideal.axioms[OF idealK])
qed
subsection {* Properties of Principal Ideals *}
text {* @{text "\<zero>"} generates the zero ideal *}
-lemma (in ring) zero_genideal:
- shows "Idl {\<zero>} = {\<zero>}"
-apply rule
-apply (simp add: genideal_minimal zeroideal)
-apply (fast intro!: genideal_self)
-done
+lemma (in ring) zero_genideal: "Idl {\<zero>} = {\<zero>}"
+ apply rule
+ apply (simp add: genideal_minimal zeroideal)
+ apply (fast intro!: genideal_self)
+ done
text {* @{text "\<one>"} generates the unit ideal *}
-lemma (in ring) one_genideal:
- shows "Idl {\<one>} = carrier R"
+lemma (in ring) one_genideal: "Idl {\<one>} = carrier R"
proof -
- have "\<one> \<in> Idl {\<one>}" by (simp add: genideal_self')
- thus "Idl {\<one>} = carrier R" by (intro ideal.one_imp_carrier, fast intro: genideal_ideal)
+ have "\<one> \<in> Idl {\<one>}"
+ by (simp add: genideal_self')
+ then show "Idl {\<one>} = carrier R"
+ by (intro ideal.one_imp_carrier) (fast intro: genideal_ideal)
qed
text {* The zero ideal is a principal ideal *}
-corollary (in ring) zeropideal:
- shows "principalideal {\<zero>} R"
-apply (rule principalidealI)
- apply (rule zeroideal)
-apply (blast intro!: zero_closed zero_genideal[symmetric])
-done
+corollary (in ring) zeropideal: "principalideal {\<zero>} R"
+ apply (rule principalidealI)
+ apply (rule zeroideal)
+ apply (blast intro!: zero_genideal[symmetric])
+ done
text {* The unit ideal is a principal ideal *}
-corollary (in ring) onepideal:
- shows "principalideal (carrier R) R"
-apply (rule principalidealI)
- apply (rule oneideal)
-apply (blast intro!: one_closed one_genideal[symmetric])
-done
+corollary (in ring) onepideal: "principalideal (carrier R) R"
+ apply (rule principalidealI)
+ apply (rule oneideal)
+ apply (blast intro!: one_genideal[symmetric])
+ done
text {* Every principal ideal is a right coset of the carrier *}
@@ -659,28 +629,24 @@
shows "\<exists>x\<in>I. I = carrier R #> x"
proof -
interpret cring R by fact
- from generate
- obtain i
- where icarr: "i \<in> carrier R"
- and I1: "I = Idl {i}"
- by fast+
+ from generate obtain i where icarr: "i \<in> carrier R" and I1: "I = Idl {i}"
+ by fast+
- from icarr and genideal_self[of "{i}"]
- have "i \<in> Idl {i}" by fast
- hence iI: "i \<in> I" by (simp add: I1)
+ from icarr and genideal_self[of "{i}"] have "i \<in> Idl {i}"
+ by fast
+ then have iI: "i \<in> I" by (simp add: I1)
- from I1 icarr
- have I2: "I = PIdl i" by (simp add: cgenideal_eq_genideal)
+ from I1 icarr have I2: "I = PIdl i"
+ by (simp add: cgenideal_eq_genideal)
have "PIdl i = carrier R #> i"
- unfolding cgenideal_def r_coset_def
- by fast
+ unfolding cgenideal_def r_coset_def by fast
- from I2 and this
- have "I = carrier R #> i" by simp
+ with I2 have "I = carrier R #> i"
+ by simp
- from iI and this
- show "\<exists>x\<in>I. I = carrier R #> x" by fast
+ with iI show "\<exists>x\<in>I. I = carrier R #> x"
+ by fast
qed
@@ -693,16 +659,16 @@
proof (rule ccontr, clarsimp)
interpret cring R by fact
assume InR: "carrier R \<noteq> I"
- and "\<forall>a. a \<in> carrier R \<longrightarrow> (\<forall>b. a \<otimes> b \<in> I \<longrightarrow> b \<in> carrier R \<longrightarrow> a \<in> I \<or> b \<in> I)"
- hence I_prime: "\<And> a b. \<lbrakk>a \<in> carrier R; b \<in> carrier R; a \<otimes> b \<in> I\<rbrakk> \<Longrightarrow> a \<in> I \<or> b \<in> I" by simp
+ and "\<forall>a. a \<in> carrier R \<longrightarrow> (\<forall>b. a \<otimes> b \<in> I \<longrightarrow> b \<in> carrier R \<longrightarrow> a \<in> I \<or> b \<in> I)"
+ then have I_prime: "\<And> a b. \<lbrakk>a \<in> carrier R; b \<in> carrier R; a \<otimes> b \<in> I\<rbrakk> \<Longrightarrow> a \<in> I \<or> b \<in> I"
+ by simp
have "primeideal I R"
- apply (rule primeideal.intro [OF is_ideal is_cring])
- apply (rule primeideal_axioms.intro)
- apply (rule InR)
- apply (erule (2) I_prime)
- done
- from this and notprime
- show "False" by simp
+ apply (rule primeideal.intro [OF is_ideal is_cring])
+ apply (rule primeideal_axioms.intro)
+ apply (rule InR)
+ apply (erule (2) I_prime)
+ done
+ with notprime show False by simp
qed
lemma (in ideal) primeidealCE:
@@ -721,47 +687,44 @@
lemma (in cring) zeroprimeideal_domainI:
assumes pi: "primeideal {\<zero>} R"
shows "domain R"
-apply (rule domain.intro, rule is_cring)
-apply (rule domain_axioms.intro)
+ apply (rule domain.intro, rule is_cring)
+ apply (rule domain_axioms.intro)
proof (rule ccontr, simp)
interpret primeideal "{\<zero>}" "R" by (rule pi)
assume "\<one> = \<zero>"
- hence "carrier R = {\<zero>}" by (rule one_zeroD)
- from this[symmetric] and I_notcarr
- show "False" by simp
+ then have "carrier R = {\<zero>}" by (rule one_zeroD)
+ from this[symmetric] and I_notcarr show False
+ by simp
next
interpret primeideal "{\<zero>}" "R" by (rule pi)
fix a b
- assume ab: "a \<otimes> b = \<zero>"
- and carr: "a \<in> carrier R" "b \<in> carrier R"
- from ab
- have abI: "a \<otimes> b \<in> {\<zero>}" by fast
- from carr and this
- have "a \<in> {\<zero>} \<or> b \<in> {\<zero>}" by (rule I_prime)
- thus "a = \<zero> \<or> b = \<zero>" by simp
+ assume ab: "a \<otimes> b = \<zero>" and carr: "a \<in> carrier R" "b \<in> carrier R"
+ from ab have abI: "a \<otimes> b \<in> {\<zero>}"
+ by fast
+ with carr have "a \<in> {\<zero>} \<or> b \<in> {\<zero>}"
+ by (rule I_prime)
+ then show "a = \<zero> \<or> b = \<zero>" by simp
qed
-corollary (in cring) domain_eq_zeroprimeideal:
- shows "domain R = primeideal {\<zero>} R"
-apply rule
- apply (erule domain.zeroprimeideal)
-apply (erule zeroprimeideal_domainI)
-done
+corollary (in cring) domain_eq_zeroprimeideal: "domain R = primeideal {\<zero>} R"
+ apply rule
+ apply (erule domain.zeroprimeideal)
+ apply (erule zeroprimeideal_domainI)
+ done
subsection {* Maximal Ideals *}
lemma (in ideal) helper_I_closed:
assumes carr: "a \<in> carrier R" "x \<in> carrier R" "y \<in> carrier R"
- and axI: "a \<otimes> x \<in> I"
+ and axI: "a \<otimes> x \<in> I"
shows "a \<otimes> (x \<otimes> y) \<in> I"
proof -
- from axI and carr
- have "(a \<otimes> x) \<otimes> y \<in> I" by (simp add: I_r_closed)
- also from carr
- have "(a \<otimes> x) \<otimes> y = a \<otimes> (x \<otimes> y)" by (simp add: m_assoc)
- finally
- show "a \<otimes> (x \<otimes> y) \<in> I" .
+ from axI and carr have "(a \<otimes> x) \<otimes> y \<in> I"
+ by (simp add: I_r_closed)
+ also from carr have "(a \<otimes> x) \<otimes> y = a \<otimes> (x \<otimes> y)"
+ by (simp add: m_assoc)
+ finally show "a \<otimes> (x \<otimes> y) \<in> I" .
qed
lemma (in ideal) helper_max_prime:
@@ -787,19 +750,18 @@
have "\<ominus>(a \<otimes> x) \<in> I" by simp
also from acarr xcarr
have "\<ominus>(a \<otimes> x) = a \<otimes> (\<ominus>x)" by algebra
- finally
- show "a \<otimes> (\<ominus>x) \<in> I" .
- from acarr
- have "a \<otimes> \<zero> = \<zero>" by simp
+ finally show "a \<otimes> (\<ominus>x) \<in> I" .
+ from acarr have "a \<otimes> \<zero> = \<zero>" by simp
next
fix x y
assume xcarr: "x \<in> carrier R"
and ycarr: "y \<in> carrier R"
and ayI: "a \<otimes> y \<in> I"
- from ayI and acarr xcarr ycarr
- have "a \<otimes> (y \<otimes> x) \<in> I" by (simp add: helper_I_closed)
- moreover from xcarr ycarr
- have "y \<otimes> x = x \<otimes> y" by (simp add: m_comm)
+ from ayI and acarr xcarr ycarr have "a \<otimes> (y \<otimes> x) \<in> I"
+ by (simp add: helper_I_closed)
+ moreover
+ from xcarr ycarr have "y \<otimes> x = x \<otimes> y"
+ by (simp add: m_comm)
ultimately
show "a \<otimes> (x \<otimes> y) \<in> I" by simp
qed
@@ -818,40 +780,36 @@
apply (simp add: I_notcarr)
proof -
assume "\<exists>a b. a \<in> carrier R \<and> b \<in> carrier R \<and> a \<otimes> b \<in> I \<and> a \<notin> I \<and> b \<notin> I"
- from this
- obtain a b
- where acarr: "a \<in> carrier R"
- and bcarr: "b \<in> carrier R"
- and abI: "a \<otimes> b \<in> I"
- and anI: "a \<notin> I"
- and bnI: "b \<notin> I"
- by fast
+ then obtain a b where
+ acarr: "a \<in> carrier R" and
+ bcarr: "b \<in> carrier R" and
+ abI: "a \<otimes> b \<in> I" and
+ anI: "a \<notin> I" and
+ bnI: "b \<notin> I" by fast
def J \<equiv> "{x\<in>carrier R. a \<otimes> x \<in> I}"
- from is_cring and acarr
- have idealJ: "ideal J R" unfolding J_def by (rule helper_max_prime)
+ from is_cring and acarr have idealJ: "ideal J R"
+ unfolding J_def by (rule helper_max_prime)
have IsubJ: "I \<subseteq> J"
proof
fix x
assume xI: "x \<in> I"
- from this and acarr
- have "a \<otimes> x \<in> I" by (intro I_l_closed)
- from xI[THEN a_Hcarr] this
- show "x \<in> J" unfolding J_def by fast
+ with acarr have "a \<otimes> x \<in> I"
+ by (intro I_l_closed)
+ with xI[THEN a_Hcarr] show "x \<in> J"
+ unfolding J_def by fast
qed
- from abI and acarr bcarr
- have "b \<in> J" unfolding J_def by fast
- from bnI and this
- have JnI: "J \<noteq> I" by fast
+ from abI and acarr bcarr have "b \<in> J"
+ unfolding J_def by fast
+ with bnI have JnI: "J \<noteq> I" by fast
from acarr
have "a = a \<otimes> \<one>" by algebra
- from this and anI
- have "a \<otimes> \<one> \<notin> I" by simp
- from one_closed and this
- have "\<one> \<notin> J" unfolding J_def by fast
- hence Jncarr: "J \<noteq> carrier R" by fast
+ with anI have "a \<otimes> \<one> \<notin> I" by simp
+ with one_closed have "\<one> \<notin> J"
+ unfolding J_def by fast
+ then have Jncarr: "J \<noteq> carrier R" by fast
interpret ideal J R by (rule idealJ)
@@ -862,8 +820,7 @@
apply (rule a_subset)
done
- from this and JnI and Jncarr
- show "False" by simp
+ with JnI and Jncarr show False by simp
qed
qed
@@ -873,111 +830,93 @@
--"A non-zero cring that has only the two trivial ideals is a field"
lemma (in cring) trivialideals_fieldI:
assumes carrnzero: "carrier R \<noteq> {\<zero>}"
- and haveideals: "{I. ideal I R} = {{\<zero>}, carrier R}"
+ and haveideals: "{I. ideal I R} = {{\<zero>}, carrier R}"
shows "field R"
-apply (rule cring_fieldI)
-apply (rule, rule, rule)
- apply (erule Units_closed)
-defer 1
- apply rule
-defer 1
+ apply (rule cring_fieldI)
+ apply (rule, rule, rule)
+ apply (erule Units_closed)
+ defer 1
+ apply rule
+ defer 1
proof (rule ccontr, simp)
assume zUnit: "\<zero> \<in> Units R"
- hence a: "\<zero> \<otimes> inv \<zero> = \<one>" by (rule Units_r_inv)
- from zUnit
- have "\<zero> \<otimes> inv \<zero> = \<zero>" by (intro l_null, rule Units_inv_closed)
- from a[symmetric] and this
- have "\<one> = \<zero>" by simp
- hence "carrier R = {\<zero>}" by (rule one_zeroD)
- from this and carrnzero
- show "False" by simp
+ then have a: "\<zero> \<otimes> inv \<zero> = \<one>" by (rule Units_r_inv)
+ from zUnit have "\<zero> \<otimes> inv \<zero> = \<zero>"
+ by (intro l_null) (rule Units_inv_closed)
+ with a[symmetric] have "\<one> = \<zero>" by simp
+ then have "carrier R = {\<zero>}" by (rule one_zeroD)
+ with carrnzero show False by simp
next
fix x
assume xcarr': "x \<in> carrier R - {\<zero>}"
- hence xcarr: "x \<in> carrier R" by fast
- from xcarr'
- have xnZ: "x \<noteq> \<zero>" by fast
- from xcarr
- have xIdl: "ideal (PIdl x) R" by (intro cgenideal_ideal, fast)
+ then have xcarr: "x \<in> carrier R" by fast
+ from xcarr' have xnZ: "x \<noteq> \<zero>" by fast
+ from xcarr have xIdl: "ideal (PIdl x) R"
+ by (intro cgenideal_ideal) fast
- from xcarr
- have "x \<in> PIdl x" by (intro cgenideal_self, fast)
- from this and xnZ
- have "PIdl x \<noteq> {\<zero>}" by fast
- from haveideals and this
- have "PIdl x = carrier R"
- by (blast intro!: xIdl)
- hence "\<one> \<in> PIdl x" by simp
- hence "\<exists>y. \<one> = y \<otimes> x \<and> y \<in> carrier R" unfolding cgenideal_def by blast
- from this
- obtain y
- where ycarr: " y \<in> carrier R"
- and ylinv: "\<one> = y \<otimes> x"
- by fast+
- from ylinv and xcarr ycarr
- have yrinv: "\<one> = x \<otimes> y" by (simp add: m_comm)
+ from xcarr have "x \<in> PIdl x"
+ by (intro cgenideal_self) fast
+ with xnZ have "PIdl x \<noteq> {\<zero>}" by fast
+ with haveideals have "PIdl x = carrier R"
+ by (blast intro!: xIdl)
+ then have "\<one> \<in> PIdl x" by simp
+ then have "\<exists>y. \<one> = y \<otimes> x \<and> y \<in> carrier R"
+ unfolding cgenideal_def by blast
+ then obtain y where ycarr: " y \<in> carrier R" and ylinv: "\<one> = y \<otimes> x"
+ by fast+
+ from ylinv and xcarr ycarr have yrinv: "\<one> = x \<otimes> y"
+ by (simp add: m_comm)
from ycarr and ylinv[symmetric] and yrinv[symmetric]
- have "\<exists>y \<in> carrier R. y \<otimes> x = \<one> \<and> x \<otimes> y = \<one>" by fast
- from this and xcarr
- show "x \<in> Units R"
- unfolding Units_def
- by fast
+ have "\<exists>y \<in> carrier R. y \<otimes> x = \<one> \<and> x \<otimes> y = \<one>" by fast
+ with xcarr show "x \<in> Units R"
+ unfolding Units_def by fast
qed
-lemma (in field) all_ideals:
- shows "{I. ideal I R} = {{\<zero>}, carrier R}"
-apply (rule, rule)
+lemma (in field) all_ideals: "{I. ideal I R} = {{\<zero>}, carrier R}"
+ apply (rule, rule)
proof -
fix I
assume a: "I \<in> {I. ideal I R}"
- with this
- interpret ideal I R by simp
+ then interpret ideal I R by simp
show "I \<in> {{\<zero>}, carrier R}"
proof (cases "\<exists>a. a \<in> I - {\<zero>}")
- assume "\<exists>a. a \<in> I - {\<zero>}"
- from this
- obtain a
- where aI: "a \<in> I"
- and anZ: "a \<noteq> \<zero>"
- by fast+
- from aI[THEN a_Hcarr] anZ
- have aUnit: "a \<in> Units R" by (simp add: field_Units)
- hence a: "a \<otimes> inv a = \<one>" by (rule Units_r_inv)
- from aI and aUnit
- have "a \<otimes> inv a \<in> I" by (simp add: I_r_closed del: Units_r_inv)
- hence oneI: "\<one> \<in> I" by (simp add: a[symmetric])
+ case True
+ then obtain a where aI: "a \<in> I" and anZ: "a \<noteq> \<zero>"
+ by fast+
+ from aI[THEN a_Hcarr] anZ have aUnit: "a \<in> Units R"
+ by (simp add: field_Units)
+ then have a: "a \<otimes> inv a = \<one>" by (rule Units_r_inv)
+ from aI and aUnit have "a \<otimes> inv a \<in> I"
+ by (simp add: I_r_closed del: Units_r_inv)
+ then have oneI: "\<one> \<in> I" by (simp add: a[symmetric])
have "carrier R \<subseteq> I"
proof
fix x
assume xcarr: "x \<in> carrier R"
- from oneI and this
- have "\<one> \<otimes> x \<in> I" by (rule I_r_closed)
- from this and xcarr
- show "x \<in> I" by simp
+ with oneI have "\<one> \<otimes> x \<in> I" by (rule I_r_closed)
+ with xcarr show "x \<in> I" by simp
qed
- from this and a_subset
- have "I = carrier R" by fast
- thus "I \<in> {{\<zero>}, carrier R}" by fast
+ with a_subset have "I = carrier R" by fast
+ then show "I \<in> {{\<zero>}, carrier R}" by fast
next
- assume "\<not> (\<exists>a. a \<in> I - {\<zero>})"
- hence IZ: "\<And>a. a \<in> I \<Longrightarrow> a = \<zero>" by simp
+ case False
+ then have IZ: "\<And>a. a \<in> I \<Longrightarrow> a = \<zero>" by simp
have a: "I \<subseteq> {\<zero>}"
proof
fix x
assume "x \<in> I"
- hence "x = \<zero>" by (rule IZ)
- thus "x \<in> {\<zero>}" by fast
+ then have "x = \<zero>" by (rule IZ)
+ then show "x \<in> {\<zero>}" by fast
qed
have "\<zero> \<in> I" by simp
- hence "{\<zero>} \<subseteq> I" by fast
+ then have "{\<zero>} \<subseteq> I" by fast
- from this and a
- have "I = {\<zero>}" by fast
- thus "I \<in> {{\<zero>}, carrier R}" by fast
+ with a have "I = {\<zero>}" by fast
+ then show "I \<in> {{\<zero>}, carrier R}" by fast
qed
qed (simp add: zeroideal oneideal)
@@ -985,52 +924,47 @@
lemma (in cring) trivialideals_eq_field:
assumes carrnzero: "carrier R \<noteq> {\<zero>}"
shows "({I. ideal I R} = {{\<zero>}, carrier R}) = field R"
-by (fast intro!: trivialideals_fieldI[OF carrnzero] field.all_ideals)
+ by (fast intro!: trivialideals_fieldI[OF carrnzero] field.all_ideals)
text {* Like zeroprimeideal for domains *}
-lemma (in field) zeromaximalideal:
- "maximalideal {\<zero>} R"
-apply (rule maximalidealI)
- apply (rule zeroideal)
+lemma (in field) zeromaximalideal: "maximalideal {\<zero>} R"
+ apply (rule maximalidealI)
+ apply (rule zeroideal)
proof-
- from one_not_zero
- have "\<one> \<notin> {\<zero>}" by simp
- from this and one_closed
- show "carrier R \<noteq> {\<zero>}" by fast
+ from one_not_zero have "\<one> \<notin> {\<zero>}" by simp
+ with one_closed show "carrier R \<noteq> {\<zero>}" by fast
next
fix J
assume Jideal: "ideal J R"
- hence "J \<in> {I. ideal I R}"
- by fast
-
- from this and all_ideals
- show "J = {\<zero>} \<or> J = carrier R" by simp
+ then have "J \<in> {I. ideal I R}" by fast
+ with all_ideals show "J = {\<zero>} \<or> J = carrier R"
+ by simp
qed
lemma (in cring) zeromaximalideal_fieldI:
assumes zeromax: "maximalideal {\<zero>} R"
shows "field R"
-apply (rule trivialideals_fieldI, rule maximalideal.I_notcarr[OF zeromax])
-apply rule apply clarsimp defer 1
- apply (simp add: zeroideal oneideal)
+ apply (rule trivialideals_fieldI, rule maximalideal.I_notcarr[OF zeromax])
+ apply rule apply clarsimp defer 1
+ apply (simp add: zeroideal oneideal)
proof -
fix J
assume Jn0: "J \<noteq> {\<zero>}"
- and idealJ: "ideal J R"
+ and idealJ: "ideal J R"
interpret ideal J R by (rule idealJ)
- have "{\<zero>} \<subseteq> J" by (rule ccontr, simp)
+ have "{\<zero>} \<subseteq> J" by (rule ccontr) simp
from zeromax and idealJ and this and a_subset
- have "J = {\<zero>} \<or> J = carrier R" by (rule maximalideal.I_maximal)
- from this and Jn0
- show "J = carrier R" by simp
+ have "J = {\<zero>} \<or> J = carrier R"
+ by (rule maximalideal.I_maximal)
+ with Jn0 show "J = carrier R"
+ by simp
qed
-lemma (in cring) zeromaximalideal_eq_field:
- "maximalideal {\<zero>} R = field R"
-apply rule
- apply (erule zeromaximalideal_fieldI)
-apply (erule field.zeromaximalideal)
-done
+lemma (in cring) zeromaximalideal_eq_field: "maximalideal {\<zero>} R = field R"
+ apply rule
+ apply (erule zeromaximalideal_fieldI)
+ apply (erule field.zeromaximalideal)
+ done
end
--- a/src/HOL/Algebra/Ring.thy Sat Sep 03 11:10:38 2011 -0700
+++ b/src/HOL/Algebra/Ring.thy Sat Sep 03 14:33:45 2011 -0700
@@ -367,7 +367,7 @@
proof -
assume R: "x \<in> carrier R" "y \<in> carrier R"
then have "(\<ominus> x) \<otimes> y \<oplus> x \<otimes> y = (\<ominus> x \<oplus> x) \<otimes> y" by (simp add: l_distr)
- also from R have "... = \<zero>" by (simp add: l_neg l_null)
+ also from R have "... = \<zero>" by (simp add: l_neg)
finally have "(\<ominus> x) \<otimes> y \<oplus> x \<otimes> y = \<zero>" .
with R have "(\<ominus> x) \<otimes> y \<oplus> x \<otimes> y \<oplus> \<ominus> (x \<otimes> y) = \<zero> \<oplus> \<ominus> (x \<otimes> y)" by simp
with R show ?thesis by (simp add: a_assoc r_neg)
@@ -378,7 +378,7 @@
proof -
assume R: "x \<in> carrier R" "y \<in> carrier R"
then have "x \<otimes> (\<ominus> y) \<oplus> x \<otimes> y = x \<otimes> (\<ominus> y \<oplus> y)" by (simp add: r_distr)
- also from R have "... = \<zero>" by (simp add: l_neg r_null)
+ also from R have "... = \<zero>" by (simp add: l_neg)
finally have "x \<otimes> (\<ominus> y) \<oplus> x \<otimes> y = \<zero>" .
with R have "x \<otimes> (\<ominus> y) \<oplus> x \<otimes> y \<oplus> \<ominus> (x \<otimes> y) = \<zero> \<oplus> \<ominus> (x \<otimes> y)" by simp
with R show ?thesis by (simp add: a_assoc r_neg )
@@ -464,7 +464,6 @@
proof -
interpret ring R by fact
interpret cring S by fact
-ML_val {* Algebra.print_structures @{context} *}
from RS show ?thesis by algebra
qed
--- a/src/Pure/General/markup.ML Sat Sep 03 11:10:38 2011 -0700
+++ b/src/Pure/General/markup.ML Sat Sep 03 14:33:45 2011 -0700
@@ -116,6 +116,7 @@
val badN: string val bad: T
val functionN: string
val assign_execs: Properties.T
+ val removed_versions: Properties.T
val invoke_scala: string -> string -> Properties.T
val cancel_scala: string -> Properties.T
val no_output: Output.output * Output.output
@@ -367,6 +368,7 @@
val functionN = "function"
val assign_execs = [(functionN, "assign_execs")];
+val removed_versions = [(functionN, "removed_versions")];
fun invoke_scala name id = [(functionN, "invoke_scala"), (nameN, name), (idN, id)];
fun cancel_scala id = [(functionN, "cancel_scala"), (idN, id)];
--- a/src/Pure/General/markup.scala Sat Sep 03 11:10:38 2011 -0700
+++ b/src/Pure/General/markup.scala Sat Sep 03 14:33:45 2011 -0700
@@ -274,6 +274,7 @@
val Function = new Properties.String(FUNCTION)
val Assign_Execs: Properties.T = List((FUNCTION, "assign_execs"))
+ val Removed_Versions: Properties.T = List((FUNCTION, "removed_versions"))
val INVOKE_SCALA = "invoke_scala"
object Invoke_Scala
--- a/src/Pure/PIDE/document.ML Sat Sep 03 11:10:38 2011 -0700
+++ b/src/Pure/PIDE/document.ML Sat Sep 03 14:33:45 2011 -0700
@@ -30,6 +30,7 @@
val update: version_id -> version_id -> edit list -> state ->
((command_id * exec_id option) list * (string * command_id option) list) * state
val execute: version_id -> state -> state
+ val remove_versions: version_id list -> state -> state
val state: unit -> state
val change_state: (state -> state) -> unit
end;
@@ -61,11 +62,15 @@
type perspective = (command_id -> bool) * command_id option; (*visible commands, last*)
structure Entries = Linear_Set(type key = command_id val ord = int_ord);
+type exec = exec_id * (Toplevel.state * unit lazy) lazy; (*eval/print process*)
+val no_print = Lazy.value ();
+val no_exec = (no_id, Lazy.value (Toplevel.toplevel, no_print));
+
abstype node = Node of
{touched: bool,
header: node_header,
perspective: perspective,
- entries: exec_id option Entries.T, (*command entries with excecutions*)
+ entries: exec option Entries.T, (*command entries with excecutions*)
last_exec: command_id option, (*last command with exec state assignment*)
result: Toplevel.state lazy}
and version = Version of node Graph.T (*development graph wrt. static imports*)
@@ -83,7 +88,6 @@
val no_header = Exn.Exn (ERROR "Bad theory header");
val no_perspective = make_perspective [];
-val no_print = Lazy.value ();
val no_result = Lazy.value Toplevel.toplevel;
val empty_node = make_node (false, no_header, no_perspective, Entries.empty, NONE, no_result);
@@ -156,8 +160,8 @@
NONE => err_undef "command entry" id
| SOME (exec, _) => exec);
-fun the_default_entry node (SOME id) = the_default no_id (the_entry node id)
- | the_default_entry _ NONE = no_id;
+fun the_default_entry node (SOME id) = (id, (the_default no_exec (the_entry node id)))
+ | the_default_entry _ NONE = (no_id, no_exec);
fun update_entry id exec =
map_entries (Entries.update (id, exec));
@@ -237,42 +241,40 @@
abstype state = State of
{versions: version Inttab.table, (*version_id -> document content*)
commands: (string * Toplevel.transition future) Inttab.table, (*command_id -> name * transition*)
- execs: (command_id * (Toplevel.state * unit lazy) lazy) Inttab.table,
- (*exec_id -> command_id with eval/print process*)
- execution: Future.group} (*global execution process*)
+ execution: version_id * Future.group} (*current execution process*)
with
-fun make_state (versions, commands, execs, execution) =
- State {versions = versions, commands = commands, execs = execs, execution = execution};
+fun make_state (versions, commands, execution) =
+ State {versions = versions, commands = commands, execution = execution};
-fun map_state f (State {versions, commands, execs, execution}) =
- make_state (f (versions, commands, execs, execution));
+fun map_state f (State {versions, commands, execution}) =
+ make_state (f (versions, commands, execution));
val init_state =
- make_state (Inttab.make [(no_id, empty_version)],
- Inttab.make [(no_id, (Toplevel.name_of Toplevel.empty, Future.value Toplevel.empty))],
- Inttab.make [(no_id, (no_id, Lazy.value (Toplevel.toplevel, no_print)))],
- Future.new_group NONE);
+ make_state (Inttab.make [(no_id, empty_version)], Inttab.empty, (no_id, Future.new_group NONE));
(* document versions *)
fun define_version (id: version_id) version =
- map_state (fn (versions, commands, execs, execution) =>
+ map_state (fn (versions, commands, execution) =>
let val versions' = Inttab.update_new (id, version) versions
handle Inttab.DUP dup => err_dup "document version" dup
- in (versions', commands, execs, execution) end);
+ in (versions', commands, execution) end);
fun the_version (State {versions, ...}) (id: version_id) =
(case Inttab.lookup versions id of
NONE => err_undef "document version" id
| SOME version => version);
+fun delete_version (id: version_id) versions = Inttab.delete id versions
+ handle Inttab.UNDEF _ => err_undef "document version" id;
+
(* commands *)
fun define_command (id: command_id) name text =
- map_state (fn (versions, commands, execs, execution) =>
+ map_state (fn (versions, commands, execution) =>
let
val id_string = print_id id;
val future =
@@ -285,7 +287,7 @@
val commands' =
Inttab.update_new (id, (name, future)) commands
handle Inttab.DUP dup => err_dup "command" dup;
- in (versions, commands', execs, execution) end);
+ in (versions, commands', execution) end);
fun the_command (State {commands, ...}) (id: command_id) =
(case Inttab.lookup commands id of
@@ -293,23 +295,9 @@
| SOME command => command);
-(* command executions *)
-
-fun define_exec (exec_id, exec) =
- map_state (fn (versions, commands, execs, execution) =>
- let val execs' = Inttab.update_new (exec_id, exec) execs
- handle Inttab.DUP dup => err_dup "command execution" dup
- in (versions, commands, execs', execution) end);
-
-fun the_exec (State {execs, ...}) exec_id =
- (case Inttab.lookup execs exec_id of
- NONE => err_undef "command execution" exec_id
- | SOME exec => exec);
-
-
(* document execution *)
-fun cancel_execution (State {execution, ...}) = Future.cancel_group execution;
+fun cancel_execution (State {execution, ...}) = Future.cancel_group (#2 execution);
end;
@@ -398,7 +386,8 @@
fun get_common ((prev, id), exec) (found, (_, flags)) =
if found then NONE
else
- let val found' = is_none exec orelse exec <> lookup_entry node0 id
+ let val found' =
+ is_none exec orelse op <> (pairself (Option.map #1) (exec, lookup_entry node0 id));
in SOME (found', (prev, update_flags prev flags)) end;
val (found, (common, flags)) =
iterate_entries get_common node (false, (NONE, (true, true)));
@@ -411,7 +400,7 @@
fun illegal_init () = error "Illegal theory header after end of theory";
-fun new_exec state bad_init command_id' (execs, exec, init) =
+fun new_exec state bad_init command_id' (execs, command_exec, init) =
if bad_init andalso is_none init then NONE
else
let
@@ -424,8 +413,9 @@
val tr = tr0
|> modify_init
|> Toplevel.put_id (print_id exec_id');
- val exec' = (command_id', Lazy.map (fn (st, _) => run_command tr st) (snd exec));
- in SOME ((exec_id', exec') :: execs, exec', init') end;
+ val exec' = snd (snd command_exec) |> Lazy.map (fn (st, _) => run_command tr st);
+ val command_exec' = (command_id', (exec_id', exec'));
+ in SOME (command_exec' :: execs, command_exec', init') end;
fun make_required nodes =
let
@@ -489,10 +479,10 @@
val required = is_required name;
val last_visible = #2 (get_perspective node);
val (common, (visible, initial)) = last_common state last_visible node0 node;
- val common_exec = the_exec state (the_default_entry node common);
+ val common_command_exec = the_default_entry node common;
- val (execs, exec, _) =
- ([], common_exec, if initial then SOME init else NONE) |>
+ val (execs, (command_id, (_, exec)), _) =
+ ([], common_command_exec, if initial then SOME init else NONE) |>
(visible orelse required) ?
iterate_entries_after common
(fn ((prev, id), _) => fn res =>
@@ -506,14 +496,14 @@
else if exists (fn (_, (id, _)) => id0 = id) execs then SOME res
else SOME (id0 :: res)) node0 [];
- val last_exec = if #1 exec = no_id then NONE else SOME (#1 exec);
+ val last_exec = if command_id = no_id then NONE else SOME command_id;
val result =
if is_some (after_entry node last_exec) then no_result
- else Lazy.map #1 (#2 exec);
+ else Lazy.map #1 exec;
val node' = node
|> fold reset_entry no_execs
- |> fold (fn (exec_id, (id, _)) => update_entry id (SOME exec_id)) execs
+ |> fold (fn (id, exec) => update_entry id (SOME exec)) execs
|> set_last_exec last_exec
|> set_result result
|> set_touched false;
@@ -523,12 +513,11 @@
val command_execs =
map (rpair NONE) (maps #1 updated) @
- map (fn (exec_id, (command_id, _)) => (command_id, SOME exec_id)) (maps #2 updated);
+ map (fn (command_id, (exec_id, _)) => (command_id, SOME exec_id)) (maps #2 updated);
val updated_nodes = maps #3 updated;
val last_execs = map (fn (name, node) => (name, get_last_exec node)) updated_nodes;
val state' = state
- |> fold (fold define_exec o #2) updated
|> define_version new_id (fold put_node updated_nodes new_version);
in ((command_execs, last_execs), state') end;
@@ -538,14 +527,13 @@
(* execute *)
fun execute version_id state =
- state |> map_state (fn (versions, commands, execs, _) =>
+ state |> map_state (fn (versions, commands, _) =>
let
val version = the_version state version_id;
- fun force_exec _ NONE = ()
- | force_exec node (SOME exec_id) =
+ fun force_exec _ _ NONE = ()
+ | force_exec node command_id (SOME (_, exec)) =
let
- val (command_id, exec) = the_exec state exec_id;
val (_, print) = Lazy.force exec;
val _ =
if #1 (get_perspective node) command_id
@@ -553,16 +541,34 @@
else ();
in () end;
- val execution = Future.new_group NONE;
+ val group = Future.new_group NONE;
val _ =
nodes_of version |> Graph.schedule
(fn deps => fn (name, node) =>
(singleton o Future.forks)
- {name = "theory:" ^ name, group = SOME (Future.new_group (SOME execution)),
+ {name = "theory:" ^ name, group = SOME (Future.new_group (SOME group)),
deps = map (Future.task_of o #2) deps, pri = 1, interrupts = false}
- (iterate_entries (fn (_, exec) => fn () => SOME (force_exec node exec)) node));
+ (iterate_entries (fn ((_, id), exec) => fn () =>
+ SOME (force_exec node id exec)) node));
+
+ in (versions, commands, (version_id, group)) end);
+
+
+(* remove versions *)
- in (versions, commands, execs, execution) end);
+fun remove_versions ids state = state |> map_state (fn (versions, _, execution) =>
+ let
+ val _ = member (op =) ids (#1 execution) andalso
+ error ("Attempt to remove execution version " ^ print_id (#1 execution));
+
+ val versions' = fold delete_version ids versions;
+ val commands' =
+ (versions', Inttab.empty) |->
+ Inttab.fold (fn (_, version) => nodes_of version |>
+ Graph.fold (fn (_, (node, _)) => node |>
+ iterate_entries (fn ((_, id), _) =>
+ SOME o Inttab.insert (K true) (id, the_command state id))));
+ in (versions', commands', execution) end);
--- a/src/Pure/PIDE/document.scala Sat Sep 03 11:10:38 2011 -0700
+++ b/src/Pure/PIDE/document.scala Sat Sep 03 14:33:45 2011 -0700
@@ -168,15 +168,19 @@
object Change
{
- val init: Change = Change(Future.value(Version.init), Nil, Future.value(Version.init))
+ val init: Change = Change(Some(Future.value(Version.init)), Nil, Future.value(Version.init))
}
sealed case class Change(
- val previous: Future[Version],
+ val previous: Option[Future[Version]],
val edits: List[Edit_Text],
val version: Future[Version])
{
- def is_finished: Boolean = previous.is_finished && version.is_finished
+ def is_finished: Boolean =
+ (previous match { case None => true case Some(future) => future.is_finished }) &&
+ version.is_finished
+
+ def truncate: Change = copy(previous = None, edits = Nil)
}
@@ -184,16 +188,16 @@
object History
{
- val init: History = new History(List(Change.init))
+ val init: History = History(List(Change.init))
}
// FIXME pruning, purging of state
- class History(val undo_list: List[Change])
+ sealed case class History(val undo_list: List[Change])
{
require(!undo_list.isEmpty)
def tip: Change = undo_list.head
- def +(change: Change): History = new History(change :: undo_list)
+ def +(change: Change): History = copy(undo_list = change :: undo_list)
}
@@ -260,7 +264,6 @@
val commands: Map[Command_ID, Command.State] = Map(), // static markup from define_command
val execs: Map[Exec_ID, Command.State] = Map(), // dynamic markup from execution
val assignments: Map[Version_ID, State.Assignment] = Map(),
- val disposed: Set[ID] = Set(), // FIXME unused!?
val history: History = History.init)
{
private def fail[A]: A = throw new State.Fail(this)
@@ -268,7 +271,6 @@
def define_version(version: Version, assignment: State.Assignment): State =
{
val id = version.id
- if (versions.isDefinedAt(id) || disposed(id)) fail
copy(versions = versions + (id -> version),
assignments = assignments + (id -> assignment.unfinished))
}
@@ -276,7 +278,6 @@
def define_command(command: Command): State =
{
val id = command.id
- if (commands.isDefinedAt(id) || disposed(id)) fail
copy(commands = commands + (id -> command.empty_state))
}
@@ -342,7 +343,7 @@
def is_stable(change: Change): Boolean =
change.is_finished && is_assigned(change.version.get_finished)
- def recent_stable: Option[Change] = history.undo_list.find(is_stable)
+ def recent_stable: Change = history.undo_list.find(is_stable) getOrElse fail
def tip_stable: Boolean = is_stable(history.tip)
def tip_version: Version = history.tip.version.get_finished
@@ -366,10 +367,49 @@
edits: List[Edit_Text],
version: Future[Version]): (Change, State) =
{
- val change = Change(previous, edits, version)
+ val change = Change(Some(previous), edits, version)
(change, copy(history = history + change))
}
+ def prune_history(retain: Int = 0): (List[Version], State) =
+ {
+ val undo_list = history.undo_list
+ val n = undo_list.iterator.zipWithIndex.find(p => is_stable(p._1)).get._2 + 1
+ val (retained, dropped) = undo_list.splitAt(n max retain)
+
+ retained.splitAt(retained.length - 1) match {
+ case (prefix, List(last)) =>
+ val dropped_versions = dropped.map(change => change.version.get_finished)
+ val state1 = copy(history = History(prefix ::: List(last.truncate)))
+ (dropped_versions, state1)
+ case _ => fail
+ }
+ }
+
+ def removed_versions(removed: List[Version_ID]): State =
+ {
+ val versions1 = versions -- removed
+ val assignments1 = assignments -- removed
+ var commands1 = Map.empty[Command_ID, Command.State]
+ var execs1 = Map.empty[Exec_ID, Command.State]
+ for {
+ (version_id, version) <- versions1.iterator
+ val command_execs = assignments1(version_id).command_execs
+ (_, node) <- version.nodes.iterator
+ command <- node.commands.iterator
+ } {
+ val id = command.id
+ if (!commands1.isDefinedAt(id) && commands.isDefinedAt(id))
+ commands1 += (id -> commands(id))
+ if (command_execs.isDefinedAt(id)) {
+ val exec_id = command_execs(id)
+ if (!execs1.isDefinedAt(exec_id) && execs.isDefinedAt(exec_id))
+ execs1 += (exec_id -> execs(exec_id))
+ }
+ }
+ copy(versions = versions1, commands = commands1, execs = execs1, assignments = assignments1)
+ }
+
def command_state(version: Version, command: Command): Command.State =
{
require(is_assigned(version))
@@ -384,7 +424,7 @@
// persistent user-view
def snapshot(name: Node.Name, pending_edits: List[Text.Edit]): Snapshot =
{
- val stable = recent_stable.get
+ val stable = recent_stable
val latest = history.tip
// FIXME proper treatment of removed nodes
--- a/src/Pure/PIDE/isar_document.ML Sat Sep 03 11:10:38 2011 -0700
+++ b/src/Pure/PIDE/isar_document.ML Sat Sep 03 14:33:45 2011 -0700
@@ -65,6 +65,17 @@
in state2 end));
val _ =
+ Isabelle_Process.add_command "Isar_Document.remove_versions"
+ (fn [versions_yxml] => Document.change_state (fn state =>
+ let
+ val versions =
+ YXML.parse_body versions_yxml |>
+ let open XML.Decode in list int end;
+ val state1 = Document.remove_versions versions state;
+ val _ = Output.raw_message Markup.removed_versions versions_yxml;
+ in state1 end));
+
+val _ =
Isabelle_Process.add_command "Isar_Document.invoke_scala"
(fn [id, tag, res] => Invoke_Scala.fulfill_method id tag res);
--- a/src/Pure/PIDE/isar_document.scala Sat Sep 03 11:10:38 2011 -0700
+++ b/src/Pure/PIDE/isar_document.scala Sat Sep 03 14:33:45 2011 -0700
@@ -26,6 +26,20 @@
}
}
+ object Removed
+ {
+ def unapply(text: String): Option[List[Document.Version_ID]] =
+ try {
+ import XML.Decode._
+ Some(list(long)(YXML.parse_body(text)))
+ }
+ catch {
+ case ERROR(_) => None
+ case _: XML.XML_Atom => None
+ case _: XML.XML_Body => None
+ }
+ }
+
/* toplevel transactions */
@@ -188,6 +202,14 @@
input("Isar_Document.update", Document.ID(old_id), Document.ID(new_id), edits_yxml)
}
+ def remove_versions(versions: List[Document.Version])
+ {
+ val versions_yxml =
+ { import XML.Encode._
+ YXML.string_of_body(list(long)(versions.map(_.id))) }
+ input("Isar_Document.remove_versions", versions_yxml)
+ }
+
/* method invocation service */
--- a/src/Pure/System/session.scala Sat Sep 03 11:10:38 2011 -0700
+++ b/src/Pure/System/session.scala Sat Sep 03 14:33:45 2011 -0700
@@ -42,6 +42,8 @@
val output_delay = Time.seconds(0.1) // prover output (markup, common messages)
val update_delay = Time.seconds(0.5) // GUI layout updates
val load_delay = Time.seconds(0.5) // file load operations (new buffers etc.)
+ val prune_delay = Time.seconds(60.0) // prune history -- delete old versions
+ val prune_size = 0 // size of retained history
/* pervasive event buses */
@@ -180,6 +182,8 @@
val this_actor = self
var prover: Option[Isabelle_Process with Isar_Document] = None
+ var prune_next = System.currentTimeMillis() + prune_delay.ms
+
/* perspective */
@@ -239,6 +243,16 @@
//}}}
+ /* removed versions */
+
+ def handle_removed(removed: List[Document.Version_ID])
+ //{{{
+ {
+ global_state.change(_.removed_versions(removed))
+ }
+ //}}}
+
+
/* resulting changes */
def handle_change(change: Change_Node)
@@ -295,6 +309,19 @@
catch { case _: Document.State.Fail => bad_result(result) }
case _ => bad_result(result)
}
+ // FIXME separate timeout event/message!?
+ if (prover.isDefined && System.currentTimeMillis() > prune_next) {
+ val old_versions = global_state.change_yield(_.prune_history(prune_size))
+ if (!old_versions.isEmpty) prover.get.remove_versions(old_versions)
+ prune_next = System.currentTimeMillis() + prune_delay.ms
+ }
+ case Markup.Removed_Versions if result.is_raw =>
+ XML.content(result.body).mkString match {
+ case Isar_Document.Removed(removed) =>
+ try { handle_removed(removed) }
+ catch { case _: Document.State.Fail => bad_result(result) }
+ case _ => bad_result(result)
+ }
case Markup.Invoke_Scala(name, id) if result.is_raw =>
Future.fork {
val arg = XML.content(result.body).mkString
--- a/src/Tools/jEdit/src/session_dockable.scala Sat Sep 03 11:10:38 2011 -0700
+++ b/src/Tools/jEdit/src/session_dockable.scala Sat Sep 03 14:33:45 2011 -0700
@@ -80,23 +80,21 @@
Swing_Thread.now {
// FIXME correlation to changed_nodes!?
val state = Isabelle.session.current_state()
- state.recent_stable.map(change => change.version.get_finished) match {
- case None =>
- case Some(version) =>
- var nodes_status1 = nodes_status
- for {
- name <- changed_nodes
- node <- version.nodes.get(name)
- val status = Isar_Document.node_status(state, version, node)
- } nodes_status1 += (name -> status.toString)
+ val version = state.recent_stable.version.get_finished
- if (nodes_status != nodes_status1) {
- nodes_status = nodes_status1
- val order =
- Library.sort_wrt((name: Document.Node.Name) => name.theory,
- nodes_status.keySet.toList)
- status.listData = order.map(name => name.theory + " " + nodes_status(name))
- }
+ var nodes_status1 = nodes_status
+ for {
+ name <- changed_nodes
+ node <- version.nodes.get(name)
+ val status = Isar_Document.node_status(state, version, node)
+ } nodes_status1 += (name -> status.toString)
+
+ if (nodes_status != nodes_status1) {
+ nodes_status = nodes_status1
+ val order =
+ Library.sort_wrt((name: Document.Node.Name) => name.theory,
+ nodes_status.keySet.toList)
+ status.listData = order.map(name => name.theory + " " + nodes_status(name))
}
}
}