# HG changeset patch
# User wenzelm
# Date 1334429093 -7200
# Node ID 80ddf2016b6c82268dd27dd1318e8925d7e82ce8
# Parent  214bfaae738d68685ed949ba220befe42fa32a3c# Parent  ffa6e10df0911679ba7d13be3019d5fc96b98e7c
merged;

diff -r ffa6e10df091 -r 80ddf2016b6c src/HOL/IsaMakefile
--- a/src/HOL/IsaMakefile	Sat Apr 14 20:10:10 2012 +0200
+++ b/src/HOL/IsaMakefile	Sat Apr 14 20:44:53 2012 +0200
@@ -1027,7 +1027,7 @@
   ex/Quicksort.thy ex/ROOT.ML						\
   ex/Records.thy ex/ReflectionEx.thy ex/Refute_Examples.thy		\
   ex/SAT_Examples.thy ex/Serbian.thy ex/Set_Theory.thy			\
-  ex/Set_Algebras.thy ex/Simproc_Tests.thy ex/SVC_Oracle.thy		\
+  ex/Simproc_Tests.thy ex/SVC_Oracle.thy		\
   ex/sledgehammer_tactics.ML ex/Seq.thy ex/Sqrt.thy ex/Sqrt_Script.thy 	\
   ex/Sudoku.thy ex/Tarski.thy ex/Termination.thy ex/Transfer_Ex.thy	\
   ex/Tree23.thy	ex/Unification.thy ex/While_Combinator_Example.thy	\
diff -r ffa6e10df091 -r 80ddf2016b6c src/HOL/TPTP/lib/Tools/tptp_graph
--- a/src/HOL/TPTP/lib/Tools/tptp_graph	Sat Apr 14 20:10:10 2012 +0200
+++ b/src/HOL/TPTP/lib/Tools/tptp_graph	Sat Apr 14 20:44:53 2012 +0200
@@ -10,25 +10,26 @@
 #FIXME inline or move to settings
 DOT2TEX=dot2tex
 DOT=dot
-SED=sed
+PERL=perl
 PDFLATEX=pdflatex
 [ -n "$ISABELLE_PDFLATEX" ] && PDFLATEX=$ISABELLE_PDFLATEX
 DOT2TEX_VERSION="$($DOT2TEX -V 2> /dev/null)"
-DOT_VERSION="$($DOT -V 2> /dev/null)"
-SED_VERSION="$($SED --version | head -1 2> /dev/null)"
+DOT_VERSION="$($DOT -V 2>&1 | grep Graphviz)"
+PERL_VERSION="$($PERL -v | grep -e "v[0-9]\+." 2> /dev/null)"
 PDFLATEX_VERSION="$($PDFLATEX -version | head -1 2> /dev/null)"
 
 function check_deps()
 {
   #FIXME how well does this work across different platforms and/or versions of
   #      the tools?
-  for DEP in DOT2TEX_VERSION DOT_VERSION SED_VERSION PDFLATEX_VERSION
+  for DEP in DOT2TEX DOT PERL PDFLATEX
   do
-    eval DEP_VAL=\$$DEP
-    if [ -z "$DEP_VAL" ]; then
+    eval DEP_VAL=\$${DEP}
+    eval DEP_VERSION=\$${DEP}_VERSION
+    if [ -z "$DEP_VERSION" ]; then
       echo "$DEP not installed"
     else
-      echo "$DEP_VAL"
+      echo "$DEP ($DEP_VAL) : $DEP_VERSION"
     fi
   done
 }
@@ -53,7 +54,7 @@
 KEEP_TEMP=""
 NON_EXEC=""
 
-while getopts "dknX" OPT
+while getopts "dnkX" OPT
 do
   #FIXME could add "quiet" mode to send stderr (and some stdout) to /dev/null
   case "$OPT" in
@@ -106,7 +107,6 @@
   "$ISABELLE_PROCESS" -e "$LOADER" Pure
 }
 
-
 if [ "$OUTPUT_FORMAT" -eq 0 ]; then
   [ -z "$NON_EXEC" ] && generate_dot "$1" "$2"
   exit 0
@@ -114,14 +114,12 @@
 
 ## set some essential variables
 
-[ -z "$TMPDIR" ] && TMPDIR=/tmp
 WORKDIR=""
 while :
 do
-  WORKDIR="$TMPDIR/tptpgraph$RANDOM"
-  if [ ! -d "$WORKDIR" ]; then
-    break
-  fi
+  #FIXME not perfectly reliable method, but probably good enough
+  WORKDIR="${ISABELLE_TMP_PREFIX}-tptpgraph$RANDOM"
+  [ ! -d "$WORKDIR" ] && break
 done
 OUTPUT_FILENAME="$(basename "$2")"
 FILEDIR="$(cd "$(dirname "$2")"; cd "$(pwd -P)"; pwd)"
@@ -136,7 +134,7 @@
 if [ -z "$NON_EXEC" ]; then
   $DOT -Txdot "${FILENAME}.dot" \
   | $DOT2TEX -f pgf -t raw --crop > "${FILENAME}.tex"
-  $SED -i 's/_/\\_/g' "${FILENAME}.tex"
+  $PERL -w -p -e 's/_/\\_/g' "${FILENAME}.tex"
 fi
 
 if [ "$OUTPUT_FORMAT" -eq 1 ]; then
diff -r ffa6e10df091 -r 80ddf2016b6c src/HOL/ex/ROOT.ML
--- a/src/HOL/ex/ROOT.ML	Sat Apr 14 20:10:10 2012 +0200
+++ b/src/HOL/ex/ROOT.ML	Sat Apr 14 20:44:53 2012 +0200
@@ -67,7 +67,6 @@
   "Quicksort",
   "Birthday_Paradox",
   "List_to_Set_Comprehension_Examples",
-  "Set_Algebras",
   "Seq",
   "Simproc_Tests",
   "Executable_Relation"
diff -r ffa6e10df091 -r 80ddf2016b6c src/HOL/ex/Set_Algebras.thy
--- a/src/HOL/ex/Set_Algebras.thy	Sat Apr 14 20:10:10 2012 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,371 +0,0 @@
-(*  Title:      HOL/ex/Set_Algebras.thy
-    Author:     Jeremy Avigad and Kevin Donnelly; Florian Haftmann, TUM
-*)
-
-header {* Algebraic operations on sets *}
-
-theory Set_Algebras
-imports Main Interpretation_with_Defs
-begin
-
-text {*
-  This library lifts operations like addition and muliplication to
-  sets.  It was designed to support asymptotic calculations. See the
-  comments at the top of theory @{text BigO}.
-*}
-
-definition set_plus :: "'a::plus set \<Rightarrow> 'a set \<Rightarrow> 'a set"  (infixl "\<oplus>" 65) where
-  "A \<oplus> B = {c. \<exists>a\<in>A. \<exists>b\<in>B. c = a + b}"
-
-definition set_times :: "'a::times set \<Rightarrow> 'a set \<Rightarrow> 'a set"  (infixl "\<otimes>" 70) where
-  "A \<otimes> B = {c. \<exists>a\<in>A. \<exists>b\<in>B. c = a * b}"
-
-definition elt_set_plus :: "'a::plus \<Rightarrow> 'a set \<Rightarrow> 'a set"  (infixl "+o" 70) where
-  "a +o B = {c. \<exists>b\<in>B. c = a + b}"
-
-definition elt_set_times :: "'a::times \<Rightarrow> 'a set \<Rightarrow> 'a set"  (infixl "*o" 80) where
-  "a *o B = {c. \<exists>b\<in>B. c = a * b}"
-
-abbreviation (input) elt_set_eq :: "'a \<Rightarrow> 'a set \<Rightarrow> bool"  (infix "=o" 50) where
-  "x =o A \<equiv> x \<in> A"
-
-interpretation set_add!: semigroup "set_plus :: 'a::semigroup_add set \<Rightarrow> 'a set \<Rightarrow> 'a set"
-  by default (force simp add: set_plus_def add.assoc)
-
-interpretation set_add!: abel_semigroup "set_plus :: 'a::ab_semigroup_add set \<Rightarrow> 'a set \<Rightarrow> 'a set"
-  by default (force simp add: set_plus_def add.commute)
-
-interpretation set_add!: monoid "set_plus :: 'a::monoid_add set \<Rightarrow> 'a set \<Rightarrow> 'a set" "{0}"
-  by default (simp_all add: set_plus_def)
-
-interpretation set_add!: comm_monoid "set_plus :: 'a::comm_monoid_add set \<Rightarrow> 'a set \<Rightarrow> 'a set" "{0}"
-  by default (simp add: set_plus_def)
-
-interpretation set_add!: monoid_add "set_plus :: 'a::monoid_add set \<Rightarrow> 'a set \<Rightarrow> 'a set" "{0}"
-  defines listsum_set is set_add.listsum
-  by default (simp_all add: set_add.assoc)
-
-interpretation
-  set_add!: comm_monoid_add "set_plus :: 'a::comm_monoid_add set \<Rightarrow> 'a set \<Rightarrow> 'a set" "{0}"
-  defines setsum_set is set_add.setsum
-  where "monoid_add.listsum set_plus {0::'a} = listsum_set"
-proof -
-  show "class.comm_monoid_add (set_plus :: 'a set \<Rightarrow> 'a set \<Rightarrow> 'a set) {0}"
-    by default (simp_all add: set_add.commute)
-  then interpret set_add!: comm_monoid_add "set_plus :: 'a set \<Rightarrow> 'a set \<Rightarrow> 'a set" "{0}" .
-  show "monoid_add.listsum set_plus {0::'a} = listsum_set"
-    by (simp only: listsum_set_def)
-qed
-
-interpretation set_mult!: semigroup "set_times :: 'a::semigroup_mult set \<Rightarrow> 'a set \<Rightarrow> 'a set"
-  by default (force simp add: set_times_def mult.assoc)
-
-interpretation
-  set_mult!: abel_semigroup "set_times :: 'a::ab_semigroup_mult set \<Rightarrow> 'a set \<Rightarrow> 'a set"
-  by default (force simp add: set_times_def mult.commute)
-
-interpretation set_mult!: monoid "set_times :: 'a::monoid_mult set \<Rightarrow> 'a set \<Rightarrow> 'a set" "{1}"
-  by default (simp_all add: set_times_def)
-
-interpretation
-  set_mult!: comm_monoid "set_times :: 'a::comm_monoid_mult set \<Rightarrow> 'a set \<Rightarrow> 'a set" "{1}"
-  by default (simp add: set_times_def)
-
-interpretation set_mult!: monoid_mult "{1}" "set_times :: 'a::monoid_mult set \<Rightarrow> 'a set \<Rightarrow> 'a set"
-  defines power_set is set_mult.power
-  by default (simp_all add: set_mult.assoc)
-
-interpretation
-  set_mult!: comm_monoid_mult "set_times :: 'a::comm_monoid_mult set \<Rightarrow> 'a set \<Rightarrow> 'a set" "{1}"
-  defines setprod_set is set_mult.setprod
-  where "power.power {1} set_times = power_set"
-proof -
-  show "class.comm_monoid_mult (set_times :: 'a set \<Rightarrow> 'a set \<Rightarrow> 'a set) {1}"
-    by default (simp_all add: set_mult.commute)
-  then interpret set_mult!: comm_monoid_mult "set_times :: 'a set \<Rightarrow> 'a set \<Rightarrow> 'a set" "{1}" .
-  show "power.power {1} set_times = power_set"
-    by (simp add: power_set_def)
-qed
-
-lemma set_plus_intro [intro]: "a : C ==> b : D ==> a + b : C \<oplus> D"
-  by (auto simp add: set_plus_def)
-
-lemma set_plus_intro2 [intro]: "b : C ==> a + b : a +o C"
-  by (auto simp add: elt_set_plus_def)
-
-lemma set_plus_rearrange: "((a::'a::comm_monoid_add) +o C) \<oplus> (b +o D) = (a + b) +o (C \<oplus> D)"
-  apply (auto simp add: elt_set_plus_def set_plus_def add_ac)
-   apply (rule_tac x = "ba + bb" in exI)
-  apply (auto simp add: add_ac)
-  apply (rule_tac x = "aa + a" in exI)
-  apply (auto simp add: add_ac)
-  done
-
-lemma set_plus_rearrange2: "(a::'a::semigroup_add) +o (b +o C) = (a + b) +o C"
-  by (auto simp add: elt_set_plus_def add_assoc)
-
-lemma set_plus_rearrange3: "((a::'a::semigroup_add) +o B) \<oplus> C = a +o (B \<oplus> C)"
-  apply (auto simp add: elt_set_plus_def set_plus_def)
-   apply (blast intro: add_ac)
-  apply (rule_tac x = "a + aa" in exI)
-  apply (rule conjI)
-   apply (rule_tac x = "aa" in bexI)
-    apply auto
-  apply (rule_tac x = "ba" in bexI)
-   apply (auto simp add: add_ac)
-  done
-
-theorem set_plus_rearrange4: "C \<oplus> ((a::'a::comm_monoid_add) +o D) = a +o (C \<oplus> D)"
-  apply (auto intro!: simp add: elt_set_plus_def set_plus_def add_ac)
-   apply (rule_tac x = "aa + ba" in exI)
-   apply (auto simp add: add_ac)
-  done
-
-theorems set_plus_rearranges = set_plus_rearrange set_plus_rearrange2
-  set_plus_rearrange3 set_plus_rearrange4
-
-lemma set_plus_mono [intro!]: "C <= D ==> a +o C <= a +o D"
-  by (auto simp add: elt_set_plus_def)
-
-lemma set_plus_mono2 [intro]: "(C::('a::plus) set) <= D ==> E <= F ==>
-    C \<oplus> E <= D \<oplus> F"
-  by (auto simp add: set_plus_def)
-
-lemma set_plus_mono3 [intro]: "a : C ==> a +o D <= C \<oplus> D"
-  by (auto simp add: elt_set_plus_def set_plus_def)
-
-lemma set_plus_mono4 [intro]: "(a::'a::comm_monoid_add) : C ==>
-    a +o D <= D \<oplus> C"
-  by (auto simp add: elt_set_plus_def set_plus_def add_ac)
-
-lemma set_plus_mono5: "a:C ==> B <= D ==> a +o B <= C \<oplus> D"
-  apply (subgoal_tac "a +o B <= a +o D")
-   apply (erule order_trans)
-   apply (erule set_plus_mono3)
-  apply (erule set_plus_mono)
-  done
-
-lemma set_plus_mono_b: "C <= D ==> x : a +o C
-    ==> x : a +o D"
-  apply (frule set_plus_mono)
-  apply auto
-  done
-
-lemma set_plus_mono2_b: "C <= D ==> E <= F ==> x : C \<oplus> E ==>
-    x : D \<oplus> F"
-  apply (frule set_plus_mono2)
-   prefer 2
-   apply force
-  apply assumption
-  done
-
-lemma set_plus_mono3_b: "a : C ==> x : a +o D ==> x : C \<oplus> D"
-  apply (frule set_plus_mono3)
-  apply auto
-  done
-
-lemma set_plus_mono4_b: "(a::'a::comm_monoid_add) : C ==>
-    x : a +o D ==> x : D \<oplus> C"
-  apply (frule set_plus_mono4)
-  apply auto
-  done
-
-lemma set_zero_plus [simp]: "(0::'a::comm_monoid_add) +o C = C"
-  by (auto simp add: elt_set_plus_def)
-
-lemma set_zero_plus2: "(0::'a::comm_monoid_add) : A ==> B <= A \<oplus> B"
-  apply (auto intro!: simp add: set_plus_def)
-  apply (rule_tac x = 0 in bexI)
-   apply (rule_tac x = x in bexI)
-    apply (auto simp add: add_ac)
-  done
-
-lemma set_plus_imp_minus: "(a::'a::ab_group_add) : b +o C ==> (a - b) : C"
-  by (auto simp add: elt_set_plus_def add_ac diff_minus)
-
-lemma set_minus_imp_plus: "(a::'a::ab_group_add) - b : C ==> a : b +o C"
-  apply (auto simp add: elt_set_plus_def add_ac diff_minus)
-  apply (subgoal_tac "a = (a + - b) + b")
-   apply (rule bexI, assumption, assumption)
-  apply (auto simp add: add_ac)
-  done
-
-lemma set_minus_plus: "((a::'a::ab_group_add) - b : C) = (a : b +o C)"
-  by (rule iffI, rule set_minus_imp_plus, assumption, rule set_plus_imp_minus,
-    assumption)
-
-lemma set_times_intro [intro]: "a : C ==> b : D ==> a * b : C \<otimes> D"
-  by (auto simp add: set_times_def)
-
-lemma set_times_intro2 [intro!]: "b : C ==> a * b : a *o C"
-  by (auto simp add: elt_set_times_def)
-
-lemma set_times_rearrange: "((a::'a::comm_monoid_mult) *o C) \<otimes>
-    (b *o D) = (a * b) *o (C \<otimes> D)"
-  apply (auto simp add: elt_set_times_def set_times_def)
-   apply (rule_tac x = "ba * bb" in exI)
-   apply (auto simp add: mult_ac)
-  apply (rule_tac x = "aa * a" in exI)
-  apply (auto simp add: mult_ac)
-  done
-
-lemma set_times_rearrange2: "(a::'a::semigroup_mult) *o (b *o C) =
-    (a * b) *o C"
-  by (auto simp add: elt_set_times_def mult_assoc)
-
-lemma set_times_rearrange3: "((a::'a::semigroup_mult) *o B) \<otimes> C =
-    a *o (B \<otimes> C)"
-  apply (auto simp add: elt_set_times_def set_times_def)
-   apply (blast intro: mult_ac)
-  apply (rule_tac x = "a * aa" in exI)
-  apply (rule conjI)
-   apply (rule_tac x = "aa" in bexI)
-    apply auto
-  apply (rule_tac x = "ba" in bexI)
-   apply (auto simp add: mult_ac)
-  done
-
-theorem set_times_rearrange4: "C \<otimes> ((a::'a::comm_monoid_mult) *o D) =
-    a *o (C \<otimes> D)"
-  apply (auto intro!: simp add: elt_set_times_def set_times_def
-    mult_ac)
-   apply (rule_tac x = "aa * ba" in exI)
-   apply (auto simp add: mult_ac)
-  done
-
-theorems set_times_rearranges = set_times_rearrange set_times_rearrange2
-  set_times_rearrange3 set_times_rearrange4
-
-lemma set_times_mono [intro]: "C <= D ==> a *o C <= a *o D"
-  by (auto simp add: elt_set_times_def)
-
-lemma set_times_mono2 [intro]: "(C::('a::times) set) <= D ==> E <= F ==>
-    C \<otimes> E <= D \<otimes> F"
-  by (auto simp add: set_times_def)
-
-lemma set_times_mono3 [intro]: "a : C ==> a *o D <= C \<otimes> D"
-  by (auto simp add: elt_set_times_def set_times_def)
-
-lemma set_times_mono4 [intro]: "(a::'a::comm_monoid_mult) : C ==>
-    a *o D <= D \<otimes> C"
-  by (auto simp add: elt_set_times_def set_times_def mult_ac)
-
-lemma set_times_mono5: "a:C ==> B <= D ==> a *o B <= C \<otimes> D"
-  apply (subgoal_tac "a *o B <= a *o D")
-   apply (erule order_trans)
-   apply (erule set_times_mono3)
-  apply (erule set_times_mono)
-  done
-
-lemma set_times_mono_b: "C <= D ==> x : a *o C
-    ==> x : a *o D"
-  apply (frule set_times_mono)
-  apply auto
-  done
-
-lemma set_times_mono2_b: "C <= D ==> E <= F ==> x : C \<otimes> E ==>
-    x : D \<otimes> F"
-  apply (frule set_times_mono2)
-   prefer 2
-   apply force
-  apply assumption
-  done
-
-lemma set_times_mono3_b: "a : C ==> x : a *o D ==> x : C \<otimes> D"
-  apply (frule set_times_mono3)
-  apply auto
-  done
-
-lemma set_times_mono4_b: "(a::'a::comm_monoid_mult) : C ==>
-    x : a *o D ==> x : D \<otimes> C"
-  apply (frule set_times_mono4)
-  apply auto
-  done
-
-lemma set_one_times [simp]: "(1::'a::comm_monoid_mult) *o C = C"
-  by (auto simp add: elt_set_times_def)
-
-lemma set_times_plus_distrib: "(a::'a::semiring) *o (b +o C)=
-    (a * b) +o (a *o C)"
-  by (auto simp add: elt_set_plus_def elt_set_times_def ring_distribs)
-
-lemma set_times_plus_distrib2: "(a::'a::semiring) *o (B \<oplus> C) =
-    (a *o B) \<oplus> (a *o C)"
-  apply (auto simp add: set_plus_def elt_set_times_def ring_distribs)
-   apply blast
-  apply (rule_tac x = "b + bb" in exI)
-  apply (auto simp add: ring_distribs)
-  done
-
-lemma set_times_plus_distrib3: "((a::'a::semiring) +o C) \<otimes> D <=
-    a *o D \<oplus> C \<otimes> D"
-  apply (auto simp add:
-    elt_set_plus_def elt_set_times_def set_times_def
-    set_plus_def ring_distribs)
-  apply auto
-  done
-
-theorems set_times_plus_distribs =
-  set_times_plus_distrib
-  set_times_plus_distrib2
-
-lemma set_neg_intro: "(a::'a::ring_1) : (- 1) *o C ==>
-    - a : C"
-  by (auto simp add: elt_set_times_def)
-
-lemma set_neg_intro2: "(a::'a::ring_1) : C ==>
-    - a : (- 1) *o C"
-  by (auto simp add: elt_set_times_def)
-
-lemma set_plus_image:
-  fixes S T :: "'n::semigroup_add set" shows "S \<oplus> T = (\<lambda>(x, y). x + y) ` (S \<times> T)"
-  unfolding set_plus_def by (fastforce simp: image_iff)
-
-lemma set_setsum_alt:
-  assumes fin: "finite I"
-  shows "setsum_set S I = {setsum s I |s. \<forall>i\<in>I. s i \<in> S i}"
-    (is "_ = ?setsum I")
-using fin
-proof induct
-  case (insert x F)
-  have "setsum_set S (insert x F) = S x \<oplus> ?setsum F"
-    using insert.hyps by auto
-  also have "...= {s x + setsum s F |s. \<forall> i\<in>insert x F. s i \<in> S i}"
-  proof -
-    {
-      fix y s assume "y \<in> S x" "\<forall>i\<in>F. s i \<in> S i"
-      then have "\<exists>s'. y + setsum s F = s' x + setsum s' F \<and> (\<forall>i\<in>insert x F. s' i \<in> S i)"
-        using insert.hyps
-        by (intro exI[of _ "\<lambda>i. if i \<in> F then s i else y"]) (auto simp add: set_plus_def)
-    }
-    then show ?thesis
-      unfolding set_plus_def by auto
-  qed
-  finally show ?case
-    using insert.hyps by auto
-qed auto
-
-lemma setsum_set_cond_linear:
-  fixes f :: "('a::comm_monoid_add) set \<Rightarrow> ('b::comm_monoid_add) set"
-  assumes [intro!]: "\<And>A B. P A  \<Longrightarrow> P B  \<Longrightarrow> P (A \<oplus> B)" "P {0}"
-    and f: "\<And>A B. P A  \<Longrightarrow> P B \<Longrightarrow> f (A \<oplus> B) = f A \<oplus> f B" "f {0} = {0}"
-  assumes all: "\<And>i. i \<in> I \<Longrightarrow> P (S i)"
-  shows "f (setsum_set S I) = setsum_set (f \<circ> S) I"
-proof cases
-  assume "finite I" from this all show ?thesis
-  proof induct
-    case (insert x F)
-    from `finite F` `\<And>i. i \<in> insert x F \<Longrightarrow> P (S i)` have "P (setsum_set S F)"
-      by induct auto
-    with insert show ?case
-      by (simp, subst f) auto
-  qed (auto intro!: f)
-qed (auto intro!: f)
-
-lemma setsum_set_linear:
-  fixes f :: "('a::comm_monoid_add) set => ('b::comm_monoid_add) set"
-  assumes "\<And>A B. f(A) \<oplus> f(B) = f(A \<oplus> B)" "f {0} = {0}"
-  shows "f (setsum_set S I) = setsum_set (f \<circ> S) I"
-  using setsum_set_cond_linear[of "\<lambda>x. True" f I S] assms by auto
-
-end