--- a/etc/options Tue Aug 08 13:31:48 2017 +0200
+++ b/etc/options Tue Aug 08 22:40:05 2017 +0200
@@ -155,6 +155,9 @@
public option editor_output_delay : real = 0.1
-- "delay for prover output (markup, common messages etc.)"
+public option editor_consolidate_delay : real = 1.0
+ -- "delay to consolidate status of command evaluation (execution forks)"
+
public option editor_prune_delay : real = 15
-- "delay to prune history (delete old versions)"
--- a/src/HOL/Number_Theory/Cong.thy Tue Aug 08 13:31:48 2017 +0200
+++ b/src/HOL/Number_Theory/Cong.thy Tue Aug 08 22:40:05 2017 +0200
@@ -1,6 +1,9 @@
(* Title: HOL/Number_Theory/Cong.thy
- Authors: Christophe Tabacznyj, Lawrence C. Paulson, Amine Chaieb,
- Thomas M. Rasmussen, Jeremy Avigad
+ Author: Christophe Tabacznyj
+ Author: Lawrence C. Paulson
+ Author: Amine Chaieb
+ Author: Thomas M. Rasmussen
+ Author: Jeremy Avigad
Defines congruence (notation: [x = y] (mod z)) for natural numbers and
integers.
@@ -26,12 +29,13 @@
section \<open>Congruence\<close>
theory Cong
-imports "~~/src/HOL/Computational_Algebra/Primes"
+ imports "~~/src/HOL/Computational_Algebra/Primes"
begin
subsection \<open>Turn off \<open>One_nat_def\<close>\<close>
-lemma power_eq_one_eq_nat [simp]: "((x::nat)^m = 1) = (m = 0 | x = 1)"
+lemma power_eq_one_eq_nat [simp]: "x^m = 1 \<longleftrightarrow> m = 0 \<or> x = 1"
+ for x m :: nat
by (induct m) auto
declare mod_pos_pos_trivial [simp]
@@ -40,7 +44,7 @@
subsection \<open>Main definitions\<close>
class cong =
- fixes cong :: "'a \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> bool" ("(1[_ = _] '(()mod _'))")
+ fixes cong :: "'a \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> bool" ("(1[_ = _] '(()mod _'))")
begin
abbreviation notcong :: "'a \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> bool" ("(1[_ \<noteq> _] '(()mod _'))")
@@ -48,26 +52,27 @@
end
-(* definitions for the natural numbers *)
+
+subsubsection \<open>Definitions for the natural numbers\<close>
instantiation nat :: cong
begin
definition cong_nat :: "nat \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> bool"
- where "cong_nat x y m = ((x mod m) = (y mod m))"
+ where "cong_nat x y m \<longleftrightarrow> x mod m = y mod m"
instance ..
end
-(* definitions for the integers *)
+subsubsection \<open>Definitions for the integers\<close>
instantiation int :: cong
begin
definition cong_int :: "int \<Rightarrow> int \<Rightarrow> int \<Rightarrow> bool"
- where "cong_int x y m = ((x mod m) = (y mod m))"
+ where "cong_int x y m \<longleftrightarrow> x mod m = y mod m"
instance ..
@@ -78,253 +83,259 @@
lemma transfer_nat_int_cong:
- "(x::int) >= 0 \<Longrightarrow> y >= 0 \<Longrightarrow> m >= 0 \<Longrightarrow>
- ([(nat x) = (nat y)] (mod (nat m))) = ([x = y] (mod m))"
+ "x \<ge> 0 \<Longrightarrow> y \<ge> 0 \<Longrightarrow> m \<ge> 0 \<Longrightarrow> [nat x = nat y] (mod (nat m)) \<longleftrightarrow> [x = y] (mod m)"
+ for x y m :: int
unfolding cong_int_def cong_nat_def
by (metis Divides.transfer_int_nat_functions(2) nat_0_le nat_mod_distrib)
-declare transfer_morphism_nat_int[transfer add return:
- transfer_nat_int_cong]
+declare transfer_morphism_nat_int [transfer add return: transfer_nat_int_cong]
-lemma transfer_int_nat_cong:
- "[(int x) = (int y)] (mod (int m)) = [x = y] (mod m)"
- apply (auto simp add: cong_int_def cong_nat_def)
- apply (auto simp add: zmod_int [symmetric])
- done
+lemma transfer_int_nat_cong: "[int x = int y] (mod (int m)) = [x = y] (mod m)"
+ by (auto simp add: cong_int_def cong_nat_def) (auto simp add: zmod_int [symmetric])
-declare transfer_morphism_int_nat[transfer add return:
- transfer_int_nat_cong]
+declare transfer_morphism_int_nat [transfer add return: transfer_int_nat_cong]
subsection \<open>Congruence\<close>
(* was zcong_0, etc. *)
-lemma cong_0_nat [simp, presburger]: "([(a::nat) = b] (mod 0)) = (a = b)"
- unfolding cong_nat_def by auto
+lemma cong_0_nat [simp, presburger]: "[a = b] (mod 0) \<longleftrightarrow> a = b"
+ for a b :: nat
+ by (auto simp: cong_nat_def)
-lemma cong_0_int [simp, presburger]: "([(a::int) = b] (mod 0)) = (a = b)"
- unfolding cong_int_def by auto
+lemma cong_0_int [simp, presburger]: "[a = b] (mod 0) \<longleftrightarrow> a = b"
+ for a b :: int
+ by (auto simp: cong_int_def)
-lemma cong_1_nat [simp, presburger]: "[(a::nat) = b] (mod 1)"
- unfolding cong_nat_def by auto
+lemma cong_1_nat [simp, presburger]: "[a = b] (mod 1)"
+ for a b :: nat
+ by (auto simp: cong_nat_def)
-lemma cong_Suc_0_nat [simp, presburger]: "[(a::nat) = b] (mod Suc 0)"
- unfolding cong_nat_def by auto
+lemma cong_Suc_0_nat [simp, presburger]: "[a = b] (mod Suc 0)"
+ for a b :: nat
+ by (auto simp: cong_nat_def)
-lemma cong_1_int [simp, presburger]: "[(a::int) = b] (mod 1)"
- unfolding cong_int_def by auto
+lemma cong_1_int [simp, presburger]: "[a = b] (mod 1)"
+ for a b :: int
+ by (auto simp: cong_int_def)
-lemma cong_refl_nat [simp]: "[(k::nat) = k] (mod m)"
- unfolding cong_nat_def by auto
+lemma cong_refl_nat [simp]: "[k = k] (mod m)"
+ for k :: nat
+ by (auto simp: cong_nat_def)
-lemma cong_refl_int [simp]: "[(k::int) = k] (mod m)"
- unfolding cong_int_def by auto
+lemma cong_refl_int [simp]: "[k = k] (mod m)"
+ for k :: int
+ by (auto simp: cong_int_def)
-lemma cong_sym_nat: "[(a::nat) = b] (mod m) \<Longrightarrow> [b = a] (mod m)"
- unfolding cong_nat_def by auto
+lemma cong_sym_nat: "[a = b] (mod m) \<Longrightarrow> [b = a] (mod m)"
+ for a b :: nat
+ by (auto simp: cong_nat_def)
-lemma cong_sym_int: "[(a::int) = b] (mod m) \<Longrightarrow> [b = a] (mod m)"
- unfolding cong_int_def by auto
+lemma cong_sym_int: "[a = b] (mod m) \<Longrightarrow> [b = a] (mod m)"
+ for a b :: int
+ by (auto simp: cong_int_def)
-lemma cong_sym_eq_nat: "[(a::nat) = b] (mod m) = [b = a] (mod m)"
- unfolding cong_nat_def by auto
+lemma cong_sym_eq_nat: "[a = b] (mod m) = [b = a] (mod m)"
+ for a b :: nat
+ by (auto simp: cong_nat_def)
-lemma cong_sym_eq_int: "[(a::int) = b] (mod m) = [b = a] (mod m)"
- unfolding cong_int_def by auto
+lemma cong_sym_eq_int: "[a = b] (mod m) = [b = a] (mod m)"
+ for a b :: int
+ by (auto simp: cong_int_def)
-lemma cong_trans_nat [trans]:
- "[(a::nat) = b] (mod m) \<Longrightarrow> [b = c] (mod m) \<Longrightarrow> [a = c] (mod m)"
- unfolding cong_nat_def by auto
+lemma cong_trans_nat [trans]: "[a = b] (mod m) \<Longrightarrow> [b = c] (mod m) \<Longrightarrow> [a = c] (mod m)"
+ for a b c :: nat
+ by (auto simp: cong_nat_def)
-lemma cong_trans_int [trans]:
- "[(a::int) = b] (mod m) \<Longrightarrow> [b = c] (mod m) \<Longrightarrow> [a = c] (mod m)"
- unfolding cong_int_def by auto
+lemma cong_trans_int [trans]: "[a = b] (mod m) \<Longrightarrow> [b = c] (mod m) \<Longrightarrow> [a = c] (mod m)"
+ for a b c :: int
+ by (auto simp: cong_int_def)
-lemma cong_add_nat:
- "[(a::nat) = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow> [a + c = b + d] (mod m)"
- unfolding cong_nat_def by (metis mod_add_cong)
+lemma cong_add_nat: "[a = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow> [a + c = b + d] (mod m)"
+ for a b c :: nat
+ unfolding cong_nat_def by (metis mod_add_cong)
-lemma cong_add_int:
- "[(a::int) = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow> [a + c = b + d] (mod m)"
- unfolding cong_int_def by (metis mod_add_cong)
+lemma cong_add_int: "[a = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow> [a + c = b + d] (mod m)"
+ for a b c :: int
+ unfolding cong_int_def by (metis mod_add_cong)
-lemma cong_diff_int:
- "[(a::int) = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow> [a - c = b - d] (mod m)"
- unfolding cong_int_def by (metis mod_diff_cong)
+lemma cong_diff_int: "[a = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow> [a - c = b - d] (mod m)"
+ for a b c :: int
+ unfolding cong_int_def by (metis mod_diff_cong)
lemma cong_diff_aux_int:
- "[(a::int) = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow>
- (a::int) >= c \<Longrightarrow> b >= d \<Longrightarrow> [tsub a c = tsub b d] (mod m)"
+ "[a = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow>
+ a \<ge> c \<Longrightarrow> b \<ge> d \<Longrightarrow> [tsub a c = tsub b d] (mod m)"
+ for a b c d :: int
by (metis cong_diff_int tsub_eq)
lemma cong_diff_nat:
- assumes"[a = b] (mod m)" "[c = d] (mod m)" "(a::nat) >= c" "b >= d"
+ fixes a b c d :: nat
+ assumes "[a = b] (mod m)" "[c = d] (mod m)" "a \<ge> c" "b \<ge> d"
shows "[a - c = b - d] (mod m)"
using assms by (rule cong_diff_aux_int [transferred])
-lemma cong_mult_nat:
- "[(a::nat) = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow> [a * c = b * d] (mod m)"
- unfolding cong_nat_def by (metis mod_mult_cong)
+lemma cong_mult_nat: "[a = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow> [a * c = b * d] (mod m)"
+ for a b c d :: nat
+ unfolding cong_nat_def by (metis mod_mult_cong)
-lemma cong_mult_int:
- "[(a::int) = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow> [a * c = b * d] (mod m)"
- unfolding cong_int_def by (metis mod_mult_cong)
-
-lemma cong_exp_nat: "[(x::nat) = y] (mod n) \<Longrightarrow> [x^k = y^k] (mod n)"
- by (induct k) (auto simp add: cong_mult_nat)
+lemma cong_mult_int: "[a = b] (mod m) \<Longrightarrow> [c = d] (mod m) \<Longrightarrow> [a * c = b * d] (mod m)"
+ for a b c d :: int
+ unfolding cong_int_def by (metis mod_mult_cong)
-lemma cong_exp_int: "[(x::int) = y] (mod n) \<Longrightarrow> [x^k = y^k] (mod n)"
- by (induct k) (auto simp add: cong_mult_int)
+lemma cong_exp_nat: "[x = y] (mod n) \<Longrightarrow> [x^k = y^k] (mod n)"
+ for x y :: nat
+ by (induct k) (auto simp: cong_mult_nat)
-lemma cong_sum_nat [rule_format]:
- "(\<forall>x\<in>A. [((f x)::nat) = g x] (mod m)) \<longrightarrow>
- [(\<Sum>x\<in>A. f x) = (\<Sum>x\<in>A. g x)] (mod m)"
- apply (cases "finite A")
- apply (induct set: finite)
- apply (auto intro: cong_add_nat)
- done
+lemma cong_exp_int: "[x = y] (mod n) \<Longrightarrow> [x^k = y^k] (mod n)"
+ for x y :: int
+ by (induct k) (auto simp: cong_mult_int)
-lemma cong_sum_int [rule_format]:
- "(\<forall>x\<in>A. [((f x)::int) = g x] (mod m)) \<longrightarrow>
- [(\<Sum>x\<in>A. f x) = (\<Sum>x\<in>A. g x)] (mod m)"
- apply (cases "finite A")
- apply (induct set: finite)
- apply (auto intro: cong_add_int)
- done
+lemma cong_sum_nat: "(\<And>x. x \<in> A \<Longrightarrow> [f x = g x] (mod m)) \<Longrightarrow> [(\<Sum>x\<in>A. f x) = (\<Sum>x\<in>A. g x)] (mod m)"
+ for f g :: "'a \<Rightarrow> nat"
+ by (induct A rule: infinite_finite_induct) (auto intro: cong_add_nat)
+
+lemma cong_sum_int: "(\<And>x. x \<in> A \<Longrightarrow> [f x = g x] (mod m)) \<Longrightarrow> [(\<Sum>x\<in>A. f x) = (\<Sum>x\<in>A. g x)] (mod m)"
+ for f g :: "'a \<Rightarrow> int"
+ by (induct A rule: infinite_finite_induct) (auto intro: cong_add_int)
-lemma cong_prod_nat [rule_format]:
- "(\<forall>x\<in>A. [((f x)::nat) = g x] (mod m)) \<longrightarrow>
- [(\<Prod>x\<in>A. f x) = (\<Prod>x\<in>A. g x)] (mod m)"
- apply (cases "finite A")
- apply (induct set: finite)
- apply (auto intro: cong_mult_nat)
- done
+lemma cong_prod_nat: "(\<And>x. x \<in> A \<Longrightarrow> [f x = g x] (mod m)) \<Longrightarrow> [(\<Prod>x\<in>A. f x) = (\<Prod>x\<in>A. g x)] (mod m)"
+ for f g :: "'a \<Rightarrow> nat"
+ by (induct A rule: infinite_finite_induct) (auto intro: cong_mult_nat)
-lemma cong_prod_int [rule_format]:
- "(\<forall>x\<in>A. [((f x)::int) = g x] (mod m)) \<longrightarrow>
- [(\<Prod>x\<in>A. f x) = (\<Prod>x\<in>A. g x)] (mod m)"
- apply (cases "finite A")
- apply (induct set: finite)
- apply (auto intro: cong_mult_int)
- done
+lemma cong_prod_int: "(\<And>x. x \<in> A \<Longrightarrow> [f x = g x] (mod m)) \<Longrightarrow> [(\<Prod>x\<in>A. f x) = (\<Prod>x\<in>A. g x)] (mod m)"
+ for f g :: "'a \<Rightarrow> int"
+ by (induct A rule: infinite_finite_induct) (auto intro: cong_mult_int)
-lemma cong_scalar_nat: "[(a::nat)= b] (mod m) \<Longrightarrow> [a * k = b * k] (mod m)"
+lemma cong_scalar_nat: "[a = b] (mod m) \<Longrightarrow> [a * k = b * k] (mod m)"
+ for a b k :: nat
by (rule cong_mult_nat) simp_all
-lemma cong_scalar_int: "[(a::int)= b] (mod m) \<Longrightarrow> [a * k = b * k] (mod m)"
+lemma cong_scalar_int: "[a = b] (mod m) \<Longrightarrow> [a * k = b * k] (mod m)"
+ for a b k :: int
by (rule cong_mult_int) simp_all
-lemma cong_scalar2_nat: "[(a::nat)= b] (mod m) \<Longrightarrow> [k * a = k * b] (mod m)"
+lemma cong_scalar2_nat: "[a = b] (mod m) \<Longrightarrow> [k * a = k * b] (mod m)"
+ for a b k :: nat
by (rule cong_mult_nat) simp_all
-lemma cong_scalar2_int: "[(a::int)= b] (mod m) \<Longrightarrow> [k * a = k * b] (mod m)"
+lemma cong_scalar2_int: "[a = b] (mod m) \<Longrightarrow> [k * a = k * b] (mod m)"
+ for a b k :: int
by (rule cong_mult_int) simp_all
-lemma cong_mult_self_nat: "[(a::nat) * m = 0] (mod m)"
- unfolding cong_nat_def by auto
+lemma cong_mult_self_nat: "[a * m = 0] (mod m)"
+ for a m :: nat
+ by (auto simp: cong_nat_def)
-lemma cong_mult_self_int: "[(a::int) * m = 0] (mod m)"
- unfolding cong_int_def by auto
+lemma cong_mult_self_int: "[a * m = 0] (mod m)"
+ for a m :: int
+ by (auto simp: cong_int_def)
-lemma cong_eq_diff_cong_0_int: "[(a::int) = b] (mod m) = [a - b = 0] (mod m)"
+lemma cong_eq_diff_cong_0_int: "[a = b] (mod m) = [a - b = 0] (mod m)"
+ for a b :: int
by (metis cong_add_int cong_diff_int cong_refl_int diff_add_cancel diff_self)
-lemma cong_eq_diff_cong_0_aux_int: "a >= b \<Longrightarrow>
- [(a::int) = b] (mod m) = [tsub a b = 0] (mod m)"
+lemma cong_eq_diff_cong_0_aux_int: "a \<ge> b \<Longrightarrow> [a = b] (mod m) = [tsub a b = 0] (mod m)"
+ for a b :: int
by (subst tsub_eq, assumption, rule cong_eq_diff_cong_0_int)
lemma cong_eq_diff_cong_0_nat:
- assumes "(a::nat) >= b"
+ fixes a b :: nat
+ assumes "a \<ge> b"
shows "[a = b] (mod m) = [a - b = 0] (mod m)"
using assms by (rule cong_eq_diff_cong_0_aux_int [transferred])
lemma cong_diff_cong_0'_nat:
- "[(x::nat) = y] (mod n) \<longleftrightarrow>
- (if x <= y then [y - x = 0] (mod n) else [x - y = 0] (mod n))"
+ "[x = y] (mod n) \<longleftrightarrow> (if x \<le> y then [y - x = 0] (mod n) else [x - y = 0] (mod n))"
+ for x y :: nat
by (metis cong_eq_diff_cong_0_nat cong_sym_nat nat_le_linear)
-lemma cong_altdef_nat: "(a::nat) >= b \<Longrightarrow> [a = b] (mod m) = (m dvd (a - b))"
+lemma cong_altdef_nat: "a \<ge> b \<Longrightarrow> [a = b] (mod m) \<longleftrightarrow> m dvd (a - b)"
+ for a b :: nat
apply (subst cong_eq_diff_cong_0_nat, assumption)
apply (unfold cong_nat_def)
apply (simp add: dvd_eq_mod_eq_0 [symmetric])
done
-lemma cong_altdef_int: "[(a::int) = b] (mod m) = (m dvd (a - b))"
+lemma cong_altdef_int: "[a = b] (mod m) \<longleftrightarrow> m dvd (a - b)"
+ for a b :: int
by (metis cong_int_def mod_eq_dvd_iff)
-lemma cong_abs_int: "[(x::int) = y] (mod abs m) = [x = y] (mod m)"
+lemma cong_abs_int: "[x = y] (mod abs m) \<longleftrightarrow> [x = y] (mod m)"
+ for x y :: int
by (simp add: cong_altdef_int)
lemma cong_square_int:
- fixes a::int
- shows "\<lbrakk> prime p; 0 < a; [a * a = 1] (mod p) \<rbrakk>
- \<Longrightarrow> [a = 1] (mod p) \<or> [a = - 1] (mod p)"
+ "prime p \<Longrightarrow> 0 < a \<Longrightarrow> [a * a = 1] (mod p) \<Longrightarrow> [a = 1] (mod p) \<or> [a = - 1] (mod p)"
+ for a :: int
apply (simp only: cong_altdef_int)
apply (subst prime_dvd_mult_eq_int [symmetric], assumption)
apply (auto simp add: field_simps)
done
-lemma cong_mult_rcancel_int:
- "coprime k (m::int) \<Longrightarrow> [a * k = b * k] (mod m) = [a = b] (mod m)"
+lemma cong_mult_rcancel_int: "coprime k m \<Longrightarrow> [a * k = b * k] (mod m) = [a = b] (mod m)"
+ for a k m :: int
by (metis cong_altdef_int left_diff_distrib coprime_dvd_mult_iff gcd.commute)
-lemma cong_mult_rcancel_nat:
- "coprime k (m::nat) \<Longrightarrow> [a * k = b * k] (mod m) = [a = b] (mod m)"
+lemma cong_mult_rcancel_nat: "coprime k m \<Longrightarrow> [a * k = b * k] (mod m) = [a = b] (mod m)"
+ for a k m :: nat
by (metis cong_mult_rcancel_int [transferred])
-lemma cong_mult_lcancel_nat:
- "coprime k (m::nat) \<Longrightarrow> [k * a = k * b ] (mod m) = [a = b] (mod m)"
+lemma cong_mult_lcancel_nat: "coprime k m \<Longrightarrow> [k * a = k * b ] (mod m) = [a = b] (mod m)"
+ for a k m :: nat
by (simp add: mult.commute cong_mult_rcancel_nat)
-lemma cong_mult_lcancel_int:
- "coprime k (m::int) \<Longrightarrow> [k * a = k * b] (mod m) = [a = b] (mod m)"
+lemma cong_mult_lcancel_int: "coprime k m \<Longrightarrow> [k * a = k * b] (mod m) = [a = b] (mod m)"
+ for a k m :: int
by (simp add: mult.commute cong_mult_rcancel_int)
(* was zcong_zgcd_zmult_zmod *)
lemma coprime_cong_mult_int:
- "[(a::int) = b] (mod m) \<Longrightarrow> [a = b] (mod n) \<Longrightarrow> coprime m n
- \<Longrightarrow> [a = b] (mod m * n)"
-by (metis divides_mult cong_altdef_int)
+ "[a = b] (mod m) \<Longrightarrow> [a = b] (mod n) \<Longrightarrow> coprime m n \<Longrightarrow> [a = b] (mod m * n)"
+ for a b :: int
+ by (metis divides_mult cong_altdef_int)
lemma coprime_cong_mult_nat:
- assumes "[(a::nat) = b] (mod m)" and "[a = b] (mod n)" and "coprime m n"
- shows "[a = b] (mod m * n)"
- by (metis assms coprime_cong_mult_int [transferred])
+ "[a = b] (mod m) \<Longrightarrow> [a = b] (mod n) \<Longrightarrow> coprime m n \<Longrightarrow> [a = b] (mod m * n)"
+ for a b :: nat
+ by (metis coprime_cong_mult_int [transferred])
-lemma cong_less_imp_eq_nat: "0 \<le> (a::nat) \<Longrightarrow>
- a < m \<Longrightarrow> 0 \<le> b \<Longrightarrow> b < m \<Longrightarrow> [a = b] (mod m) \<Longrightarrow> a = b"
+lemma cong_less_imp_eq_nat: "0 \<le> a \<Longrightarrow> a < m \<Longrightarrow> 0 \<le> b \<Longrightarrow> b < m \<Longrightarrow> [a = b] (mod m) \<Longrightarrow> a = b"
+ for a b :: nat
by (auto simp add: cong_nat_def)
-lemma cong_less_imp_eq_int: "0 \<le> (a::int) \<Longrightarrow>
- a < m \<Longrightarrow> 0 \<le> b \<Longrightarrow> b < m \<Longrightarrow> [a = b] (mod m) \<Longrightarrow> a = b"
+lemma cong_less_imp_eq_int: "0 \<le> a \<Longrightarrow> a < m \<Longrightarrow> 0 \<le> b \<Longrightarrow> b < m \<Longrightarrow> [a = b] (mod m) \<Longrightarrow> a = b"
+ for a b :: int
by (auto simp add: cong_int_def)
-lemma cong_less_unique_nat:
- "0 < (m::nat) \<Longrightarrow> (\<exists>!b. 0 \<le> b \<and> b < m \<and> [a = b] (mod m))"
+lemma cong_less_unique_nat: "0 < m \<Longrightarrow> (\<exists>!b. 0 \<le> b \<and> b < m \<and> [a = b] (mod m))"
+ for a m :: nat
by (auto simp: cong_nat_def) (metis mod_less_divisor mod_mod_trivial)
-lemma cong_less_unique_int:
- "0 < (m::int) \<Longrightarrow> (\<exists>!b. 0 \<le> b \<and> b < m \<and> [a = b] (mod m))"
+lemma cong_less_unique_int: "0 < m \<Longrightarrow> (\<exists>!b. 0 \<le> b \<and> b < m \<and> [a = b] (mod m))"
+ for a m :: int
by (auto simp: cong_int_def) (metis mod_mod_trivial pos_mod_conj)
-lemma cong_iff_lin_int: "([(a::int) = b] (mod m)) = (\<exists>k. b = a + m * k)"
+lemma cong_iff_lin_int: "[a = b] (mod m) \<longleftrightarrow> (\<exists>k. b = a + m * k)"
+ for a b :: int
apply (auto simp add: cong_altdef_int dvd_def)
apply (rule_tac [!] x = "-k" in exI, auto)
done
-lemma cong_iff_lin_nat:
- "([(a::nat) = b] (mod m)) \<longleftrightarrow> (\<exists>k1 k2. b + k1 * m = a + k2 * m)" (is "?lhs = ?rhs")
-proof (rule iffI)
- assume eqm: ?lhs
+lemma cong_iff_lin_nat: "([a = b] (mod m)) \<longleftrightarrow> (\<exists>k1 k2. b + k1 * m = a + k2 * m)"
+ (is "?lhs = ?rhs")
+ for a b :: nat
+proof
+ assume ?lhs
show ?rhs
proof (cases "b \<le> a")
case True
- then show ?rhs using eqm
+ with \<open>?lhs\<close> show ?rhs
by (metis cong_altdef_nat dvd_def le_add_diff_inverse add_0_right mult_0 mult.commute)
next
case False
- then show ?rhs using eqm
+ with \<open>?lhs\<close> show ?rhs
apply (subst (asm) cong_sym_eq_nat)
apply (auto simp: cong_altdef_nat)
apply (metis add_0_right add_diff_inverse dvd_div_mult_self less_or_eq_imp_le mult_0)
@@ -336,26 +347,32 @@
by (metis cong_nat_def mod_mult_self2 mult.commute)
qed
-lemma cong_gcd_eq_int: "[(a::int) = b] (mod m) \<Longrightarrow> gcd a m = gcd b m"
+lemma cong_gcd_eq_int: "[a = b] (mod m) \<Longrightarrow> gcd a m = gcd b m"
+ for a b :: int
by (metis cong_int_def gcd_red_int)
-lemma cong_gcd_eq_nat:
- "[(a::nat) = b] (mod m) \<Longrightarrow>gcd a m = gcd b m"
+lemma cong_gcd_eq_nat: "[a = b] (mod m) \<Longrightarrow> gcd a m = gcd b m"
+ for a b :: nat
by (metis cong_gcd_eq_int [transferred])
-lemma cong_imp_coprime_nat: "[(a::nat) = b] (mod m) \<Longrightarrow> coprime a m \<Longrightarrow> coprime b m"
+lemma cong_imp_coprime_nat: "[a = b] (mod m) \<Longrightarrow> coprime a m \<Longrightarrow> coprime b m"
+ for a b :: nat
by (auto simp add: cong_gcd_eq_nat)
-lemma cong_imp_coprime_int: "[(a::int) = b] (mod m) \<Longrightarrow> coprime a m \<Longrightarrow> coprime b m"
+lemma cong_imp_coprime_int: "[a = b] (mod m) \<Longrightarrow> coprime a m \<Longrightarrow> coprime b m"
+ for a b :: int
by (auto simp add: cong_gcd_eq_int)
-lemma cong_cong_mod_nat: "[(a::nat) = b] (mod m) = [a mod m = b mod m] (mod m)"
+lemma cong_cong_mod_nat: "[a = b] (mod m) \<longleftrightarrow> [a mod m = b mod m] (mod m)"
+ for a b :: nat
by (auto simp add: cong_nat_def)
-lemma cong_cong_mod_int: "[(a::int) = b] (mod m) = [a mod m = b mod m] (mod m)"
+lemma cong_cong_mod_int: "[a = b] (mod m) \<longleftrightarrow> [a mod m = b mod m] (mod m)"
+ for a b :: int
by (auto simp add: cong_int_def)
-lemma cong_minus_int [iff]: "[(a::int) = b] (mod -m) = [a = b] (mod m)"
+lemma cong_minus_int [iff]: "[a = b] (mod - m) \<longleftrightarrow> [a = b] (mod m)"
+ for a b :: int
by (metis cong_iff_lin_int minus_equation_iff mult_minus_left mult_minus_right)
(*
@@ -375,115 +392,158 @@
done
*)
-lemma cong_add_lcancel_nat:
- "[(a::nat) + x = a + y] (mod n) \<longleftrightarrow> [x = y] (mod n)"
+lemma cong_add_lcancel_nat: "[a + x = a + y] (mod n) \<longleftrightarrow> [x = y] (mod n)"
+ for a x y :: nat
by (simp add: cong_iff_lin_nat)
-lemma cong_add_lcancel_int:
- "[(a::int) + x = a + y] (mod n) \<longleftrightarrow> [x = y] (mod n)"
+lemma cong_add_lcancel_int: "[a + x = a + y] (mod n) \<longleftrightarrow> [x = y] (mod n)"
+ for a x y :: int
by (simp add: cong_iff_lin_int)
-lemma cong_add_rcancel_nat: "[(x::nat) + a = y + a] (mod n) \<longleftrightarrow> [x = y] (mod n)"
+lemma cong_add_rcancel_nat: "[x + a = y + a] (mod n) \<longleftrightarrow> [x = y] (mod n)"
+ for a x y :: nat
by (simp add: cong_iff_lin_nat)
-lemma cong_add_rcancel_int: "[(x::int) + a = y + a] (mod n) \<longleftrightarrow> [x = y] (mod n)"
+lemma cong_add_rcancel_int: "[x + a = y + a] (mod n) \<longleftrightarrow> [x = y] (mod n)"
+ for a x y :: int
by (simp add: cong_iff_lin_int)
-lemma cong_add_lcancel_0_nat: "[(a::nat) + x = a] (mod n) \<longleftrightarrow> [x = 0] (mod n)"
- by (simp add: cong_iff_lin_nat)
-
-lemma cong_add_lcancel_0_int: "[(a::int) + x = a] (mod n) \<longleftrightarrow> [x = 0] (mod n)"
- by (simp add: cong_iff_lin_int)
-
-lemma cong_add_rcancel_0_nat: "[x + (a::nat) = a] (mod n) \<longleftrightarrow> [x = 0] (mod n)"
+lemma cong_add_lcancel_0_nat: "[a + x = a] (mod n) \<longleftrightarrow> [x = 0] (mod n)"
+ for a x :: nat
by (simp add: cong_iff_lin_nat)
-lemma cong_add_rcancel_0_int: "[x + (a::int) = a] (mod n) \<longleftrightarrow> [x = 0] (mod n)"
+lemma cong_add_lcancel_0_int: "[a + x = a] (mod n) \<longleftrightarrow> [x = 0] (mod n)"
+ for a x :: int
by (simp add: cong_iff_lin_int)
-lemma cong_dvd_modulus_nat: "[(x::nat) = y] (mod m) \<Longrightarrow> n dvd m \<Longrightarrow>
- [x = y] (mod n)"
+lemma cong_add_rcancel_0_nat: "[x + a = a] (mod n) \<longleftrightarrow> [x = 0] (mod n)"
+ for a x :: nat
+ by (simp add: cong_iff_lin_nat)
+
+lemma cong_add_rcancel_0_int: "[x + a = a] (mod n) \<longleftrightarrow> [x = 0] (mod n)"
+ for a x :: int
+ by (simp add: cong_iff_lin_int)
+
+lemma cong_dvd_modulus_nat: "[x = y] (mod m) \<Longrightarrow> n dvd m \<Longrightarrow> [x = y] (mod n)"
+ for x y :: nat
apply (auto simp add: cong_iff_lin_nat dvd_def)
- apply (rule_tac x="k1 * k" in exI)
- apply (rule_tac x="k2 * k" in exI)
+ apply (rule_tac x= "k1 * k" in exI)
+ apply (rule_tac x= "k2 * k" in exI)
apply (simp add: field_simps)
done
-lemma cong_dvd_modulus_int: "[(x::int) = y] (mod m) \<Longrightarrow> n dvd m \<Longrightarrow> [x = y] (mod n)"
+lemma cong_dvd_modulus_int: "[x = y] (mod m) \<Longrightarrow> n dvd m \<Longrightarrow> [x = y] (mod n)"
+ for x y :: int
by (auto simp add: cong_altdef_int dvd_def)
-lemma cong_dvd_eq_nat: "[(x::nat) = y] (mod n) \<Longrightarrow> n dvd x \<longleftrightarrow> n dvd y"
- unfolding cong_nat_def by (auto simp add: dvd_eq_mod_eq_0)
+lemma cong_dvd_eq_nat: "[x = y] (mod n) \<Longrightarrow> n dvd x \<longleftrightarrow> n dvd y"
+ for x y :: nat
+ by (auto simp: cong_nat_def dvd_eq_mod_eq_0)
-lemma cong_dvd_eq_int: "[(x::int) = y] (mod n) \<Longrightarrow> n dvd x \<longleftrightarrow> n dvd y"
- unfolding cong_int_def by (auto simp add: dvd_eq_mod_eq_0)
+lemma cong_dvd_eq_int: "[x = y] (mod n) \<Longrightarrow> n dvd x \<longleftrightarrow> n dvd y"
+ for x y :: int
+ by (auto simp: cong_int_def dvd_eq_mod_eq_0)
-lemma cong_mod_nat: "(n::nat) ~= 0 \<Longrightarrow> [a mod n = a] (mod n)"
+lemma cong_mod_nat: "n \<noteq> 0 \<Longrightarrow> [a mod n = a] (mod n)"
+ for a n :: nat
by (simp add: cong_nat_def)
-lemma cong_mod_int: "(n::int) ~= 0 \<Longrightarrow> [a mod n = a] (mod n)"
+lemma cong_mod_int: "n \<noteq> 0 \<Longrightarrow> [a mod n = a] (mod n)"
+ for a n :: int
by (simp add: cong_int_def)
-lemma mod_mult_cong_nat: "(a::nat) ~= 0 \<Longrightarrow> b ~= 0
- \<Longrightarrow> [x mod (a * b) = y] (mod a) \<longleftrightarrow> [x = y] (mod a)"
+lemma mod_mult_cong_nat: "a \<noteq> 0 \<Longrightarrow> b \<noteq> 0 \<Longrightarrow> [x mod (a * b) = y] (mod a) \<longleftrightarrow> [x = y] (mod a)"
+ for a b :: nat
by (simp add: cong_nat_def mod_mult2_eq mod_add_left_eq)
-lemma neg_cong_int: "([(a::int) = b] (mod m)) = ([-a = -b] (mod m))"
+lemma neg_cong_int: "[a = b] (mod m) \<longleftrightarrow> [- a = - b] (mod m)"
+ for a b :: int
by (metis cong_int_def minus_minus mod_minus_cong)
-lemma cong_modulus_neg_int: "([(a::int) = b] (mod m)) = ([a = b] (mod -m))"
+lemma cong_modulus_neg_int: "[a = b] (mod m) \<longleftrightarrow> [a = b] (mod - m)"
+ for a b :: int
by (auto simp add: cong_altdef_int)
-lemma mod_mult_cong_int: "(a::int) ~= 0 \<Longrightarrow> b ~= 0
- \<Longrightarrow> [x mod (a * b) = y] (mod a) \<longleftrightarrow> [x = y] (mod a)"
- apply (cases "b > 0", simp add: cong_int_def mod_mod_cancel mod_add_left_eq)
- apply (subst (1 2) cong_modulus_neg_int)
- apply (unfold cong_int_def)
- apply (subgoal_tac "a * b = (-a * -b)")
- apply (erule ssubst)
- apply (subst zmod_zmult2_eq)
- apply (auto simp add: mod_add_left_eq mod_minus_right div_minus_right)
- apply (metis mod_diff_left_eq mod_diff_right_eq mod_mult_self1_is_0 diff_zero)+
+lemma mod_mult_cong_int: "a \<noteq> 0 \<Longrightarrow> b \<noteq> 0 \<Longrightarrow> [x mod (a * b) = y] (mod a) \<longleftrightarrow> [x = y] (mod a)"
+ for a b :: int
+proof (cases "b > 0")
+ case True
+ then show ?thesis
+ by (simp add: cong_int_def mod_mod_cancel mod_add_left_eq)
+next
+ case False
+ then show ?thesis
+ apply (subst (1 2) cong_modulus_neg_int)
+ apply (unfold cong_int_def)
+ apply (subgoal_tac "a * b = (- a * - b)")
+ apply (erule ssubst)
+ apply (subst zmod_zmult2_eq)
+ apply (auto simp add: mod_add_left_eq mod_minus_right div_minus_right)
+ apply (metis mod_diff_left_eq mod_diff_right_eq mod_mult_self1_is_0 diff_zero)+
+ done
+qed
+
+lemma cong_to_1_nat:
+ fixes a :: nat
+ assumes "[a = 1] (mod n)"
+ shows "n dvd (a - 1)"
+proof (cases "a = 0")
+ case True
+ then show ?thesis by force
+next
+ case False
+ with assms show ?thesis by (metis cong_altdef_nat leI less_one)
+qed
+
+lemma cong_0_1_nat': "[0 = Suc 0] (mod n) \<longleftrightarrow> n = Suc 0"
+ by (auto simp: cong_nat_def)
+
+lemma cong_0_1_nat: "[0 = 1] (mod n) \<longleftrightarrow> n = 1"
+ for n :: nat
+ by (auto simp: cong_nat_def)
+
+lemma cong_0_1_int: "[0 = 1] (mod n) \<longleftrightarrow> n = 1 \<or> n = - 1"
+ for n :: int
+ by (auto simp: cong_int_def zmult_eq_1_iff)
+
+lemma cong_to_1'_nat: "[a = 1] (mod n) \<longleftrightarrow> a = 0 \<and> n = 1 \<or> (\<exists>m. a = 1 + m * n)"
+ for a :: nat
+ by (metis add.right_neutral cong_0_1_nat cong_iff_lin_nat cong_to_1_nat
+ dvd_div_mult_self leI le_add_diff_inverse less_one mult_eq_if)
+
+lemma cong_le_nat: "y \<le> x \<Longrightarrow> [x = y] (mod n) \<longleftrightarrow> (\<exists>q. x = q * n + y)"
+ for x y :: nat
+ by (metis cong_altdef_nat Nat.le_imp_diff_is_add dvd_def mult.commute)
+
+lemma cong_solve_nat:
+ fixes a :: nat
+ assumes "a \<noteq> 0"
+ shows "\<exists>x. [a * x = gcd a n] (mod n)"
+proof (cases "n = 0")
+ case True
+ then show ?thesis by force
+next
+ case False
+ then show ?thesis
+ using bezout_nat [of a n, OF \<open>a \<noteq> 0\<close>]
+ by auto (metis cong_add_rcancel_0_nat cong_mult_self_nat mult.commute)
+qed
+
+lemma cong_solve_int: "a \<noteq> 0 \<Longrightarrow> \<exists>x. [a * x = gcd a n] (mod n)"
+ for a :: int
+ apply (cases "n = 0")
+ apply (cases "a \<ge> 0")
+ apply auto
+ apply (rule_tac x = "-1" in exI)
+ apply auto
+ apply (insert bezout_int [of a n], auto)
+ apply (metis cong_iff_lin_int mult.commute)
done
-lemma cong_to_1_nat: "([(a::nat) = 1] (mod n)) \<Longrightarrow> (n dvd (a - 1))"
- apply (cases "a = 0", force)
- by (metis cong_altdef_nat leI less_one)
-
-lemma cong_0_1_nat': "[(0::nat) = Suc 0] (mod n) = (n = Suc 0)"
- unfolding cong_nat_def by auto
-
-lemma cong_0_1_nat: "[(0::nat) = 1] (mod n) = (n = 1)"
- unfolding cong_nat_def by auto
-
-lemma cong_0_1_int: "[(0::int) = 1] (mod n) = ((n = 1) | (n = -1))"
- unfolding cong_int_def by (auto simp add: zmult_eq_1_iff)
-
-lemma cong_to_1'_nat: "[(a::nat) = 1] (mod n) \<longleftrightarrow>
- a = 0 \<and> n = 1 \<or> (\<exists>m. a = 1 + m * n)"
-by (metis add.right_neutral cong_0_1_nat cong_iff_lin_nat cong_to_1_nat dvd_div_mult_self leI le_add_diff_inverse less_one mult_eq_if)
-
-lemma cong_le_nat: "(y::nat) <= x \<Longrightarrow> [x = y] (mod n) \<longleftrightarrow> (\<exists>q. x = q * n + y)"
- by (metis cong_altdef_nat Nat.le_imp_diff_is_add dvd_def mult.commute)
-
-lemma cong_solve_nat: "(a::nat) \<noteq> 0 \<Longrightarrow> EX x. [a * x = gcd a n] (mod n)"
- apply (cases "n = 0")
- apply force
- apply (frule bezout_nat [of a n], auto)
- by (metis cong_add_rcancel_0_nat cong_mult_self_nat mult.commute)
-
-lemma cong_solve_int: "(a::int) \<noteq> 0 \<Longrightarrow> EX x. [a * x = gcd a n] (mod n)"
- apply (cases "n = 0")
- apply (cases "a \<ge> 0")
- apply auto
- apply (rule_tac x = "-1" in exI)
- apply auto
- apply (insert bezout_int [of a n], auto)
- by (metis cong_iff_lin_int mult.commute)
-
lemma cong_solve_dvd_nat:
- assumes a: "(a::nat) \<noteq> 0" and b: "gcd a n dvd d"
- shows "EX x. [a * x = d] (mod n)"
+ fixes a :: nat
+ assumes a: "a \<noteq> 0" and b: "gcd a n dvd d"
+ shows "\<exists>x. [a * x = d] (mod n)"
proof -
from cong_solve_nat [OF a] obtain x where "[a * x = gcd a n](mod n)"
by auto
@@ -499,7 +559,7 @@
lemma cong_solve_dvd_int:
assumes a: "(a::int) \<noteq> 0" and b: "gcd a n dvd d"
- shows "EX x. [a * x = d] (mod n)"
+ shows "\<exists>x. [a * x = d] (mod n)"
proof -
from cong_solve_int [OF a] obtain x where "[a * x = gcd a n](mod n)"
by auto
@@ -513,54 +573,62 @@
by auto
qed
-lemma cong_solve_coprime_nat: "coprime (a::nat) n \<Longrightarrow> EX x. [a * x = 1] (mod n)"
- apply (cases "a = 0")
- apply force
- apply (metis cong_solve_nat)
- done
+lemma cong_solve_coprime_nat:
+ fixes a :: nat
+ assumes "coprime a n"
+ shows "\<exists>x. [a * x = 1] (mod n)"
+proof (cases "a = 0")
+ case True
+ with assms show ?thesis by force
+next
+ case False
+ with assms show ?thesis by (metis cong_solve_nat)
+qed
-lemma cong_solve_coprime_int: "coprime (a::int) n \<Longrightarrow> EX x. [a * x = 1] (mod n)"
+lemma cong_solve_coprime_int: "coprime (a::int) n \<Longrightarrow> \<exists>x. [a * x = 1] (mod n)"
apply (cases "a = 0")
- apply auto
- apply (cases "n \<ge> 0")
- apply auto
+ apply auto
+ apply (cases "n \<ge> 0")
+ apply auto
apply (metis cong_solve_int)
done
lemma coprime_iff_invertible_nat:
- "m > 0 \<Longrightarrow> coprime a m = (EX x. [a * x = Suc 0] (mod m))"
+ "m > 0 \<Longrightarrow> coprime a m = (\<exists>x. [a * x = Suc 0] (mod m))"
by (metis One_nat_def cong_gcd_eq_nat cong_solve_coprime_nat coprime_lmult gcd.commute gcd_Suc_0)
-
-lemma coprime_iff_invertible_int: "m > (0::int) \<Longrightarrow> coprime a m = (EX x. [a * x = 1] (mod m))"
+
+lemma coprime_iff_invertible_int: "m > 0 \<Longrightarrow> coprime a m \<longleftrightarrow> (\<exists>x. [a * x = 1] (mod m))"
+ for m :: int
apply (auto intro: cong_solve_coprime_int)
apply (metis cong_int_def coprime_mul_eq gcd_1_int gcd.commute gcd_red_int)
done
-lemma coprime_iff_invertible'_nat: "m > 0 \<Longrightarrow> coprime a m =
- (EX x. 0 \<le> x & x < m & [a * x = Suc 0] (mod m))"
+lemma coprime_iff_invertible'_nat:
+ "m > 0 \<Longrightarrow> coprime a m \<longleftrightarrow> (\<exists>x. 0 \<le> x \<and> x < m \<and> [a * x = Suc 0] (mod m))"
apply (subst coprime_iff_invertible_nat)
- apply auto
+ apply auto
apply (auto simp add: cong_nat_def)
apply (metis mod_less_divisor mod_mult_right_eq)
done
-lemma coprime_iff_invertible'_int: "m > (0::int) \<Longrightarrow> coprime a m =
- (EX x. 0 <= x & x < m & [a * x = 1] (mod m))"
+lemma coprime_iff_invertible'_int:
+ "m > 0 \<Longrightarrow> coprime a m \<longleftrightarrow> (\<exists>x. 0 \<le> x \<and> x < m \<and> [a * x = 1] (mod m))"
+ for m :: int
apply (subst coprime_iff_invertible_int)
- apply (auto simp add: cong_int_def)
+ apply (auto simp add: cong_int_def)
apply (metis mod_mult_right_eq pos_mod_conj)
done
-lemma cong_cong_lcm_nat: "[(x::nat) = y] (mod a) \<Longrightarrow>
- [x = y] (mod b) \<Longrightarrow> [x = y] (mod lcm a b)"
+lemma cong_cong_lcm_nat: "[x = y] (mod a) \<Longrightarrow> [x = y] (mod b) \<Longrightarrow> [x = y] (mod lcm a b)"
+ for x y :: nat
apply (cases "y \<le> x")
apply (metis cong_altdef_nat lcm_least)
apply (meson cong_altdef_nat cong_sym_nat lcm_least_iff nat_le_linear)
done
-lemma cong_cong_lcm_int: "[(x::int) = y] (mod a) \<Longrightarrow>
- [x = y] (mod b) \<Longrightarrow> [x = y] (mod lcm a b)"
- by (auto simp add: cong_altdef_int lcm_least) [1]
+lemma cong_cong_lcm_int: "[x = y] (mod a) \<Longrightarrow> [x = y] (mod b) \<Longrightarrow> [x = y] (mod lcm a b)"
+ for x y :: int
+ by (auto simp add: cong_altdef_int lcm_least)
lemma cong_cong_prod_coprime_nat [rule_format]: "finite A \<Longrightarrow>
(\<forall>i\<in>A. (\<forall>j\<in>A. i \<noteq> j \<longrightarrow> coprime (m i) (m j))) \<longrightarrow>
@@ -581,162 +649,168 @@
done
lemma binary_chinese_remainder_aux_nat:
- assumes a: "coprime (m1::nat) m2"
- shows "EX b1 b2. [b1 = 1] (mod m1) \<and> [b1 = 0] (mod m2) \<and>
- [b2 = 0] (mod m1) \<and> [b2 = 1] (mod m2)"
+ fixes m1 m2 :: nat
+ assumes a: "coprime m1 m2"
+ shows "\<exists>b1 b2. [b1 = 1] (mod m1) \<and> [b1 = 0] (mod m2) \<and> [b2 = 0] (mod m1) \<and> [b2 = 1] (mod m2)"
proof -
- from cong_solve_coprime_nat [OF a] obtain x1 where one: "[m1 * x1 = 1] (mod m2)"
+ from cong_solve_coprime_nat [OF a] obtain x1 where 1: "[m1 * x1 = 1] (mod m2)"
by auto
from a have b: "coprime m2 m1"
by (subst gcd.commute)
- from cong_solve_coprime_nat [OF b] obtain x2 where two: "[m2 * x2 = 1] (mod m1)"
+ from cong_solve_coprime_nat [OF b] obtain x2 where 2: "[m2 * x2 = 1] (mod m1)"
by auto
have "[m1 * x1 = 0] (mod m1)"
- by (subst mult.commute, rule cong_mult_self_nat)
+ by (subst mult.commute) (rule cong_mult_self_nat)
moreover have "[m2 * x2 = 0] (mod m2)"
- by (subst mult.commute, rule cong_mult_self_nat)
- moreover note one two
- ultimately show ?thesis by blast
+ by (subst mult.commute) (rule cong_mult_self_nat)
+ ultimately show ?thesis
+ using 1 2 by blast
qed
lemma binary_chinese_remainder_aux_int:
- assumes a: "coprime (m1::int) m2"
- shows "EX b1 b2. [b1 = 1] (mod m1) \<and> [b1 = 0] (mod m2) \<and>
- [b2 = 0] (mod m1) \<and> [b2 = 1] (mod m2)"
+ fixes m1 m2 :: int
+ assumes a: "coprime m1 m2"
+ shows "\<exists>b1 b2. [b1 = 1] (mod m1) \<and> [b1 = 0] (mod m2) \<and> [b2 = 0] (mod m1) \<and> [b2 = 1] (mod m2)"
proof -
- from cong_solve_coprime_int [OF a] obtain x1 where one: "[m1 * x1 = 1] (mod m2)"
+ from cong_solve_coprime_int [OF a] obtain x1 where 1: "[m1 * x1 = 1] (mod m2)"
by auto
from a have b: "coprime m2 m1"
by (subst gcd.commute)
- from cong_solve_coprime_int [OF b] obtain x2 where two: "[m2 * x2 = 1] (mod m1)"
+ from cong_solve_coprime_int [OF b] obtain x2 where 2: "[m2 * x2 = 1] (mod m1)"
by auto
have "[m1 * x1 = 0] (mod m1)"
- by (subst mult.commute, rule cong_mult_self_int)
+ by (subst mult.commute) (rule cong_mult_self_int)
moreover have "[m2 * x2 = 0] (mod m2)"
- by (subst mult.commute, rule cong_mult_self_int)
- moreover note one two
- ultimately show ?thesis by blast
+ by (subst mult.commute) (rule cong_mult_self_int)
+ ultimately show ?thesis
+ using 1 2 by blast
qed
lemma binary_chinese_remainder_nat:
- assumes a: "coprime (m1::nat) m2"
- shows "EX x. [x = u1] (mod m1) \<and> [x = u2] (mod m2)"
+ fixes m1 m2 :: nat
+ assumes a: "coprime m1 m2"
+ shows "\<exists>x. [x = u1] (mod m1) \<and> [x = u2] (mod m2)"
proof -
from binary_chinese_remainder_aux_nat [OF a] obtain b1 b2
- where "[b1 = 1] (mod m1)" and "[b1 = 0] (mod m2)" and
- "[b2 = 0] (mod m1)" and "[b2 = 1] (mod m2)"
+ where "[b1 = 1] (mod m1)" and "[b1 = 0] (mod m2)"
+ and "[b2 = 0] (mod m1)" and "[b2 = 1] (mod m2)"
by blast
let ?x = "u1 * b1 + u2 * b2"
have "[?x = u1 * 1 + u2 * 0] (mod m1)"
apply (rule cong_add_nat)
- apply (rule cong_scalar2_nat)
- apply (rule \<open>[b1 = 1] (mod m1)\<close>)
+ apply (rule cong_scalar2_nat)
+ apply (rule \<open>[b1 = 1] (mod m1)\<close>)
apply (rule cong_scalar2_nat)
apply (rule \<open>[b2 = 0] (mod m1)\<close>)
done
then have "[?x = u1] (mod m1)" by simp
have "[?x = u1 * 0 + u2 * 1] (mod m2)"
apply (rule cong_add_nat)
- apply (rule cong_scalar2_nat)
- apply (rule \<open>[b1 = 0] (mod m2)\<close>)
+ apply (rule cong_scalar2_nat)
+ apply (rule \<open>[b1 = 0] (mod m2)\<close>)
apply (rule cong_scalar2_nat)
apply (rule \<open>[b2 = 1] (mod m2)\<close>)
done
- then have "[?x = u2] (mod m2)" by simp
- with \<open>[?x = u1] (mod m1)\<close> show ?thesis by blast
+ then have "[?x = u2] (mod m2)"
+ by simp
+ with \<open>[?x = u1] (mod m1)\<close> show ?thesis
+ by blast
qed
lemma binary_chinese_remainder_int:
- assumes a: "coprime (m1::int) m2"
- shows "EX x. [x = u1] (mod m1) \<and> [x = u2] (mod m2)"
+ fixes m1 m2 :: int
+ assumes a: "coprime m1 m2"
+ shows "\<exists>x. [x = u1] (mod m1) \<and> [x = u2] (mod m2)"
proof -
from binary_chinese_remainder_aux_int [OF a] obtain b1 b2
- where "[b1 = 1] (mod m1)" and "[b1 = 0] (mod m2)" and
- "[b2 = 0] (mod m1)" and "[b2 = 1] (mod m2)"
+ where "[b1 = 1] (mod m1)" and "[b1 = 0] (mod m2)"
+ and "[b2 = 0] (mod m1)" and "[b2 = 1] (mod m2)"
by blast
let ?x = "u1 * b1 + u2 * b2"
have "[?x = u1 * 1 + u2 * 0] (mod m1)"
apply (rule cong_add_int)
- apply (rule cong_scalar2_int)
- apply (rule \<open>[b1 = 1] (mod m1)\<close>)
+ apply (rule cong_scalar2_int)
+ apply (rule \<open>[b1 = 1] (mod m1)\<close>)
apply (rule cong_scalar2_int)
apply (rule \<open>[b2 = 0] (mod m1)\<close>)
done
then have "[?x = u1] (mod m1)" by simp
have "[?x = u1 * 0 + u2 * 1] (mod m2)"
apply (rule cong_add_int)
- apply (rule cong_scalar2_int)
- apply (rule \<open>[b1 = 0] (mod m2)\<close>)
+ apply (rule cong_scalar2_int)
+ apply (rule \<open>[b1 = 0] (mod m2)\<close>)
apply (rule cong_scalar2_int)
apply (rule \<open>[b2 = 1] (mod m2)\<close>)
done
then have "[?x = u2] (mod m2)" by simp
- with \<open>[?x = u1] (mod m1)\<close> show ?thesis by blast
+ with \<open>[?x = u1] (mod m1)\<close> show ?thesis
+ by blast
qed
-lemma cong_modulus_mult_nat: "[(x::nat) = y] (mod m * n) \<Longrightarrow>
- [x = y] (mod m)"
+lemma cong_modulus_mult_nat: "[x = y] (mod m * n) \<Longrightarrow> [x = y] (mod m)"
+ for x y :: nat
apply (cases "y \<le> x")
- apply (simp add: cong_altdef_nat)
- apply (erule dvd_mult_left)
+ apply (simp add: cong_altdef_nat)
+ apply (erule dvd_mult_left)
apply (rule cong_sym_nat)
apply (subst (asm) cong_sym_eq_nat)
apply (simp add: cong_altdef_nat)
apply (erule dvd_mult_left)
done
-lemma cong_modulus_mult_int: "[(x::int) = y] (mod m * n) \<Longrightarrow>
- [x = y] (mod m)"
+lemma cong_modulus_mult_int: "[x = y] (mod m * n) \<Longrightarrow> [x = y] (mod m)"
+ for x y :: int
apply (simp add: cong_altdef_int)
apply (erule dvd_mult_left)
done
-lemma cong_less_modulus_unique_nat:
- "[(x::nat) = y] (mod m) \<Longrightarrow> x < m \<Longrightarrow> y < m \<Longrightarrow> x = y"
+lemma cong_less_modulus_unique_nat: "[x = y] (mod m) \<Longrightarrow> x < m \<Longrightarrow> y < m \<Longrightarrow> x = y"
+ for x y :: nat
by (simp add: cong_nat_def)
lemma binary_chinese_remainder_unique_nat:
- assumes a: "coprime (m1::nat) m2"
+ fixes m1 m2 :: nat
+ assumes a: "coprime m1 m2"
and nz: "m1 \<noteq> 0" "m2 \<noteq> 0"
shows "\<exists>!x. x < m1 * m2 \<and> [x = u1] (mod m1) \<and> [x = u2] (mod m2)"
proof -
- from binary_chinese_remainder_nat [OF a] obtain y where
- "[y = u1] (mod m1)" and "[y = u2] (mod m2)"
+ from binary_chinese_remainder_nat [OF a] obtain y
+ where "[y = u1] (mod m1)" and "[y = u2] (mod m2)"
by blast
let ?x = "y mod (m1 * m2)"
from nz have less: "?x < m1 * m2"
by auto
- have one: "[?x = u1] (mod m1)"
+ have 1: "[?x = u1] (mod m1)"
apply (rule cong_trans_nat)
- prefer 2
- apply (rule \<open>[y = u1] (mod m1)\<close>)
+ prefer 2
+ apply (rule \<open>[y = u1] (mod m1)\<close>)
apply (rule cong_modulus_mult_nat)
apply (rule cong_mod_nat)
using nz apply auto
done
- have two: "[?x = u2] (mod m2)"
+ have 2: "[?x = u2] (mod m2)"
apply (rule cong_trans_nat)
- prefer 2
- apply (rule \<open>[y = u2] (mod m2)\<close>)
+ prefer 2
+ apply (rule \<open>[y = u2] (mod m2)\<close>)
apply (subst mult.commute)
apply (rule cong_modulus_mult_nat)
apply (rule cong_mod_nat)
using nz apply auto
done
- have "ALL z. z < m1 * m2 \<and> [z = u1] (mod m1) \<and> [z = u2] (mod m2) \<longrightarrow> z = ?x"
+ have "\<forall>z. z < m1 * m2 \<and> [z = u1] (mod m1) \<and> [z = u2] (mod m2) \<longrightarrow> z = ?x"
proof clarify
fix z
assume "z < m1 * m2"
assume "[z = u1] (mod m1)" and "[z = u2] (mod m2)"
have "[?x = z] (mod m1)"
apply (rule cong_trans_nat)
- apply (rule \<open>[?x = u1] (mod m1)\<close>)
+ apply (rule \<open>[?x = u1] (mod m1)\<close>)
apply (rule cong_sym_nat)
apply (rule \<open>[z = u1] (mod m1)\<close>)
done
moreover have "[?x = z] (mod m2)"
apply (rule cong_trans_nat)
- apply (rule \<open>[?x = u2] (mod m2)\<close>)
+ apply (rule \<open>[?x = u2] (mod m2)\<close>)
apply (rule cong_sym_nat)
apply (rule \<open>[z = u2] (mod m2)\<close>)
done
@@ -744,32 +818,30 @@
by (auto intro: coprime_cong_mult_nat a)
with \<open>z < m1 * m2\<close> \<open>?x < m1 * m2\<close> show "z = ?x"
apply (intro cong_less_modulus_unique_nat)
- apply (auto, erule cong_sym_nat)
+ apply (auto, erule cong_sym_nat)
done
qed
- with less one two show ?thesis by auto
+ with less 1 2 show ?thesis by auto
qed
lemma chinese_remainder_aux_nat:
fixes A :: "'a set"
and m :: "'a \<Rightarrow> nat"
assumes fin: "finite A"
- and cop: "ALL i : A. (ALL j : A. i \<noteq> j \<longrightarrow> coprime (m i) (m j))"
- shows "EX b. (ALL i : A. [b i = 1] (mod m i) \<and> [b i = 0] (mod (\<Prod>j \<in> A - {i}. m j)))"
+ and cop: "\<forall>i \<in> A. (\<forall>j \<in> A. i \<noteq> j \<longrightarrow> coprime (m i) (m j))"
+ shows "\<exists>b. (\<forall>i \<in> A. [b i = 1] (mod m i) \<and> [b i = 0] (mod (\<Prod>j \<in> A - {i}. m j)))"
proof (rule finite_set_choice, rule fin, rule ballI)
fix i
- assume "i : A"
+ assume "i \<in> A"
with cop have "coprime (\<Prod>j \<in> A - {i}. m j) (m i)"
- by (intro prod_coprime, auto)
- then have "EX x. [(\<Prod>j \<in> A - {i}. m j) * x = 1] (mod m i)"
+ by (intro prod_coprime) auto
+ then have "\<exists>x. [(\<Prod>j \<in> A - {i}. m j) * x = 1] (mod m i)"
by (elim cong_solve_coprime_nat)
then obtain x where "[(\<Prod>j \<in> A - {i}. m j) * x = 1] (mod m i)"
by auto
- moreover have "[(\<Prod>j \<in> A - {i}. m j) * x = 0]
- (mod (\<Prod>j \<in> A - {i}. m j))"
+ moreover have "[(\<Prod>j \<in> A - {i}. m j) * x = 0] (mod (\<Prod>j \<in> A - {i}. m j))"
by (subst mult.commute, rule cong_mult_self_nat)
- ultimately show "\<exists>a. [a = 1] (mod m i) \<and> [a = 0]
- (mod prod m (A - {i}))"
+ ultimately show "\<exists>a. [a = 1] (mod m i) \<and> [a = 0] (mod prod m (A - {i}))"
by blast
qed
@@ -778,37 +850,35 @@
and m :: "'a \<Rightarrow> nat"
and u :: "'a \<Rightarrow> nat"
assumes fin: "finite A"
- and cop: "ALL i:A. (ALL j : A. i \<noteq> j \<longrightarrow> coprime (m i) (m j))"
- shows "EX x. (ALL i:A. [x = u i] (mod m i))"
+ and cop: "\<forall>i \<in> A. \<forall>j \<in> A. i \<noteq> j \<longrightarrow> coprime (m i) (m j)"
+ shows "\<exists>x. \<forall>i \<in> A. [x = u i] (mod m i)"
proof -
- from chinese_remainder_aux_nat [OF fin cop] obtain b where
- bprop: "ALL i:A. [b i = 1] (mod m i) \<and>
- [b i = 0] (mod (\<Prod>j \<in> A - {i}. m j))"
+ from chinese_remainder_aux_nat [OF fin cop]
+ obtain b where b: "\<forall>i \<in> A. [b i = 1] (mod m i) \<and> [b i = 0] (mod (\<Prod>j \<in> A - {i}. m j))"
by blast
let ?x = "\<Sum>i\<in>A. (u i) * (b i)"
- show "?thesis"
+ show ?thesis
proof (rule exI, clarify)
fix i
- assume a: "i : A"
+ assume a: "i \<in> A"
show "[?x = u i] (mod m i)"
proof -
- from fin a have "?x = (\<Sum>j \<in> {i}. u j * b j) +
- (\<Sum>j \<in> A - {i}. u j * b j)"
- by (subst sum.union_disjoint [symmetric], auto intro: sum.cong)
+ from fin a have "?x = (\<Sum>j \<in> {i}. u j * b j) + (\<Sum>j \<in> A - {i}. u j * b j)"
+ by (subst sum.union_disjoint [symmetric]) (auto intro: sum.cong)
then have "[?x = u i * b i + (\<Sum>j \<in> A - {i}. u j * b j)] (mod m i)"
by auto
also have "[u i * b i + (\<Sum>j \<in> A - {i}. u j * b j) =
u i * 1 + (\<Sum>j \<in> A - {i}. u j * 0)] (mod m i)"
apply (rule cong_add_nat)
- apply (rule cong_scalar2_nat)
- using bprop a apply blast
+ apply (rule cong_scalar2_nat)
+ using b a apply blast
apply (rule cong_sum_nat)
apply (rule cong_scalar2_nat)
- using bprop apply auto
+ using b apply auto
apply (rule cong_dvd_modulus_nat)
- apply (drule (1) bspec)
- apply (erule conjE)
- apply assumption
+ apply (drule (1) bspec)
+ apply (erule conjE)
+ apply assumption
apply rule
using fin a apply auto
done
@@ -833,36 +903,35 @@
and u :: "'a \<Rightarrow> nat"
assumes fin: "finite A"
and nz: "\<forall>i\<in>A. m i \<noteq> 0"
- and cop: "\<forall>i\<in>A. (\<forall>j\<in>A. i \<noteq> j \<longrightarrow> coprime (m i) (m j))"
+ and cop: "\<forall>i\<in>A. \<forall>j\<in>A. i \<noteq> j \<longrightarrow> coprime (m i) (m j)"
shows "\<exists>!x. x < (\<Prod>i\<in>A. m i) \<and> (\<forall>i\<in>A. [x = u i] (mod m i))"
proof -
from chinese_remainder_nat [OF fin cop]
- obtain y where one: "(ALL i:A. [y = u i] (mod m i))"
+ obtain y where one: "(\<forall>i\<in>A. [y = u i] (mod m i))"
by blast
let ?x = "y mod (\<Prod>i\<in>A. m i)"
from fin nz have prodnz: "(\<Prod>i\<in>A. m i) \<noteq> 0"
by auto
then have less: "?x < (\<Prod>i\<in>A. m i)"
by auto
- have cong: "ALL i:A. [?x = u i] (mod m i)"
+ have cong: "\<forall>i\<in>A. [?x = u i] (mod m i)"
apply auto
apply (rule cong_trans_nat)
- prefer 2
+ prefer 2
using one apply auto
apply (rule cong_dvd_modulus_nat)
- apply (rule cong_mod_nat)
+ apply (rule cong_mod_nat)
using prodnz apply auto
apply rule
- apply (rule fin)
+ apply (rule fin)
apply assumption
done
- have unique: "ALL z. z < (\<Prod>i\<in>A. m i) \<and>
- (ALL i:A. [z = u i] (mod m i)) \<longrightarrow> z = ?x"
- proof (clarify)
+ have unique: "\<forall>z. z < (\<Prod>i\<in>A. m i) \<and> (\<forall>i\<in>A. [z = u i] (mod m i)) \<longrightarrow> z = ?x"
+ proof clarify
fix z
assume zless: "z < (\<Prod>i\<in>A. m i)"
- assume zcong: "(ALL i:A. [z = u i] (mod m i))"
- have "ALL i:A. [?x = z] (mod m i)"
+ assume zcong: "(\<forall>i\<in>A. [z = u i] (mod m i))"
+ have "\<forall>i\<in>A. [?x = z] (mod m i)"
apply clarify
apply (rule cong_trans_nat)
using cong apply (erule bspec)
@@ -871,14 +940,16 @@
done
with fin cop have "[?x = z] (mod (\<Prod>i\<in>A. m i))"
apply (intro coprime_cong_prod_nat)
- apply auto
+ apply auto
done
with zless less show "z = ?x"
apply (intro cong_less_modulus_unique_nat)
- apply (auto, erule cong_sym_nat)
+ apply auto
+ apply (erule cong_sym_nat)
done
qed
- from less cong unique show ?thesis by blast
+ from less cong unique show ?thesis
+ by blast
qed
end
--- a/src/Pure/Concurrent/future.ML Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/Concurrent/future.ML Tue Aug 08 22:40:05 2017 +0200
@@ -40,7 +40,7 @@
val promise: (unit -> unit) -> 'a future
val fulfill_result: 'a future -> 'a Exn.result -> unit
val fulfill: 'a future -> 'a -> unit
- val group_snapshot: group -> task list
+ val snapshot: group list -> task list
val shutdown: unit -> unit
end;
@@ -638,11 +638,11 @@
fun fulfill x res = fulfill_result x (Exn.Res res);
-(* group snapshot *)
+(* snapshot: current tasks of groups *)
-fun group_snapshot group =
- SYNCHRONIZED "group_snapshot" (fn () =>
- Task_Queue.group_tasks (! queue) group);
+fun snapshot groups =
+ SYNCHRONIZED "snapshot" (fn () =>
+ Task_Queue.group_tasks (! queue) groups);
(* shutdown *)
--- a/src/Pure/Concurrent/task_queue.ML Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/Concurrent/task_queue.ML Tue Aug 08 22:40:05 2017 +0200
@@ -29,7 +29,7 @@
val waiting: task -> task list -> (unit -> 'a) -> 'a
type queue
val empty: queue
- val group_tasks: queue -> group -> task list
+ val group_tasks: queue -> group list -> task list
val known_task: queue -> task -> bool
val all_passive: queue -> bool
val status: queue -> {ready: int, pending: int, running: int, passive: int, urgent: int}
@@ -222,7 +222,11 @@
fun make_queue groups jobs urgent = Queue {groups = groups, jobs = jobs, urgent = urgent};
val empty = make_queue Inttab.empty Task_Graph.empty 0;
-fun group_tasks (Queue {groups, ...}) group = Tasks.keys (get_tasks groups (group_id group));
+fun group_tasks (Queue {groups, ...}) gs =
+ fold (fn g => fn tasks => Tasks.merge (op =) (tasks, get_tasks groups (group_id g)))
+ gs Tasks.empty
+ |> Tasks.keys;
+
fun known_task (Queue {jobs, ...}) task = can (Task_Graph.get_entry jobs) task;
--- a/src/Pure/PIDE/command.ML Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/PIDE/command.ML Tue Aug 08 22:40:05 2017 +0200
@@ -12,6 +12,7 @@
val read: Keyword.keywords -> theory -> Path.T-> (unit -> theory) ->
blob list * int -> Token.T list -> Toplevel.transition
type eval
+ val eval_exec_id: eval -> Document_ID.exec
val eval_eq: eval * eval -> bool
val eval_running: eval -> bool
val eval_finished: eval -> bool
--- a/src/Pure/PIDE/command.scala Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/PIDE/command.scala Tue Aug 08 22:40:05 2017 +0200
@@ -213,6 +213,9 @@
results: Results = Results.empty,
markups: Markups = Markups.empty)
{
+ lazy val consolidated: Boolean =
+ status.exists(markup => markup.name == Markup.CONSOLIDATED)
+
lazy val protocol_status: Protocol.Status =
{
val warnings =
--- a/src/Pure/PIDE/document.ML Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/PIDE/document.ML Tue Aug 08 22:40:05 2017 +0200
@@ -24,6 +24,7 @@
val command_exec: state -> string -> Document_ID.command -> Command.exec option
val remove_versions: Document_ID.version list -> state -> state
val start_execution: state -> state
+ val consolidate_execution: state -> unit
val update: Document_ID.version -> Document_ID.version -> edit list -> state ->
Document_ID.exec list * (Document_ID.command * Document_ID.exec list) list * state
val state: unit -> state
@@ -59,16 +60,17 @@
keywords: Keyword.keywords option, (*outer syntax keywords*)
perspective: perspective, (*command perspective*)
entries: Command.exec option Entries.T, (*command entries with executions*)
- result: Command.eval option} (*result of last execution*)
+ result: Command.eval option, (*result of last execution*)
+ consolidated: unit lazy} (*consolidation status of eval forks*)
and version = Version of node String_Graph.T (*development graph wrt. static imports*)
with
-fun make_node (header, keywords, perspective, entries, result) =
+fun make_node (header, keywords, perspective, entries, result, consolidated) =
Node {header = header, keywords = keywords, perspective = perspective,
- entries = entries, result = result};
+ entries = entries, result = result, consolidated = consolidated};
-fun map_node f (Node {header, keywords, perspective, entries, result}) =
- make_node (f (header, keywords, perspective, entries, result));
+fun map_node f (Node {header, keywords, perspective, entries, result, consolidated}) =
+ make_node (f (header, keywords, perspective, entries, result, consolidated));
fun make_perspective (required, command_ids, overlays) : perspective =
{required = required,
@@ -80,7 +82,7 @@
{master = "", header = Thy_Header.make ("", Position.none) [] [], errors = []};
val no_perspective = make_perspective (false, [], []);
-val empty_node = make_node (no_header, NONE, no_perspective, Entries.empty, NONE);
+val empty_node = make_node (no_header, NONE, no_perspective, Entries.empty, NONE, Lazy.value ());
fun is_no_perspective ({required, visible, visible_last, overlays}: perspective) =
not required andalso
@@ -88,12 +90,13 @@
is_none visible_last andalso
Inttab.is_empty overlays;
-fun is_empty_node (Node {header, keywords, perspective, entries, result}) =
+fun is_empty_node (Node {header, keywords, perspective, entries, result, consolidated}) =
header = no_header andalso
is_none keywords andalso
is_no_perspective perspective andalso
Entries.is_empty entries andalso
- is_none result;
+ is_none result andalso
+ Lazy.is_finished consolidated;
(* basic components *)
@@ -104,14 +107,15 @@
| _ => Path.current);
fun set_header master header errors =
- map_node (fn (_, keywords, perspective, entries, result) =>
- ({master = master, header = header, errors = errors}, keywords, perspective, entries, result));
+ map_node (fn (_, keywords, perspective, entries, result, consolidated) =>
+ ({master = master, header = header, errors = errors},
+ keywords, perspective, entries, result, consolidated));
fun get_header (Node {header, ...}) = header;
fun set_keywords keywords =
- map_node (fn (header, _, perspective, entries, result) =>
- (header, keywords, perspective, entries, result));
+ map_node (fn (header, _, perspective, entries, result, consolidated) =>
+ (header, keywords, perspective, entries, result, consolidated));
fun get_keywords (Node {keywords, ...}) = keywords;
@@ -134,8 +138,8 @@
fun get_perspective (Node {perspective, ...}) = perspective;
fun set_perspective args =
- map_node (fn (header, keywords, _, entries, result) =>
- (header, keywords, make_perspective args, entries, result));
+ map_node (fn (header, keywords, _, entries, result, consolidated) =>
+ (header, keywords, make_perspective args, entries, result, consolidated));
val required_node = #required o get_perspective;
val visible_command = Inttab.defined o #visible o get_perspective;
@@ -144,8 +148,8 @@
val overlays = Inttab.lookup_list o #overlays o get_perspective;
fun map_entries f =
- map_node (fn (header, keywords, perspective, entries, result) =>
- (header, keywords, perspective, f entries, result));
+ map_node (fn (header, keywords, perspective, entries, result, consolidated) =>
+ (header, keywords, perspective, f entries, result, consolidated));
fun get_entries (Node {entries, ...}) = entries;
@@ -158,14 +162,8 @@
fun get_result (Node {result, ...}) = result;
fun set_result result =
- map_node (fn (header, keywords, perspective, entries, _) =>
- (header, keywords, perspective, entries, result));
-
-fun changed_result node node' =
- (case (get_result node, get_result node') of
- (SOME eval, SOME eval') => not (Command.eval_eq (eval, eval'))
- | (NONE, NONE) => false
- | _ => true);
+ map_node (fn (header, keywords, perspective, entries, _, consolidated) =>
+ (header, keywords, perspective, entries, result, consolidated));
fun pending_result node =
(case get_result node of
@@ -177,6 +175,35 @@
SOME eval => Command.eval_finished eval
| NONE => false);
+fun finished_result_theory node =
+ finished_result node andalso
+ let val st = Command.eval_result_state (the (get_result node))
+ in (Toplevel.end_theory Position.none st; true) handle ERROR _ => false end;
+
+val reset_consolidated =
+ map_node (fn (header, keywords, perspective, entries, result, _) =>
+ (header, keywords, perspective, entries, result, Lazy.lazy I));
+
+fun check_consolidated (node as Node {consolidated, ...}) =
+ Lazy.is_finished consolidated orelse
+ finished_result_theory node andalso
+ let
+ val result_id = Command.eval_exec_id (the (get_result node));
+ val eval_ids =
+ iterate_entries (fn (_, opt_exec) => fn eval_ids =>
+ (case opt_exec of
+ SOME (eval, _) => SOME (cons (Command.eval_exec_id eval) eval_ids)
+ | NONE => NONE)) node [];
+ in
+ (case Execution.snapshot eval_ids of
+ [] =>
+ (Lazy.force consolidated;
+ Position.setmp_thread_data (Position.id_only (Document_ID.print result_id))
+ (fn () => Output.status (Markup.markup_only Markup.consolidated)) ();
+ true)
+ | _ => false)
+ end;
+
fun get_node nodes name = String_Graph.get_node nodes name
handle String_Graph.UNDEF _ => empty_node;
fun default_node name = String_Graph.default_node (name, empty_node);
@@ -400,10 +427,16 @@
val the_command_name = #1 oo the_command;
+
+(* execution *)
+
+fun get_execution (State {execution, ...}) = execution;
+fun get_execution_version state = the_version state (#version_id (get_execution state));
+
fun command_exec state node_name command_id =
let
- val State {execution = {version_id, ...}, ...} = state;
- val node = get_node (nodes_of (the_version state version_id)) node_name;
+ val version = get_execution_version state;
+ val node = get_node (nodes_of version) node_name;
in the_entry node command_id end;
end;
@@ -492,6 +525,10 @@
{version_id = version_id, execution_id = execution_id, delay_request = delay_request'};
in (versions, blobs, commands, execution') end));
+fun consolidate_execution state =
+ String_Graph.fold (fn (_, (node, _)) => fn () => ignore (check_consolidated node))
+ (nodes_of (get_execution_version state)) ();
+
(** document update **)
@@ -702,11 +739,13 @@
val removed = maps (removed_execs node0) assign_update;
val _ = List.app Execution.cancel removed;
+ val result_changed =
+ not (eq_option Command.eval_eq (get_result node0, result));
val node' = node
|> assign_update_apply assigned_execs
- |> set_result result;
+ |> set_result result
+ |> result_changed ? reset_consolidated;
val assigned_node = SOME (name, node');
- val result_changed = changed_result node0 node';
in ((removed, assign_update, assigned_node, result_changed), node') end
else (([], [], NONE, false), node)
end))))
--- a/src/Pure/PIDE/document.scala Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/PIDE/document.scala Tue Aug 08 22:40:05 2017 +0200
@@ -453,6 +453,7 @@
def node_name: Node.Name
def node: Node
+ def node_consolidated: Boolean
def commands_loading: List[Command]
def commands_loading_ranges(pred: Node.Name => Boolean): List[Text.Range]
@@ -791,6 +792,11 @@
} yield tree).toList
}
+ def node_consolidated(version: Version, name: Node.Name): Boolean =
+ !name.is_theory ||
+ version.nodes(name).commands.reverse.iterator.
+ flatMap(command_states(version, _)).exists(_.consolidated)
+
// persistent user-view
def snapshot(name: Node.Name = Node.Name.empty, pending_edits: List[Text.Edit] = Nil)
: Snapshot =
@@ -835,6 +841,8 @@
val node_name: Node.Name = name
val node: Node = version.nodes(name)
+ def node_consolidated: Boolean = state.node_consolidated(version, node_name)
+
val commands_loading: List[Command] =
if (node_name.is_theory) Nil
else version.nodes.commands_loading(node_name)
--- a/src/Pure/PIDE/execution.ML Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/PIDE/execution.ML Tue Aug 08 22:40:05 2017 +0200
@@ -80,8 +80,7 @@
| NONE => []);
fun snapshot exec_ids =
- change_state_result (fn state =>
- (maps Future.group_snapshot (maps (exec_groups state) exec_ids), state));
+ change_state_result (`(fn state => Future.snapshot (maps (exec_groups state) exec_ids)));
fun join exec_ids =
(case snapshot exec_ids of
--- a/src/Pure/PIDE/markup.ML Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/PIDE/markup.ML Tue Aug 08 22:40:05 2017 +0200
@@ -159,6 +159,7 @@
val runningN: string val running: T
val finishedN: string val finished: T
val failedN: string val failed: T
+ val consolidatedN: string val consolidated: T
val exec_idN: string
val initN: string
val statusN: string val status: T
@@ -555,6 +556,7 @@
val (runningN, running) = markup_elem "running";
val (finishedN, finished) = markup_elem "finished";
val (failedN, failed) = markup_elem "failed";
+val (consolidatedN, consolidated) = markup_elem "consolidated";
(* messages *)
--- a/src/Pure/PIDE/markup.scala Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/PIDE/markup.scala Tue Aug 08 22:40:05 2017 +0200
@@ -423,6 +423,7 @@
val RUNNING = "running"
val FINISHED = "finished"
val FAILED = "failed"
+ val CONSOLIDATED = "consolidated"
/* interactive documents */
--- a/src/Pure/PIDE/protocol.ML Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/PIDE/protocol.ML Tue Aug 08 22:40:05 2017 +0200
@@ -58,6 +58,10 @@
end);
val _ =
+ Isabelle_Process.protocol_command "Document.consolidate_execution"
+ (fn [] => Document.consolidate_execution (Document.state ()));
+
+val _ =
Isabelle_Process.protocol_command "Document.discontinue_execution"
(fn [] => Execution.discontinue ());
--- a/src/Pure/PIDE/protocol.scala Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/PIDE/protocol.scala Tue Aug 08 22:40:05 2017 +0200
@@ -352,6 +352,9 @@
/* execution */
+ def consolidate_execution(): Unit =
+ protocol_command("Document.consolidate_execution")
+
def discontinue_execution(): Unit =
protocol_command("Document.discontinue_execution")
--- a/src/Pure/PIDE/session.scala Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/PIDE/session.scala Tue Aug 08 22:40:05 2017 +0200
@@ -130,6 +130,7 @@
/* dynamic session options */
def output_delay: Time = session_options.seconds("editor_output_delay")
+ def consolidate_delay: Time = session_options.seconds("editor_consolidate_delay")
def prune_delay: Time = session_options.seconds("editor_prune_delay")
def prune_size: Int = session_options.int("editor_prune_size")
def syslog_limit: Int = session_options.int("editor_syslog_limit")
@@ -191,6 +192,7 @@
private case class Cancel_Exec(exec_id: Document_ID.Exec)
private case class Protocol_Command(name: String, args: List[String])
private case class Update_Options(options: Options)
+ private case object Consolidate_Execution
private case object Prune_History
@@ -519,6 +521,9 @@
prover.get.terminate
}
+ case Consolidate_Execution =>
+ if (prover.defined) prover.get.consolidate_execution()
+
case Prune_History =>
if (prover.defined) {
val old_versions = global_state.change_result(_.remove_versions(prune_size))
@@ -564,6 +569,28 @@
}
}
+ private val consolidator: Thread =
+ Standard_Thread.fork("Session.consolidator", daemon = true) {
+ try {
+ while (true) {
+ Thread.sleep(consolidate_delay.ms)
+
+ val state = global_state.value
+ state.stable_tip_version match {
+ case None =>
+ case Some(version) =>
+ val consolidated =
+ version.nodes.iterator.forall(
+ { case (name, _) =>
+ resources.session_base.loaded_theory(name) ||
+ state.node_consolidated(version, name) })
+ if (!consolidated) manager.send(Consolidate_Execution)
+ }
+ }
+ }
+ catch { case Exn.Interrupt() => }
+ }
+
/* main operations */
@@ -602,6 +629,8 @@
change_parser.shutdown()
change_buffer.shutdown()
+ consolidator.interrupt
+ consolidator.join
manager.shutdown()
dispatcher.shutdown()
--- a/src/Pure/Thy/thy_info.ML Tue Aug 08 13:31:48 2017 +0200
+++ b/src/Pure/Thy/thy_info.ML Tue Aug 08 22:40:05 2017 +0200
@@ -156,8 +156,8 @@
let
val _ = Execution.join [exec_id];
val res = Exn.capture Thm.consolidate_theory theory;
- val errs = maps Task_Queue.group_status (Execution.peek exec_id);
- in res :: map Exn.Exn errs end;
+ val exns = maps Task_Queue.group_status (Execution.peek exec_id);
+ in res :: map Exn.Exn exns end;
datatype task =
Task of Path.T * string list * (theory list -> result) |