--- a/Admin/components/components.sha1 Thu Apr 02 11:45:03 2020 +0200
+++ b/Admin/components/components.sha1 Thu Apr 02 13:04:24 2020 +0200
@@ -266,6 +266,7 @@
3eca4b80710996fff87ed1340dcea2c5f6ebf4f7 scala-2.11.8.tar.gz
0004e53f885fb165b50c95686dec40d99ab0bdbd scala-2.12.0.tar.gz
059cbdc58d36e3ac1fffcccd9139ecd34f271882 scala-2.12.10.tar.gz
+82056106aa6fd37c159ea76d16096c20a749cccd scala-2.12.11.tar.gz
74a8c3dab3a25a87357996ab3e95d825dc820fd0 scala-2.12.2.tar.gz
d66796a68ec3254b46b17b1f8ee5bcc56a93aacf scala-2.12.3.tar.gz
1636556167dff2c191baf502c23f12e09181ef78 scala-2.12.4.tar.gz
--- a/Admin/components/main Thu Apr 02 11:45:03 2020 +0200
+++ b/Admin/components/main Thu Apr 02 13:04:24 2020 +0200
@@ -14,7 +14,7 @@
opam-2.0.6
polyml-5.8.1-20200228
postgresql-42.2.9
-scala-2.12.10
+scala-2.12.11
smbc-0.4.1
spass-3.8ds-1
sqlite-jdbc-3.30.1
--- a/CONTRIBUTORS Thu Apr 02 11:45:03 2020 +0200
+++ b/CONTRIBUTORS Thu Apr 02 13:04:24 2020 +0200
@@ -3,6 +3,10 @@
listed as an author in one of the source files of this Isabelle distribution.
+Contributions to this Isabelle version
+--------------------------------------
+
+
Contributions to Isabelle2020
-----------------------------
--- a/NEWS Thu Apr 02 11:45:03 2020 +0200
+++ b/NEWS Thu Apr 02 13:04:24 2020 +0200
@@ -4,6 +4,11 @@
(Note: Isabelle/jEdit shows a tree-view of the NEWS file in Sidekick.)
+New in this Isabelle version
+----------------------------
+
+
+
New in Isabelle2020 (April 2020)
--------------------------------
--- a/README_REPOSITORY Thu Apr 02 11:45:03 2020 +0200
+++ b/README_REPOSITORY Thu Apr 02 13:04:24 2020 +0200
@@ -34,8 +34,6 @@
./bin/isabelle jedit -l HOL
- ./bin/isabelle jedit -b -f #optional: force fresh build of Isabelle/Scala
-
4. Access documentation (bash shell commands):
./bin/isabelle build_doc -a
@@ -48,11 +46,9 @@
Mercurial https://www.mercurial-scm.org belongs to source code
management systems that follow the so-called paradigm of "distributed
-version control". This means plain revision control without the
-legacy of CVS or SVN (and without the extra complexity introduced by
-git). See also http://hginit.com/ for an introduction to the main
-ideas. The Mercurial book http://hgbook.red-bean.com/ explains many
-more details.
+version control". This means plain versioning without the legacy of
+SVN and the extra complexity of GIT. See also
+https://www.mercurial-scm.org/learn
Mercurial offers some flexibility in organizing the flow of changes,
both between individual developers and designated pull/push areas that
@@ -100,7 +96,7 @@
as follows:
[ui]
- username = XXX
+ username = ABC
Isabelle contributors are free to choose either a short "login name"
(for accounts at TU Munich) or a "full name" -- with or without mail
@@ -136,8 +132,7 @@
quite easy to publish changed clones again on the web, using the
ad-hoc command "hg serve -v", or the hgweb.cgi or hgwebdir.cgi scripts
that are included in the Mercurial distribution, and send a "pull
-request" to someone else. There are also public hosting services for
-Mercurial repositories, notably Bitbucket.
+request" to someone else.
The downstream/upstream mode of operation is quite common in the
distributed version control community, and works well for occasional
--- a/etc/options Thu Apr 02 11:45:03 2020 +0200
+++ b/etc/options Thu Apr 02 13:04:24 2020 +0200
@@ -123,6 +123,9 @@
option system_heaps : bool = false
-- "store session heaps in $ISABELLE_HEAPS_SYSTEM, not $ISABELLE_HEAPS"
+option pide_build : bool = false
+ -- "build session heaps via PIDE"
+
section "ML System"
--- a/src/Doc/System/Environment.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Doc/System/Environment.thy Thu Apr 02 13:04:24 2020 +0200
@@ -390,8 +390,8 @@
\<^medskip>
This is how to invoke a function body with proper return code and printing
of errors, and without printing of a redundant \<^verbatim>\<open>val it = (): unit\<close> result:
- @{verbatim [display] \<open>isabelle process -e 'Command_Line.tool0 (fn () => writeln "OK")'\<close>}
- @{verbatim [display] \<open>isabelle process -e 'Command_Line.tool0 (fn () => error "Bad")'\<close>}
+ @{verbatim [display] \<open>isabelle process -e 'Command_Line.tool (fn () => writeln "OK")'\<close>}
+ @{verbatim [display] \<open>isabelle process -e 'Command_Line.tool (fn () => error "Bad")'\<close>}
\<close>
--- a/src/HOL/Analysis/Abstract_Euclidean_Space.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Abstract_Euclidean_Space.thy Thu Apr 02 13:04:24 2020 +0200
@@ -158,7 +158,7 @@
by (simp add: contractible_imp_path_connected_space)
lemma connected_Euclidean_space: "connected_space (Euclidean_space n)"
- by (simp add: contractible_Euclidean_space contractible_imp_connected_space)
+ by (simp add: contractible_imp_connected_space)
lemma locally_path_connected_Euclidean_space:
"locally_path_connected_space (Euclidean_space n)"
--- a/src/HOL/Analysis/Abstract_Topology.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Abstract_Topology.thy Thu Apr 02 13:04:24 2020 +0200
@@ -2383,12 +2383,6 @@
by (simp add: closed_map_id continuous_closed_imp_quotient_map)
qed
-lemma homeomorphic_maps_i [simp]:"homeomorphic_maps X Y id id \<longleftrightarrow> Y = X"
- by (metis (full_types) eq_id_iff homeomorphic_maps_id)
-
-lemma homeomorphic_map_i [simp]: "homeomorphic_map X Y id \<longleftrightarrow> Y = X"
- by (metis (no_types) eq_id_iff homeomorphic_map_id)
-
lemma homeomorphic_map_compose:
assumes "homeomorphic_map X Y f" "homeomorphic_map Y X'' g"
shows "homeomorphic_map X X'' (g \<circ> f)"
--- a/src/HOL/Analysis/Arcwise_Connected.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Arcwise_Connected.thy Thu Apr 02 13:04:24 2020 +0200
@@ -1789,13 +1789,13 @@
have "False" if "\<xi> \<in> F n" "u < \<xi>" "\<xi> < v" for \<xi>
proof -
have "\<xi> \<notin> {z..v}"
- by (metis DiffI disjoint_iff_not_equal less_irrefl singletonD that v(3))
+ by (metis DiffI disjoint_iff_not_equal less_irrefl singletonD that(1,3) v(3))
moreover have "\<xi> \<notin> {w..z} \<inter> F n"
by (metis equals0D wzF_null)
ultimately have "\<xi> \<in> {u..w}"
using that by auto
then show ?thesis
- by (metis DiffI disjoint_iff_not_equal less_eq_real_def not_le singletonD that u(3))
+ by (metis DiffI disjoint_iff_not_equal less_eq_real_def not_le singletonD that(1,2) u(3))
qed
moreover
have "\<lbrakk>\<xi> \<in> F n; v < \<xi>; \<xi> < u\<rbrakk> \<Longrightarrow> False" for \<xi>
@@ -1811,7 +1811,7 @@
by (metis dist_norm dist_triangle_half_r less_irrefl)
qed (auto simp: open_segment_commute)
show ?thesis
- unfolding \<phi>_def by (metis (no_types, hide_lams) INT_I Inf_lower2 rangeI that F01 subsetCE pqF)
+ unfolding \<phi>_def by (metis (no_types, hide_lams) INT_I Inf_lower2 rangeI that(3) F01 subsetCE pqF)
qed
show "closed {0..1::real}" by auto
qed (meson \<phi>_def)
@@ -1972,7 +1972,7 @@
show "pathstart (subpath u v g) = a" "pathfinish (subpath u v g) = b"
by (simp_all add: \<open>a = g u\<close> \<open>b = g v\<close>)
show "path_image (subpath u v g) \<subseteq> path_image p"
- by (metis \<open>arc g\<close> \<open>u \<in> {0..1}\<close> \<open>v \<in> {0..1}\<close> arc_imp_path order_trans pag path_image_def path_image_subpath_subset ph)
+ by (metis \<open>u \<in> {0..1}\<close> \<open>v \<in> {0..1}\<close> order_trans pag path_image_def path_image_subpath_subset ph)
show "arc (subpath u v g)"
using \<open>arc g\<close> \<open>a = g u\<close> \<open>b = g v\<close> \<open>u \<in> {0..1}\<close> \<open>v \<in> {0..1}\<close> arc_subpath_arc \<open>a \<noteq> b\<close> by blast
qed
@@ -2049,7 +2049,7 @@
and g: "pathstart g = y" "pathfinish g = z"
using \<open>y \<noteq> z\<close> by (force simp: path_connected_arcwise)
have "compact (g -` frontier S \<inter> {0..1})"
- apply (simp add: compact_eq_bounded_closed bounded_Int bounded_closed_interval)
+ apply (simp add: compact_eq_bounded_closed bounded_Int)
apply (rule closed_vimage_Int)
using \<open>arc g\<close> apply (auto simp: arc_def path_def)
done
--- a/src/HOL/Analysis/Ball_Volume.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Ball_Volume.thy Thu Apr 02 13:04:24 2020 +0200
@@ -46,7 +46,7 @@
(auto intro!: derivative_eq_intros continuous_intros simp: set_borel_measurable_def)
also have "\<dots> = (\<integral>\<^sup>+ x. 2 * ennreal ((1 - x\<^sup>2) powr (real n / 2) * indicator {0..1} x) \<partial>lborel)"
by (intro nn_integral_cong_AE AE_I[of _ _ "{0}"])
- (auto simp: indicator_def powr_minus powr_half_sqrt field_split_simps ennreal_mult' mult_ac)
+ (auto simp: indicator_def powr_minus powr_half_sqrt field_split_simps ennreal_mult')
also have "\<dots> = (\<integral>\<^sup>+ x. ennreal ((1 - x\<^sup>2) powr (real n / 2) * indicator {0..1} x) \<partial>lborel) +
(\<integral>\<^sup>+ x. ennreal ((1 - x\<^sup>2) powr (real n / 2) * indicator {0..1} x) \<partial>lborel)"
(is "_ = ?I + _") by (simp add: mult_2 nn_integral_add)
@@ -137,7 +137,7 @@
proof (cases "y \<in> {-r<..<r}")
case True
hence "y\<^sup>2 < r\<^sup>2" by (subst real_sqrt_less_iff [symmetric]) auto
- thus ?thesis by (subst insert.IH) (auto simp: real_sqrt_less_iff)
+ thus ?thesis by (subst insert.IH) (auto)
qed (insert elim, auto)
qed
qed
--- a/src/HOL/Analysis/Bochner_Integration.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Bochner_Integration.thy Thu Apr 02 13:04:24 2020 +0200
@@ -403,7 +403,7 @@
from g have "simple_bochner_integral M (\<lambda>x. f (g x)) =
(\<Sum>y\<in>g ` space M. measure M {x \<in> space M. g x = y} *\<^sub>R f y)"
by (intro simple_bochner_integral_partition)
- (auto simp: simple_bochner_integrable_compose2[where p="\<lambda>x y. f x"] zero
+ (auto simp: simple_bochner_integrable_compose2[where p="\<lambda>x y. f x"]
elim: simple_bochner_integrable.cases)
also have "\<dots> = f (simple_bochner_integral M g)"
by (simp add: simple_bochner_integral_def sum scale)
@@ -1379,7 +1379,7 @@
lemma integral_minus_iff[simp]:
"integrable M (\<lambda>x. - f x ::'a::{banach, second_countable_topology}) \<longleftrightarrow> integrable M f"
unfolding integrable_iff_bounded
- by (auto intro: borel_measurable_uminus[of "\<lambda>x. - f x" M, simplified])
+ by (auto)
lemma integrable_indicator_iff:
"integrable M (indicator A::_ \<Rightarrow> real) \<longleftrightarrow> A \<inter> space M \<in> sets M \<and> emeasure M (A \<inter> space M) < \<infinity>"
@@ -1634,7 +1634,7 @@
with seq show "\<exists>N. \<forall>n\<ge>N. 0 \<le> integral\<^sup>L M (U n)"
by auto
qed
- qed (auto simp: integrable_mult_left_iff)
+ qed (auto)
also have "\<dots> = integral\<^sup>L M f"
using nonneg by (auto intro!: integral_cong_AE)
finally show ?thesis .
@@ -1657,7 +1657,7 @@
by (simp add: integrable_indicator_iff ennreal_indicator emeasure_eq_ennreal_measure)
next
case (mult f c) then show ?case
- by (auto simp add: integrable_mult_left_iff nn_integral_cmult ennreal_mult integral_nonneg_AE)
+ by (auto simp add: nn_integral_cmult ennreal_mult integral_nonneg_AE)
next
case (add g f)
then have "integrable M f" "integrable M g"
@@ -2756,7 +2756,7 @@
by (auto split: split_indicator simp: eq_commute[of x] cong: conj_cong)
qed
also have "\<dots> = (\<Sum>a\<in>A. f a * measure M {a})"
- using finite by (subst integral_sum) (auto simp add: integrable_mult_left_iff)
+ using finite by (subst integral_sum) (auto)
finally show ?thesis .
qed
--- a/src/HOL/Analysis/Borel_Space.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Borel_Space.thy Thu Apr 02 13:04:24 2020 +0200
@@ -1758,7 +1758,7 @@
also have "\<dots> < ?I i / 2 + ?I i / 2"
by (intro add_strict_mono d less_trans[OF _ j] *)
also have "\<dots> \<le> ?I i"
- by (simp add: field_simps of_nat_Suc)
+ by (simp add: field_simps)
finally show "dist (f y) (f z) \<le> ?I i"
by simp
qed
--- a/src/HOL/Analysis/Bounded_Linear_Function.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Bounded_Linear_Function.thy Thu Apr 02 13:04:24 2020 +0200
@@ -420,7 +420,7 @@
using b
by (simp add: inner_sum_left inner_Basis if_distrib cong: if_cong) (simp add: sum.swap)
also have "\<dots> = (\<Sum>i\<in>Basis. (x \<bullet> i * (f i \<bullet> b)))"
- using b by (simp add: sum.delta)
+ using b by (simp)
also have "\<dots> = f x \<bullet> b"
by (metis (mono_tags, lifting) Linear_Algebra.linear_componentwise linear_axioms)
finally show "(\<Sum>j\<in>Basis. \<Sum>i\<in>Basis. (x \<bullet> i * (f i \<bullet> j)) *\<^sub>R j) \<bullet> b = f x \<bullet> b" .
--- a/src/HOL/Analysis/Cartesian_Space.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Cartesian_Space.thy Thu Apr 02 13:04:24 2020 +0200
@@ -1436,7 +1436,7 @@
using idplus [OF \<open>m \<noteq> n\<close>] by simp
qed
then show ?thesis
- by (metis \<open>linear f\<close> matrix_vector_mul)
+ by (metis \<open>linear f\<close> matrix_vector_mul(2))
qed
end
\ No newline at end of file
--- a/src/HOL/Analysis/Change_Of_Vars.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Change_Of_Vars.thy Thu Apr 02 13:04:24 2020 +0200
@@ -543,7 +543,7 @@
also have "\<dots> = norm (f' x (y - x) - (f y - f x)) / r"
using \<open>r > 0\<close> by (simp add: divide_simps scale_right_diff_distrib [symmetric])
also have "\<dots> \<le> norm (f y - (f x + f' x (y - x))) / norm (y - x)"
- using that \<open>r > 0\<close> False by (simp add: algebra_simps field_split_simps dist_norm norm_minus_commute mult_right_mono)
+ using that \<open>r > 0\<close> False by (simp add: field_split_simps dist_norm norm_minus_commute mult_right_mono)
also have "\<dots> < k"
using that \<open>0 < \<zeta>\<close> by (simp add: dist_commute r_def \<zeta> [OF \<open>y \<in> S\<close> False])
finally show "dist (f' x ((y - x) /\<^sub>R r)) ((f y - f x) /\<^sub>R r) < k" .
@@ -1656,7 +1656,7 @@
show "linear ((*v) (matrix (f' x) - B))"
by (rule matrix_vector_mul_linear)
have "((\<lambda>y. ((f x + f' x (y - x)) - f y) /\<^sub>R norm (y - x)) \<longlongrightarrow> 0) (at x within S)"
- using tendsto_minus [OF lim_df] by (simp add: algebra_simps field_split_simps)
+ using tendsto_minus [OF lim_df] by (simp add: field_split_simps)
then show "((\<lambda>y. (matrix (f' x) - B) *v (y - x) /\<^sub>R norm (y - x)) \<longlongrightarrow> 0) (at x within S)"
proof (rule Lim_transform)
have "((\<lambda>y. ((f y + B *v x - (f x + B *v y)) /\<^sub>R norm (y - x))) \<longlongrightarrow> 0) (at x within S)"
@@ -1724,7 +1724,7 @@
then show "((\<lambda>y. (matrix (f' x) - B) *v (y - x) /\<^sub>R
norm (y - x) - (f x + f' x (y - x) - f y) /\<^sub>R norm (y - x)) \<longlongrightarrow> 0)
(at x within S)"
- by (simp add: algebra_simps diff lin_df matrix_vector_mul_linear scalar_mult_eq_scaleR)
+ by (simp add: algebra_simps diff lin_df scalar_mult_eq_scaleR)
qed
qed (use x in \<open>simp; auto simp: not_less\<close>)
ultimately have "f' x = (*v) B"
@@ -2168,7 +2168,7 @@
proof (rule order_trans [OF measT])
have "?DVU = (d * 2 * (4 * B) ^ (?n - 1)) * norm (v - u)^?n"
using \<open>c > 0\<close>
- apply (simp add: algebra_simps power_mult_distrib)
+ apply (simp add: algebra_simps)
by (metis Suc_pred power_Suc zero_less_card_finite)
also have "\<dots> \<le> (e / (2*c) ^ ?m / (?m ^ ?m)) * norm(v - u) ^ ?n"
by (rule mult_right_mono [OF d]) auto
@@ -2239,7 +2239,7 @@
using \<open>c > 0\<close> by (simp add: content_cbox_if_cart)
finally have "sum ?\<mu> \<F> \<le> (2 ^ ?m * c ^ ?m)" .
then show ?thesis
- using \<open>e > 0\<close> \<open>c > 0\<close> by (auto simp: field_split_simps mult_less_0_iff)
+ using \<open>e > 0\<close> \<open>c > 0\<close> by (auto simp: field_split_simps)
qed
finally show ?thesis .
qed
@@ -2384,7 +2384,7 @@
done
ultimately show ?thesis
using \<open>y > 0\<close> integral_restrict_Int [of S "{t. h n (g t) = y}" "\<lambda>t. \<bar>det (matrix (g' t))\<bar> * y"]
- apply (simp add: integrable_on_indicator integrable_on_cmult_iff integral_indicator)
+ apply (simp add: integrable_on_indicator integral_indicator)
apply (simp add: indicator_def if_distrib cong: if_cong)
done
qed
--- a/src/HOL/Analysis/Complex_Analysis_Basics.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Complex_Analysis_Basics.thy Thu Apr 02 13:04:24 2020 +0200
@@ -489,7 +489,7 @@
lemma analytic_on_sum [analytic_intros]:
"(\<And>i. i \<in> I \<Longrightarrow> (f i) analytic_on S) \<Longrightarrow> (\<lambda>x. sum (\<lambda>i. f i x) I) analytic_on S"
- by (induct I rule: infinite_finite_induct) (auto simp: analytic_on_const analytic_on_add)
+ by (induct I rule: infinite_finite_induct) (auto simp: analytic_on_add)
lemma deriv_left_inverse:
assumes "f holomorphic_on S" and "g holomorphic_on T"
@@ -579,11 +579,11 @@
lemma deriv_cmult_at:
"f analytic_on {z} \<Longrightarrow> deriv (\<lambda>w. c * f w) z = c * deriv f z"
-by (auto simp: complex_derivative_mult_at deriv_const analytic_on_const)
+by (auto simp: complex_derivative_mult_at)
lemma deriv_cmult_right_at:
"f analytic_on {z} \<Longrightarrow> deriv (\<lambda>w. f w * c) z = deriv f z * c"
-by (auto simp: complex_derivative_mult_at deriv_const analytic_on_const)
+by (auto simp: complex_derivative_mult_at)
subsection\<^marker>\<open>tag unimportant\<close>\<open>Complex differentiation of sequences and series\<close>
@@ -758,7 +758,7 @@
apply (rule field_differentiable_bound
[where f' = "\<lambda>w. f (Suc n) w * (z - w)^n / (fact n)"
and S = "closed_segment w z", OF convex_closed_segment])
- apply (auto simp: ends_in_segment DERIV_subset [OF sum_deriv wzs]
+ apply (auto simp: DERIV_subset [OF sum_deriv wzs]
norm_divide norm_mult norm_power divide_le_cancel cmod_bound)
done
also have "... \<le> B * norm (z - w) ^ Suc n / (fact n)"
--- a/src/HOL/Analysis/Complex_Transcendental.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Complex_Transcendental.thy Thu Apr 02 13:04:24 2020 +0200
@@ -612,7 +612,7 @@
apply (simp add: cos_add cmod_power2 cos_of_real sin_of_real Complex_eq)
apply (simp add: cos_exp_eq sin_exp_eq exp_minus exp_of_real Re_divide Im_divide power_divide)
apply (simp only: left_diff_distrib [symmetric] power_mult_distrib sin_squared_eq)
- apply (simp add: power2_eq_square algebra_simps field_split_simps)
+ apply (simp add: power2_eq_square field_split_simps)
done
lemma norm_sin_squared:
@@ -621,7 +621,7 @@
apply (simp add: sin_add cmod_power2 cos_of_real sin_of_real cos_double_cos exp_double Complex_eq)
apply (simp add: cos_exp_eq sin_exp_eq exp_minus exp_of_real Re_divide Im_divide power_divide)
apply (simp only: left_diff_distrib [symmetric] power_mult_distrib cos_squared_eq)
- apply (simp add: power2_eq_square algebra_simps field_split_simps)
+ apply (simp add: power2_eq_square field_split_simps)
done
lemma exp_uminus_Im: "exp (- Im z) \<le> exp (cmod z)"
@@ -1102,7 +1102,7 @@
by auto
lemma Arg2pi_cnj_eq_inverse: "z\<noteq>0 \<Longrightarrow> Arg2pi (cnj z) = Arg2pi (inverse z)"
- apply (simp add: Arg2pi_eq_iff field_split_simps complex_norm_square [symmetric] mult.commute)
+ apply (simp add: Arg2pi_eq_iff field_split_simps complex_norm_square [symmetric])
by (metis of_real_power zero_less_norm_iff zero_less_power)
lemma Arg2pi_cnj: "Arg2pi(cnj z) = (if z \<in> \<real> then Arg2pi z else 2*pi - Arg2pi z)"
@@ -1946,7 +1946,7 @@
by (metis Arg_eq_0 Arg_inverse inverse_inverse_eq)
lemma Arg_cnj_eq_inverse: "z\<noteq>0 \<Longrightarrow> Arg (cnj z) = Arg (inverse z)"
- apply (simp add: Arg_eq_iff field_split_simps complex_norm_square [symmetric] mult.commute)
+ apply (simp add: Arg_eq_iff field_split_simps complex_norm_square [symmetric])
by (metis of_real_power zero_less_norm_iff zero_less_power)
lemma Arg_cnj: "Arg(cnj z) = (if z \<in> \<real> then Arg z else - Arg z)"
@@ -2936,7 +2936,7 @@
unfolding Arctan_def scaleR_conv_of_real
apply (intro derivative_eq_intros | simp add: nz0 *)+
using nz0 nz1 zz
- apply (simp add: algebra_simps field_split_simps power2_eq_square)
+ apply (simp add: field_split_simps power2_eq_square)
apply algebra
done
qed
@@ -3014,7 +3014,7 @@
have "\<exists>c. \<forall>u\<in>ball 0 1. Arctan u - G u = c"
proof (rule has_field_derivative_zero_constant)
fix u :: complex assume "u \<in> ball 0 1"
- hence u: "norm u < 1" by (simp add: dist_0_norm)
+ hence u: "norm u < 1" by (simp)
define K where "K = (norm u + 1) / 2"
from u and abs_Im_le_cmod[of u] have Im_u: "\<bar>Im u\<bar> < 1" by linarith
from u have K: "0 \<le> K" "norm u < K" "K < 1" by (simp_all add: K_def)
@@ -3634,7 +3634,7 @@
assumes "z\<^sup>2 \<noteq> 1" shows "cos(Arcsin z) \<noteq> 0"
proof -
have eq: "(\<i> * z * (csqrt (1 - z\<^sup>2)))\<^sup>2 = z\<^sup>2 * (z\<^sup>2 - 1)"
- by (simp add: power_mult_distrib algebra_simps)
+ by (simp add: algebra_simps)
have "\<i> * z * (csqrt (1 - z\<^sup>2)) \<noteq> z\<^sup>2 - 1"
proof
assume "\<i> * z * (csqrt (1 - z\<^sup>2)) = z\<^sup>2 - 1"
@@ -3665,7 +3665,7 @@
assumes "z\<^sup>2 \<noteq> 1" shows "sin(Arccos z) \<noteq> 0"
proof -
have eq: "(\<i> * z * (csqrt (1 - z\<^sup>2)))\<^sup>2 = -(z\<^sup>2) * (1 - z\<^sup>2)"
- by (simp add: power_mult_distrib algebra_simps)
+ by (simp add: algebra_simps)
have "\<i> * z * (csqrt (1 - z\<^sup>2)) \<noteq> 1 - z\<^sup>2"
proof
assume "\<i> * z * (csqrt (1 - z\<^sup>2)) = 1 - z\<^sup>2"
@@ -3971,7 +3971,7 @@
shows "exp(2 * of_real pi * \<i> * of_nat j / of_nat n)^n = 1"
proof -
have *: "of_nat j * (complex_of_real pi * 2) = complex_of_real (2 * real j * pi)"
- by (simp add: of_real_numeral)
+ by (simp)
then show ?thesis
apply (simp add: exp_of_nat_mult [symmetric] mult_ac exp_Euler)
apply (simp only: * cos_of_real sin_of_real)
@@ -4006,7 +4006,7 @@
note * = this
show ?thesis
using assms
- by (simp add: exp_eq field_split_simps mult_ac of_real_numeral *)
+ by (simp add: exp_eq field_split_simps *)
qed
corollary bij_betw_roots_unity:
--- a/src/HOL/Analysis/Convex_Euclidean_Space.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Convex_Euclidean_Space.thy Thu Apr 02 13:04:24 2020 +0200
@@ -346,7 +346,7 @@
proof-
have "{a..b} = {a..} \<inter> {..b}" by auto
also have "interior \<dots> = {a<..} \<inter> {..<b}"
- by (simp add: interior_real_atLeast interior_real_atMost)
+ by (simp)
also have "\<dots> = {a<..<b}" by auto
finally show ?thesis .
qed
--- a/src/HOL/Analysis/Cross3.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Cross3.thy Thu Apr 02 13:04:24 2020 +0200
@@ -100,7 +100,7 @@
lemma cross_basis_nonzero:
"u \<noteq> 0 \<Longrightarrow> u \<times> axis 1 1 \<noteq> 0 \<or> u \<times> axis 2 1 \<noteq> 0 \<or> u \<times> axis 3 1 \<noteq> 0"
- by (clarsimp simp add: axis_def cross3_simps) (metis vector_3 exhaust_3)
+ by (clarsimp simp add: axis_def cross3_simps) (metis exhaust_3)
lemma cross_dot_cancel:
fixes x::"real^3"
--- a/src/HOL/Analysis/Derivative.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Derivative.thy Thu Apr 02 13:04:24 2020 +0200
@@ -1056,7 +1056,7 @@
by (rule openE)
then have "\<exists>c. \<forall>x\<in>ball a e. f x = c"
by (intro has_derivative_zero_constant)
- (auto simp: at_within_open[OF _ open_ball] f convex_ball)
+ (auto simp: at_within_open[OF _ open_ball] f)
with \<open>0<e\<close> have "\<forall>x\<in>ball a e. f a = f x"
by auto
then show "eventually (\<lambda>b. f a = f b) (at a within s)"
@@ -2187,7 +2187,7 @@
show "((\<lambda>y. (exp (y *\<^sub>R A) - exp (t *\<^sub>R A) - (y - t) *\<^sub>R (exp (t *\<^sub>R A) * A)) /\<^sub>R norm (y - t)) \<longlongrightarrow> 0)
(at t within T)"
by (rule Lim_transform_eventually)
- (auto simp: algebra_simps field_split_simps exp_add_commuting[symmetric])
+ (auto simp: field_split_simps exp_add_commuting[symmetric])
qed (rule bounded_linear_scaleR_left)
lemma exp_times_scaleR_commute: "exp (t *\<^sub>R A) * A = A * exp (t *\<^sub>R A)"
--- a/src/HOL/Analysis/Elementary_Metric_Spaces.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Elementary_Metric_Spaces.thy Thu Apr 02 13:04:24 2020 +0200
@@ -109,7 +109,7 @@
qed
lemma open_contains_ball: "open S \<longleftrightarrow> (\<forall>x\<in>S. \<exists>e>0. ball x e \<subseteq> S)"
- by (simp add: open_dist subset_eq mem_ball Ball_def dist_commute)
+ by (simp add: open_dist subset_eq Ball_def dist_commute)
lemma openI [intro?]: "(\<And>x. x\<in>S \<Longrightarrow> \<exists>e>0. ball x e \<subseteq> S) \<Longrightarrow> open S"
by (auto simp: open_contains_ball)
--- a/src/HOL/Analysis/Elementary_Normed_Spaces.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Elementary_Normed_Spaces.thy Thu Apr 02 13:04:24 2020 +0200
@@ -798,7 +798,7 @@
corollary cobounded_imp_unbounded:
fixes S :: "'a::{real_normed_vector, perfect_space} set"
shows "bounded (- S) \<Longrightarrow> \<not> bounded S"
- using bounded_Un [of S "-S"] by (simp add: sup_compl_top)
+ using bounded_Un [of S "-S"] by (simp)
subsection\<^marker>\<open>tag unimportant\<close>\<open>Relations among convergence and absolute convergence for power series\<close>
--- a/src/HOL/Analysis/Embed_Measure.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Embed_Measure.thy Thu Apr 02 13:04:24 2020 +0200
@@ -251,7 +251,7 @@
have fg[simp]: "\<And>A. inj_on (map_prod f g) A" "\<And>A. inj_on f A" "\<And>A. inj_on g A"
using f g by (auto simp: inj_on_def)
- note complete_lattice_class.Sup_insert[simp del] ccSup_insert[simp del] SUP_insert[simp del]
+ note complete_lattice_class.Sup_insert[simp del] ccSup_insert[simp del]
ccSUP_insert[simp del]
show sets: "sets ?L = sets (embed_measure (M \<Otimes>\<^sub>M N) (map_prod f g))"
unfolding map_prod_def[symmetric]
--- a/src/HOL/Analysis/Equivalence_Lebesgue_Henstock_Integration.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Equivalence_Lebesgue_Henstock_Integration.thy Thu Apr 02 13:04:24 2020 +0200
@@ -3357,7 +3357,7 @@
have eq: "?g =
(\<lambda>x. \<Sum>i\<in>Basis. ((\<lambda>y. \<Sum>j\<in>Basis. if j = i then y *\<^sub>R j else 0) \<circ>
(\<lambda>x. norm(\<Sum>j\<in>Basis. if j = i then (x \<bullet> i) *\<^sub>R j else 0)) \<circ> f) x)"
- by (simp add: sum.delta)
+ by (simp)
have *: "(\<lambda>y. \<Sum>j\<in>Basis. if j = i then y *\<^sub>R j else 0) \<circ>
(\<lambda>x. norm (\<Sum>j\<in>Basis. if j = i then (x \<bullet> i) *\<^sub>R j else 0)) \<circ> f
absolutely_integrable_on S"
--- a/src/HOL/Analysis/Equivalence_Measurable_On_Borel.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Equivalence_Measurable_On_Borel.thy Thu Apr 02 13:04:24 2020 +0200
@@ -742,7 +742,7 @@
show "continuous_on UNIV (g \<circ> (\<theta> n))" for n :: nat
unfolding \<theta>_def
apply (intro continuous_on_compose2 [OF contg] continuous_intros conth)
- apply (auto simp: aibi * mem_box less_max_iff_disj min_less_iff_disj algebra_simps field_split_simps)
+ apply (auto simp: aibi * mem_box less_max_iff_disj min_less_iff_disj field_split_simps)
done
show "(\<lambda>n. (g \<circ> \<theta> n) x) \<longlonglongrightarrow> g (f x)"
if "x \<notin> N" for x
--- a/src/HOL/Analysis/Extended_Real_Limits.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Extended_Real_Limits.thy Thu Apr 02 13:04:24 2020 +0200
@@ -304,7 +304,7 @@
fix P d
assume "0 < d" and "\<forall>y. y \<in> S \<longrightarrow> y \<noteq> x \<and> dist y x < d \<longrightarrow> P y"
then have "S \<inter> ball x d - {x} \<subseteq> {x. P x}"
- by (auto simp: zero_less_dist_iff dist_commute)
+ by (auto simp: dist_commute)
then show "\<exists>r>0. Inf (f ` (Collect P)) \<le> Inf (f ` (S \<inter> ball x r - {x}))"
by (intro exI[of _ d] INF_mono conjI \<open>0 < d\<close>) auto
next
@@ -324,7 +324,7 @@
fix P d
assume "0 < d" and "\<forall>y. y \<in> S \<longrightarrow> y \<noteq> x \<and> dist y x < d \<longrightarrow> P y"
then have "S \<inter> ball x d - {x} \<subseteq> {x. P x}"
- by (auto simp: zero_less_dist_iff dist_commute)
+ by (auto simp: dist_commute)
then show "\<exists>r>0. Sup (f ` (S \<inter> ball x r - {x})) \<le> Sup (f ` (Collect P))"
by (intro exI[of _ d] SUP_mono conjI \<open>0 < d\<close>) auto
next
--- a/src/HOL/Analysis/FPS_Convergence.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/FPS_Convergence.thy Thu Apr 02 13:04:24 2020 +0200
@@ -429,7 +429,7 @@
have "(\<lambda>n. norm (c * z) ^ n /\<^sub>R fact n) sums exp (norm (c * z))"
by (rule exp_converges)
also have "(\<lambda>n. norm (c * z) ^ n /\<^sub>R fact n) = (\<lambda>n. norm (fps_nth (fps_exp c) n * z ^ n))"
- by (rule ext) (simp add: norm_divide norm_mult norm_power field_split_simps power_mult_distrib)
+ by (rule ext) (simp add: norm_divide norm_mult norm_power field_split_simps)
finally have "summable \<dots>" by (simp add: sums_iff)
thus "summable (\<lambda>n. fps_nth (fps_exp c) n * z ^ n)"
by (rule summable_norm_cancel)
@@ -585,7 +585,7 @@
lemma eval_fps_exp [simp]:
fixes c :: "'a :: {banach, real_normed_field}"
shows "eval_fps (fps_exp c) z = exp (c * z)" unfolding eval_fps_def exp_def
- by (simp add: eval_fps_def exp_def scaleR_conv_of_real field_split_simps power_mult_distrib)
+ by (simp add: eval_fps_def exp_def scaleR_conv_of_real field_split_simps)
text \<open>
The case of division is more complicated and will therefore not be handled here.
--- a/src/HOL/Analysis/Fashoda_Theorem.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Fashoda_Theorem.thy Thu Apr 02 13:04:24 2020 +0200
@@ -677,10 +677,10 @@
path_image(linepath(pathfinish g)(vector[(pathfinish g)$1,a$2 - 1])) \<union>
path_image(linepath(vector[(pathfinish g)$1,a$2 - 1])(vector[b$1 + 1,a$2 - 1])) \<union>
path_image(linepath(vector[b$1 + 1,a$2 - 1])(vector[b$1 + 1,b$2 + 3]))" using assms(1-2)
- by(auto simp add: path_image_join path_linepath)
+ by(auto simp add: path_image_join)
have abab: "cbox a b \<subseteq> cbox ?a ?b"
unfolding interval_cbox_cart[symmetric]
- by (auto simp add:less_eq_vec_def forall_2 vector_2)
+ by (auto simp add:less_eq_vec_def forall_2)
obtain z where
"z \<in> path_image
(linepath (vector [a $ 1 - 2, a $ 2 - 2]) (vector [pathstart f $ 1, a $ 2 - 2]) +++
--- a/src/HOL/Analysis/Function_Metric.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Function_Metric.thy Thu Apr 02 13:04:24 2020 +0200
@@ -187,7 +187,7 @@
have "dist x y \<le> 2 * Max {dist (x (from_nat n)) (y (from_nat n))|n. n \<le> N} + (1/2)^N"
by (rule dist_fun_le_dist_first_terms)
also have "... \<le> 2 * f + e / 8"
- apply (rule add_mono) using ** \<open>2^N > 8/e\<close> by(auto simp add: algebra_simps field_split_simps)
+ apply (rule add_mono) using ** \<open>2^N > 8/e\<close> by(auto simp add: field_split_simps)
also have "... \<le> e/2 + e/8"
unfolding f_def by auto
also have "... < e"
@@ -331,7 +331,7 @@
also have "... < (1/2)^k * min e 1"
using C \<open>m \<ge> N\<close> \<open>n \<ge> N\<close> by auto
finally have "min (dist (u m i) (u n i)) 1 < min e 1"
- by (auto simp add: algebra_simps field_split_simps)
+ by (auto simp add: field_split_simps)
then show "dist (u m i) (u n i) < e" by auto
qed
then show "\<exists>N. \<forall>m n. N \<le> m \<and> N \<le> n \<longrightarrow> dist (u m i) (u n i) < e"
@@ -371,7 +371,7 @@
using dist_fun_le_dist_first_terms by auto
also have "... \<le> 2 * e/4 + e/4"
apply (rule add_mono)
- using ** \<open>2^N > 4/e\<close> less_imp_le by (auto simp add: algebra_simps field_split_simps)
+ using ** \<open>2^N > 4/e\<close> less_imp_le by (auto simp add: field_split_simps)
also have "... < e" by auto
finally show ?thesis by simp
qed
--- a/src/HOL/Analysis/Function_Topology.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Function_Topology.thy Thu Apr 02 13:04:24 2020 +0200
@@ -198,7 +198,7 @@
have "(\<Pi>\<^sub>E i\<in>I. topspace (T i)) \<in> {(\<Pi>\<^sub>E i\<in>I. X i) |X. (\<forall>i. openin (T i) (X i)) \<and> finite {i. X i \<noteq> topspace (T i)}}"
using openin_topspace not_finite_existsD by auto
then show "(\<Pi>\<^sub>E i\<in>I. topspace (T i)) \<subseteq> topspace (product_topology T I)"
- unfolding product_topology_def using PiE_def by (auto simp add: topology_generated_by_topspace)
+ unfolding product_topology_def using PiE_def by (auto)
qed
lemma product_topology_basis:
--- a/src/HOL/Analysis/Further_Topology.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Further_Topology.thy Thu Apr 02 13:04:24 2020 +0200
@@ -3682,7 +3682,7 @@
qed
show "disjoint \<V>"
apply (clarsimp simp add: \<V>_def pairwise_def disjnt_def add.commute [of _ "x*y" for x y]
- image_add_ball ball_eq_ball_iff)
+ ball_eq_ball_iff)
apply (rule disjoint_ballI)
apply (auto simp: dist_norm neq_iff)
by (metis norm_minus_commute xy)+
@@ -5321,7 +5321,7 @@
assumes "connected S" and C: "C \<in> components(- S)" shows "connected(frontier C)"
apply (rule connected_frontier_simple)
using C in_components_connected apply blast
- by (metis Compl_eq_Diff_UNIV connected_UNIV assms top_greatest component_complement_connected)
+ by (metis assms component_complement_connected)
lemma connected_frontier_disjoint:
fixes S :: "'a :: euclidean_space set"
--- a/src/HOL/Analysis/Gamma_Function.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Gamma_Function.thy Thu Apr 02 13:04:24 2020 +0200
@@ -395,7 +395,7 @@
from d have "\<lceil>2 * (cmod z + d)\<rceil> \<ge> \<lceil>0::real\<rceil>"
by (intro ceiling_mono mult_nonneg_nonneg add_nonneg_nonneg) simp_all
hence "2 * (norm z + d) \<le> of_nat (nat \<lceil>2 * (norm z + d)\<rceil>)" unfolding N_def
- by (simp_all add: le_of_int_ceiling)
+ by (simp_all)
also have "... \<le> of_nat N" unfolding N_def
by (subst of_nat_le_iff) (rule max.coboundedI2, rule max.cobounded1)
finally have "of_nat N \<ge> 2 * (norm z + d)" .
@@ -540,7 +540,7 @@
also have "\<dots> = z * of_real (harm n) - (\<Sum>k=1..n. ln (1 + z / of_nat k))"
by (simp add: harm_def sum_subtractf sum_distrib_left divide_inverse)
also from n have "\<dots> - ?g n = 0"
- by (simp add: ln_Gamma_series_def sum_subtractf algebra_simps Ln_of_nat)
+ by (simp add: ln_Gamma_series_def sum_subtractf algebra_simps)
finally show "(\<Sum>k<n. ?f k) - ?g n = 0" .
qed
show "(\<lambda>n. (\<Sum>k<n. ?f k) - ?g n) \<longlonglongrightarrow> 0" by (subst tendsto_cong[OF A]) simp_all
@@ -583,7 +583,7 @@
with t_nz have "?f n t = 1 / (of_nat (Suc n) * (1 + of_nat (Suc n)/t))"
by (simp add: field_split_simps eq_neg_iff_add_eq_0 del: of_nat_Suc)
also have "norm \<dots> = inverse (of_nat (Suc n)) * inverse (norm (of_nat (Suc n)/t + 1))"
- by (simp add: norm_divide norm_mult field_split_simps add_ac del: of_nat_Suc)
+ by (simp add: norm_divide norm_mult field_split_simps del: of_nat_Suc)
also {
from z t_nz ball[OF t] have "of_nat (Suc n) / (4 * norm z) \<le> of_nat (Suc n) / (2 * norm t)"
by (intro divide_left_mono mult_pos_pos) simp_all
@@ -1110,7 +1110,7 @@
pochhammer z (Suc (Suc n)) / (fact n * exp (z * of_real (ln (of_nat n))))"
by (subst pochhammer_rec) (simp add: rGamma_series_def field_simps exp_add exp_of_real)
also from n have "\<dots> = ?f n * rGamma_series z n"
- by (subst pochhammer_rec') (simp_all add: field_split_simps rGamma_series_def add_ac)
+ by (subst pochhammer_rec') (simp_all add: field_split_simps rGamma_series_def)
finally show "?f n * rGamma_series z n = z * rGamma_series (z + 1) n" ..
qed
moreover have "(\<lambda>n. ?f n * rGamma_series z n) \<longlonglongrightarrow> ((z+1) * 0 + 1) * rGamma z"
@@ -1175,7 +1175,7 @@
have "1/2 > (0::real)" by simp
from tendstoD[OF assms, OF this]
show "eventually (\<lambda>n. g n / Gamma_series z n * Gamma_series z n = g n) sequentially"
- by (force elim!: eventually_mono simp: dist_real_def dist_0_norm)
+ by (force elim!: eventually_mono simp: dist_real_def)
from assms have "(\<lambda>n. g n / Gamma_series z n * Gamma_series z n) \<longlonglongrightarrow> 1 * Gamma z"
by (intro tendsto_intros)
thus "(\<lambda>n. g n / Gamma_series z n * Gamma_series z n) \<longlonglongrightarrow> Gamma z" by simp
@@ -1189,7 +1189,7 @@
proof (rule Lim_transform_eventually)
have "1/2 > (0::real)" by simp
from tendstoD[OF assms(2), OF this] show "eventually (\<lambda>n. g n * f n / f n = g n) sequentially"
- by (force elim!: eventually_mono simp: dist_real_def dist_0_norm)
+ by (force elim!: eventually_mono simp: dist_real_def)
from assms have "(\<lambda>n. g n * f n / f n) \<longlonglongrightarrow> 1 / rGamma z"
by (intro tendsto_divide assms) (simp_all add: rGamma_eq_zero_iff)
thus "(\<lambda>n. g n * f n / f n) \<longlonglongrightarrow> Gamma z" by (simp add: Gamma_def divide_inverse)
@@ -1409,13 +1409,13 @@
\<longlonglongrightarrow> d) - euler_mascheroni *\<^sub>R 1 in (\<lambda>y. (rGamma y - rGamma z +
rGamma z * d * (y - z)) /\<^sub>R cmod (y - z)) \<midarrow>z\<rightarrow> 0"
by (simp add: has_field_derivative_def has_derivative_def Digamma_def sums_def [abs_def]
- netlimit_at of_real_def[symmetric] suminf_def)
+ of_real_def[symmetric] suminf_def)
next
fix n :: nat
from has_field_derivative_rGamma_complex_nonpos_Int[of n]
show "let z = - of_nat n in (\<lambda>y. (rGamma y - rGamma z - (- 1) ^ n * prod of_nat {1..n} *
(y - z)) /\<^sub>R cmod (y - z)) \<midarrow>z\<rightarrow> 0"
- by (simp add: has_field_derivative_def has_derivative_def fact_prod netlimit_at Let_def)
+ by (simp add: has_field_derivative_def has_derivative_def fact_prod Let_def)
next
fix z :: complex
from rGamma_series_complex_converges[of z] have "rGamma_series z \<longlonglongrightarrow> rGamma z"
@@ -1535,7 +1535,7 @@
fix n :: nat assume n: "n > 0"
have "Re (rGamma_series (of_real x) n) =
Re (of_real (pochhammer x (Suc n)) / (fact n * exp (of_real (x * ln (real_of_nat n)))))"
- using n by (simp add: rGamma_series_def powr_def Ln_of_nat pochhammer_of_real)
+ using n by (simp add: rGamma_series_def powr_def pochhammer_of_real)
also from n have "\<dots> = Re (of_real ((pochhammer x (Suc n)) /
(fact n * (exp (x * ln (real_of_nat n))))))"
by (subst exp_of_real) simp
@@ -1569,7 +1569,7 @@
\<longlonglongrightarrow> d) - euler_mascheroni *\<^sub>R 1 in (\<lambda>y. (rGamma y - rGamma x +
rGamma x * d * (y - x)) /\<^sub>R norm (y - x)) \<midarrow>x\<rightarrow> 0"
by (simp add: has_field_derivative_def has_derivative_def Digamma_def sums_def [abs_def]
- netlimit_at of_real_def[symmetric] suminf_def)
+ of_real_def[symmetric] suminf_def)
next
fix n :: nat
have "(rGamma has_field_derivative (-1)^n * fact n) (at (- of_nat n :: real))"
@@ -1577,7 +1577,7 @@
simp: Polygamma_of_real rGamma_real_def [abs_def])
thus "let x = - of_nat n in (\<lambda>y. (rGamma y - rGamma x - (- 1) ^ n * prod of_nat {1..n} *
(y - x)) /\<^sub>R norm (y - x)) \<midarrow>x::real\<rightarrow> 0"
- by (simp add: has_field_derivative_def has_derivative_def fact_prod netlimit_at Let_def)
+ by (simp add: has_field_derivative_def has_derivative_def fact_prod Let_def)
next
fix x :: real
have "rGamma_series x \<longlonglongrightarrow> rGamma x"
@@ -1619,7 +1619,7 @@
assume xn: "x > 0" "n > 0"
have "Ln (complex_of_real x / of_nat k + 1) = of_real (ln (x / of_nat k + 1))" if "k \<ge> 1" for k
using that xn by (subst Ln_of_real [symmetric]) (auto intro!: add_nonneg_pos simp: field_simps)
- with xn show ?thesis by (simp add: ln_Gamma_series_def Ln_of_nat Ln_of_real)
+ with xn show ?thesis by (simp add: ln_Gamma_series_def Ln_of_real)
qed
lemma ln_Gamma_real_converges:
@@ -2061,7 +2061,7 @@
by (intro not_in_Ints_imp_not_in_nonpos_Ints) simp_all
with lim[of "1/2 :: 'a"] have "?h \<longlonglongrightarrow> 2 * Gamma (1/2 :: 'a)" by (simp add: exp_of_real)
from LIMSEQ_unique[OF this lim[OF assms]] z' show ?thesis
- by (simp add: field_split_simps Gamma_eq_zero_iff ring_distribs exp_diff exp_of_real ac_simps)
+ by (simp add: field_split_simps Gamma_eq_zero_iff ring_distribs exp_diff exp_of_real)
qed
text \<open>
@@ -2126,13 +2126,13 @@
have h_eq: "h t = h2 t" if "abs (Re t) < 1" for t
proof -
- from that have t: "t \<in> \<int> \<longleftrightarrow> t = 0" by (auto elim!: Ints_cases simp: dist_0_norm)
+ from that have t: "t \<in> \<int> \<longleftrightarrow> t = 0" by (auto elim!: Ints_cases)
hence "h t = a*cot (a*t) - 1/t + Digamma (1 + t) - Digamma (1 - t)"
unfolding h_def using Digamma_plus1[of t] by (force simp: field_simps a_def)
also have "a*cot (a*t) - 1/t = (F t) / (G t)"
using t by (auto simp add: divide_simps sin_eq_0 cot_def a_def F_def G_def)
also have "\<dots> = (\<Sum>n. f n * (a*t)^n) / (\<Sum>n. g n * (a*t)^n)"
- using sums[of t] that by (simp add: sums_iff dist_0_norm)
+ using sums[of t] that by (simp add: sums_iff)
finally show "h t = h2 t" by (simp only: h2_def)
qed
@@ -2167,7 +2167,7 @@
have d: "abs (Re d) < 1" "norm z < norm d" by (simp_all add: d_def norm_mult del: of_real_add)
have "eventually (\<lambda>z. h z = h2 z) (nhds z)"
using eventually_nhds_in_nhd[of z ?A] using h_eq z
- by (auto elim!: eventually_mono simp: dist_0_norm)
+ by (auto elim!: eventually_mono)
moreover from sums(2)[OF z] z have nz: "(\<Sum>n. g n * (a * z) ^ n) \<noteq> 0"
unfolding G_def by (auto simp: sums_iff sin_eq_0 a_def)
@@ -2326,7 +2326,7 @@
show "g z = of_real pi * Gamma (1 + z) * Gamma (1 - z) * ?t z"
proof (cases "z = 0")
assume z': "z \<noteq> 0"
- with z have z'': "z \<notin> \<int>\<^sub>\<le>\<^sub>0" "z \<notin> \<int>" by (auto elim!: Ints_cases simp: dist_0_norm)
+ with z have z'': "z \<notin> \<int>\<^sub>\<le>\<^sub>0" "z \<notin> \<int>" by (auto elim!: Ints_cases)
from Gamma_plus1[OF this(1)] have "Gamma z = Gamma (z + 1) / z" by simp
with z'' z' show ?thesis by (simp add: g_def ac_simps)
qed (simp add: g_def)
@@ -2471,7 +2471,7 @@
show "\<forall>z\<in>B. norm (h' z) \<le> M/2"
proof
fix t :: complex assume t: "t \<in> B"
- from h'_eq[of t] t have "h' t = (h' (t/2) + h' ((t+1)/2)) / 4" by (simp add: dist_0_norm)
+ from h'_eq[of t] t have "h' t = (h' (t/2) + h' ((t+1)/2)) / 4" by (simp)
also have "norm \<dots> = norm (h' (t/2) + h' ((t+1)/2)) / 4" by simp
also have "norm (h' (t/2) + h' ((t+1)/2)) \<le> norm (h' (t/2)) + norm (h' ((t+1)/2))"
by (rule norm_triangle_ineq)
@@ -2482,7 +2482,7 @@
also have "(M + M) / 4 = M / 2" by simp
finally show "norm (h' t) \<le> M/2" by - simp_all
qed
- qed (insert bdd, auto simp: cball_eq_empty)
+ qed (insert bdd, auto)
hence "M \<le> 0" by simp
finally show "h' z = 0" by simp
qed
@@ -2512,7 +2512,7 @@
with c have A: "h z * g z = 0" for z by simp
hence "(g has_field_derivative 0) (at z)" for z using g_g'[of z] by simp
hence "\<exists>c'. \<forall>z\<in>UNIV. g z = c'" by (intro has_field_derivative_zero_constant) simp_all
- then obtain c' where c: "\<And>z. g z = c'" by (force simp: dist_0_norm)
+ then obtain c' where c: "\<And>z. g z = c'" by (force)
from this[of 0] have "c' = pi" unfolding g_def by simp
with c have "g z = pi" by simp
@@ -2547,7 +2547,7 @@
lemma Gamma_reflection_complex':
"Gamma z * Gamma (- z :: complex) = - of_real pi / (z * sin (of_real pi * z))"
- using rGamma_reflection_complex'[of z] by (force simp add: Gamma_def field_split_simps mult_ac)
+ using rGamma_reflection_complex'[of z] by (force simp add: Gamma_def field_split_simps)
@@ -2675,7 +2675,7 @@
from z have z': "z \<noteq> 0" by auto
have "eventually (\<lambda>n. ?r' n = ?r n) sequentially"
- using z by (auto simp: field_split_simps Gamma_series_def ring_distribs exp_diff ln_div add_ac
+ using z by (auto simp: field_split_simps Gamma_series_def ring_distribs exp_diff ln_div
intro: eventually_mono eventually_gt_at_top[of "0::nat"] dest: pochhammer_eq_0_imp_nonpos_Int)
moreover have "?r' \<longlonglongrightarrow> exp (z * of_real (ln 1))"
by (intro tendsto_intros LIMSEQ_Suc_n_over_n) simp_all
@@ -2819,7 +2819,7 @@
have "(\<lambda>n. of_nat ((k + n) choose n) / of_real (exp (of_nat k * ln (real_of_nat n))))
\<longlonglongrightarrow> 1 / Gamma (of_nat (Suc k) :: 'a)" (is "?f \<longlonglongrightarrow> _")
using Gamma_gbinomial[of "of_nat k :: 'a"]
- by (simp add: binomial_gbinomial add_ac Gamma_def field_split_simps exp_of_real [symmetric] exp_minus)
+ by (simp add: binomial_gbinomial Gamma_def field_split_simps exp_of_real [symmetric] exp_minus)
also have "Gamma (of_nat (Suc k)) = fact k" by (simp add: Gamma_fact)
finally show "?f \<longlonglongrightarrow> 1 / fact k" .
@@ -2862,7 +2862,7 @@
next
case False
with \<open>z = 0\<close> show ?thesis
- by (simp_all add: Beta_pole1 one_minus_of_nat_in_nonpos_Ints_iff gbinomial_1)
+ by (simp_all add: Beta_pole1 one_minus_of_nat_in_nonpos_Ints_iff)
qed
next
case False
@@ -2885,7 +2885,7 @@
have "(z gchoose n) = Gamma (z + 2) / (z + 1) / (fact n * Gamma (z - of_nat n + 1))"
by (subst gbinomial_Beta[OF assms]) (simp_all add: Beta_def Gamma_fact [symmetric] add_ac)
also from assms have "Gamma (z + 2) / (z + 1) = Gamma (z + 1)"
- using Gamma_plus1[of "z+1"] by (auto simp add: field_split_simps mult_ac add_ac)
+ using Gamma_plus1[of "z+1"] by (auto simp add: field_split_simps)
finally show ?thesis .
qed
@@ -3073,7 +3073,7 @@
have "eventually (\<lambda>n. Gamma_series z n =
of_nat n powr z * fact n / pochhammer z (n+1)) sequentially"
using eventually_gt_at_top[of "0::nat"]
- by eventually_elim (simp add: powr_def algebra_simps Ln_of_nat Gamma_series_def)
+ by eventually_elim (simp add: powr_def algebra_simps Gamma_series_def)
from this and Gamma_series_LIMSEQ[of z]
have C: "(\<lambda>k. of_nat k powr z * fact k / pochhammer z (k+1)) \<longlonglongrightarrow> Gamma z"
by (blast intro: Lim_transform_eventually)
@@ -3441,7 +3441,7 @@
fix n :: nat and x :: real assume x: "x \<in> ball 0 1"
{
fix k :: nat assume k: "k \<ge> 1"
- from x have "x^2 < 1" by (auto simp: dist_0_norm abs_square_less_1)
+ from x have "x^2 < 1" by (auto simp: abs_square_less_1)
also from k have "\<dots> \<le> of_nat k^2" by simp
finally have "(1 - x^2 / of_nat k^2) \<in> {0..1}" using k
by (simp_all add: field_simps del: of_nat_Suc)
@@ -3470,7 +3470,7 @@
by (simp add: eval_nat_numeral)
from sums_divide[OF this, of "x^3 * pi"] x
have "(\<lambda>n. - (sin_coeff (n+3) * pi^(n+2) * x^n)) sums ((1 - sin (pi*x) / (pi*x)) / x^2)"
- by (simp add: field_split_simps eval_nat_numeral power_mult_distrib mult_ac)
+ by (simp add: field_split_simps eval_nat_numeral)
with x have "(\<lambda>n. - (sin_coeff (n+3) * pi^(n+2) * x^n)) sums (g x / x^2)"
by (simp add: g_def)
hence "f' x = g x / x^2" by (simp add: sums_iff f'_def)
@@ -3485,7 +3485,7 @@
assume x: "x \<noteq> 0"
from summable_divide[OF sums_summable[OF sums_split_initial_segment[OF
sin_converges[of "pi*x"]], of 3], of "-pi*x^3"] x
- show ?thesis by (simp add: mult_ac power_mult_distrib field_split_simps eval_nat_numeral)
+ show ?thesis by (simp add: field_split_simps eval_nat_numeral)
qed (simp only: summable_0_powser)
qed
hence "f' \<midarrow> 0 \<rightarrow> f' 0" by (simp add: isCont_def)
--- a/src/HOL/Analysis/Henstock_Kurzweil_Integration.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Henstock_Kurzweil_Integration.thy Thu Apr 02 13:04:24 2020 +0200
@@ -1526,7 +1526,7 @@
apply (rule sum.cong)
using assms
apply simp
- apply (metis abs_of_nonneg assms(1) content_pos_le division_ofD(4))
+ apply (metis abs_of_nonneg content_pos_le)
done
have e: "0 \<le> e"
using assms(2) norm_ge_zero order_trans by blast
--- a/src/HOL/Analysis/Homeomorphism.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Homeomorphism.thy Thu Apr 02 13:04:24 2020 +0200
@@ -1993,7 +1993,7 @@
have "q' t = (h \<circ> (*\<^sub>R) 2) t" if "0 \<le> t" "t \<le> 1/2" for t
proof (rule covering_space_lift_unique [OF cov, of q' 0 "h \<circ> (*\<^sub>R) 2" "{0..1/2}" "f \<circ> g \<circ> (*\<^sub>R) 2" t])
show "q' 0 = (h \<circ> (*\<^sub>R) 2) 0"
- by (metis \<open>pathstart q' = pathstart q\<close> comp_def h pastq pathstart_def pth_4(2))
+ by (metis \<open>pathstart q' = pathstart q\<close> comp_def h(3) pastq pathstart_def pth_4(2))
show "continuous_on {0..1/2} (f \<circ> g \<circ> (*\<^sub>R) 2)"
apply (intro continuous_intros continuous_on_compose continuous_on_path [OF \<open>path g\<close>] continuous_on_subset [OF contf])
using g(2) path_image_def by fastforce+
--- a/src/HOL/Analysis/Homotopy.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Homotopy.thy Thu Apr 02 13:04:24 2020 +0200
@@ -901,7 +901,7 @@
apply (rule pip [unfolded path_image_def, THEN subsetD])
apply (rule image_eqI, blast)
apply (simp add: algebra_simps)
- by (metis add_mono_thms_linordered_semiring(1) affine_ineq linear mult.commute mult.left_neutral mult_right_mono not_le
+ by (metis add_mono_thms_linordered_semiring(1) affine_ineq linear mult.commute mult.left_neutral mult_right_mono
add.commute zero_le_numeral)
have qs: "\<And>a b. \<lbrakk>4 * b \<le> 3; \<not> b * 2 \<le> 1\<rbrakk> \<Longrightarrow> q (4 * b - 2) \<in> s"
using path_image_def piq by fastforce
--- a/src/HOL/Analysis/Improper_Integral.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Improper_Integral.thy Thu Apr 02 13:04:24 2020 +0200
@@ -445,7 +445,7 @@
obtain u v where K: "K = cbox u v" "K \<noteq> {}" "K \<subseteq> cbox a b"
using K cbox_division_memE [OF _ div] by (meson div_subset_cbox)
with i show "extend K \<noteq> {}" "extend K \<subseteq> cbox a b"
- apply (auto simp: extend_def subset_box box_ne_empty sum_if_inner)
+ apply (auto simp: extend_def subset_box box_ne_empty)
by fastforce
qed
have int_extend_disjoint:
@@ -468,7 +468,7 @@
and xv: "\<And>k. k \<in> Basis - {i} \<Longrightarrow> x \<bullet> k < v \<bullet> k"
and wx: "\<And>k. k \<in> Basis - {i} \<Longrightarrow> w \<bullet> k < x \<bullet> k"
and xz: "\<And>k. k \<in> Basis - {i} \<Longrightarrow> x \<bullet> k < z \<bullet> k"
- using that K1 K2 i by (auto simp: extend_def box_ne_empty sum_if_inner mem_box)
+ using that K1 K2 i by (auto simp: extend_def box_ne_empty mem_box)
have "box u v \<noteq> {}" "box w z \<noteq> {}"
using cboxes interior_cbox by (auto simp: content_eq_0_interior dest: mt)
then obtain q s
@@ -630,7 +630,7 @@
show "\<Union>Dlec \<subseteq> cbox a b'"
using Dlec_def div S by (auto simp: b'_def division_of_def mem_box)
show "(\<forall>K\<in>Dlec. K \<inter> {x. x \<bullet> i = a \<bullet> i} \<noteq> {}) \<or> (\<forall>K\<in>Dlec. K \<inter> {x. x \<bullet> i = b' \<bullet> i} \<noteq> {})"
- using nonmt by (fastforce simp: Dlec_def b'_def sum_if_inner i)
+ using nonmt by (fastforce simp: Dlec_def b'_def i)
qed (use i Dlec_def in auto)
moreover
have "(\<Sum>K\<in>Dlec. content K / (interval_upperbound K \<bullet> i - interval_lowerbound K \<bullet> i)) =
@@ -640,7 +640,7 @@
unfolding Dlec_def using \<open>finite \<D>\<close> apply (auto simp: sum.mono_neutral_left)
done
moreover have "(b' \<bullet> i - a \<bullet> i) = (c - a \<bullet> i)"
- by (simp add: b'_def sum_if_inner i)
+ by (simp add: b'_def i)
ultimately
have lec: "(c - a \<bullet> i) * (\<Sum>K\<in>\<D>. ((\<lambda>K. content K / (interval_upperbound K \<bullet> i - interval_lowerbound K \<bullet> i)) \<circ> ((\<lambda>K. K \<inter> {x. x \<bullet> i \<le> c}))) K)
\<le> content(cbox a b')"
@@ -657,7 +657,7 @@
show "\<Union>Dgec \<subseteq> cbox a' b"
using Dgec_def div S by (auto simp: a'_def division_of_def mem_box)
show "(\<forall>K\<in>Dgec. K \<inter> {x. x \<bullet> i = a' \<bullet> i} \<noteq> {}) \<or> (\<forall>K\<in>Dgec. K \<inter> {x. x \<bullet> i = b \<bullet> i} \<noteq> {})"
- using nonmt by (fastforce simp: Dgec_def a'_def sum_if_inner i)
+ using nonmt by (fastforce simp: Dgec_def a'_def i)
qed (use i Dgec_def in auto)
moreover
have "(\<Sum>K\<in>Dgec. content K / (interval_upperbound K \<bullet> i - interval_lowerbound K \<bullet> i)) =
@@ -667,7 +667,7 @@
unfolding Dgec_def using \<open>finite \<D>\<close> apply (auto simp: sum.mono_neutral_left)
done
moreover have "(b \<bullet> i - a' \<bullet> i) = (b \<bullet> i - c)"
- by (simp add: a'_def sum_if_inner i)
+ by (simp add: a'_def i)
ultimately
have gec: "(b \<bullet> i - c) * (\<Sum>K\<in>\<D>. ((\<lambda>K. content K / (interval_upperbound K \<bullet> i - interval_lowerbound K \<bullet> i)) \<circ> ((\<lambda>K. K \<inter> {x. x \<bullet> i \<ge> c}))) K)
\<le> content(cbox a' b)"
@@ -679,7 +679,7 @@
proof
assume c: "c = a \<bullet> i"
then have "a' = a"
- apply (simp add: sum_if_inner i a'_def cong: if_cong)
+ apply (simp add: i a'_def cong: if_cong)
using euclidean_representation [of a] sum.cong [OF refl, of Basis "\<lambda>i. (a \<bullet> i) *\<^sub>R i"] by presburger
then have "content (cbox a' b) \<le> 2 * content (cbox a b)" by simp
moreover
@@ -701,7 +701,7 @@
next
assume c: "c = b \<bullet> i"
then have "b' = b"
- apply (simp add: sum_if_inner i b'_def cong: if_cong)
+ apply (simp add: i b'_def cong: if_cong)
using euclidean_representation [of b] sum.cong [OF refl, of Basis "\<lambda>i. (b \<bullet> i) *\<^sub>R i"] by presburger
then have "content (cbox a b') \<le> 2 * content (cbox a b)" by simp
moreover
@@ -726,14 +726,14 @@
have prod_if: "(\<Prod>k\<in>Basis \<inter> - {i}. f k) = (\<Prod>k\<in>Basis. f k) / f i" if "f i \<noteq> (0::real)" for f
using that mk_disjoint_insert [OF i]
apply (clarsimp simp add: field_split_simps)
- by (metis Int_insert_left_if0 finite_Basis finite_insert le_iff_inf mult.commute order_refl prod.insert subset_Compl_singleton)
+ by (metis Int_insert_left_if0 finite_Basis finite_insert le_iff_inf order_refl prod.insert subset_Compl_singleton)
have abc: "a \<bullet> i < c" "c < b \<bullet> i"
using False assms by auto
then have "(\<Sum>K\<in>\<D>. ((\<lambda>K. content K / (interval_upperbound K \<bullet> i - interval_lowerbound K \<bullet> i)) \<circ> ((\<lambda>K. K \<inter> {x. x \<bullet> i \<le> c}))) K)
\<le> content(cbox a b') / (c - a \<bullet> i)"
"(\<Sum>K\<in>\<D>. ((\<lambda>K. content K / (interval_upperbound K \<bullet> i - interval_lowerbound K \<bullet> i)) \<circ> ((\<lambda>K. K \<inter> {x. x \<bullet> i \<ge> c}))) K)
\<le> content(cbox a' b) / (b \<bullet> i - c)"
- using lec gec by (simp_all add: field_split_simps mult.commute)
+ using lec gec by (simp_all add: field_split_simps)
moreover
have "(\<Sum>K\<in>\<D>. content K / (interval_upperbound K \<bullet> i - interval_lowerbound K \<bullet> i))
\<le> (\<Sum>K\<in>\<D>. ((\<lambda>K. content K / (interval_upperbound K \<bullet> i - interval_lowerbound K \<bullet> i)) \<circ> ((\<lambda>K. K \<inter> {x. x \<bullet> i \<le> c}))) K) +
@@ -780,7 +780,7 @@
\<le> 2 * content (cbox a b) / (b \<bullet> i - a \<bullet> i)"
by linarith
then show ?thesis
- using abc by (simp add: field_split_simps mult.commute)
+ using abc by (simp add: field_split_simps)
qed
qed
@@ -856,7 +856,7 @@
have "gauge (\<lambda>x. ball x
(\<epsilon> * (INF m\<in>Basis. b \<bullet> m - a \<bullet> m) / ((8 * norm (f x) + 8) * content (cbox a b))))"
using \<open>0 < content (cbox a b)\<close> \<open>0 < \<epsilon>\<close> a_less_b
- apply (auto simp: gauge_def field_split_simps mult_less_0_iff zero_less_mult_iff add_nonneg_eq_0_iff finite_less_Inf_iff)
+ apply (auto simp: gauge_def field_split_simps add_nonneg_eq_0_iff finite_less_Inf_iff)
apply (meson add_increasing measure_nonneg mult_nonneg_nonneg norm_ge_zero not_le zero_le_numeral)
done
then have "gauge \<gamma>"
@@ -936,7 +936,7 @@
by simp
also have "... < \<epsilon> * (b \<bullet> i - a \<bullet> i) / dist u v / (4 * content (cbox a b))"
using duv dist_uv contab_gt0
- apply (simp add: field_split_simps algebra_simps mult_less_0_iff zero_less_mult_iff split: if_split_asm)
+ apply (simp add: field_split_simps split: if_split_asm)
by (meson add_nonneg_nonneg linorder_not_le measure_nonneg mult_nonneg_nonneg norm_ge_zero zero_le_numeral)
also have "... = \<epsilon> * (b \<bullet> i - a \<bullet> i) / norm (v - u) / (4 * content (cbox a b))"
by (simp add: dist_norm norm_minus_commute)
@@ -1239,7 +1239,7 @@
obtain u v where uv: "K = cbox u v"
using T''_tagged \<open>(x,K) \<in> T''\<close> by blast
then have "connected K"
- by (simp add: is_interval_cbox is_interval_connected)
+ by (simp add: is_interval_connected)
then have "(\<exists>z \<in> K. z \<bullet> i = c)"
using y connected_ivt_component by fastforce
then show ?thesis
@@ -1883,7 +1883,7 @@
then obtain m::nat where m: "floor(n * f x) = int m"
using nonneg_int_cases zero_le_floor by blast
then have kn: "real k / real n \<le> f x \<longleftrightarrow> k \<le> m" for k
- using \<open>n \<noteq> 0\<close> by (simp add: field_split_simps mult.commute) linarith
+ using \<open>n \<noteq> 0\<close> by (simp add: field_split_simps) linarith
then have "Suc n / real n \<le> f x \<longleftrightarrow> Suc n \<le> m"
by blast
have "real n * f x \<le> real n"
@@ -1894,7 +1894,7 @@
by (subst sum.inter_restrict) (auto simp: kn)
also have "\<dots> < inverse n"
using \<open>m \<le> n\<close> \<open>n \<noteq> 0\<close> m
- by (simp add: min_absorb2 field_split_simps mult.commute) linarith
+ by (simp add: min_absorb2 field_split_simps) linarith
finally show ?thesis .
qed
@@ -2222,7 +2222,7 @@
proof (subst has_integral_cong)
show "g x * f x - g a * f x = (g b - g a) * h x *\<^sub>R f x"
if "x \<in> {a..b}" for x
- using 1 that by (simp add: h_def field_split_simps algebra_simps)
+ using 1 that by (simp add: h_def field_split_simps)
show "((\<lambda>x. (g b - g a) * h x *\<^sub>R f x) has_integral (g b - g a) * integral {c..b} f) {a..b}"
using has_integral_mult_right [OF c, of "g b - g a"] .
qed
--- a/src/HOL/Analysis/Infinite_Set_Sum.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Infinite_Set_Sum.thy Thu Apr 02 13:04:24 2020 +0200
@@ -154,7 +154,7 @@
lemma abs_summable_on_altdef':
"A \<subseteq> B \<Longrightarrow> f abs_summable_on A \<longleftrightarrow> set_integrable (count_space B) A f"
unfolding abs_summable_on_def set_integrable_def
- by (metis (no_types) Pow_iff abs_summable_on_def inf.orderE integrable_restrict_space restrict_count_space_subset set_integrable_def sets_count_space space_count_space)
+ by (metis (no_types) Pow_iff abs_summable_on_def inf.orderE integrable_restrict_space restrict_count_space_subset sets_count_space space_count_space)
lemma abs_summable_on_norm_iff [simp]:
"(\<lambda>x. norm (f x)) abs_summable_on A \<longleftrightarrow> f abs_summable_on A"
--- a/src/HOL/Analysis/Jordan_Curve.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Jordan_Curve.thy Thu Apr 02 13:04:24 2020 +0200
@@ -624,7 +624,7 @@
then show "connected (- closure (inside (?\<Theta>1 \<union> ?\<Theta>)))"
by (metis Compl_Un outside_inside co_out1c closure_Un_frontier)
have if2: "- (inside (?\<Theta>2 \<union> ?\<Theta>) \<union> frontier (inside (?\<Theta>2 \<union> ?\<Theta>))) = - ?\<Theta>2 \<inter> - ?\<Theta> \<inter> - inside (?\<Theta>2 \<union> ?\<Theta>)"
- by (metis (no_types, lifting) Int_commute Jordan_inside_outside c c2 compl_sup path_image_join path_image_reversepath pathfinish_join pathfinish_reversepath pathstart_join pathstart_reversepath sp closure_Un_frontier fr_out(2))
+ by (metis (no_types, lifting) Int_commute Jordan_inside_outside c c2 compl_sup path_image_join path_image_reversepath pathfinish_join pathfinish_reversepath pathstart_join pathstart_reversepath sp(3) closure_Un_frontier fr_out(2))
then show "connected (- closure (inside (?\<Theta>2 \<union> ?\<Theta>)))"
by (metis Compl_Un outside_inside co_out2c closure_Un_frontier)
have "connected(?\<Theta>)"
--- a/src/HOL/Analysis/Lipschitz.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Lipschitz.thy Thu Apr 02 13:04:24 2020 +0200
@@ -684,7 +684,7 @@
from this elim d[of "rx (ry (rt n))"]
have "\<dots> < dist (f (?t n) (?y n)) (f (?t n) (?x n)) / rx (ry (rt (n)))"
using lx'(2) ly'(2) lt'(2) \<open>0 < rx _\<close>
- by (auto simp add: field_split_simps algebra_simps strict_mono_def)
+ by (auto simp add: field_split_simps strict_mono_def)
also have "\<dots> \<le> diameter ?S / n"
by (force intro!: \<open>0 < n\<close> strict_mono_def xy diameter_bounded_bound frac_le
compact_imp_bounded compact t
--- a/src/HOL/Analysis/Measure_Space.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Measure_Space.thy Thu Apr 02 13:04:24 2020 +0200
@@ -1574,7 +1574,7 @@
by (cases "emeasure M A" rule: ennreal_cases) (auto simp: measure_def)
lemma measure_zero_top: "emeasure M A = top \<Longrightarrow> measure M A = 0"
- by (simp add: measure_def enn2ereal_top)
+ by (simp add: measure_def)
lemma measure_eq_emeasure_eq_ennreal: "0 \<le> x \<Longrightarrow> emeasure M A = ennreal x \<Longrightarrow> measure M A = x"
using emeasure_eq_ennreal_measure[of M A]
--- a/src/HOL/Analysis/Nonnegative_Lebesgue_Integration.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Nonnegative_Lebesgue_Integration.thy Thu Apr 02 13:04:24 2020 +0200
@@ -166,7 +166,7 @@
(if y = f x then y * indicator (f -` {y} \<inter> space M) x else 0))"
by (auto intro!: sum.cong)
also have "... = f x * indicator (f -` {f x} \<inter> space M) x"
- using assms by (auto dest: simple_functionD simp: sum.delta)
+ using assms by (auto dest: simple_functionD)
also have "... = f x" using x by (auto simp: indicator_def)
finally show ?thesis by auto
qed
@@ -327,10 +327,10 @@
{ fix d :: nat
have "\<lfloor>2^d::real\<rfloor> * \<lfloor>2^m * enn2real (min (of_nat m) (u x))\<rfloor> \<le>
\<lfloor>2^d * (2^m * enn2real (min (of_nat m) (u x)))\<rfloor>"
- by (rule le_mult_floor) (auto simp: enn2real_nonneg)
+ by (rule le_mult_floor) (auto)
also have "\<dots> \<le> \<lfloor>2^d * (2^m * enn2real (min (of_nat d + of_nat m) (u x)))\<rfloor>"
by (intro floor_mono mult_mono enn2real_mono min.mono)
- (auto simp: enn2real_nonneg min_less_iff_disj of_nat_less_top)
+ (auto simp: min_less_iff_disj of_nat_less_top)
finally have "f m x \<le> f (m + d) x"
unfolding f_def
by (auto simp: field_simps power_add * simp del: of_int_mult) }
@@ -348,7 +348,7 @@
by (cases "u x" rule: ennreal_cases)
(auto split: split_min intro!: floor_mono)
then have "f i ` space M \<subseteq> (\<lambda>n. real_of_int n / 2^i) ` {0 .. of_nat i * 2^i}"
- unfolding floor_of_int by (auto simp: f_def enn2real_nonneg intro!: imageI)
+ unfolding floor_of_int by (auto simp: f_def intro!: imageI)
then show "finite (f i ` space M)"
by (rule finite_subset) auto
show "f i \<in> borel_measurable M"
@@ -680,7 +680,7 @@
proof cases
assume "finite P"
from this assms show ?thesis
- by induct (auto simp: simple_function_sum simple_integral_add sum_nonneg)
+ by induct (auto)
qed auto
lemma simple_integral_mult[simp]:
@@ -1090,8 +1090,7 @@
by (subst nn_integral_eq_simple_integral) (auto simp: simple_integral_indicator)
lemma nn_integral_cmult_indicator: "A \<in> sets M \<Longrightarrow> (\<integral>\<^sup>+ x. c * indicator A x \<partial>M) = c * emeasure M A"
- by (subst nn_integral_eq_simple_integral)
- (auto simp: simple_function_indicator simple_integral_indicator)
+ by (subst nn_integral_eq_simple_integral) (auto)
lemma nn_integral_indicator':
assumes [measurable]: "A \<inter> space M \<in> sets M"
@@ -1120,7 +1119,7 @@
lemma nn_integral_indicator_singleton'[simp]:
assumes [measurable]: "{y} \<in> sets M"
shows "(\<integral>\<^sup>+x. ennreal (f x * indicator {y} x) \<partial>M) = f y * emeasure M {y}"
- by (subst nn_integral_set_ennreal[symmetric]) (simp add: nn_integral_indicator_singleton)
+ by (subst nn_integral_set_ennreal[symmetric]) (simp)
lemma nn_integral_add:
"f \<in> borel_measurable M \<Longrightarrow> g \<in> borel_measurable M \<Longrightarrow> (\<integral>\<^sup>+ x. f x + g x \<partial>M) = integral\<^sup>N M f + integral\<^sup>N M g"
--- a/src/HOL/Analysis/Ordered_Euclidean_Space.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Ordered_Euclidean_Space.thy Thu Apr 02 13:04:24 2020 +0200
@@ -48,7 +48,7 @@
lemma inner_Basis_inf_left: "i \<in> Basis \<Longrightarrow> inf x y \<bullet> i = inf (x \<bullet> i) (y \<bullet> i)"
and inner_Basis_sup_left: "i \<in> Basis \<Longrightarrow> sup x y \<bullet> i = sup (x \<bullet> i) (y \<bullet> i)"
- by (simp_all add: eucl_inf eucl_sup inner_sum_left inner_Basis if_distrib comm_monoid_add_class.sum.delta
+ by (simp_all add: eucl_inf eucl_sup inner_sum_left inner_Basis if_distrib
cong: if_cong)
lemma inner_Basis_INF_left: "i \<in> Basis \<Longrightarrow> (INF x\<in>X. f x) \<bullet> i = (INF x\<in>X. f x \<bullet> i)"
@@ -118,7 +118,7 @@
hence "Inf ?proj = x \<bullet> b"
by (auto intro!: conditionally_complete_lattice_class.cInf_eq_minimum)
hence "x \<bullet> b = Inf X \<bullet> b"
- by (auto simp: eucl_Inf inner_sum_left inner_Basis if_distrib \<open>b \<in> Basis\<close> sum.delta
+ by (auto simp: eucl_Inf inner_sum_left inner_Basis if_distrib \<open>b \<in> Basis\<close>
cong: if_cong)
with x show "\<exists>x. x \<in> X \<and> x \<bullet> b = Inf X \<bullet> b \<and> (\<forall>y. y \<in> X \<longrightarrow> x \<bullet> b \<le> y \<bullet> b)" by blast
qed
@@ -140,7 +140,7 @@
hence "Sup ?proj = x \<bullet> b"
by (auto intro!: cSup_eq_maximum)
hence "x \<bullet> b = Sup X \<bullet> b"
- by (auto simp: eucl_Sup[where 'a='a] inner_sum_left inner_Basis if_distrib \<open>b \<in> Basis\<close> sum.delta
+ by (auto simp: eucl_Sup[where 'a='a] inner_sum_left inner_Basis if_distrib \<open>b \<in> Basis\<close>
cong: if_cong)
with x show "\<exists>x. x \<in> X \<and> x \<bullet> b = Sup X \<bullet> b \<and> (\<forall>y. y \<in> X \<longrightarrow> y \<bullet> b \<le> x \<bullet> b)" by blast
qed
--- a/src/HOL/Analysis/Path_Connected.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Path_Connected.thy Thu Apr 02 13:04:24 2020 +0200
@@ -511,7 +511,7 @@
} note ** = this
show ?thesis
using assms
- apply (simp add: arc_def simple_path_def path_join, clarify)
+ apply (simp add: arc_def simple_path_def, clarify)
apply (simp add: joinpaths_def split: if_split_asm)
apply (force dest: inj_onD [OF injg1])
apply (metis *)
--- a/src/HOL/Analysis/Polytope.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Polytope.thy Thu Apr 02 13:04:24 2020 +0200
@@ -994,13 +994,13 @@
"a \<noteq> 0 \<Longrightarrow> {x. a \<bullet> x = b} facet_of {x. a \<bullet> x \<le> b}"
unfolding facet_of_def hyperplane_eq_empty
by (auto simp: hyperplane_face_of_halfspace_ge hyperplane_face_of_halfspace_le
- DIM_positive Suc_leI of_nat_diff aff_dim_halfspace_le)
+ Suc_leI of_nat_diff aff_dim_halfspace_le)
lemma hyperplane_facet_of_halfspace_ge:
"a \<noteq> 0 \<Longrightarrow> {x. a \<bullet> x = b} facet_of {x. a \<bullet> x \<ge> b}"
unfolding facet_of_def hyperplane_eq_empty
by (auto simp: hyperplane_face_of_halfspace_le hyperplane_face_of_halfspace_ge
- DIM_positive Suc_leI of_nat_diff aff_dim_halfspace_ge)
+ Suc_leI of_nat_diff aff_dim_halfspace_ge)
lemma facet_of_halfspace_le:
"F facet_of {x. a \<bullet> x \<le> b} \<longleftrightarrow> a \<noteq> 0 \<and> F = {x. a \<bullet> x = b}"
@@ -1316,7 +1316,7 @@
apply (rule_tac x="u/x" in exI)
apply (rule_tac x="v/x" in exI)
apply (rule_tac x="w/x" in exI)
- using x apply (auto simp: algebra_simps field_split_simps)
+ using x apply (auto simp: field_split_simps)
done
ultimately show ?thesis by force
qed
@@ -1445,14 +1445,14 @@
have "x = (((1 - v) * ub) *\<^sub>R b + (v * uc) *\<^sub>R c) /\<^sub>R ux"
by (metis \<open>ux \<noteq> 0\<close> uxx mult.commute right_inverse scaleR_one scaleR_scaleR)
also have "... = (1 - v * uc / ux) *\<^sub>R b + (v * uc / ux) *\<^sub>R c"
- using \<open>ux \<noteq> 0\<close> equx apply (auto simp: algebra_simps field_split_simps)
+ using \<open>ux \<noteq> 0\<close> equx apply (auto simp: field_split_simps)
by (metis add.commute add_diff_eq add_divide_distrib diff_add_cancel scaleR_add_left)
finally have "x = (1 - v * uc / ux) *\<^sub>R b + (v * uc / ux) *\<^sub>R c" .
then have "x \<in> open_segment b c"
apply (simp add: in_segment \<open>b \<noteq> c\<close>)
apply (rule_tac x="(v * uc) / ux" in exI)
using \<open>0 \<le> ux\<close> \<open>ux \<noteq> 0\<close> \<open>0 < uc\<close> \<open>0 < v\<close> \<open>0 < ub\<close> \<open>v < 1\<close> equx
- apply (force simp: algebra_simps field_split_simps)
+ apply (force simp: field_split_simps)
done
then show ?thesis
by (rule face_ofD [OF F _ b c \<open>x \<in> F\<close>])
@@ -2116,7 +2116,7 @@
done
then show ?thesis
using \<open>0 < inff\<close> awlt [OF that] mult_strict_left_mono
- by (fastforce simp add: algebra_simps field_split_simps split: if_split_asm)
+ by (fastforce simp add: field_split_simps split: if_split_asm)
next
case False
with \<open>0 < inff\<close> have "inff * (a j \<bullet> y - a j \<bullet> w) \<le> 0"
--- a/src/HOL/Analysis/Product_Topology.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Product_Topology.thy Thu Apr 02 13:04:24 2020 +0200
@@ -290,7 +290,7 @@
next
case False
then show ?thesis
- by (simp add: continuous_compose_quotient_map_eq quotient_map_fst)
+ by (simp add: continuous_compose_quotient_map_eq)
qed
lemma continuous_map_of_snd:
@@ -302,7 +302,7 @@
next
case False
then show ?thesis
- by (simp add: continuous_compose_quotient_map_eq quotient_map_snd)
+ by (simp add: continuous_compose_quotient_map_eq)
qed
lemma continuous_map_prod_top:
--- a/src/HOL/Analysis/Regularity.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Regularity.thy Thu Apr 02 13:04:24 2020 +0200
@@ -53,7 +53,7 @@
hence "1/n > 0" "e * 2 powr - n > 0" by (auto)
from M_space[OF \<open>1/n>0\<close>]
have "(\<lambda>k. measure M (\<Union>i\<in>{0..k}. cball (from_nat_into X i) (1/real n))) \<longlonglongrightarrow> measure M (space M)"
- unfolding emeasure_eq_measure by (auto simp: measure_nonneg)
+ unfolding emeasure_eq_measure by (auto)
from metric_LIMSEQ_D[OF this \<open>0 < e * 2 powr -n\<close>]
obtain k where "dist (measure M (\<Union>i\<in>{0..k}. cball (from_nat_into X i) (1/real n))) (measure M (space M)) <
e * 2 powr -n"
@@ -95,7 +95,7 @@
also have "\<dots> \<le> (\<Sum>n. emeasure M (space M - B n))"
by (rule emeasure_subadditive_countably) (auto simp: summable_def)
also have "\<dots> \<le> (\<Sum>n. ennreal (e*2 powr - real (Suc n)))"
- using B_compl_le by (intro suminf_le) (simp_all add: measure_nonneg emeasure_eq_measure ennreal_leI)
+ using B_compl_le by (intro suminf_le) (simp_all add: emeasure_eq_measure ennreal_leI)
also have "\<dots> \<le> (\<Sum>n. ennreal (e * (1 / 2) ^ Suc n))"
by (simp add: powr_minus powr_realpow field_simps del: of_nat_Suc)
also have "\<dots> = ennreal e * (\<Sum>n. ennreal ((1 / 2) ^ Suc n))"
@@ -268,7 +268,7 @@
also have "(\<lambda>n. \<Sum>i<n. M (D i)) \<longlonglongrightarrow> (\<Sum>i. M (D i))"
by (intro summable_LIMSEQ) auto
finally have measure_LIMSEQ: "(\<lambda>n. \<Sum>i<n. measure M (D i)) \<longlonglongrightarrow> measure M (\<Union>i. D i)"
- by (simp add: emeasure_eq_measure measure_nonneg sum_nonneg)
+ by (simp add: emeasure_eq_measure sum_nonneg)
have "(\<Union>i. D i) \<in> sets M" using \<open>range D \<subseteq> sets M\<close> by auto
case 1
@@ -282,12 +282,12 @@
then obtain n0 where n0: "\<bar>(\<Sum>i<n0. measure M (D i)) - measure M (\<Union>i. D i)\<bar> < e/2"
unfolding choice_iff by blast
have "ennreal (\<Sum>i<n0. measure M (D i)) = (\<Sum>i<n0. M (D i))"
- by (auto simp add: emeasure_eq_measure sum_nonneg measure_nonneg)
+ by (auto simp add: emeasure_eq_measure)
also have "\<dots> \<le> (\<Sum>i. M (D i))" by (rule sum_le_suminf) auto
also have "\<dots> = M (\<Union>i. D i)" by (simp add: M)
also have "\<dots> = measure M (\<Union>i. D i)" by (simp add: emeasure_eq_measure)
finally have n0: "measure M (\<Union>i. D i) - (\<Sum>i<n0. measure M (D i)) < e/2"
- using n0 by (auto simp: measure_nonneg sum_nonneg)
+ using n0 by (auto simp: sum_nonneg)
have "\<forall>i. \<exists>K. K \<subseteq> D i \<and> compact K \<and> emeasure M (D i) \<le> emeasure M K + e/(2*Suc n0)"
proof
fix i
@@ -351,7 +351,7 @@
have "ennreal (measure M ?U - measure M (\<Union>i. D i)) = M ?U - M (\<Union>i. D i)"
using U(1,2)
by (subst ennreal_minus[symmetric])
- (auto intro!: finite_measure_mono simp: sb measure_nonneg emeasure_eq_measure)
+ (auto intro!: finite_measure_mono simp: sb emeasure_eq_measure)
also have "\<dots> = M (?U - (\<Union>i. D i))" using U \<open>(\<Union>i. D i) \<in> sets M\<close>
by (subst emeasure_Diff) (auto simp: sb)
also have "\<dots> \<le> M (\<Union>i. U i - D i)" using U \<open>range D \<subseteq> sets M\<close>
@@ -361,7 +361,7 @@
also have "\<dots> \<le> (\<Sum>i. ennreal e/(2 powr Suc i))" using U \<open>range D \<subseteq> sets M\<close>
using \<open>0<e\<close>
by (intro suminf_le, subst emeasure_Diff)
- (auto simp: emeasure_Diff emeasure_eq_measure sb measure_nonneg ennreal_minus
+ (auto simp: emeasure_Diff emeasure_eq_measure sb ennreal_minus
finite_measure_mono divide_ennreal ennreal_less_iff
intro: less_imp_le)
also have "\<dots> \<le> (\<Sum>n. ennreal (e * (1 / 2) ^ Suc n))"
--- a/src/HOL/Analysis/Simplex_Content.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Simplex_Content.thy Thu Apr 02 13:04:24 2020 +0200
@@ -252,7 +252,7 @@
((a + b + c) - 2 * c)"
unfolding power2_eq_square by (simp add: s_def a_def b_def c_def algebra_simps)
also have "\<dots> = 16 * s * (s - a) * (s - b) * (s - c)"
- by (simp add: s_def field_split_simps mult_ac)
+ by (simp add: s_def field_split_simps)
finally have "content (convex hull {A, B, C}) ^ 2 = s * (s - a) * (s - b) * (s - c)"
by simp
also have "\<dots> = sqrt (s * (s - a) * (s - b) * (s - c)) ^ 2"
--- a/src/HOL/Analysis/Starlike.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Starlike.thy Thu Apr 02 13:04:24 2020 +0200
@@ -5199,7 +5199,7 @@
using \<open>T \<subseteq> S\<close> apply (auto simp: \<open>a \<notin> S\<close> cc0)
done
also have "... = c a + (1 - c a)"
- by (metis \<open>a \<notin> S\<close> fun_upd_other sum.cong sumSS')
+ by (metis \<open>a \<notin> S\<close> fun_upd_other sum.cong sumSS'(1))
finally show "sum (cc(a := c a)) (insert a (T \<inter> T')) = 1"
by simp
have "(\<Sum>x\<in>insert a (T \<inter> T'). (cc(a := c a)) x *\<^sub>R x) = c a *\<^sub>R a + (\<Sum>x \<in> T \<inter> T'. (cc(a := c a)) x *\<^sub>R x)"
--- a/src/HOL/Analysis/Summation_Tests.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Summation_Tests.thy Thu Apr 02 13:04:24 2020 +0200
@@ -149,7 +149,7 @@
also have "Discrete.log k = n" if "k \<in> {2^n..<2^Suc n}" for k using that by (intro Discrete.log_eqI) simp_all
hence "(\<Sum>k = 2^n..<2^Suc n. f (2^Discrete.log k)) = (\<Sum>(_::nat) = 2^n..<2^Suc n. f (2^n))"
by (intro sum.cong) simp_all
- also have "\<dots> = 2^n * f (2^n)" by (simp add: of_nat_power)
+ also have "\<dots> = 2^n * f (2^n)" by (simp)
finally show ?case by simp
qed simp
@@ -163,7 +163,7 @@
also have "Discrete.log k = n" if "k \<in> {2^n..<2^Suc n}" for k using that by (intro Discrete.log_eqI) simp_all
hence "(\<Sum>k = 2^n..<2^Suc n. f (2*2^Discrete.log k)) = (\<Sum>(_::nat) = 2^n..<2^Suc n. f (2^Suc n))"
by (intro sum.cong) simp_all
- also have "\<dots> = 2^n * f (2^Suc n)" by (simp add: of_nat_power)
+ also have "\<dots> = 2^n * f (2^Suc n)" by (simp)
finally show ?case by simp
qed simp
--- a/src/HOL/Analysis/Tagged_Division.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Tagged_Division.thy Thu Apr 02 13:04:24 2020 +0200
@@ -2447,7 +2447,7 @@
finally show "a \<bullet> i + real ?k * (b \<bullet> i - a \<bullet> i) / 2 ^ n \<le> x \<bullet> i" .
next
have "x \<bullet> i \<le> a \<bullet> i + (2 ^ n * (x \<bullet> i - a \<bullet> i) / (b \<bullet> i - a \<bullet> i)) * (b \<bullet> i - a \<bullet> i) / 2 ^ n"
- using abi_less by (simp add: field_split_simps algebra_simps)
+ using abi_less by (simp add: field_split_simps)
also have "... \<le> a \<bullet> i + (real ?k + 1) * (b \<bullet> i - a \<bullet> i) / 2 ^ n"
apply (intro add_left_mono mult_right_mono divide_right_mono of_nat_floor)
using aibi [OF \<open>i \<in> Basis\<close>] xab
@@ -2488,12 +2488,12 @@
proof -
have dd: "w / m \<le> v / n \<and> (v+1) / n \<le> (w+1) / m
\<Longrightarrow> inverse n \<le> inverse m" for w m v n::real
- by (auto simp: field_split_simps algebra_simps)
+ by (auto simp: field_split_simps)
have bjaj: "b \<bullet> j - a \<bullet> j > 0"
using \<open>j \<in> Basis\<close> \<open>box a b \<noteq> {}\<close> box_eq_empty(1) by fastforce
have "((g j) / 2 ^ m) * (b \<bullet> j - a \<bullet> j) \<le> ((f j) / 2 ^ n) * (b \<bullet> j - a \<bullet> j) \<and>
(((f j) + 1) / 2 ^ n) * (b \<bullet> j - a \<bullet> j) \<le> (((g j) + 1) / 2 ^ m) * (b \<bullet> j - a \<bullet> j)"
- using that \<open>j \<in> Basis\<close> by (simp add: subset_box algebra_simps field_split_simps aibi)
+ using that \<open>j \<in> Basis\<close> by (simp add: subset_box field_split_simps aibi)
then have "((g j) / 2 ^ m) \<le> ((f j) / 2 ^ n) \<and>
((real(f j) + 1) / 2 ^ n) \<le> ((real(g j) + 1) / 2 ^ m)"
by (metis bjaj mult.commute of_nat_1 of_nat_add real_mult_le_cancel_iff2)
--- a/src/HOL/Analysis/Weierstrass_Theorems.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Analysis/Weierstrass_Theorems.thy Thu Apr 02 13:04:24 2020 +0200
@@ -110,7 +110,7 @@
then have "(\<Sum>k\<le>n. (k - n * x)\<^sup>2 * Bernstein n k x)/n^2 = x * (1 - x) / n"
by (simp add: power2_eq_square)
then show ?thesis
- using n by (simp add: sum_divide_distrib field_split_simps mult.commute power2_commute)
+ using n by (simp add: sum_divide_distrib field_split_simps power2_commute)
qed
{ fix k
assume k: "k \<le> n"
@@ -158,7 +158,7 @@
also have "... < e"
apply (simp add: field_simps)
using \<open>d>0\<close> nbig e \<open>n>0\<close>
- apply (simp add: field_split_simps algebra_simps)
+ apply (simp add: field_split_simps)
using ed0 by linarith
finally have "\<bar>f x - (\<Sum>k\<le>n. f (real k / real n) * Bernstein n k x)\<bar> < e" .
}
@@ -576,7 +576,7 @@
define B where "B j = {x \<in> S. f x \<ge> (j + 1/3)*e}" for j :: nat
have ngt: "(n-1) * e \<ge> normf f" "n\<ge>1"
using e
- apply (simp_all add: n_def field_simps of_nat_Suc)
+ apply (simp_all add: n_def field_simps)
by (metis real_nat_ceiling_ge mult.commute not_less pos_less_divide_eq)
then have ge_fx: "(n-1) * e \<ge> f x" if "x \<in> S" for x
using f normf_upper that by fastforce
@@ -646,7 +646,7 @@
then have "t \<in> B i"
using Anj e ge_fx [OF t] \<open>1 \<le> n\<close> fpos [OF t] t
apply (simp add: A_def B_def)
- apply (clarsimp simp add: field_simps of_nat_diff not_le of_nat_Suc)
+ apply (clarsimp simp add: field_simps of_nat_diff not_le)
apply (rule order_trans [of _ "e * 2 + (e * (real d * 3) + e * (real i * 3))"])
apply auto
done
@@ -693,7 +693,7 @@
apply simp
apply (rule order_trans [OF _ sum_bounded_below [OF less_imp_le [OF ****]]])
using True
- apply (simp_all add: of_nat_Suc of_nat_diff)
+ apply (simp_all add: of_nat_diff)
done
also have "... \<le> g t"
using jn e
@@ -744,7 +744,7 @@
have "\<not> real (Suc n) < inverse e"
using \<open>N \<le> n\<close> N using less_imp_inverse_less by force
then have "1 / (1 + real n) \<le> e"
- using e by (simp add: field_simps of_nat_Suc)
+ using e by (simp add: field_simps)
then have "\<bar>f x - g x\<bar> < e"
using n(2) x by auto
} note * = this
@@ -927,7 +927,7 @@
show ?case
apply (rule_tac x="\<lambda>i. c" in exI)
apply (rule_tac x=0 in exI)
- apply (auto simp: mult_ac of_nat_Suc)
+ apply (auto simp: mult_ac)
done
case (add f1 f2)
then obtain a1 n1 a2 n2 where
@@ -1328,7 +1328,7 @@
also have "... = (\<Sum>j\<in>B. if j = i then x \<bullet> i else 0)"
by (rule sum.cong; simp)
also have "... = i \<bullet> x"
- by (simp add: \<open>finite B\<close> that inner_commute sum.delta)
+ by (simp add: \<open>finite B\<close> that inner_commute)
finally show ?thesis .
qed
qed
--- a/src/HOL/Computational_Algebra/Polynomial.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Computational_Algebra/Polynomial.thy Thu Apr 02 13:04:24 2020 +0200
@@ -4367,11 +4367,11 @@
define m where "m = (GREATEST m. \<not>c dvd coeff b m)"
assume "\<not>[:c:] dvd b"
hence A: "\<exists>i. \<not>c dvd coeff b i" by (subst (asm) const_poly_dvd_iff) blast
- have B: "\<forall>i. \<not>c dvd coeff b i \<longrightarrow> i \<le> degree b"
+ have B: "\<And>i. \<not>c dvd coeff b i \<Longrightarrow> i \<le> degree b"
by (auto intro: le_degree)
have coeff_m: "\<not>c dvd coeff b m" unfolding m_def by (rule GreatestI_ex_nat[OF A B])
have "i \<le> m" if "\<not>c dvd coeff b i" for i
- unfolding m_def by (rule Greatest_le_nat[OF that B])
+ unfolding m_def by (metis (mono_tags, lifting) B Greatest_le_nat that)
hence dvd_b: "c dvd coeff b i" if "i > m" for i using that by force
have "c dvd coeff a i" for i
--- a/src/HOL/Computational_Algebra/Polynomial_Factorial.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Computational_Algebra/Polynomial_Factorial.thy Thu Apr 02 13:04:24 2020 +0200
@@ -286,11 +286,11 @@
define m where "m = (GREATEST m. \<not>c dvd coeff b m)"
assume "\<not>[:c:] dvd b"
hence A: "\<exists>i. \<not>c dvd coeff b i" by (subst (asm) const_poly_dvd_iff) blast
- have B: "\<forall>i. \<not>c dvd coeff b i \<longrightarrow> i \<le> degree b"
+ have B: "\<And>i. \<not>c dvd coeff b i \<Longrightarrow> i \<le> degree b"
by (auto intro: le_degree)
have coeff_m: "\<not>c dvd coeff b m" unfolding m_def by (rule GreatestI_ex_nat[OF A B])
have "i \<le> m" if "\<not>c dvd coeff b i" for i
- unfolding m_def by (rule Greatest_le_nat[OF that B])
+ unfolding m_def by (blast intro!: Greatest_le_nat that B)
hence dvd_b: "c dvd coeff b i" if "i > m" for i using that by force
have "c dvd coeff a i" for i
--- a/src/HOL/Data_Structures/AVL_Map.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Data_Structures/AVL_Map.thy Thu Apr 02 13:04:24 2020 +0200
@@ -18,7 +18,8 @@
fun delete :: "'a::linorder \<Rightarrow> ('a*'b) avl_tree \<Rightarrow> ('a*'b) avl_tree" where
"delete _ Leaf = Leaf" |
"delete x (Node l ((a,b), h) r) = (case cmp x a of
- EQ \<Rightarrow> del_root (Node l ((a,b), h) r) |
+ EQ \<Rightarrow> if l = Leaf then r
+ else let (l', ab') = split_max l in balR l' ab' r |
LT \<Rightarrow> balR (delete x l) (a,b) r |
GT \<Rightarrow> balL l (a,b) (delete x r))"
@@ -34,7 +35,7 @@
"sorted1(inorder t) \<Longrightarrow> inorder (delete x t) = del_list x (inorder t)"
by(induction t)
(auto simp: del_list_simps inorder_balL inorder_balR
- inorder_del_root inorder_split_maxD split: prod.splits)
+ inorder_split_maxD split: prod.splits)
subsection \<open>AVL invariants\<close>
@@ -120,7 +121,8 @@
case 1
show ?case
proof(cases "x = a")
- case True with Node 1 show ?thesis by (auto simp:avl_del_root)
+ case True with Node 1 show ?thesis
+ using avl_split_max[of l] by (auto simp: avl_balR split: prod.split)
next
case False
show ?thesis
@@ -133,11 +135,8 @@
case 2
show ?case
proof(cases "x = a")
- case True
- with 1 have "height (Node l (n, h) r) = height(del_root (Node l (n, h) r))
- \<or> height (Node l (n, h) r) = height(del_root (Node l (n, h) r)) + 1"
- by (subst height_del_root,simp_all)
- with True show ?thesis by simp
+ case True then show ?thesis using 1 avl_split_max[of l]
+ by(auto simp: balR_def max_absorb2 split!: if_splits prod.split tree.split)
next
case False
show ?thesis
--- a/src/HOL/Data_Structures/AVL_Set.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Data_Structures/AVL_Set.thy Thu Apr 02 13:04:24 2020 +0200
@@ -1,6 +1,6 @@
(*
Author: Tobias Nipkow, Daniel Stüwe
-Largely derived from AFP entry AVL.
+Based on the AFP entry AVL.
*)
section "AVL Tree Implementation of Sets"
@@ -33,26 +33,26 @@
"node l a r = Node l (a, max (ht l) (ht r) + 1) r"
definition balL :: "'a avl_tree \<Rightarrow> 'a \<Rightarrow> 'a avl_tree \<Rightarrow> 'a avl_tree" where
-"balL l a r =
- (if ht l = ht r + 2 then
- case l of
- Node bl (b, _) br \<Rightarrow>
- if ht bl < ht br then
- case br of
- Node cl (c, _) cr \<Rightarrow> node (node bl b cl) c (node cr a r)
- else node bl b (node br a r)
- else node l a r)"
+"balL AB b C =
+ (if ht AB = ht C + 2 then
+ case AB of
+ Node A (a, _) B \<Rightarrow>
+ if ht A \<ge> ht B then node A a (node B b C)
+ else
+ case B of
+ Node B\<^sub>1 (ab, _) B\<^sub>2 \<Rightarrow> node (node A a B\<^sub>1) ab (node B\<^sub>2 b C)
+ else node AB b C)"
definition balR :: "'a avl_tree \<Rightarrow> 'a \<Rightarrow> 'a avl_tree \<Rightarrow> 'a avl_tree" where
-"balR l a r =
- (if ht r = ht l + 2 then
- case r of
- Node bl (b, _) br \<Rightarrow>
- if ht bl > ht br then
- case bl of
- Node cl (c, _) cr \<Rightarrow> node (node l a cl) c (node cr b br)
- else node (node l a bl) b br
- else node l a r)"
+"balR A a BC =
+ (if ht BC = ht A + 2 then
+ case BC of
+ Node B (b, _) C \<Rightarrow>
+ if ht B \<le> ht C then node (node A a B) b C
+ else
+ case B of
+ Node B\<^sub>1 (ab, _) B\<^sub>2 \<Rightarrow> node (node A a B\<^sub>1) ab (node B\<^sub>2 b C)
+ else node A a BC)"
fun insert :: "'a::linorder \<Rightarrow> 'a avl_tree \<Rightarrow> 'a avl_tree" where
"insert x Leaf = Node Leaf (x, 1) Leaf" |
@@ -67,18 +67,12 @@
lemmas split_max_induct = split_max.induct[case_names Node Leaf]
-fun del_root :: "'a avl_tree \<Rightarrow> 'a avl_tree" where
-"del_root (Node Leaf (a,_) r) = r" |
-"del_root (Node l (a,_) Leaf) = l" |
-"del_root (Node l (a,_) r) = (let (l', a') = split_max l in balR l' a' r)"
-
-lemmas del_root_cases = del_root.cases[split_format(complete), case_names Leaf_t Node_Leaf Node_Node]
-
fun delete :: "'a::linorder \<Rightarrow> 'a avl_tree \<Rightarrow> 'a avl_tree" where
"delete _ Leaf = Leaf" |
"delete x (Node l (a, n) r) =
(case cmp x a of
- EQ \<Rightarrow> del_root (Node l (a, n) r) |
+ EQ \<Rightarrow> if l = Leaf then r
+ else let (l', a') = split_max l in balR l' a' r |
LT \<Rightarrow> balR (delete x l) a r |
GT \<Rightarrow> balL l a (delete x r))"
@@ -112,16 +106,10 @@
by(induction t arbitrary: t' rule: split_max.induct)
(auto simp: inorder_balL split: if_splits prod.splits tree.split)
-lemma inorder_del_root:
- "inorder (del_root (Node l ah r)) = inorder l @ inorder r"
-by(cases "Node l ah r" rule: del_root.cases)
- (auto simp: inorder_balL inorder_balR inorder_split_maxD split: if_splits prod.splits)
-
theorem inorder_delete:
"sorted(inorder t) \<Longrightarrow> inorder (delete x t) = del_list x (inorder t)"
by(induction t)
- (auto simp: del_list_simps inorder_balL inorder_balR
- inorder_del_root inorder_split_maxD split: prod.splits)
+ (auto simp: del_list_simps inorder_balL inorder_balR inorder_split_maxD split: prod.splits)
subsection \<open>AVL invariants\<close>
@@ -136,6 +124,8 @@
lemma ht_height[simp]: "avl t \<Longrightarrow> ht t = height t"
by (cases t rule: tree2_cases) simp_all
+text \<open>First, a fast but relatively manual proof with many lemmas:\<close>
+
lemma height_balL:
"\<lbrakk> height l = height r + 2; avl l; avl r \<rbrakk> \<Longrightarrow>
height (balL l a r) = height r + 2 \<or>
@@ -207,9 +197,7 @@
qed
qed
-(* It appears that these two properties need to be proved simultaneously: *)
-
-text\<open>Insertion maintains the AVL property:\<close>
+text\<open>Insertion maintains the AVL property. Requires simultaneous proof.\<close>
theorem avl_insert:
assumes "avl t"
@@ -276,6 +264,15 @@
qed
qed simp_all
+text \<open>Now an automatic proof without lemmas:\<close>
+
+theorem avl_insert_auto: "avl t \<Longrightarrow>
+ avl(insert x t) \<and> height (insert x t) \<in> {height t, height t + 1}"
+apply (induction t rule: tree2_induct)
+ apply (auto split!: if_splits)
+ apply (auto simp: balL_def balR_def node_def max_absorb2 split!: tree.splits)
+done
+
subsubsection \<open>Deletion maintains AVL balance\<close>
@@ -298,58 +295,6 @@
apply (auto split:prod.splits simp del:avl.simps) by arith+
qed auto
-lemma avl_del_root:
- assumes "avl t" and "t \<noteq> Leaf"
- shows "avl(del_root t)"
-using assms
-proof (cases t rule:del_root_cases)
- case (Node_Node ll ln lh lr n h rl rn rh rr)
- let ?l = "Node ll (ln, lh) lr"
- let ?r = "Node rl (rn, rh) rr"
- let ?l' = "fst (split_max ?l)"
- from \<open>avl t\<close> and Node_Node have "avl ?r" by simp
- from \<open>avl t\<close> and Node_Node have "avl ?l" by simp
- hence "avl(?l')" "height ?l = height(?l') \<or>
- height ?l = height(?l') + 1" by (rule avl_split_max,simp)+
- with \<open>avl t\<close> Node_Node have "height ?l' = height ?r \<or> height ?l' = height ?r + 1
- \<or> height ?r = height ?l' + 1 \<or> height ?r = height ?l' + 2" by fastforce
- with \<open>avl ?l'\<close> \<open>avl ?r\<close> have "avl(balR ?l' (snd(split_max ?l)) ?r)"
- by (rule avl_balR)
- with Node_Node show ?thesis by (auto split:prod.splits)
-qed simp_all
-
-lemma height_del_root:
- assumes "avl t" and "t \<noteq> Leaf"
- shows "height t = height(del_root t) \<or> height t = height(del_root t) + 1"
-using assms
-proof (cases t rule: del_root_cases)
- case (Node_Node ll lx lh lr x h rl rx rh rr)
- let ?l = "Node ll (lx, lh) lr"
- let ?r = "Node rl (rx, rh) rr"
- let ?l' = "fst (split_max ?l)"
- let ?t' = "balR ?l' (snd(split_max ?l)) ?r"
- from \<open>avl t\<close> and Node_Node have "avl ?r" by simp
- from \<open>avl t\<close> and Node_Node have "avl ?l" by simp
- hence "avl(?l')" by (rule avl_split_max,simp)
- have l'_height: "height ?l = height ?l' \<or> height ?l = height ?l' + 1" using \<open>avl ?l\<close> by (intro avl_split_max) auto
- have t_height: "height t = 1 + max (height ?l) (height ?r)" using \<open>avl t\<close> Node_Node by simp
- have "height t = height ?t' \<or> height t = height ?t' + 1" using \<open>avl t\<close> Node_Node
- proof(cases "height ?r = height ?l' + 2")
- case False
- show ?thesis using l'_height t_height False
- by (subst height_balR2[OF \<open>avl ?l'\<close> \<open>avl ?r\<close> False])+ arith
- next
- case True
- show ?thesis
- proof(cases rule: disjE[OF height_balR[OF True \<open>avl ?l'\<close> \<open>avl ?r\<close>, of "snd (split_max ?l)"]])
- case 1 thus ?thesis using l'_height t_height True by arith
- next
- case 2 thus ?thesis using l'_height t_height True by arith
- qed
- qed
- thus ?thesis using Node_Node by (auto split:prod.splits)
-qed simp_all
-
text\<open>Deletion maintains the AVL property:\<close>
theorem avl_delete:
@@ -361,7 +306,8 @@
case 1
show ?case
proof(cases "x = a")
- case True with Node 1 show ?thesis by (auto simp:avl_del_root)
+ case True with Node 1 show ?thesis
+ using avl_split_max[of l] by (auto simp: avl_balR split: prod.split)
next
case False
show ?thesis
@@ -374,11 +320,8 @@
case 2
show ?case
proof(cases "x = a")
- case True
- with 1 have "height (Node l (a,n) r) = height(del_root (Node l (a,n) r))
- \<or> height (Node l (a,n) r) = height(del_root (Node l (a,n) r)) + 1"
- by (subst height_del_root,simp_all)
- with True show ?thesis by simp
+ case True then show ?thesis using 1 avl_split_max[of l]
+ by(auto simp: balR_def max_absorb2 split!: if_splits prod.split tree.split)
next
case False
show ?thesis
--- a/src/HOL/Equiv_Relations.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Equiv_Relations.thy Thu Apr 02 13:04:24 2020 +0200
@@ -34,21 +34,21 @@
unfolding refl_on_def by blast
lemma equiv_comp_eq: "equiv A r \<Longrightarrow> r\<inverse> O r = r"
- apply (unfold equiv_def)
- apply clarify
- apply (rule equalityI)
- apply (iprover intro: sym_trans_comp_subset refl_on_comp_subset)+
- done
+ unfolding equiv_def
+ by (iprover intro: sym_trans_comp_subset refl_on_comp_subset equalityI)
text \<open>Second half.\<close>
-lemma comp_equivI: "r\<inverse> O r = r \<Longrightarrow> Domain r = A \<Longrightarrow> equiv A r"
- apply (unfold equiv_def refl_on_def sym_def trans_def)
- apply (erule equalityE)
- apply (subgoal_tac "\<forall>x y. (x, y) \<in> r \<longrightarrow> (y, x) \<in> r")
- apply fast
- apply fast
- done
+lemma comp_equivI:
+ assumes "r\<inverse> O r = r" "Domain r = A"
+ shows "equiv A r"
+proof -
+ have *: "\<And>x y. (x, y) \<in> r \<Longrightarrow> (y, x) \<in> r"
+ using assms by blast
+ show ?thesis
+ unfolding equiv_def refl_on_def sym_def trans_def
+ using assms by (auto intro: *)
+qed
subsection \<open>Equivalence classes\<close>
@@ -58,10 +58,7 @@
unfolding equiv_def trans_def sym_def by blast
theorem equiv_class_eq: "equiv A r \<Longrightarrow> (a, b) \<in> r \<Longrightarrow> r``{a} = r``{b}"
- apply (assumption | rule equalityI equiv_class_subset)+
- apply (unfold equiv_def sym_def)
- apply blast
- done
+ by (intro equalityI equiv_class_subset; force simp add: equiv_def sym_def)
lemma equiv_class_self: "equiv A r \<Longrightarrow> a \<in> A \<Longrightarrow> a \<in> r``{a}"
unfolding equiv_def refl_on_def by blast
@@ -91,7 +88,7 @@
definition quotient :: "'a set \<Rightarrow> ('a \<times> 'a) set \<Rightarrow> 'a set set" (infixl "'/'/" 90)
where "A//r = (\<Union>x \<in> A. {r``{x}})" \<comment> \<open>set of equiv classes\<close>
-lemma quotientI: "x \<in> A ==> r``{x} \<in> A//r"
+lemma quotientI: "x \<in> A \<Longrightarrow> r``{x} \<in> A//r"
unfolding quotient_def by blast
lemma quotientE: "X \<in> A//r \<Longrightarrow> (\<And>x. X = r``{x} \<Longrightarrow> x \<in> A \<Longrightarrow> P) \<Longrightarrow> P"
@@ -101,32 +98,31 @@
unfolding equiv_def refl_on_def quotient_def by blast
lemma quotient_disj: "equiv A r \<Longrightarrow> X \<in> A//r \<Longrightarrow> Y \<in> A//r \<Longrightarrow> X = Y \<or> X \<inter> Y = {}"
- apply (unfold quotient_def)
- apply clarify
- apply (rule equiv_class_eq)
- apply assumption
- apply (unfold equiv_def trans_def sym_def)
- apply blast
- done
+ unfolding quotient_def equiv_def trans_def sym_def by blast
lemma quotient_eqI:
- "equiv A r \<Longrightarrow> X \<in> A//r \<Longrightarrow> Y \<in> A//r \<Longrightarrow> x \<in> X \<Longrightarrow> y \<in> Y \<Longrightarrow> (x, y) \<in> r \<Longrightarrow> X = Y"
- apply (clarify elim!: quotientE)
- apply (rule equiv_class_eq)
- apply assumption
- apply (unfold equiv_def sym_def trans_def)
- apply blast
- done
+ assumes "equiv A r" "X \<in> A//r" "Y \<in> A//r" and xy: "x \<in> X" "y \<in> Y" "(x, y) \<in> r"
+ shows "X = Y"
+proof -
+ obtain a b where "a \<in> A" and a: "X = r `` {a}" and "b \<in> A" and b: "Y = r `` {b}"
+ using assms by (auto elim!: quotientE)
+ then have "(a,b) \<in> r"
+ using xy \<open>equiv A r\<close> unfolding equiv_def sym_def trans_def by blast
+ then show ?thesis
+ unfolding a b by (rule equiv_class_eq [OF \<open>equiv A r\<close>])
+qed
lemma quotient_eq_iff:
- "equiv A r \<Longrightarrow> X \<in> A//r \<Longrightarrow> Y \<in> A//r \<Longrightarrow> x \<in> X \<Longrightarrow> y \<in> Y \<Longrightarrow> X = Y \<longleftrightarrow> (x, y) \<in> r"
- apply (rule iffI)
- prefer 2
- apply (blast del: equalityI intro: quotient_eqI)
- apply (clarify elim!: quotientE)
- apply (unfold equiv_def sym_def trans_def)
- apply blast
- done
+ assumes "equiv A r" "X \<in> A//r" "Y \<in> A//r" and xy: "x \<in> X" "y \<in> Y"
+ shows "X = Y \<longleftrightarrow> (x, y) \<in> r"
+proof
+ assume L: "X = Y"
+ with assms show "(x, y) \<in> r"
+ unfolding equiv_def sym_def trans_def by (blast elim!: quotientE)
+next
+ assume \<section>: "(x, y) \<in> r" show "X = Y"
+ by (rule quotient_eqI) (use \<section> assms in \<open>blast+\<close>)
+qed
lemma eq_equiv_class_iff2: "equiv A r \<Longrightarrow> x \<in> A \<Longrightarrow> y \<in> A \<Longrightarrow> {x}//r = {y}//r \<longleftrightarrow> (x, y) \<in> r"
by (simp add: quotient_def eq_equiv_class_iff)
@@ -189,22 +185,22 @@
\<comment> \<open>lemma required to prove \<open>UN_equiv_class\<close>\<close>
by auto
-lemma UN_equiv_class: "equiv A r \<Longrightarrow> f respects r \<Longrightarrow> a \<in> A \<Longrightarrow> (\<Union>x \<in> r``{a}. f x) = f a"
+lemma UN_equiv_class:
+ assumes "equiv A r" "f respects r" "a \<in> A"
+ shows "(\<Union>x \<in> r``{a}. f x) = f a"
\<comment> \<open>Conversion rule\<close>
- apply (rule equiv_class_self [THEN UN_constant_eq])
- apply assumption
- apply assumption
- apply (unfold equiv_def congruent_def sym_def)
- apply (blast del: equalityI)
- done
+proof -
+ have \<section>: "\<forall>x\<in>r `` {a}. f x = f a"
+ using assms unfolding equiv_def congruent_def sym_def by blast
+ show ?thesis
+ by (iprover intro: assms UN_constant_eq [OF equiv_class_self \<section>])
+qed
lemma UN_equiv_class_type:
- "equiv A r \<Longrightarrow> f respects r \<Longrightarrow> X \<in> A//r \<Longrightarrow> (\<And>x. x \<in> A \<Longrightarrow> f x \<in> B) \<Longrightarrow> (\<Union>x \<in> X. f x) \<in> B"
- apply (unfold quotient_def)
- apply clarify
- apply (subst UN_equiv_class)
- apply auto
- done
+ assumes r: "equiv A r" "f respects r" and X: "X \<in> A//r" and AB: "\<And>x. x \<in> A \<Longrightarrow> f x \<in> B"
+ shows "(\<Union>x \<in> X. f x) \<in> B"
+ using assms unfolding quotient_def
+ by (auto simp: UN_equiv_class [OF r])
text \<open>
Sufficient conditions for injectiveness. Could weaken premises!
@@ -213,19 +209,23 @@
\<close>
lemma UN_equiv_class_inject:
- "equiv A r \<Longrightarrow> f respects r \<Longrightarrow>
- (\<Union>x \<in> X. f x) = (\<Union>y \<in> Y. f y) \<Longrightarrow> X \<in> A//r ==> Y \<in> A//r
- \<Longrightarrow> (\<And>x y. x \<in> A \<Longrightarrow> y \<in> A \<Longrightarrow> f x = f y \<Longrightarrow> (x, y) \<in> r)
- \<Longrightarrow> X = Y"
- apply (unfold quotient_def)
- apply clarify
- apply (rule equiv_class_eq)
- apply assumption
- apply (subgoal_tac "f x = f xa")
- apply blast
- apply (erule box_equals)
- apply (assumption | rule UN_equiv_class)+
- done
+ assumes "equiv A r" "f respects r"
+ and eq: "(\<Union>x \<in> X. f x) = (\<Union>y \<in> Y. f y)"
+ and X: "X \<in> A//r" and Y: "Y \<in> A//r"
+ and fr: "\<And>x y. x \<in> A \<Longrightarrow> y \<in> A \<Longrightarrow> f x = f y \<Longrightarrow> (x, y) \<in> r"
+ shows "X = Y"
+proof -
+ obtain a b where "a \<in> A" and a: "X = r `` {a}" and "b \<in> A" and b: "Y = r `` {b}"
+ using assms by (auto elim!: quotientE)
+ then have "\<Union> (f ` r `` {a}) = f a" "\<Union> (f ` r `` {b}) = f b"
+ by (iprover intro: UN_equiv_class [OF \<open>equiv A r\<close>] assms)+
+ then have "f a = f b"
+ using eq unfolding a b by (iprover intro: trans sym)
+ then have "(a,b) \<in> r"
+ using fr \<open>a \<in> A\<close> \<open>b \<in> A\<close> by blast
+ then show ?thesis
+ unfolding a b by (rule equiv_class_eq [OF \<open>equiv A r\<close>])
+qed
subsection \<open>Defining binary operations upon equivalence classes\<close>
@@ -253,15 +253,20 @@
unfolding congruent_def congruent2_def equiv_def refl_on_def by blast
lemma congruent2_implies_congruent_UN:
- "equiv A1 r1 \<Longrightarrow> equiv A2 r2 \<Longrightarrow> congruent2 r1 r2 f \<Longrightarrow> a \<in> A2 \<Longrightarrow>
- congruent r1 (\<lambda>x1. \<Union>x2 \<in> r2``{a}. f x1 x2)"
- apply (unfold congruent_def)
- apply clarify
- apply (rule equiv_type [THEN subsetD, THEN SigmaE2], assumption+)
- apply (simp add: UN_equiv_class congruent2_implies_congruent)
- apply (unfold congruent2_def equiv_def refl_on_def)
- apply (blast del: equalityI)
- done
+ assumes "equiv A1 r1" "equiv A2 r2" "congruent2 r1 r2 f" "a \<in> A2"
+ shows "congruent r1 (\<lambda>x1. \<Union>x2 \<in> r2``{a}. f x1 x2)"
+ unfolding congruent_def
+proof clarify
+ fix c d
+ assume cd: "(c,d) \<in> r1"
+ then have "c \<in> A1" "d \<in> A1"
+ using \<open>equiv A1 r1\<close> by (auto elim!: equiv_type [THEN subsetD, THEN SigmaE2])
+ with assms show "\<Union> (f c ` r2 `` {a}) = \<Union> (f d ` r2 `` {a})"
+ proof (simp add: UN_equiv_class congruent2_implies_congruent)
+ show "f c a = f d a"
+ using assms cd unfolding congruent2_def equiv_def refl_on_def by blast
+ qed
+qed
lemma UN_equiv_class2:
"equiv A1 r1 \<Longrightarrow> equiv A2 r2 \<Longrightarrow> congruent2 r1 r2 f \<Longrightarrow> a1 \<in> A1 \<Longrightarrow> a2 \<in> A2 \<Longrightarrow>
@@ -273,11 +278,10 @@
\<Longrightarrow> X1 \<in> A1//r1 \<Longrightarrow> X2 \<in> A2//r2
\<Longrightarrow> (\<And>x1 x2. x1 \<in> A1 \<Longrightarrow> x2 \<in> A2 \<Longrightarrow> f x1 x2 \<in> B)
\<Longrightarrow> (\<Union>x1 \<in> X1. \<Union>x2 \<in> X2. f x1 x2) \<in> B"
- apply (unfold quotient_def)
- apply clarify
- apply (blast intro: UN_equiv_class_type congruent2_implies_congruent_UN
- congruent2_implies_congruent quotientI)
- done
+ unfolding quotient_def
+ by (blast intro: UN_equiv_class_type congruent2_implies_congruent_UN
+ congruent2_implies_congruent quotientI)
+
lemma UN_UN_split_split_eq:
"(\<Union>(x1, x2) \<in> X. \<Union>(y1, y2) \<in> Y. A x1 x2 y1 y2) =
@@ -293,60 +297,63 @@
\<Longrightarrow> congruent2 r1 r2 f"
\<comment> \<open>Suggested by John Harrison -- the two subproofs may be\<close>
\<comment> \<open>\<^emph>\<open>much\<close> simpler than the direct proof.\<close>
- apply (unfold congruent2_def equiv_def refl_on_def)
- apply clarify
- apply (blast intro: trans)
- done
+ unfolding congruent2_def equiv_def refl_on_def
+ by (blast intro: trans)
lemma congruent2_commuteI:
assumes equivA: "equiv A r"
and commute: "\<And>y z. y \<in> A \<Longrightarrow> z \<in> A \<Longrightarrow> f y z = f z y"
and congt: "\<And>y z w. w \<in> A \<Longrightarrow> (y,z) \<in> r \<Longrightarrow> f w y = f w z"
shows "f respects2 r"
- apply (rule congruent2I [OF equivA equivA])
- apply (rule commute [THEN trans])
- apply (rule_tac [3] commute [THEN trans, symmetric])
- apply (rule_tac [5] sym)
- apply (rule congt | assumption |
- erule equivA [THEN equiv_type, THEN subsetD, THEN SigmaE2])+
- done
+proof (rule congruent2I [OF equivA equivA])
+ note eqv = equivA [THEN equiv_type, THEN subsetD, THEN SigmaE2]
+ show "\<And>y z w. \<lbrakk>w \<in> A; (y, z) \<in> r\<rbrakk> \<Longrightarrow> f y w = f z w"
+ by (iprover intro: commute [THEN trans] sym congt elim: eqv)
+ show "\<And>y z w. \<lbrakk>w \<in> A; (y, z) \<in> r\<rbrakk> \<Longrightarrow> f w y = f w z"
+ by (iprover intro: congt elim: eqv)
+qed
subsection \<open>Quotients and finiteness\<close>
text \<open>Suggested by Florian Kammüller\<close>
-lemma finite_quotient: "finite A \<Longrightarrow> r \<subseteq> A \<times> A \<Longrightarrow> finite (A//r)"
- \<comment> \<open>recall @{thm equiv_type}\<close>
- apply (rule finite_subset)
- apply (erule_tac [2] finite_Pow_iff [THEN iffD2])
- apply (unfold quotient_def)
- apply blast
- done
+lemma finite_quotient:
+ assumes "finite A" "r \<subseteq> A \<times> A"
+ shows "finite (A//r)"
+ \<comment> \<open>recall @{thm equiv_type}\<close>
+proof -
+ have "A//r \<subseteq> Pow A"
+ using assms unfolding quotient_def by blast
+ moreover have "finite (Pow A)"
+ using assms by simp
+ ultimately show ?thesis
+ by (iprover intro: finite_subset)
+qed
lemma finite_equiv_class: "finite A \<Longrightarrow> r \<subseteq> A \<times> A \<Longrightarrow> X \<in> A//r \<Longrightarrow> finite X"
- apply (unfold quotient_def)
- apply (rule finite_subset)
- prefer 2 apply assumption
- apply blast
- done
+ unfolding quotient_def
+ by (erule rev_finite_subset) blast
-lemma equiv_imp_dvd_card: "finite A \<Longrightarrow> equiv A r \<Longrightarrow> \<forall>X \<in> A//r. k dvd card X \<Longrightarrow> k dvd card A"
- apply (rule Union_quotient [THEN subst [where P="\<lambda>A. k dvd card A"]])
- apply assumption
- apply (rule dvd_partition)
- prefer 3 apply (blast dest: quotient_disj)
- apply (simp_all add: Union_quotient equiv_type)
- done
+lemma equiv_imp_dvd_card:
+ assumes "finite A" "equiv A r" "\<And>X. X \<in> A//r \<Longrightarrow> k dvd card X"
+ shows "k dvd card A"
+proof (rule Union_quotient [THEN subst])
+ show "k dvd card (\<Union> (A // r))"
+ apply (rule dvd_partition)
+ using assms
+ by (auto simp: Union_quotient dest: quotient_disj)
+qed (use assms in blast)
-lemma card_quotient_disjoint: "finite A \<Longrightarrow> inj_on (\<lambda>x. {x} // r) A \<Longrightarrow> card (A//r) = card A"
- apply (simp add:quotient_def)
- apply (subst card_UN_disjoint)
- apply assumption
- apply simp
- apply (fastforce simp add:inj_on_def)
- apply simp
- done
+lemma card_quotient_disjoint:
+ assumes "finite A" "inj_on (\<lambda>x. {x} // r) A"
+ shows "card (A//r) = card A"
+proof -
+ have "\<forall>i\<in>A. \<forall>j\<in>A. i \<noteq> j \<longrightarrow> r `` {j} \<noteq> r `` {i}"
+ using assms by (fastforce simp add: quotient_def inj_on_def)
+ with assms show ?thesis
+ by (simp add: quotient_def card_UN_disjoint)
+qed
subsection \<open>Projection\<close>
--- a/src/HOL/Fun.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Fun.thy Thu Apr 02 13:04:24 2020 +0200
@@ -738,7 +738,7 @@
by (simp add: fun_eq_iff)
lemma fun_upd_twist: "a \<noteq> c \<Longrightarrow> (m(a := b))(c := d) = (m(c := d))(a := b)"
- by (rule ext) auto
+ by auto
lemma inj_on_fun_updI: "inj_on f A \<Longrightarrow> y \<notin> f ` A \<Longrightarrow> inj_on (f(x := y)) A"
by (auto simp: inj_on_def)
--- a/src/HOL/HOL.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/HOL.thy Thu Apr 02 13:04:24 2020 +0200
@@ -249,11 +249,7 @@
| |
c = d *)
lemma box_equals: "\<lbrakk>a = b; a = c; b = d\<rbrakk> \<Longrightarrow> c = d"
- apply (rule trans)
- apply (rule trans)
- apply (rule sym)
- apply assumption+
- done
+ by (iprover intro: sym trans)
text \<open>For calculational reasoning:\<close>
@@ -268,25 +264,17 @@
text \<open>Similar to \<open>AP_THM\<close> in Gordon's HOL.\<close>
lemma fun_cong: "(f :: 'a \<Rightarrow> 'b) = g \<Longrightarrow> f x = g x"
- apply (erule subst)
- apply (rule refl)
- done
+ by (iprover intro: refl elim: subst)
text \<open>Similar to \<open>AP_TERM\<close> in Gordon's HOL and FOL's \<open>subst_context\<close>.\<close>
lemma arg_cong: "x = y \<Longrightarrow> f x = f y"
- apply (erule subst)
- apply (rule refl)
- done
+ by (iprover intro: refl elim: subst)
lemma arg_cong2: "\<lbrakk>a = b; c = d\<rbrakk> \<Longrightarrow> f a c = f b d"
- apply (erule ssubst)+
- apply (rule refl)
- done
+ by (iprover intro: refl elim: subst)
lemma cong: "\<lbrakk>f = g; (x::'a) = y\<rbrakk> \<Longrightarrow> f x = g y"
- apply (erule subst)+
- apply (rule refl)
- done
+ by (iprover intro: refl elim: subst)
ML \<open>fun cong_tac ctxt = Cong_Tac.cong_tac ctxt @{thm cong}\<close>
@@ -324,20 +312,15 @@
subsubsection \<open>Universal quantifier (1)\<close>
lemma spec: "\<forall>x::'a. P x \<Longrightarrow> P x"
- apply (unfold All_def)
- apply (rule eqTrueE)
- apply (erule fun_cong)
- done
+ unfolding All_def by (iprover intro: eqTrueE fun_cong)
lemma allE:
- assumes major: "\<forall>x. P x"
- and minor: "P x \<Longrightarrow> R"
+ assumes major: "\<forall>x. P x" and minor: "P x \<Longrightarrow> R"
shows R
by (iprover intro: minor major [THEN spec])
lemma all_dupE:
- assumes major: "\<forall>x. P x"
- and minor: "\<lbrakk>P x; \<forall>x. P x\<rbrakk> \<Longrightarrow> R"
+ assumes major: "\<forall>x. P x" and minor: "\<lbrakk>P x; \<forall>x. P x\<rbrakk> \<Longrightarrow> R"
shows R
by (iprover intro: minor major major [THEN spec])
@@ -350,9 +333,7 @@
\<close>
lemma FalseE: "False \<Longrightarrow> P"
- apply (unfold False_def)
- apply (erule spec)
- done
+ unfolding False_def by (erule spec)
lemma False_neq_True: "False = True \<Longrightarrow> P"
by (erule eqTrueE [THEN FalseE])
@@ -363,29 +344,17 @@
lemma notI:
assumes "P \<Longrightarrow> False"
shows "\<not> P"
- apply (unfold not_def)
- apply (iprover intro: impI assms)
- done
+ unfolding not_def by (iprover intro: impI assms)
lemma False_not_True: "False \<noteq> True"
- apply (rule notI)
- apply (erule False_neq_True)
- done
+ by (iprover intro: notI elim: False_neq_True)
lemma True_not_False: "True \<noteq> False"
- apply (rule notI)
- apply (drule sym)
- apply (erule False_neq_True)
- done
+ by (iprover intro: notI dest: sym elim: False_neq_True)
lemma notE: "\<lbrakk>\<not> P; P\<rbrakk> \<Longrightarrow> R"
- apply (unfold not_def)
- apply (erule mp [THEN FalseE])
- apply assumption
- done
-
-lemma notI2: "(P \<Longrightarrow> \<not> Pa) \<Longrightarrow> (P \<Longrightarrow> Pa) \<Longrightarrow> \<not> P"
- by (erule notE [THEN notI]) (erule meta_mp)
+ unfolding not_def
+ by (iprover intro: mp [THEN FalseE])
subsubsection \<open>Implication\<close>
@@ -397,7 +366,7 @@
text \<open>Reduces \<open>Q\<close> to \<open>P \<longrightarrow> Q\<close>, allowing substitution in \<open>P\<close>.\<close>
lemma rev_mp: "\<lbrakk>P; P \<longrightarrow> Q\<rbrakk> \<Longrightarrow> Q"
- by (iprover intro: mp)
+ by (rule mp)
lemma contrapos_nn:
assumes major: "\<not> Q"
@@ -510,10 +479,10 @@
assumes major: "P \<and> Q"
and minor: "\<lbrakk>P; Q\<rbrakk> \<Longrightarrow> R"
shows R
- apply (rule minor)
- apply (rule major [THEN conjunct1])
- apply (rule major [THEN conjunct2])
- done
+proof (rule minor)
+ show P by (rule major [THEN conjunct1])
+ show Q by (rule major [THEN conjunct2])
+qed
lemma context_conjI:
assumes P "P \<Longrightarrow> Q"
@@ -533,14 +502,18 @@
subsubsection \<open>Classical logic\<close>
lemma classical:
- assumes prem: "\<not> P \<Longrightarrow> P"
+ assumes "\<not> P \<Longrightarrow> P"
shows P
- apply (rule True_or_False [THEN disjE, THEN eqTrueE])
- apply assumption
- apply (rule notI [THEN prem, THEN eqTrueI])
- apply (erule subst)
- apply assumption
- done
+proof (rule True_or_False [THEN disjE])
+ show P if "P = True"
+ using that by (iprover intro: eqTrueE)
+ show P if "P = False"
+ proof (intro notI assms)
+ assume P
+ with that show False
+ by (iprover elim: subst)
+ qed
+qed
lemmas ccontr = FalseE [THEN classical]
@@ -550,16 +523,12 @@
assumes premp: P
and premnot: "\<not> R \<Longrightarrow> \<not> P"
shows R
- apply (rule ccontr)
- apply (erule notE [OF premnot premp])
- done
+ by (iprover intro: ccontr notE [OF premnot premp])
+
text \<open>Double negation law.\<close>
lemma notnotD: "\<not>\<not> P \<Longrightarrow> P"
- apply (rule classical)
- apply (erule notE)
- apply assumption
- done
+ by (iprover intro: ccontr notE )
lemma contrapos_pp:
assumes p1: Q
@@ -583,19 +552,15 @@
by (iprover intro: ex_prem [THEN exE] ex1I eq)
lemma ex1E:
- assumes major: "\<exists>!x. P x"
- and minor: "\<And>x. \<lbrakk>P x; \<forall>y. P y \<longrightarrow> y = x\<rbrakk> \<Longrightarrow> R"
+ assumes major: "\<exists>!x. P x" and minor: "\<And>x. \<lbrakk>P x; \<forall>y. P y \<longrightarrow> y = x\<rbrakk> \<Longrightarrow> R"
shows R
- apply (rule major [unfolded Ex1_def, THEN exE])
- apply (erule conjE)
- apply (iprover intro: minor)
- done
+proof (rule major [unfolded Ex1_def, THEN exE])
+ show "\<And>x. P x \<and> (\<forall>y. P y \<longrightarrow> y = x) \<Longrightarrow> R"
+ by (iprover intro: minor elim: conjE)
+qed
lemma ex1_implies_ex: "\<exists>!x. P x \<Longrightarrow> \<exists>x. P x"
- apply (erule ex1E)
- apply (rule exI)
- apply assumption
- done
+ by (iprover intro: exI elim: ex1E)
subsubsection \<open>Classical intro rules for disjunction and existential quantifiers\<close>
@@ -613,22 +578,18 @@
Note that \<open>\<not> P\<close> is the second case, not the first.
\<close>
lemma case_split [case_names True False]:
- assumes prem1: "P \<Longrightarrow> Q"
- and prem2: "\<not> P \<Longrightarrow> Q"
+ assumes "P \<Longrightarrow> Q" "\<not> P \<Longrightarrow> Q"
shows Q
- apply (rule excluded_middle [THEN disjE])
- apply (erule prem2)
- apply (erule prem1)
- done
+ using excluded_middle [of P]
+ by (iprover intro: assms elim: disjE)
text \<open>Classical implies (\<open>\<longrightarrow>\<close>) elimination.\<close>
lemma impCE:
assumes major: "P \<longrightarrow> Q"
and minor: "\<not> P \<Longrightarrow> R" "Q \<Longrightarrow> R"
shows R
- apply (rule excluded_middle [of P, THEN disjE])
- apply (iprover intro: minor major [THEN mp])+
- done
+ using excluded_middle [of P]
+ by (iprover intro: minor major [THEN mp] elim: disjE)+
text \<open>
This version of \<open>\<longrightarrow>\<close> elimination works on \<open>Q\<close> before \<open>P\<close>. It works best for
@@ -639,9 +600,8 @@
assumes major: "P \<longrightarrow> Q"
and minor: "Q \<Longrightarrow> R" "\<not> P \<Longrightarrow> R"
shows R
- apply (rule excluded_middle [of P, THEN disjE])
- apply (iprover intro: minor major [THEN mp])+
- done
+ using assms by (elim impCE)
+
text \<open>Classical \<open>\<longleftrightarrow>\<close> elimination.\<close>
lemma iffCE:
@@ -874,9 +834,7 @@
ML \<open>val HOL_cs = claset_of \<^context>\<close>
lemma contrapos_np: "\<not> Q \<Longrightarrow> (\<not> P \<Longrightarrow> Q) \<Longrightarrow> P"
- apply (erule swap)
- apply (erule (1) meta_mp)
- done
+ by (erule swap)
declare ex_ex1I [rule del, intro! 2]
and ex1I [intro]
@@ -889,15 +847,13 @@
text \<open>Better than \<open>ex1E\<close> for classical reasoner: needs no quantifier duplication!\<close>
lemma alt_ex1E [elim!]:
assumes major: "\<exists>!x. P x"
- and prem: "\<And>x. \<lbrakk>P x; \<forall>y y'. P y \<and> P y' \<longrightarrow> y = y'\<rbrakk> \<Longrightarrow> R"
+ and minor: "\<And>x. \<lbrakk>P x; \<forall>y y'. P y \<and> P y' \<longrightarrow> y = y'\<rbrakk> \<Longrightarrow> R"
shows R
- apply (rule ex1E [OF major])
- apply (rule prem)
- apply assumption
- apply (rule allI)+
- apply (tactic \<open>eresolve_tac \<^context> [Classical.dup_elim \<^context> @{thm allE}] 1\<close>)
- apply iprover
- done
+proof (rule ex1E [OF major minor])
+ show "\<forall>y y'. P y \<and> P y' \<longrightarrow> y = y'" if "P x" and \<section>: "\<forall>y. P y \<longrightarrow> y = x" for x
+ using \<open>P x\<close> \<section> \<section> by fast
+qed assumption
+
ML \<open>
structure Blast = Blast
@@ -1101,12 +1057,12 @@
unfolding If_def by blast
lemma if_split: "P (if Q then x else y) = ((Q \<longrightarrow> P x) \<and> (\<not> Q \<longrightarrow> P y))"
- apply (rule case_split [of Q])
- apply (simplesubst if_P)
- prefer 3
- apply (simplesubst if_not_P)
- apply blast+
- done
+proof (rule case_split [of Q])
+ show ?thesis if Q
+ using that by (simplesubst if_P) blast+
+ show ?thesis if "\<not> Q"
+ using that by (simplesubst if_not_P) blast+
+qed
lemma if_split_asm: "P (if Q then x else y) = (\<not> ((Q \<and> \<not> P x) \<or> (\<not> Q \<and> \<not> P y)))"
by (simplesubst if_split) blast
@@ -1150,20 +1106,15 @@
lemma simp_impliesI:
assumes PQ: "(PROP P \<Longrightarrow> PROP Q)"
shows "PROP P =simp=> PROP Q"
- apply (unfold simp_implies_def)
- apply (rule PQ)
- apply assumption
- done
+ unfolding simp_implies_def
+ by (iprover intro: PQ)
lemma simp_impliesE:
assumes PQ: "PROP P =simp=> PROP Q"
and P: "PROP P"
and QR: "PROP Q \<Longrightarrow> PROP R"
shows "PROP R"
- apply (rule QR)
- apply (rule PQ [unfolded simp_implies_def])
- apply (rule P)
- done
+ by (iprover intro: QR P PQ [unfolded simp_implies_def])
lemma simp_implies_cong:
assumes PP' :"PROP P \<equiv> PROP P'"
@@ -1658,22 +1609,32 @@
lemma ex1_eq [iff]: "\<exists>!x. x = t" "\<exists>!x. t = x"
by blast+
-lemma choice_eq: "(\<forall>x. \<exists>!y. P x y) = (\<exists>!f. \<forall>x. P x (f x))"
- apply (rule iffI)
- apply (rule_tac a = "\<lambda>x. THE y. P x y" in ex1I)
- apply (fast dest!: theI')
- apply (fast intro: the1_equality [symmetric])
- apply (erule ex1E)
- apply (rule allI)
- apply (rule ex1I)
- apply (erule spec)
- apply (erule_tac x = "\<lambda>z. if z = x then y else f z" in allE)
- apply (erule impE)
- apply (rule allI)
- apply (case_tac "xa = x")
- apply (drule_tac [3] x = x in fun_cong)
- apply simp_all
- done
+lemma choice_eq: "(\<forall>x. \<exists>!y. P x y) = (\<exists>!f. \<forall>x. P x (f x))" (is "?lhs = ?rhs")
+proof (intro iffI allI)
+ assume L: ?lhs
+ then have \<section>: "\<forall>x. P x (THE y. P x y)"
+ by (best intro: theI')
+ show ?rhs
+ by (rule ex1I) (use L \<section> in \<open>fast+\<close>)
+next
+ fix x
+ assume R: ?rhs
+ then obtain f where f: "\<forall>x. P x (f x)" and f1: "\<And>y. (\<forall>x. P x (y x)) \<Longrightarrow> y = f"
+ by (blast elim: ex1E)
+ show "\<exists>!y. P x y"
+ proof (rule ex1I)
+ show "P x (f x)"
+ using f by blast
+ show "y = f x" if "P x y" for y
+ proof -
+ have "P z (if z = x then y else f z)" for z
+ using f that by (auto split: if_split)
+ with f1 [of "\<lambda>z. if z = x then y else f z"] f
+ show ?thesis
+ by (auto simp add: split: if_split_asm dest: fun_cong)
+ qed
+ qed
+qed
lemmas eq_sym_conv = eq_commute
--- a/src/HOL/Induct/Comb.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Induct/Comb.thy Thu Apr 02 13:04:24 2020 +0200
@@ -10,12 +10,10 @@
begin
text \<open>
- Curiously, combinators do not include free variables.
-
+ Combinator terms do not have free variables.
Example taken from @{cite camilleri92}.
\<close>
-
subsection \<open>Definitions\<close>
text \<open>Datatype definition of combinators \<open>S\<close> and \<open>K\<close>.\<close>
@@ -29,36 +27,32 @@
(multi-step) reductions, \<open>\<rightarrow>\<close>.
\<close>
-inductive_set contract :: "(comb*comb) set"
- and contract_rel1 :: "[comb,comb] \<Rightarrow> bool" (infixl "\<rightarrow>\<^sup>1" 50)
-where
- "x \<rightarrow>\<^sup>1 y == (x,y) \<in> contract"
-| K: "K\<bullet>x\<bullet>y \<rightarrow>\<^sup>1 x"
-| S: "S\<bullet>x\<bullet>y\<bullet>z \<rightarrow>\<^sup>1 (x\<bullet>z)\<bullet>(y\<bullet>z)"
-| Ap1: "x\<rightarrow>\<^sup>1y \<Longrightarrow> x\<bullet>z \<rightarrow>\<^sup>1 y\<bullet>z"
-| Ap2: "x\<rightarrow>\<^sup>1y \<Longrightarrow> z\<bullet>x \<rightarrow>\<^sup>1 z\<bullet>y"
+inductive contract1 :: "[comb,comb] \<Rightarrow> bool" (infixl "\<rightarrow>\<^sup>1" 50)
+ where
+ K: "K\<bullet>x\<bullet>y \<rightarrow>\<^sup>1 x"
+ | S: "S\<bullet>x\<bullet>y\<bullet>z \<rightarrow>\<^sup>1 (x\<bullet>z)\<bullet>(y\<bullet>z)"
+ | Ap1: "x \<rightarrow>\<^sup>1 y \<Longrightarrow> x\<bullet>z \<rightarrow>\<^sup>1 y\<bullet>z"
+ | Ap2: "x \<rightarrow>\<^sup>1 y \<Longrightarrow> z\<bullet>x \<rightarrow>\<^sup>1 z\<bullet>y"
abbreviation
- contract_rel :: "[comb,comb] \<Rightarrow> bool" (infixl "\<rightarrow>" 50) where
- "x \<rightarrow> y == (x,y) \<in> contract\<^sup>*"
+ contract :: "[comb,comb] \<Rightarrow> bool" (infixl "\<rightarrow>" 50) where
+ "contract \<equiv> contract1\<^sup>*\<^sup>*"
text \<open>
Inductive definition of parallel contractions, \<open>\<Rrightarrow>\<^sup>1\<close> and
(multi-step) parallel reductions, \<open>\<Rrightarrow>\<close>.
\<close>
-inductive_set parcontract :: "(comb*comb) set"
- and parcontract_rel1 :: "[comb,comb] \<Rightarrow> bool" (infixl "\<Rrightarrow>\<^sup>1" 50)
-where
- "x \<Rrightarrow>\<^sup>1 y == (x,y) \<in> parcontract"
-| refl: "x \<Rrightarrow>\<^sup>1 x"
-| K: "K\<bullet>x\<bullet>y \<Rrightarrow>\<^sup>1 x"
-| S: "S\<bullet>x\<bullet>y\<bullet>z \<Rrightarrow>\<^sup>1 (x\<bullet>z)\<bullet>(y\<bullet>z)"
-| Ap: "[| x\<Rrightarrow>\<^sup>1y; z\<Rrightarrow>\<^sup>1w |] ==> x\<bullet>z \<Rrightarrow>\<^sup>1 y\<bullet>w"
+inductive parcontract1 :: "[comb,comb] \<Rightarrow> bool" (infixl "\<Rrightarrow>\<^sup>1" 50)
+ where
+ refl: "x \<Rrightarrow>\<^sup>1 x"
+ | K: "K\<bullet>x\<bullet>y \<Rrightarrow>\<^sup>1 x"
+ | S: "S\<bullet>x\<bullet>y\<bullet>z \<Rrightarrow>\<^sup>1 (x\<bullet>z)\<bullet>(y\<bullet>z)"
+ | Ap: "\<lbrakk>x \<Rrightarrow>\<^sup>1 y; z \<Rrightarrow>\<^sup>1 w\<rbrakk> \<Longrightarrow> x\<bullet>z \<Rrightarrow>\<^sup>1 y\<bullet>w"
abbreviation
- parcontract_rel :: "[comb,comb] \<Rightarrow> bool" (infixl "\<Rrightarrow>" 50) where
- "x \<Rrightarrow> y == (x,y) \<in> parcontract\<^sup>*"
+ parcontract :: "[comb,comb] \<Rightarrow> bool" (infixl "\<Rrightarrow>" 50) where
+ "parcontract \<equiv> parcontract1\<^sup>*\<^sup>*"
text \<open>
Misc definitions.
@@ -66,37 +60,55 @@
definition
I :: comb where
- "I = S\<bullet>K\<bullet>K"
+ "I \<equiv> S\<bullet>K\<bullet>K"
definition
- diamond :: "('a * 'a)set \<Rightarrow> bool" where
+ diamond :: "([comb,comb] \<Rightarrow> bool) \<Rightarrow> bool" where
\<comment> \<open>confluence; Lambda/Commutation treats this more abstractly\<close>
- "diamond(r) = (\<forall>x y. (x,y) \<in> r -->
- (\<forall>y'. (x,y') \<in> r -->
- (\<exists>z. (y,z) \<in> r & (y',z) \<in> r)))"
+ "diamond r \<equiv> \<forall>x y. r x y \<longrightarrow>
+ (\<forall>y'. r x y' \<longrightarrow>
+ (\<exists>z. r y z \<and> r y' z))"
subsection \<open>Reflexive/Transitive closure preserves Church-Rosser property\<close>
-text\<open>So does the Transitive closure, with a similar proof\<close>
+text\<open>Remark: So does the Transitive closure, with a similar proof\<close>
text\<open>Strip lemma.
The induction hypothesis covers all but the last diamond of the strip.\<close>
-lemma diamond_strip_lemmaE [rule_format]:
- "[| diamond(r); (x,y) \<in> r\<^sup>* |] ==>
- \<forall>y'. (x,y') \<in> r --> (\<exists>z. (y',z) \<in> r\<^sup>* & (y,z) \<in> r)"
-apply (unfold diamond_def)
-apply (erule rtrancl_induct)
-apply (meson rtrancl_refl)
-apply (meson rtrancl_trans r_into_rtrancl)
-done
+lemma strip_lemma [rule_format]:
+ assumes "diamond r" and r: "r\<^sup>*\<^sup>* x y" "r x y'"
+ shows "\<exists>z. r\<^sup>*\<^sup>* y' z \<and> r y z"
+ using r
+proof (induction rule: rtranclp_induct)
+ case base
+ then show ?case
+ by blast
+next
+ case (step y z)
+ then show ?case
+ using \<open>diamond r\<close> unfolding diamond_def
+ by (metis rtranclp.rtrancl_into_rtrancl)
+qed
-lemma diamond_rtrancl: "diamond(r) \<Longrightarrow> diamond(r\<^sup>*)"
-apply (simp (no_asm_simp) add: diamond_def)
-apply (rule impI [THEN allI, THEN allI])
-apply (erule rtrancl_induct, blast)
-apply (meson rtrancl_trans r_into_rtrancl diamond_strip_lemmaE)
-done
+proposition diamond_rtrancl:
+ assumes "diamond r"
+ shows "diamond(r\<^sup>*\<^sup>*)"
+ unfolding diamond_def
+proof (intro strip)
+ fix x y y'
+ assume "r\<^sup>*\<^sup>* x y" "r\<^sup>*\<^sup>* x y'"
+ then show "\<exists>z. r\<^sup>*\<^sup>* y z \<and> r\<^sup>*\<^sup>* y' z"
+ proof (induction rule: rtranclp_induct)
+ case base
+ then show ?case
+ by blast
+ next
+ case (step y z)
+ then show ?case
+ by (meson assms strip_lemma rtranclp.rtrancl_into_rtrancl)
+ qed
+qed
subsection \<open>Non-contraction results\<close>
@@ -104,33 +116,29 @@
text \<open>Derive a case for each combinator constructor.\<close>
inductive_cases
- K_contractE [elim!]: "K \<rightarrow>\<^sup>1 r"
+ K_contractE [elim!]: "K \<rightarrow>\<^sup>1 r"
and S_contractE [elim!]: "S \<rightarrow>\<^sup>1 r"
and Ap_contractE [elim!]: "p\<bullet>q \<rightarrow>\<^sup>1 r"
-declare contract.K [intro!] contract.S [intro!]
-declare contract.Ap1 [intro] contract.Ap2 [intro]
+declare contract1.K [intro!] contract1.S [intro!]
+declare contract1.Ap1 [intro] contract1.Ap2 [intro]
-lemma I_contract_E [elim!]: "I \<rightarrow>\<^sup>1 z \<Longrightarrow> P"
-by (unfold I_def, blast)
+lemma I_contract_E [iff]: "\<not> I \<rightarrow>\<^sup>1 z"
+ unfolding I_def by blast
-lemma K1_contractD [elim!]: "K\<bullet>x \<rightarrow>\<^sup>1 z \<Longrightarrow> (\<exists>x'. z = K\<bullet>x' & x \<rightarrow>\<^sup>1 x')"
-by blast
+lemma K1_contractD [elim!]: "K\<bullet>x \<rightarrow>\<^sup>1 z \<Longrightarrow> (\<exists>x'. z = K\<bullet>x' \<and> x \<rightarrow>\<^sup>1 x')"
+ by blast
lemma Ap_reduce1 [intro]: "x \<rightarrow> y \<Longrightarrow> x\<bullet>z \<rightarrow> y\<bullet>z"
-apply (erule rtrancl_induct)
-apply (blast intro: rtrancl_trans)+
-done
+ by (induction rule: rtranclp_induct; blast intro: rtranclp_trans)
lemma Ap_reduce2 [intro]: "x \<rightarrow> y \<Longrightarrow> z\<bullet>x \<rightarrow> z\<bullet>y"
-apply (erule rtrancl_induct)
-apply (blast intro: rtrancl_trans)+
-done
+ by (induction rule: rtranclp_induct; blast intro: rtranclp_trans)
text \<open>Counterexample to the diamond property for \<^term>\<open>x \<rightarrow>\<^sup>1 y\<close>\<close>
-lemma not_diamond_contract: "~ diamond(contract)"
-by (unfold diamond_def, metis S_contractE contract.K)
+lemma not_diamond_contract: "\<not> diamond(contract1)"
+ unfolding diamond_def by (metis S_contractE contract1.K)
subsection \<open>Results about Parallel Contraction\<close>
@@ -142,55 +150,52 @@
and S_parcontractE [elim!]: "S \<Rrightarrow>\<^sup>1 r"
and Ap_parcontractE [elim!]: "p\<bullet>q \<Rrightarrow>\<^sup>1 r"
-declare parcontract.intros [intro]
-
-(*** Basic properties of parallel contraction ***)
+declare parcontract1.intros [intro]
subsection \<open>Basic properties of parallel contraction\<close>
+text\<open>The rules below are not essential but make proofs much faster\<close>
-lemma K1_parcontractD [dest!]: "K\<bullet>x \<Rrightarrow>\<^sup>1 z \<Longrightarrow> (\<exists>x'. z = K\<bullet>x' & x \<Rrightarrow>\<^sup>1 x')"
-by blast
+lemma K1_parcontractD [dest!]: "K\<bullet>x \<Rrightarrow>\<^sup>1 z \<Longrightarrow> (\<exists>x'. z = K\<bullet>x' \<and> x \<Rrightarrow>\<^sup>1 x')"
+ by blast
-lemma S1_parcontractD [dest!]: "S\<bullet>x \<Rrightarrow>\<^sup>1 z \<Longrightarrow> (\<exists>x'. z = S\<bullet>x' & x \<Rrightarrow>\<^sup>1 x')"
-by blast
+lemma S1_parcontractD [dest!]: "S\<bullet>x \<Rrightarrow>\<^sup>1 z \<Longrightarrow> (\<exists>x'. z = S\<bullet>x' \<and> x \<Rrightarrow>\<^sup>1 x')"
+ by blast
-lemma S2_parcontractD [dest!]:
- "S\<bullet>x\<bullet>y \<Rrightarrow>\<^sup>1 z \<Longrightarrow> (\<exists>x' y'. z = S\<bullet>x'\<bullet>y' & x \<Rrightarrow>\<^sup>1 x' & y \<Rrightarrow>\<^sup>1 y')"
-by blast
-
-text\<open>The rules above are not essential but make proofs much faster\<close>
+lemma S2_parcontractD [dest!]: "S\<bullet>x\<bullet>y \<Rrightarrow>\<^sup>1 z \<Longrightarrow> (\<exists>x' y'. z = S\<bullet>x'\<bullet>y' \<and> x \<Rrightarrow>\<^sup>1 x' \<and> y \<Rrightarrow>\<^sup>1 y')"
+ by blast
text\<open>Church-Rosser property for parallel contraction\<close>
-lemma diamond_parcontract: "diamond parcontract"
-apply (unfold diamond_def)
-apply (rule impI [THEN allI, THEN allI])
-apply (erule parcontract.induct, fast+)
-done
+proposition diamond_parcontract: "diamond parcontract1"
+proof -
+ have "(\<exists>z. w \<Rrightarrow>\<^sup>1 z \<and> y' \<Rrightarrow>\<^sup>1 z)" if "y \<Rrightarrow>\<^sup>1 w" "y \<Rrightarrow>\<^sup>1 y'" for w y y'
+ using that by (induction arbitrary: y' rule: parcontract1.induct) fast+
+ then show ?thesis
+ by (auto simp: diamond_def)
+qed
-text \<open>
- \<^medskip>
- Equivalence of \<^prop>\<open>p \<rightarrow> q\<close> and \<^prop>\<open>p \<Rrightarrow> q\<close>.
-\<close>
+subsection \<open>Equivalence of \<^prop>\<open>p \<rightarrow> q\<close> and \<^prop>\<open>p \<Rrightarrow> q\<close>.\<close>
-lemma contract_subset_parcontract: "contract \<subseteq> parcontract"
-by (auto, erule contract.induct, blast+)
+lemma contract_imp_parcontract: "x \<rightarrow>\<^sup>1 y \<Longrightarrow> x \<Rrightarrow>\<^sup>1 y"
+ by (induction rule: contract1.induct; blast)
text\<open>Reductions: simply throw together reflexivity, transitivity and
the one-step reductions\<close>
-declare r_into_rtrancl [intro] rtrancl_trans [intro]
-
-(*Example only: not used*)
-lemma reduce_I: "I\<bullet>x \<rightarrow> x"
-by (unfold I_def, blast)
+proposition reduce_I: "I\<bullet>x \<rightarrow> x"
+ unfolding I_def
+ by (meson contract1.K contract1.S r_into_rtranclp rtranclp.rtrancl_into_rtrancl)
-lemma parcontract_subset_reduce: "parcontract \<subseteq> contract\<^sup>*"
-by (auto, erule parcontract.induct, blast+)
+lemma parcontract_imp_reduce: "x \<Rrightarrow>\<^sup>1 y \<Longrightarrow> x \<rightarrow> y"
+proof (induction rule: parcontract1.induct)
+ case (Ap x y z w)
+ then show ?case
+ by (meson Ap_reduce1 Ap_reduce2 rtranclp_trans)
+qed auto
-lemma reduce_eq_parreduce: "contract\<^sup>* = parcontract\<^sup>*"
-by (metis contract_subset_parcontract parcontract_subset_reduce rtrancl_subset)
+lemma reduce_eq_parreduce: "x \<rightarrow> y \<longleftrightarrow> x \<Rrightarrow> y"
+ by (metis contract_imp_parcontract parcontract_imp_reduce predicate2I rtranclp_subset)
-theorem diamond_reduce: "diamond(contract\<^sup>*)"
-by (simp add: reduce_eq_parreduce diamond_rtrancl diamond_parcontract)
+theorem diamond_reduce: "diamond(contract)"
+ using diamond_parcontract diamond_rtrancl reduce_eq_parreduce by presburger
end
--- a/src/HOL/Int.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Int.thy Thu Apr 02 13:04:24 2020 +0200
@@ -136,21 +136,23 @@
by (cases "k = 0") (simp_all add: distrib_right add_strict_mono)
qed
-lemma zero_le_imp_eq_int: "0 \<le> k \<Longrightarrow> \<exists>n. k = int n"
- for k :: int
- apply transfer
- apply clarsimp
- apply (rule_tac x="a - b" in exI)
- apply simp
- done
+lemma zero_le_imp_eq_int:
+ assumes "k \<ge> (0::int)" shows "\<exists>n. k = int n"
+proof -
+ have "b \<le> a \<Longrightarrow> \<exists>n::nat. a = n + b" for a b
+ by (rule_tac x="a - b" in exI) simp
+ with assms show ?thesis
+ by transfer auto
+qed
-lemma zero_less_imp_eq_int: "0 < k \<Longrightarrow> \<exists>n>0. k = int n"
- for k :: int
- apply transfer
- apply clarsimp
- apply (rule_tac x="a - b" in exI)
- apply simp
- done
+lemma zero_less_imp_eq_int:
+ assumes "k > (0::int)" shows "\<exists>n>0. k = int n"
+proof -
+ have "b < a \<Longrightarrow> \<exists>n::nat. n>0 \<and> a = n + b" for a b
+ by (rule_tac x="a - b" in exI) simp
+ with assms show ?thesis
+ by transfer auto
+qed
lemma zmult_zless_mono2: "i < j \<Longrightarrow> 0 < k \<Longrightarrow> k * i < k * j"
for i j k :: int
@@ -185,12 +187,12 @@
lemma zless_iff_Suc_zadd: "w < z \<longleftrightarrow> (\<exists>n. z = w + int (Suc n))"
for w z :: int
- apply transfer
- apply auto
- apply (rename_tac a b c d)
- apply (rule_tac x="c+b - Suc(a+d)" in exI)
- apply arith
- done
+proof -
+ have "\<And>a b c d. a + d < c + b \<Longrightarrow> \<exists>n. c + b = Suc (a + n + d)"
+ by (rule_tac x="c+b - Suc(a+d)" in exI) arith
+ then show ?thesis
+ by transfer auto
+qed
lemma zabs_less_one_iff [simp]: "\<bar>z\<bar> < 1 \<longleftrightarrow> z = 0" (is "?lhs \<longleftrightarrow> ?rhs")
for z :: int
@@ -471,16 +473,16 @@
qed
instance int :: no_top
- apply standard
- apply (rule_tac x="x + 1" in exI)
- apply simp
- done
+proof
+ show "\<And>x::int. \<exists>y. x < y"
+ by (rule_tac x="x + 1" in exI) simp
+qed
instance int :: no_bot
- apply standard
- apply (rule_tac x="x - 1" in exI)
- apply simp
- done
+proof
+ show "\<And>x::int. \<exists>y. y < x"
+ by (rule_tac x="x - 1" in exI) simp
+qed
subsection \<open>Magnitude of an Integer, as a Natural Number: \<open>nat\<close>\<close>
@@ -732,12 +734,14 @@
for a :: "'a::linordered_idom"
by (force dest: order_less_le_trans simp add: abs_if linorder_not_less)
-lemma negD: "x < 0 \<Longrightarrow> \<exists>n. x = - (int (Suc n))"
- apply transfer
- apply clarsimp
- apply (rule_tac x="b - Suc a" in exI)
- apply arith
- done
+lemma negD:
+ assumes "x < 0" shows "\<exists>n. x = - (int (Suc n))"
+proof -
+ have "\<And>a b. a < b \<Longrightarrow> \<exists>n. Suc (a + n) = b"
+ by (rule_tac x="b - Suc a" in exI) arith
+ with assms show ?thesis
+ by transfer auto
+qed
subsection \<open>Cases and induction\<close>
@@ -754,13 +758,17 @@
text \<open>This is the default, with a negative case.\<close>
lemma int_cases [case_names nonneg neg, cases type: int]:
- "(\<And>n. z = int n \<Longrightarrow> P) \<Longrightarrow> (\<And>n. z = - (int (Suc n)) \<Longrightarrow> P) \<Longrightarrow> P"
- apply (cases "z < 0")
- apply (blast dest!: negD)
- apply (simp add: linorder_not_less del: of_nat_Suc)
- apply auto
- apply (blast dest: nat_0_le [THEN sym])
- done
+ assumes pos: "\<And>n. z = int n \<Longrightarrow> P" and neg: "\<And>n. z = - (int (Suc n)) \<Longrightarrow> P"
+ shows P
+proof (cases "z < 0")
+ case True
+ with neg show ?thesis
+ by (blast dest!: negD)
+next
+ case False
+ with pos show ?thesis
+ by (force simp add: linorder_not_less dest: nat_0_le [THEN sym])
+qed
lemma int_cases3 [case_names zero pos neg]:
fixes k :: int
@@ -891,31 +899,19 @@
by (subst of_nat_numeral [symmetric], rule Ints_of_nat)
lemma Ints_add [simp]: "a \<in> \<int> \<Longrightarrow> b \<in> \<int> \<Longrightarrow> a + b \<in> \<int>"
- apply (auto simp add: Ints_def)
- apply (rule range_eqI)
- apply (rule of_int_add [symmetric])
- done
+ by (force simp add: Ints_def simp flip: of_int_add intro: range_eqI)
lemma Ints_minus [simp]: "a \<in> \<int> \<Longrightarrow> -a \<in> \<int>"
- apply (auto simp add: Ints_def)
- apply (rule range_eqI)
- apply (rule of_int_minus [symmetric])
- done
+ by (force simp add: Ints_def simp flip: of_int_minus intro: range_eqI)
lemma minus_in_Ints_iff: "-x \<in> \<int> \<longleftrightarrow> x \<in> \<int>"
using Ints_minus[of x] Ints_minus[of "-x"] by auto
lemma Ints_diff [simp]: "a \<in> \<int> \<Longrightarrow> b \<in> \<int> \<Longrightarrow> a - b \<in> \<int>"
- apply (auto simp add: Ints_def)
- apply (rule range_eqI)
- apply (rule of_int_diff [symmetric])
- done
+ by (force simp add: Ints_def simp flip: of_int_diff intro: range_eqI)
lemma Ints_mult [simp]: "a \<in> \<int> \<Longrightarrow> b \<in> \<int> \<Longrightarrow> a * b \<in> \<int>"
- apply (auto simp add: Ints_def)
- apply (rule range_eqI)
- apply (rule of_int_mult [symmetric])
- done
+ by (force simp add: Ints_def simp flip: of_int_mult intro: range_eqI)
lemma Ints_power [simp]: "a \<in> \<int> \<Longrightarrow> a ^ n \<in> \<int>"
by (induct n) simp_all
@@ -1234,12 +1230,15 @@
of_nat_nat [OF assms] of_nat_nat [OF ge_0], simp)
qed
-lemma nat_mult_distrib_neg: "z \<le> 0 \<Longrightarrow> nat (z * z') = nat (- z) * nat (- z')"
- for z z' :: int
- apply (rule trans)
- apply (rule_tac [2] nat_mult_distrib)
- apply auto
- done
+lemma nat_mult_distrib_neg:
+ assumes "z \<le> (0::int)" shows "nat (z * z') = nat (- z) * nat (- z')" (is "?L = ?R")
+proof -
+ have "?L = nat (- z * - z')"
+ using assms by auto
+ also have "... = ?R"
+ by (rule nat_mult_distrib) (use assms in auto)
+ finally show ?thesis .
+qed
lemma nat_abs_mult_distrib: "nat \<bar>w * z\<bar> = nat \<bar>w\<bar> * nat \<bar>z\<bar>"
by (cases "z = 0 \<or> w = 0")
@@ -1332,16 +1331,14 @@
(* `set:int': dummy construction *)
theorem int_gr_induct [case_names base step, induct set: int]:
fixes i k :: int
- assumes gr: "k < i"
- and base: "P (k + 1)"
- and step: "\<And>i. k < i \<Longrightarrow> P i \<Longrightarrow> P (i + 1)"
+ assumes "k < i" "P (k + 1)" "\<And>i. k < i \<Longrightarrow> P i \<Longrightarrow> P (i + 1)"
shows "P i"
- apply (rule int_ge_induct[of "k + 1"])
- using gr apply arith
- apply (rule base)
- apply (rule step)
- apply simp_all
- done
+proof -
+ have "k+1 \<le> i"
+ using assms by auto
+ then show ?thesis
+ by (induction i rule: int_ge_induct) (auto simp: assms)
+qed
theorem int_le_induct [consumes 1, case_names base step]:
fixes i k :: int
@@ -1367,16 +1364,14 @@
theorem int_less_induct [consumes 1, case_names base step]:
fixes i k :: int
- assumes less: "i < k"
- and base: "P (k - 1)"
- and step: "\<And>i. i < k \<Longrightarrow> P i \<Longrightarrow> P (i - 1)"
+ assumes "i < k" "P (k - 1)" "\<And>i. i < k \<Longrightarrow> P i \<Longrightarrow> P (i - 1)"
shows "P i"
- apply (rule int_le_induct[of _ "k - 1"])
- using less apply arith
- apply (rule base)
- apply (rule step)
- apply simp_all
- done
+proof -
+ have "i \<le> k-1"
+ using assms by auto
+ then show ?thesis
+ by (induction i rule: int_le_induct) (auto simp: assms)
+qed
theorem int_induct [case_names base step1 step2]:
fixes k :: int
@@ -1401,26 +1396,30 @@
subsection \<open>Intermediate value theorems\<close>
+lemma nat_ivt_aux:
+ "\<lbrakk>\<forall>i<n. \<bar>f (Suc i) - f i\<bar> \<le> 1; f 0 \<le> k; k \<le> f n\<rbrakk> \<Longrightarrow> \<exists>i \<le> n. f i = k"
+ for m n :: nat and k :: int
+proof (induct n)
+ case (Suc n)
+ show ?case
+ proof (cases "k = f (Suc n)")
+ case False
+ with Suc have "k \<le> f n"
+ by auto
+ with Suc show ?thesis
+ by (auto simp add: abs_if split: if_split_asm intro: le_SucI)
+ qed (use Suc in auto)
+qed auto
+
lemma nat_intermed_int_val:
- "\<exists>i. m \<le> i \<and> i \<le> n \<and> f i = k"
- if "\<forall>i. m \<le> i \<and> i < n \<longrightarrow> \<bar>f (Suc i) - f i\<bar> \<le> 1"
- "m \<le> n" "f m \<le> k" "k \<le> f n"
- for m n :: nat and k :: int
+ fixes m n :: nat and k :: int
+ assumes "\<forall>i. m \<le> i \<and> i < n \<longrightarrow> \<bar>f (Suc i) - f i\<bar> \<le> 1" "m \<le> n" "f m \<le> k" "k \<le> f n"
+ shows "\<exists>i. m \<le> i \<and> i \<le> n \<and> f i = k"
proof -
- have "(\<forall>i<n. \<bar>f (Suc i) - f i\<bar> \<le> 1) \<Longrightarrow> f 0 \<le> k \<Longrightarrow> k \<le> f n
- \<Longrightarrow> (\<exists>i \<le> n. f i = k)"
- for n :: nat and f
- apply (induct n)
- apply auto
- apply (erule_tac x = n in allE)
- apply (case_tac "k = f (Suc n)")
- apply (auto simp add: abs_if split: if_split_asm intro: le_SucI)
- done
- from this [of "n - m" "f \<circ> plus m"] that show ?thesis
- apply auto
- apply (rule_tac x = "m + i" in exI)
- apply auto
- done
+ obtain i where "i \<le> n - m" "k = f (m + i)"
+ using nat_ivt_aux [of "n - m" "f \<circ> plus m" k] assms by auto
+ with assms show ?thesis
+ by (rule_tac x = "m + i" in exI) auto
qed
lemma nat0_intermed_int_val:
@@ -1465,14 +1464,12 @@
by (auto dest: pos_zmult_eq_1_iff_lemma)
qed
-lemma zmult_eq_1_iff: "m * n = 1 \<longleftrightarrow> (m = 1 \<and> n = 1) \<or> (m = - 1 \<and> n = - 1)"
+lemma zmult_eq_1_iff: "m * n = 1 \<longleftrightarrow> (m = 1 \<and> n = 1) \<or> (m = - 1 \<and> n = - 1)" (is "?L = ?R")
for m n :: int
- apply (rule iffI)
- apply (frule pos_zmult_eq_1_iff_lemma)
- apply (simp add: mult.commute [of m])
- apply (frule pos_zmult_eq_1_iff_lemma)
- apply auto
- done
+proof
+ assume L: ?L show ?R
+ using pos_zmult_eq_1_iff_lemma [OF L] L by force
+qed auto
lemma infinite_UNIV_int [simp]: "\<not> finite (UNIV::int set)"
proof
@@ -1677,13 +1674,12 @@
using nat_less_eq_zless[of a "numeral x ^ n"]
by (cases "a < 0") (auto simp: nat_power_eq less_le_trans[where y=0])
-lemma zdvd_imp_le: "z dvd n \<Longrightarrow> 0 < n \<Longrightarrow> z \<le> n"
- for n z :: int
- apply (cases n)
- apply auto
- apply (cases z)
- apply (auto simp add: dvd_imp_le)
- done
+lemma zdvd_imp_le: "z \<le> n" if "z dvd n" "0 < n" for n z :: int
+proof (cases n)
+ case (nonneg n)
+ show ?thesis
+ by (cases z) (use nonneg dvd_imp_le that in auto)
+qed (use that in auto)
lemma zdvd_period:
fixes a d :: int
--- a/src/HOL/List.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/List.thy Thu Apr 02 13:04:24 2020 +0200
@@ -853,7 +853,7 @@
"(Suc n \<le> length xs) = (\<exists>x ys. xs = x # ys \<and> n \<le> length ys)"
by (metis Suc_le_D[of n] Suc_le_mono[of n] Suc_length_conv[of _ xs])
-lemma impossible_Cons: "length xs \<le> length ys ==> xs = x # ys = False"
+lemma impossible_Cons: "length xs \<le> length ys \<Longrightarrow> xs = x # ys = False"
by (induct xs) auto
lemma list_induct2 [consumes 1, case_names Nil Cons]:
@@ -972,7 +972,7 @@
lemma append_eq_append_conv [simp]:
"length xs = length ys \<or> length us = length vs
- ==> (xs@us = ys@vs) = (xs=ys \<and> us=vs)"
+ \<Longrightarrow> (xs@us = ys@vs) = (xs=ys \<and> us=vs)"
by (induct xs arbitrary: ys; case_tac ys; force)
lemma append_eq_append_conv2: "(xs @ ys = zs @ ts) =
@@ -998,19 +998,19 @@
lemma self_append_conv2 [iff]: "(ys = xs @ ys) = (xs = [])"
using append_same_eq [of "[]"] by auto
-lemma hd_Cons_tl: "xs \<noteq> [] ==> hd xs # tl xs = xs"
+lemma hd_Cons_tl: "xs \<noteq> [] \<Longrightarrow> hd xs # tl xs = xs"
by (fact list.collapse)
lemma hd_append: "hd (xs @ ys) = (if xs = [] then hd ys else hd xs)"
by (induct xs) auto
-lemma hd_append2 [simp]: "xs \<noteq> [] ==> hd (xs @ ys) = hd xs"
+lemma hd_append2 [simp]: "xs \<noteq> [] \<Longrightarrow> hd (xs @ ys) = hd xs"
by (simp add: hd_append split: list.split)
lemma tl_append: "tl (xs @ ys) = (case xs of [] \<Rightarrow> tl ys | z#zs \<Rightarrow> zs @ ys)"
by (simp split: list.split)
-lemma tl_append2 [simp]: "xs \<noteq> [] ==> tl (xs @ ys) = tl xs @ ys"
+lemma tl_append2 [simp]: "xs \<noteq> [] \<Longrightarrow> tl (xs @ ys) = tl xs @ ys"
by (simp add: tl_append split: list.split)
@@ -1031,16 +1031,14 @@
text \<open>Trivial rules for solving \<open>@\<close>-equations automatically.\<close>
-lemma eq_Nil_appendI: "xs = ys ==> xs = [] @ ys"
-by simp
-
-lemma Cons_eq_appendI:
-"[| x # xs1 = ys; xs = xs1 @ zs |] ==> x # xs = ys @ zs"
-by (drule sym) simp
-
-lemma append_eq_appendI:
-"[| xs @ xs1 = zs; ys = xs1 @ us |] ==> xs @ ys = zs @ us"
-by (drule sym) simp
+lemma eq_Nil_appendI: "xs = ys \<Longrightarrow> xs = [] @ ys"
+ by simp
+
+lemma Cons_eq_appendI: "\<lbrakk>x # xs1 = ys; xs = xs1 @ zs\<rbrakk> \<Longrightarrow> x # xs = ys @ zs"
+ by auto
+
+lemma append_eq_appendI: "\<lbrakk>xs @ xs1 = zs; ys = xs1 @ us\<rbrakk> \<Longrightarrow> xs @ ys = zs @ us"
+ by auto
text \<open>
@@ -1100,7 +1098,7 @@
lemma map_tl: "map f (tl xs) = tl (map f xs)"
by (cases xs) simp_all
-lemma map_ext: "(\<And>x. x \<in> set xs \<longrightarrow> f x = g x) ==> map f xs = map g xs"
+lemma map_ext: "(\<And>x. x \<in> set xs \<longrightarrow> f x = g x) \<Longrightarrow> map f xs = map g xs"
by (induct xs) simp_all
lemma map_ident [simp]: "map (\<lambda>x. x) = (\<lambda>xs. xs)"
@@ -1175,16 +1173,16 @@
by(blast dest:map_inj_on)
lemma map_injective:
- "map f xs = map f ys ==> inj f ==> xs = ys"
+ "map f xs = map f ys \<Longrightarrow> inj f \<Longrightarrow> xs = ys"
by (induct ys arbitrary: xs) (auto dest!:injD)
lemma inj_map_eq_map[simp]: "inj f \<Longrightarrow> (map f xs = map f ys) = (xs = ys)"
by(blast dest:map_injective)
-lemma inj_mapI: "inj f ==> inj (map f)"
+lemma inj_mapI: "inj f \<Longrightarrow> inj (map f)"
by (iprover dest: map_injective injD intro: inj_onI)
-lemma inj_mapD: "inj (map f) ==> inj f"
+lemma inj_mapD: "inj (map f) \<Longrightarrow> inj f"
by (metis (no_types, hide_lams) injI list.inject list.simps(9) the_inv_f_f)
lemma inj_map[iff]: "inj (map f) = inj f"
@@ -1260,13 +1258,16 @@
by(simp add:inj_on_def)
lemma rev_induct [case_names Nil snoc]:
- "[| P []; !!x xs. P xs ==> P (xs @ [x]) |] ==> P xs"
-apply(simplesubst rev_rev_ident[symmetric])
-apply(rule_tac list = "rev xs" in list.induct, simp_all)
-done
+ assumes "P []" and "\<And>x xs. P xs \<Longrightarrow> P (xs @ [x])"
+ shows "P xs"
+proof -
+ have "P (rev (rev xs))"
+ by (rule_tac list = "rev xs" in list.induct, simp_all add: assms)
+ then show ?thesis by simp
+qed
lemma rev_exhaust [case_names Nil snoc]:
- "(xs = [] ==> P) ==>(!!ys y. xs = ys @ [y] ==> P) ==> P"
+ "(xs = [] \<Longrightarrow> P) \<Longrightarrow>(\<And>ys y. xs = ys @ [y] \<Longrightarrow> P) \<Longrightarrow> P"
by (induct xs rule: rev_induct) auto
lemmas rev_cases = rev_exhaust
@@ -1475,10 +1476,10 @@
"length(filter P xs) + length(filter (\<lambda>x. \<not>P x) xs) = length xs"
by(induct xs) simp_all
-lemma filter_True [simp]: "\<forall>x \<in> set xs. P x ==> filter P xs = xs"
+lemma filter_True [simp]: "\<forall>x \<in> set xs. P x \<Longrightarrow> filter P xs = xs"
by (induct xs) auto
-lemma filter_False [simp]: "\<forall>x \<in> set xs. \<not> P x ==> filter P xs = []"
+lemma filter_False [simp]: "\<forall>x \<in> set xs. \<not> P x \<Longrightarrow> filter P xs = []"
by (induct xs) auto
lemma filter_empty_conv: "(filter P xs = []) = (\<forall>x\<in>set xs. \<not> P x)"
@@ -1664,13 +1665,13 @@
lemma rev_concat: "rev (concat xs) = concat (map rev (rev xs))"
by (induct xs) auto
-lemma concat_eq_concat_iff: "\<forall>(x, y) \<in> set (zip xs ys). length x = length y ==> length xs = length ys ==> (concat xs = concat ys) = (xs = ys)"
+lemma concat_eq_concat_iff: "\<forall>(x, y) \<in> set (zip xs ys). length x = length y \<Longrightarrow> length xs = length ys \<Longrightarrow> (concat xs = concat ys) = (xs = ys)"
proof (induct xs arbitrary: ys)
case (Cons x xs ys)
thus ?case by (cases ys) auto
qed (auto)
-lemma concat_injective: "concat xs = concat ys ==> length xs = length ys ==> \<forall>(x, y) \<in> set (zip xs ys). length x = length y ==> xs = ys"
+lemma concat_injective: "concat xs = concat ys \<Longrightarrow> length xs = length ys \<Longrightarrow> \<forall>(x, y) \<in> set (zip xs ys). length x = length y \<Longrightarrow> xs = ys"
by (simp add: concat_eq_concat_iff)
lemma concat_eq_appendD:
@@ -1725,7 +1726,7 @@
lemma nth_append_length_plus[simp]: "(xs @ ys) ! (length xs + n) = ys ! n"
by (induct xs) auto
-lemma nth_map [simp]: "n < length xs ==> (map f xs)!n = f(xs!n)"
+lemma nth_map [simp]: "n < length xs \<Longrightarrow> (map f xs)!n = f(xs!n)"
proof (induct xs arbitrary: n)
case (Cons x xs)
then show ?case
@@ -1856,13 +1857,13 @@
by (induct xs arbitrary: i) (auto split: nat.split)
lemma nth_list_update:
- "i < length xs==> (xs[i:=x])!j = (if i = j then x else xs!j)"
+ "i < length xs\<Longrightarrow> (xs[i:=x])!j = (if i = j then x else xs!j)"
by (induct xs arbitrary: i j) (auto simp add: nth_Cons split: nat.split)
-lemma nth_list_update_eq [simp]: "i < length xs ==> (xs[i:=x])!i = x"
+lemma nth_list_update_eq [simp]: "i < length xs \<Longrightarrow> (xs[i:=x])!i = x"
by (simp add: nth_list_update)
-lemma nth_list_update_neq [simp]: "i \<noteq> j ==> xs[i:=x]!j = xs!j"
+lemma nth_list_update_neq [simp]: "i \<noteq> j \<Longrightarrow> xs[i:=x]!j = xs!j"
by (induct xs arbitrary: i j) (auto simp add: nth_Cons split: nat.split)
lemma list_update_id[simp]: "xs[i := xs!i] = xs"
@@ -1879,7 +1880,7 @@
by (simp only: length_0_conv[symmetric] length_list_update)
lemma list_update_same_conv:
- "i < length xs ==> (xs[i := x] = xs) = (xs!i = x)"
+ "i < length xs \<Longrightarrow> (xs[i := x] = xs) = (xs!i = x)"
by (induct xs arbitrary: i) (auto split: nat.split)
lemma list_update_append1:
@@ -2105,10 +2106,10 @@
lemma length_drop [simp]: "length (drop n xs) = (length xs - n)"
by (induct n arbitrary: xs) (auto, case_tac xs, auto)
-lemma take_all [simp]: "length xs \<le> n ==> take n xs = xs"
+lemma take_all [simp]: "length xs \<le> n \<Longrightarrow> take n xs = xs"
by (induct n arbitrary: xs) (auto, case_tac xs, auto)
-lemma drop_all [simp]: "length xs \<le> n ==> drop n xs = []"
+lemma drop_all [simp]: "length xs \<le> n \<Longrightarrow> drop n xs = []"
by (induct n arbitrary: xs) (auto, case_tac xs, auto)
lemma take_append [simp]:
@@ -2206,7 +2207,7 @@
lemma take_rev: "take n (rev xs) = rev (drop (length xs - n) xs)"
by (cases "length xs < n") (auto simp: rev_drop)
-lemma nth_take [simp]: "i < n ==> (take n xs)!i = xs!i"
+lemma nth_take [simp]: "i < n \<Longrightarrow> (take n xs)!i = xs!i"
proof (induct xs arbitrary: i n)
case Nil
then show ?case by simp
@@ -2216,7 +2217,7 @@
qed
lemma nth_drop [simp]:
- "n \<le> length xs ==> (drop n xs)!i = xs!(n + i)"
+ "n \<le> length xs \<Longrightarrow> (drop n xs)!i = xs!(n + i)"
proof (induct n arbitrary: xs)
case 0
then show ?case by simp
@@ -2226,13 +2227,13 @@
qed
lemma butlast_take:
- "n \<le> length xs ==> butlast (take n xs) = take (n - 1) xs"
+ "n \<le> length xs \<Longrightarrow> butlast (take n xs) = take (n - 1) xs"
by (simp add: butlast_conv_take min.absorb1 min.absorb2)
lemma butlast_drop: "butlast (drop n xs) = drop n (butlast xs)"
by (simp add: butlast_conv_take drop_take ac_simps)
-lemma take_butlast: "n < length xs ==> take n (butlast xs) = take n xs"
+lemma take_butlast: "n < length xs \<Longrightarrow> take n (butlast xs) = take n xs"
by (simp add: butlast_conv_take min.absorb1)
lemma drop_butlast: "drop n (butlast xs) = butlast (drop n xs)"
@@ -2390,7 +2391,7 @@
by (induct xs) auto
lemma dropWhile_append2 [simp]:
- "(\<And>x. x \<in> set xs \<Longrightarrow> P(x)) ==> dropWhile P (xs @ ys) = dropWhile P ys"
+ "(\<And>x. x \<in> set xs \<Longrightarrow> P(x)) \<Longrightarrow> dropWhile P (xs @ ys) = dropWhile P ys"
by (induct xs) auto
lemma dropWhile_append3:
@@ -2419,10 +2420,10 @@
"(dropWhile P xs = y#ys) = (xs = takeWhile P xs @ y # ys \<and> \<not> P y)"
by(induct xs, auto)
-lemma distinct_takeWhile[simp]: "distinct xs ==> distinct (takeWhile P xs)"
+lemma distinct_takeWhile[simp]: "distinct xs \<Longrightarrow> distinct (takeWhile P xs)"
by (induct xs) (auto dest: set_takeWhileD)
-lemma distinct_dropWhile[simp]: "distinct xs ==> distinct (dropWhile P xs)"
+lemma distinct_dropWhile[simp]: "distinct xs \<Longrightarrow> distinct (dropWhile P xs)"
by (induct xs) auto
lemma takeWhile_map: "takeWhile P (map f xs) = map f (takeWhile (P \<circ> f) xs)"
@@ -2582,12 +2583,12 @@
by (induct xs ys rule:list_induct2') auto
lemma zip_append [simp]:
- "[| length xs = length us |] ==>
+ "\<lbrakk>length xs = length us\<rbrakk> \<Longrightarrow>
zip (xs@ys) (us@vs) = zip xs us @ zip ys vs"
by (simp add: zip_append1)
lemma zip_rev:
- "length xs = length ys ==> zip (rev xs) (rev ys) = rev (zip xs ys)"
+ "length xs = length ys \<Longrightarrow> zip (rev xs) (rev ys) = rev (zip xs ys)"
by (induct rule:list_induct2, simp_all)
lemma zip_map_map:
@@ -2622,7 +2623,7 @@
by(induct xs) auto
lemma nth_zip [simp]:
- "[| i < length xs; i < length ys|] ==> (zip xs ys)!i = (xs!i, ys!i)"
+ "\<lbrakk>i < length xs; i < length ys\<rbrakk> \<Longrightarrow> (zip xs ys)!i = (xs!i, ys!i)"
proof (induct ys arbitrary: i xs)
case (Cons y ys)
then show ?case
@@ -2804,7 +2805,7 @@
subsubsection \<open>\<^const>\<open>list_all2\<close>\<close>
lemma list_all2_lengthD [intro?]:
- "list_all2 P xs ys ==> length xs = length ys"
+ "list_all2 P xs ys \<Longrightarrow> length xs = length ys"
by (simp add: list_all2_iff)
lemma list_all2_Nil [iff, code]: "list_all2 P [] ys = (ys = [])"
@@ -2892,8 +2893,8 @@
by (force simp add: list_all2_iff set_zip)
lemma list_all2_trans:
- assumes tr: "!!a b c. P1 a b ==> P2 b c ==> P3 a c"
- shows "!!bs cs. list_all2 P1 as bs ==> list_all2 P2 bs cs ==> list_all2 P3 as cs"
+ assumes tr: "!!a b c. P1 a b \<Longrightarrow> P2 b c \<Longrightarrow> P3 a c"
+ shows "!!bs cs. list_all2 P1 as bs \<Longrightarrow> list_all2 P2 bs cs \<Longrightarrow> list_all2 P3 as cs"
(is "!!bs cs. PROP ?Q as bs cs")
proof (induct as)
fix x xs bs assume I1: "!!bs cs. PROP ?Q xs bs cs"
@@ -3224,7 +3225,7 @@
lemmas upt_rec_numeral[simp] = upt_rec[of "numeral m" "numeral n"] for m n
-lemma upt_conv_Nil [simp]: "j \<le> i ==> [i..<j] = []"
+lemma upt_conv_Nil [simp]: "j \<le> i \<Longrightarrow> [i..<j] = []"
by (subst upt_rec) simp
lemma upt_eq_Nil_conv[simp]: "([i..<j] = []) = (j = 0 \<or> j \<le> i)"
@@ -3238,11 +3239,11 @@
by (simp add: upt_rec)
qed simp
-lemma upt_Suc_append: "i \<le> j ==> [i..<(Suc j)] = [i..<j]@[j]"
+lemma upt_Suc_append: "i \<le> j \<Longrightarrow> [i..<(Suc j)] = [i..<j]@[j]"
\<comment> \<open>Only needed if \<open>upt_Suc\<close> is deleted from the simpset.\<close>
by simp
-lemma upt_conv_Cons: "i < j ==> [i..<j] = i # [Suc i..<j]"
+lemma upt_conv_Cons: "i < j \<Longrightarrow> [i..<j] = i # [Suc i..<j]"
by (simp add: upt_rec)
lemma upt_conv_Cons_Cons: \<comment> \<open>no precondition\<close>
@@ -3253,14 +3254,14 @@
case True then show ?thesis by (simp add: upt_conv_Cons)
qed
-lemma upt_add_eq_append: "i<=j ==> [i..<j+k] = [i..<j]@[j..<j+k]"
+lemma upt_add_eq_append: "i<=j \<Longrightarrow> [i..<j+k] = [i..<j]@[j..<j+k]"
\<comment> \<open>LOOPS as a simprule, since \<open>j \<le> j\<close>.\<close>
by (induct k) auto
lemma length_upt [simp]: "length [i..<j] = j - i"
by (induct j) (auto simp add: Suc_diff_le)
-lemma nth_upt [simp]: "i + k < j ==> [i..<j] ! k = i + k"
+lemma nth_upt [simp]: "i + k < j \<Longrightarrow> [i..<j] ! k = i + k"
by (induct j) (auto simp add: less_Suc_eq nth_append split: nat_diff_split)
lemma hd_upt[simp]: "i < j \<Longrightarrow> hd[i..<j] = i"
@@ -3272,7 +3273,7 @@
lemma last_upt[simp]: "i < j \<Longrightarrow> last[i..<j] = j - 1"
by(cases j)(auto simp: upt_Suc_append)
-lemma take_upt [simp]: "i+m \<le> n ==> take m [i..<n] = [i..<i+m]"
+lemma take_upt [simp]: "i+m \<le> n \<Longrightarrow> take m [i..<n] = [i..<i+m]"
proof (induct m arbitrary: i)
case (Suc m)
then show ?case
@@ -3288,7 +3289,7 @@
lemma map_add_upt: "map (\<lambda>i. i + n) [0..<m] = [n..<m + n]"
by (induct m) simp_all
-lemma nth_map_upt: "i < n-m ==> (map f [m..<n]) ! i = f(m+i)"
+lemma nth_map_upt: "i < n-m \<Longrightarrow> (map f [m..<n]) ! i = f(m+i)"
proof (induct n m arbitrary: i rule: diff_induct)
case (3 x y)
then show ?case
@@ -3324,7 +3325,7 @@
\<Longrightarrow> xs = ys"
by (simp add: list_all2_conv_all_nth nth_equalityI)
-lemma take_equalityI: "(\<forall>i. take i xs = take i ys) ==> xs = ys"
+lemma take_equalityI: "(\<forall>i. take i xs = take i ys) \<Longrightarrow> xs = ys"
\<comment> \<open>The famous take-lemma.\<close>
by (metis length_take min.commute order_refl take_all)
@@ -3403,10 +3404,11 @@
qed
lemma nth_upto[simp]: "i + int k \<le> j \<Longrightarrow> [i..j] ! k = i + int k"
- apply(induction i j arbitrary: k rule: upto.induct)
-apply(subst upto_rec1)
-apply(auto simp add: nth_Cons')
-done
+proof(induction i j arbitrary: k rule: upto.induct)
+ case (1 i j)
+ then show ?case
+ by (auto simp add: upto_rec1 [of i j] nth_Cons')
+qed
lemma upto_split1:
"i \<le> j \<Longrightarrow> j \<le> k \<Longrightarrow> [i..k] = [i..j-1] @ [j..k]"
@@ -3454,7 +3456,7 @@
lemma distinct_remdups [iff]: "distinct (remdups xs)"
by (induct xs) auto
-lemma distinct_remdups_id: "distinct xs ==> remdups xs = xs"
+lemma distinct_remdups_id: "distinct xs \<Longrightarrow> remdups xs = xs"
by (induct xs, auto)
lemma remdups_id_iff_distinct [simp]: "remdups xs = xs \<longleftrightarrow> distinct xs"
@@ -3491,17 +3493,18 @@
"distinct (map f xs) \<Longrightarrow> distinct (map f (filter P xs))"
by (induct xs) auto
-lemma distinct_filter [simp]: "distinct xs ==> distinct (filter P xs)"
+lemma distinct_filter [simp]: "distinct xs \<Longrightarrow> distinct (filter P xs)"
by (induct xs) auto
lemma distinct_upt[simp]: "distinct[i..<j]"
by (induct j) auto
lemma distinct_upto[simp]: "distinct[i..j]"
-apply(induct i j rule:upto.induct)
-apply(subst upto.simps)
-apply(simp)
-done
+proof (induction i j rule: upto.induct)
+ case (1 i j)
+ then show ?case
+ by (simp add: upto.simps [of i])
+qed
lemma distinct_take[simp]: "distinct xs \<Longrightarrow> distinct (take i xs)"
proof (induct xs arbitrary: i)
@@ -3531,10 +3534,10 @@
by auto
next
case False
+ have "set (take i xs) \<inter> set (drop (Suc i) xs) = {}"
+ by (metis True d disjoint_insert(1) distinct_append id_take_nth_drop list.set(2))
then show ?thesis
- using d anot \<open>i < length xs\<close>
- apply (simp add: upd_conv_take_nth_drop)
- by (metis disjoint_insert(1) distinct_append id_take_nth_drop set_simps(2))
+ using d False anot \<open>i < length xs\<close> by (simp add: upd_conv_take_nth_drop)
qed
next
case False with d show ?thesis by auto
@@ -3547,8 +3550,9 @@
\<rbrakk> \<Longrightarrow> distinct (concat xs)"
by (induct xs) auto
-text \<open>It is best to avoid this indexed version of distinct, but
-sometimes it is useful.\<close>
+text \<open>An iff-version of @{thm distinct_concat} is available further down as \<open>distinct_concat_iff\<close>.\<close>
+
+text \<open>It is best to avoid the following indexed version of distinct, but sometimes it is useful.\<close>
lemma distinct_conv_nth: "distinct xs = (\<forall>i < size xs. \<forall>j < size xs. i \<noteq> j \<longrightarrow> xs!i \<noteq> xs!j)"
proof (induct xs)
@@ -3580,21 +3584,20 @@
set(xs[n := x]) = insert x (set xs - {xs!n})"
by(auto simp: set_eq_iff in_set_conv_nth nth_list_update nth_eq_iff_index_eq)
-lemma distinct_swap[simp]: "\<lbrakk> i < size xs; j < size xs \<rbrakk> \<Longrightarrow>
+lemma distinct_swap[simp]: "\<lbrakk> i < size xs; j < size xs\<rbrakk> \<Longrightarrow>
distinct(xs[i := xs!j, j := xs!i]) = distinct xs"
apply (simp add: distinct_conv_nth nth_list_update)
-apply safe
-apply metis+
-done
+ apply (safe; metis)
+ done
lemma set_swap[simp]:
"\<lbrakk> i < size xs; j < size xs \<rbrakk> \<Longrightarrow> set(xs[i := xs!j, j := xs!i]) = set xs"
by(simp add: set_conv_nth nth_list_update) metis
-lemma distinct_card: "distinct xs ==> card (set xs) = size xs"
+lemma distinct_card: "distinct xs \<Longrightarrow> card (set xs) = size xs"
by (induct xs) auto
-lemma card_distinct: "card (set xs) = size xs ==> distinct xs"
+lemma card_distinct: "card (set xs) = size xs \<Longrightarrow> distinct xs"
proof (induct xs)
case (Cons x xs)
show ?case
@@ -3822,18 +3825,12 @@
using f_mono by (simp add: mono_iff_le_Suc)
next
have "?f' ` {0 ..< length (x1 # xs)} = f ` {Suc 0 ..< length (x1 # x2 # xs)}"
- apply safe
- apply fastforce
- subgoal for \<dots> x by (cases x) auto
- done
+ using less_Suc_eq_0_disj by auto
also have "\<dots> = f ` {0 ..< length (x1 # x2 # xs)}"
proof -
have "f 0 = f (Suc 0)" using \<open>x1 = x2\<close> f_nth[of 0] by simp
then show ?thesis
- apply safe
- apply fastforce
- subgoal for \<dots> x by (cases x) auto
- done
+ using less_Suc_eq_0_disj by auto
qed
also have "\<dots> = {0 ..< length ys}" by fact
finally show "?f' ` {0 ..< length (x1 # xs)} = {0 ..< length ys}" .
@@ -3842,7 +3839,7 @@
next
assume "x1 \<noteq> x2"
- have "2 \<le> length ys"
+ have two: "Suc (Suc 0) \<le> length ys"
proof -
have "2 = card {f 0, f 1}" using \<open>x1 \<noteq> x2\<close> f_nth[of 0] by auto
also have "\<dots> \<le> card (f ` {0..< length (x1 # x2 # xs)})"
@@ -3862,26 +3859,18 @@
then have "Suc 0 \<noteq> f i" for i using \<open>f 0 = 0\<close>
by (cases i) fastforce+
then have "Suc 0 \<notin> f ` {0 ..< length (x1 # x2 # xs)}" by auto
- then show False using f_img \<open>2 \<le> length ys\<close> by auto
+ then show False using f_img two by auto
qed
obtain ys' where "ys = x1 # x2 # ys'"
- using \<open>2 \<le> length ys\<close> f_nth[of 0] f_nth[of 1]
- apply (cases ys)
- apply (rename_tac [2] ys', case_tac [2] ys')
- apply (auto simp: \<open>f 0 = 0\<close> \<open>f (Suc 0) = Suc 0\<close>)
- done
+ using two f_nth[of 0] f_nth[of 1]
+ by (auto simp: Suc_le_length_iff \<open>f 0 = 0\<close> \<open>f (Suc 0) = Suc 0\<close>)
+
+ have Suc0_le_f_Suc: "Suc 0 \<le> f (Suc i)" for i
+ by (metis Suc_le_mono \<open>f (Suc 0) = Suc 0\<close> f_mono le0 mono_def)
define f' where "f' x = f (Suc x) - 1" for x
-
- { fix i
- have "Suc 0 \<le> f (Suc 0)" using f_nth[of 0] \<open>x1 \<noteq> x2\<close> \<open>f 0 = 0\<close> by auto
- also have "\<dots> \<le> f (Suc i)" using f_mono by (rule monoD) arith
- finally have "Suc 0 \<le> f (Suc i)" .
- } note Suc0_le_f_Suc = this
-
- { fix i have "f (Suc i) = Suc (f' i)"
+ have f_Suc: "f (Suc i) = Suc (f' i)" for i
using Suc0_le_f_Suc[of i] by (auto simp: f'_def)
- } note f_Suc = this
have "remdups_adj (x2 # xs) = (x2 # ys')"
proof (intro "3.hyps" exI conjI impI allI)
@@ -3904,15 +3893,15 @@
qed
lemma hd_remdups_adj[simp]: "hd (remdups_adj xs) = hd xs"
-by (induction xs rule: remdups_adj.induct) simp_all
+ by (induction xs rule: remdups_adj.induct) simp_all
lemma remdups_adj_Cons: "remdups_adj (x # xs) =
(case remdups_adj xs of [] \<Rightarrow> [x] | y # xs \<Rightarrow> if x = y then y # xs else x # y # xs)"
-by (induct xs arbitrary: x) (auto split: list.splits)
+ by (induct xs arbitrary: x) (auto split: list.splits)
lemma remdups_adj_append_two:
"remdups_adj (xs @ [x,y]) = remdups_adj (xs @ [x]) @ (if x = y then [] else [y])"
-by (induct xs rule: remdups_adj.induct, simp_all)
+ by (induct xs rule: remdups_adj.induct, simp_all)
lemma remdups_adj_adjacent:
"Suc i < length (remdups_adj xs) \<Longrightarrow> remdups_adj xs ! i \<noteq> remdups_adj xs ! Suc i"
@@ -4059,8 +4048,8 @@
proof (induction xs arbitrary: X)
case (Cons x xs)
then show ?case
- apply (auto simp: sum.If_cases sum.remove)
- by (metis (no_types) Cons.IH Cons.prems(2) diff_eq sum.remove)
+ using sum.remove [of X x "count_list xs"]
+ by (auto simp: sum.If_cases simp flip: diff_eq)
qed simp
@@ -4191,6 +4180,14 @@
"x \<in> set xs \<Longrightarrow> length (removeAll x xs) < length xs"
by (auto dest: length_filter_less simp add: removeAll_filter_not_eq)
+lemma distinct_concat_iff: "distinct (concat xs) \<longleftrightarrow>
+ distinct (removeAll [] xs) \<and>
+ (\<forall>ys. ys \<in> set xs \<longrightarrow> distinct ys) \<and>
+ (\<forall>ys zs. ys \<in> set xs \<and> zs \<in> set xs \<and> ys \<noteq> zs \<longrightarrow> set ys \<inter> set zs = {})"
+apply (induct xs)
+ apply(simp_all, safe, auto)
+by (metis Int_iff UN_I empty_iff equals0I set_empty)
+
subsubsection \<open>\<^const>\<open>replicate\<close>\<close>
@@ -4237,16 +4234,16 @@
"filter P (replicate n x) = (if P x then replicate n x else [])"
by(induct n) auto
-lemma hd_replicate [simp]: "n \<noteq> 0 ==> hd (replicate n x) = x"
+lemma hd_replicate [simp]: "n \<noteq> 0 \<Longrightarrow> hd (replicate n x) = x"
by (induct n) auto
lemma tl_replicate [simp]: "tl (replicate n x) = replicate (n - 1) x"
by (induct n) auto
-lemma last_replicate [simp]: "n \<noteq> 0 ==> last (replicate n x) = x"
+lemma last_replicate [simp]: "n \<noteq> 0 \<Longrightarrow> last (replicate n x) = x"
by (atomize (full), induct n) auto
-lemma nth_replicate[simp]: "i < n ==> (replicate n x)!i = x"
+lemma nth_replicate[simp]: "i < n \<Longrightarrow> (replicate n x)!i = x"
by (induct n arbitrary: i)(auto simp: nth_Cons split: nat.split)
text\<open>Courtesy of Matthias Daum (2 lemmas):\<close>
@@ -4273,7 +4270,7 @@
lemma set_replicate_Suc: "set (replicate (Suc n) x) = {x}"
by (induct n) auto
-lemma set_replicate [simp]: "n \<noteq> 0 ==> set (replicate n x) = {x}"
+lemma set_replicate [simp]: "n \<noteq> 0 \<Longrightarrow> set (replicate n x) = {x}"
by (fast dest!: not0_implies_Suc intro!: set_replicate_Suc)
lemma set_replicate_conv_if: "set (replicate n x) = (if n = 0 then {} else {x})"
@@ -4495,8 +4492,7 @@
proof (cases "n mod length xs = 0")
case True
then show ?thesis
- apply (simp add: mod_Suc)
- by (simp add: False Suc.hyps drop_Suc rotate1_hd_tl take_Suc)
+ by (auto simp add: mod_Suc False Suc.hyps drop_Suc rotate1_hd_tl take_Suc Suc_length_conv)
next
case False
with \<open>xs \<noteq> []\<close> Suc
@@ -4508,37 +4504,37 @@
qed simp
lemma rotate_conv_mod: "rotate n xs = rotate (n mod length xs) xs"
-by(simp add:rotate_drop_take)
+ by(simp add:rotate_drop_take)
lemma rotate_id[simp]: "n mod length xs = 0 \<Longrightarrow> rotate n xs = xs"
-by(simp add:rotate_drop_take)
+ by(simp add:rotate_drop_take)
lemma length_rotate1[simp]: "length(rotate1 xs) = length xs"
-by (cases xs) simp_all
+ by (cases xs) simp_all
lemma length_rotate[simp]: "length(rotate n xs) = length xs"
-by (induct n arbitrary: xs) (simp_all add:rotate_def)
+ by (induct n arbitrary: xs) (simp_all add:rotate_def)
lemma distinct1_rotate[simp]: "distinct(rotate1 xs) = distinct xs"
-by (cases xs) auto
+ by (cases xs) auto
lemma distinct_rotate[simp]: "distinct(rotate n xs) = distinct xs"
-by (induct n) (simp_all add:rotate_def)
+ by (induct n) (simp_all add:rotate_def)
lemma rotate_map: "rotate n (map f xs) = map f (rotate n xs)"
-by(simp add:rotate_drop_take take_map drop_map)
+ by(simp add:rotate_drop_take take_map drop_map)
lemma set_rotate1[simp]: "set(rotate1 xs) = set xs"
-by (cases xs) auto
+ by (cases xs) auto
lemma set_rotate[simp]: "set(rotate n xs) = set xs"
-by (induct n) (simp_all add:rotate_def)
+ by (induct n) (simp_all add:rotate_def)
lemma rotate1_is_Nil_conv[simp]: "(rotate1 xs = []) = (xs = [])"
-by (cases xs) auto
+ by (cases xs) auto
lemma rotate_is_Nil_conv[simp]: "(rotate n xs = []) = (xs = [])"
-by (induct n) (simp_all add:rotate_def)
+ by (induct n) (simp_all add:rotate_def)
lemma rotate_rev:
"rotate n (rev xs) = rev(rotate (length xs - (n mod length xs)) xs)"
@@ -4564,21 +4560,20 @@
subsubsection \<open>\<^const>\<open>nths\<close> --- a generalization of \<^const>\<open>nth\<close> to sets\<close>
lemma nths_empty [simp]: "nths xs {} = []"
-by (auto simp add: nths_def)
+ by (auto simp add: nths_def)
lemma nths_nil [simp]: "nths [] A = []"
-by (auto simp add: nths_def)
+ by (auto simp add: nths_def)
lemma nths_all: "\<forall>i < length xs. i \<in> I \<Longrightarrow> nths xs I = xs"
apply (simp add: nths_def)
apply (subst filter_True)
- apply (clarsimp simp: in_set_zip subset_iff)
-apply simp
+ apply (auto simp: in_set_zip subset_iff)
done
lemma length_nths:
"length (nths xs I) = card{i. i < length xs \<and> i \<in> I}"
-by(simp add: nths_def length_filter_conv_card cong:conj_cong)
+ by(simp add: nths_def length_filter_conv_card cong:conj_cong)
lemma nths_shift_lemma_Suc:
"map fst (filter (\<lambda>p. P(Suc(snd p))) (zip xs is)) =
@@ -4612,46 +4607,41 @@
qed (auto simp: nths_def)
lemma nths_map: "nths (map f xs) I = map f (nths xs I)"
-by(induction xs arbitrary: I) (simp_all add: nths_Cons)
+ by(induction xs arbitrary: I) (simp_all add: nths_Cons)
lemma set_nths: "set(nths xs I) = {xs!i|i. i<size xs \<and> i \<in> I}"
-by (induct xs arbitrary: I) (auto simp: nths_Cons nth_Cons split:nat.split dest!: gr0_implies_Suc)
+ by (induct xs arbitrary: I) (auto simp: nths_Cons nth_Cons split:nat.split dest!: gr0_implies_Suc)
lemma set_nths_subset: "set(nths xs I) \<subseteq> set xs"
-by(auto simp add:set_nths)
+ by(auto simp add:set_nths)
lemma notin_set_nthsI[simp]: "x \<notin> set xs \<Longrightarrow> x \<notin> set(nths xs I)"
-by(auto simp add:set_nths)
+ by(auto simp add:set_nths)
lemma in_set_nthsD: "x \<in> set(nths xs I) \<Longrightarrow> x \<in> set xs"
-by(auto simp add:set_nths)
+ by(auto simp add:set_nths)
lemma nths_singleton [simp]: "nths [x] A = (if 0 \<in> A then [x] else [])"
-by (simp add: nths_Cons)
+ by (simp add: nths_Cons)
lemma distinct_nthsI[simp]: "distinct xs \<Longrightarrow> distinct (nths xs I)"
-by (induct xs arbitrary: I) (auto simp: nths_Cons)
+ by (induct xs arbitrary: I) (auto simp: nths_Cons)
lemma nths_upt_eq_take [simp]: "nths l {..<n} = take n l"
-by (induct l rule: rev_induct)
- (simp_all split: nat_diff_split add: nths_append)
+ by (induct l rule: rev_induct) (simp_all split: nat_diff_split add: nths_append)
lemma nths_nths: "nths (nths xs A) B = nths xs {i \<in> A. \<exists>j \<in> B. card {i' \<in> A. i' < i} = j}"
-apply(induction xs arbitrary: A B)
-apply(auto simp add: nths_Cons card_less_Suc card_less_Suc2)
-done
+ by (induction xs arbitrary: A B) (auto simp add: nths_Cons card_less_Suc card_less_Suc2)
lemma drop_eq_nths: "drop n xs = nths xs {i. i \<ge> n}"
-apply(induction xs arbitrary: n)
-apply (auto simp add: nths_Cons nths_all drop_Cons' intro: arg_cong2[where f=nths, OF refl])
-done
+ by (induction xs arbitrary: n) (auto simp add: nths_Cons nths_all drop_Cons' intro: arg_cong2[where f=nths, OF refl])
lemma nths_drop: "nths (drop n xs) I = nths xs ((+) n ` I)"
by(force simp: drop_eq_nths nths_nths simp flip: atLeastLessThan_iff
intro: arg_cong2[where f=nths, OF refl])
lemma filter_eq_nths: "filter P xs = nths xs {i. i<length xs \<and> P(xs!i)}"
-by(induction xs) (auto simp: nths_Cons)
+ by(induction xs) (auto simp: nths_Cons)
lemma filter_in_nths:
"distinct xs \<Longrightarrow> filter (%x. x \<in> set (nths xs s)) xs = nths xs s"
@@ -4732,18 +4722,20 @@
subsubsection \<open>\<^const>\<open>splice\<close>\<close>
lemma splice_Nil2 [simp]: "splice xs [] = xs"
-by (cases xs) simp_all
+ by (cases xs) simp_all
lemma length_splice[simp]: "length(splice xs ys) = length xs + length ys"
-by (induct xs ys rule: splice.induct) auto
+ by (induct xs ys rule: splice.induct) auto
lemma split_Nil_iff[simp]: "splice xs ys = [] \<longleftrightarrow> xs = [] \<and> ys = []"
-by (induct xs ys rule: splice.induct) auto
+ by (induct xs ys rule: splice.induct) auto
lemma splice_replicate[simp]: "splice (replicate m x) (replicate n x) = replicate (m+n) x"
-apply(induction "replicate m x" "replicate n x" arbitrary: m n rule: splice.induct)
-apply (auto simp add: Cons_replicate_eq dest: gr0_implies_Suc)
-done
+proof (induction "replicate m x" "replicate n x" arbitrary: m n rule: splice.induct)
+ case (2 x xs)
+ then show ?case
+ by (auto simp add: Cons_replicate_eq dest: gr0_implies_Suc)
+qed auto
subsubsection \<open>\<^const>\<open>shuffles\<close>\<close>
@@ -4768,7 +4760,7 @@
by (induct xs ys rule: shuffles.induct) auto
lemma splice_in_shuffles [simp, intro]: "splice xs ys \<in> shuffles xs ys"
-by (induction xs ys rule: splice.induct) (simp_all add: Cons_in_shuffles_iff shuffles_commutes)
+ by (induction xs ys rule: splice.induct) (simp_all add: Cons_in_shuffles_iff shuffles_commutes)
lemma Nil_in_shufflesI: "xs = [] \<Longrightarrow> ys = [] \<Longrightarrow> [] \<in> shuffles xs ys"
by simp
@@ -5001,13 +4993,13 @@
subsubsection \<open>\<^const>\<open>min\<close> and \<^const>\<open>arg_min\<close>\<close>
lemma min_list_Min: "xs \<noteq> [] \<Longrightarrow> min_list xs = Min (set xs)"
-by (induction xs rule: induct_list012)(auto)
+ by (induction xs rule: induct_list012)(auto)
lemma f_arg_min_list_f: "xs \<noteq> [] \<Longrightarrow> f (arg_min_list f xs) = Min (f ` (set xs))"
-by(induction f xs rule: arg_min_list.induct) (auto simp: min_def intro!: antisym)
+ by(induction f xs rule: arg_min_list.induct) (auto simp: min_def intro!: antisym)
lemma arg_min_list_in: "xs \<noteq> [] \<Longrightarrow> arg_min_list f xs \<in> set xs"
-by(induction xs rule: induct_list012) (auto simp: Let_def)
+ by(induction xs rule: induct_list012) (auto simp: Let_def)
subsubsection \<open>(In)finiteness\<close>
@@ -5811,19 +5803,19 @@
lemma sorted_list_of_set_empty:
"sorted_list_of_set {} = []"
-by (fact sorted_list_of_set.empty)
+ by (fact sorted_list_of_set.empty)
lemma sorted_list_of_set_insert [simp]:
"finite A \<Longrightarrow> sorted_list_of_set (insert x A) = insort x (sorted_list_of_set (A - {x}))"
-by (fact sorted_list_of_set.insert_remove)
+ by (fact sorted_list_of_set.insert_remove)
lemma sorted_list_of_set_eq_Nil_iff [simp]:
"finite A \<Longrightarrow> sorted_list_of_set A = [] \<longleftrightarrow> A = {}"
-by (auto simp: sorted_list_of_set.remove)
+ by (auto simp: sorted_list_of_set.remove)
lemma set_sorted_list_of_set [simp]:
"finite A \<Longrightarrow> set (sorted_list_of_set A) = A"
-by(induct A rule: finite_induct) (simp_all add: set_insort_key)
+ by(induct A rule: finite_induct) (simp_all add: set_insort_key)
lemma sorted_sorted_list_of_set [simp]: "sorted (sorted_list_of_set A)"
proof (cases "finite A")
@@ -5894,13 +5886,13 @@
"listsp A []"
"listsp A (x # xs)"
-lemma listsp_mono [mono]: "A \<le> B ==> listsp A \<le> listsp B"
+lemma listsp_mono [mono]: "A \<le> B \<Longrightarrow> listsp A \<le> listsp B"
by (rule predicate1I, erule listsp.induct, blast+)
lemmas lists_mono = listsp_mono [to_set]
lemma listsp_infI:
- assumes l: "listsp A l" shows "listsp B l ==> listsp (inf A B) l" using l
+ assumes l: "listsp A l" shows "listsp B l \<Longrightarrow> listsp (inf A B) l" using l
by induct blast+
lemmas lists_IntI = listsp_infI [to_set]
@@ -5930,12 +5922,12 @@
lemmas in_lists_conv_set [code_unfold] = in_listsp_conv_set [to_set]
-lemma in_listspD [dest!]: "listsp A xs ==> \<forall>x\<in>set xs. A x"
+lemma in_listspD [dest!]: "listsp A xs \<Longrightarrow> \<forall>x\<in>set xs. A x"
by (rule in_listsp_conv_set [THEN iffD1])
lemmas in_listsD [dest!] = in_listspD [to_set]
-lemma in_listspI [intro!]: "\<forall>x\<in>set xs. A x ==> listsp A xs"
+lemma in_listspI [intro!]: "\<forall>x\<in>set xs. A x \<Longrightarrow> listsp A xs"
by (rule in_listsp_conv_set [THEN iffD2])
lemmas in_listsI [intro!] = in_listspI [to_set]
@@ -6025,24 +6017,31 @@
lemma lexn_length:
"(xs, ys) \<in> lexn r n \<Longrightarrow> length xs = n \<and> length ys = n"
-by (induct n arbitrary: xs ys) auto
-
-lemma wf_lex [intro!]: "wf r ==> wf (lex r)"
+ by (induct n arbitrary: xs ys) auto
+
+lemma wf_lex [intro!]:
+ assumes "wf r" shows "wf (lex r)"
unfolding lex_def
- apply (rule wf_UN)
- apply (simp add: wf_lexn)
- apply (metis DomainE Int_emptyI RangeE lexn_length)
- done
+proof (rule wf_UN)
+ show "wf (lexn r i)" for i
+ by (simp add: assms wf_lexn)
+ show "\<And>i j. lexn r i \<noteq> lexn r j \<Longrightarrow> Domain (lexn r i) \<inter> Range (lexn r j) = {}"
+ by (metis DomainE Int_emptyI RangeE lexn_length)
+qed
+
lemma lexn_conv:
"lexn r n =
{(xs,ys). length xs = n \<and> length ys = n \<and>
(\<exists>xys x y xs' ys'. xs= xys @ x#xs' \<and> ys= xys @ y # ys' \<and> (x, y) \<in> r)}"
-apply (induct n, simp)
-apply (simp add: image_Collect lex_prod_def, safe, blast)
- apply (rule_tac x = "ab # xys" in exI, simp)
-apply (case_tac xys, simp_all, blast)
-done
+proof (induction n)
+ case (Suc n)
+ then show ?case
+ apply (simp add: image_Collect lex_prod_def, safe, blast)
+ apply (rule_tac x = "ab # xys" in exI, simp)
+ apply (case_tac xys; force)
+ done
+qed auto
text\<open>By Mathias Fleury:\<close>
proposition lexn_transI:
@@ -6121,7 +6120,7 @@
(\<exists>xys x y xs' ys'. xs = xys @ x # xs' \<and> ys = xys @ y # ys' \<and> (x, y) \<in> r)}"
by (force simp add: lex_def lexn_conv)
-lemma wf_lenlex [intro!]: "wf r ==> wf (lenlex r)"
+lemma wf_lenlex [intro!]: "wf r \<Longrightarrow> wf (lenlex r)"
by (unfold lenlex_def) blast
lemma lenlex_conv:
@@ -6152,18 +6151,21 @@
by (meson lex_transI trans_inv_image trans_less_than trans_lex_prod)
lemma Nil_notin_lex [iff]: "([], ys) \<notin> lex r"
-by (simp add: lex_conv)
+ by (simp add: lex_conv)
lemma Nil2_notin_lex [iff]: "(xs, []) \<notin> lex r"
-by (simp add:lex_conv)
+ by (simp add:lex_conv)
lemma Cons_in_lex [simp]:
- "((x # xs, y # ys) \<in> lex r) =
- ((x, y) \<in> r \<and> length xs = length ys \<or> x = y \<and> (xs, ys) \<in> lex r)"
- apply (simp add: lex_conv)
- apply (rule iffI)
- prefer 2 apply (blast intro: Cons_eq_appendI, clarify)
- by (metis hd_append append_Nil list.sel(1) list.sel(3) tl_append2)
+ "(x # xs, y # ys) \<in> lex r \<longleftrightarrow> (x, y) \<in> r \<and> length xs = length ys \<or> x = y \<and> (xs, ys) \<in> lex r"
+ (is "?lhs = ?rhs")
+proof
+ assume ?lhs then show ?rhs
+ by (simp add: lex_conv) (metis hd_append list.sel(1) list.sel(3) tl_append2)
+next
+ assume ?rhs then show ?lhs
+ by (simp add: lex_conv) (blast intro: Cons_eq_appendI)
+qed
lemma Nil_lenlex_iff1 [simp]: "([], ns) \<in> lenlex r \<longleftrightarrow> ns \<noteq> []"
and Nil_lenlex_iff2 [simp]: "(ns,[]) \<notin> lenlex r"
@@ -6181,24 +6183,23 @@
lemma lex_append_rightI:
"(xs, ys) \<in> lex r \<Longrightarrow> length vs = length us \<Longrightarrow> (xs @ us, ys @ vs) \<in> lex r"
-by (fastforce simp: lex_def lexn_conv)
+ by (fastforce simp: lex_def lexn_conv)
lemma lex_append_leftI:
"(ys, zs) \<in> lex r \<Longrightarrow> (xs @ ys, xs @ zs) \<in> lex r"
-by (induct xs) auto
+ by (induct xs) auto
lemma lex_append_leftD:
"\<forall>x. (x,x) \<notin> r \<Longrightarrow> (xs @ ys, xs @ zs) \<in> lex r \<Longrightarrow> (ys, zs) \<in> lex r"
-by (induct xs) auto
+ by (induct xs) auto
lemma lex_append_left_iff:
"\<forall>x. (x,x) \<notin> r \<Longrightarrow> (xs @ ys, xs @ zs) \<in> lex r \<longleftrightarrow> (ys, zs) \<in> lex r"
-by(metis lex_append_leftD lex_append_leftI)
+ by(metis lex_append_leftD lex_append_leftI)
lemma lex_take_index:
assumes "(xs, ys) \<in> lex r"
- obtains i where "i < length xs" and "i < length ys" and "take i xs =
-take i ys"
+ obtains i where "i < length xs" and "i < length ys" and "take i xs = take i ys"
and "(xs ! i, ys ! i) \<in> r"
proof -
obtain n us x xs' y ys' where "(xs, ys) \<in> lexn r n" and "length xs = n" and "length ys = n"
@@ -6225,40 +6226,47 @@
by (unfold lexord_def, induct_tac x, auto)
lemma lexord_cons_cons[simp]:
- "((a # x, b # y) \<in> lexord r) = ((a,b)\<in> r \<or> (a = b \<and> (x,y)\<in> lexord r))"
- unfolding lexord_def
- apply (safe, simp_all)
- apply (metis hd_append list.sel(1))
+ "(a # x, b # y) \<in> lexord r \<longleftrightarrow> (a,b)\<in> r \<or> (a = b \<and> (x,y)\<in> lexord r)" (is "?lhs = ?rhs")
+proof
+ assume ?lhs
+ then show ?rhs
+ apply (simp add: lexord_def)
apply (metis hd_append list.sel(1) list.sel(3) tl_append2)
- apply blast
- by (meson Cons_eq_appendI)
+ done
+qed (auto simp add: lexord_def; (blast | meson Cons_eq_appendI))
lemmas lexord_simps = lexord_Nil_left lexord_Nil_right lexord_cons_cons
lemma lexord_append_rightI: "\<exists> b z. y = b # z \<Longrightarrow> (x, x @ y) \<in> lexord r"
-by (induct_tac x, auto)
+ by (induct_tac x, auto)
lemma lexord_append_left_rightI:
- "(a,b) \<in> r \<Longrightarrow> (u @ a # x, u @ b # y) \<in> lexord r"
-by (induct_tac u, auto)
+ "(a,b) \<in> r \<Longrightarrow> (u @ a # x, u @ b # y) \<in> lexord r"
+ by (induct_tac u, auto)
lemma lexord_append_leftI: " (u,v) \<in> lexord r \<Longrightarrow> (x @ u, x @ v) \<in> lexord r"
-by (induct x, auto)
+ by (induct x, auto)
lemma lexord_append_leftD:
- "\<lbrakk> (x @ u, x @ v) \<in> lexord r; (\<forall>a. (a,a) \<notin> r) \<rbrakk> \<Longrightarrow> (u,v) \<in> lexord r"
-by (erule rev_mp, induct_tac x, auto)
+ "\<lbrakk>(x @ u, x @ v) \<in> lexord r; (\<forall>a. (a,a) \<notin> r) \<rbrakk> \<Longrightarrow> (u,v) \<in> lexord r"
+ by (erule rev_mp, induct_tac x, auto)
lemma lexord_take_index_conv:
"((x,y) \<in> lexord r) =
((length x < length y \<and> take (length x) y = x) \<or>
(\<exists>i. i < min(length x)(length y) \<and> take i x = take i y \<and> (x!i,y!i) \<in> r))"
- apply (unfold lexord_def Let_def, clarsimp)
- apply (rule_tac f = "(% a b. a \<or> b)" in arg_cong2)
- apply (metis Cons_nth_drop_Suc append_eq_conv_conj drop_all list.simps(3) not_le)
- apply auto
- apply (rule_tac x ="length u" in exI, simp)
- by (metis id_take_nth_drop)
+proof -
+ have "(\<exists>a v. y = x @ a # v) = (length x < length y \<and> take (length x) y = x)"
+ by (metis Cons_nth_drop_Suc append_eq_conv_conj drop_all list.simps(3) not_le)
+ moreover
+ have "(\<exists>u a b. (a, b) \<in> r \<and> (\<exists>v. x = u @ a # v) \<and> (\<exists>w. y = u @ b # w)) =
+ (\<exists>i<length x. i < length y \<and> take i x = take i y \<and> (x ! i, y ! i) \<in> r)"
+ apply safe
+ using less_iff_Suc_add apply auto[1]
+ by (metis id_take_nth_drop)
+ ultimately show ?thesis
+ by (auto simp: lexord_def Let_def)
+qed
\<comment> \<open>lexord is extension of partial ordering List.lex\<close>
lemma lexord_lex: "(x,y) \<in> lex r = ((x,y) \<in> lexord r \<and> length x = length y)"
@@ -6539,10 +6547,10 @@
unfolding measures_def
by auto
-lemma measures_less: "f x < f y ==> (x, y) \<in> measures (f#fs)"
+lemma measures_less: "f x < f y \<Longrightarrow> (x, y) \<in> measures (f#fs)"
by simp
-lemma measures_lesseq: "f x \<le> f y ==> (x, y) \<in> measures fs ==> (x, y) \<in> measures (f#fs)"
+lemma measures_lesseq: "f x \<le> f y \<Longrightarrow> (x, y) \<in> measures fs \<Longrightarrow> (x, y) \<in> measures (f#fs)"
by auto
@@ -6685,7 +6693,7 @@
for r :: "('a \<times> 'b) set"
where
Nil: "([],[]) \<in> listrel r"
- | Cons: "[| (x,y) \<in> r; (xs,ys) \<in> listrel r |] ==> (x#xs, y#ys) \<in> listrel r"
+ | Cons: "\<lbrakk>(x,y) \<in> r; (xs,ys) \<in> listrel r\<rbrakk> \<Longrightarrow> (x#xs, y#ys) \<in> listrel r"
inductive_cases listrel_Nil1 [elim!]: "([],xs) \<in> listrel r"
inductive_cases listrel_Nil2 [elim!]: "(xs,[]) \<in> listrel r"
--- a/src/HOL/Map.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Map.thy Thu Apr 02 13:04:24 2020 +0200
@@ -110,18 +110,19 @@
lemma map_upd_Some_unfold:
"((m(a\<mapsto>b)) x = Some y) = (x = a \<and> b = y \<or> x \<noteq> a \<and> m x = Some y)"
-by auto
+ by auto
lemma image_map_upd [simp]: "x \<notin> A \<Longrightarrow> m(x \<mapsto> y) ` A = m ` A"
-by auto
+ by auto
-lemma finite_range_updI: "finite (range f) \<Longrightarrow> finite (range (f(a\<mapsto>b)))"
-unfolding image_def
-apply (simp (no_asm_use) add:full_SetCompr_eq)
-apply (rule finite_subset)
- prefer 2 apply assumption
-apply (auto)
-done
+lemma finite_range_updI:
+ assumes "finite (range f)" shows "finite (range (f(a\<mapsto>b)))"
+proof -
+ have "range (f(a\<mapsto>b)) \<subseteq> insert (Some b) (range f)"
+ by auto
+ then show ?thesis
+ by (rule finite_subset) (use assms in auto)
+qed
subsection \<open>@{term [source] map_of}\<close>
@@ -143,21 +144,19 @@
lemma map_of_eq_Some_iff [simp]:
"distinct(map fst xys) \<Longrightarrow> (map_of xys x = Some y) = ((x,y) \<in> set xys)"
-apply (induct xys)
- apply simp
-apply (auto simp: map_of_eq_None_iff [symmetric])
-done
+proof (induct xys)
+ case (Cons xy xys)
+ then show ?case
+ by (cases xy) (auto simp flip: map_of_eq_None_iff)
+qed auto
lemma Some_eq_map_of_iff [simp]:
"distinct(map fst xys) \<Longrightarrow> (Some y = map_of xys x) = ((x,y) \<in> set xys)"
by (auto simp del: map_of_eq_Some_iff simp: map_of_eq_Some_iff [symmetric])
-lemma map_of_is_SomeI [simp]: "\<lbrakk> distinct(map fst xys); (x,y) \<in> set xys \<rbrakk>
- \<Longrightarrow> map_of xys x = Some y"
-apply (induct xys)
- apply simp
-apply force
-done
+lemma map_of_is_SomeI [simp]:
+ "\<lbrakk>distinct(map fst xys); (x,y) \<in> set xys\<rbrakk> \<Longrightarrow> map_of xys x = Some y"
+ by simp
lemma map_of_zip_is_None [simp]:
"length xs = length ys \<Longrightarrow> (map_of (zip xs ys) x = None) = (x \<notin> set xs)"
@@ -233,12 +232,11 @@
by (induct xs) (simp_all add: fun_eq_iff)
lemma finite_range_map_of: "finite (range (map_of xys))"
-apply (induct xys)
- apply (simp_all add: image_constant)
-apply (rule finite_subset)
- prefer 2 apply assumption
-apply auto
-done
+proof (induct xys)
+ case (Cons a xys)
+ then show ?case
+ using finite_range_updI by fastforce
+qed auto
lemma map_of_SomeD: "map_of xs k = Some y \<Longrightarrow> (k, y) \<in> set xs"
by (induct xs) (auto split: if_splits)
@@ -334,23 +332,24 @@
by (rule ext) (auto simp: map_add_def dom_def split: option.split)
lemma map_of_append[simp]: "map_of (xs @ ys) = map_of ys ++ map_of xs"
-unfolding map_add_def
-apply (induct xs)
- apply simp
-apply (rule ext)
-apply (simp split: option.split)
-done
+ unfolding map_add_def
+proof (induct xs)
+ case (Cons a xs)
+ then show ?case
+ by (force split: option.split)
+qed auto
lemma finite_range_map_of_map_add:
"finite (range f) \<Longrightarrow> finite (range (f ++ map_of l))"
-apply (induct l)
- apply (auto simp del: fun_upd_apply)
-apply (erule finite_range_updI)
-done
+proof (induct l)
+case (Cons a l)
+ then show ?case
+ by (metis finite_range_updI map_add_upd map_of.simps(2))
+qed auto
lemma inj_on_map_add_dom [iff]:
"inj_on (m ++ m') (dom m') = inj_on m' (dom m')"
-by (fastforce simp: map_add_def dom_def inj_on_def split: option.splits)
+ by (fastforce simp: map_add_def dom_def inj_on_def split: option.splits)
lemma map_upds_fold_map_upd:
"m(ks[\<mapsto>]vs) = foldl (\<lambda>m (k, v). m(k \<mapsto> v)) m (zip ks vs)"
@@ -369,46 +368,46 @@
subsection \<open>@{term [source] restrict_map}\<close>
lemma restrict_map_to_empty [simp]: "m|`{} = empty"
-by (simp add: restrict_map_def)
+ by (simp add: restrict_map_def)
lemma restrict_map_insert: "f |` (insert a A) = (f |` A)(a := f a)"
-by (auto simp: restrict_map_def)
+ by (auto simp: restrict_map_def)
lemma restrict_map_empty [simp]: "empty|`D = empty"
-by (simp add: restrict_map_def)
+ by (simp add: restrict_map_def)
lemma restrict_in [simp]: "x \<in> A \<Longrightarrow> (m|`A) x = m x"
-by (simp add: restrict_map_def)
+ by (simp add: restrict_map_def)
lemma restrict_out [simp]: "x \<notin> A \<Longrightarrow> (m|`A) x = None"
-by (simp add: restrict_map_def)
+ by (simp add: restrict_map_def)
lemma ran_restrictD: "y \<in> ran (m|`A) \<Longrightarrow> \<exists>x\<in>A. m x = Some y"
-by (auto simp: restrict_map_def ran_def split: if_split_asm)
+ by (auto simp: restrict_map_def ran_def split: if_split_asm)
lemma dom_restrict [simp]: "dom (m|`A) = dom m \<inter> A"
-by (auto simp: restrict_map_def dom_def split: if_split_asm)
+ by (auto simp: restrict_map_def dom_def split: if_split_asm)
lemma restrict_upd_same [simp]: "m(x\<mapsto>y)|`(-{x}) = m|`(-{x})"
-by (rule ext) (auto simp: restrict_map_def)
+ by (rule ext) (auto simp: restrict_map_def)
lemma restrict_restrict [simp]: "m|`A|`B = m|`(A\<inter>B)"
-by (rule ext) (auto simp: restrict_map_def)
+ by (rule ext) (auto simp: restrict_map_def)
lemma restrict_fun_upd [simp]:
"m(x := y)|`D = (if x \<in> D then (m|`(D-{x}))(x := y) else m|`D)"
-by (simp add: restrict_map_def fun_eq_iff)
+ by (simp add: restrict_map_def fun_eq_iff)
lemma fun_upd_None_restrict [simp]:
"(m|`D)(x := None) = (if x \<in> D then m|`(D - {x}) else m|`D)"
-by (simp add: restrict_map_def fun_eq_iff)
+ by (simp add: restrict_map_def fun_eq_iff)
lemma fun_upd_restrict: "(m|`D)(x := y) = (m|`(D-{x}))(x := y)"
-by (simp add: restrict_map_def fun_eq_iff)
+ by (simp add: restrict_map_def fun_eq_iff)
lemma fun_upd_restrict_conv [simp]:
"x \<in> D \<Longrightarrow> (m|`D)(x := y) = (m|`(D-{x}))(x := y)"
-by (simp add: restrict_map_def fun_eq_iff)
+ by (rule fun_upd_restrict)
lemma map_of_map_restrict:
"map_of (map (\<lambda>k. (k, f k)) ks) = (Some \<circ> f) |` set ks"
@@ -416,47 +415,62 @@
lemma restrict_complement_singleton_eq:
"f |` (- {x}) = f(x := None)"
- by (simp add: restrict_map_def fun_eq_iff)
+ by auto
subsection \<open>@{term [source] map_upds}\<close>
lemma map_upds_Nil1 [simp]: "m([] [\<mapsto>] bs) = m"
-by (simp add: map_upds_def)
+ by (simp add: map_upds_def)
lemma map_upds_Nil2 [simp]: "m(as [\<mapsto>] []) = m"
-by (simp add:map_upds_def)
+ by (simp add:map_upds_def)
lemma map_upds_Cons [simp]: "m(a#as [\<mapsto>] b#bs) = (m(a\<mapsto>b))(as[\<mapsto>]bs)"
-by (simp add:map_upds_def)
+ by (simp add:map_upds_def)
-lemma map_upds_append1 [simp]: "size xs < size ys \<Longrightarrow>
- m(xs@[x] [\<mapsto>] ys) = m(xs [\<mapsto>] ys)(x \<mapsto> ys!size xs)"
-apply(induct xs arbitrary: ys m)
- apply (clarsimp simp add: neq_Nil_conv)
-apply (case_tac ys)
- apply simp
-apply simp
-done
+lemma map_upds_append1 [simp]:
+ "size xs < size ys \<Longrightarrow> m(xs@[x] [\<mapsto>] ys) = m(xs [\<mapsto>] ys)(x \<mapsto> ys!size xs)"
+proof (induct xs arbitrary: ys m)
+ case Nil
+ then show ?case
+ by (auto simp: neq_Nil_conv)
+next
+ case (Cons a xs)
+ then show ?case
+ by (cases ys) auto
+qed
lemma map_upds_list_update2_drop [simp]:
"size xs \<le> i \<Longrightarrow> m(xs[\<mapsto>]ys[i:=y]) = m(xs[\<mapsto>]ys)"
-apply (induct xs arbitrary: m ys i)
- apply simp
-apply (case_tac ys)
- apply simp
-apply (simp split: nat.split)
-done
+proof (induct xs arbitrary: m ys i)
+ case Nil
+ then show ?case
+ by auto
+next
+ case (Cons a xs)
+ then show ?case
+ by (cases ys) (use Cons in \<open>auto split: nat.split\<close>)
+qed
+text \<open>Something weirdly sensitive about this proof, which needs only four lines in apply style\<close>
lemma map_upd_upds_conv_if:
"(f(x\<mapsto>y))(xs [\<mapsto>] ys) =
(if x \<in> set(take (length ys) xs) then f(xs [\<mapsto>] ys)
else (f(xs [\<mapsto>] ys))(x\<mapsto>y))"
-apply (induct xs arbitrary: x y ys f)
- apply simp
-apply (case_tac ys)
- apply (auto split: if_split simp: fun_upd_twist)
-done
+proof (induct xs arbitrary: x y ys f)
+ case (Cons a xs)
+ show ?case
+ proof (cases ys)
+ case (Cons z zs)
+ then show ?thesis
+ using Cons.hyps
+ apply (auto split: if_split simp: fun_upd_twist)
+ using Cons.hyps apply fastforce+
+ done
+ qed auto
+qed auto
+
lemma map_upds_twist [simp]:
"a \<notin> set as \<Longrightarrow> m(a\<mapsto>b)(as[\<mapsto>]bs) = m(as[\<mapsto>]bs)(a\<mapsto>b)"
@@ -464,39 +478,42 @@
lemma map_upds_apply_nontin [simp]:
"x \<notin> set xs \<Longrightarrow> (f(xs[\<mapsto>]ys)) x = f x"
-apply (induct xs arbitrary: ys)
- apply simp
-apply (case_tac ys)
- apply (auto simp: map_upd_upds_conv_if)
-done
+proof (induct xs arbitrary: ys)
+ case (Cons a xs)
+ then show ?case
+ by (cases ys) (auto simp: map_upd_upds_conv_if)
+qed auto
lemma fun_upds_append_drop [simp]:
"size xs = size ys \<Longrightarrow> m(xs@zs[\<mapsto>]ys) = m(xs[\<mapsto>]ys)"
-apply (induct xs arbitrary: m ys)
- apply simp
-apply (case_tac ys)
- apply simp_all
-done
+proof (induct xs arbitrary: ys)
+ case (Cons a xs)
+ then show ?case
+ by (cases ys) (auto simp: map_upd_upds_conv_if)
+qed auto
lemma fun_upds_append2_drop [simp]:
"size xs = size ys \<Longrightarrow> m(xs[\<mapsto>]ys@zs) = m(xs[\<mapsto>]ys)"
-apply (induct xs arbitrary: m ys)
- apply simp
-apply (case_tac ys)
- apply simp_all
-done
-
+proof (induct xs arbitrary: ys)
+ case (Cons a xs)
+ then show ?case
+ by (cases ys) (auto simp: map_upd_upds_conv_if)
+qed auto
lemma restrict_map_upds[simp]:
"\<lbrakk> length xs = length ys; set xs \<subseteq> D \<rbrakk>
\<Longrightarrow> m(xs [\<mapsto>] ys)|`D = (m|`(D - set xs))(xs [\<mapsto>] ys)"
-apply (induct xs arbitrary: m ys)
- apply simp
-apply (case_tac ys)
- apply simp
-apply (simp add: Diff_insert [symmetric] insert_absorb)
-apply (simp add: map_upd_upds_conv_if)
-done
+proof (induct xs arbitrary: m ys)
+ case (Cons a xs)
+ then show ?case
+ proof (cases ys)
+ case (Cons z zs)
+ with Cons.hyps Cons.prems show ?thesis
+ apply (simp add: insert_absorb flip: Diff_insert)
+ apply (auto simp add: map_upd_upds_conv_if)
+ done
+ qed auto
+qed auto
subsection \<open>@{term [source] dom}\<close>
@@ -537,11 +554,12 @@
lemma dom_map_upds [simp]:
"dom(m(xs[\<mapsto>]ys)) = set(take (length ys) xs) \<union> dom m"
-apply (induct xs arbitrary: m ys)
- apply simp
-apply (case_tac ys)
- apply auto
-done
+proof (induct xs arbitrary: ys)
+ case (Cons a xs)
+ then show ?case
+ by (cases ys) (auto simp: map_upd_upds_conv_if)
+qed auto
+
lemma dom_map_add [simp]: "dom (m ++ n) = dom n \<union> dom m"
by (auto simp: dom_def)
@@ -638,12 +656,9 @@
lemma ran_empty [simp]: "ran empty = {}"
by (auto simp: ran_def)
-lemma ran_map_upd [simp]: "m a = None \<Longrightarrow> ran(m(a\<mapsto>b)) = insert b (ran m)"
+lemma ran_map_upd [simp]: "m a = None \<Longrightarrow> ran(m(a\<mapsto>b)) = insert b (ran m)"
unfolding ran_def
-apply auto
-apply (subgoal_tac "aa \<noteq> a")
- apply auto
-done
+ by force
lemma ran_map_add:
assumes "dom m1 \<inter> dom m2 = {}"
@@ -712,11 +727,11 @@
lemma map_le_upds [simp]:
"f \<subseteq>\<^sub>m g \<Longrightarrow> f(as [\<mapsto>] bs) \<subseteq>\<^sub>m g(as [\<mapsto>] bs)"
-apply (induct as arbitrary: f g bs)
- apply simp
-apply (case_tac bs)
- apply auto
-done
+proof (induct as arbitrary: f g bs)
+ case (Cons a as)
+ then show ?case
+ by (cases bs) (use Cons in auto)
+qed auto
lemma map_le_implies_dom_le: "(f \<subseteq>\<^sub>m g) \<Longrightarrow> (dom f \<subseteq> dom g)"
by (fastforce simp add: map_le_def dom_def)
@@ -728,11 +743,8 @@
by (auto simp add: map_le_def dom_def)
lemma map_le_antisym: "\<lbrakk> f \<subseteq>\<^sub>m g; g \<subseteq>\<^sub>m f \<rbrakk> \<Longrightarrow> f = g"
-unfolding map_le_def
-apply (rule ext)
-apply (case_tac "x \<in> dom f", simp)
-apply (case_tac "x \<in> dom g", simp, fastforce)
-done
+ unfolding map_le_def
+ by (metis ext domIff)
lemma map_le_map_add [simp]: "f \<subseteq>\<^sub>m g ++ f"
by (fastforce simp: map_le_def)
--- a/src/HOL/Nat.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Nat.thy Thu Apr 02 13:04:24 2020 +0200
@@ -65,15 +65,15 @@
by (rule iffI, rule Suc_Rep_inject) simp_all
lemma nat_induct0:
- assumes "P 0"
- and "\<And>n. P n \<Longrightarrow> P (Suc n)"
+ assumes "P 0" and "\<And>n. P n \<Longrightarrow> P (Suc n)"
shows "P n"
- using assms
- apply (unfold Zero_nat_def Suc_def)
- apply (rule Rep_Nat_inverse [THEN subst]) \<comment> \<open>types force good instantiation\<close>
- apply (erule Nat_Rep_Nat [THEN Nat.induct])
- apply (iprover elim: Nat_Abs_Nat_inverse [THEN subst])
- done
+proof -
+ have "P (Abs_Nat (Rep_Nat n))"
+ using assms unfolding Zero_nat_def Suc_def
+ by (iprover intro: Nat_Rep_Nat [THEN Nat.induct] elim: Nat_Abs_Nat_inverse [THEN subst])
+ then show ?thesis
+ by (simp add: Rep_Nat_inverse)
+qed
free_constructors case_nat for "0 :: nat" | Suc pred
where "pred (0 :: nat) = (0 :: nat)"
@@ -87,11 +87,7 @@
setup \<open>Sign.mandatory_path "old"\<close>
old_rep_datatype "0 :: nat" Suc
- apply (erule nat_induct0)
- apply assumption
- apply (rule nat.inject)
- apply (rule nat.distinct(1))
- done
+ by (erule nat_induct0) auto
setup \<open>Sign.parent_path\<close>
@@ -356,18 +352,11 @@
qed
lemma one_eq_mult_iff [simp]: "Suc 0 = m * n \<longleftrightarrow> m = Suc 0 \<and> n = Suc 0"
- apply (rule trans)
- apply (rule_tac [2] mult_eq_1_iff)
- apply fastforce
- done
-
-lemma nat_mult_eq_1_iff [simp]: "m * n = 1 \<longleftrightarrow> m = 1 \<and> n = 1"
- for m n :: nat
- unfolding One_nat_def by (rule mult_eq_1_iff)
-
-lemma nat_1_eq_mult_iff [simp]: "1 = m * n \<longleftrightarrow> m = 1 \<and> n = 1"
- for m n :: nat
- unfolding One_nat_def by (rule one_eq_mult_iff)
+ by (simp add: eq_commute flip: mult_eq_1_iff)
+
+lemma nat_mult_eq_1_iff [simp]: "m * n = 1 \<longleftrightarrow> m = 1 \<and> n = 1"
+ and nat_1_eq_mult_iff [simp]: "1 = m * n \<longleftrightarrow> m = 1 \<and> n = 1" for m n :: nat
+ by auto
lemma mult_cancel1 [simp]: "k * m = k * n \<longleftrightarrow> m = n \<or> k = 0"
for k m n :: nat
@@ -584,22 +573,23 @@
and less: "m < n \<Longrightarrow> P"
and eq: "m = n \<Longrightarrow> P"
shows P
- apply (rule major [THEN lessE])
- apply (rule eq)
- apply blast
- apply (rule less)
- apply blast
- done
+proof (rule major [THEN lessE])
+ show "Suc n = Suc m \<Longrightarrow> P"
+ using eq by blast
+ show "\<And>j. \<lbrakk>m < j; Suc n = Suc j\<rbrakk> \<Longrightarrow> P"
+ by (blast intro: less)
+qed
lemma Suc_lessE:
assumes major: "Suc i < k"
and minor: "\<And>j. i < j \<Longrightarrow> k = Suc j \<Longrightarrow> P"
shows P
- apply (rule major [THEN lessE])
- apply (erule lessI [THEN minor])
- apply (erule Suc_lessD [THEN minor])
- apply assumption
- done
+proof (rule major [THEN lessE])
+ show "k = Suc (Suc i) \<Longrightarrow> P"
+ using lessI minor by iprover
+ show "\<And>j. \<lbrakk>Suc i < j; k = Suc j\<rbrakk> \<Longrightarrow> P"
+ using Suc_lessD minor by iprover
+qed
lemma Suc_less_SucD: "Suc m < Suc n \<Longrightarrow> m < n"
by simp
@@ -786,12 +776,16 @@
by (induct k) simp_all
text \<open>strict, in both arguments\<close>
-lemma add_less_mono: "i < j \<Longrightarrow> k < l \<Longrightarrow> i + k < j + l"
- for i j k l :: nat
- apply (rule add_less_mono1 [THEN less_trans], assumption+)
- apply (induct j)
- apply simp_all
- done
+lemma add_less_mono:
+ fixes i j k l :: nat
+ assumes "i < j" "k < l" shows "i + k < j + l"
+proof -
+ have "i + k < j + k"
+ by (simp add: add_less_mono1 assms)
+ also have "... < j + l"
+ using \<open>i < j\<close> by (induction j) (auto simp: assms)
+ finally show ?thesis .
+qed
lemma less_imp_Suc_add: "m < n \<Longrightarrow> \<exists>k. n = Suc (m + k)"
proof (induct n)
@@ -969,42 +963,55 @@
for P :: "nat \<Rightarrow> bool"
by (rule Least_equality[OF _ le0])
-lemma Least_Suc: "P n \<Longrightarrow> \<not> P 0 \<Longrightarrow> (LEAST n. P n) = Suc (LEAST m. P (Suc m))"
- apply (cases n)
- apply auto
- apply (frule LeastI)
- apply (drule_tac P = "\<lambda>x. P (Suc x)" in LeastI)
- apply (subgoal_tac " (LEAST x. P x) \<le> Suc (LEAST x. P (Suc x))")
- apply (erule_tac [2] Least_le)
- apply (cases "LEAST x. P x")
- apply auto
- apply (drule_tac P = "\<lambda>x. P (Suc x)" in Least_le)
- apply (blast intro: order_antisym)
- done
+lemma Least_Suc:
+ assumes "P n" "\<not> P 0"
+ shows "(LEAST n. P n) = Suc (LEAST m. P (Suc m))"
+proof (cases n)
+ case (Suc m)
+ show ?thesis
+ proof (rule antisym)
+ show "(LEAST x. P x) \<le> Suc (LEAST x. P (Suc x))"
+ using assms Suc by (force intro: LeastI Least_le)
+ have \<section>: "P (LEAST x. P x)"
+ by (blast intro: LeastI assms)
+ show "Suc (LEAST m. P (Suc m)) \<le> (LEAST n. P n)"
+ proof (cases "(LEAST n. P n)")
+ case 0
+ then show ?thesis
+ using \<section> by (simp add: assms)
+ next
+ case Suc
+ with \<section> show ?thesis
+ by (auto simp: Least_le)
+ qed
+ qed
+qed (use assms in auto)
lemma Least_Suc2: "P n \<Longrightarrow> Q m \<Longrightarrow> \<not> P 0 \<Longrightarrow> \<forall>k. P (Suc k) = Q k \<Longrightarrow> Least P = Suc (Least Q)"
by (erule (1) Least_Suc [THEN ssubst]) simp
-lemma ex_least_nat_le: "\<not> P 0 \<Longrightarrow> P n \<Longrightarrow> \<exists>k\<le>n. (\<forall>i<k. \<not> P i) \<and> P k"
- for P :: "nat \<Rightarrow> bool"
- apply (cases n)
- apply blast
- apply (rule_tac x="LEAST k. P k" in exI)
- apply (blast intro: Least_le dest: not_less_Least intro: LeastI_ex)
- done
-
-lemma ex_least_nat_less: "\<not> P 0 \<Longrightarrow> P n \<Longrightarrow> \<exists>k<n. (\<forall>i\<le>k. \<not> P i) \<and> P (k + 1)"
- for P :: "nat \<Rightarrow> bool"
- apply (cases n)
- apply blast
- apply (frule (1) ex_least_nat_le)
- apply (erule exE)
- apply (case_tac k)
- apply simp
- apply (rename_tac k1)
- apply (rule_tac x=k1 in exI)
- apply (auto simp add: less_eq_Suc_le)
- done
+lemma ex_least_nat_le:
+ fixes P :: "nat \<Rightarrow> bool"
+ assumes "P n" "\<not> P 0"
+ shows "\<exists>k\<le>n. (\<forall>i<k. \<not> P i) \<and> P k"
+proof (cases n)
+ case (Suc m)
+ with assms show ?thesis
+ by (blast intro: Least_le LeastI_ex dest: not_less_Least)
+qed (use assms in auto)
+
+lemma ex_least_nat_less:
+ fixes P :: "nat \<Rightarrow> bool"
+ assumes "P n" "\<not> P 0"
+ shows "\<exists>k<n. (\<forall>i\<le>k. \<not> P i) \<and> P (Suc k)"
+proof (cases n)
+ case (Suc m)
+ then obtain k where k: "k \<le> n" "\<forall>i<k. \<not> P i" "P k"
+ using ex_least_nat_le [OF assms] by blast
+ show ?thesis
+ by (cases k) (use assms k less_eq_Suc_le in auto)
+qed (use assms in auto)
+
lemma nat_less_induct:
fixes P :: "nat \<Rightarrow> bool"
@@ -1070,11 +1077,10 @@
assumes "P 0"
and "\<And>n. n > 0 \<Longrightarrow> \<not> P n \<Longrightarrow> \<exists>m. m < n \<and> \<not> P m"
shows "P n"
- apply (rule infinite_descent)
- using assms
- apply (case_tac "n > 0")
- apply auto
- done
+proof (rule infinite_descent)
+ show "\<And>n. \<not> P n \<Longrightarrow> \<exists>m<n. \<not> P m"
+ using assms by (case_tac "n > 0") auto
+qed
text \<open>
Infinite descent using a mapping to \<open>nat\<close>:
@@ -1178,14 +1184,11 @@
lemma not_add_less1 [iff]: "\<not> i + j < i"
for i j :: nat
- apply (rule notI)
- apply (drule add_lessD1)
- apply (erule less_irrefl [THEN notE])
- done
+ by simp
lemma not_add_less2 [iff]: "\<not> j + i < i"
for i j :: nat
- by (simp add: add.commute)
+ by simp
lemma add_leD1: "m + k \<le> n \<Longrightarrow> m \<le> n"
for k m n :: nat
@@ -1193,9 +1196,7 @@
lemma add_leD2: "m + k \<le> n \<Longrightarrow> k \<le> n"
for k m n :: nat
- apply (simp add: add.commute)
- apply (erule add_leD1)
- done
+ by (force simp add: add.commute dest: add_leD1)
lemma add_leE: "m + k \<le> n \<Longrightarrow> (m \<le> n \<Longrightarrow> k \<le> n \<Longrightarrow> R) \<Longrightarrow> R"
for k m n :: nat
@@ -1213,10 +1214,7 @@
by (induct m n rule: diff_induct) simp_all
lemma diff_less_Suc: "m - n < Suc m"
- apply (induct m n rule: diff_induct)
- apply (erule_tac [3] less_SucE)
- apply (simp_all add: less_Suc_eq)
- done
+ by (induct m n rule: diff_induct) (auto simp: less_Suc_eq)
lemma diff_le_self [simp]: "m - n \<le> m"
for m n :: nat
@@ -1345,12 +1343,26 @@
lemma mult_less_cancel2 [simp]: "m * k < n * k \<longleftrightarrow> 0 < k \<and> m < n"
for k m n :: nat
- apply (safe intro!: mult_less_mono1)
- apply (cases k)
- apply auto
- apply (simp add: linorder_not_le [symmetric])
- apply (blast intro: mult_le_mono1)
- done
+proof (intro iffI conjI)
+ assume m: "m * k < n * k"
+ then show "0 < k"
+ by (cases k) auto
+ show "m < n"
+ proof (cases k)
+ case 0
+ then show ?thesis
+ using m by auto
+ next
+ case (Suc k')
+ then show ?thesis
+ using m
+ by (simp flip: linorder_not_le) (blast intro: add_mono mult_le_mono1)
+ qed
+next
+ assume "0 < k \<and> m < n"
+ then show "m * k < n * k"
+ by (blast intro: mult_less_mono1)
+qed
lemma mult_less_cancel1 [simp]: "k * m < k * n \<longleftrightarrow> 0 < k \<and> m < n"
for k m n :: nat
@@ -1379,16 +1391,18 @@
by (cases m) (auto intro: le_add1)
text \<open>Lemma for \<open>gcd\<close>\<close>
-lemma mult_eq_self_implies_10: "m = m * n \<Longrightarrow> n = 1 \<or> m = 0"
- for m n :: nat
- apply (drule sym)
- apply (rule disjCI)
- apply (rule linorder_cases)
- defer
- apply assumption
- apply (drule mult_less_mono2)
- apply auto
- done
+lemma mult_eq_self_implies_10:
+ fixes m n :: nat
+ assumes "m = m * n" shows "n = 1 \<or> m = 0"
+proof (rule disjCI)
+ assume "m \<noteq> 0"
+ show "n = 1"
+ proof (cases n "1::nat" rule: linorder_cases)
+ case greater
+ show ?thesis
+ using assms mult_less_mono2 [OF greater, of m] \<open>m \<noteq> 0\<close> by auto
+ qed (use assms \<open>m \<noteq> 0\<close> in auto)
+qed
lemma mono_times_nat:
fixes n :: nat
@@ -1849,28 +1863,20 @@
by (simp add: Nats_def)
lemma Nats_0 [simp]: "0 \<in> \<nat>"
- apply (simp add: Nats_def)
- apply (rule range_eqI)
- apply (rule of_nat_0 [symmetric])
- done
+ using of_nat_0 [symmetric] unfolding Nats_def
+ by (rule range_eqI)
lemma Nats_1 [simp]: "1 \<in> \<nat>"
- apply (simp add: Nats_def)
- apply (rule range_eqI)
- apply (rule of_nat_1 [symmetric])
- done
+ using of_nat_1 [symmetric] unfolding Nats_def
+ by (rule range_eqI)
lemma Nats_add [simp]: "a \<in> \<nat> \<Longrightarrow> b \<in> \<nat> \<Longrightarrow> a + b \<in> \<nat>"
- apply (auto simp add: Nats_def)
- apply (rule range_eqI)
- apply (rule of_nat_add [symmetric])
- done
+ unfolding Nats_def using of_nat_add [symmetric]
+ by (blast intro: range_eqI)
lemma Nats_mult [simp]: "a \<in> \<nat> \<Longrightarrow> b \<in> \<nat> \<Longrightarrow> a * b \<in> \<nat>"
- apply (auto simp add: Nats_def)
- apply (rule range_eqI)
- apply (rule of_nat_mult [symmetric])
- done
+ unfolding Nats_def using of_nat_mult [symmetric]
+ by (blast intro: range_eqI)
lemma Nats_cases [cases set: Nats]:
assumes "x \<in> \<nat>"
@@ -2303,21 +2309,21 @@
qed
qed
-lemma GreatestI_nat:
- "\<lbrakk> P(k::nat); \<forall>y. P y \<longrightarrow> y \<le> b \<rbrakk> \<Longrightarrow> P (Greatest P)"
-apply(drule (1) ex_has_greatest_nat)
-using GreatestI2_order by auto
-
-lemma Greatest_le_nat:
- "\<lbrakk> P(k::nat); \<forall>y. P y \<longrightarrow> y \<le> b \<rbrakk> \<Longrightarrow> k \<le> (Greatest P)"
-apply(frule (1) ex_has_greatest_nat)
-using GreatestI2_order[where P=P and Q=\<open>\<lambda>x. k \<le> x\<close>] by auto
+lemma
+ fixes k::nat
+ assumes "P k" and minor: "\<And>y. P y \<Longrightarrow> y \<le> b"
+ shows GreatestI_nat: "P (Greatest P)"
+ and Greatest_le_nat: "k \<le> Greatest P"
+proof -
+ obtain x where "P x" "\<And>y. P y \<Longrightarrow> y \<le> x"
+ using assms ex_has_greatest_nat by blast
+ with \<open>P k\<close> show "P (Greatest P)" "k \<le> Greatest P"
+ using GreatestI2_order by blast+
+qed
lemma GreatestI_ex_nat:
- "\<lbrakk> \<exists>k::nat. P k; \<forall>y. P y \<longrightarrow> y \<le> b \<rbrakk> \<Longrightarrow> P (Greatest P)"
-apply (erule exE)
-apply (erule (1) GreatestI_nat)
-done
+ "\<lbrakk> \<exists>k::nat. P k; \<And>y. P y \<Longrightarrow> y \<le> b \<rbrakk> \<Longrightarrow> P (Greatest P)"
+ by (blast intro: GreatestI_nat)
subsection \<open>Monotonicity of \<open>funpow\<close>\<close>
@@ -2363,11 +2369,16 @@
for k m n :: nat
unfolding dvd_def by (blast intro: right_diff_distrib' [symmetric])
-lemma dvd_diffD: "k dvd m - n \<Longrightarrow> k dvd n \<Longrightarrow> n \<le> m \<Longrightarrow> k dvd m"
- for k m n :: nat
- apply (erule linorder_not_less [THEN iffD2, THEN add_diff_inverse, THEN subst])
- apply (blast intro: dvd_add)
- done
+lemma dvd_diffD:
+ fixes k m n :: nat
+ assumes "k dvd m - n" "k dvd n" "n \<le> m"
+ shows "k dvd m"
+proof -
+ have "k dvd n + (m - n)"
+ using assms by (blast intro: dvd_add)
+ with assms show ?thesis
+ by simp
+qed
lemma dvd_diffD1: "k dvd m - n \<Longrightarrow> k dvd m \<Longrightarrow> n \<le> m \<Longrightarrow> k dvd n"
for k m n :: nat
@@ -2384,13 +2395,19 @@
then show ?thesis ..
qed
-lemma dvd_mult_cancel1: "0 < m \<Longrightarrow> m * n dvd m \<longleftrightarrow> n = 1"
- for m n :: nat
- apply auto
- apply (subgoal_tac "m * n dvd m * 1")
- apply (drule dvd_mult_cancel)
- apply auto
- done
+lemma dvd_mult_cancel1:
+ fixes m n :: nat
+ assumes "0 < m"
+ shows "m * n dvd m \<longleftrightarrow> n = 1"
+proof
+ assume "m * n dvd m"
+ then have "m * n dvd m * 1"
+ by simp
+ then have "n dvd 1"
+ by (iprover intro: assms dvd_mult_cancel)
+ then show "n = 1"
+ by auto
+qed auto
lemma dvd_mult_cancel2: "0 < m \<Longrightarrow> n * m dvd m \<longleftrightarrow> n = 1"
for m n :: nat
@@ -2442,14 +2459,6 @@
for n :: nat
by (fact mult_1_right)
-lemma nat_add_left_cancel: "k + m = k + n \<longleftrightarrow> m = n"
- for k m n :: nat
- by (fact add_left_cancel)
-
-lemma nat_add_right_cancel: "m + k = n + k \<longleftrightarrow> m = n"
- for k m n :: nat
- by (fact add_right_cancel)
-
lemma diff_mult_distrib: "(m - n) * k = (m * k) - (n * k)"
for k m n :: nat
by (fact left_diff_distrib')
@@ -2458,13 +2467,10 @@
for k m n :: nat
by (fact right_diff_distrib')
-lemma le_add_diff: "k \<le> n \<Longrightarrow> m \<le> n + m - k"
- for k m n :: nat
- by (fact le_add_diff) (* FIXME delete *)
-
+(*Used in AUTO2 and Groups.le_diff_conv2 (with variables renamed) doesn't work for some reason*)
lemma le_diff_conv2: "k \<le> j \<Longrightarrow> (i \<le> j - k) = (i + k \<le> j)"
for i j k :: nat
- by (fact le_diff_conv2) (* FIXME delete *)
+ by (fact le_diff_conv2)
lemma diff_self_eq_0 [simp]: "m - m = 0"
for m :: nat
--- a/src/HOL/Quotient.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Quotient.thy Thu Apr 02 13:04:24 2020 +0200
@@ -253,27 +253,29 @@
fixes P::"'a \<Rightarrow> bool"
and x::"'a"
assumes a: "equivp R2"
- shows "(Ball (Respects (R1 ===> R2)) (\<lambda>f. P (f x)) = All (\<lambda>f. P (f x)))"
- apply(rule iffI)
- apply(rule allI)
- apply(drule_tac x="\<lambda>y. f x" in bspec)
- apply(simp add: in_respects rel_fun_def)
- apply(rule impI)
- using a equivp_reflp_symp_transp[of "R2"]
- apply (auto elim: equivpE reflpE)
- done
+ shows "(Ball (Respects (R1 ===> R2)) (\<lambda>f. P (f x)) = All (\<lambda>f. P (f x)))"
+proof (intro allI iffI)
+ fix f
+ assume "\<forall>f \<in> Respects (R1 ===> R2). P (f x)"
+ moreover have "(\<lambda>y. f x) \<in> Respects (R1 ===> R2)"
+ using a equivp_reflp_symp_transp[of "R2"]
+ by(auto simp add: in_respects rel_fun_def elim: equivpE reflpE)
+ ultimately show "P (f x)"
+ by auto
+qed auto
lemma bex_reg_eqv_range:
assumes a: "equivp R2"
shows "(Bex (Respects (R1 ===> R2)) (\<lambda>f. P (f x)) = Ex (\<lambda>f. P (f x)))"
- apply(auto)
- apply(rule_tac x="\<lambda>y. f x" in bexI)
- apply(simp)
- apply(simp add: Respects_def in_respects rel_fun_def)
- apply(rule impI)
- using a equivp_reflp_symp_transp[of "R2"]
- apply (auto elim: equivpE reflpE)
- done
+proof -
+ { fix f
+ assume "P (f x)"
+ have "(\<lambda>y. f x) \<in> Respects (R1 ===> R2)"
+ using a equivp_reflp_symp_transp[of "R2"]
+ by (auto simp add: Respects_def in_respects rel_fun_def elim: equivpE reflpE) }
+ then show ?thesis
+ by auto
+qed
(* Next four lemmas are unused *)
lemma all_reg:
@@ -322,35 +324,42 @@
assumes q: "Quotient3 R1 Abs1 Rep1"
and a: "(R1 ===> R2) f g"
shows "(R1 ===> R2) (Babs (Respects R1) f) (Babs (Respects R1) g)"
- apply (auto simp add: Babs_def in_respects rel_fun_def)
- apply (subgoal_tac "x \<in> Respects R1 \<and> y \<in> Respects R1")
- using a apply (simp add: Babs_def rel_fun_def)
- apply (simp add: in_respects rel_fun_def)
- using Quotient3_rel[OF q]
- by metis
+proof (clarsimp simp add: Babs_def in_respects rel_fun_def)
+ fix x y
+ assume "R1 x y"
+ then have "x \<in> Respects R1 \<and> y \<in> Respects R1"
+ unfolding in_respects rel_fun_def using Quotient3_rel[OF q]by metis
+ then show "R2 (Babs (Respects R1) f x) (Babs (Respects R1) g y)"
+ using \<open>R1 x y\<close> a by (simp add: Babs_def rel_fun_def)
+qed
lemma babs_prs:
assumes q1: "Quotient3 R1 Abs1 Rep1"
and q2: "Quotient3 R2 Abs2 Rep2"
- shows "((Rep1 ---> Abs2) (Babs (Respects R1) ((Abs1 ---> Rep2) f))) = f"
- apply (rule ext)
- apply (simp add:)
- apply (subgoal_tac "Rep1 x \<in> Respects R1")
- apply (simp add: Babs_def Quotient3_abs_rep[OF q1] Quotient3_abs_rep[OF q2])
- apply (simp add: in_respects Quotient3_rel_rep[OF q1])
- done
+shows "((Rep1 ---> Abs2) (Babs (Respects R1) ((Abs1 ---> Rep2) f))) = f"
+proof -
+ { fix x
+ have "Rep1 x \<in> Respects R1"
+ by (simp add: in_respects Quotient3_rel_rep[OF q1])
+ then have "Abs2 (Babs (Respects R1) ((Abs1 ---> Rep2) f) (Rep1 x)) = f x"
+ by (simp add: Babs_def Quotient3_abs_rep[OF q1] Quotient3_abs_rep[OF q2])
+ }
+ then show ?thesis
+ by force
+qed
lemma babs_simp:
assumes q: "Quotient3 R1 Abs Rep"
shows "((R1 ===> R2) (Babs (Respects R1) f) (Babs (Respects R1) g)) = ((R1 ===> R2) f g)"
- apply(rule iffI)
- apply(simp_all only: babs_rsp[OF q])
- apply(auto simp add: Babs_def rel_fun_def)
- apply(metis Babs_def in_respects Quotient3_rel[OF q])
- done
+ (is "?lhs = ?rhs")
+proof
+ assume ?lhs
+ then show ?rhs
+ unfolding rel_fun_def by (metis Babs_def in_respects Quotient3_rel[OF q])
+qed (simp add: babs_rsp[OF q])
-(* If a user proves that a particular functional relation
- is an equivalence this may be useful in regularising *)
+text \<open>If a user proves that a particular functional relation
+ is an equivalence, this may be useful in regularising\<close>
lemma babs_reg_eqv:
shows "equivp R \<Longrightarrow> Babs (Respects R) P = P"
by (simp add: fun_eq_iff Babs_def in_respects equivp_reflp)
@@ -372,7 +381,8 @@
shows "Ex1 (\<lambda>x. x \<in> Respects R \<and> f x) = Ex1 (\<lambda>x. x \<in> Respects R \<and> g x)"
using a by (auto elim: rel_funE simp add: Ex1_def in_respects)
-(* 2 lemmas needed for cleaning of quantifiers *)
+text \<open>Two lemmas needed for cleaning of quantifiers\<close>
+
lemma all_prs:
assumes a: "Quotient3 R absf repf"
shows "Ball (Respects R) ((absf ---> id) f) = All f"
@@ -410,10 +420,10 @@
lemma ex1_prs:
assumes "Quotient3 R absf repf"
shows "((absf ---> id) ---> id) (Bex1_rel R) f = Ex1 f"
- apply (auto simp: Bex1_rel_def Respects_def)
- apply (metis Quotient3_def assms)
- apply (metis (full_types) Quotient3_def assms)
- by (meson Quotient3_rel assms)
+ (is "?lhs = ?rhs")
+ using assms
+ apply (auto simp add: Bex1_rel_def Respects_def)
+ by (metis (full_types) Quotient3_def)+
lemma bex1_bexeq_reg:
shows "(\<exists>!x\<in>Respects R. P x) \<longrightarrow> (Bex1_rel R (\<lambda>x. P x))"
@@ -543,7 +553,6 @@
subsection \<open>Quotient composition\<close>
-
lemma OOO_quotient3:
fixes R1 :: "'a \<Rightarrow> 'a \<Rightarrow> bool"
fixes Abs1 :: "'a \<Rightarrow> 'b" and Rep1 :: "'b \<Rightarrow> 'a"
@@ -558,29 +567,35 @@
proof -
have *: "(R1 OOO R2') r r \<and> (R1 OOO R2') s s \<and> (Abs2 \<circ> Abs1) r = (Abs2 \<circ> Abs1) s
\<longleftrightarrow> (R1 OOO R2') r s" for r s
- apply safe
- subgoal for a b c d
- apply simp
- apply (rule_tac b="Rep1 (Abs1 r)" in relcomppI)
- using Quotient3_refl1 R1 rep_abs_rsp apply fastforce
- apply (rule_tac b="Rep1 (Abs1 s)" in relcomppI)
- apply (metis (full_types) Rep1 Abs1 Quotient3_rel R2 Quotient3_refl1 [OF R1] Quotient3_refl2 [OF R1] Quotient3_rel_abs [OF R1])
- by (metis Quotient3_rel R1 rep_abs_rsp_left)
- subgoal for x y
- apply (drule Abs1)
- apply (erule Quotient3_refl2 [OF R1])
- apply (erule Quotient3_refl1 [OF R1])
- apply (drule Quotient3_refl1 [OF R2], drule Rep1)
- by (metis (full_types) Quotient3_def R1 relcompp.relcompI)
- subgoal for x y
- apply (drule Abs1)
- apply (erule Quotient3_refl2 [OF R1])
- apply (erule Quotient3_refl1 [OF R1])
- apply (drule Quotient3_refl2 [OF R2], drule Rep1)
- by (metis (full_types) Quotient3_def R1 relcompp.relcompI)
- subgoal for x y
- by simp (metis (full_types) Abs1 Quotient3_rel R1 R2)
- done
+ proof (intro iffI conjI; clarify)
+ show "(R1 OOO R2') r s"
+ if r: "R1 r a" "R2' a b" "R1 b r" and eq: "(Abs2 \<circ> Abs1) r = (Abs2 \<circ> Abs1) s"
+ and s: "R1 s c" "R2' c d" "R1 d s" for a b c d
+ proof -
+ have "R1 r (Rep1 (Abs1 r))"
+ using r Quotient3_refl1 R1 rep_abs_rsp by fastforce
+ moreover have "R2' (Rep1 (Abs1 r)) (Rep1 (Abs1 s))"
+ using that
+ apply (simp add: )
+ apply (metis (full_types) Rep1 Abs1 Quotient3_rel R2 Quotient3_refl1 [OF R1] Quotient3_refl2 [OF R1] Quotient3_rel_abs [OF R1])
+ done
+ moreover have "R1 (Rep1 (Abs1 s)) s"
+ by (metis s Quotient3_rel R1 rep_abs_rsp_left)
+ ultimately show ?thesis
+ by (metis relcomppI)
+ qed
+ next
+ fix x y
+ assume xy: "R1 r x" "R2' x y" "R1 y s"
+ then have "R2 (Abs1 x) (Abs1 y)"
+ by (iprover dest: Abs1 elim: Quotient3_refl1 [OF R1] Quotient3_refl2 [OF R1])
+ then have "R2' (Rep1 (Abs1 x)) (Rep1 (Abs1 x))" "R2' (Rep1 (Abs1 y)) (Rep1 (Abs1 y))"
+ by (simp_all add: Quotient3_refl1 [OF R2] Quotient3_refl2 [OF R2] Rep1)
+ with \<open>R1 r x\<close> \<open>R1 y s\<close> show "(R1 OOO R2') r r" "(R1 OOO R2') s s"
+ by (metis (full_types) Quotient3_def R1 relcompp.relcompI)+
+ show "(Abs2 \<circ> Abs1) r = (Abs2 \<circ> Abs1) s"
+ using xy by simp (metis (full_types) Abs1 Quotient3_rel R1 R2)
+ qed
show ?thesis
apply (rule Quotient3I)
using * apply (simp_all add: o_def Quotient3_abs_rep [OF R2] Quotient3_abs_rep [OF R1])
--- a/src/HOL/Tools/BNF/bnf_lift.ML Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Tools/BNF/bnf_lift.ML Thu Apr 02 13:04:24 2020 +0200
@@ -2012,14 +2012,10 @@
else bad_input [thm])
| NONE => (case Lifting_Info.lookup_quotients lthy absT_name of
SOME {quot_thm = qthm, ...} =>
- let
- val qthm = Thm.transfer' lthy qthm;
- in
- case [qthm] RL @{thms Quotient_eq_onp_typedef Quotient_eq_onp_type_copy} of
- thm :: _ => (thm, Typedef)
- | _ => (qthm RS @{thm Quotient_Quotient3},
- Quotient (find_equiv_thm_via_Quotient qthm))
- end
+ (case [qthm] RL @{thms Quotient_eq_onp_typedef Quotient_eq_onp_type_copy} of
+ thm :: _ => (thm, Typedef)
+ | _ => (qthm RS @{thm Quotient_Quotient3},
+ Quotient (find_equiv_thm_via_Quotient qthm)))
| NONE => (Typedef.get_info lthy absT_name |> hd |> snd |> #type_definition, Typedef))
| SOME thms => bad_input thms);
val wits = (Option.map o map) (prepare_term lthy) raw_wits;
--- a/src/HOL/Transcendental.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Transcendental.thy Thu Apr 02 13:04:24 2020 +0200
@@ -618,10 +618,6 @@
for r :: "'a::ring_1"
by (simp add: sum_subtractf)
-lemma lemma_realpow_rev_sumr:
- "(\<Sum>p<Suc n. (x ^ p) * (y ^ (n - p))) = (\<Sum>p<Suc n. (x ^ (n - p)) * (y ^ p))"
- by (subst sum.nat_diff_reindex[symmetric]) simp
-
lemma lemma_termdiff2:
fixes h :: "'a::field"
assumes h: "h \<noteq> 0"
@@ -629,26 +625,26 @@
h * (\<Sum>p< n - Suc 0. \<Sum>q< n - Suc 0 - p. (z + h) ^ q * z ^ (n - 2 - q))"
(is "?lhs = ?rhs")
proof (cases n)
- case (Suc n)
+ case (Suc m)
have 0: "\<And>x k. (\<Sum>n<Suc k. h * (z ^ x * (z ^ (k - n) * (h + z) ^ n))) =
(\<Sum>j<Suc k. h * ((h + z) ^ j * z ^ (x + k - j)))"
- apply (rule sum.cong [OF refl])
- by (simp add: power_add [symmetric] mult.commute)
- have *: "(\<Sum>i<n. z ^ i * ((z + h) ^ (n - i) - z ^ (n - i))) =
- (\<Sum>i<n. \<Sum>j<n - i. h * ((z + h) ^ j * z ^ (n - Suc j)))"
- apply (rule sum.cong [OF refl])
- apply (clarsimp simp add: less_iff_Suc_add sum_distrib_left diff_power_eq_sum ac_simps 0
- simp del: sum.lessThan_Suc power_Suc)
- done
- have "h * ?lhs = h * ?rhs"
- apply (simp add: right_diff_distrib diff_divide_distrib h mult.assoc [symmetric])
- using Suc
- apply (simp add: diff_power_eq_sum h right_diff_distrib [symmetric] mult.assoc
+ by (auto simp add: power_add [symmetric] mult.commute intro: sum.cong)
+ have *: "(\<Sum>i<m. z ^ i * ((z + h) ^ (m - i) - z ^ (m - i))) =
+ (\<Sum>i<m. \<Sum>j<m - i. h * ((z + h) ^ j * z ^ (m - Suc j)))"
+ by (force simp add: less_iff_Suc_add sum_distrib_left diff_power_eq_sum ac_simps 0
+ simp del: sum.lessThan_Suc power_Suc intro: sum.cong)
+ have "h * ?lhs = (z + h) ^ n - z ^ n - h * of_nat n * z ^ (n - Suc 0)"
+ by (simp add: right_diff_distrib diff_divide_distrib h mult.assoc [symmetric])
+ also have "... = h * ((\<Sum>p<Suc m. (z + h) ^ p * z ^ (m - p)) - of_nat (Suc m) * z ^ m)"
+ by (simp add: Suc diff_power_eq_sum h right_diff_distrib [symmetric] mult.assoc
del: power_Suc sum.lessThan_Suc of_nat_Suc)
- apply (subst lemma_realpow_rev_sumr)
- apply (subst sumr_diff_mult_const2)
- apply (simp add: lemma_termdiff1 sum_distrib_left *)
- done
+ also have "... = h * ((\<Sum>p<Suc m. (z + h) ^ (m - p) * z ^ p) - of_nat (Suc m) * z ^ m)"
+ by (subst sum.nat_diff_reindex[symmetric]) simp
+ also have "... = h * (\<Sum>i<Suc m. (z + h) ^ (m - i) * z ^ i - z ^ m)"
+ by (simp add: sum_subtractf)
+ also have "... = h * ?rhs"
+ by (simp add: lemma_termdiff1 sum_distrib_left Suc *)
+ finally have "h * ?lhs = h * ?rhs" .
then show ?thesis
by (simp add: h)
qed auto
@@ -656,12 +652,15 @@
lemma real_sum_nat_ivl_bounded2:
fixes K :: "'a::linordered_semidom"
- assumes f: "\<And>p::nat. p < n \<Longrightarrow> f p \<le> K"
- and K: "0 \<le> K"
+ assumes f: "\<And>p::nat. p < n \<Longrightarrow> f p \<le> K" and K: "0 \<le> K"
shows "sum f {..<n-k} \<le> of_nat n * K"
- apply (rule order_trans [OF sum_mono [OF f]])
- apply (auto simp: mult_right_mono K)
- done
+proof -
+ have "sum f {..<n-k} \<le> (\<Sum>i<n - k. K)"
+ by (rule sum_mono [OF f]) auto
+ also have "... \<le> of_nat n * K"
+ by (auto simp: mult_right_mono K)
+ finally show ?thesis .
+qed
lemma lemma_termdiff3:
fixes h z :: "'a::real_normed_field"
@@ -678,21 +677,23 @@
proof (rule mult_right_mono [OF _ norm_ge_zero])
from norm_ge_zero 2 have K: "0 \<le> K"
by (rule order_trans)
- have le_Kn: "\<And>i j n. i + j = n \<Longrightarrow> norm ((z + h) ^ i * z ^ j) \<le> K ^ n"
- apply (erule subst)
- apply (simp only: norm_mult norm_power power_add)
- apply (intro mult_mono power_mono 2 3 norm_ge_zero zero_le_power K)
- done
+ have le_Kn: "norm ((z + h) ^ i * z ^ j) \<le> K ^ n" if "i + j = n" for i j n
+ proof -
+ have "norm (z + h) ^ i * norm z ^ j \<le> K ^ i * K ^ j"
+ by (intro mult_mono power_mono 2 3 norm_ge_zero zero_le_power K)
+ also have "... = K^n"
+ by (metis power_add that)
+ finally show ?thesis
+ by (simp add: norm_mult norm_power)
+ qed
+ then have "\<And>p q.
+ \<lbrakk>p < n; q < n - Suc 0\<rbrakk> \<Longrightarrow> norm ((z + h) ^ q * z ^ (n - 2 - q)) \<le> K ^ (n - 2)"
+ by simp
+ then
show "norm (\<Sum>p<n - Suc 0. \<Sum>q<n - Suc 0 - p. (z + h) ^ q * z ^ (n - 2 - q)) \<le>
of_nat n * (of_nat (n - Suc 0) * K ^ (n - 2))"
- apply (intro
- order_trans [OF norm_sum]
- real_sum_nat_ivl_bounded2
- mult_nonneg_nonneg
- of_nat_0_le_iff
- zero_le_power K)
- apply (rule le_Kn, simp)
- done
+ by (intro order_trans [OF norm_sum]
+ real_sum_nat_ivl_bounded2 mult_nonneg_nonneg of_nat_0_le_iff zero_le_power K)
qed
also have "\<dots> = of_nat n * of_nat (n - Suc 0) * K ^ (n - 2) * norm h"
by (simp only: mult.assoc)
@@ -775,39 +776,30 @@
then have "summable (\<lambda>n. of_nat n * diffs (\<lambda>n. norm (c n)) n * r ^ (n - Suc 0))"
by (rule diffs_equiv [THEN sums_summable])
also have "(\<lambda>n. of_nat n * diffs (\<lambda>n. norm (c n)) n * r ^ (n - Suc 0)) =
- (\<lambda>n. diffs (\<lambda>m. of_nat (m - Suc 0) * norm (c m) * inverse r) n * (r ^ n))"
- apply (rule ext)
- apply (case_tac n)
- apply (simp_all add: diffs_def r_neq_0)
- done
+ (\<lambda>n. diffs (\<lambda>m. of_nat (m - Suc 0) * norm (c m) * inverse r) n * (r ^ n))"
+ by (simp add: diffs_def r_neq_0 fun_eq_iff split: nat_diff_split)
finally have "summable
(\<lambda>n. of_nat n * (of_nat (n - Suc 0) * norm (c n) * inverse r) * r ^ (n - Suc 0))"
by (rule diffs_equiv [THEN sums_summable])
also have
"(\<lambda>n. of_nat n * (of_nat (n - Suc 0) * norm (c n) * inverse r) * r ^ (n - Suc 0)) =
(\<lambda>n. norm (c n) * of_nat n * of_nat (n - Suc 0) * r ^ (n - 2))"
- apply (rule ext)
- apply (case_tac n, simp)
- apply (rename_tac nat)
- apply (case_tac nat, simp)
- apply (simp add: r_neq_0)
- done
+ by (rule ext) (simp add: r_neq_0 split: nat_diff_split)
finally show "summable (\<lambda>n. norm (c n) * of_nat n * of_nat (n - Suc 0) * r ^ (n - 2))" .
next
- fix h :: 'a
- fix n :: nat
+ fix h :: 'a and n
assume h: "h \<noteq> 0"
assume "norm h < r - norm x"
then have "norm x + norm h < r" by simp
- with norm_triangle_ineq have xh: "norm (x + h) < r"
+ with norm_triangle_ineq
+ have xh: "norm (x + h) < r"
by (rule order_le_less_trans)
- show "norm (c n * (((x + h) ^ n - x^n) / h - of_nat n * x ^ (n - Suc 0))) \<le>
+ have "norm (((x + h) ^ n - x ^ n) / h - of_nat n * x ^ (n - Suc 0))
+ \<le> real n * (real (n - Suc 0) * (r ^ (n - 2) * norm h))"
+ by (metis (mono_tags, lifting) h mult.assoc lemma_termdiff3 less_eq_real_def r1 xh)
+ then show "norm (c n * (((x + h) ^ n - x^n) / h - of_nat n * x ^ (n - Suc 0))) \<le>
norm (c n) * of_nat n * of_nat (n - Suc 0) * r ^ (n - 2) * norm h"
- apply (simp only: norm_mult mult.assoc)
- apply (rule mult_left_mono [OF _ norm_ge_zero])
- apply (simp add: mult.assoc [symmetric])
- apply (metis h lemma_termdiff3 less_eq_real_def r1 xh)
- done
+ by (simp only: norm_mult mult.assoc mult_left_mono [OF _ norm_ge_zero])
qed
qed
@@ -900,12 +892,10 @@
and K: "norm x < norm K"
shows "DERIV (\<lambda>x. \<Sum>n. c n * x^n) x :> (\<Sum>n. diffs c n * x^n)"
proof -
- have K2: "norm ((of_real (norm K) + of_real (norm x)) / 2 :: 'a) < norm K"
- using K
- apply (auto simp: norm_divide field_simps)
- apply (rule le_less_trans [of _ "of_real (norm K) + of_real (norm x)"])
- apply (auto simp: mult_2_right norm_triangle_mono)
- done
+ have "norm K + norm x < norm K + norm K"
+ using K by force
+ then have K2: "norm ((of_real (norm K) + of_real (norm x)) / 2 :: 'a) < norm K"
+ by (auto simp: norm_triangle_lt norm_divide field_simps)
then have [simp]: "norm ((of_real (norm K) + of_real (norm x)) :: 'a) < norm K * 2"
by simp
have "summable (\<lambda>n. c n * (of_real (norm x + norm K) / 2) ^ n)"
@@ -915,11 +905,8 @@
moreover have "\<And>x. norm x < norm K \<Longrightarrow> summable (\<lambda>n. diffs(diffs c) n * x ^ n)"
by (blast intro: sm termdiff_converges powser_inside)
ultimately show ?thesis
- apply (rule termdiffs [where K = "of_real (norm x + norm K) / 2"])
- using K
- apply (auto simp: field_simps)
- apply (simp flip: of_real_add)
- done
+ by (rule termdiffs [where K = "of_real (norm x + norm K) / 2"])
+ (use K in \<open>auto simp: field_simps simp flip: of_real_add\<close>)
qed
lemma termdiffs_strong_converges_everywhere:
@@ -999,11 +986,12 @@
by (blast intro: DERIV_continuous)
then have "((\<lambda>x. \<Sum>n. a n * x ^ n) \<longlongrightarrow> a 0) (at 0)"
by (simp add: continuous_within)
- then show ?thesis
- apply (rule Lim_transform)
+ moreover have "(\<lambda>x. f x - (\<Sum>n. a n * x ^ n)) \<midarrow>0\<rightarrow> 0"
apply (clarsimp simp: LIM_eq)
apply (rule_tac x=s in exI)
using s sm sums_unique by fastforce
+ ultimately show ?thesis
+ by (rule Lim_transform)
qed
lemma powser_limit_0_strong:
@@ -1015,9 +1003,7 @@
have *: "((\<lambda>x. if x = 0 then a 0 else f x) \<longlongrightarrow> a 0) (at 0)"
by (rule powser_limit_0 [OF s]) (auto simp: powser_sums_zero sm)
show ?thesis
- apply (subst LIM_equal [where g = "(\<lambda>x. if x = 0 then a 0 else f x)"])
- apply (simp_all add: *)
- done
+ by (simp add: * LIM_equal [where g = "(\<lambda>x. if x = 0 then a 0 else f x)"])
qed
@@ -1591,10 +1577,10 @@
have "1 + x \<le> (\<Sum>n<2. inverse (fact n) * x^n)"
by (auto simp: numeral_2_eq_2)
also have "\<dots> \<le> (\<Sum>n. inverse (fact n) * x^n)"
- apply (rule sum_le_suminf [OF summable_exp])
- using \<open>0 < x\<close>
- apply (auto simp add: zero_le_mult_iff)
- done
+ proof (rule sum_le_suminf [OF summable_exp])
+ show "\<forall>m\<in>- {..<2}. 0 \<le> inverse (fact m) * x ^ m"
+ using \<open>0 < x\<close> by (auto simp add: zero_le_mult_iff)
+ qed auto
finally show "1 + x \<le> exp x"
by (simp add: exp_def)
qed auto
@@ -2049,9 +2035,7 @@
proof (cases "0 \<le> x \<or> x \<le> -1")
case True
then show ?thesis
- apply (rule disjE)
- apply (simp add: exp_ge_add_one_self_aux)
- using exp_ge_zero order_trans real_add_le_0_iff by blast
+ by (meson exp_ge_add_one_self_aux exp_ge_zero order.trans real_add_le_0_iff)
next
case False
then have ln1: "ln (1 + x) \<le> x"
@@ -2463,11 +2447,12 @@
lemma powr_non_neg[simp]: "\<not>a powr x < 0" for a x::real
using powr_ge_pzero[of a x] by arith
+lemma inverse_powr: "\<And>y::real. 0 \<le> y \<Longrightarrow> inverse y powr a = inverse (y powr a)"
+ by (simp add: exp_minus ln_inverse powr_def)
+
lemma powr_divide: "\<lbrakk>0 \<le> x; 0 \<le> y\<rbrakk> \<Longrightarrow> (x / y) powr a = (x powr a) / (y powr a)"
for a b x :: real
- apply (simp add: divide_inverse positive_imp_inverse_positive powr_mult)
- apply (simp add: powr_def exp_minus [symmetric] exp_add [symmetric] ln_inverse)
- done
+ by (simp add: divide_inverse powr_mult inverse_powr)
lemma powr_add: "x powr (a + b) = (x powr a) * (x powr b)"
for a b x :: "'a::{ln,real_normed_field}"
@@ -3198,17 +3183,20 @@
lemma summable_norm_sin: "summable (\<lambda>n. norm (sin_coeff n *\<^sub>R x^n))"
for x :: "'a::{real_normed_algebra_1,banach}"
- unfolding sin_coeff_def
- apply (rule summable_comparison_test [OF _ summable_norm_exp [where x=x]])
- apply (auto simp: divide_inverse abs_mult power_abs [symmetric] zero_le_mult_iff)
- done
+proof (rule summable_comparison_test [OF _ summable_norm_exp])
+ show "\<exists>N. \<forall>n\<ge>N. norm (norm (sin_coeff n *\<^sub>R x ^ n)) \<le> norm (x ^ n /\<^sub>R fact n)"
+ unfolding sin_coeff_def
+ by (auto simp: divide_inverse abs_mult power_abs [symmetric] zero_le_mult_iff)
+qed
lemma summable_norm_cos: "summable (\<lambda>n. norm (cos_coeff n *\<^sub>R x^n))"
for x :: "'a::{real_normed_algebra_1,banach}"
- unfolding cos_coeff_def
- apply (rule summable_comparison_test [OF _ summable_norm_exp [where x=x]])
- apply (auto simp: divide_inverse abs_mult power_abs [symmetric] zero_le_mult_iff)
- done
+proof (rule summable_comparison_test [OF _ summable_norm_exp])
+ show "\<exists>N. \<forall>n\<ge>N. norm (norm (cos_coeff n *\<^sub>R x ^ n)) \<le> norm (x ^ n /\<^sub>R fact n)"
+ unfolding cos_coeff_def
+ by (auto simp: divide_inverse abs_mult power_abs [symmetric] zero_le_mult_iff)
+qed
+
lemma sin_converges: "(\<lambda>n. sin_coeff n *\<^sub>R x^n) sums sin x"
unfolding sin_def
@@ -3230,8 +3218,7 @@
by (rule sin_converges)
finally have "(\<lambda>n. of_real (sin_coeff n *\<^sub>R x^n)) sums (sin (of_real x))" .
then show ?thesis
- using sums_unique2 sums_of_real [OF sin_converges]
- by blast
+ using sums_unique2 sums_of_real [OF sin_converges] by blast
qed
corollary sin_in_Reals [simp]: "z \<in> \<real> \<Longrightarrow> sin z \<in> \<real>"
@@ -3317,44 +3304,41 @@
lemma continuous_on_cos_real: "continuous_on {a..b} cos" for a::real
using continuous_at_imp_continuous_on isCont_cos by blast
+
+context
+ fixes f :: "'a::t2_space \<Rightarrow> 'b::{real_normed_field,banach}"
+begin
+
lemma isCont_sin' [simp]: "isCont f a \<Longrightarrow> isCont (\<lambda>x. sin (f x)) a"
- for f :: "_ \<Rightarrow> 'a::{real_normed_field,banach}"
by (rule isCont_o2 [OF _ isCont_sin])
-(* FIXME a context for f would be better *)
-
lemma isCont_cos' [simp]: "isCont f a \<Longrightarrow> isCont (\<lambda>x. cos (f x)) a"
- for f :: "_ \<Rightarrow> 'a::{real_normed_field,banach}"
by (rule isCont_o2 [OF _ isCont_cos])
lemma tendsto_sin [tendsto_intros]: "(f \<longlongrightarrow> a) F \<Longrightarrow> ((\<lambda>x. sin (f x)) \<longlongrightarrow> sin a) F"
- for f :: "_ \<Rightarrow> 'a::{real_normed_field,banach}"
by (rule isCont_tendsto_compose [OF isCont_sin])
lemma tendsto_cos [tendsto_intros]: "(f \<longlongrightarrow> a) F \<Longrightarrow> ((\<lambda>x. cos (f x)) \<longlongrightarrow> cos a) F"
- for f :: "_ \<Rightarrow> 'a::{real_normed_field,banach}"
by (rule isCont_tendsto_compose [OF isCont_cos])
lemma continuous_sin [continuous_intros]: "continuous F f \<Longrightarrow> continuous F (\<lambda>x. sin (f x))"
- for f :: "_ \<Rightarrow> 'a::{real_normed_field,banach}"
unfolding continuous_def by (rule tendsto_sin)
lemma continuous_on_sin [continuous_intros]: "continuous_on s f \<Longrightarrow> continuous_on s (\<lambda>x. sin (f x))"
- for f :: "_ \<Rightarrow> 'a::{real_normed_field,banach}"
unfolding continuous_on_def by (auto intro: tendsto_sin)
+lemma continuous_cos [continuous_intros]: "continuous F f \<Longrightarrow> continuous F (\<lambda>x. cos (f x))"
+ unfolding continuous_def by (rule tendsto_cos)
+
+lemma continuous_on_cos [continuous_intros]: "continuous_on s f \<Longrightarrow> continuous_on s (\<lambda>x. cos (f x))"
+ unfolding continuous_on_def by (auto intro: tendsto_cos)
+
+end
+
lemma continuous_within_sin: "continuous (at z within s) sin"
for z :: "'a::{real_normed_field,banach}"
by (simp add: continuous_within tendsto_sin)
-lemma continuous_cos [continuous_intros]: "continuous F f \<Longrightarrow> continuous F (\<lambda>x. cos (f x))"
- for f :: "_ \<Rightarrow> 'a::{real_normed_field,banach}"
- unfolding continuous_def by (rule tendsto_cos)
-
-lemma continuous_on_cos [continuous_intros]: "continuous_on s f \<Longrightarrow> continuous_on s (\<lambda>x. cos (f x))"
- for f :: "_ \<Rightarrow> 'a::{real_normed_field,banach}"
- unfolding continuous_on_def by (auto intro: tendsto_cos)
-
lemma continuous_within_cos: "continuous (at z within s) cos"
for z :: "'a::{real_normed_field,banach}"
by (simp add: continuous_within tendsto_cos)
@@ -3369,10 +3353,10 @@
by (simp add: cos_def cos_coeff_def scaleR_conv_of_real)
lemma DERIV_fun_sin: "DERIV g x :> m \<Longrightarrow> DERIV (\<lambda>x. sin (g x)) x :> cos (g x) * m"
- by (auto intro!: derivative_intros)
+ by (fact derivative_intros)
lemma DERIV_fun_cos: "DERIV g x :> m \<Longrightarrow> DERIV (\<lambda>x. cos(g x)) x :> - sin (g x) * m"
- by (auto intro!: derivative_eq_intros)
+ by (fact derivative_intros)
subsection \<open>Deriving the Addition Formulas\<close>
@@ -3428,15 +3412,16 @@
have "(-1) ^ ((n - Suc 0) div 2) * (-1) ^ ((p - Suc n) div 2) = - ((-1 :: real) ^ (p div 2))"
if np: "odd n" "even p"
proof -
+ have "p > 0"
+ using \<open>n \<le> p\<close> neq0_conv that(1) by blast
+ then have \<section>: "(- 1::real) ^ (p div 2 - Suc 0) = - ((- 1) ^ (p div 2))"
+ using \<open>even p\<close> by (auto simp add: dvd_def power_eq_if)
from \<open>n \<le> p\<close> np have *: "n - Suc 0 + (p - Suc n) = p - Suc (Suc 0)" "Suc (Suc 0) \<le> p"
by arith+
have "(p - Suc (Suc 0)) div 2 = p div 2 - Suc 0"
by simp
- with \<open>n \<le> p\<close> np * show ?thesis
- apply (simp add: power_add [symmetric] div_add [symmetric] del: div_add)
- apply (metis (no_types) One_nat_def Suc_1 le_div_geq minus_minus
- mult.left_neutral mult_minus_left power.simps(2) zero_less_Suc)
- done
+ with \<open>n \<le> p\<close> np \<section> * show ?thesis
+ by (simp add: flip: div_add power_add)
qed
then show ?thesis
using \<open>n\<le>p\<close> by (auto simp: algebra_simps sin_coeff_def binomial_fact)
@@ -3884,22 +3869,31 @@
lemma sin_two_pi [simp]: "sin (2 * pi) = 0"
by (simp add: sin_double)
+context
+ fixes w :: "'a::{real_normed_field,banach}"
+
+begin
+
lemma sin_times_sin: "sin w * sin z = (cos (w - z) - cos (w + z)) / 2"
- for w :: "'a::{real_normed_field,banach}"
by (simp add: cos_diff cos_add)
lemma sin_times_cos: "sin w * cos z = (sin (w + z) + sin (w - z)) / 2"
- for w :: "'a::{real_normed_field,banach}"
by (simp add: sin_diff sin_add)
lemma cos_times_sin: "cos w * sin z = (sin (w + z) - sin (w - z)) / 2"
- for w :: "'a::{real_normed_field,banach}"
by (simp add: sin_diff sin_add)
lemma cos_times_cos: "cos w * cos z = (cos (w - z) + cos (w + z)) / 2"
- for w :: "'a::{real_normed_field,banach}"
by (simp add: cos_diff cos_add)
+lemma cos_double_cos: "cos (2 * w) = 2 * cos w ^ 2 - 1"
+ by (simp add: cos_double sin_squared_eq)
+
+lemma cos_double_sin: "cos (2 * w) = 1 - 2 * sin w ^ 2"
+ by (simp add: cos_double sin_squared_eq)
+
+end
+
lemma sin_plus_sin: "sin w + sin z = 2 * sin ((w + z) / 2) * cos ((w - z) / 2)"
for w :: "'a::{real_normed_field,banach}"
apply (simp add: mult.assoc sin_times_cos)
@@ -3924,14 +3918,6 @@
apply (simp add: field_simps)
done
-lemma cos_double_cos: "cos (2 * z) = 2 * cos z ^ 2 - 1"
- for z :: "'a::{real_normed_field,banach}"
- by (simp add: cos_double sin_squared_eq)
-
-lemma cos_double_sin: "cos (2 * z) = 1 - 2 * sin z ^ 2"
- for z :: "'a::{real_normed_field,banach}"
- by (simp add: cos_double sin_squared_eq)
-
lemma sin_pi_minus [simp]: "sin (pi - x) = sin x"
by (metis sin_minus sin_periodic_pi minus_minus uminus_add_conv_diff)
@@ -4074,7 +4060,7 @@
lemma cos_zero_lemma:
assumes "0 \<le> x" "cos x = 0"
- shows "\<exists>n. odd n \<and> x = of_nat n * (pi/2) \<and> n > 0"
+ shows "\<exists>n. odd n \<and> x = of_nat n * (pi/2)"
proof -
have xle: "x < (1 + real_of_int \<lfloor>x/pi\<rfloor>) * pi"
using floor_correct [of "x/pi"]
@@ -4101,12 +4087,17 @@
by (rule_tac x = "Suc (2 * n)" in exI) (simp add: algebra_simps)
qed
-lemma sin_zero_lemma: "0 \<le> x \<Longrightarrow> sin x = 0 \<Longrightarrow> \<exists>n::nat. even n \<and> x = real n * (pi/2)"
- using cos_zero_lemma [of "x + pi/2"]
- apply (clarsimp simp add: cos_add)
- apply (rule_tac x = "n - 1" in exI)
- apply (simp add: algebra_simps of_nat_diff)
- done
+lemma sin_zero_lemma:
+ assumes "0 \<le> x" "sin x = 0"
+ shows "\<exists>n::nat. even n \<and> x = real n * (pi/2)"
+proof -
+ obtain n where "odd n" and n: "x + pi/2 = of_nat n * (pi/2)" "n > 0"
+ using cos_zero_lemma [of "x + pi/2"] assms by (auto simp add: cos_add)
+ then have "x = real (n - 1) * (pi / 2)"
+ by (simp add: algebra_simps of_nat_diff)
+ then show ?thesis
+ by (simp add: \<open>odd n\<close>)
+qed
lemma cos_zero_iff:
"cos x = 0 \<longleftrightarrow> ((\<exists>n. odd n \<and> x = real n * (pi/2)) \<or> (\<exists>n. odd n \<and> x = - (real n * (pi/2))))"
@@ -4146,7 +4137,7 @@
using that assms by (auto simp: sin_zero_iff)
qed auto
-lemma cos_zero_iff_int: "cos x = 0 \<longleftrightarrow> (\<exists>n. odd n \<and> x = of_int n * (pi/2))"
+lemma cos_zero_iff_int: "cos x = 0 \<longleftrightarrow> (\<exists>i. odd i \<and> x = of_int i * (pi/2))"
proof -
have 1: "\<And>n. odd n \<Longrightarrow> \<exists>i. odd i \<and> real n = real_of_int i"
by (metis even_of_nat of_int_of_nat_eq)
@@ -4159,15 +4150,21 @@
by (force simp: cos_zero_iff intro!: 1 2 3)
qed
-lemma sin_zero_iff_int: "sin x = 0 \<longleftrightarrow> (\<exists>n. even n \<and> x = of_int n * (pi/2))"
+lemma sin_zero_iff_int: "sin x = 0 \<longleftrightarrow> (\<exists>i. even i \<and> x = of_int i * (pi/2))" (is "?lhs = ?rhs")
proof safe
- assume "sin x = 0"
+ assume ?lhs
+ then consider (plus) n where "even n" "x = real n * (pi/2)" | (minus) n where "even n" "x = - (real n * (pi/2))"
+ using sin_zero_iff by auto
then show "\<exists>n. even n \<and> x = of_int n * (pi/2)"
- apply (simp add: sin_zero_iff, safe)
- apply (metis even_of_nat of_int_of_nat_eq)
- apply (rule_tac x="- (int n)" in exI)
- apply simp
- done
+ proof cases
+ case plus
+ then show ?rhs
+ by (metis even_of_nat of_int_of_nat_eq)
+ next
+ case minus
+ then show ?thesis
+ by (rule_tac x="- (int n)" in exI) simp
+ qed
next
fix i :: int
assume "even i"
@@ -4175,12 +4172,16 @@
by (cases i rule: int_cases2, simp_all add: sin_zero_iff)
qed
-lemma sin_zero_iff_int2: "sin x = 0 \<longleftrightarrow> (\<exists>n::int. x = of_int n * pi)"
- apply (simp only: sin_zero_iff_int)
- apply (safe elim!: evenE)
- apply (simp_all add: field_simps)
- using dvd_triv_left apply fastforce
- done
+lemma sin_zero_iff_int2: "sin x = 0 \<longleftrightarrow> (\<exists>i::int. x = of_int i * pi)"
+proof -
+ have "sin x = 0 \<longleftrightarrow> (\<exists>i. even i \<and> x = real_of_int i * (pi / 2))"
+ by (auto simp: sin_zero_iff_int)
+ also have "... = (\<exists>j. x = real_of_int (2*j) * (pi / 2))"
+ using dvd_triv_left by blast
+ also have "... = (\<exists>i::int. x = of_int i * pi)"
+ by auto
+ finally show ?thesis .
+qed
lemma sin_npi_int [simp]: "sin (pi * of_int n) = 0"
by (simp add: sin_zero_iff_int2)
@@ -4252,15 +4253,14 @@
lemma sin_x_le_x:
fixes x :: real
- assumes x: "x \<ge> 0"
+ assumes "x \<ge> 0"
shows "sin x \<le> x"
proof -
let ?f = "\<lambda>x. x - sin x"
- from x have "?f x \<ge> ?f 0"
- apply (rule DERIV_nonneg_imp_nondecreasing)
- apply (intro allI impI exI[of _ "1 - cos x" for x])
- apply (auto intro!: derivative_eq_intros simp: field_simps)
- done
+ have "\<And>u. \<lbrakk>0 \<le> u; u \<le> x\<rbrakk> \<Longrightarrow> \<exists>y. (?f has_real_derivative 1 - cos u) (at u)"
+ by (auto intro!: derivative_eq_intros simp: field_simps)
+ then have "?f x \<ge> ?f 0"
+ by (metis cos_le_one diff_ge_0_iff_ge DERIV_nonneg_imp_nondecreasing [OF assms])
then show "sin x \<le> x" by simp
qed
@@ -4270,11 +4270,10 @@
shows "sin x \<ge> - x"
proof -
let ?f = "\<lambda>x. x + sin x"
- from x have "?f x \<ge> ?f 0"
- apply (rule DERIV_nonneg_imp_nondecreasing)
- apply (intro allI impI exI[of _ "1 + cos x" for x])
- apply (auto intro!: derivative_eq_intros simp: field_simps real_0_le_add_iff)
- done
+ have \<section>: "\<And>u. \<lbrakk>0 \<le> u; u \<le> x\<rbrakk> \<Longrightarrow> \<exists>y. (?f has_real_derivative 1 + cos u) (at u)"
+ by (auto intro!: derivative_eq_intros simp: field_simps)
+ have "?f x \<ge> ?f 0"
+ by (rule DERIV_nonneg_imp_nondecreasing [OF assms]) (use \<section> real_0_le_add_iff in force)
then show "sin x \<ge> -x" by simp
qed
@@ -4409,9 +4408,8 @@
have "cos(3 * x) = cos(2*x + x)"
by simp
also have "\<dots> = 4 * cos x ^ 3 - 3 * cos x"
- apply (simp only: cos_add cos_double sin_double)
- apply (simp add: * field_simps power2_eq_square power3_eq_cube)
- done
+ unfolding cos_add cos_double sin_double
+ by (simp add: * field_simps power2_eq_square power3_eq_cube)
finally show ?thesis .
qed
@@ -4482,12 +4480,18 @@
by (metis Ints_of_int sin_integer_2pi)
lemma sincos_principal_value: "\<exists>y. (- pi < y \<and> y \<le> pi) \<and> (sin y = sin x \<and> cos y = cos x)"
- apply (rule exI [where x="pi - (2 * pi) * frac ((pi - x) / (2 * pi))"])
- apply (auto simp: field_simps frac_lt_1)
- apply (simp_all add: frac_def field_simps)
- apply (simp_all add: add_divide_distrib diff_divide_distrib)
- apply (simp_all add: sin_add cos_add mult.assoc [symmetric])
- done
+proof -
+ define y where "y \<equiv> pi - (2 * pi) * frac ((pi - x) / (2 * pi))"
+ have "-pi < y"" y \<le> pi"
+ by (auto simp: field_simps frac_lt_1 y_def)
+ moreover
+ have "sin y = sin x" "cos y = cos x"
+ unfolding y_def
+ apply (simp_all add: frac_def divide_simps sin_add cos_add)
+ by (metis sin_int_2pin cos_int_2pin diff_zero add.right_neutral mult.commute mult.left_neutral mult_zero_left)+
+ ultimately
+ show ?thesis by metis
+qed
subsection \<open>Tangent\<close>
@@ -5238,10 +5242,11 @@
qed (use assms isCont_arccos in auto)
lemma DERIV_arctan: "DERIV arctan x :> inverse (1 + x\<^sup>2)"
-proof (rule DERIV_inverse_function [where f=tan and a="x - 1" and b="x + 1"])
- show "(tan has_real_derivative 1 + x\<^sup>2) (at (arctan x))"
- apply (rule derivative_eq_intros | simp)+
+proof (rule DERIV_inverse_function)
+ have "inverse ((cos (arctan x))\<^sup>2) = 1 + x\<^sup>2"
by (metis arctan cos_arctan_not_zero power_inverse tan_sec)
+ then show "(tan has_real_derivative 1 + x\<^sup>2) (at (arctan x))"
+ by (auto intro!: derivative_eq_intros)
show "\<And>y. \<lbrakk>x - 1 < y; y < x + 1\<rbrakk> \<Longrightarrow> tan (arctan y) = y"
using tan_arctan by blast
show "1 + x\<^sup>2 \<noteq> 0"
@@ -5999,19 +6004,15 @@
assumes "x \<noteq> 0"
shows "arctan (1 / x) = sgn x * pi/2 - arctan x"
proof (rule arctan_unique)
+ have \<section>: "x > 0 \<Longrightarrow> arctan x < pi"
+ using arctan_bounded [of x] by linarith
show "- (pi/2) < sgn x * pi/2 - arctan x"
- using arctan_bounded [of x] assms
- unfolding sgn_real_def
- apply (auto simp: arctan algebra_simps)
- apply (drule zero_less_arctan_iff [THEN iffD2], arith)
- done
+ using assms by (auto simp: sgn_real_def arctan algebra_simps \<section>)
show "sgn x * pi/2 - arctan x < pi/2"
using arctan_bounded [of "- x"] assms
- unfolding sgn_real_def arctan_minus
- by (auto simp: algebra_simps)
+ by (auto simp: algebra_simps sgn_real_def arctan_minus)
show "tan (sgn x * pi/2 - arctan x) = 1 / x"
- unfolding tan_inverse [of "arctan x", unfolded tan_arctan]
- unfolding sgn_real_def
+ unfolding tan_inverse [of "arctan x", unfolded tan_arctan] sgn_real_def
by (simp add: tan_def cos_arctan sin_arctan sin_diff cos_diff)
qed
@@ -6032,18 +6033,18 @@
by (rule power2_le_imp_le [OF _ zero_le_one])
(simp add: power_divide divide_le_eq not_sum_power2_lt_zero)
-lemmas cos_arccos_lemma1 = cos_arccos_abs [OF cos_x_y_le_one]
-
-lemmas sin_arccos_lemma1 = sin_arccos_abs [OF cos_x_y_le_one]
-
lemma polar_Ex: "\<exists>r::real. \<exists>a. x = r * cos a \<and> y = r * sin a"
proof -
- have polar_ex1: "0 < y \<Longrightarrow> \<exists>r a. x = r * cos a \<and> y = r * sin a" for y
- apply (rule exI [where x = "sqrt (x\<^sup>2 + y\<^sup>2)"])
- apply (rule exI [where x = "arccos (x / sqrt (x\<^sup>2 + y\<^sup>2))"])
- apply (simp add: cos_arccos_lemma1 sin_arccos_lemma1 power_divide
- real_sqrt_mult [symmetric] right_diff_distrib)
- done
+ have polar_ex1: "\<exists>r a. x = r * cos a \<and> y = r * sin a" if "0 < y" for y
+ proof -
+ have "x = sqrt (x\<^sup>2 + y\<^sup>2) * cos (arccos (x / sqrt (x\<^sup>2 + y\<^sup>2)))"
+ by (simp add: cos_arccos_abs [OF cos_x_y_le_one])
+ moreover have "y = sqrt (x\<^sup>2 + y\<^sup>2) * sin (arccos (x / sqrt (x\<^sup>2 + y\<^sup>2)))"
+ using that
+ by (simp add: sin_arccos_abs [OF cos_x_y_le_one] power_divide right_diff_distrib flip: real_sqrt_mult)
+ ultimately show ?thesis
+ by blast
+ qed
show ?thesis
proof (cases "0::real" y rule: linorder_cases)
case less
@@ -6083,24 +6084,24 @@
assumes m: "\<And>i. i > m \<Longrightarrow> a i = 0"
and n: "\<And>j. j > n \<Longrightarrow> b j = 0"
shows "(\<Sum>i\<le>m. (a i) * x ^ i) * (\<Sum>j\<le>n. (b j) * x ^ j) =
- (\<Sum>r\<le>m + n. (\<Sum>k\<le>r. (a k) * (b (r - k))) * x ^ r)"
-proof -
+ (\<Sum>r\<le>m + n. (\<Sum>k\<le>r. (a k) * (b (r - k))) * x ^ r)"
+proof -
+ have "\<And>i j. \<lbrakk>m + n - i < j; a i \<noteq> 0\<rbrakk> \<Longrightarrow> b j = 0"
+ by (meson le_add_diff leI le_less_trans m n)
+ then have \<section>: "(\<Sum>(i,j)\<in>(SIGMA i:{..m+n}. {m+n - i<..m+n}). a i * x ^ i * (b j * x ^ j)) = 0"
+ by (clarsimp simp add: sum_Un Sigma_interval_disjoint intro!: sum.neutral)
have "(\<Sum>i\<le>m. (a i) * x ^ i) * (\<Sum>j\<le>n. (b j) * x ^ j) = (\<Sum>i\<le>m. \<Sum>j\<le>n. (a i * x ^ i) * (b j * x ^ j))"
by (rule sum_product)
also have "\<dots> = (\<Sum>i\<le>m + n. \<Sum>j\<le>n + m. a i * x ^ i * (b j * x ^ j))"
using assms by (auto simp: sum_up_index_split)
also have "\<dots> = (\<Sum>r\<le>m + n. \<Sum>j\<le>m + n - r. a r * x ^ r * (b j * x ^ j))"
- apply (simp add: add_ac sum.Sigma product_atMost_eq_Un)
- apply (clarsimp simp add: sum_Un Sigma_interval_disjoint intro!: sum.neutral)
- apply (metis add_diff_assoc2 add.commute add_lessD1 leD m n nat_le_linear neqE)
- done
+ by (simp add: add_ac sum.Sigma product_atMost_eq_Un sum_Un Sigma_interval_disjoint \<section>)
also have "\<dots> = (\<Sum>(i,j)\<in>{(i,j). i+j \<le> m+n}. (a i * x ^ i) * (b j * x ^ j))"
by (auto simp: pairs_le_eq_Sigma sum.Sigma)
+ also have "... = (\<Sum>k\<le>m + n. \<Sum>i\<le>k. a i * x ^ i * (b (k - i) * x ^ (k - i)))"
+ by (rule sum.triangle_reindex_eq)
also have "\<dots> = (\<Sum>r\<le>m + n. (\<Sum>k\<le>r. (a k) * (b (r - k))) * x ^ r)"
- apply (subst sum.triangle_reindex_eq)
- apply (auto simp: algebra_simps sum_distrib_left intro!: sum.cong)
- apply (metis le_add_diff_inverse power_add)
- done
+ by (auto simp: algebra_simps sum_distrib_left simp flip: power_add intro!: sum.cong)
finally show ?thesis .
qed
@@ -6109,7 +6110,7 @@
assumes m: "\<And>i. i > m \<Longrightarrow> a i = 0"
and n: "\<And>j. j > n \<Longrightarrow> b j = 0"
shows "(\<Sum>i\<le>m. (a i) * x ^ i) * (\<Sum>j\<le>n. (b j) * x ^ j) =
- (\<Sum>r\<le>m + n. (\<Sum>k\<le>r. (a k) * (b (r - k))) * x ^ r)"
+ (\<Sum>r\<le>m + n. (\<Sum>k\<le>r. (a k) * (b (r - k))) * x ^ r)"
using polynomial_product [of m a n b x] assms
by (simp only: of_nat_mult [symmetric] of_nat_power [symmetric]
of_nat_eq_iff Int.int_sum [symmetric])
@@ -6148,10 +6149,10 @@
have "(\<Sum>i=Suc j..n. a i * y^(i - j - 1)) = (\<Sum>k<n-j. a(j+k+1) * y^k)"
if "j < n" for j :: nat
proof -
- have h: "bij_betw (\<lambda>i. i - (j + 1)) {Suc j..n} (lessThan (n-j))"
- apply (auto simp: bij_betw_def inj_on_def)
- apply (rule_tac x="x + Suc j" in image_eqI, auto)
- done
+ have "\<And>k. k < n - j \<Longrightarrow> k \<in> (\<lambda>i. i - Suc j) ` {Suc j..n}"
+ by (rule_tac x="k + Suc j" in image_eqI, auto)
+ then have h: "bij_betw (\<lambda>i. i - (j + 1)) {Suc j..n} (lessThan (n-j))"
+ by (auto simp: bij_betw_def inj_on_def)
then show ?thesis
by (auto simp: sum.reindex_bij_betw [OF h, symmetric] intro: sum.cong_simp)
qed
--- a/src/HOL/Transitive_Closure.thy Thu Apr 02 11:45:03 2020 +0200
+++ b/src/HOL/Transitive_Closure.thy Thu Apr 02 13:04:24 2020 +0200
@@ -87,9 +87,7 @@
lemma r_into_rtrancl [intro]: "\<And>p. p \<in> r \<Longrightarrow> p \<in> r\<^sup>*"
\<comment> \<open>\<open>rtrancl\<close> of \<open>r\<close> contains \<open>r\<close>\<close>
- apply (simp only: split_tupled_all)
- apply (erule rtrancl_refl [THEN rtrancl_into_rtrancl])
- done
+ by (simp add: split_tupled_all rtrancl_refl [THEN rtrancl_into_rtrancl])
lemma r_into_rtranclp [intro]: "r x y \<Longrightarrow> r\<^sup>*\<^sup>* x y"
\<comment> \<open>\<open>rtrancl\<close> of \<open>r\<close> contains \<open>r\<close>\<close>
@@ -97,10 +95,11 @@
lemma rtranclp_mono: "r \<le> s \<Longrightarrow> r\<^sup>*\<^sup>* \<le> s\<^sup>*\<^sup>*"
\<comment> \<open>monotonicity of \<open>rtrancl\<close>\<close>
- apply (rule predicate2I)
- apply (erule rtranclp.induct)
- apply (rule_tac [2] rtranclp.rtrancl_into_rtrancl, blast+)
- done
+proof (rule predicate2I)
+ show "s\<^sup>*\<^sup>* x y" if "r \<le> s" "r\<^sup>*\<^sup>* x y" for x y
+ using \<open>r\<^sup>*\<^sup>* x y\<close> \<open>r \<le> s\<close>
+ by (induction rule: rtranclp.induct) (blast intro: rtranclp.rtrancl_into_rtrancl)+
+qed
lemma mono_rtranclp[mono]: "(\<And>a b. x a b \<longrightarrow> y a b) \<Longrightarrow> x\<^sup>*\<^sup>* a b \<longrightarrow> y\<^sup>*\<^sup>* a b"
using rtranclp_mono[of x y] by auto
@@ -164,9 +163,7 @@
qed
lemma rtrancl_Int_subset: "Id \<subseteq> s \<Longrightarrow> (r\<^sup>* \<inter> s) O r \<subseteq> s \<Longrightarrow> r\<^sup>* \<subseteq> s"
- apply clarify
- apply (erule rtrancl_induct, auto)
- done
+ by (fastforce elim: rtrancl_induct)
lemma converse_rtranclp_into_rtranclp: "r a b \<Longrightarrow> r\<^sup>*\<^sup>* b c \<Longrightarrow> r\<^sup>*\<^sup>* a c"
by (rule rtranclp_trans) iprover+
@@ -176,27 +173,23 @@
text \<open>\<^medskip> More \<^term>\<open>r\<^sup>*\<close> equations and inclusions.\<close>
lemma rtranclp_idemp [simp]: "(r\<^sup>*\<^sup>*)\<^sup>*\<^sup>* = r\<^sup>*\<^sup>*"
- apply (auto intro!: order_antisym)
- apply (erule rtranclp_induct)
- apply (rule rtranclp.rtrancl_refl)
- apply (blast intro: rtranclp_trans)
- done
+proof -
+ have "r\<^sup>*\<^sup>*\<^sup>*\<^sup>* x y \<Longrightarrow> r\<^sup>*\<^sup>* x y" for x y
+ by (induction rule: rtranclp_induct) (blast intro: rtranclp_trans)+
+ then show ?thesis
+ by (auto intro!: order_antisym)
+qed
lemmas rtrancl_idemp [simp] = rtranclp_idemp [to_set]
lemma rtrancl_idemp_self_comp [simp]: "R\<^sup>* O R\<^sup>* = R\<^sup>*"
- apply (rule set_eqI)
- apply (simp only: split_tupled_all)
- apply (blast intro: rtrancl_trans)
- done
+ by (force intro: rtrancl_trans)
lemma rtrancl_subset_rtrancl: "r \<subseteq> s\<^sup>* \<Longrightarrow> r\<^sup>* \<subseteq> s\<^sup>*"
-by (drule rtrancl_mono, simp)
+ by (drule rtrancl_mono, simp)
lemma rtranclp_subset: "R \<le> S \<Longrightarrow> S \<le> R\<^sup>*\<^sup>* \<Longrightarrow> S\<^sup>*\<^sup>* = R\<^sup>*\<^sup>*"
- apply (drule rtranclp_mono)
- apply (drule rtranclp_mono, simp)
- done
+ by (fastforce dest: rtranclp_mono)
lemmas rtrancl_subset = rtranclp_subset [to_set]
@@ -319,11 +312,15 @@
subsection \<open>Transitive closure\<close>
-lemma trancl_mono: "\<And>p. p \<in> r\<^sup>+ \<Longrightarrow> r \<subseteq> s \<Longrightarrow> p \<in> s\<^sup>+"
- apply (simp add: split_tupled_all)
- apply (erule trancl.induct)
- apply (iprover dest: subsetD)+
- done
+lemma trancl_mono:
+ assumes "p \<in> r\<^sup>+" "r \<subseteq> s"
+ shows "p \<in> s\<^sup>+"
+proof -
+ have "\<lbrakk>(a, b) \<in> r\<^sup>+; r \<subseteq> s\<rbrakk> \<Longrightarrow> (a, b) \<in> s\<^sup>+" for a b
+ by (induction rule: trancl.induct) (iprover dest: subsetD)+
+ with assms show ?thesis
+ by (cases p) force
+qed
lemma r_into_trancl': "\<And>p. p \<in> r \<Longrightarrow> p \<in> r\<^sup>+"
by (simp only: split_tupled_all) (erule r_into_trancl)
@@ -342,12 +339,19 @@
lemmas rtrancl_into_trancl1 = rtranclp_into_tranclp1 [to_set]
-lemma rtranclp_into_tranclp2: "r a b \<Longrightarrow> r\<^sup>*\<^sup>* b c \<Longrightarrow> r\<^sup>+\<^sup>+ a c"
+lemma rtranclp_into_tranclp2:
+ assumes "r a b" "r\<^sup>*\<^sup>* b c" shows "r\<^sup>+\<^sup>+ a c"
\<comment> \<open>intro rule from \<open>r\<close> and \<open>rtrancl\<close>\<close>
- apply (erule rtranclp.cases, iprover)
- apply (rule rtranclp_trans [THEN rtranclp_into_tranclp1])
- apply (simp | rule r_into_rtranclp)+
- done
+ using \<open>r\<^sup>*\<^sup>* b c\<close>
+proof (cases rule: rtranclp.cases)
+ case rtrancl_refl
+ with assms show ?thesis
+ by iprover
+next
+ case rtrancl_into_rtrancl
+ with assms show ?thesis
+ by (auto intro: rtranclp_trans [THEN rtranclp_into_tranclp1])
+qed
lemmas rtrancl_into_trancl2 = rtranclp_into_tranclp2 [to_set]
@@ -384,9 +388,7 @@
using assms by cases simp_all
lemma trancl_Int_subset: "r \<subseteq> s \<Longrightarrow> (r\<^sup>+ \<inter> s) O r \<subseteq> s \<Longrightarrow> r\<^sup>+ \<subseteq> s"
- apply clarify
- apply (erule trancl_induct, auto)
- done
+ by (fastforce simp add: elim: trancl_induct)
lemma trancl_unfold: "r\<^sup>+ = r \<union> r\<^sup>+ O r"
by (auto intro: trancl_into_trancl elim: tranclE)
@@ -418,10 +420,7 @@
using assms(2,1) by induct iprover+
lemma trancl_id [simp]: "trans r \<Longrightarrow> r\<^sup>+ = r"
- apply auto
- apply (erule trancl_induct, assumption)
- apply (unfold trans_def, blast)
- done
+ unfolding trans_def by (fastforce simp add: elim: trancl_induct)
lemma rtranclp_tranclp_tranclp:
assumes "r\<^sup>*\<^sup>* x y"
@@ -435,19 +434,30 @@
lemmas trancl_into_trancl2 = tranclp_into_tranclp2 [to_set]
-lemma tranclp_converseI: "(r\<^sup>+\<^sup>+)\<inverse>\<inverse> x y \<Longrightarrow> (r\<inverse>\<inverse>)\<^sup>+\<^sup>+ x y"
- apply (drule conversepD)
- apply (erule tranclp_induct)
- apply (iprover intro: conversepI tranclp_trans)+
- done
+lemma tranclp_converseI:
+ assumes "(r\<^sup>+\<^sup>+)\<inverse>\<inverse> x y" shows "(r\<inverse>\<inverse>)\<^sup>+\<^sup>+ x y"
+ using conversepD [OF assms]
+proof (induction rule: tranclp_induct)
+ case (base y)
+ then show ?case
+ by (iprover intro: conversepI)
+next
+ case (step y z)
+ then show ?case
+ by (iprover intro: conversepI tranclp_trans)
+qed
lemmas trancl_converseI = tranclp_converseI [to_set]
-lemma tranclp_converseD: "(r\<inverse>\<inverse>)\<^sup>+\<^sup>+ x y \<Longrightarrow> (r\<^sup>+\<^sup>+)\<inverse>\<inverse> x y"
- apply (rule conversepI)
- apply (erule tranclp_induct)
- apply (iprover dest: conversepD intro: tranclp_trans)+
- done
+lemma tranclp_converseD:
+ assumes "(r\<inverse>\<inverse>)\<^sup>+\<^sup>+ x y" shows "(r\<^sup>+\<^sup>+)\<inverse>\<inverse> x y"
+proof -
+ have "r\<^sup>+\<^sup>+ y x"
+ using assms
+ by (induction rule: tranclp_induct) (iprover dest: conversepD intro: tranclp_trans)+
+ then show ?thesis
+ by (rule conversepI)
+qed
lemmas trancl_converseD = tranclp_converseD [to_set]
@@ -463,17 +473,21 @@
assumes major: "r\<^sup>+\<^sup>+ a b"
and cases: "\<And>y. r y b \<Longrightarrow> P y" "\<And>y z. r y z \<Longrightarrow> r\<^sup>+\<^sup>+ z b \<Longrightarrow> P z \<Longrightarrow> P y"
shows "P a"
- apply (rule tranclp_induct [OF tranclp_converseI, OF conversepI, OF major])
- apply (blast intro: cases)
- apply (blast intro: assms dest!: tranclp_converseD)
- done
+proof -
+ have "r\<inverse>\<inverse>\<^sup>+\<^sup>+ b a"
+ by (intro tranclp_converseI conversepI major)
+ then show ?thesis
+ by (induction rule: tranclp_induct) (blast intro: cases dest: tranclp_converseD)+
+qed
lemmas converse_trancl_induct = converse_tranclp_induct [to_set]
lemma tranclpD: "R\<^sup>+\<^sup>+ x y \<Longrightarrow> \<exists>z. R x z \<and> R\<^sup>*\<^sup>* z y"
- apply (erule converse_tranclp_induct, auto)
- apply (blast intro: rtranclp_trans)
- done
+proof (induction rule: converse_tranclp_induct)
+ case (step u v)
+ then show ?case
+ by (blast intro: rtranclp_trans)
+qed auto
lemmas tranclD = tranclpD [to_set]
@@ -492,7 +506,7 @@
by iprover
next
case rtrancl_into_rtrancl
- from this have "tranclp r y z"
+ then have "tranclp r y z"
by (iprover intro: rtranclp_into_tranclp1)
with \<open>r x y\<close> step show P
by iprover
@@ -513,17 +527,15 @@
lemma trancl_subset_Sigma_aux: "(a, b) \<in> r\<^sup>* \<Longrightarrow> r \<subseteq> A \<times> A \<Longrightarrow> a = b \<or> a \<in> A"
by (induct rule: rtrancl_induct) auto
-lemma trancl_subset_Sigma: "r \<subseteq> A \<times> A \<Longrightarrow> r\<^sup>+ \<subseteq> A \<times> A"
- apply (clarsimp simp:)
- apply (erule tranclE)
- apply (blast dest!: trancl_into_rtrancl trancl_subset_Sigma_aux)+
- done
+lemma trancl_subset_Sigma:
+ assumes "r \<subseteq> A \<times> A" shows "r\<^sup>+ \<subseteq> A \<times> A"
+proof (rule trancl_Int_subset [OF assms])
+ show "(r\<^sup>+ \<inter> A \<times> A) O r \<subseteq> A \<times> A"
+ using assms by auto
+qed
lemma reflclp_tranclp [simp]: "(r\<^sup>+\<^sup>+)\<^sup>=\<^sup>= = r\<^sup>*\<^sup>*"
- apply (safe intro!: order_antisym)
- apply (erule tranclp_into_rtranclp)
- apply (blast elim: rtranclp.cases dest: rtranclp_into_tranclp1)
- done
+ by (fast elim: rtranclp.cases tranclp_into_rtranclp dest: rtranclp_into_tranclp1)
lemmas reflcl_trancl [simp] = reflclp_tranclp [to_set]
@@ -629,19 +641,14 @@
qed
lemma trancl_subset_Field2: "r\<^sup>+ \<subseteq> Field r \<times> Field r"
- apply clarify
- apply (erule trancl_induct)
- apply (auto simp: Field_def)
- done
+ by (rule trancl_Int_subset) (auto simp: Field_def)
lemma finite_trancl[simp]: "finite (r\<^sup>+) = finite r"
proof
show "finite (r\<^sup>+) \<Longrightarrow> finite r"
by (blast intro: r_into_trancl' finite_subset)
show "finite r \<Longrightarrow> finite (r\<^sup>+)"
- apply (rule trancl_subset_Field2 [THEN finite_subset])
- apply (auto simp: finite_Field)
- done
+ by (auto simp: finite_Field trancl_subset_Field2 [THEN finite_subset])
qed
lemma finite_rtrancl_Image[simp]: assumes "finite R" "finite A" shows "finite (R\<^sup>* `` A)"
@@ -665,9 +672,7 @@
next
case (step y z)
with xz \<open>single_valued r\<close> show ?case
- apply (auto simp: elim: converse_rtranclE dest: single_valuedD)
- apply (blast intro: rtrancl_trans)
- done
+ by (auto elim: converse_rtranclE dest: single_valuedD intro: rtrancl_trans)
qed
lemma r_r_into_trancl: "(a, b) \<in> R \<Longrightarrow> (b, c) \<in> R \<Longrightarrow> (a, c) \<in> R\<^sup>+"
@@ -676,12 +681,14 @@
lemma trancl_into_trancl: "(a, b) \<in> r\<^sup>+ \<Longrightarrow> (b, c) \<in> r \<Longrightarrow> (a, c) \<in> r\<^sup>+"
by (induct rule: trancl_induct) (fast intro: r_r_into_trancl trancl_trans)+
-lemma tranclp_rtranclp_tranclp: "r\<^sup>+\<^sup>+ a b \<Longrightarrow> r\<^sup>*\<^sup>* b c \<Longrightarrow> r\<^sup>+\<^sup>+ a c"
- apply (drule tranclpD)
- apply (elim exE conjE)
- apply (drule rtranclp_trans, assumption)
- apply (drule (2) rtranclp_into_tranclp2)
- done
+lemma tranclp_rtranclp_tranclp:
+ assumes "r\<^sup>+\<^sup>+ a b" "r\<^sup>*\<^sup>* b c" shows "r\<^sup>+\<^sup>+ a c"
+proof -
+ obtain z where "r a z" "r\<^sup>*\<^sup>* z c"
+ using assms by (iprover dest: tranclpD rtranclp_trans)
+ then show ?thesis
+ by (blast dest: rtranclp_into_tranclp2)
+qed
lemma rtranclp_conversep: "r\<inverse>\<inverse>\<^sup>*\<^sup>* = r\<^sup>*\<^sup>*\<inverse>\<inverse>"
by(auto simp add: fun_eq_iff intro: rtranclp_converseI rtranclp_converseD)
@@ -717,13 +724,13 @@
lemma symclpI [simp, intro?]:
shows symclpI1: "r x y \<Longrightarrow> symclp r x y"
- and symclpI2: "r y x \<Longrightarrow> symclp r x y"
-by(simp_all add: symclp_def)
+ and symclpI2: "r y x \<Longrightarrow> symclp r x y"
+ by(simp_all add: symclp_def)
lemma symclpE [consumes 1, cases pred]:
assumes "symclp r x y"
obtains (base) "r x y" | (sym) "r y x"
-using assms by(auto simp add: symclp_def)
+ using assms by(auto simp add: symclp_def)
lemma symclp_pointfree: "symclp r = sup r r\<inverse>\<inverse>"
by(auto simp add: symclp_def fun_eq_iff)
@@ -962,12 +969,10 @@
lemma trancl_power: "p \<in> R\<^sup>+ \<longleftrightarrow> (\<exists>n > 0. p \<in> R ^^ n)"
proof -
- have "((a, b) \<in> R\<^sup>+) = (\<exists>n>0. (a, b) \<in> R ^^ n)" for a b
+ have "(a, b) \<in> R\<^sup>+ \<longleftrightarrow> (\<exists>n>0. (a, b) \<in> R ^^ n)" for a b
proof safe
show "(a, b) \<in> R\<^sup>+ \<Longrightarrow> \<exists>n>0. (a, b) \<in> R ^^ n"
- apply (drule tranclD2)
- apply (fastforce simp: rtrancl_is_UN_relpow relcomp_unfold)
- done
+ by (fastforce simp: rtrancl_is_UN_relpow relcomp_unfold dest: tranclD2)
show "(a, b) \<in> R\<^sup>+" if "n > 0" "(a, b) \<in> R ^^ n" for n
proof (cases n)
case (Suc m)
@@ -1117,17 +1122,23 @@
fixes R :: "('a \<times> 'a) set"
assumes "finite R"
shows "R^^k \<subseteq> (\<Union>n\<in>{n. n \<le> card R}. R^^n)"
- apply (cases k, force)
- apply (use relpow_finite_bounded1[OF assms, of k] in auto)
- done
+proof (cases k)
+ case (Suc k')
+ then show ?thesis
+ using relpow_finite_bounded1[OF assms, of k] by auto
+qed force
lemma rtrancl_finite_eq_relpow: "finite R \<Longrightarrow> R\<^sup>* = (\<Union>n\<in>{n. n \<le> card R}. R^^n)"
by (fastforce simp: rtrancl_power dest: relpow_finite_bounded)
-lemma trancl_finite_eq_relpow: "finite R \<Longrightarrow> R\<^sup>+ = (\<Union>n\<in>{n. 0 < n \<and> n \<le> card R}. R^^n)"
- apply (auto simp: trancl_power)
- apply (auto dest: relpow_finite_bounded1)
- done
+lemma trancl_finite_eq_relpow:
+ assumes "finite R" shows "R\<^sup>+ = (\<Union>n\<in>{n. 0 < n \<and> n \<le> card R}. R^^n)"
+proof -
+ have "\<And>a b n. \<lbrakk>0 < n; (a, b) \<in> R ^^ n\<rbrakk> \<Longrightarrow> \<exists>x>0. x \<le> card R \<and> (a, b) \<in> R ^^ x"
+ using assms by (auto dest: relpow_finite_bounded1)
+ then show ?thesis
+ by (auto simp: trancl_power)
+qed
lemma finite_relcomp[simp,intro]:
assumes "finite R" and "finite S"
@@ -1189,7 +1200,7 @@
show ?thesis
proof (cases "i = 1")
case True
- from this \<open>(a, b) \<in> R ^^ i\<close> show ?thesis
+ with \<open>(a, b) \<in> R ^^ i\<close> show ?thesis
by (auto simp: ntrancl_def)
next
case False
--- a/src/Pure/Admin/afp.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/afp.scala Thu Apr 02 13:04:24 2020 +0200
@@ -166,7 +166,7 @@
/* dependency graph */
private def sessions_deps(entry: AFP.Entry): List[String] =
- entry.sessions.flatMap(sessions_structure.imports_graph.imm_preds(_)).distinct.sorted
+ entry.sessions.flatMap(sessions_structure.imports_graph.imm_preds).distinct.sorted
lazy val entries_graph: Graph[String, Unit] =
{
@@ -214,7 +214,7 @@
case 1 | 2 =>
val graph = sessions_structure.build_graph.restrict(sessions.toSet)
val force_part1 =
- graph.all_preds(graph.all_succs(AFP.force_partition1.filter(graph.defined(_)))).toSet
+ graph.all_preds(graph.all_succs(AFP.force_partition1.filter(graph.defined))).toSet
val (part1, part2) = graph.keys.partition(a => force_part1(a) || graph.is_isolated(a))
if (n == 1) part1 else part2
case _ => error("Bad AFP partition: " + n + " (should be 0, 1, 2)")
--- a/src/Pure/Admin/build_fonts.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/build_fonts.scala Thu Apr 02 13:04:24 2020 +0200
@@ -284,7 +284,7 @@
val domain =
(for ((name, index) <- targets if index == 0)
yield Fontforge.font_domain(target_dir + hinted_path(false) + name))
- .flatten.toSet.toList.sorted
+ .flatten.distinct.sorted
Fontforge.execute(
Fontforge.commands(
--- a/src/Pure/Admin/build_history.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/build_history.scala Thu Apr 02 13:04:24 2020 +0200
@@ -18,7 +18,6 @@
val engine = "build_history"
val log_prefix = engine + "_"
- val META_INFO_MARKER = "\fmeta_info = "
/* augment settings */
@@ -282,8 +281,7 @@
val theory_timings =
try {
store.read_theory_timings(db, session_name).map(ps =>
- Build_Log.Log_File.print_props(Build_Log.THEORY_TIMING_MARKER,
- (Build_Log.SESSION_NAME, session_name) :: ps))
+ Protocol.Theory_Timing_Marker((Build_Log.SESSION_NAME, session_name) :: ps))
}
catch { case ERROR(_) => Nil }
@@ -357,10 +355,10 @@
build_out_progress.echo("Writing log file " + log_path.ext("xz") + " ...")
File.write_xz(log_path.ext("xz"),
terminate_lines(
- Build_Log.Log_File.print_props(META_INFO_MARKER, meta_info) :: build_result.out_lines :::
+ Protocol.Meta_Info_Marker(meta_info) :: build_result.out_lines :::
session_build_info :::
- ml_statistics.map(Build_Log.Log_File.print_props(Build_Log.ML_STATISTICS_MARKER, _)) :::
- session_errors.map(Build_Log.Log_File.print_props(Build_Log.ERROR_MESSAGE_MARKER, _)) :::
+ ml_statistics.map(Protocol.ML_Statistics_Marker.apply) :::
+ session_errors.map(Protocol.Error_Message_Marker.apply) :::
heap_sizes), XZ.options(6))
@@ -395,7 +393,7 @@
def main(args: Array[String])
{
- Command_Line.tool0 {
+ Command_Line.tool {
var afp_rev: Option[String] = None
var multicore_base = false
var components_base: Path = Components.default_components_base
@@ -454,7 +452,7 @@
"B" -> (_ => multicore_base = true),
"C:" -> (arg => components_base = Path.explode(arg)),
"H:" -> (arg => heap = Some(Value.Int.parse(arg))),
- "M:" -> (arg => multicore_list = space_explode(',', arg).map(Multicore.parse(_))),
+ "M:" -> (arg => multicore_list = space_explode(',', arg).map(Multicore.parse)),
"N:" -> (arg => isabelle_identifier = arg),
"P:" -> (arg => afp_partition = Value.Int.parse(arg)),
"U:" -> (arg => max_heap = Some(Value.Int.parse(arg))),
--- a/src/Pure/Admin/build_jdk.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/build_jdk.scala Thu Apr 02 13:04:24 2020 +0200
@@ -106,7 +106,7 @@
}
val dir_entry =
- File.read_dir(tmp_dir).filterNot(suppress_name(_)) match {
+ File.read_dir(tmp_dir).filterNot(suppress_name) match {
case List(s) => s
case _ => error("Archive contains multiple directories")
}
@@ -144,7 +144,7 @@
val extracted = archives.map(extract_archive(dir, _))
val version =
- extracted.map(_._1).toSet.toList match {
+ extracted.map(_._1).distinct match {
case List(version) => version
case Nil => error("No archives")
case versions =>
@@ -232,7 +232,7 @@
val more_args = getopts(args)
if (more_args.isEmpty) getopts.usage()
- val archives = more_args.map(Path.explode(_))
+ val archives = more_args.map(Path.explode)
val progress = new Console_Progress()
build_jdk(archives = archives, progress = progress, target_dir = target_dir)
--- a/src/Pure/Admin/build_log.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/build_log.scala Thu Apr 02 13:04:24 2020 +0200
@@ -103,17 +103,17 @@
def plain_name(name: String): String =
{
- List(".log", ".log.gz", ".log.xz", ".gz", ".xz").find(name.endsWith(_)) match {
+ List(".log", ".log.gz", ".log.xz", ".gz", ".xz").find(name.endsWith) match {
case Some(s) => Library.try_unsuffix(s, name).get
case None => name
}
}
def apply(name: String, lines: List[String]): Log_File =
- new Log_File(plain_name(name), lines)
+ new Log_File(plain_name(name), lines.map(Library.trim_line))
def apply(name: String, text: String): Log_File =
- Log_File(name, Library.trim_split_lines(text))
+ new Log_File(plain_name(name), Library.trim_split_lines(text))
def apply(file: JFile): Log_File =
{
@@ -138,8 +138,8 @@
{
val name = file.getName
- prefixes.exists(name.startsWith(_)) &&
- suffixes.exists(name.endsWith(_)) &&
+ prefixes.exists(name.startsWith) &&
+ suffixes.exists(name.endsWith) &&
name != "isatest.log" &&
name != "afp-test.log" &&
name != "main.log"
@@ -179,20 +179,14 @@
def tune(s: String): String =
Word.implode(
Word.explode(s) match {
- case a :: "M\uFFFDr" :: bs => tune_weekday(a) :: "Mär" :: bs.map(tune_timezone(_))
- case a :: bs => tune_weekday(a) :: bs.map(tune_timezone(_))
+ case a :: "M\uFFFDr" :: bs => tune_weekday(a) :: "Mär" :: bs.map(tune_timezone)
+ case a :: bs => tune_weekday(a) :: bs.map(tune_timezone)
case Nil => Nil
}
)
Date.Format.make(fmts, tune)
}
-
-
- /* inlined content */
-
- def print_props(marker: String, props: Properties.T): String =
- marker + YXML.string_of_body(XML.Encode.properties(Properties.encode_lines(props)))
}
class Log_File private(val name: String, val lines: List[String])
@@ -217,13 +211,13 @@
}
- /* inlined content */
+ /* inlined text */
- def find[A](f: String => Option[A]): Option[A] =
- lines.iterator.map(f).find(_.isDefined).map(_.get)
+ def filter(Marker: Protocol_Message.Marker): List[String] =
+ for (Marker(text) <- lines) yield text
- def find_line(marker: String): Option[String] =
- find(Library.try_unprefix(marker, _))
+ def find(Marker: Protocol_Message.Marker): Option[String] =
+ lines.collectFirst({ case Marker(text) => text })
def find_match(regexes: List[Regex]): Option[String] =
regexes match {
@@ -249,25 +243,17 @@
/* properties (YXML) */
- val xml_cache = XML.make_cache()
+ val xml_cache: XML.Cache = XML.make_cache()
def parse_props(text: String): Properties.T =
- try {
- xml_cache.props(Properties.decode_lines(XML.Decode.properties(YXML.parse_body(text))))
- }
+ try { xml_cache.props(XML.Decode.properties(YXML.parse_body(text))) }
catch { case _: XML.Error => log_file.err("malformed properties") }
- def filter_lines(marker: String): List[String] =
- for (line <- lines; s <- Library.try_unprefix(marker, line)) yield s
-
- def filter_props(marker: String): List[Properties.T] =
- for (s <- filter_lines(marker) if YXML.detect(s)) yield parse_props(s)
+ def filter_props(marker: Protocol_Message.Marker): List[Properties.T] =
+ for (text <- filter(marker) if YXML.detect(text)) yield parse_props(text)
- def find_props(marker: String): Option[Properties.T] =
- find_line(marker) match {
- case Some(text) if YXML.detect(text) => Some(parse_props(text))
- case _ => None
- }
+ def find_props(marker: Protocol_Message.Marker): Option[Properties.T] =
+ for (text <- find(marker) if YXML.detect(text)) yield parse_props(text)
/* parse various formats */
@@ -304,7 +290,7 @@
Properties.get(settings, c.name)
def get_date(c: SQL.Column): Option[Date] =
- get(c).map(Log_File.Date_Format.parse(_))
+ get(c).map(Log_File.Date_Format.parse)
}
object Identify
@@ -401,9 +387,8 @@
}
log_file.lines match {
- case line :: _ if line.startsWith(Build_History.META_INFO_MARKER) =>
- Meta_Info(log_file.find_props(Build_History.META_INFO_MARKER).get,
- log_file.get_all_settings)
+ case line :: _ if Protocol.Meta_Info_Marker.test_yxml(line) =>
+ Meta_Info(log_file.find_props(Protocol.Meta_Info_Marker).get, log_file.get_all_settings)
case Identify.Start(log_file.Strict_Date(start)) :: _ =>
parse(Identify.engine(log_file), "", start, Identify.No_End,
@@ -446,9 +431,6 @@
/** build info: toplevel output of isabelle build or Admin/build_history **/
- val THEORY_TIMING_MARKER = "\ftheory_timing = "
- val ML_STATISTICS_MARKER = "\fML_statistics = "
- val ERROR_MESSAGE_MARKER = "\ferror_message = "
val SESSION_NAME = "session_name"
object Session_Status extends Enumeration
@@ -514,9 +496,8 @@
object Theory_Timing
{
def unapply(line: String): Option[(String, (String, Timing))] =
- {
- val line1 = line.replace('~', '-')
- Library.try_unprefix(THEORY_TIMING_MARKER, line1).map(log_file.parse_props(_)) match {
+ Protocol.Theory_Timing_Marker.unapply(line.replace('~', '-')).map(log_file.parse_props)
+ match {
case Some((SESSION_NAME, name) :: props) =>
(props, props) match {
case (Markup.Name(thy), Markup.Timing_Properties(t)) => Some((name, thy -> t))
@@ -524,7 +505,6 @@
}
case _ => None
}
- }
}
var chapter = Map.empty[String, String]
@@ -586,24 +566,24 @@
case Heap(name, Value.Long(size)) =>
heap_sizes += (name -> size)
- case _ if line.startsWith(THEORY_TIMING_MARKER) && YXML.detect(line) =>
+ case _ if Protocol.Theory_Timing_Marker.test_yxml(line) =>
line match {
case Theory_Timing(name, theory_timing) =>
theory_timings += (name -> (theory_timings.getOrElse(name, Map.empty) + theory_timing))
case _ => log_file.err("malformed theory_timing " + quote(line))
}
- case _ if parse_ml_statistics && line.startsWith(ML_STATISTICS_MARKER) && YXML.detect(line) =>
- Library.try_unprefix(ML_STATISTICS_MARKER, line).map(log_file.parse_props(_)) match {
+ case _ if parse_ml_statistics && Protocol.ML_Statistics_Marker.test_yxml(line) =>
+ Protocol.ML_Statistics_Marker.unapply(line).map(log_file.parse_props) match {
case Some((SESSION_NAME, name) :: props) =>
ml_statistics += (name -> (props :: ml_statistics.getOrElse(name, Nil)))
case _ => log_file.err("malformed ML_statistics " + quote(line))
}
- case _ if line.startsWith(ERROR_MESSAGE_MARKER) && YXML.detect(line) =>
- Library.try_unprefix(ERROR_MESSAGE_MARKER, line).map(log_file.parse_props(_)) match {
+ case _ if Protocol.Error_Message_Marker.test_yxml(line) =>
+ Protocol.Error_Message_Marker.unapply(line).map(log_file.parse_props) match {
case Some(List((SESSION_NAME, name), (Markup.CONTENT, msg))) =>
- errors += (name -> (Library.decode_lines(msg) :: errors.getOrElse(name, Nil)))
+ errors += (name -> (msg :: errors.getOrElse(name, Nil)))
case _ => log_file.err("malformed error message " + quote(line))
}
@@ -663,12 +643,16 @@
task_statistics: Boolean): Session_Info =
{
Session_Info(
- session_timing = log_file.find_props("\fTiming = ") getOrElse Nil,
- command_timings = if (command_timings) log_file.filter_props("\fcommand_timing = ") else Nil,
- theory_timings = if (theory_timings) log_file.filter_props(THEORY_TIMING_MARKER) else Nil,
- ml_statistics = if (ml_statistics) log_file.filter_props(ML_STATISTICS_MARKER) else Nil,
- task_statistics = if (task_statistics) log_file.filter_props("\ftask_statistics = ") else Nil,
- errors = log_file.filter_lines(ERROR_MESSAGE_MARKER).map(Library.decode_lines(_)))
+ session_timing = log_file.find_props(Protocol.Timing_Marker) getOrElse Nil,
+ command_timings =
+ if (command_timings) log_file.filter_props(Protocol.Command_Timing_Marker) else Nil,
+ theory_timings =
+ if (theory_timings) log_file.filter_props(Protocol.Theory_Timing_Marker) else Nil,
+ ml_statistics =
+ if (ml_statistics) log_file.filter_props(Protocol.ML_Statistics_Marker) else Nil,
+ task_statistics =
+ if (task_statistics) log_file.filter_props(Protocol.Task_Statistics_Marker) else Nil,
+ errors = log_file.filter(Protocol.Error_Message_Marker))
}
def compress_errors(errors: List[String], cache: XZ.Cache = XZ.cache()): Option[Bytes] =
@@ -681,7 +665,7 @@
def uncompress_errors(bytes: Bytes, cache: XZ.Cache = XZ.cache()): List[String] =
if (bytes.isEmpty) Nil
else {
- XML.Decode.list(YXML.string_of_body(_))(YXML.parse_body(bytes.uncompress(cache = cache).text))
+ XML.Decode.list(YXML.string_of_body)(YXML.parse_body(bytes.uncompress(cache = cache).text))
}
@@ -754,7 +738,7 @@
/* earliest pull date for repository version (PostgreSQL queries) */
- def pull_date(afp: Boolean = false) =
+ def pull_date(afp: Boolean = false): SQL.Column =
if (afp) SQL.Column.date("afp_pull_date")
else SQL.Column.date("pull_date")
@@ -1110,7 +1094,7 @@
files.filter(file => status.exists(_.required(file))).
grouped(options.int("build_log_transaction_size") max 1))
{
- val log_files = Par_List.map[JFile, Log_File](Log_File.apply _, file_group)
+ val log_files = Par_List.map[JFile, Log_File](Log_File.apply, file_group)
db.transaction { log_files.foreach(log_file => status.foreach(_.update(log_file))) }
}
}
@@ -1182,7 +1166,7 @@
res.timing(Data.ml_timing_elapsed, Data.ml_timing_cpu, Data.ml_timing_gc),
sources = res.get_string(Data.sources),
heap_size = res.get_long(Data.heap_size),
- status = res.get_string(Data.status).map(Session_Status.withName(_)),
+ status = res.get_string(Data.status).map(Session_Status.withName),
errors = uncompress_errors(res.bytes(Data.errors), cache = xz_cache),
ml_statistics =
if (ml_statistics) {
--- a/src/Pure/Admin/build_polyml.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/build_polyml.scala Thu Apr 02 13:04:24 2020 +0200
@@ -256,7 +256,7 @@
val isabelle_tool1 =
Isabelle_Tool("build_polyml", "build Poly/ML from sources", args =>
{
- Command_Line.tool0 {
+ Command_Line.tool {
var msys_root: Option[Path] = None
var arch_64 = false
var sha1_root: Option[Path] = None
@@ -295,7 +295,7 @@
val isabelle_tool2 =
Isabelle_Tool("build_polyml_component", "make skeleton for Poly/ML component", args =>
{
- Command_Line.tool0 {
+ Command_Line.tool {
var sha1_root: Option[Path] = None
val getopts = Getopts("""
--- a/src/Pure/Admin/build_release.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/build_release.scala Thu Apr 02 13:04:24 2020 +0200
@@ -163,7 +163,7 @@
terminate_lines("#bundled components" ::
(for {
(catalog, bundled) <- catalogs.iterator
- val path = Components.admin(dir) + Path.basic(catalog)
+ path = Components.admin(dir) + Path.basic(catalog)
if path.is_file
line <- split_lines(File.read(path))
if line.nonEmpty && !line.startsWith("#") && !line.startsWith("jedit_build")
@@ -196,7 +196,7 @@
if (Components.check_dir(Components.contrib(dir, name))) Some(contrib_name(name))
else None
case _ => if (Bundled.detect(line)) None else Some(line)
- }) ::: more_names.map(contrib_name(_)))
+ }) ::: more_names.map(contrib_name))
}
def make_contrib(dir: Path)
@@ -428,7 +428,6 @@
val bundle_infos = platform_families.map(release.bundle_info)
for (bundle_info <- bundle_infos) {
- val bundle_archive = release.dist_dir + bundle_info.path
val isabelle_name = release.dist_name
val platform = bundle_info.platform
@@ -776,7 +775,7 @@
def main(args: Array[String])
{
- Command_Line.tool0 {
+ Command_Line.tool {
var afp_rev = ""
var components_base: Path = Components.default_components_base
var official_release = false
--- a/src/Pure/Admin/components.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/components.scala Thu Apr 02 13:04:24 2020 +0200
@@ -38,7 +38,7 @@
/* component collections */
- val default_components_base = Path.explode("$ISABELLE_COMPONENTS_BASE")
+ val default_components_base: Path = Path.explode("$ISABELLE_COMPONENTS_BASE")
def admin(dir: Path): Path = dir + Path.explode("Admin/components")
@@ -125,7 +125,7 @@
case _ => error("Bad components.sha1 entry: " + quote(line))
})
- def write_components_sha1(entries: List[SHA1_Digest]) =
+ def write_components_sha1(entries: List[SHA1_Digest]): Unit =
File.write(components_sha1, entries.sortBy(_.file_name).mkString("", "\n", "\n"))
--- a/src/Pure/Admin/isabelle_cronjob.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/isabelle_cronjob.scala Thu Apr 02 13:04:24 2020 +0200
@@ -18,14 +18,14 @@
/* global resources: owned by main cronjob */
val backup = "lxbroy10:cronjob"
- val main_dir = Path.explode("~/cronjob")
- val main_state_file = main_dir + Path.explode("run/main.state")
- val current_log = main_dir + Path.explode("run/main.log") // owned by log service
- val cumulative_log = main_dir + Path.explode("log/main.log") // owned by log service
+ val main_dir: Path = Path.explode("~/cronjob")
+ val main_state_file: Path = main_dir + Path.explode("run/main.state")
+ val current_log: Path = main_dir + Path.explode("run/main.log") // owned by log service
+ val cumulative_log: Path = main_dir + Path.explode("log/main.log") // owned by log service
val isabelle_repos_source = "https://isabelle.sketis.net/repos/isabelle"
- val isabelle_repos = main_dir + Path.explode("isabelle")
- val afp_repos = main_dir + Path.explode("AFP")
+ val isabelle_repos: Path = main_dir + Path.explode("isabelle")
+ val afp_repos: Path = main_dir + Path.explode("AFP")
val build_log_dirs =
List(Path.explode("~/log"), Path.explode("~/afp/log"), Path.explode("~/cronjob/log"))
@@ -42,7 +42,7 @@
def get_rev(): String = Mercurial.repository(isabelle_repos).id()
def get_afp_rev(): String = Mercurial.repository(afp_repos).id()
- val init =
+ val init: Logger_Task =
Logger_Task("init", logger =>
{
Isabelle_Devel.make_index()
@@ -61,7 +61,7 @@
Files.createSymbolicLink(Isabelle_Devel.cronjob_log.file.toPath, current_log.file.toPath)
})
- val exit =
+ val exit: Logger_Task =
Logger_Task("exit", logger =>
{
Isabelle_System.bash(
@@ -72,7 +72,7 @@
/* build release */
- val build_release =
+ val build_release: Logger_Task =
Logger_Task("build_release", logger =>
{
Isabelle_Devel.release_snapshot(logger.options, rev = get_rev(), afp_rev = get_afp_rev())
@@ -81,7 +81,7 @@
/* integrity test of build_history vs. build_history_base */
- val build_history_base =
+ val build_history_base: Logger_Task =
Logger_Task("build_history_base", logger =>
{
using(logger.ssh_context.open_session("lxbroy10"))(ssh =>
@@ -147,9 +147,9 @@
sealed case class Remote_Build(
description: String,
host: String,
+ actual_host: String = "",
user: String = "",
port: Int = 0,
- ssh_host: String = "",
proxy_host: String = "",
proxy_user: String = "",
proxy_port: Int = 0,
@@ -166,7 +166,7 @@
active: Boolean = true)
{
def ssh_session(context: SSH.Context): SSH.Session =
- context.open_session(host = proper_string(ssh_host) getOrElse host, user = user, port = port,
+ context.open_session(host = host, user = user, port = port, actual_host = actual_host,
proxy_host = proxy_host, proxy_user = proxy_user, proxy_port = proxy_port,
permissive = proxy_host.nonEmpty)
@@ -216,7 +216,6 @@
List(
Remote_Build("AFP bulky", "lrzcloud1", self_update = true,
proxy_host = "lxbroy10", proxy_user = "i21isatest",
- ssh_host = "10.155.208.96",
options = "-m64 -M6 -U30000 -s10 -t AFP",
args = "-g large -g slow",
afp = true,
@@ -291,18 +290,18 @@
detect = Build_Log.Prop.build_tags + " = " + SQL.string("skip_proofs"),
history_base = "2c0f24e927dd")),
List(
- Remote_Build("macOS 10.12 Sierra", "macbroy30", options = "-m32 -M2", args = "-a",
+ Remote_Build("Mac OS X 10.12 Sierra", "macbroy30", options = "-m32 -M2", args = "-a",
detect = Build_Log.Prop.build_start + " > date '2017-03-03'")),
List(Remote_Build("Mac OS X 10.10 Yosemite", "macbroy31", options = "-m32 -M2", args = "-a")),
- List(Remote_Build("macOS 10.13 High Sierra", "lapbroy68",
+ List(Remote_Build("Mac OS X 10.13 High Sierra", "lapbroy68",
options = "-m32 -M1,2,4 -e ISABELLE_GHC_SETUP=true",
self_update = true, args = "-a -d '~~/src/Benchmarks'")),
- List(Remote_Build("macOS 10.14 Mojave", "lapnipkow3",
+ List(Remote_Build("Mac OS X 10.14 Mojave", "lapnipkow3",
options = "-m32 -M1,2 -e ISABELLE_GHC_SETUP=true",
self_update = true, args = "-a -d '~~/src/Benchmarks'")),
- List(Remote_Build("macOS 10.15 Catalina", "laramac01", user = "makarius",
+ List(Remote_Build("Mac OS X 10.15 Catalina", "laramac01", user = "makarius",
proxy_host = "laraserver", proxy_user = "makarius",
- self_update = true, options = "-m32 -M1,2,4 -e ISABELLE_GHC_SETUP=true",
+ self_update = true, options = "-m32 -M4 -e ISABELLE_GHC_SETUP=true",
args = "-a -d '~~/src/Benchmarks'")),
List(
Remote_Build("Windows", "vmnipkow9", historic = true, history = 90, self_update = true,
@@ -339,9 +338,8 @@
val remote_builds2: List[List[Remote_Build]] =
List(
List(
- Remote_Build("AFP2", "lrzcloud2", self_update = true,
+ Remote_Build("AFP2", "lrzcloud2", actual_host = "10.195.2.10", self_update = true,
proxy_host = "lxbroy10", proxy_user = "i21isatest",
- ssh_host = "10.195.2.10",
options = "-m32 -M1x8 -t AFP" +
" -e ISABELLE_GHC=ghc" +
" -e ISABELLE_MLTON=mlton" +
@@ -350,9 +348,8 @@
args = "-a -X large -X slow",
afp = true,
detect = Build_Log.Prop.build_tags + " = " + SQL.string("AFP")),
- Remote_Build("AFP bulky2", "lrzcloud2", self_update = true,
+ Remote_Build("AFP bulky2", "lrzcloud2", actual_host = "10.195.2.10", self_update = true,
proxy_host = "lxbroy10", proxy_user = "i21isatest",
- ssh_host = "10.195.2.10",
options = "-m64 -M8 -U30000 -s10 -t AFP",
args = "-g large -g slow",
afp = true,
@@ -417,7 +414,7 @@
def shutdown() { thread.shutdown() }
- val hostname = Isabelle_System.hostname()
+ val hostname: String = Isabelle_System.hostname()
def log(date: Date, task_name: String, msg: String): Unit =
if (task_name != "")
@@ -582,7 +579,7 @@
def main(args: Array[String])
{
- Command_Line.tool0 {
+ Command_Line.tool {
var force = false
var verbose = false
var exclude_task = Set.empty[String]
--- a/src/Pure/Admin/isabelle_devel.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/isabelle_devel.scala Thu Apr 02 13:04:24 2020 +0200
@@ -14,8 +14,8 @@
val BUILD_STATUS = "build_status"
val CRONJOB_LOG = "cronjob-main.log"
- val root = Path.explode("~/html-data/devel")
- val cronjob_log = root + Path.basic(CRONJOB_LOG)
+ val root: Path = Path.explode("~/html-data/devel")
+ val cronjob_log: Path = root + Path.basic(CRONJOB_LOG)
/* index */
--- a/src/Pure/Admin/jenkins.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/jenkins.scala Thu Apr 02 13:04:24 2020 +0200
@@ -43,7 +43,7 @@
options: Options, job_names: List[String], dir: Path, progress: Progress = No_Progress)
{
val store = Sessions.store(options)
- val infos = job_names.flatMap(build_job_infos(_))
+ val infos = job_names.flatMap(build_job_infos)
Par_List.map((info: Job_Info) => info.download_log(store, dir, progress), infos)
}
@@ -106,13 +106,13 @@
Isabelle_System.mkdirs(log_dir)
val ml_statistics =
- session_logs.map(_._1).toSet.toList.sorted.flatMap(session_name =>
+ session_logs.map(_._1).distinct.sorted.flatMap(session_name =>
read_ml_statistics(store, session_name).
map(props => (Build_Log.SESSION_NAME -> session_name) :: props))
File.write_xz(log_path,
terminate_lines(Url.read(main_log) ::
- ml_statistics.map(Build_Log.Log_File.print_props(Build_Log.ML_STATISTICS_MARKER, _))),
+ ml_statistics.map(Protocol.ML_Statistics_Marker.apply)),
XZ.options(6))
}
}
--- a/src/Pure/Admin/other_isabelle.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Admin/other_isabelle.scala Thu Apr 02 13:04:24 2020 +0200
@@ -62,7 +62,7 @@
val etc_preferences: Path = etc + Path.explode("preferences")
def copy_fonts(target_dir: Path): Unit =
- Isabelle_Fonts.make_entries(getenv = getenv(_), hidden = true).
+ Isabelle_Fonts.make_entries(getenv = getenv, hidden = true).
foreach(entry => File.copy(entry.path, target_dir))
--- a/src/Pure/General/csv.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/csv.scala Thu Apr 02 13:04:24 2020 +0200
@@ -20,7 +20,7 @@
sealed case class Record(fields: Any*)
{
- override def toString: String = fields.iterator.map(print_field(_)).mkString(",")
+ override def toString: String = fields.iterator.map(print_field).mkString(",")
}
sealed case class File(name: String, header: List[String], records: List[Record])
--- a/src/Pure/General/date.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/date.scala Thu Apr 02 13:04:24 2020 +0200
@@ -33,7 +33,7 @@
}
def apply(pats: String*): Format =
- make(pats.toList.map(Date.Formatter.pattern(_)))
+ make(pats.toList.map(Date.Formatter.pattern))
val default: Format = Format("dd-MMM-uuuu HH:mm:ss xx")
val date: Format = Format("dd-MMM-uuuu")
@@ -56,7 +56,7 @@
def variants(pats: List[String], locs: List[Locale] = Nil): List[DateTimeFormatter] =
pats.flatMap(pat => {
val fmt = pattern(pat)
- if (locs.isEmpty) List(fmt) else locs.map(fmt.withLocale(_))
+ if (locs.isEmpty) List(fmt) else locs.map(fmt.withLocale)
})
@tailrec def try_variants(fmts: List[DateTimeFormatter], str: String,
--- a/src/Pure/General/exn.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/exn.scala Thu Apr 02 13:04:24 2020 +0200
@@ -70,7 +70,7 @@
def release_first[A](results: List[Result[A]]): List[A] =
results.find({ case Exn(exn) => !is_interrupt(exn) case _ => false }) match {
case Some(Exn(exn)) => throw exn
- case _ => results.map(release(_))
+ case _ => results.map(release)
}
--- a/src/Pure/General/file.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/file.scala Thu Apr 02 13:04:24 2020 +0200
@@ -213,7 +213,7 @@
val line =
try { reader.readLine}
catch { case _: IOException => null }
- if (line == null) None else Some(line)
+ Option(line)
}
def read_lines(reader: BufferedReader, progress: String => Unit): List[String] =
--- a/src/Pure/General/graph.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/graph.scala Thu Apr 02 13:04:24 2020 +0200
@@ -123,9 +123,9 @@
(Map.empty[Key, Long] /: xs)(reach(0))
}
def node_height(count: Key => Long): Map[Key, Long] =
- reachable_length(count, imm_preds(_), maximals)
+ reachable_length(count, imm_preds, maximals)
def node_depth(count: Key => Long): Map[Key, Long] =
- reachable_length(count, imm_succs(_), minimals)
+ reachable_length(count, imm_succs, minimals)
/*reachable nodes with size limit*/
def reachable_limit(
@@ -138,7 +138,7 @@
{
val (n, rs) = res
if (rs.contains(x)) res
- else ((n + count(x), rs + x) /: next(x))(reach _)
+ else ((n + count(x), rs + x) /: next(x))(reach)
}
@tailrec def reachs(size: Long, rs: Keys, rest: List[Key]): Keys =
--- a/src/Pure/General/json.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/json.scala Thu Apr 02 13:04:24 2020 +0200
@@ -9,6 +9,7 @@
package isabelle
+import scala.util.matching.Regex
import scala.util.parsing.combinator.Parsers
import scala.util.parsing.combinator.lexical.Scanners
import scala.util.parsing.input.CharArrayReader.EofCh
@@ -61,14 +62,14 @@
def errorToken(msg: String): Token = Token(Kind.ERROR, msg)
val white_space: String = " \t\n\r"
- override val whiteSpace = ("[" + white_space + "]+").r
+ override val whiteSpace: Regex = ("[" + white_space + "]+").r
def whitespace: Parser[Any] = many(character(white_space.contains(_)))
- val letter: Parser[String] = one(character(Symbol.is_ascii_letter(_)))
- val letters1: Parser[String] = many1(character(Symbol.is_ascii_letter(_)))
+ val letter: Parser[String] = one(character(Symbol.is_ascii_letter))
+ val letters1: Parser[String] = many1(character(Symbol.is_ascii_letter))
- def digits: Parser[String] = many(character(Symbol.is_ascii_digit(_)))
- def digits1: Parser[String] = many1(character(Symbol.is_ascii_digit(_)))
+ def digits: Parser[String] = many(character(Symbol.is_ascii_digit))
+ def digits1: Parser[String] = many1(character(Symbol.is_ascii_digit))
/* keyword */
@@ -114,8 +115,8 @@
one(character("eE".contains(_))) ~ maybe(character("-+".contains(_))) ~ digits1 ^^
{ case a ~ b ~ c => a + b + c }
- def zero = one(character(c => c == '0'))
- def nonzero = one(character(c => c != '0' && Symbol.is_ascii_digit(c)))
+ def zero: Parser[String] = one(character(c => c == '0'))
+ def nonzero: Parser[String] = one(character(c => c != '0' && Symbol.is_ascii_digit(c)))
def positive: Parser[String] = nonzero ~ digits ^^ { case a ~ b => a + b }
@@ -326,7 +327,7 @@
object Seconds
{
def unapply(json: T): Option[Time] =
- Double.unapply(json).map(Time.seconds(_))
+ Double.unapply(json).map(Time.seconds)
}
}
@@ -402,9 +403,9 @@
: Option[List[A]] = value_default(obj, name, Value.List.unapply(_, unapply), default)
def strings(obj: T, name: String): Option[List[String]] =
- list(obj, name, JSON.Value.String.unapply _)
+ list(obj, name, JSON.Value.String.unapply)
def strings_default(obj: T, name: String, default: => List[String] = Nil): Option[List[String]] =
- list_default(obj, name, JSON.Value.String.unapply _, default)
+ list_default(obj, name, JSON.Value.String.unapply, default)
def seconds(obj: T, name: String): Option[Time] =
value(obj, name, Value.Seconds.unapply)
--- a/src/Pure/General/linear_set.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/linear_set.scala Thu Apr 02 13:04:24 2020 +0200
@@ -17,7 +17,7 @@
object Linear_Set extends SetFactory[Linear_Set]
{
private val empty_val: Linear_Set[Nothing] = new Linear_Set[Nothing](None, None, Map(), Map())
- override def empty[A] = empty_val.asInstanceOf[Linear_Set[A]]
+ override def empty[A]: Linear_Set[A] = empty_val.asInstanceOf[Linear_Set[A]]
implicit def canBuildFrom[A]: CanBuildFrom[Coll, A, Linear_Set[A]] = setCanBuildFrom[A]
def newBuilder[A]: Builder[A, Linear_Set[A]] = new SetBuilder[A, Linear_Set[A]](empty[A])
--- a/src/Pure/General/mercurial.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/mercurial.scala Thu Apr 02 13:04:24 2020 +0200
@@ -44,7 +44,7 @@
def find_repository(start: Path, ssh: SSH.System = SSH.Local): Option[Repository] =
{
- def find(root: Path): Option[Repository] =
+ @tailrec def find(root: Path): Option[Repository] =
if (is_repository(root, ssh)) Some(repository(root, ssh = ssh))
else if (root.is_root) None
else find(root + Path.parent)
@@ -82,7 +82,7 @@
val root: Path = ssh.expand_path(root_path)
def root_url: String = ssh.hg_url + root.implode
- override def toString: String = ssh.prefix + root.implode
+ override def toString: String = ssh.hg_url + root.implode
def command(name: String, args: String = "", options: String = "",
repository: Boolean = true): Process_Result =
@@ -95,7 +95,7 @@
}
def add(files: List[Path]): Unit =
- hg.command("add", files.map(ssh.bash_path(_)).mkString(" "))
+ hg.command("add", files.map(ssh.bash_path).mkString(" "))
def archive(target: String, rev: String = "", options: String = ""): Unit =
hg.command("archive", opt_rev(rev) + " " + Bash.string(target), options).check
--- a/src/Pure/General/multi_map.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/multi_map.scala Thu Apr 02 13:04:24 2020 +0200
@@ -14,7 +14,7 @@
object Multi_Map extends ImmutableMapFactory[Multi_Map]
{
private val empty_val: Multi_Map[Any, Nothing] = new Multi_Map[Any, Nothing](Map.empty)
- override def empty[A, B] = empty_val.asInstanceOf[Multi_Map[A, B]]
+ override def empty[A, B]: Multi_Map[A, B] = empty_val.asInstanceOf[Multi_Map[A, B]]
implicit def canBuildFrom[A, B]: CanBuildFrom[Coll, (A, B), Multi_Map[A, B]] =
new MapCanBuildFrom[A, B]
@@ -63,7 +63,7 @@
override def stringPrefix = "Multi_Map"
- override def empty = Multi_Map.empty
+ override def empty: Multi_Map[A, Nothing] = Multi_Map.empty
override def isEmpty: Boolean = rep.isEmpty
override def keySet: Set[A] = rep.keySet
--- a/src/Pure/General/output.ML Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/output.ML Thu Apr 02 13:04:24 2020 +0200
@@ -59,7 +59,6 @@
val report_fn: (output list -> unit) Unsynchronized.ref
val result_fn: (Properties.T -> output list -> unit) Unsynchronized.ref
val protocol_message_fn: Output_Primitives.protocol_message_fn Unsynchronized.ref
- val init_channels: unit -> unit
end;
structure Private_Output: PRIVATE_OUTPUT =
--- a/src/Pure/General/output.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/output.scala Thu Apr 02 13:04:24 2020 +0200
@@ -15,11 +15,11 @@
def writeln_text(msg: String): String = clean_yxml(msg)
- def warning_text(msg: String): String =
- Library.prefix_lines("### ", clean_yxml(msg))
+ def warning_prefix(s: String): String = Library.prefix_lines("### ", s)
+ def warning_text(msg: String): String = warning_prefix(clean_yxml(msg))
- def error_message_text(msg: String): String =
- Library.prefix_lines("*** ", clean_yxml(msg))
+ def error_prefix(s: String): String = Library.prefix_lines("*** ", s)
+ def error_message_text(msg: String): String = error_prefix(clean_yxml(msg))
def writeln(msg: String, stdout: Boolean = false, include_empty: Boolean = false)
{
--- a/src/Pure/General/output_primitives.ML Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/output_primitives.ML Thu Apr 02 13:04:24 2020 +0200
@@ -49,6 +49,7 @@
| Text of string;
type body = tree list;
+
end;
--- a/src/Pure/General/path.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/path.scala Thu Apr 02 13:04:24 2020 +0200
@@ -73,7 +73,7 @@
val current: Path = new Path(Nil)
val root: Path = new Path(List(Root("")))
def named_root(s: String): Path = new Path(List(root_elem(s)))
- def make(elems: List[String]): Path = new Path(elems.reverse.map(basic_elem(_)))
+ def make(elems: List[String]): Path = new Path(elems.reverse.map(basic_elem))
def basic(s: String): Path = new Path(List(basic_elem(s)))
def variable(s: String): Path = new Path(List(variable_elem(s)))
val parent: Path = new Path(List(Parent))
--- a/src/Pure/General/pretty.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/pretty.scala Thu Apr 02 13:04:24 2020 +0200
@@ -6,6 +6,8 @@
package isabelle
+import scala.annotation.tailrec
+
object Pretty
{
@@ -69,7 +71,7 @@
{
val indent1 = force_nat(indent)
- def body_length(prts: List[Tree], len: Double): Double =
+ @tailrec def body_length(prts: List[Tree], len: Double): Double =
{
val (line, rest) =
Library.take_prefix[Tree]({ case Break(true, _, _) => false case _ => true }, prts)
@@ -104,7 +106,7 @@
private def force_break(tree: Tree): Tree =
tree match { case Break(false, wd, ind) => Break(true, wd, ind) case _ => tree }
- private def force_all(trees: List[Tree]): List[Tree] = trees.map(force_break(_))
+ private def force_all(trees: List[Tree]): List[Tree] = trees.map(force_break)
private def force_next(trees: List[Tree]): List[Tree] =
trees match {
@@ -113,8 +115,8 @@
case t :: ts => t :: force_next(ts)
}
- val default_margin = 76.0
- val default_breakgain = default_margin / 20
+ val default_margin: Double = 76.0
+ val default_breakgain: Double = default_margin / 20
def formatted(input: XML.Body,
margin: Double = default_margin,
--- a/src/Pure/General/properties.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/properties.scala Thu Apr 02 13:04:24 2020 +0200
@@ -67,7 +67,7 @@
XML.Decode.list(XML.Decode.properties)(YXML.parse_body(bs.uncompress(cache = cache).text))
xml_cache match {
case None => ps
- case Some(cache) => ps.map(cache.props(_))
+ case Some(cache) => ps.map(cache.props)
}
}
}
--- a/src/Pure/General/scan.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/scan.scala Thu Apr 02 13:04:24 2020 +0200
@@ -10,10 +10,10 @@
import scala.annotation.tailrec
import scala.collection.{IndexedSeq, Traversable, TraversableOnce}
import scala.collection.immutable.PagedSeq
+import scala.util.matching.Regex
import scala.util.parsing.input.{OffsetPosition, Position => InputPosition,
Reader, CharSequenceReader}
import scala.util.parsing.combinator.RegexParsers
-
import java.io.{File => JFile, BufferedInputStream, FileInputStream, InputStream}
import java.net.URL
@@ -39,7 +39,7 @@
trait Parsers extends RegexParsers
{
- override val whiteSpace = "".r
+ override val whiteSpace: Regex = "".r
/* optional termination */
@@ -237,7 +237,7 @@
{
require(depth >= 0)
- val comment_text =
+ val comment_text: Parser[List[String]] =
rep1(many1(sym => sym != "*" && sym != "(") | """\*(?!\))|\((?!\*)""".r)
def apply(in: Input) =
@@ -399,7 +399,7 @@
else this ++ other.raw_iterator
def -- (remove: Traversable[String]): Lexicon =
- if (remove.exists(contains(_)))
+ if (remove.exists(contains))
Lexicon.empty ++ iterator.filterNot(a => remove.exists(b => a == b))
else this
--- a/src/Pure/General/sql.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/sql.scala Thu Apr 02 13:04:24 2020 +0200
@@ -37,7 +37,7 @@
}
def string(s: String): Source =
- s.iterator.map(escape_char(_)).mkString("'", "", "'")
+ s.iterator.map(escape_char).mkString("'", "", "'")
def ident(s: String): Source =
Long_Name.implode(Long_Name.explode(s).map(a => quote(a.replace("\"", "\"\""))))
@@ -288,7 +288,7 @@
}
def date(column: Column): Date = stmt.db.date(res, column)
- def timing(c1: Column, c2: Column, c3: Column) =
+ def timing(c1: Column, c2: Column, c3: Column): Timing =
Timing(Time.ms(long(c1)), Time.ms(long(c2)), Time.ms(long(c3)))
def get[A](column: Column, f: Column => A): Option[A] =
@@ -296,13 +296,13 @@
val x = f(column)
if (rep.wasNull) None else Some(x)
}
- def get_bool(column: Column): Option[Boolean] = get(column, bool _)
- def get_int(column: Column): Option[Int] = get(column, int _)
- def get_long(column: Column): Option[Long] = get(column, long _)
- def get_double(column: Column): Option[Double] = get(column, double _)
- def get_string(column: Column): Option[String] = get(column, string _)
- def get_bytes(column: Column): Option[Bytes] = get(column, bytes _)
- def get_date(column: Column): Option[Date] = get(column, date _)
+ def get_bool(column: Column): Option[Boolean] = get(column, bool)
+ def get_int(column: Column): Option[Int] = get(column, int)
+ def get_long(column: Column): Option[Long] = get(column, long)
+ def get_double(column: Column): Option[Double] = get(column, double)
+ def get_string(column: Column): Option[String] = get(column, string)
+ def get_bytes(column: Column): Option[Bytes] = get(column, bytes)
+ def get_date(column: Column): Option[Date] = get(column, date)
}
--- a/src/Pure/General/ssh.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/ssh.scala Thu Apr 02 13:04:24 2020 +0200
@@ -10,6 +10,7 @@
import java.io.{InputStream, OutputStream, ByteArrayOutputStream}
import scala.collection.mutable
+import scala.util.matching.Regex
import com.jcraft.jsch.{JSch, Logger => JSch_Logger, Session => JSch_Session, SftpException,
OpenSSHConfig, UserInfo, Channel => JSch_Channel, ChannelExec, ChannelSftp, SftpATTRS}
@@ -21,7 +22,7 @@
object Target
{
- val User_Host = "^([^@]+)@(.+)$".r
+ val User_Host: Regex = "^([^@]+)@(.+)$".r
def parse(s: String): (String, String) =
s match {
@@ -76,17 +77,19 @@
jsch.setKnownHosts(File.platform_path(known_hosts))
val identity_files =
- space_explode(':', options.string("ssh_identity_files")).map(Path.explode(_))
+ space_explode(':', options.string("ssh_identity_files")).map(Path.explode)
for (identity_file <- identity_files if identity_file.is_file)
jsch.addIdentity(File.platform_path(identity_file))
new Context(options, jsch)
}
- def open_session(options: Options, host: String, user: String = "", port: Int = 0,
+ def open_session(options: Options,
+ host: String, user: String = "", port: Int = 0, actual_host: String = "",
proxy_host: String = "", proxy_user: String = "", proxy_port: Int = 0,
permissive: Boolean = false): Session =
- init_context(options).open_session(host = host, user = user, port = port,
+ init_context(options).open_session(
+ host = host, user = user, port = port, actual_host = actual_host,
proxy_host = proxy_host, proxy_user = proxy_user, proxy_port = proxy_port,
permissive = permissive)
@@ -120,16 +123,18 @@
proper_string(nominal_user) getOrElse user)
}
- def open_session(host: String, user: String = "", port: Int = 0,
+ def open_session(
+ host: String, user: String = "", port: Int = 0, actual_host: String = "",
proxy_host: String = "", proxy_user: String = "", proxy_port: Int = 0,
permissive: Boolean = false): Session =
{
- if (proxy_host == "") connect_session(host = host, user = user, port = port)
+ val connect_host = proper_string(actual_host) getOrElse host
+ if (proxy_host == "") connect_session(host = connect_host, user = user, port = port)
else {
val proxy = connect_session(host = proxy_host, port = proxy_port, user = proxy_user)
val fw =
- try { proxy.port_forwarding(remote_host = host, remote_port = make_port(port)) }
+ try { proxy.port_forwarding(remote_host = connect_host, remote_port = make_port(port)) }
catch { case exn: Throwable => proxy.close; throw exn }
try {
@@ -317,9 +322,6 @@
override def hg_url: String =
"ssh://" + user_prefix(nominal_user) + nominal_host + "/"
- override def prefix: String =
- user_prefix(session.getUserName) + host + port_suffix(session.getPort) + ":"
-
override def toString: String =
user_prefix(session.getUserName) + host + port_suffix(session.getPort) +
(if (session.isConnected) "" else " (disconnected)")
@@ -430,12 +432,12 @@
def read_file(path: Path, local_path: Path): Unit =
sftp.get(remote_path(path), File.platform_path(local_path))
def read_bytes(path: Path): Bytes = using(open_input(path))(Bytes.read_stream(_))
- def read(path: Path): String = using(open_input(path))(File.read_stream(_))
+ def read(path: Path): String = using(open_input(path))(File.read_stream)
def write_file(path: Path, local_path: Path): Unit =
sftp.put(File.platform_path(local_path), remote_path(path))
def write_bytes(path: Path, bytes: Bytes): Unit =
- using(open_output(path))(bytes.write_stream(_))
+ using(open_output(path))(bytes.write_stream)
def write(path: Path, text: String): Unit =
using(open_output(path))(stream => Bytes(text).write_stream(stream))
@@ -480,7 +482,6 @@
trait System
{
def hg_url: String = ""
- def prefix: String = ""
def expand_path(path: Path): Path = path.expand
def bash_path(path: Path): String = File.bash_path(path)
--- a/src/Pure/General/symbol.ML Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/symbol.ML Thu Apr 02 13:04:24 2020 +0200
@@ -501,10 +501,9 @@
(* length *)
fun sym_len s =
- if not (is_printable s) then (0: int)
- else if String.isPrefix "\092<long" s then 2
- else if String.isPrefix "\092<Long" s then 2
- else 1;
+ if String.isPrefix "\092<long" s orelse String.isPrefix "\092<Long" s then 2
+ else if is_printable s then 1
+ else 0;
fun sym_length ss = fold (fn s => fn n => sym_len s + n) ss 0;
--- a/src/Pure/General/symbol.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/symbol.scala Thu Apr 02 13:04:24 2020 +0200
@@ -23,6 +23,7 @@
/* spaces */
+ val space_char = ' '
val space = " "
private val static_spaces = space * 4000
@@ -37,6 +38,8 @@
/* ASCII characters */
+ def is_ascii_printable(c: Char): Boolean = space_char <= c && c <= '~'
+
def is_ascii_letter(c: Char): Boolean = 'A' <= c && c <= 'Z' || 'a' <= c && c <= 'z'
def is_ascii_digit(c: Char): Boolean = '0' <= c && c <= '9'
@@ -113,8 +116,8 @@
{
private val matcher = new Matcher(text)
private var i = 0
- def hasNext = i < text.length
- def next =
+ def hasNext: Boolean = i < text.length
+ def next: Symbol =
{
val n = matcher(i, text.length)
val s =
@@ -135,10 +138,10 @@
def length(text: CharSequence): Int = iterator(text).length
def trim_blanks(text: CharSequence): String =
- Library.trim(is_blank(_), explode(text)).mkString
+ Library.trim(is_blank, explode(text)).mkString
def all_blank(str: String): Boolean =
- iterator(str).forall(is_blank(_))
+ iterator(str).forall(is_blank)
def trim_blank_lines(text: String): String =
cat_lines(split_lines(text).dropWhile(all_blank).reverse.dropWhile(all_blank).reverse)
@@ -191,7 +194,7 @@
if (i < 0) sym
else index(i).chr + sym - index(i).sym
}
- def decode(symbol_range: Range): Text.Range = symbol_range.map(decode(_))
+ def decode(symbol_range: Range): Text.Range = symbol_range.map(decode)
override def hashCode: Int = hash
override def equals(that: Any): Boolean =
@@ -448,7 +451,7 @@
/* classification */
- val letters = recode_set(
+ val letters: Set[String] = recode_set(
"A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M",
"N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z",
"a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m",
@@ -481,12 +484,12 @@
"\\<Xi>", "\\<Pi>", "\\<Sigma>", "\\<Upsilon>", "\\<Phi>",
"\\<Psi>", "\\<Omega>")
- val blanks = recode_set(space, "\t", "\n", "\u000B", "\f", "\r", "\r\n")
+ val blanks: Set[String] = recode_set(space, "\t", "\n", "\u000B", "\f", "\r", "\r\n")
val sym_chars =
Set("!", "#", "$", "%", "&", "*", "+", "-", "/", "<", "=", ">", "?", "@", "^", "_", "|", "~")
- val symbolic = recode_set((for { (sym, _) <- symbols; if raw_symbolic(sym) } yield sym): _*)
+ val symbolic: Set[String] = recode_set((for {(sym, _) <- symbols; if raw_symbolic(sym)} yield sym): _*)
/* misc symbols */
@@ -654,4 +657,23 @@
def esub_decoded: Symbol = symbols.esub_decoded
def bsup_decoded: Symbol = symbols.bsup_decoded
def esup_decoded: Symbol = symbols.esup_decoded
+
+
+ /* metric */
+
+ def is_printable(sym: Symbol): Boolean =
+ if (is_ascii(sym)) is_ascii_printable(sym(0))
+ else !is_control(sym)
+
+ object Metric extends Pretty.Metric
+ {
+ val unit = 1.0
+ def apply(str: String): Double =
+ (for (s <- iterator(str)) yield {
+ val sym = encode(s)
+ if (sym.startsWith("\\<long") || sym.startsWith("\\<Long")) 2
+ else if (is_printable(sym)) 1
+ else 0
+ }).sum
+ }
}
--- a/src/Pure/General/url.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/url.scala Thu Apr 02 13:04:24 2020 +0200
@@ -24,7 +24,7 @@
}
else c.toString
- def escape_special(s: String): String = s.iterator.map(escape_special(_)).mkString
+ def escape_special(s: String): String = s.iterator.map(escape_special).mkString
def escape_name(name: String): String =
name.iterator.map({ case '\'' => "%27" case c => c.toString }).mkString
--- a/src/Pure/General/value.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/value.scala Thu Apr 02 13:04:24 2020 +0200
@@ -70,7 +70,7 @@
val s = t.seconds
if (s.toInt.toDouble == s) s.toInt.toString else t.toString
}
- def unapply(s: java.lang.String): Option[Time] = Double.unapply(s).map(Time.seconds(_))
+ def unapply(s: java.lang.String): Option[Time] = Double.unapply(s).map(Time.seconds)
def parse(s: java.lang.String): Time =
unapply(s) getOrElse error("Bad real (for seconds): " + quote(s))
}
--- a/src/Pure/General/word.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/General/word.scala Thu Apr 02 13:04:24 2020 +0200
@@ -53,11 +53,11 @@
}
def unapply(str: String): Option[Case] =
if (str.nonEmpty) {
- if (Codepoint.iterator(str).forall(Character.isLowerCase(_))) Some(Lowercase)
- else if (Codepoint.iterator(str).forall(Character.isUpperCase(_))) Some(Uppercase)
+ if (Codepoint.iterator(str).forall(Character.isLowerCase)) Some(Lowercase)
+ else if (Codepoint.iterator(str).forall(Character.isUpperCase)) Some(Uppercase)
else {
val it = Codepoint.iterator(str)
- if (Character.isUpperCase(it.next) && it.forall(Character.isLowerCase(_)))
+ if (Character.isUpperCase(it.next) && it.forall(Character.isLowerCase))
Some(Capitalized)
else None
}
--- a/src/Pure/Isar/keyword.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Isar/keyword.scala Thu Apr 02 13:04:24 2020 +0200
@@ -169,7 +169,7 @@
val kinds1 = kinds + (name -> kind)
val load_commands1 =
if (kind == THY_LOAD) {
- if (!Symbol.iterator(name).forall(Symbol.is_ascii(_)))
+ if (!Symbol.iterator(name).forall(Symbol.is_ascii))
error("Bad theory load command " + quote(name))
load_commands + (name -> exts)
}
--- a/src/Pure/Isar/line_structure.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Isar/line_structure.scala Thu Apr 02 13:04:24 2020 +0200
@@ -9,7 +9,7 @@
object Line_Structure
{
- val init = Line_Structure()
+ val init: Line_Structure = Line_Structure()
}
sealed case class Line_Structure(
--- a/src/Pure/Isar/outer_syntax.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Isar/outer_syntax.scala Thu Apr 02 13:04:24 2020 +0200
@@ -193,7 +193,7 @@
if (tok.is_ignored) ignored += tok
else if (keywords.is_before_command(tok) ||
tok.is_command &&
- (!content.exists(keywords.is_before_command(_)) || content.exists(_.is_command)))
+ (!content.exists(keywords.is_before_command) || content.exists(_.is_command)))
{ flush(); content += tok }
else { content ++= ignored; ignored.clear; content += tok }
}
--- a/src/Pure/Isar/token.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Isar/token.scala Thu Apr 02 13:04:24 2020 +0200
@@ -249,9 +249,9 @@
private class Token_Reader(tokens: List[Token], val pos: Pos) extends Reader
{
- def first = tokens.head
- def rest = new Token_Reader(tokens.tail, pos.advance(first))
- def atEnd = tokens.isEmpty
+ def first: Token = tokens.head
+ def rest: Token_Reader = new Token_Reader(tokens.tail, pos.advance(first))
+ def atEnd: Boolean = tokens.isEmpty
}
def reader(tokens: List[Token], start: Token.Pos): Reader =
@@ -321,8 +321,8 @@
source.startsWith(Symbol.open) ||
source.startsWith(Symbol.open_decoded))
- def is_open_bracket: Boolean = is_keyword && Word.open_brackets.exists(is_keyword(_))
- def is_close_bracket: Boolean = is_keyword && Word.close_brackets.exists(is_keyword(_))
+ def is_open_bracket: Boolean = is_keyword && Word.open_brackets.exists(is_keyword)
+ def is_close_bracket: Boolean = is_keyword && Word.close_brackets.exists(is_keyword)
def is_begin: Boolean = is_keyword("begin")
def is_end: Boolean = is_command("end")
@@ -341,7 +341,7 @@
{
val s = content
is_name && Path.is_wellformed(s) &&
- !s.exists(Symbol.is_ascii_blank(_)) &&
+ !s.exists(Symbol.is_ascii_blank) &&
!Path.is_reserved(s)
}
}
--- a/src/Pure/ML/ml_console.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/ML/ml_console.scala Thu Apr 02 13:04:24 2020 +0200
@@ -50,6 +50,9 @@
if (more_args.nonEmpty) getopts.usage()
+ val sessions_structure = Sessions.load_structure(options, dirs = dirs)
+ val store = Sessions.store(options)
+
// build logic
if (!no_build && !raw_ml_system) {
val progress = new Console_Progress()
@@ -62,10 +65,10 @@
// process loop
val process =
- ML_Process(options, logic = logic, args = List("-i"), dirs = dirs, redirect = true,
+ ML_Process(options, sessions_structure, store,
+ logic = logic, args = List("-i"), redirect = true,
modes = if (raw_ml_system) Nil else modes ::: List("ASCII"),
raw_ml_system = raw_ml_system,
- store = Some(Sessions.store(options)),
session_base =
if (raw_ml_system) None
else Some(Sessions.base_info(
@@ -78,7 +81,9 @@
rc
}
tty_loop.join
- process_result.join
+
+ val rc = process_result.join
+ if (rc != 0) sys.exit(rc)
}
}
}
--- a/src/Pure/ML/ml_process.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/ML/ml_process.scala Thu Apr 02 13:04:24 2020 +0200
@@ -13,31 +13,28 @@
object ML_Process
{
def apply(options: Options,
+ sessions_structure: Sessions.Structure,
+ store: Sessions.Store,
logic: String = "",
+ raw_ml_system: Boolean = false,
+ use_prelude: List[String] = Nil,
+ eval_main: String = "",
args: List[String] = Nil,
- dirs: List[Path] = Nil,
modes: List[String] = Nil,
- raw_ml_system: Boolean = false,
cwd: JFile = null,
env: Map[String, String] = Isabelle_System.settings(),
redirect: Boolean = false,
cleanup: () => Unit = () => (),
- sessions_structure: Option[Sessions.Structure] = None,
- session_base: Option[Sessions.Base] = None,
- store: Option[Sessions.Store] = None): Bash.Process =
+ session_base: Option[Sessions.Base] = None): Bash.Process =
{
val logic_name = Isabelle_System.default_logic(logic)
- val _store = store.getOrElse(Sessions.store(options))
-
- val sessions_structure1 =
- sessions_structure.getOrElse(Sessions.load_structure(options, dirs = dirs))
val heaps: List[String] =
if (raw_ml_system) Nil
else {
- sessions_structure1.selection(Sessions.Selection.session(logic_name)).
+ sessions_structure.selection(Sessions.Selection.session(logic_name)).
build_requirements(List(logic_name)).
- map(a => File.platform_path(_store.the_heap(a)))
+ map(a => File.platform_path(store.the_heap(a)))
}
val eval_init =
@@ -96,8 +93,8 @@
ML_Syntax.print_pair(ML_Syntax.print_string_bytes, ML_Syntax.print_properties))(list)
List("Resources.init_session_base" +
- " {session_positions = " + print_sessions(sessions_structure1.session_positions) +
- ", session_directories = " + print_table(sessions_structure1.dest_session_directories) +
+ " {session_positions = " + print_sessions(sessions_structure.session_positions) +
+ ", session_directories = " + print_table(sessions_structure.dest_session_directories) +
", docs = " + print_list(base.doc_names) +
", global_theories = " + print_table(base.global_theories.toList) +
", loaded_theories = " + print_list(base.loaded_theories.keys) + "}")
@@ -105,9 +102,11 @@
// process
val eval_process =
- if (heaps.isEmpty)
- List("PolyML.print_depth " + ML_Syntax.print_int(options.int("ML_print_depth")))
- else List("Isabelle_Process.init ()")
+ proper_string(eval_main).getOrElse(
+ if (heaps.isEmpty) {
+ "PolyML.print_depth " + ML_Syntax.print_int(options.int("ML_print_depth"))
+ }
+ else "Isabelle_Process.init ()")
// ISABELLE_TMP
val isabelle_tmp = Isabelle_System.tmp_dir("process")
@@ -128,8 +127,8 @@
// bash
val bash_args =
ml_runtime_options :::
- (eval_init ::: eval_modes ::: eval_options ::: eval_session_base ::: eval_process)
- .flatMap(eval => List("--eval", eval)) ::: args
+ (eval_init ::: eval_modes ::: eval_options ::: eval_session_base).flatMap(List("--eval", _)) :::
+ use_prelude.flatMap(List("--use", _)) ::: List("--eval", eval_process) ::: args
Bash.process(
"exec " + options.string("ML_process_policy") + """ "$ML_HOME/poly" -q """ +
@@ -182,8 +181,12 @@
val more_args = getopts(args)
if (args.isEmpty || more_args.nonEmpty) getopts.usage()
- val rc = ML_Process(options, logic = logic, args = eval_args, dirs = dirs, modes = modes).
- result().print_stdout.rc
+ val sessions_structure = Sessions.load_structure(options, dirs = dirs)
+ val store = Sessions.store(options)
+
+ val rc =
+ ML_Process(options, sessions_structure, store, logic = logic, args = eval_args, modes = modes)
+ .result().print_stdout.rc
sys.exit(rc)
})
}
--- a/src/Pure/ML/ml_statistics.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/ML/ml_statistics.scala Thu Apr 02 13:04:24 2020 +0200
@@ -208,7 +208,7 @@
chart(fields._1, fields._2)
def show_frames(fields: List[ML_Statistics.Fields] = ML_Statistics.main_fields): Unit =
- fields.map(chart(_)).foreach(c =>
+ fields.map(chart).foreach(c =>
GUI_Thread.later {
new Frame {
iconImage = GUI.isabelle_image()
--- a/src/Pure/ML/ml_syntax.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/ML/ml_syntax.scala Thu Apr 02 13:04:24 2020 +0200
@@ -37,13 +37,13 @@
private def print_symbol(s: Symbol.Symbol): String =
if (s.startsWith("\\<")) s
- else UTF8.bytes(s).iterator.map(print_byte(_)).mkString
+ else UTF8.bytes(s).iterator.map(print_byte).mkString
def print_string_bytes(str: String): String =
- quote(UTF8.bytes(str).iterator.map(print_byte(_)).mkString)
+ quote(UTF8.bytes(str).iterator.map(print_byte).mkString)
def print_string_symbols(str: String): String =
- quote(Symbol.iterator(str).map(print_symbol(_)).mkString)
+ quote(Symbol.iterator(str).map(print_symbol).mkString)
/* pair */
@@ -61,5 +61,5 @@
/* properties */
def print_properties(props: Properties.T): String =
- print_list(print_pair(print_string_bytes(_), print_string_bytes(_))(_))(props)
+ print_list(print_pair(print_string_bytes, print_string_bytes))(props)
}
--- a/src/Pure/PIDE/document.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/document.scala Thu Apr 02 13:04:24 2020 +0200
@@ -95,12 +95,12 @@
copy(errors = errors.map(msg1 => Exn.cat_message(msg1, msg2)))
}
- val no_header = Header()
+ val no_header: Header = Header()
def bad_header(msg: String): Header = Header(errors = List(msg))
object Name
{
- val empty = Name("")
+ val empty: Name = Name("")
object Ordering extends scala.math.Ordering[Name]
{
@@ -375,7 +375,7 @@
}
def purge_suppressed: Option[Nodes] =
- graph.keys_iterator.filter(is_suppressed(_)).toList match {
+ graph.keys_iterator.filter(is_suppressed).toList match {
case Nil => None
case del => Some(new Nodes((graph /: del)(_.del_node(_))))
}
@@ -527,7 +527,7 @@
object Snapshot
{
- val init = State.init.snapshot()
+ val init: Snapshot = State.init.snapshot()
}
abstract class Snapshot
@@ -737,13 +737,13 @@
{
execs.get(id) match {
case Some(st) =>
- val new_st = st.accumulate(self_id(st), other_id _, message, xml_cache)
+ val new_st = st.accumulate(self_id(st), other_id, message, xml_cache)
val execs1 = execs + (id -> new_st)
(new_st, copy(execs = execs1, commands_redirection = redirection(new_st)))
case None =>
commands.get(id) match {
case Some(st) =>
- val new_st = st.accumulate(self_id(st), other_id _, message, xml_cache)
+ val new_st = st.accumulate(self_id(st), other_id, message, xml_cache)
val commands1 = commands + (id -> new_st)
(new_st, copy(commands = commands1, commands_redirection = redirection(new_st)))
case None => fail
@@ -1039,11 +1039,11 @@
/* local node content */
- def convert(offset: Text.Offset) = (offset /: edits)((i, edit) => edit.convert(i))
- def revert(offset: Text.Offset) = (offset /: reverse_edits)((i, edit) => edit.revert(i))
+ def convert(offset: Text.Offset): Text.Offset = (offset /: edits)((i, edit) => edit.convert(i))
+ def revert(offset: Text.Offset): Text.Offset = (offset /: reverse_edits)((i, edit) => edit.revert(i))
- def convert(range: Text.Range) = range.map(convert(_))
- def revert(range: Text.Range) = range.map(revert(_))
+ def convert(range: Text.Range): Text.Range = range.map(convert)
+ def revert(range: Text.Range): Text.Range = range.map(revert)
val node_name: Node.Name = name
val node: Node = version.nodes(name)
@@ -1166,7 +1166,7 @@
case some => Some(some)
}
}
- for (Text.Info(r, Some(x)) <- cumulate(range, None, elements, result1 _, status))
+ for (Text.Info(r, Some(x)) <- cumulate(range, None, elements, result1, status))
yield Text.Info(r, x)
}
--- a/src/Pure/PIDE/document_id.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/document_id.scala Thu Apr 02 13:04:24 2020 +0200
@@ -17,7 +17,7 @@
type Exec = Generic
val none: Generic = 0
- val make = Counter.make()
+ val make: Counter = Counter.make()
def apply(id: Generic): String = Value.Long.apply(id)
def unapply(s: String): Option[Generic] = Value.Long.unapply(s)
--- a/src/Pure/PIDE/document_status.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/document_status.scala Thu Apr 02 13:04:24 2020 +0200
@@ -55,7 +55,7 @@
runs = runs)
}
- val empty = make(Iterator.empty)
+ val empty: Command_Status = make(Iterator.empty)
def merge(status_iterator: Iterator[Command_Status]): Command_Status =
if (status_iterator.hasNext) {
--- a/src/Pure/PIDE/headless.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/headless.scala Thu Apr 02 13:04:24 2020 +0200
@@ -224,7 +224,7 @@
}
else result
- val (load_theories, load_state1) = load_state.next(dep_graph, finished_theory(_))
+ val (load_theories, load_state1) = load_state.next(dep_graph, finished_theory)
(load_theories,
copy(already_committed = already_committed1, result = result1, load_state = load_state1))
@@ -350,7 +350,7 @@
(theory_progress, st.update(nodes_status1))
})
- theory_progress.foreach(progress.theory(_))
+ theory_progress.foreach(progress.theory)
check_state()
@@ -396,8 +396,8 @@
object Resources
{
- def apply(base_info: Sessions.Base_Info, log: Logger = No_Logger): Resources =
- new Resources(base_info, log = log)
+ def apply(options: Options, base_info: Sessions.Base_Info, log: Logger = No_Logger): Resources =
+ new Resources(options, base_info, log = log)
def make(
options: Options,
@@ -410,7 +410,7 @@
val base_info =
Sessions.base_info(options, session_name, dirs = session_dirs,
include_sessions = include_sessions, progress = progress)
- apply(base_info, log = log)
+ apply(options, base_info, log = log)
}
final class Theory private[Headless](
@@ -496,7 +496,7 @@
lazy val theory_graph: Document.Node.Name.Graph[Unit] =
Document.Node.Name.make_graph(
for ((name, theory) <- theories.toList)
- yield ((name, ()), theory.node_header.imports.filter(theories.isDefinedAt(_))))
+ yield ((name, ()), theory.node_header.imports.filter(theories.isDefinedAt)))
def is_required(name: Document.Node.Name): Boolean = required.isDefinedAt(name)
@@ -542,7 +542,7 @@
: ((List[Document.Node.Name], List[Document.Node.Name], List[Document.Edit_Text]), State) =
{
val all_nodes = theory_graph.topological_order
- val purge = nodes.getOrElse(all_nodes).filterNot(is_required(_)).toSet
+ val purge = nodes.getOrElse(all_nodes).filterNot(is_required).toSet
val retain = theory_graph.all_preds(all_nodes.filterNot(purge)).toSet
val (retained, purged) = all_nodes.partition(retain)
@@ -554,6 +554,7 @@
}
class Resources private[Headless](
+ val options: Options,
val session_base_info: Sessions.Base_Info,
log: Logger = No_Logger)
extends isabelle.Resources(
@@ -561,7 +562,7 @@
{
resources =>
- def options: Options = session_base_info.options
+ val store: Sessions.Store = Sessions.store(options)
/* session */
@@ -570,28 +571,11 @@
{
val session = new Session(session_base_info.session, options, resources)
- val session_error = Future.promise[String]
- var session_phase: Session.Consumer[Session.Phase] = null
- session_phase =
- Session.Consumer(getClass.getName) {
- case Session.Ready =>
- session.phase_changed -= session_phase
- session_error.fulfill("")
- case Session.Terminated(result) if !result.ok =>
- session.phase_changed -= session_phase
- session_error.fulfill("Session start failed: return code " + result.rc)
- case _ =>
- }
- session.phase_changed += session_phase
+ progress.echo("Starting session " + session_base_info.session + " ...")
+ Isabelle_Process(session, options, session_base_info.sessions_structure, store,
+ logic = session_base_info.session, modes = print_mode).await_startup
- progress.echo("Starting session " + session_base_info.session + " ...")
- Isabelle_Process.start(session, options,
- logic = session_base_info.session, dirs = session_base_info.dirs, modes = print_mode)
-
- session_error.join match {
- case "" => session
- case msg => session.stop(); error(msg)
- }
+ session
}
--- a/src/Pure/PIDE/markup.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/markup.scala Thu Apr 02 13:04:24 2020 +0200
@@ -58,8 +58,8 @@
/* basic markup */
- val Empty = Markup("", Nil)
- val Broken = Markup("broken", Nil)
+ val Empty: Markup = Markup("", Nil)
+ val Broken: Markup = Markup("broken", Nil)
class Markup_String(val name: String, prop: String)
{
@@ -625,57 +625,10 @@
/* export */
val EXPORT = "export"
-
- object Export
- {
- sealed case class Args(
- id: Option[String],
- serial: Long,
- theory_name: String,
- name: String,
- executable: Boolean,
- compress: Boolean,
- strict: Boolean)
- {
- def compound_name: String = isabelle.Export.compound_name(theory_name, name)
- }
-
- val THEORY_NAME = "theory_name"
- val EXECUTABLE = "executable"
- val COMPRESS = "compress"
- val STRICT = "strict"
-
- def dest_inline(props: Properties.T): Option[(Args, Path)] =
- props match {
- case
- List(
- (SERIAL, Value.Long(serial)),
- (THEORY_NAME, theory_name),
- (NAME, name),
- (EXECUTABLE, Value.Boolean(executable)),
- (COMPRESS, Value.Boolean(compress)),
- (STRICT, Value.Boolean(strict)),
- (FILE, file)) if isabelle.Path.is_valid(file) =>
- val args = Args(None, serial, theory_name, name, executable, compress, strict)
- Some((args, isabelle.Path.explode(file)))
- case _ => None
- }
-
- def unapply(props: Properties.T): Option[Args] =
- props match {
- case List(
- (FUNCTION, EXPORT),
- (ID, id),
- (SERIAL, Value.Long(serial)),
- (THEORY_NAME, theory_name),
- (NAME, name),
- (EXECUTABLE, Value.Boolean(executable)),
- (COMPRESS, Value.Boolean(compress)),
- (STRICT, Value.Boolean(strict))) =>
- Some(Args(proper_string(id), serial, theory_name, name, executable, compress, strict))
- case _ => None
- }
- }
+ val THEORY_NAME = "theory_name"
+ val EXECUTABLE = "executable"
+ val COMPRESS = "compress"
+ val STRICT = "strict"
/* debugger output */
--- a/src/Pure/PIDE/protocol.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/protocol.scala Thu Apr 02 13:04:24 2020 +0200
@@ -9,6 +9,19 @@
object Protocol
{
+ /* markers for inlined messages */
+
+ val Loading_Theory_Marker = Protocol_Message.Marker("loading_theory")
+ val Export_Marker = Protocol_Message.Marker("export")
+ val Meta_Info_Marker = Protocol_Message.Marker("meta_info")
+ val Timing_Marker = Protocol_Message.Marker("Timing")
+ val Command_Timing_Marker = Protocol_Message.Marker("command_timing")
+ val Theory_Timing_Marker = Protocol_Message.Marker("theory_timing")
+ val ML_Statistics_Marker = Protocol_Message.Marker("ML_statistics")
+ val Task_Statistics_Marker = Protocol_Message.Marker("task_statistics")
+ val Error_Message_Marker = Protocol_Message.Marker("error_message")
+
+
/* document editing */
object Commands_Accepted
@@ -32,7 +45,7 @@
case a :: bs => (a, bs)
case _ => throw new XML.XML_Body(body)
}
- Some(triple(long, list(string), list(decode_upd _))(Symbol.decode_yxml(text)))
+ Some(triple(long, list(string), list(decode_upd))(Symbol.decode_yxml(text)))
}
catch {
case ERROR(_) => None
@@ -89,6 +102,12 @@
/* result messages */
+ def is_message(pred: XML.Elem => Boolean, body: XML.Body): Boolean =
+ body match {
+ case List(elem: XML.Elem) => pred(elem)
+ case _ => false
+ }
+
def is_result(msg: XML.Tree): Boolean =
msg match {
case XML.Elem(Markup(Markup.RESULT, _), _) => true
@@ -150,12 +169,76 @@
def is_exported(msg: XML.Tree): Boolean =
is_writeln(msg) || is_warning(msg) || is_legacy(msg) || is_error(msg)
- def message_text(msg: XML.Tree): String =
+ def message_text(body: XML.Body,
+ margin: Double = Pretty.default_margin,
+ breakgain: Double = Pretty.default_breakgain,
+ metric: Pretty.Metric = Pretty.Default_Metric): String =
+ {
+ val text =
+ Pretty.string_of(Protocol_Message.expose_no_reports(body),
+ margin = margin, breakgain = breakgain, metric = metric)
+
+ if (is_message(is_warning, body) || is_message(is_legacy, body)) Output.warning_prefix(text)
+ else if (is_message(is_error, body)) Output.error_prefix(text)
+ else text
+ }
+
+
+ /* export */
+
+ object Export
{
- val text = Pretty.string_of(List(msg))
- if (is_warning(msg) || is_legacy(msg)) Library.prefix_lines("### ", text)
- else if (is_error(msg)) Library.prefix_lines("*** ", text)
- else text
+ sealed case class Args(
+ id: Option[String],
+ serial: Long,
+ theory_name: String,
+ name: String,
+ executable: Boolean,
+ compress: Boolean,
+ strict: Boolean)
+ {
+ def compound_name: String = isabelle.Export.compound_name(theory_name, name)
+ }
+
+ object Marker
+ {
+ def unapply(line: String): Option[(Args, Path)] =
+ line match {
+ case Export_Marker(text) =>
+ val props = XML.Decode.properties(YXML.parse_body(text))
+ props match {
+ case
+ List(
+ (Markup.SERIAL, Value.Long(serial)),
+ (Markup.THEORY_NAME, theory_name),
+ (Markup.NAME, name),
+ (Markup.EXECUTABLE, Value.Boolean(executable)),
+ (Markup.COMPRESS, Value.Boolean(compress)),
+ (Markup.STRICT, Value.Boolean(strict)),
+ (Markup.FILE, file)) if isabelle.Path.is_valid(file) =>
+ val args = Args(None, serial, theory_name, name, executable, compress, strict)
+ Some((args, isabelle.Path.explode(file)))
+ case _ => None
+ }
+ case _ => None
+ }
+ }
+
+ def unapply(props: Properties.T): Option[Args] =
+ props match {
+ case
+ List(
+ (Markup.FUNCTION, Markup.EXPORT),
+ (Markup.ID, id),
+ (Markup.SERIAL, Value.Long(serial)),
+ (Markup.THEORY_NAME, theory_name),
+ (Markup.NAME, name),
+ (Markup.EXECUTABLE, Value.Boolean(executable)),
+ (Markup.COMPRESS, Value.Boolean(compress)),
+ (Markup.STRICT, Value.Boolean(strict))) =>
+ Some(Args(proper_string(id), serial, theory_name, name, executable, compress, strict))
+ case _ => None
+ }
}
@@ -310,7 +393,7 @@
def define_commands_bulk(commands: List[Command])
{
val (irregular, regular) = commands.partition(command => YXML.detect(command.source))
- irregular.foreach(define_command(_))
+ irregular.foreach(define_command)
regular match {
case Nil =>
case List(command) => define_command(command)
--- a/src/Pure/PIDE/protocol_message.ML Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/protocol_message.ML Thu Apr 02 13:04:24 2020 +0200
@@ -6,7 +6,8 @@
signature PROTOCOL_MESSAGE =
sig
- val inline: string -> Properties.T -> unit
+ val marker_text: string -> string -> unit
+ val marker: string -> Properties.T -> unit
val command_positions: string -> XML.body -> XML.body
val command_positions_yxml: string -> string -> string
end;
@@ -14,8 +15,11 @@
structure Protocol_Message: PROTOCOL_MESSAGE =
struct
-fun inline a args =
- writeln ("\f" ^ a ^ " = " ^ YXML.string_of_body (XML.Encode.properties args));
+fun marker_text a text =
+ Output.physical_writeln ("\f" ^ a ^ " = " ^ encode_lines text);
+
+fun marker a props =
+ marker_text a (YXML.string_of_body (XML.Encode.properties props));
fun command_positions id =
--- a/src/Pure/PIDE/protocol_message.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/protocol_message.scala Thu Apr 02 13:04:24 2020 +0200
@@ -9,6 +9,34 @@
object Protocol_Message
{
+ /* message markers */
+
+ object Marker
+ {
+ def apply(a: String): Marker =
+ new Marker { override def name: String = a }
+
+ def test(line: String): Boolean = line.startsWith("\f")
+ }
+
+ abstract class Marker private
+ {
+ def name: String
+ val prefix: String = "\f" + name + " = "
+
+ def apply(text: String): String = prefix + Library.encode_lines(text)
+ def apply(props: Properties.T): String = apply(YXML.string_of_body(XML.Encode.properties(props)))
+
+ def test(line: String): Boolean = line.startsWith(prefix)
+ def test_yxml(line: String): Boolean = test(line) && YXML.detect(line)
+
+ def unapply(line: String): Option[String] =
+ Library.try_unprefix(prefix, line).map(Library.decode_lines)
+
+ override def toString: String = "Marker(" + quote(name) + ")"
+ }
+
+
/* inlined reports */
private val report_elements =
@@ -25,6 +53,14 @@
case t => t
}
+ def expose_no_reports(body: XML.Body): XML.Body =
+ body flatMap {
+ case XML.Wrapped_Elem(markup, body, ts) => List(XML.Wrapped_Elem(markup, body, expose_no_reports(ts)))
+ case XML.Elem(Markup(Markup.NO_REPORT, _), ts) => ts
+ case XML.Elem(markup, ts) => List(XML.Elem(markup, expose_no_reports(ts)))
+ case t => List(t)
+ }
+
def reports(props: Properties.T, body: XML.Body): List[XML.Elem] =
body flatMap {
case XML.Wrapped_Elem(Markup(Markup.REPORT, ps), body, ts) =>
--- a/src/Pure/PIDE/prover.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/prover.scala Thu Apr 02 13:04:24 2020 +0200
@@ -32,20 +32,20 @@
def properties: Properties.T = message.markup.properties
def body: XML.Body = message.body
- def is_init = kind == Markup.INIT
- def is_exit = kind == Markup.EXIT
- def is_stdout = kind == Markup.STDOUT
- def is_stderr = kind == Markup.STDERR
- def is_system = kind == Markup.SYSTEM
- def is_status = kind == Markup.STATUS
- def is_report = kind == Markup.REPORT
- def is_syslog = is_init || is_exit || is_system || is_stderr
+ def is_init: Boolean = kind == Markup.INIT
+ def is_exit: Boolean = kind == Markup.EXIT
+ def is_stdout: Boolean = kind == Markup.STDOUT
+ def is_stderr: Boolean = kind == Markup.STDERR
+ def is_system: Boolean = kind == Markup.SYSTEM
+ def is_status: Boolean = kind == Markup.STATUS
+ def is_report: Boolean = kind == Markup.REPORT
+ def is_syslog: Boolean = is_init || is_exit || is_system || is_stderr
override def toString: String =
{
val res =
if (is_status || is_report) message.body.map(_.toString).mkString
- else Pretty.string_of(message.body)
+ else Pretty.string_of(message.body, metric = Symbol.Metric)
if (properties.isEmpty)
kind.toString + " [[" + res + "]]"
else
@@ -114,6 +114,8 @@
private val process_manager = Standard_Thread.fork("process_manager")
{
+ val stdout = physical_output(false)
+
val (startup_failed, startup_errors) =
{
var finished: Option[Boolean] = None
@@ -127,7 +129,7 @@
}
catch { case _: IOException => finished = Some(false) }
}
- Thread.sleep(10)
+ Thread.sleep(50)
}
(finished.isEmpty || !finished.get, result.toString.trim)
}
@@ -136,13 +138,13 @@
if (startup_failed) {
terminate_process()
process_result.join
+ stdout.join
exit_message(Process_Result(127))
}
else {
val (command_stream, message_stream) = channel.rendezvous()
command_input_init(command_stream)
- val stdout = physical_output(false)
val stderr = physical_output(true)
val message = message_output(message_stream)
--- a/src/Pure/PIDE/rendering.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/rendering.scala Thu Apr 02 13:04:24 2020 +0200
@@ -21,20 +21,20 @@
// background
val unprocessed1, running1, canceled, bad, intensify, entity, active, active_result,
markdown_bullet1, markdown_bullet2, markdown_bullet3, markdown_bullet4 = Value
- val background_colors = values
+ val background_colors: ValueSet = values
// foreground
val quoted, antiquoted = Value
- val foreground_colors = values -- background_colors
+ val foreground_colors: ValueSet = values -- background_colors
// message underline
val writeln, information, warning, legacy, error = Value
- val message_underline_colors = values -- background_colors -- foreground_colors
+ val message_underline_colors: ValueSet = values -- background_colors -- foreground_colors
// message background
val writeln_message, information_message, tracing_message,
warning_message, legacy_message, error_message = Value
- val message_background_colors =
+ val message_background_colors: ValueSet =
values -- background_colors -- foreground_colors -- message_underline_colors
// text
@@ -42,7 +42,7 @@
tfree, tvar, free, skolem, bound, `var`, inner_numeral, inner_quoted,
inner_cartouche, comment1, comment2, comment3, dynamic, class_parameter,
antiquote, raw_text, plain_text = Value
- val text_colors =
+ val text_colors: ValueSet =
values -- background_colors -- foreground_colors -- message_underline_colors --
message_background_colors
--- a/src/Pure/PIDE/session.ML Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/session.ML Thu Apr 02 13:04:24 2020 +0200
@@ -9,7 +9,7 @@
val get_name: unit -> string
val welcome: unit -> string
val get_keywords: unit -> Keyword.keywords
- val init: HTML.symbols -> bool -> bool -> Path.T -> string -> string -> (string * string) list ->
+ val init: HTML.symbols -> bool -> Path.T -> string -> string -> (string * string) list ->
(Path.T * Path.T) list -> Path.T -> string -> string * string -> bool -> unit
val shutdown: unit -> unit
val finish: unit -> unit
@@ -48,13 +48,13 @@
(* init *)
-fun init symbols build info info_path doc doc_output doc_variants doc_files graph_file
+fun init symbols info info_path doc doc_output doc_variants doc_files graph_file
parent (chapter, name) verbose =
(Synchronized.change session (fn ({name = parent_name, ...}, parent_finished) =>
if parent_name <> parent orelse not parent_finished then
error ("Unfinished parent session " ^ quote parent ^ " for " ^ quote name)
else ({chapter = chapter, name = name}, false));
- Present.init symbols build info info_path (if doc = "false" then "" else doc)
+ Present.init symbols info info_path (if doc = "false" then "" else doc)
doc_output doc_variants doc_files graph_file (chapter, name) verbose);
--- a/src/Pure/PIDE/session.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/session.scala Thu Apr 02 13:04:24 2020 +0200
@@ -61,7 +61,10 @@
/* events */
//{{{
- case class Statistics(props: Properties.T)
+ case class Command_Timing(props: Properties.T)
+ case class Theory_Timing(props: Properties.T)
+ case class Runtime_Statistics(props: Properties.T)
+ case class Task_Statistics(props: Properties.T)
case class Global_Options(options: Options)
case object Caret_Focus
case class Raw_Edits(doc_blobs: Document.Blobs, edits: List[Document.Edit_Text])
@@ -175,7 +178,10 @@
/* outlets */
- val statistics = new Session.Outlet[Session.Statistics](dispatcher)
+ val command_timings = new Session.Outlet[Session.Command_Timing](dispatcher)
+ val theory_timings = new Session.Outlet[Session.Theory_Timing](dispatcher)
+ val runtime_statistics = new Session.Outlet[Session.Runtime_Statistics](dispatcher)
+ val task_statistics = new Session.Outlet[Session.Task_Statistics](dispatcher)
val global_options = new Session.Outlet[Session.Global_Options](dispatcher)
val caret_focus = new Session.Outlet[Session.Caret_Focus.type](dispatcher)
val raw_edits = new Session.Outlet[Session.Raw_Edits](dispatcher)
@@ -213,7 +219,7 @@
private val _phase = Synchronized[Session.Phase](Session.Inactive)
private def phase_=(new_phase: Session.Phase): Unit = _phase.change(_ => post_phase(new_phase))
- def phase = _phase.value
+ def phase: Session.Phase = _phase.value
def is_ready: Boolean = phase == Session.Ready
@@ -480,13 +486,14 @@
init_protocol_handler(name)
case Protocol.Command_Timing(state_id, timing) if prover.defined =>
+ command_timings.post(Session.Command_Timing(msg.properties.tail))
val message = XML.elem(Markup.STATUS, List(XML.Elem(Markup.Timing(timing), Nil)))
change_command(_.accumulate(state_id, xml_cache.elem(message), xml_cache))
case Protocol.Theory_Timing(_, _) =>
- // FIXME
+ theory_timings.post(Session.Theory_Timing(msg.properties.tail))
- case Markup.Export(args)
+ case Protocol.Export(args)
if args.id.isDefined && Value.Long.unapply(args.id.get).isDefined =>
val id = Value.Long.unapply(args.id.get).get
val export = Export.make_entry("", args, msg.bytes, cache = xz_cache)
@@ -526,10 +533,10 @@
}
case Markup.ML_Statistics(props) =>
- statistics.post(Session.Statistics(props))
+ runtime_statistics.post(Session.Runtime_Statistics(props))
case Markup.Task_Statistics(props) =>
- // FIXME
+ task_statistics.post(Session.Task_Statistics(props))
case _ => bad_output()
}
@@ -566,15 +573,15 @@
//{{{
arg match {
case output: Prover.Output =>
- if (output.is_stdout || output.is_stderr)
- raw_output_messages.post(output)
- else handle_output(output)
-
if (output.is_syslog) {
syslog += output.message
syslog_messages.post(output)
}
+ if (output.is_stdout || output.is_stderr)
+ raw_output_messages.post(output)
+ else handle_output(output)
+
all_messages.post(output)
case input: Prover.Input =>
@@ -645,7 +652,7 @@
case Session.Change_Flush if prover.defined =>
val state = global_state.value
if (!state.removing_versions)
- postponed_changes.flush(state).foreach(handle_change(_))
+ postponed_changes.flush(state).foreach(handle_change)
case bad =>
if (verbose) Output.warning("Ignoring bad message: " + bad.toString)
--- a/src/Pure/PIDE/xml.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/xml.scala Thu Apr 02 13:04:24 2020 +0200
@@ -217,7 +217,7 @@
else
lookup(x) match {
case Some(y) => y
- case None => x.map(cache_tree(_))
+ case None => x.map(cache_tree)
}
}
--- a/src/Pure/PIDE/yxml.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/PIDE/yxml.scala Thu Apr 02 13:04:24 2020 +0200
@@ -21,10 +21,10 @@
val is_X = (c: Char) => c == X
val is_Y = (c: Char) => c == Y
- val X_string = X.toString
- val Y_string = Y.toString
- val XY_string = X_string + Y_string
- val XYX_string = XY_string + X_string
+ val X_string: String = X.toString
+ val Y_string: String = Y.toString
+ val XY_string: String = X_string + Y_string
+ val XYX_string: String = XY_string + X_string
def detect(s: String): Boolean = s.exists(c => c == X || c == Y)
def detect_elem(s: String): Boolean = s.startsWith(XY_string)
--- a/src/Pure/System/bash.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/bash.scala Thu Apr 02 13:04:24 2020 +0200
@@ -35,10 +35,10 @@
def string(s: String): String =
if (s == "") "\"\""
- else UTF8.bytes(s).iterator.map(bash_chr(_)).mkString
+ else UTF8.bytes(s).iterator.map(bash_chr).mkString
def strings(ss: List[String]): String =
- ss.iterator.map(Bash.string(_)).mkString(" ")
+ ss.iterator.map(Bash.string).mkString(" ")
/* process and result */
--- a/src/Pure/System/command_line.ML Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/command_line.ML Thu Apr 02 13:04:24 2020 +0200
@@ -6,8 +6,7 @@
signature COMMAND_LINE =
sig
- val tool: (unit -> int) -> unit
- val tool0: (unit -> unit) -> unit
+ val tool: (unit -> unit) -> unit
end;
structure Command_Line: COMMAND_LINE =
@@ -17,11 +16,8 @@
Thread_Attributes.uninterruptible (fn restore_attributes => fn () =>
let
val rc =
- restore_attributes body () handle exn =>
- Exn.capture_exit 2 (fn () => (Runtime.exn_error_message exn; raise exn)) ();
+ (restore_attributes body (); 0)
+ handle exn => Exn.capture_exit 2 (fn () => (Runtime.exn_error_message exn; raise exn)) ();
in exit rc end) ();
-fun tool0 body = tool (fn () => (body (); 0));
-
end;
-
--- a/src/Pure/System/command_line.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/command_line.scala Thu Apr 02 13:04:24 2020 +0200
@@ -23,10 +23,10 @@
var debug = false
- def tool(body: => Int): Nothing =
+ def tool(body: => Unit): Nothing =
{
val rc =
- try { body }
+ try { body; 0 }
catch {
case exn: Throwable =>
Output.error_message(Exn.message(exn) + (if (debug) "\n" + Exn.trace(exn) else ""))
@@ -35,6 +35,6 @@
sys.exit(rc)
}
- def tool0(body: => Unit): Nothing = tool { body; 0 }
+ def ML_tool(body: List[String]): String =
+ "Command_Line.tool (fn () => (" + body.mkString("; ") + "));"
}
-
--- a/src/Pure/System/getopts.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/getopts.scala Thu Apr 02 13:04:24 2020 +0200
@@ -7,6 +7,9 @@
package isabelle
+import scala.annotation.tailrec
+
+
object Getopts
{
def apply(usage_text: String, option_specs: (String, String => Unit)*): Getopts =
@@ -44,7 +47,7 @@
cat_error(msg, "The error(s) above occurred in command-line option " + print_option(opt))
}
- private def getopts(args: List[List[Char]]): List[List[Char]] =
+ @tailrec private def getopts(args: List[List[Char]]): List[List[Char]] =
args match {
case List('-', '-') :: rest_args => rest_args
case ('-' :: opt :: rest_opts) :: rest_args if is_option0(opt) && rest_opts.nonEmpty =>
--- a/src/Pure/System/invoke_scala.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/invoke_scala.scala Thu Apr 02 13:04:24 2020 +0200
@@ -123,6 +123,6 @@
val functions =
List(
- Markup.INVOKE_SCALA -> invoke_scala _,
- Markup.CANCEL_SCALA -> cancel_scala _)
+ Markup.INVOKE_SCALA -> invoke_scala,
+ Markup.CANCEL_SCALA -> cancel_scala)
}
--- a/src/Pure/System/isabelle_process.ML Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/isabelle_process.ML Thu Apr 02 13:04:24 2020 +0200
@@ -9,10 +9,12 @@
val is_active: unit -> bool
val protocol_command: string -> (string list -> unit) -> unit
val reset_tracing: Document_ID.exec -> unit
+ exception EXIT of int
val crashes: exn list Synchronized.var
val init_options: unit -> unit
val init_options_interactive: unit -> unit
val init: unit -> unit
+ val init_build: unit -> unit
end;
structure Isabelle_Process: ISABELLE_PROCESS =
@@ -27,6 +29,9 @@
val _ = Output.add_mode isabelle_processN Output.default_output Output.default_escape;
val _ = Markup.add_mode isabelle_processN YXML.output_markup;
+val protocol_modes1 = [Syntax_Trans.no_bracketsN, Syntax_Trans.no_type_bracketsN];
+val protocol_modes2 = [isabelle_processN, Pretty.symbolicN];
+
(* protocol commands *)
@@ -91,16 +96,41 @@
end);
-(* output channels *)
+(* init protocol -- uninterruptible *)
+
+exception EXIT of int;
+
+val crashes = Synchronized.var "Isabelle_Process.crashes" ([]: exn list);
+
+local
+
+fun recover crash =
+ (Synchronized.change crashes (cons crash);
+ Output.physical_stderr
+ "Recovered from Isabelle process crash -- see also Isabelle_Process.crashes\n");
-val serial_props = Markup.serial_properties o serial;
+in
+
+fun init_protocol modes = Thread_Attributes.uninterruptible (fn _ => fn (address, password) =>
+ let
+ val _ = SHA1.test_samples ()
+ handle exn as Fail msg => (Output.physical_stderr (msg ^ "\n"); Exn.reraise exn);
-fun init_channels out_stream =
- let
+ val _ = Output.physical_stderr Symbol.STX;
+
+
+ (* streams *)
+
+ val (in_stream, out_stream) = Socket_IO.open_streams address;
+ val _ = Byte_Message.write_line out_stream password;
+
val _ = TextIO.StreamIO.setBufferMode (TextIO.getOutstream TextIO.stdOut, IO.LINE_BUF);
val _ = TextIO.StreamIO.setBufferMode (TextIO.getOutstream TextIO.stdErr, IO.LINE_BUF);
val _ = BinIO.StreamIO.setBufferMode (BinIO.getOutstream out_stream, IO.BLOCK_BUF);
+
+ (* messages *)
+
val msg_channel = Message_Channel.make out_stream;
fun message name props body =
@@ -115,88 +145,75 @@
(false, SOME id') => props @ [(Markup.idN, id')]
| _ => props);
in message name props' (XML.blob ss) end;
- in
- Private_Output.status_fn := standard_message [] Markup.statusN;
- Private_Output.report_fn := standard_message [] Markup.reportN;
- Private_Output.result_fn :=
- (fn props => fn s => standard_message (props @ serial_props ()) Markup.resultN s);
- Private_Output.writeln_fn := (fn s => standard_message (serial_props ()) Markup.writelnN s);
- Private_Output.state_fn := (fn s => standard_message (serial_props ()) Markup.stateN s);
- Private_Output.information_fn :=
- (fn s => standard_message (serial_props ()) Markup.informationN s);
- Private_Output.tracing_fn :=
- (fn s => (update_tracing (); standard_message (serial_props ()) Markup.tracingN s));
- Private_Output.warning_fn := (fn s => standard_message (serial_props ()) Markup.warningN s);
- Private_Output.legacy_fn := (fn s => standard_message (serial_props ()) Markup.legacyN s);
- Private_Output.error_message_fn :=
- (fn (i, s) => standard_message (Markup.serial_properties i) Markup.errorN s);
- Private_Output.system_message_fn :=
- (fn ss => message Markup.systemN [] (XML.blob ss));
- Private_Output.protocol_message_fn :=
- (fn props => fn body => message Markup.protocolN props body);
+
+ val serial_props = Markup.serial_properties o serial;
- Session.init_protocol_handlers ();
- message Markup.initN [] [XML.Text (Session.welcome ())];
- msg_channel
- end;
+ val message_context =
+ Unsynchronized.setmp Private_Output.status_fn
+ (standard_message [] Markup.statusN) #>
+ Unsynchronized.setmp Private_Output.report_fn
+ (standard_message [] Markup.reportN) #>
+ Unsynchronized.setmp Private_Output.result_fn
+ (fn props => fn s => standard_message (props @ serial_props ()) Markup.resultN s) #>
+ Unsynchronized.setmp Private_Output.writeln_fn
+ (fn s => standard_message (serial_props ()) Markup.writelnN s) #>
+ Unsynchronized.setmp Private_Output.state_fn
+ (fn s => standard_message (serial_props ()) Markup.stateN s) #>
+ Unsynchronized.setmp Private_Output.information_fn
+ (fn s => standard_message (serial_props ()) Markup.informationN s) #>
+ Unsynchronized.setmp Private_Output.tracing_fn
+ (fn s => (update_tracing (); standard_message (serial_props ()) Markup.tracingN s)) #>
+ Unsynchronized.setmp Private_Output.warning_fn
+ (fn s => standard_message (serial_props ()) Markup.warningN s) #>
+ Unsynchronized.setmp Private_Output.legacy_fn
+ (fn s => standard_message (serial_props ()) Markup.legacyN s) #>
+ Unsynchronized.setmp Private_Output.error_message_fn
+ (fn (i, s) => standard_message (Markup.serial_properties i) Markup.errorN s) #>
+ Unsynchronized.setmp Private_Output.system_message_fn
+ (fn ss => message Markup.systemN [] (XML.blob ss)) #>
+ Unsynchronized.setmp Private_Output.protocol_message_fn
+ (fn props => fn body => message Markup.protocolN props body) #>
+ Unsynchronized.setmp print_mode
+ ((! print_mode @ #1 modes) |> fold (update op =) (#2 modes));
-(* protocol loop -- uninterruptible *)
-
-val crashes = Synchronized.var "Isabelle_Process.crashes" ([]: exn list);
-
-local
+ (* protocol *)
-fun recover crash =
- (Synchronized.change crashes (cons crash);
- Output.physical_stderr
- "Recovered from Isabelle process crash -- see also Isabelle_Process.crashes\n");
-
-in
+ fun protocol_loop () =
+ let
+ val continue =
+ (case Byte_Message.read_message in_stream of
+ NONE => false
+ | SOME [] => (Output.system_message "Isabelle process: no input"; true)
+ | SOME (name :: args) => (run_command name args; true))
+ handle exn as EXIT _ => Exn.reraise exn
+ | exn => (Runtime.exn_system_message exn handle crash => recover crash; true);
+ in if continue then protocol_loop () else () end;
-fun loop stream =
- let
- val continue =
- (case Byte_Message.read_message stream of
- NONE => false
- | SOME [] => (Output.system_message "Isabelle process: no input"; true)
- | SOME (name :: args) => (run_command name args; true))
- handle exn => (Runtime.exn_system_message exn handle crash => recover crash; true);
+ fun protocol () =
+ (Session.init_protocol_handlers ();
+ message Markup.initN [] [XML.Text (Session.welcome ())];
+ protocol_loop ());
+
+ val result = Exn.capture (message_context protocol) ();
+
+
+ (* shutdown *)
+
+ val _ = Future.shutdown ();
+ val _ = Execution.reset ();
+ val _ = Message_Channel.shutdown msg_channel;
+ val _ = BinIO.closeIn in_stream;
+ val _ = BinIO.closeOut out_stream;
in
- if continue then loop stream
- else (Future.shutdown (); Execution.reset (); ())
- end;
+ (case result of
+ Exn.Exn (EXIT rc) => exit rc
+ | _ => Exn.release result)
+ end);
end;
-(* init protocol *)
-
-val default_modes1 = [Syntax_Trans.no_bracketsN, Syntax_Trans.no_type_bracketsN];
-val default_modes2 = [isabelle_processN, Pretty.symbolicN];
-
-val init_protocol = Thread_Attributes.uninterruptible (fn _ => fn (address, password) =>
- let
- val _ = SHA1.test_samples ()
- handle exn as Fail msg => (Output.physical_stderr (msg ^ "\n"); Exn.reraise exn);
- val _ = Output.physical_stderr Symbol.STX;
-
- val _ = Context.put_generic_context NONE;
- val _ =
- Unsynchronized.change print_mode
- (fn mode => (mode @ default_modes1) |> fold (update op =) default_modes2);
-
- val (in_stream, out_stream) = Socket_IO.open_streams address;
- val _ = Byte_Message.write_line out_stream password;
- val msg_channel = init_channels out_stream;
- val _ = loop in_stream;
- val _ = Message_Channel.shutdown msg_channel;
- val _ = Private_Output.init_channels ();
-
- val _ = print_mode := [];
- in () end);
-
-
(* init options *)
fun init_options () =
@@ -218,14 +235,17 @@
(* generic init *)
-fun init () =
+fun init_modes modes =
let
val address = Options.default_string \<^system_option>\<open>system_channel_address\<close>;
val password = Options.default_string \<^system_option>\<open>system_channel_password\<close>;
in
if address <> "" andalso password <> ""
- then init_protocol (address, password)
+ then init_protocol modes (address, password)
else init_options ()
end;
+fun init () = init_modes (protocol_modes1, protocol_modes2);
+fun init_build () = init_modes ([], protocol_modes2);
+
end;
--- a/src/Pure/System/isabelle_process.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/isabelle_process.scala Thu Apr 02 13:04:24 2020 +0200
@@ -12,39 +12,18 @@
object Isabelle_Process
{
- def start(session: Session,
+ def apply(
+ session: Session,
options: Options,
+ sessions_structure: Sessions.Structure,
+ store: Sessions.Store,
logic: String = "",
- args: List[String] = Nil,
- dirs: List[Path] = Nil,
+ raw_ml_system: Boolean = false,
+ use_prelude: List[String] = Nil,
+ eval_main: String = "",
modes: List[String] = Nil,
cwd: JFile = null,
- env: Map[String, String] = Isabelle_System.settings(),
- sessions_structure: Option[Sessions.Structure] = None,
- store: Option[Sessions.Store] = None,
- phase_changed: Session.Phase => Unit = null)
- {
- if (phase_changed != null)
- session.phase_changed += Session.Consumer("Isabelle_Process")(phase_changed)
-
- session.start(receiver =>
- Isabelle_Process(options, logic = logic, args = args, dirs = dirs, modes = modes,
- cwd = cwd, env = env, receiver = receiver, xml_cache = session.xml_cache,
- sessions_structure = sessions_structure, store = store))
- }
-
- def apply(
- options: Options,
- logic: String = "",
- args: List[String] = Nil,
- dirs: List[Path] = Nil,
- modes: List[String] = Nil,
- cwd: JFile = null,
- env: Map[String, String] = Isabelle_System.settings(),
- receiver: Prover.Receiver = (msg: Prover.Message) => Output.writeln(msg.toString, stdout = true),
- xml_cache: XML.Cache = XML.make_cache(),
- sessions_structure: Option[Sessions.Structure] = None,
- store: Option[Sessions.Store] = None): Prover =
+ env: Map[String, String] = Isabelle_System.settings()): Isabelle_Process =
{
val channel = System_Channel()
val process =
@@ -52,12 +31,44 @@
val channel_options =
options.string.update("system_channel_address", channel.address).
string.update("system_channel_password", channel.password)
- ML_Process(channel_options, logic = logic, args = args, dirs = dirs, modes = modes,
- cwd = cwd, env = env, sessions_structure = sessions_structure, store = store)
+ ML_Process(channel_options, sessions_structure, store,
+ logic = logic, raw_ml_system = raw_ml_system,
+ use_prelude = use_prelude, eval_main = eval_main,
+ modes = modes, cwd = cwd, env = env)
}
catch { case exn @ ERROR(_) => channel.shutdown(); throw exn }
process.stdin.close
- new Prover(receiver, xml_cache, channel, process)
+ new Isabelle_Process(session, channel, process)
}
}
+
+class Isabelle_Process private(session: Session, channel: System_Channel, process: Bash.Process)
+{
+ private val startup = Future.promise[String]
+ private val terminated = Future.promise[Process_Result]
+
+ session.phase_changed +=
+ Session.Consumer(getClass.getName) {
+ case Session.Ready =>
+ startup.fulfill("")
+ case Session.Terminated(result) =>
+ if (!result.ok && !startup.is_finished) {
+ val syslog = session.syslog_content()
+ val err = "Session startup failed" + (if (syslog.isEmpty) "" else ":\n" + syslog)
+ startup.fulfill(err)
+ }
+ terminated.fulfill(result)
+ case _ =>
+ }
+
+ session.start(receiver => new Prover(receiver, session.xml_cache, channel, process))
+
+ def await_startup(): Isabelle_Process =
+ startup.join match {
+ case "" => this
+ case err => session.stop(); error(err)
+ }
+
+ def join(): Process_Result = terminated.join
+}
\ No newline at end of file
--- a/src/Pure/System/isabelle_tool.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/isabelle_tool.scala Thu Apr 02 13:04:24 2020 +0200
@@ -108,7 +108,7 @@
private def find_internal(name: String): Option[List[String] => Unit] =
internal_tools.collectFirst({
case tool if tool.name == name =>
- args => Command_Line.tool0 { tool.body(args) }
+ args => Command_Line.tool { tool.body(args) }
})
@@ -116,7 +116,7 @@
def main(args: Array[String])
{
- Command_Line.tool0 {
+ Command_Line.tool {
args.toList match {
case Nil | List("-?") =>
val tool_descriptions =
--- a/src/Pure/System/numa.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/numa.scala Thu Apr 02 13:04:24 2020 +0200
@@ -26,7 +26,7 @@
}
if (numa_nodes_linux.is_file) {
- space_explode(',', File.read(numa_nodes_linux).trim).flatMap(read(_))
+ space_explode(',', File.read(numa_nodes_linux).trim).flatMap(read)
}
else Nil
}
--- a/src/Pure/System/options.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/options.scala Thu Apr 02 13:04:24 2020 +0200
@@ -55,7 +55,7 @@
case word :: rest if word == strip => rest
case _ => words
}
- Word.implode(words1.map(Word.perhaps_capitalize(_)))
+ Word.implode(words1.map(Word.perhaps_capitalize))
}
def unknown: Boolean = typ == Unknown
@@ -70,19 +70,19 @@
private val OPTIONS = Path.explode("etc/options")
private val PREFS = Path.explode("$ISABELLE_HOME_USER/etc/preferences")
- val options_syntax =
+ val options_syntax: Outer_Syntax =
Outer_Syntax.empty + ":" + "=" + "--" + Symbol.comment + Symbol.comment_decoded +
(SECTION, Keyword.DOCUMENT_HEADING) +
(PUBLIC, Keyword.BEFORE_COMMAND) +
(OPTION, Keyword.THY_DECL)
- val prefs_syntax = Outer_Syntax.empty + "="
+ val prefs_syntax: Outer_Syntax = Outer_Syntax.empty + "="
trait Parser extends Parse.Parser
{
- val option_name = atom("option name", _.is_name)
- val option_type = atom("option type", _.is_name)
- val option_value =
+ val option_name: Parser[String] = atom("option name", _.is_name)
+ val option_type: Parser[String] = atom("option type", _.is_name)
+ val option_value: Parser[String] =
opt(token("-", tok => tok.is_sym_ident && tok.content == "-")) ~ atom("nat", _.is_nat) ^^
{ case s ~ n => if (s.isDefined) "-" + n else n } |
atom("option value", tok => tok.is_name || tok.is_float)
--- a/src/Pure/System/process_result.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/process_result.scala Thu Apr 02 13:04:24 2020 +0200
@@ -15,7 +15,11 @@
{
def out: String = cat_lines(out_lines)
def err: String = cat_lines(err_lines)
- def errors(errs: List[String]): Process_Result = copy(err_lines = err_lines ::: errs)
+
+ def output(outs: List[String]): Process_Result =
+ copy(out_lines = out_lines ::: outs.flatMap(split_lines))
+ def errors(errs: List[String]): Process_Result =
+ copy(err_lines = err_lines ::: errs.flatMap(split_lines))
def error(err: String): Process_Result = errors(List(err))
def was_timeout: Process_Result = copy(rc = 1, timeout = true)
--- a/src/Pure/System/progress.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/System/progress.scala Thu Apr 02 13:04:24 2020 +0200
@@ -34,7 +34,7 @@
def echo_error_message(msg: String) { echo(Output.error_message_text(msg)) }
def timeit[A](message: String = "", enabled: Boolean = true)(e: => A): A =
- Timing.timeit(message, enabled, echo(_))(e)
+ Timing.timeit(message, enabled, echo)(e)
def stopped: Boolean = false
def interrupt_handler[A](e: => A): A = e
--- a/src/Pure/Thy/export.ML Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Thy/export.ML Thu Apr 02 13:04:24 2020 +0200
@@ -83,7 +83,7 @@
let
val path = Path.expand (Path.explode ("$ISABELLE_EXPORT_TMP/export" ^ serial_string ()));
val _ = YXML.write_body path body;
- in Protocol_Message.inline (#2 function) (tl args @ [(Markup.fileN, Path.implode path)]) end
+ in Protocol_Message.marker (#2 function) (tl args @ [(Markup.fileN, Path.implode path)]) end
else raise Output.Protocol_Message props
| [] => raise Output.Protocol_Message props);
--- a/src/Pure/Thy/export.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Thy/export.scala Thu Apr 02 13:04:24 2020 +0200
@@ -143,7 +143,7 @@
regex.pattern.matcher(compound_name(theory_name, name)).matches
}
- def make_entry(session_name: String, args: Markup.Export.Args, body: Bytes,
+ def make_entry(session_name: String, args: Protocol.Export.Args, body: Bytes,
cache: XZ.Cache = XZ.cache()): Entry =
{
Entry(session_name, args.theory_name, args.name, args.executable,
@@ -213,7 +213,7 @@
(results, true)
})
- def apply(session_name: String, args: Markup.Export.Args, body: Bytes): Unit =
+ def apply(session_name: String, args: Protocol.Export.Args, body: Bytes): Unit =
consumer.send(make_entry(session_name, args, body, cache = cache) -> args.strict)
def shutdown(close: Boolean = false): List[String] =
@@ -312,7 +312,7 @@
// list
if (export_list) {
(for ((theory_name, name) <- export_names) yield compound_name(theory_name, name)).
- sorted.foreach(progress.echo(_))
+ sorted.foreach(progress.echo)
}
// export
@@ -348,7 +348,7 @@
/* Isabelle tool wrapper */
- val default_export_dir = Path.explode("export")
+ val default_export_dir: Path = Path.explode("export")
val isabelle_tool = Isabelle_Tool("export", "retrieve theory exports", args =>
{
--- a/src/Pure/Thy/export_theory.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Thy/export_theory.scala Thu Apr 02 13:04:24 2020 +0200
@@ -23,7 +23,7 @@
else None
def theories: List[Theory] =
- theory_graph.topological_order.flatMap(theory(_))
+ theory_graph.topological_order.flatMap(theory)
}
def read_session(
--- a/src/Pure/Thy/file_format.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Thy/file_format.scala Thu Apr 02 13:04:24 2020 +0200
@@ -56,7 +56,7 @@
trait File_Format
{
def format_name: String
- override def toString = format_name
+ override def toString: String = format_name
def file_ext: String
def detect(name: String): Boolean = name.endsWith("." + file_ext)
--- a/src/Pure/Thy/html.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Thy/html.scala Thu Apr 02 13:04:24 2020 +0200
@@ -368,7 +368,7 @@
(if (entry.is_italic) List(" font-style: italic;") else Nil) :::
List("}"))
- ("/* Isabelle fonts */" :: Isabelle_Fonts.fonts(hidden = true).map(font_face(_)))
+ ("/* Isabelle fonts */" :: Isabelle_Fonts.fonts(hidden = true).map(font_face))
.mkString("", "\n\n", "\n")
}
--- a/src/Pure/Thy/latex.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Thy/latex.scala Thu Apr 02 13:04:24 2020 +0200
@@ -10,6 +10,7 @@
import java.io.{File => JFile}
import scala.annotation.tailrec
+import scala.util.matching.Regex
object Latex
@@ -102,7 +103,7 @@
object File_Line_Error
{
- val Pattern = """^(.*?\.\w\w\w):(\d+): (.*)$""".r
+ val Pattern: Regex = """^(.*?\.\w\w\w):(\d+): (.*)$""".r
def unapply(line: String): Option[(Path, Int, String)] =
line match {
case Pattern(file, Value.Int(line), message) =>
--- a/src/Pure/Thy/present.ML Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Thy/present.ML Thu Apr 02 13:04:24 2020 +0200
@@ -10,7 +10,7 @@
val theory_qualifier: theory -> string
val document_option: Options.T -> {enabled: bool, disabled: bool}
val document_variants: Options.T -> (string * string) list
- val init: HTML.symbols -> bool -> bool -> Path.T -> string -> string -> (string * string) list ->
+ val init: HTML.symbols -> bool -> Path.T -> string -> string -> (string * string) list ->
(Path.T * Path.T) list -> Path.T -> string * string -> bool -> unit
val finish: unit -> unit
val theory_output: theory -> string list -> unit
@@ -165,28 +165,25 @@
(* init session *)
-fun init symbols build info info_path doc document_output doc_variants doc_files graph_file
+fun init symbols info info_path doc document_output doc_variants doc_files graph_file
(chapter, name) verbose =
- if not build andalso not info andalso doc = "" then
- (Synchronized.change browser_info (K empty_browser_info); session_info := NONE)
- else
- let
- val doc_output =
- if document_output = "" then NONE else SOME (Path.explode document_output);
+ let
+ val doc_output =
+ if document_output = "" then NONE else SOME (Path.explode document_output);
+
+ val documents = if doc = "" orelse null doc_files then [] else doc_variants;
+ val readme = if File.exists readme_html_path then SOME readme_html_path else NONE;
- val documents = if doc = "" orelse null doc_files then [] else doc_variants;
- val readme = if File.exists readme_html_path then SOME readme_html_path else NONE;
-
- val docs =
- (case readme of NONE => [] | SOME p => [(Url.File p, "README")]) @
- map (fn (name, _) => (Url.File (Path.ext doc (Path.basic name)), name)) documents;
- in
- session_info :=
- SOME (make_session_info (symbols, name, chapter, info_path, info, doc,
- doc_output, doc_files, graph_file, documents, verbose, readme));
- Synchronized.change browser_info (K empty_browser_info);
- add_html_index (0, HTML.begin_session_index symbols name (Url.File session_graph_path) docs)
- end;
+ val docs =
+ (case readme of NONE => [] | SOME p => [(Url.File p, "README")]) @
+ map (fn (name, _) => (Url.File (Path.ext doc (Path.basic name)), name)) documents;
+ in
+ session_info :=
+ SOME (make_session_info (symbols, name, chapter, info_path, info, doc,
+ doc_output, doc_files, graph_file, documents, verbose, readme));
+ Synchronized.change browser_info (K empty_browser_info);
+ add_html_index (0, HTML.begin_session_index symbols name (Url.File session_graph_path) docs)
+ end;
(* isabelle tool wrappers *)
--- a/src/Pure/Thy/sessions.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Thy/sessions.scala Thu Apr 02 13:04:24 2020 +0200
@@ -143,21 +143,19 @@
val doc_names = Doc.doc_names()
+ val bootstrap =
+ Sessions.Base.bootstrap(
+ sessions_structure.session_directories,
+ sessions_structure.global_theories)
+
val session_bases =
- (Map.empty[String, Base] /: sessions_structure.imports_topological_order)({
+ (Map("" -> bootstrap) /: sessions_structure.imports_topological_order)({
case (session_bases, session_name) =>
progress.expose_interrupt()
val info = sessions_structure(session_name)
try {
- val parent_base: Sessions.Base =
- info.parent match {
- case None =>
- Base.bootstrap(
- sessions_structure.session_directories,
- sessions_structure.global_theories)
- case Some(parent) => session_bases(parent)
- }
+ val parent_base = session_bases(info.parent.getOrElse(""))
val imports_base: Sessions.Base =
{
@@ -235,7 +233,7 @@
(Graph_Display.empty_graph /: required_subgraph.topological_order)(
{ case (g, session) =>
val a = session_node(session)
- val bs = required_subgraph.imm_preds(session).toList.map(session_node(_))
+ val bs = required_subgraph.imm_preds(session).toList.map(session_node)
((g /: (a :: bs))(_.default_node(_, Nil)) /: bs)(_.add_edge(_, a)) })
(graph0 /: dependencies.entries)(
@@ -271,7 +269,7 @@
if !ok(path.canonical_file)
path1 = File.relative_path(info.dir.canonical, path).getOrElse(path)
} yield (path1, name)).toList
- val bad_dirs = (for { (path1, _) <- bad } yield path1.toString).toSet.toList.sorted
+ val bad_dirs = (for { (path1, _) <- bad } yield path1.toString).distinct.sorted
val errs1 =
for { (path1, name) <- bad }
@@ -336,8 +334,6 @@
/* base info */
sealed case class Base_Info(
- options: Options,
- dirs: List[Path],
session: String,
sessions_structure: Structure,
errors: List[String],
@@ -371,7 +367,7 @@
deps.get(ancestor.get) match {
case Some(ancestor_base)
if !selected_sessions.imports_requirements(List(ancestor.get)).contains(session) =>
- ancestor_base.loaded_theories.defined(_)
+ ancestor_base.loaded_theories.defined _
case _ =>
error("Bad ancestor " + quote(ancestor.get) + " for session " + quote(session))
}
@@ -420,7 +416,7 @@
val deps1 = Sessions.deps(selected_sessions1, progress = progress)
- Base_Info(options, dirs, session1, full_sessions1, deps1.errors, deps1(session1), infos1)
+ Base_Info(session1, full_sessions1, deps1.errors, deps1(session1), infos1)
}
@@ -654,7 +650,7 @@
def check_sessions(names: List[String])
{
- val bad_sessions = SortedSet(names.filterNot(defined(_)): _*).toList
+ val bad_sessions = SortedSet(names.filterNot(defined): _*).toList
if (bad_sessions.nonEmpty)
error("Undefined session(s): " + commas_quote(bad_sessions))
}
@@ -746,8 +742,8 @@
/* parser */
- val ROOT = Path.explode("ROOT")
- val ROOTS = Path.explode("ROOTS")
+ val ROOT: Path = Path.explode("ROOT")
+ val ROOTS: Path = Path.explode("ROOTS")
private val CHAPTER = "chapter"
private val SESSION = "session"
@@ -761,7 +757,7 @@
private val DOCUMENT_FILES = "document_files"
private val EXPORT_FILES = "export_files"
- val root_syntax =
+ val root_syntax: Outer_Syntax =
Outer_Syntax.empty + "(" + ")" + "+" + "," + "=" + "[" + "]" +
GLOBAL + IN +
(CHAPTER, Keyword.THY_DECL) +
@@ -897,7 +893,7 @@
def directories(dirs: List[Path], select_dirs: List[Path]): List[(Boolean, Path)] =
{
- val default_dirs = Isabelle_System.components().filter(is_session_dir(_))
+ val default_dirs = Isabelle_System.components().filter(is_session_dir)
for { (select, dir) <- (default_dirs ::: dirs).map((false, _)) ::: select_dirs.map((true, _)) }
yield (select, dir.canonical)
}
@@ -1075,7 +1071,7 @@
input_dirs.map(_ + heap(name)).find(_.is_file)
def find_heap_digest(name: String): Option[String] =
- find_heap(name).flatMap(read_heap_digest(_))
+ find_heap(name).flatMap(read_heap_digest)
def the_heap(name: String): Path =
find_heap(name) getOrElse
@@ -1107,7 +1103,7 @@
if (output || has_session_info(db, name)) Some(db) else { db.close; None }
}
else if (output) Some(SQLite.open_database(output_database(name)))
- else input_dirs.map(_ + database(name)).find(_.is_file).map(SQLite.open_database(_))
+ else input_dirs.map(_ + database(name)).find(_.is_file).map(SQLite.open_database)
}
def open_database(name: String, output: Boolean = false): SQL.Database =
--- a/src/Pure/Thy/thy_syntax.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Thy/thy_syntax.scala Thu Apr 02 13:04:24 2020 +0200
@@ -136,7 +136,7 @@
val new_commands = insert_text(Some(cmd), text) - cmd
edit_text(rest.toList ::: es, new_commands)
- case Some((cmd, cmd_start)) =>
+ case Some((cmd, _)) =>
edit_text(es, insert_text(Some(cmd), e.text))
case None =>
--- a/src/Pure/Tools/build.ML Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/build.ML Thu Apr 02 13:04:24 2020 +0200
@@ -58,7 +58,7 @@
val timing_props =
[("threads", threads)] @ Markup.timing_properties timing @ [("factor", factor)];
- val _ = writeln ("\fTiming = " ^ YXML.string_of_body (XML.Encode.properties timing_props));
+ val _ = Protocol_Message.marker "Timing" timing_props;
val _ =
if verbose then
Output.physical_stderr ("Timing " ^ name ^ " (" ^
@@ -73,7 +73,7 @@
(case props of
function :: args =>
if function = Markup.ML_statistics orelse function = Markup.task_statistics then
- Protocol_Message.inline (#2 function) args
+ Protocol_Message.marker (#2 function) args
else if function = Markup.command_timing then
let
val name = the_default "" (Properties.get args Markup.nameN);
@@ -86,15 +86,16 @@
if is_significant then
(case approximative_id name pos of
SOME id =>
- Protocol_Message.inline (#2 function) (Markup.command_timing_properties id elapsed)
+ Protocol_Message.marker (#2 function)
+ (Markup.command_timing_properties id elapsed)
| NONE => ())
else ()
end
else if function = Markup.theory_timing then
- Protocol_Message.inline (#2 function) args
+ Protocol_Message.marker (#2 function) args
else
(case Markup.dest_loading_theory props of
- SOME name => writeln ("\floading_theory = " ^ name)
+ SOME name => Protocol_Message.marker_text "loading_theory" name
| NONE => Export.protocol_message props output)
| [] => raise Output.Protocol_Message props);
@@ -133,7 +134,6 @@
datatype args = Args of
{symbol_codes: (string * int) list,
command_timings: Properties.T list,
- do_output: bool,
verbose: bool,
browser_info: Path.T,
document_files: (Path.T * Path.T) list,
@@ -154,20 +154,20 @@
let
open XML.Decode;
val position = Position.of_properties o properties;
- val (symbol_codes, (command_timings, (do_output, (verbose, (browser_info,
+ val (symbol_codes, (command_timings, (verbose, (browser_info,
(document_files, (graph_file, (parent_name, (chapter, (name, (master_dir,
(theories, (session_positions, (session_directories, (doc_names, (global_theories,
- (loaded_theories, bibtex_entries))))))))))))))))) =
- pair (list (pair string int)) (pair (list properties) (pair bool (pair bool (pair string
+ (loaded_theories, bibtex_entries)))))))))))))))) =
+ pair (list (pair string int)) (pair (list properties) (pair bool (pair string
(pair (list (pair string string)) (pair string (pair string (pair string (pair string
(pair string
(pair (((list (pair Options.decode (list (pair string position))))))
(pair (list (pair string properties))
(pair (list (pair string string)) (pair (list string)
- (pair (list (pair string string)) (pair (list string) (list string)))))))))))))))))
+ (pair (list (pair string string)) (pair (list string) (list string))))))))))))))))
(YXML.parse_body yxml);
in
- Args {symbol_codes = symbol_codes, command_timings = command_timings, do_output = do_output,
+ Args {symbol_codes = symbol_codes, command_timings = command_timings,
verbose = verbose, browser_info = Path.explode browser_info,
document_files = map (apply2 Path.explode) document_files,
graph_file = Path.explode graph_file, parent_name = parent_name, chapter = chapter,
@@ -177,7 +177,7 @@
bibtex_entries = bibtex_entries}
end;
-fun build_session (Args {symbol_codes, command_timings, do_output, verbose, browser_info,
+fun build_session (Args {symbol_codes, command_timings, verbose, browser_info,
document_files, graph_file, parent_name, chapter, name, master_dir, theories, session_positions,
session_directories, doc_names, global_theories, loaded_theories, bibtex_entries}) =
let
@@ -194,7 +194,6 @@
val _ =
Session.init
symbols
- do_output
(Options.default_bool "browser_info")
browser_info
(Options.default_string "document")
@@ -217,34 +216,51 @@
val _ = Resources.finish_session_base ();
val _ = Par_Exn.release_all [res1, res2];
+ val _ =
+ if name = Context.PureN then Theory.install_pure (Thy_Info.get_theory Context.PureN) else ();
in () end;
-(*command-line tool*)
+
+(* command-line tool *)
+
+fun inline_errors exn =
+ Runtime.exn_message_list exn
+ |> List.app (fn msg => Protocol_Message.marker_text "error_message" (YXML.content_of msg));
+
fun build args_file =
let
val _ = SHA1.test_samples ();
val _ = Options.load_default ();
val _ = Isabelle_Process.init_options ();
val args = decode_args (File.read (Path.explode args_file));
- fun error_message msg = writeln ("\ferror_message = " ^ encode_lines (YXML.content_of msg));
val _ =
Unsynchronized.setmp Private_Output.protocol_message_fn protocol_message
build_session args
- handle exn => (List.app error_message (Runtime.exn_message_list exn); Exn.reraise exn);
+ handle exn => (inline_errors exn; Exn.reraise exn);
val _ = Private_Output.protocol_message_fn := Output.protocol_message_undefined;
val _ = Options.reset_default ();
in () end;
-(*PIDE version*)
+
+(* PIDE version *)
+
+fun build_session_finished errs =
+ XML.Encode.list XML.Encode.string errs
+ |> Output.protocol_message Markup.build_session_finished;
+
val _ =
Isabelle_Process.protocol_command "build_session"
(fn [args_yxml] =>
let
val args = decode_args args_yxml;
- val result = (build_session args; "") handle exn =>
- (Runtime.exn_message exn handle _ (*sic!*) =>
- "Exception raised, but failed to print details!");
- in Output.protocol_message Markup.build_session_finished [XML.Text result] end
+ val errs =
+ Future.interruptible_task (fn () =>
+ (build_session args; []) handle exn =>
+ (Runtime.exn_message_list exn handle _ (*sic!*) =>
+ (build_session_finished ["CRASHED"];
+ raise Isabelle_Process.EXIT 1))) ();
+ val _ = build_session_finished errs;
+ in if null errs then () else raise Isabelle_Process.EXIT 1 end
| _ => raise Match);
end;
--- a/src/Pure/Tools/build.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/build.scala Thu Apr 02 13:04:24 2020 +0200
@@ -8,7 +8,7 @@
package isabelle
-import scala.collection.SortedSet
+import scala.collection.{SortedSet, mutable}
import scala.annotation.tailrec
@@ -153,16 +153,19 @@
class Handler(progress: Progress, session: Session, session_name: String)
extends Session.Protocol_Handler
{
- val result_error: Promise[String] = Future.promise
+ val build_session_errors: Promise[List[String]] = Future.promise
- override def exit() { result_error.cancel }
+ override def exit() { build_session_errors.cancel }
private def build_session_finished(msg: Prover.Protocol_Output): Boolean =
{
- val error_message =
- try { Pretty.string_of(Symbol.decode_yxml(msg.text)) }
- catch { case ERROR(msg) => msg }
- result_error.fulfill(error_message)
+ val errors =
+ try {
+ for (err <- XML.Decode.list(x => x)(Symbol.decode_yxml(msg.text))) yield
+ Pretty.string_of(Protocol_Message.expose_no_reports(err), metric = Symbol.Metric)
+ }
+ catch { case ERROR(err) => List(err) }
+ build_session_errors.fulfill(errors)
session.send_stop()
true
}
@@ -177,8 +180,8 @@
val functions =
List(
- Markup.BUILD_SESSION_FINISHED -> build_session_finished _,
- Markup.LOADING_THEORY -> loading_theory _)
+ Markup.BUILD_SESSION_FINISHED -> build_session_finished,
+ Markup.LOADING_THEORY -> loading_theory)
}
@@ -189,15 +192,14 @@
val info: Sessions.Info,
deps: Sessions.Deps,
store: Sessions.Store,
- do_output: Boolean,
+ do_store: Boolean,
verbose: Boolean,
- pide: Boolean,
val numa_node: Option[Int],
command_timings: List[Properties.T])
{
- val options = NUMA.policy_options(info.options, numa_node)
+ private val options = NUMA.policy_options(info.options, numa_node)
- val sessions_structure = deps.sessions_structure
+ private val sessions_structure = deps.sessions_structure
private val graph_file = Isabelle_System.tmp_file("session_graph", "pdf")
isabelle.graphview.Graph_File.write(options, graph_file, deps(name).session_graph_display)
@@ -209,27 +211,27 @@
private val future_result: Future[Process_Result] =
Future.thread("build") {
val parent = info.parent.getOrElse("")
- val base = deps(name)
+ val base = deps(parent)
val args_yxml =
YXML.string_of_body(
{
import XML.Encode._
- pair(list(pair(string, int)), pair(list(properties), pair(bool, pair(bool,
+ pair(list(pair(string, int)), pair(list(properties), pair(bool,
pair(Path.encode, pair(list(pair(Path.encode, Path.encode)), pair(string,
pair(string, pair(string, pair(string, pair(Path.encode,
pair(list(pair(Options.encode, list(pair(string, properties)))),
pair(list(pair(string, properties)),
pair(list(pair(string, string)),
pair(list(string), pair(list(pair(string, string)),
- pair(list(string), list(string))))))))))))))))))(
- (Symbol.codes, (command_timings, (do_output, (verbose,
+ pair(list(string), list(string)))))))))))))))))(
+ (Symbol.codes, (command_timings, (verbose,
(store.browser_info, (info.document_files, (File.standard_path(graph_file),
(parent, (info.chapter, (name, (Path.current,
(info.theories,
(sessions_structure.session_positions,
(sessions_structure.dest_session_directories,
(base.doc_names, (base.global_theories.toList,
- (base.loaded_theories.keys, info.bibtex_entries.map(_.info)))))))))))))))))))
+ (base.loaded_theories.keys, info.bibtex_entries.map(_.info))))))))))))))))))
})
val env =
@@ -237,82 +239,111 @@
("ISABELLE_EXPORT_TMP" -> File.standard_path(export_tmp_dir)) +
("ISABELLE_ML_DEBUGGER" -> options.bool("ML_debugger").toString)
- def save_heap: String =
- (if (info.theories.isEmpty) "" else "ML_Heap.share_common_data (); ") +
- "ML_Heap.save_child " +
- ML_Syntax.print_string_bytes(File.platform_path(store.output_heap(name)))
+ val is_pure = Sessions.is_pure(name)
+
+ val use_prelude = if (is_pure) Thy_Header.ml_roots.map(_._1) else Nil
- if (pide && !Sessions.is_pure(name)) {
+ val eval_store =
+ if (do_store) {
+ (if (info.theories.nonEmpty) List("ML_Heap.share_common_data ()") else Nil) :::
+ List("ML_Heap.save_child " +
+ ML_Syntax.print_string_bytes(File.platform_path(store.output_heap(name))))
+ }
+ else Nil
+
+ if (options.bool("pide_build")) {
val resources = new Resources(sessions_structure, deps(parent))
val session = new Session(options, resources)
val handler = new Handler(progress, session, name)
session.init_protocol_handler(handler)
- val session_result = Future.promise[Process_Result]
+ val stdout = new StringBuilder(1000)
+ val messages = new mutable.ListBuffer[String]
+ val command_timings = new mutable.ListBuffer[Properties.T]
+ val theory_timings = new mutable.ListBuffer[Properties.T]
+ val runtime_statistics = new mutable.ListBuffer[Properties.T]
+ val task_statistics = new mutable.ListBuffer[Properties.T]
- Isabelle_Process.start(session, options, logic = parent, cwd = info.dir.file, env = env,
- sessions_structure = Some(sessions_structure), store = Some(store),
- phase_changed =
- {
- case Session.Ready => session.protocol_command("build_session", args_yxml)
- case Session.Terminated(result) => session_result.fulfill(result)
+ val consumer =
+ Session.Consumer[Any]("build_session_output") {
+ case msg: Prover.Output =>
+ val message = msg.message
+ if (msg.is_stdout) {
+ stdout ++= Symbol.encode(XML.content(message))
+ }
+ else if (Protocol.is_exported(message)) {
+ messages +=
+ Symbol.encode(Protocol.message_text(List(message), metric = Symbol.Metric))
+ }
+ case Session.Command_Timing(props) => command_timings += props
+ case Session.Theory_Timing(props) => theory_timings += props
+ case Session.Runtime_Statistics(props) => runtime_statistics += props
+ case Session.Task_Statistics(props) => task_statistics += props
case _ =>
- })
+ }
+
+ session.all_messages += consumer
+ session.command_timings += consumer
+ session.theory_timings += consumer
+ session.runtime_statistics += consumer
+ session.task_statistics += consumer
+
+ val eval_main = Command_Line.ML_tool("Isabelle_Process.init_build ()" :: eval_store)
+
+ val process =
+ Isabelle_Process(session, options, sessions_structure, store,
+ logic = parent, raw_ml_system = is_pure,
+ use_prelude = use_prelude, eval_main = eval_main,
+ cwd = info.dir.file, env = env).await_startup
- val result = session_result.join
- handler.result_error.join match {
- case "" => result
- case msg =>
- result.copy(
- rc = result.rc max 1,
- out_lines = result.out_lines ::: split_lines(Output.error_message_text(msg)))
+ session.protocol_command("build_session", args_yxml)
+
+ val process_result = process.join
+ val process_output =
+ stdout.toString :: messages.toList :::
+ command_timings.toList.map(Protocol.Command_Timing_Marker.apply) :::
+ theory_timings.toList.map(Protocol.Theory_Timing_Marker.apply) :::
+ runtime_statistics.toList.map(Protocol.ML_Statistics_Marker.apply) :::
+ task_statistics.toList.map(Protocol.Task_Statistics_Marker.apply)
+
+ val result = process_result.output(process_output)
+ handler.build_session_errors.join match {
+ case Nil => result
+ case errors =>
+ result.error_rc.output(
+ errors.flatMap(s => split_lines(Output.error_message_text(s))) :::
+ errors.map(Protocol.Error_Message_Marker.apply))
}
}
else {
val args_file = Isabelle_System.tmp_file("build")
File.write(args_file, args_yxml)
- val eval =
- "Command_Line.tool0 (fn () => (" +
- "Build.build " + ML_Syntax.print_string_bytes(File.standard_path(args_file)) +
- (if (Sessions.is_pure(name)) "; Theory.install_pure (Thy_Info.get_theory Context.PureN)"
- else "") + (if (do_output) "; " + save_heap else "") + "));"
+ val eval_build =
+ "Build.build " + ML_Syntax.print_string_bytes(File.standard_path(args_file))
+ val eval_main = Command_Line.ML_tool(eval_build :: eval_store)
val process =
- if (Sessions.is_pure(name)) {
- ML_Process(options, raw_ml_system = true, cwd = info.dir.file,
- args =
- (for ((root, _) <- Thy_Header.ml_roots) yield List("--use", root)).flatten :::
- List("--eval", eval),
- env = env, sessions_structure = Some(deps.sessions_structure), store = Some(store),
- cleanup = () => args_file.delete)
- }
- else {
- ML_Process(options, parent, List("--eval", eval), cwd = info.dir.file,
- env = env, sessions_structure = Some(deps.sessions_structure), store = Some(store),
- cleanup = () => args_file.delete)
- }
+ ML_Process(options, deps.sessions_structure, store,
+ logic = parent, raw_ml_system = is_pure,
+ use_prelude = use_prelude, eval_main = eval_main,
+ cwd = info.dir.file, env = env, cleanup = () => args_file.delete)
process.result(
- progress_stdout = (line: String) =>
- Library.try_unprefix("\floading_theory = ", line) match {
- case Some(theory) =>
+ progress_stdout =
+ {
+ case Protocol.Loading_Theory_Marker(theory) =>
progress.theory(Progress.Theory(theory, session = name))
- case None =>
- for {
- text <- Library.try_unprefix("\fexport = ", line)
- (args, path) <-
- Markup.Export.dest_inline(XML.Decode.properties(YXML.parse_body(text)))
- } {
- val body =
- try { Bytes.read(path) }
- catch {
- case ERROR(msg) =>
- error("Failed to read export " + quote(args.compound_name) + "\n" + msg)
- }
- path.file.delete
- export_consumer(name, args, body)
- }
+ case Protocol.Export.Marker((args, path)) =>
+ val body =
+ try { Bytes.read(path) }
+ catch {
+ case ERROR(msg) =>
+ error("Failed to read export " + quote(args.compound_name) + "\n" + msg)
+ }
+ path.file.delete
+ export_consumer(name, args, body)
+ case _ =>
},
progress_limit =
options.int("process_output_limit") match {
@@ -337,7 +368,7 @@
{
val result0 = future_result.join
val result1 =
- export_consumer.shutdown(close = true).map(Output.error_message_text(_)) match {
+ export_consumer.shutdown(close = true).map(Output.error_message_text) match {
case Nil => result0
case errs => result0.errors(errs).error_rc
}
@@ -363,7 +394,7 @@
else result1
val heap_digest =
- if (result2.ok && do_output && store.output_heap(name).is_file)
+ if (result2.ok && do_store && store.output_heap(name).is_file)
Some(Sessions.write_heap_digest(store.output_heap(name)))
else None
@@ -381,7 +412,7 @@
def cancelled(name: String): Boolean = results(name)._1.isEmpty
def apply(name: String): Process_Result = results(name)._1.getOrElse(Process_Result(1))
def info(name: String): Sessions.Info = results(name)._2
- val rc =
+ val rc: Int =
(0 /: results.iterator.map(
{ case (_, (Some(r), _)) => r.rc case (_, (None, _)) => 1 }))(_ max _)
def ok: Boolean = rc == 0
@@ -407,7 +438,6 @@
soft_build: Boolean = false,
verbose: Boolean = false,
export_files: Boolean = false,
- pide: Boolean = false,
requirements: Boolean = false,
all_sessions: Boolean = false,
base_sessions: List[String] = Nil,
@@ -544,7 +574,7 @@
val (process_result, heap_digest) = job.join
- val log_lines = process_result.out_lines.filterNot(_.startsWith("\f"))
+ val log_lines = process_result.out_lines.filterNot(Protocol_Message.Marker.test)
val process_result_tail =
{
val tail = job.info.options.int("process_output_tail")
@@ -581,7 +611,7 @@
}
// messages
- process_result.err_lines.foreach(progress.echo(_))
+ process_result.err_lines.foreach(progress.echo)
if (process_result.ok)
progress.echo("Finished " + name + " (" + process_result.timing.message_resources + ")")
@@ -595,14 +625,14 @@
//}}}
case None if running.size < (max_jobs max 1) =>
//{{{ check/start next job
- pending.dequeue(running.isDefinedAt(_)) match {
+ pending.dequeue(running.isDefinedAt) match {
case Some((name, info)) =>
val ancestor_results =
deps.sessions_structure.build_requirements(List(name)).filterNot(_ == name).
map(results(_))
val ancestor_heaps = ancestor_results.flatMap(_.heap_digest)
- val do_output = build_heap || Sessions.is_pure(name) || queue.is_inner(name)
+ val do_store = build_heap || Sessions.is_pure(name) || queue.is_inner(name)
val (current, heap_digest) =
{
@@ -617,7 +647,7 @@
build.sources == sources_stamp(deps, name) &&
build.input_heaps == ancestor_heaps &&
build.output_heap == heap_digest &&
- !(do_output && heap_digest.isEmpty)
+ !(do_store && heap_digest.isEmpty)
(current, heap_digest)
case None => (false, None)
}
@@ -635,14 +665,14 @@
results + (name -> Result(false, heap_digest, Some(Process_Result(1)), info)))
}
else if (ancestor_results.forall(_.ok) && !progress.stopped) {
- progress.echo((if (do_output) "Building " else "Running ") + name + " ...")
+ progress.echo((if (do_store) "Building " else "Running ") + name + " ...")
store.clean_output(name)
using(store.open_database(name, output = true))(store.init_session_info(_, name))
- val numa_node = numa_nodes.next(used_node(_))
+ val numa_node = numa_nodes.next(used_node)
val job =
- new Job(progress, name, info, deps, store, do_output, verbose, pide = pide,
+ new Job(progress, name, info, deps, store, do_store, verbose,
numa_node, queue.command_timings(name))
loop(pending, running + (name -> (ancestor_heaps, job)), results)
}
@@ -730,7 +760,6 @@
var base_sessions: List[String] = Nil
var select_dirs: List[Path] = Nil
var numa_shuffling = false
- var pide = false
var requirements = false
var soft_build = false
var exclude_session_groups: List[String] = Nil
@@ -756,7 +785,6 @@
-B NAME include session NAME and all descendants
-D DIR include session directory and select its sessions
-N cyclic shuffling of NUMA CPU nodes (performance tuning)
- -P build via PIDE protocol
-R operate on requirements of selected sessions
-S soft build: only observe changes of sources, not heap images
-X NAME exclude sessions from group NAME and all descendants
@@ -781,7 +809,6 @@
"B:" -> (arg => base_sessions = base_sessions ::: List(arg)),
"D:" -> (arg => select_dirs = select_dirs ::: List(Path.explode(arg))),
"N" -> (_ => numa_shuffling = true),
- "P" -> (_ => pide = true),
"R" -> (_ => requirements = true),
"S" -> (_ => soft_build = true),
"X:" -> (arg => exclude_session_groups = exclude_session_groups ::: List(arg)),
@@ -831,7 +858,6 @@
soft_build = soft_build,
verbose = verbose,
export_files = export_files,
- pide = pide,
requirements = requirements,
all_sessions = all_sessions,
base_sessions = base_sessions,
--- a/src/Pure/Tools/debugger.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/debugger.scala Thu Apr 02 13:04:24 2020 +0200
@@ -23,7 +23,7 @@
{
def size: Int = debug_states.length + 1
def reset: Context = copy(index = 0)
- def select(i: Int) = copy(index = i + 1)
+ def select(i: Int): Context = copy(index = i + 1)
def thread_state: Option[Debug_State] = debug_states.headOption
@@ -143,8 +143,8 @@
val functions =
List(
- Markup.DEBUGGER_STATE -> debugger_state _,
- Markup.DEBUGGER_OUTPUT -> debugger_output _)
+ Markup.DEBUGGER_STATE -> debugger_state,
+ Markup.DEBUGGER_OUTPUT -> debugger_output)
}
}
--- a/src/Pure/Tools/doc.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/doc.scala Thu Apr 02 13:04:24 2020 +0200
@@ -46,7 +46,7 @@
private def release_notes(): List[Entry] =
Section("Release Notes", true) ::
- Path.split(Isabelle_System.getenv_strict("ISABELLE_DOCS_RELEASE_NOTES")).flatMap(text_file(_))
+ Path.split(Isabelle_System.getenv_strict("ISABELLE_DOCS_RELEASE_NOTES")).flatMap(text_file)
private def examples(): List[Entry] =
Section("Examples", true) ::
--- a/src/Pure/Tools/dump.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/dump.scala Thu Apr 02 13:04:24 2020 +0200
@@ -363,7 +363,7 @@
session.use_theories(used_theories.map(_.theory),
unicode_symbols = unicode_symbols,
progress = progress,
- commit = Some(Consumer.apply _))
+ commit = Some(Consumer.apply))
val bad_theories = Consumer.shutdown()
val bad_msgs =
@@ -463,7 +463,7 @@
Dump cumulative PIDE session database, with the following aspects:
""" + Library.prefix_lines(" ", show_aspects) + "\n",
- "A:" -> (arg => aspects = Library.distinct(space_explode(',', arg)).map(the_aspect(_))),
+ "A:" -> (arg => aspects = Library.distinct(space_explode(',', arg)).map(the_aspect)),
"B:" -> (arg => base_sessions = base_sessions ::: List(arg)),
"D:" -> (arg => select_dirs = select_dirs ::: List(Path.explode(arg))),
"O:" -> (arg => output_dir = Path.explode(arg)),
--- a/src/Pure/Tools/fontforge.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/fontforge.scala Thu Apr 02 13:04:24 2020 +0200
@@ -38,7 +38,7 @@
}
if (s.nonEmpty && s(0) == '\\') err('\\')
- s.iterator.map(escape(_)).mkString(q.toString, "", q.toString)
+ s.iterator.map(escape).mkString(q.toString, "", q.toString)
}
def file_name(path: Path): Script = string(File.standard_path(path))
@@ -121,7 +121,7 @@
}
def set: Script =
- List(fontname, familyname, fullname, weight, copyright, fontversion).map(string(_)).
+ List(fontname, familyname, fullname, weight, copyright, fontversion).map(string).
mkString("SetFontNames(", ",", ")")
}
--- a/src/Pure/Tools/phabricator.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/phabricator.scala Thu Apr 02 13:04:24 2020 +0200
@@ -39,7 +39,7 @@
val daemon_user = "phabricator"
- val sshd_config = Path.explode("/etc/ssh/sshd_config")
+ val sshd_config: Path = Path.explode("/etc/ssh/sshd_config")
/* installation parameters */
@@ -59,7 +59,7 @@
val default_mailers: Path = Path.explode("mailers.json")
- val default_system_port = SSH.default_port
+ val default_system_port: Int = SSH.default_port
val alternative_system_port = 222
val default_server_port = 2222
@@ -69,7 +69,7 @@
/** global configuration **/
- val global_config = Path.explode("/etc/" + isabelle_phabricator_name(ext = "conf"))
+ val global_config: Path = Path.explode("/etc/" + isabelle_phabricator_name(ext = "conf"))
def global_config_script(
init: String = "",
--- a/src/Pure/Tools/print_operation.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/print_operation.scala Thu Apr 02 13:04:24 2020 +0200
@@ -38,6 +38,6 @@
true
}
- val functions = List(Markup.PRINT_OPERATIONS -> put _)
+ val functions = List(Markup.PRINT_OPERATIONS -> put)
}
}
--- a/src/Pure/Tools/profiling_report.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/profiling_report.scala Thu Apr 02 13:04:24 2020 +0200
@@ -32,7 +32,7 @@
val isabelle_tool =
Isabelle_Tool("profiling_report", "report Poly/ML profiling information from log files", args =>
{
- Command_Line.tool0 {
+ Command_Line.tool {
val getopts =
Getopts("""
Usage: isabelle profiling_report [LOGS ...]
--- a/src/Pure/Tools/server.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/server.scala Thu Apr 02 13:04:24 2020 +0200
@@ -35,8 +35,8 @@
def split(msg: String): (String, String) =
{
- val name = msg.takeWhile(is_name_char(_))
- val argument = msg.substring(name.length).dropWhile(Symbol.is_ascii_blank(_))
+ val name = msg.takeWhile(is_name_char)
+ val argument = msg.substring(name.length).dropWhile(Symbol.is_ascii_blank)
(name, argument)
}
@@ -607,7 +607,7 @@
Exn.capture(server_socket.accept) match {
case Exn.Res(socket) =>
Standard_Thread.fork("server_connection")
- { using(Server.Connection(socket))(handle(_)) }
+ { using(Server.Connection(socket))(handle) }
case Exn.Exn(_) => finished = true
}
}
--- a/src/Pure/Tools/server_commands.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/server_commands.scala Thu Apr 02 13:04:24 2020 +0200
@@ -46,10 +46,10 @@
}
def command(args: Args, progress: Progress = No_Progress)
- : (JSON.Object.T, Build.Results, Sessions.Base_Info) =
+ : (JSON.Object.T, Build.Results, Options, Sessions.Base_Info) =
{
val options = Options.init(prefs = args.preferences, opts = args.options)
- val dirs = args.dirs.map(Path.explode(_))
+ val dirs = args.dirs.map(Path.explode)
val base_info =
Sessions.base_info(options, args.session, progress = progress, dirs = dirs,
@@ -85,7 +85,7 @@
"timing" -> result.timing.json)
}))
- if (results.ok) (results_json, results, base_info)
+ if (results.ok) (results_json, results, options, base_info)
else throw new Server.Error("Session build failed: return code " + results.rc, results_json)
}
}
@@ -106,11 +106,11 @@
def command(args: Args, progress: Progress = No_Progress, log: Logger = No_Logger)
: (JSON.Object.T, (UUID.T, Headless.Session)) =
{
- val base_info =
- try { Session_Build.command(args.build, progress = progress)._3 }
+ val (_, _, options, base_info) =
+ try { Session_Build.command(args.build, progress = progress) }
catch { case exn: Server.Error => error(exn.message) }
- val resources = Headless.Resources(base_info, log = log)
+ val resources = Headless.Resources(options, base_info, log = log)
val session = resources.start_session(print_mode = args.print_mode, progress = progress)
--- a/src/Pure/Tools/simplifier_trace.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/simplifier_trace.scala Thu Apr 02 13:04:24 2020 +0200
@@ -123,22 +123,22 @@
def handle_results(session: Session, id: Document_ID.Command, results: Command.Results): Context =
{
val slot = Future.promise[Context]
- manager.send(Handle_Results(session, id, results, slot))
+ the_manager(session).send(Handle_Results(session, id, results, slot))
slot.join
}
- def generate_trace(results: Command.Results): Trace =
+ def generate_trace(session: Session, results: Command.Results): Trace =
{
val slot = Future.promise[Trace]
- manager.send(Generate_Trace(results, slot))
+ the_manager(session).send(Generate_Trace(results, slot))
slot.join
}
- def clear_memory() =
- manager.send(Clear_Memory)
+ def clear_memory(session: Session): Unit =
+ the_manager(session).send(Clear_Memory)
- def send_reply(session: Session, serial: Long, answer: Answer) =
- manager.send(Reply(session, serial, answer))
+ def send_reply(session: Session, serial: Long, answer: Answer): Unit =
+ the_manager(session).send(Reply(session, serial, answer))
def make_manager: Consumer_Thread[Any] =
{
@@ -283,10 +283,10 @@
)
}
- private val manager_variable = Synchronized[Option[Consumer_Thread[Any]]](None)
+ private val managers = Synchronized(Map.empty[Session, Consumer_Thread[Any]])
- def manager: Consumer_Thread[Any] =
- manager_variable.value match {
+ def the_manager(session: Session): Consumer_Thread[Any] =
+ managers.value.get(session) match {
case Some(thread) if thread.is_active => thread
case _ => error("Bad Simplifier_Trace.manager thread")
}
@@ -296,25 +296,36 @@
class Handler extends Session.Protocol_Handler
{
- try { manager }
- catch { case ERROR(_) => manager_variable.change(_ => Some(make_manager)) }
+ private var the_session: Session = null
+
+ override def init(session: Session)
+ {
+ try { the_manager(session) }
+ catch { case ERROR(_) => managers.change(map => map + (session -> make_manager)) }
+ the_session = session
+ }
- override def exit() =
+ override def exit()
{
- manager.send(Clear_Memory)
- manager.shutdown()
- manager_variable.change(_ => None)
+ val session = the_session
+ if (session != null) {
+ val manager = the_manager(session)
+ manager.send(Clear_Memory)
+ manager.shutdown()
+ managers.change(map => map - session)
+ the_session = null
+ }
}
private def cancel(msg: Prover.Protocol_Output): Boolean =
msg.properties match {
case Markup.Simp_Trace_Cancel(serial) =>
- manager.send(Cancel(serial))
+ the_manager(the_session).send(Cancel(serial))
true
case _ =>
false
}
- val functions = List(Markup.SIMP_TRACE_CANCEL -> cancel _)
+ val functions = List(Markup.SIMP_TRACE_CANCEL -> cancel)
}
}
--- a/src/Pure/Tools/spell_checker.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/spell_checker.scala Thu Apr 02 13:04:24 2020 +0200
@@ -66,8 +66,8 @@
class Dictionary private[Spell_Checker](val path: Path)
{
- val lang = path.drop_ext.file_name
- val user_path = Path.explode("$ISABELLE_HOME_USER/dictionaries") + Path.basic(lang)
+ val lang: String = path.drop_ext.file_name
+ val user_path: Path = Path.explode("$ISABELLE_HOME_USER/dictionaries") + Path.basic(lang)
override def toString: String = lang
}
--- a/src/Pure/Tools/update_cartouches.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/Tools/update_cartouches.scala Thu Apr 02 13:04:24 2020 +0200
@@ -7,13 +7,16 @@
package isabelle
+import scala.util.matching.Regex
+
+
object Update_Cartouches
{
/* update cartouches */
private val Verbatim_Body = """(?s)[ \t]*(.*?)[ \t]*""".r
- val Text_Antiq = """(?s)@\{\s*text\b\s*(.+)\}""".r
+ val Text_Antiq: Regex = """(?s)@\{\s*text\b\s*(.+)\}""".r
def update_text(content: String): String =
{
--- a/src/Pure/library.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/library.scala Thu Apr 02 13:04:24 2020 +0200
@@ -140,7 +140,7 @@
else s
def trim_split_lines(s: String): List[String] =
- split_lines(trim_line(s)).map(trim_line(_))
+ split_lines(trim_line(s)).map(trim_line)
def isolate_substring(s: String): String = new String(s.toCharArray)
@@ -204,7 +204,7 @@
def is_regex_meta(c: Char): Boolean = """()[]{}\^$|?*+.<>-=!""".contains(c)
def escape_regex(s: String): String =
- if (s.exists(is_regex_meta(_))) {
+ if (s.exists(is_regex_meta)) {
(for (c <- s.iterator)
yield { if (is_regex_meta(c)) "\\" + c.toString else c.toString }).mkString
}
--- a/src/Pure/term.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Pure/term.scala Thu Apr 02 13:04:24 2020 +0200
@@ -50,7 +50,7 @@
override def toString: String =
"TVar(" + name + (if (sort.isEmpty) "" else "," + sort) + ")"
}
- val dummyT = Type("dummy")
+ val dummyT: Type = Type("dummy")
sealed abstract class Term
{
@@ -143,7 +143,7 @@
lookup(x) getOrElse store(Indexname(cache_string(x.name), x.index))
protected def cache_sort(x: Sort): Sort =
- if (x.isEmpty) Nil else lookup(x) getOrElse store(x.map(cache_string(_)))
+ if (x.isEmpty) Nil else lookup(x) getOrElse store(x.map(cache_string))
protected def cache_typ(x: Typ): Typ =
{
@@ -166,7 +166,7 @@
else {
lookup(x) match {
case Some(y) => y
- case None => store(x.map(cache_typ(_)))
+ case None => store(x.map(cache_typ))
}
}
}
--- a/src/Tools/Graphview/graph_file.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/Graphview/graph_file.scala Thu Apr 02 13:04:24 2020 +0200
@@ -30,8 +30,8 @@
}
val name = file.getName
- if (name.endsWith(".png")) Graphics_File.write_png(file, paint _, w, h)
- else if (name.endsWith(".pdf")) Graphics_File.write_pdf(file, paint _, w, h)
+ if (name.endsWith(".png")) Graphics_File.write_png(file, paint, w, h)
+ else if (name.endsWith(".pdf")) Graphics_File.write_pdf(file, paint, w, h)
else error("Bad type of file: " + quote(name) + " (.png or .pdf expected)")
}
--- a/src/Tools/Graphview/graphview.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/Graphview/graphview.scala Thu Apr 02 13:04:24 2020 +0200
@@ -82,7 +82,7 @@
}
else node.toString
- _layout = Layout.make(options, metrics, node_text _, visible_graph)
+ _layout = Layout.make(options, metrics, node_text, visible_graph)
}
--- a/src/Tools/Graphview/layout.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/Graphview/layout.scala Thu Apr 02 13:04:24 2020 +0200
@@ -104,7 +104,7 @@
val lines = split_lines(node_text(a, content))
val w2 = metrics.node_width2(lines)
val h2 = metrics.node_height2(lines.length)
- ((Node(a), Info(0.0, 0.0, w2, h2, lines)), bs.toList.map(Node(_)))
+ ((Node(a), Info(0.0, 0.0, w2, h2, lines)), bs.toList.map(Node))
}).toList)
val initial_levels: Levels =
--- a/src/Tools/Graphview/model.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/Graphview/model.scala Thu Apr 02 13:04:24 2020 +0200
@@ -18,7 +18,7 @@
val events = new Mutator_Event.Bus
private var _mutators : List[Mutator.Info] = Nil
- def apply() = _mutators
+ def apply(): List[Mutator.Info] = _mutators
def apply(mutators: List[Mutator.Info])
{
_mutators = mutators
--- a/src/Tools/Graphview/mutator.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/Graphview/mutator.scala Thu Apr 02 13:04:24 2020 +0200
@@ -173,6 +173,6 @@
trait Filter extends Mutator
{
- def mutate(full_graph: Graph_Display.Graph, graph: Graph_Display.Graph) = filter(graph)
+ def mutate(full_graph: Graph_Display.Graph, graph: Graph_Display.Graph): Graph_Display.Graph = filter(graph)
def filter(graph: Graph_Display.Graph): Graph_Display.Graph
}
--- a/src/Tools/Graphview/mutator_dialog.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/Graphview/mutator_dialog.scala Thu Apr 02 13:04:24 2020 +0200
@@ -110,7 +110,7 @@
filter_panel.repaint
}
- val filter_panel = new BoxPanel(Orientation.Vertical) {}
+ val filter_panel: BoxPanel = new BoxPanel(Orientation.Vertical) {}
private val mutator_box = new ComboBox[Mutator](container.available)
--- a/src/Tools/VSCode/extension/README.md Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/VSCode/extension/README.md Thu Apr 02 13:04:24 2020 +0200
@@ -1,15 +1,14 @@
# Isabelle Prover IDE support
This extension connects VSCode to the Isabelle Prover IDE infrastructure: it
-requires Isabelle2020.
+requires a repository version of Isabelle.
The implementation is centered around the VSCode Language Server protocol, but
with many add-ons that are specific to VSCode and Isabelle/PIDE.
See also:
- * <https://isabelle.in.tum.de/website-Isabelle2020>
- * <https://isabelle.in.tum.de/repos/isabelle/file/Isabelle2020/src/Tools/VSCode>
+ * <https://isabelle.in.tum.de/repos/isabelle/file/tip/src/Tools/VSCode>
* <https://github.com/Microsoft/language-server-protocol>
@@ -59,8 +58,8 @@
### Isabelle/VSCode Installation
- * Download Isabelle2020 from <https://isabelle.in.tum.de/website-Isabelle2020>
- or any of its mirror sites.
+ * Download a recent Isabelle development snapshot from
+ <https://isabelle.in.tum.de/devel/release_snapshot>
* Unpack and run the main Isabelle/jEdit application as usual, to ensure that
the logic image is built properly and Isabelle works as expected.
@@ -69,7 +68,7 @@
* Open the VSCode *Extensions* view and install the following:
- + *Isabelle2020* (needs to fit to the underlying Isabelle release).
+ + *Isabelle* (needs to fit to the underlying Isabelle release).
+ *Prettify Symbols Mode* (important for display of Isabelle symbols).
@@ -90,17 +89,17 @@
+ Linux:
```
- "isabelle.home": "/home/makarius/Isabelle2020"
+ "isabelle.home": "/home/makarius/Isabelle"
```
+ Mac OS X:
```
- "isabelle.home": "/Users/makarius/Isabelle.app/Isabelle2020"
+ "isabelle.home": "/Users/makarius/Isabelle.app/Isabelle"
```
+ Windows:
```
- "isabelle.home": "C:\\Users\\makarius\\Isabelle2020"
+ "isabelle.home": "C:\\Users\\makarius\\Isabelle"
```
* Restart the VSCode application to ensure that all extensions are properly
--- a/src/Tools/VSCode/extension/package.json Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/VSCode/extension/package.json Thu Apr 02 13:04:24 2020 +0200
@@ -1,6 +1,6 @@
{
- "name": "Isabelle2020",
- "displayName": "Isabelle2020",
+ "name": "Isabelle",
+ "displayName": "Isabelle",
"description": "Isabelle Prover IDE",
"keywords": [
"theorem prover",
--- a/src/Tools/VSCode/src/grammar.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/VSCode/src/grammar.scala Thu Apr 02 13:04:24 2020 +0200
@@ -23,7 +23,7 @@
def generate(keywords: Keyword.Keywords): JSON.S =
{
val (minor_keywords, operators) =
- keywords.minor.iterator.toList.partition(Symbol.is_ascii_identifier(_))
+ keywords.minor.iterator.toList.partition(Symbol.is_ascii_identifier)
def major_keywords(pred: String => Boolean): List[String] =
(for {
@@ -39,7 +39,7 @@
def grouped_names(as: List[String]): String =
- JSON.Format("\\b(" + as.sorted.map(Library.escape_regex(_)).mkString("|") + ")\\b")
+ JSON.Format("\\b(" + as.sorted.map(Library.escape_regex).mkString("|") + ")\\b")
"""{
"name": "Isabelle",
--- a/src/Tools/VSCode/src/server.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/VSCode/src/server.scala Thu Apr 02 13:04:24 2020 +0200
@@ -140,7 +140,7 @@
}
private val file_watcher =
- File_Watcher(sync_documents(_), options.seconds("vscode_load_delay"))
+ File_Watcher(sync_documents, options.seconds("vscode_load_delay"))
private def close_document(file: JFile)
{
@@ -305,21 +305,12 @@
dynamic_output.init()
- var session_phase: Session.Consumer[Session.Phase] = null
- session_phase =
- Session.Consumer(getClass.getName) {
- case Session.Ready =>
- session.phase_changed -= session_phase
- reply_ok("Welcome to Isabelle/" + base_info.session + " (" + Distribution.version + ")")
- case Session.Terminated(result) if !result.ok =>
- session.phase_changed -= session_phase
- reply_error("Prover startup failed: return code " + result.rc)
- case _ =>
- }
- session.phase_changed += session_phase
-
- Isabelle_Process.start(session, options, modes = modes,
- sessions_structure = Some(base_info.sessions_structure), logic = base_info.session)
+ try {
+ Isabelle_Process(session, options, base_info.sessions_structure, Sessions.store(options),
+ modes = modes, logic = base_info.session).await_startup
+ reply_ok("Welcome to Isabelle/" + base_info.session + " (" + Distribution.version + ")")
+ }
+ catch { case ERROR(msg) => reply_error(msg) }
}
}
@@ -485,7 +476,7 @@
channel.read() match {
case Some(json) =>
json match {
- case bulk: List[_] => bulk.foreach(handle(_))
+ case bulk: List[_] => bulk.foreach(handle)
case _ => handle(json)
}
loop()
--- a/src/Tools/VSCode/src/vscode_resources.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/VSCode/src/vscode_resources.scala Thu Apr 02 13:04:24 2020 +0200
@@ -345,7 +345,7 @@
output_text(XML.content(xml))
def output_pretty(body: XML.Body, margin: Int): String =
- output_text(Pretty.string_of(body, margin = margin))
+ output_text(Pretty.string_of(body, margin = margin, metric = Symbol.Metric))
def output_pretty_tooltip(body: XML.Body): String = output_pretty(body, tooltip_margin)
def output_pretty_message(body: XML.Body): String = output_pretty(body, message_margin)
--- a/src/Tools/jEdit/src/completion_popup.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/completion_popup.scala Thu Apr 02 13:04:24 2020 +0200
@@ -10,7 +10,7 @@
import isabelle._
import java.awt.{Color, Font, Point, BorderLayout, Dimension}
-import java.awt.event.{KeyEvent, MouseEvent, MouseAdapter, FocusAdapter, FocusEvent}
+import java.awt.event.{KeyEvent, KeyListener, MouseEvent, MouseAdapter, FocusAdapter, FocusEvent}
import java.io.{File => JFile}
import javax.swing.{JPanel, JComponent, JLayeredPane, SwingUtilities}
import javax.swing.border.LineBorder
@@ -18,7 +18,6 @@
import scala.swing.{ListView, ScrollPane}
import scala.swing.event.MouseClicked
-
import org.gjt.sp.jedit.View
import org.gjt.sp.jedit.textarea.{JEditTextArea, TextArea, Selection}
import org.gjt.sp.jedit.gui.{HistoryTextField, KeyEventWorkaround}
@@ -399,7 +398,7 @@
/* activation */
private val outer_key_listener =
- JEdit_Lib.key_listener(key_typed = input _)
+ JEdit_Lib.key_listener(key_typed = input)
private def activate()
{
@@ -570,7 +569,7 @@
GUI_Thread.require {}
require(items.nonEmpty)
- val multi = items.length > 1
+ val multi: Boolean = items.length > 1
/* actions */
@@ -621,7 +620,7 @@
/* event handling */
- val inner_key_listener =
+ val inner_key_listener: KeyListener =
JEdit_Lib.key_listener(
key_pressed = (e: KeyEvent) =>
{
@@ -655,7 +654,7 @@
}
propagate(e)
},
- key_typed = propagate _
+ key_typed = propagate
)
list_view.peer.addKeyListener(inner_key_listener)
--- a/src/Tools/jEdit/src/debugger_dockable.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/debugger_dockable.scala Thu Apr 02 13:04:24 2020 +0200
@@ -74,7 +74,7 @@
val pretty_text_area = new Pretty_Text_Area(view)
- override def detach_operation = pretty_text_area.detach_operation
+ override def detach_operation: Option[() => Unit] = pretty_text_area.detach_operation
private def handle_resize()
{
@@ -208,22 +208,22 @@
private val continue_button = new Button("Continue") {
tooltip = "Continue program on current thread, until next breakpoint"
- reactions += { case ButtonClicked(_) => thread_selection().map(debugger.continue(_)) }
+ reactions += { case ButtonClicked(_) => thread_selection().map(debugger.continue) }
}
private val step_button = new Button("Step") {
tooltip = "Single-step in depth-first order"
- reactions += { case ButtonClicked(_) => thread_selection().map(debugger.step(_)) }
+ reactions += { case ButtonClicked(_) => thread_selection().map(debugger.step) }
}
private val step_over_button = new Button("Step over") {
tooltip = "Single-step within this function"
- reactions += { case ButtonClicked(_) => thread_selection().map(debugger.step_over(_)) }
+ reactions += { case ButtonClicked(_) => thread_selection().map(debugger.step_over) }
}
private val step_out_button = new Button("Step out") {
tooltip = "Single-step outside this function"
- reactions += { case ButtonClicked(_) => thread_selection().map(debugger.step_out(_)) }
+ reactions += { case ButtonClicked(_) => thread_selection().map(debugger.step_out) }
}
private val context_label = new Label("Context:") {
@@ -318,7 +318,7 @@
/* main panel */
- val main_panel = new SplitPane(Orientation.Vertical) {
+ val main_panel: SplitPane = new SplitPane(Orientation.Vertical) {
oneTouchExpandable = true
leftComponent = tree_pane
rightComponent = Component.wrap(pretty_text_area)
--- a/src/Tools/jEdit/src/document_model.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/document_model.scala Thu Apr 02 13:04:24 2020 +0200
@@ -81,7 +81,7 @@
private val state = Synchronized(State()) // owned by GUI thread
def get_models(): Map[Document.Node.Name, Document_Model] = state.value.models
- def get(name: Document.Node.Name): Option[Document_Model] = get_models.get(name)
+ def get(name: Document.Node.Name): Option[Document_Model] = get_models().get(name)
def get(buffer: JEditBuffer): Option[Buffer_Model] = state.value.buffer_models.get(buffer)
def document_blobs(): Document.Blobs = state.value.document_blobs
@@ -313,7 +313,7 @@
val preview =
HTTP.get(preview_root, arg =>
for {
- query <- Library.try_unprefix(preview_root + "?", arg.uri.toString).map(Url.decode(_))
+ query <- Library.try_unprefix(preview_root + "?", arg.uri.toString).map(Url.decode)
name = Library.perhaps_unprefix(plain_text_prefix, query)
model <- get(PIDE.resources.node_name(name))
}
@@ -348,7 +348,7 @@
if (hidden) Text.Perspective.empty
else {
val view_ranges = document_view_ranges(snapshot)
- val load_ranges = snapshot.commands_loading_ranges(PIDE.editor.visible_node(_))
+ val load_ranges = snapshot.commands_loading_ranges(PIDE.editor.visible_node)
Text.Perspective(view_ranges ::: load_ranges)
}
val overlays = PIDE.editor.node_overlays(node_name)
@@ -589,7 +589,7 @@
if (reparse || edits.nonEmpty || last_perspective != perspective) {
pending.clear
last_perspective = perspective
- node_edits(node_header, edits, perspective)
+ node_edits(node_header(), edits, perspective)
}
else Nil
}
--- a/src/Tools/jEdit/src/document_view.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/document_view.scala Thu Apr 02 13:04:24 2020 +0200
@@ -137,7 +137,7 @@
JEdit_Lib.buffer_lock(buffer) {
val rendering = get_rendering()
- for (i <- 0 until physical_lines.length) {
+ for (i <- physical_lines.indices) {
if (physical_lines(i) != -1) {
val line_range = Text.Range(start(i), end(i))
@@ -241,7 +241,7 @@
text_area.revalidate()
text_area.repaint()
Isabelle.structure_matchers(JEdit_Lib.buffer_mode(text_area.getBuffer)).
- foreach(text_area.addStructureMatcher(_))
+ foreach(text_area.addStructureMatcher)
session.raw_edits += main
session.commands_changed += main
}
@@ -253,7 +253,7 @@
session.raw_edits -= main
session.commands_changed -= main
Isabelle.structure_matchers(JEdit_Lib.buffer_mode(text_area.getBuffer)).
- foreach(text_area.removeStructureMatcher(_))
+ foreach(text_area.removeStructureMatcher)
text_overview.foreach(_.revoke())
text_overview.foreach(text_area.removeLeftOfScrollBar(_))
text_area.removeCaretListener(caret_listener)
--- a/src/Tools/jEdit/src/isabelle.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/isabelle.scala Thu Apr 02 13:04:24 2020 +0200
@@ -406,8 +406,8 @@
private def enclose_input(text_area: JEditTextArea, s1: String, s2: String)
{
- s1.foreach(text_area.userInput(_))
- s2.foreach(text_area.userInput(_))
+ s1.foreach(text_area.userInput)
+ s2.foreach(text_area.userInput)
s2.foreach(_ => text_area.goToPrevCharacter(false))
}
--- a/src/Tools/jEdit/src/isabelle_options.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/isabelle_options.scala Thu Apr 02 13:04:24 2020 +0200
@@ -39,7 +39,7 @@
class Isabelle_Options1 extends Isabelle_Options("isabelle-general")
{
- val options = PIDE.options
+ val options: JEdit_Options = PIDE.options
private val predefined =
List(JEdit_Sessions.logic_selector(options, false),
--- a/src/Tools/jEdit/src/isabelle_sidekick.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/isabelle_sidekick.scala Thu Apr 02 13:04:24 2020 +0200
@@ -53,11 +53,11 @@
}
override def getLongString: String = _name
override def getName: String = _name
- override def setName(name: String) = _name = name
+ override def setName(name: String): Unit = _name = name
override def getStart: Position = _start
- override def setStart(start: Position) = _start = start
+ override def setStart(start: Position): Unit = _start = start
override def getEnd: Position = _end
- override def setEnd(end: Position) = _end = end
+ override def setEnd(end: Position): Unit = _end = end
override def toString: String = _name
}
@@ -148,19 +148,19 @@
class Isabelle_Sidekick_Default extends
Isabelle_Sidekick_Structure("isabelle",
- PIDE.resources.theory_node_name, Document_Structure.parse_sections _)
+ PIDE.resources.theory_node_name, Document_Structure.parse_sections)
class Isabelle_Sidekick_Context extends
Isabelle_Sidekick_Structure("isabelle-context",
- PIDE.resources.theory_node_name, Document_Structure.parse_blocks _)
+ PIDE.resources.theory_node_name, Document_Structure.parse_blocks)
class Isabelle_Sidekick_Options extends
Isabelle_Sidekick_Structure("isabelle-options",
- _ => Some(Document.Node.Name("options")), Document_Structure.parse_sections _)
+ _ => Some(Document.Node.Name("options")), Document_Structure.parse_sections)
class Isabelle_Sidekick_Root extends
Isabelle_Sidekick_Structure("isabelle-root",
- _ => Some(Document.Node.Name("ROOT")), Document_Structure.parse_sections _)
+ _ => Some(Document.Node.Name("ROOT")), Document_Structure.parse_sections)
class Isabelle_Sidekick_ML extends
Isabelle_Sidekick_Structure("isabelle-ml",
@@ -257,7 +257,7 @@
case _ =>
}
offset += line.length + 1
- if (!line.forall(Character.isSpaceChar(_))) end_offset = offset
+ if (!line.forall(Character.isSpaceChar)) end_offset = offset
}
if (!stopped) { close2; close1 }
--- a/src/Tools/jEdit/src/isabelle_vfs.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/isabelle_vfs.scala Thu Apr 02 13:04:24 2020 +0200
@@ -77,7 +77,7 @@
else {
val files = _listFiles(vfs_session, parent, component)
if (files == null) null
- else files.find(_.getPath == url) getOrElse null
+ else files.find(_.getPath == url).orNull
}
}
}
--- a/src/Tools/jEdit/src/jedit_editor.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/jedit_editor.scala Thu Apr 02 13:04:24 2020 +0200
@@ -202,7 +202,7 @@
case doc: Doc.Text_File if doc.name == name => doc.path
case doc: Doc.Doc if doc.name == name => doc.path}).map(path =>
new Hyperlink {
- override val external = !path.is_file
+ override val external: Boolean = !path.is_file
def follow(view: View): Unit = goto_doc(view, path)
override def toString: String = "doc " + quote(name)
})
--- a/src/Tools/jEdit/src/jedit_lib.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/jedit_lib.scala Thu Apr 02 13:04:24 2020 +0200
@@ -160,7 +160,7 @@
else view.getEditPanes().iterator.filter(_ != null).map(_.getTextArea).filter(_ != null)
def jedit_text_areas(): Iterator[JEditTextArea] =
- jedit_views().flatMap(jedit_text_areas(_))
+ jedit_views().flatMap(jedit_text_areas)
def jedit_text_areas(buffer: JEditBuffer): Iterator[JEditTextArea] =
jedit_text_areas().filter(_.getBuffer == buffer)
@@ -319,8 +319,8 @@
def string_width(s: String): Double =
painter.getFont.getStringBounds(s, painter.getFontRenderContext).getWidth
- val unit = string_width(Symbol.space) max 1.0
- val average = string_width("mix") / (3 * unit)
+ val unit: Double = string_width(Symbol.space) max 1.0
+ val average: Double = string_width("mix") / (3 * unit)
def apply(s: String): Double = if (s == "\n") 1.0 else string_width(s) / unit
}
--- a/src/Tools/jEdit/src/jedit_options.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/jedit_options.scala Thu Apr 02 13:04:24 2020 +0200
@@ -129,7 +129,7 @@
case None => if (filter(opt.name)) List(make_component(opt)) else Nil
}
value.sections.sortBy(_._1).map(
- { case (a, opts) => (a, opts.sortBy(_.title("jedit")).flatMap(mk_component _)) })
+ { case (a, opts) => (a, opts.sortBy(_.title("jedit")).flatMap(mk_component)) })
.filterNot(_._2.isEmpty)
}
}
--- a/src/Tools/jEdit/src/jedit_rendering.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/jedit_rendering.scala Thu Apr 02 13:04:24 2020 +0200
@@ -300,11 +300,11 @@
def tooltip(range: Text.Range, control: Boolean): Option[Text.Info[XML.Body]] =
{
val elements = if (control) Rendering.tooltip_elements else Rendering.tooltip_message_elements
- tooltips(elements, range).map(info => info.map(Pretty.fbreaks(_)))
+ tooltips(elements, range).map(info => info.map(Pretty.fbreaks))
}
- lazy val tooltip_close_icon = JEdit_Lib.load_icon(options.string("tooltip_close_icon"))
- lazy val tooltip_detach_icon = JEdit_Lib.load_icon(options.string("tooltip_detach_icon"))
+ lazy val tooltip_close_icon: Icon = JEdit_Lib.load_icon(options.string("tooltip_close_icon"))
+ lazy val tooltip_detach_icon: Icon = JEdit_Lib.load_icon(options.string("tooltip_detach_icon"))
/* gutter */
@@ -378,7 +378,7 @@
else
snapshot.cumulate(range, current_color, Rendering.text_color_elements, _ =>
{
- case (_, Text.Info(_, elem)) => Rendering.text_color.get(elem.name).map(color(_))
+ case (_, Text.Info(_, elem)) => Rendering.text_color.get(elem.name).map(color)
})
}
--- a/src/Tools/jEdit/src/jedit_resources.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/jedit_resources.scala Thu Apr 02 13:04:24 2020 +0200
@@ -37,7 +37,7 @@
/* document node name */
def node_name(path: String): Document.Node.Name =
- JEdit_Lib.check_file(path).flatMap(find_theory(_)) getOrElse {
+ JEdit_Lib.check_file(path).flatMap(find_theory) getOrElse {
val vfs = VFSManager.getVFSForPath(path)
val node = if (vfs.isInstanceOf[FileVFS]) MiscUtilities.resolveSymlinks(path) else path
val theory = theory_name(Sessions.DRAFT, Thy_Header.theory_name(node))
--- a/src/Tools/jEdit/src/jedit_sessions.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/jedit_sessions.scala Thu Apr 02 13:04:24 2020 +0200
@@ -135,15 +135,17 @@
def session_start(options0: Options)
{
+ val session = PIDE.session
val options = session_options(options0)
+ val sessions_structure = PIDE.resources.session_base_info.sessions_structure
+ val store = Sessions.store(options)
- Isabelle_Process.start(PIDE.session, options,
- sessions_structure = Some(PIDE.resources.session_base_info.sessions_structure),
+ session.phase_changed += PIDE.plugin.session_phase_changed
+
+ Isabelle_Process(session, options, sessions_structure, store,
logic = PIDE.resources.session_name,
- store = Some(Sessions.store(options)),
modes =
(space_explode(',', options.string("jedit_print_mode")) :::
- space_explode(',', Isabelle_System.getenv("JEDIT_PRINT_MODE"))).reverse,
- phase_changed = PIDE.plugin.session_phase_changed)
+ space_explode(',', Isabelle_System.getenv("JEDIT_PRINT_MODE"))).reverse)
}
}
--- a/src/Tools/jEdit/src/monitor_dockable.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/monitor_dockable.scala Thu Apr 02 13:04:24 2020 +0200
@@ -108,7 +108,7 @@
private val main =
Session.Consumer[Any](getClass.getName) {
- case stats: Session.Statistics =>
+ case stats: Session.Runtime_Statistics =>
add_statistics(stats.props)
update_delay.invoke()
@@ -118,13 +118,13 @@
override def init()
{
- PIDE.session.statistics += main
+ PIDE.session.runtime_statistics += main
PIDE.session.global_options += main
}
override def exit()
{
- PIDE.session.statistics -= main
+ PIDE.session.runtime_statistics -= main
PIDE.session.global_options -= main
}
}
--- a/src/Tools/jEdit/src/output_dockable.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/output_dockable.scala Thu Apr 02 13:04:24 2020 +0200
@@ -32,7 +32,7 @@
val pretty_text_area = new Pretty_Text_Area(view)
set_content(pretty_text_area)
- override def detach_operation = pretty_text_area.detach_operation
+ override def detach_operation: Option[() => Unit] = pretty_text_area.detach_operation
private def handle_resize()
@@ -58,7 +58,7 @@
}
val new_output =
- if (!restriction.isDefined || restriction.get.contains(command))
+ if (restriction.isEmpty || restriction.get.contains(command))
Rendering.output_messages(results)
else current_output
--- a/src/Tools/jEdit/src/plugin.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/plugin.scala Thu Apr 02 13:04:24 2020 +0200
@@ -150,7 +150,7 @@
}
else Nil
- (thy_files1 ::: thy_files2 ::: aux_files).filterNot(models.isDefinedAt(_))
+ (thy_files1 ::: thy_files2 ::: aux_files).filterNot(models.isDefinedAt)
}
if (required_files.nonEmpty) {
try {
@@ -184,12 +184,12 @@
if (Document_Model.sync_files(changed)) PIDE.editor.invoke_generated()
lazy val file_watcher: File_Watcher =
- File_Watcher(file_watcher_action _, options.seconds("editor_load_delay"))
+ File_Watcher(file_watcher_action, options.seconds("editor_load_delay"))
/* session phase */
- val session_phase_changed: Session.Phase => Unit =
+ val session_phase_changed: Session.Consumer[Session.Phase] = Session.Consumer("Isabelle/jEdit")
{
case Session.Terminated(result) if !result.ok =>
GUI_Thread.later {
@@ -460,11 +460,11 @@
completion_history.load()
spell_checker.update(options.value)
- JEdit_Lib.jedit_views.foreach(init_title(_))
+ JEdit_Lib.jedit_views.foreach(init_title)
isabelle.jedit_base.Syntax_Style.set_style_extender(Syntax_Style.Extender)
init_mode_provider()
- JEdit_Lib.jedit_text_areas.foreach(Completion_Popup.Text_Area.init _)
+ JEdit_Lib.jedit_text_areas.foreach(Completion_Popup.Text_Area.init)
http_server.start
@@ -489,7 +489,7 @@
isabelle.jedit_base.Syntax_Style.dummy_style_extender()
exit_mode_provider()
- JEdit_Lib.jedit_text_areas.foreach(Completion_Popup.Text_Area.exit _)
+ JEdit_Lib.jedit_text_areas.foreach(Completion_Popup.Text_Area.exit)
if (startup_failure.isEmpty) {
options.value.save_prefs()
--- a/src/Tools/jEdit/src/pretty_tooltip.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/pretty_tooltip.scala Thu Apr 02 13:04:24 2020 +0200
@@ -146,7 +146,7 @@
}
def dismiss_descendant(parent: JComponent): Unit =
- descendant(parent).foreach(dismiss(_))
+ descendant(parent).foreach(dismiss)
def dismissed_all(): Boolean =
{
@@ -203,7 +203,7 @@
/* text area */
- val pretty_text_area =
+ val pretty_text_area: Pretty_Text_Area =
new Pretty_Text_Area(view, () => Pretty_Tooltip.dismiss(tip), true) {
override def get_background() = Some(rendering.tooltip_color)
}
@@ -262,7 +262,7 @@
val formatted = Pretty.formatted(info.info, margin = margin, metric = metric)
val lines =
XML.traverse_text(formatted)(if (XML.text_length(formatted) == 0) 0 else 1)(
- (n: Int, s: String) => n + s.iterator.filter(_ == '\n').length)
+ (n: Int, s: String) => n + s.iterator.count(_ == '\n'))
val h = painter.getLineHeight * lines + geometry.deco_height
val margin1 =
--- a/src/Tools/jEdit/src/query_dockable.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/query_dockable.scala Thu Apr 02 13:04:24 2020 +0200
@@ -302,7 +302,7 @@
select_operation()
set_content(operations_pane)
- override def detach_operation =
+ override def detach_operation: Option[() => Unit] =
get_operation() match {
case None => None
case Some(op) => op.pretty_text_area.detach_operation
--- a/src/Tools/jEdit/src/rich_text_area.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/rich_text_area.scala Thu Apr 02 13:04:24 2020 +0200
@@ -159,15 +159,15 @@
private val highlight_area =
new Active_Area[Color](
- (rendering: JEdit_Rendering) => rendering.highlight _, None)
+ (rendering: JEdit_Rendering) => rendering.highlight, None)
private val hyperlink_area =
new Active_Area[PIDE.editor.Hyperlink](
- (rendering: JEdit_Rendering) => rendering.hyperlink _, Some(Cursor.HAND_CURSOR))
+ (rendering: JEdit_Rendering) => rendering.hyperlink, Some(Cursor.HAND_CURSOR))
private val active_area =
new Active_Area[XML.Elem](
- (rendering: JEdit_Rendering) => rendering.active _, Some(Cursor.DEFAULT_CURSOR))
+ (rendering: JEdit_Rendering) => rendering.active, Some(Cursor.DEFAULT_CURSOR))
private val active_areas =
List((highlight_area, true), (hyperlink_area, true), (active_area, false))
@@ -292,7 +292,7 @@
robust_rendering { rendering =>
val fm = text_area.getPainter.getFontMetrics
- for (i <- 0 until physical_lines.length) {
+ for (i <- physical_lines.indices) {
if (physical_lines(i) != -1) {
val line_range = Text.Range(start(i), end(i) min buffer.getLength)
@@ -479,7 +479,7 @@
((w - b + 1) / 2, c - b / 2, w - b, line_height - b)
}
- for (i <- 0 until physical_lines.length) {
+ for (i <- physical_lines.indices) {
val line = physical_lines(i)
if (line != -1) {
val line_range = Text.Range(start(i), end(i) min buffer.getLength)
@@ -525,7 +525,7 @@
{
robust_rendering { rendering =>
val search_pattern = get_search_pattern()
- for (i <- 0 until physical_lines.length) {
+ for (i <- physical_lines.indices) {
if (physical_lines(i) != -1) {
val line_range = Text.Range(start(i), end(i) min buffer.getLength)
--- a/src/Tools/jEdit/src/scala_console.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/scala_console.scala Thu Apr 02 13:04:24 2020 +0200
@@ -30,7 +30,7 @@
def find_jars(start: String): List[String] =
if (start != null)
File.find_files(new JFile(start), file => file.getName.endsWith(".jar")).
- map(File.absolute_name(_))
+ map(File.absolute_name)
else Nil
val initial_class_path =
--- a/src/Tools/jEdit/src/session_build.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/session_build.scala Thu Apr 02 13:04:24 2020 +0200
@@ -40,7 +40,7 @@
private class Dialog(view: View) extends JDialog(view)
{
- val options = PIDE.options.value
+ val options: Options = PIDE.options.value
/* text */
--- a/src/Tools/jEdit/src/simplifier_trace_dockable.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/simplifier_trace_dockable.scala Thu Apr 02 13:04:24 2020 +0200
@@ -64,7 +64,7 @@
private def show_trace()
{
- val trace = Simplifier_Trace.generate_trace(current_results)
+ val trace = Simplifier_Trace.generate_trace(PIDE.session, current_results)
new Simplifier_Trace_Window(view, current_snapshot, trace)
}
@@ -181,7 +181,7 @@
new Button("Clear memory") {
reactions += {
case ButtonClicked(_) =>
- Simplifier_Trace.clear_memory()
+ Simplifier_Trace.clear_memory(PIDE.session)
}
}))
--- a/src/Tools/jEdit/src/sledgehammer_dockable.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/sledgehammer_dockable.scala Thu Apr 02 13:04:24 2020 +0200
@@ -30,7 +30,7 @@
val pretty_text_area = new Pretty_Text_Area(view)
set_content(pretty_text_area)
- override def detach_operation = pretty_text_area.detach_operation
+ override def detach_operation: Option[() => Unit] = pretty_text_area.detach_operation
/* query operation */
@@ -50,7 +50,7 @@
}
private val sledgehammer =
- new Query_Operation(PIDE.editor, view, "sledgehammer", consume_status _,
+ new Query_Operation(PIDE.editor, view, "sledgehammer", consume_status,
(snapshot, results, body) =>
pretty_text_area.update(snapshot, results, Pretty.separate(body)))
--- a/src/Tools/jEdit/src/state_dockable.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/state_dockable.scala Thu Apr 02 13:04:24 2020 +0200
@@ -29,7 +29,7 @@
val pretty_text_area = new Pretty_Text_Area(view)
set_content(pretty_text_area)
- override def detach_operation = pretty_text_area.detach_operation
+ override def detach_operation: Option[() => Unit] = pretty_text_area.detach_operation
private val print_state =
new Query_Operation(PIDE.editor, view, "print_state", _ => (),
--- a/src/Tools/jEdit/src/symbols_dockable.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/symbols_dockable.scala Thu Apr 02 13:04:24 2020 +0200
@@ -174,7 +174,7 @@
}
for (page <- pages)
- page.title = Word.implode(Word.explode('_', page.title).map(Word.perhaps_capitalize(_)))
+ page.title = Word.implode(Word.explode('_', page.title).map(Word.perhaps_capitalize))
}
set_content(group_tabs)
@@ -200,7 +200,7 @@
}
case _ =>
})
- comp.revalidate
+ comp.revalidate()
comp.repaint()
}
case _: Session.Commands_Changed => abbrevs_refresh_delay.invoke()
--- a/src/Tools/jEdit/src/syntax_style.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/syntax_style.scala Thu Apr 02 13:04:24 2020 +0200
@@ -99,9 +99,9 @@
}
private def control_style(sym: String): Option[Byte => Byte] =
- if (sym == Symbol.sub_decoded) Some(subscript(_))
- else if (sym == Symbol.sup_decoded) Some(superscript(_))
- else if (sym == Symbol.bold_decoded) Some(bold(_))
+ if (sym == Symbol.sub_decoded) Some(subscript)
+ else if (sym == Symbol.sup_decoded) Some(superscript)
+ else if (sym == Symbol.bold_decoded) Some(bold)
else None
def extended(text: CharSequence): Map[Text.Offset, Byte => Byte] =
--- a/src/Tools/jEdit/src/text_structure.scala Thu Apr 02 11:45:03 2020 +0200
+++ b/src/Tools/jEdit/src/text_structure.scala Thu Apr 02 13:04:24 2020 +0200
@@ -21,7 +21,7 @@
class Navigator(syntax: Outer_Syntax, buffer: JEditBuffer, comments: Boolean)
{
- val limit = PIDE.options.value.int("jedit_structure_limit") max 0
+ val limit: Int = PIDE.options.value.int("jedit_structure_limit") max 0
def iterator(line: Int, lim: Int = limit): Iterator[Text.Info[Token]] =
{
@@ -137,7 +137,7 @@
else i })
def indent_extra: Int =
- if (prev_span.exists(keywords.is_quasi_command(_))) indent_size
+ if (prev_span.exists(keywords.is_quasi_command)) indent_size
else 0
val indent =