# HG changeset patch
# User haftmann
# Date 1236757557 -3600
# Node ID aad3cd70e25a2f5f298ad004c6425da76735271e
# Parent  699afca335277d9b7cf3eff68e71e13c20c81db2# Parent  836b71e950b52c7be9b62c0ae47872d00c53633e
merged

diff -r 699afca33527 -r aad3cd70e25a src/HOL/Code_Eval.thy
--- a/src/HOL/Code_Eval.thy	Tue Mar 10 22:50:19 2009 +0100
+++ b/src/HOL/Code_Eval.thy	Wed Mar 11 08:45:57 2009 +0100
@@ -134,6 +134,10 @@
 lemma [code, code del]: "(term_of \<Colon> typerep \<Rightarrow> term) = term_of" ..
 lemma [code, code del]: "(term_of \<Colon> term \<Rightarrow> term) = term_of" ..
 lemma [code, code del]: "(term_of \<Colon> message_string \<Rightarrow> term) = term_of" ..
+lemma [code, code del]:
+  "(Code_Eval.term_of \<Colon> 'a::{type, term_of} Predicate.pred \<Rightarrow> Code_Eval.term) = Code_Eval.term_of" ..
+lemma [code, code del]:
+  "(Code_Eval.term_of \<Colon> 'a::{type, term_of} Predicate.seq \<Rightarrow> Code_Eval.term) = Code_Eval.term_of" ..
 
 lemma term_of_char [unfolded typerep_fun_def typerep_char_def typerep_nibble_def, code]: "Code_Eval.term_of c =
     (let (n, m) = nibble_pair_of_char c
diff -r 699afca33527 -r aad3cd70e25a src/HOL/Decision_Procs/Decision_Procs.thy
--- a/src/HOL/Decision_Procs/Decision_Procs.thy	Tue Mar 10 22:50:19 2009 +0100
+++ b/src/HOL/Decision_Procs/Decision_Procs.thy	Wed Mar 11 08:45:57 2009 +0100
@@ -1,5 +1,7 @@
+header {* Various decision procedures. typically involving reflection *}
+
 theory Decision_Procs
-imports Cooper Ferrack MIR Approximation Dense_Linear_Order
+imports Cooper Ferrack MIR Approximation Dense_Linear_Order "ex/Approximation_Ex" "ex/Dense_Linear_Order_Ex"
 begin
 
 end
\ No newline at end of file
diff -r 699afca33527 -r aad3cd70e25a src/HOL/Decision_Procs/ex/Approximation_Ex.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Decision_Procs/ex/Approximation_Ex.thy	Wed Mar 11 08:45:57 2009 +0100
@@ -0,0 +1,52 @@
+(*  Title:      HOL/ex/ApproximationEx.thy
+    Author:     Johannes Hoelzl <hoelzl@in.tum.de> 2009
+*)
+
+theory Approximation_Ex
+imports Complex_Main "~~/src/HOL/Decision_Procs/Approximation"
+begin
+
+text {*
+
+Here are some examples how to use the approximation method.
+
+The parameter passed to the method specifies the precision used by the computations, it is specified
+as number of bits to calculate. When a variable is used it needs to be bounded by an interval. This
+interval is specified as a conjunction of the lower and upper bound. It must have the form
+@{text "\<lbrakk> l\<^isub>1 \<le> x\<^isub>1 \<and> x\<^isub>1 \<le> u\<^isub>1 ; \<dots> ; l\<^isub>n \<le> x\<^isub>n \<and> x\<^isub>n \<le> u\<^isub>n \<rbrakk> \<Longrightarrow> F"} where @{term F} is the formula, and
+@{text "x\<^isub>1, \<dots>, x\<^isub>n"} are the variables. The lower bounds @{text "l\<^isub>1, \<dots>, l\<^isub>n"} and the upper bounds
+@{text "u\<^isub>1, \<dots>, u\<^isub>n"} must either be integer numerals, floating point numbers or of the form
+@{term "m * pow2 e"} to specify a exact floating point value.
+
+*}
+
+section "Compute some transcendental values"
+
+lemma "\<bar> ln 2 - 544531980202654583340825686620847 / 785593587443817081832229725798400 \<bar> < inverse (2^51) "
+  by (approximation 80)
+
+lemma "\<bar> exp 1.626 - 5.083499996273 \<bar> < (inverse 10 ^ 10 :: real)"
+  by (approximation 80)
+
+lemma "\<bar> sqrt 2 - 1.4142135623730951 \<bar> < inverse 10 ^ 16"
+  by (approximation 80)
+   
+lemma "\<bar> pi - 3.1415926535897932385 \<bar> < inverse 10 ^ 18"
+  by (approximation 80)
+
+section "Use variable ranges"
+
+lemma "0.5 \<le> x \<and> x \<le> 4.5 \<Longrightarrow> \<bar> arctan x - 0.91 \<bar> < 0.455"
+  by (approximation 10)
+
+lemma "0.49 \<le> x \<and> x \<le> 4.49 \<Longrightarrow> \<bar> arctan x - 0.91 \<bar> < 0.455"
+  by (approximation 20)
+
+lemma "1 * pow2 -1 \<le> x \<and> x \<le> 9 * pow2 -1 \<Longrightarrow> \<bar> arctan x - 0.91 \<bar> < 0.455"
+  by (approximation 10)
+
+lemma "0 \<le> x \<and> x \<le> 1 \<Longrightarrow> 0 \<le> sin x"
+  by (approximation 10)
+
+end
+
diff -r 699afca33527 -r aad3cd70e25a src/HOL/Decision_Procs/ex/Dense_Linear_Order_Ex.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Decision_Procs/ex/Dense_Linear_Order_Ex.thy	Wed Mar 11 08:45:57 2009 +0100
@@ -0,0 +1,153 @@
+(* Author:     Amine Chaieb, TU Muenchen *)
+
+header {* Examples for Ferrante and Rackoff's quantifier elimination procedure *}
+
+theory Dense_Linear_Order_Ex
+imports Complex_Main "~~/src/HOL/Decision_Procs/Dense_Linear_Order"
+begin
+
+lemma
+  "\<exists>(y::'a::{ordered_field,recpower,number_ring, division_by_zero}) <2. x + 3* y < 0 \<and> x - y >0"
+  by ferrack
+
+lemma "~ (ALL x (y::'a::{ordered_field,recpower,number_ring, division_by_zero}). x < y --> 10*x < 11*y)"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. x < y --> (10*(x + 5*y + -1) < 60*y)"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. x ~= y --> x < y"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (x ~= y & 10*x ~= 9*y & 10*x < y) --> x < y"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (x ~= y & 5*x <= y) --> 500*x <= 100*y"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX (y::'a::{ordered_field,recpower,number_ring, division_by_zero}). 4*x + 3*y <= 0 & 4*x + 3*y >= -1)"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) < 0. (EX (y::'a::{ordered_field,recpower,number_ring, division_by_zero}) > 0. 7*x + y > 0 & x - y <= 9)"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (0 < x & x < 1) --> (ALL y > 1. x + y ~= 1)"
+  by ferrack
+
+lemma "EX x. (ALL (y::'a::{ordered_field,recpower,number_ring, division_by_zero}). y < 2 -->  2*(y - x) \<le> 0 )"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). x < 10 | x > 20 | (EX y. y>= 0 & y <= 10 & x+y = 20)"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. x + y < z --> y >= z --> x < 0"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. x + 7*y < 5* z & 5*y >= 7*z & x < 0"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. abs (x + y) <= z --> (abs z = z)"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. x + 7*y - 5* z < 0 & 5*y + 7*z + 3*x < 0"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. (abs (5*x+3*y+z) <= 5*x+3*y+z & abs (5*x+3*y+z) >= - (5*x+3*y+z)) | (abs (5*x+3*y+z) >= 5*x+3*y+z & abs (5*x+3*y+z) <= - (5*x+3*y+z))"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. x < y --> (EX z>0. x+z = y)"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. x < y --> (EX z>0. x+z = y)"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (EX z>0. abs (x - y) <= z )"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (ALL z<0. (z < x --> z <= y) & (z > y --> z >= x))"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (ALL z>=0. abs (3*x+7*y) <= 2*z + 1)"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (ALL z<0. (z < x --> z <= y) & (z > y --> z >= x))"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero})>0. (ALL y. (EX z. 13* abs z \<noteq> abs (12*y - x) & 5*x - 3*(abs y) <= 7*z))"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). abs (4*x + 17) < 4 & (ALL y . abs (x*34 - 34*y - 9) \<noteq> 0 \<longrightarrow> (EX z. 5*x - 3*abs y <= 7*z))"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y > abs (23*x - 9). (ALL z > abs (3*y - 19* abs x). x+z > 2*y))"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y< abs (3*x - 1). (ALL z >= (3*abs x - 1). abs (12*x - 13*y + 19*z) > abs (23*x) ))"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). abs x < 100 & (ALL y > x. (EX z<2*y - x. 5*x - 3*y <= 7*z))"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z w. 7*x<3*y --> 5*y < 7*z --> z < 2*w --> 7*(2*w-x) > 2*y"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z w. 5*x + 3*z - 17*w + abs (y - 8*x + z) <= 89"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z w. 5*x + 3*z - 17*w + 7* (y - 8*x + z) <= max y (7*z - x + w)"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z w. min (5*x + 3*z) (17*w) + 5* abs (y - 8*x + z) <= max y (7*z - x + w)"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. (EX w >= (x+y+z). w <= abs x + abs y + abs z)"
+  by ferrack
+
+lemma "~(ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y z w. 3* x + z*4 = 3*y & x + y < z & x> w & 3*x < w + y))"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (EX z w. abs (x-y) = (z-w) & z*1234 < 233*x & w ~= y)"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y z w. min (5*x + 3*z) (17*w) + 5* abs (y - 8*x + z) <= max y (7*z - x + w))"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. (ALL w >= abs (x+y+z). w >= abs x + abs y + abs z)"
+  by ferrack
+
+lemma "EX z. (ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (EX w >= (x+y+z). w <= abs x + abs y + abs z))"
+  by ferrack
+
+lemma "EX z. (ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) < abs z. (EX y w. x< y & x < z & x> w & 3*x < w + y))"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (EX z. (ALL w. abs (x-y) = abs (z-w) --> z < x & w ~= y))"
+  by ferrack
+
+lemma "EX y. (ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX z w. min (5*x + 3*z) (17*w) + 5* abs (y - 8*x + z) <= max y (7*z - x + w)))"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) z. (ALL w >= 13*x - 4*z. (EX y. w >= abs x + abs y + z))"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (ALL y < x. (EX z > (x+y).
+  (ALL w. 5*w + 10*x - z >= y --> w + 7*x + 3*z >= 2*y)))"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (ALL y. (EX z > y.
+  (ALL w . w < 13 --> w + 10*x - z >= y --> 5*w + 7*x + 13*z >= 2*y)))"
+  by ferrack
+
+lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z w. min (5*x + 3*z) (17*w) + 5* abs (y - 8*x + z) <= max y (7*z - x + w)"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y. (ALL z>19. y <= x + z & (EX w. abs (y - x) < w)))"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y. (ALL z>19. y <= x + z & (EX w. abs (x + z) < w - y)))"
+  by ferrack
+
+lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y. abs y ~= abs x & (ALL z> max x y. (EX w. w ~= y & w ~= z & 3*w - z >= x + y)))"
+  by ferrack
+
+end
diff -r 699afca33527 -r aad3cd70e25a src/HOL/FunDef.thy
--- a/src/HOL/FunDef.thy	Tue Mar 10 22:50:19 2009 +0100
+++ b/src/HOL/FunDef.thy	Wed Mar 11 08:45:57 2009 +0100
@@ -225,10 +225,10 @@
 subsection {* Concrete orders for SCNP termination proofs *}
 
 definition "pair_less = less_than <*lex*> less_than"
-definition "pair_leq = pair_less^="
+definition [code del]: "pair_leq = pair_less^="
 definition "max_strict = max_ext pair_less"
-definition "max_weak = max_ext pair_leq \<union> {({}, {})}"
-definition "min_strict = min_ext pair_less"
+definition [code del]: "max_weak = max_ext pair_leq \<union> {({}, {})}"
+definition [code del]: "min_strict = min_ext pair_less"
 definition "min_weak = min_ext pair_leq \<union> {({}, {})}"
 
 lemma wf_pair_less[simp]: "wf pair_less"
diff -r 699afca33527 -r aad3cd70e25a src/HOL/IsaMakefile
--- a/src/HOL/IsaMakefile	Tue Mar 10 22:50:19 2009 +0100
+++ b/src/HOL/IsaMakefile	Wed Mar 11 08:45:57 2009 +0100
@@ -680,6 +680,8 @@
   Decision_Procs/MIR.thy \
   Decision_Procs/mir_tac.ML \
   Decision_Procs/Decision_Procs.thy \
+  Decision_Procs/ex/Dense_Linear_Order_Ex.thy \
+  Decision_Procs/ex/Approximation_Ex.thy \
   Decision_Procs/ROOT.ML
 	@$(ISABELLE_TOOL) usedir $(OUT)/HOL Decision_Procs
 
@@ -823,13 +825,13 @@
 
 $(LOG)/HOL-ex.gz: $(OUT)/HOL Library/Commutative_Ring.thy		\
   Library/Primes.thy ex/Abstract_NAT.thy ex/Antiquote.thy		\
-  ex/ApproximationEx.thy ex/Arith_Examples.thy				\
+  ex/Arith_Examples.thy				\
   ex/Arithmetic_Series_Complex.thy ex/BT.thy ex/BinEx.thy		\
   ex/Binary.thy ex/CTL.thy ex/Chinese.thy ex/Classical.thy		\
   ex/CodegenSML_Test.thy ex/Codegenerator.thy				\
   ex/Codegenerator_Pretty.thy ex/Coherent.thy				\
   ex/Commutative_RingEx.thy ex/Commutative_Ring_Complete.thy		\
-  ex/Dense_Linear_Order_Ex.thy ex/Efficient_Nat_examples.thy		\
+  ex/Efficient_Nat_examples.thy		\
   ex/Eval_Examples.thy ex/ExecutableContent.thy				\
   ex/Formal_Power_Series_Examples.thy ex/Fundefs.thy			\
   ex/Groebner_Examples.thy ex/Guess.thy ex/HarmonicSeries.thy		\
diff -r 699afca33527 -r aad3cd70e25a src/HOL/Library/Multiset.thy
--- a/src/HOL/Library/Multiset.thy	Tue Mar 10 22:50:19 2009 +0100
+++ b/src/HOL/Library/Multiset.thy	Wed Mar 11 08:45:57 2009 +0100
@@ -1487,7 +1487,7 @@
   by auto
 
 definition "ms_strict = mult pair_less"
-definition "ms_weak = ms_strict \<union> Id"
+definition [code del]: "ms_weak = ms_strict \<union> Id"
 
 lemma ms_reduction_pair: "reduction_pair (ms_strict, ms_weak)"
 unfolding reduction_pair_def ms_strict_def ms_weak_def pair_less_def
diff -r 699afca33527 -r aad3cd70e25a src/HOL/Predicate.thy
--- a/src/HOL/Predicate.thy	Tue Mar 10 22:50:19 2009 +0100
+++ b/src/HOL/Predicate.thy	Wed Mar 11 08:45:57 2009 +0100
@@ -588,7 +588,39 @@
     by (simp add: adjunct_sup sup_assoc sup_commute sup_left_commute)
 qed
 
-declare eq_pred_def [code, code del]
+primrec contained :: "'a seq \<Rightarrow> 'a pred \<Rightarrow> bool" where
+    "contained Empty Q \<longleftrightarrow> True"
+  | "contained (Insert x P) Q \<longleftrightarrow> eval Q x \<and> P \<le> Q"
+  | "contained (Join P xq) Q \<longleftrightarrow> P \<le> Q \<and> contained xq Q"
+
+lemma single_less_eq_eval:
+  "single x \<le> P \<longleftrightarrow> eval P x"
+  by (auto simp add: single_def less_eq_pred_def mem_def)
+
+lemma contained_less_eq:
+  "contained xq Q \<longleftrightarrow> pred_of_seq xq \<le> Q"
+  by (induct xq) (simp_all add: single_less_eq_eval)
+
+lemma less_eq_pred_code [code]:
+  "Seq f \<le> Q = (case f ()
+   of Empty \<Rightarrow> True
+    | Insert x P \<Rightarrow> eval Q x \<and> P \<le> Q
+    | Join P xq \<Rightarrow> P \<le> Q \<and> contained xq Q)"
+  by (cases "f ()")
+    (simp_all add: Seq_def single_less_eq_eval contained_less_eq)
+
+lemma eq_pred_code [code]:
+  fixes P Q :: "'a::eq pred"
+  shows "eq_class.eq P Q \<longleftrightarrow> P \<le> Q \<and> Q \<le> P"
+  unfolding eq by auto
+
+lemma [code]:
+  "pred_case f P = f (eval P)"
+  by (cases P) simp
+
+lemma [code]:
+  "pred_rec f P = f (eval P)"
+  by (cases P) simp
 
 no_notation
   inf (infixl "\<sqinter>" 70) and
@@ -601,6 +633,6 @@
 
 hide (open) type pred seq
 hide (open) const Pred eval single bind if_pred not_pred
-  Empty Insert Join Seq member "apply" adjunct
+  Empty Insert Join Seq member pred_of_seq "apply" adjunct
 
 end
diff -r 699afca33527 -r aad3cd70e25a src/HOL/Tools/datatype_package.ML
--- a/src/HOL/Tools/datatype_package.ML	Tue Mar 10 22:50:19 2009 +0100
+++ b/src/HOL/Tools/datatype_package.ML	Wed Mar 11 08:45:57 2009 +0100
@@ -677,15 +677,14 @@
       val thy = ProofContext.theory_of ctxt;
       val (vs, cos) = the_datatype_spec thy dtco;
       val ty = Type (dtco, map TFree vs);
-      fun pretty_typ_br ty =
-        let
-          val p = Syntax.pretty_typ ctxt ty;
-          val s = explode (Pretty.str_of p);  (* FIXME do not inspect pretty output! *)
-        in if member (op =) s " " then Pretty.enclose "(" ")" [p] else p end;
+      fun pretty_typ_bracket (ty as Type (_, _ :: _)) =
+            Pretty.enclose "(" ")" [Syntax.pretty_typ ctxt ty]
+        | pretty_typ_bracket ty =
+            Syntax.pretty_typ ctxt ty;
       fun pretty_constr (co, tys) =
         (Pretty.block o Pretty.breaks)
           (Syntax.pretty_term ctxt (Const (co, tys ---> ty)) ::
-            map pretty_typ_br tys);
+            map pretty_typ_bracket tys);
       val pretty_datatype =
         Pretty.block
           (Pretty.command "datatype" :: Pretty.brk 1 ::
diff -r 699afca33527 -r aad3cd70e25a src/HOL/Wellfounded.thy
--- a/src/HOL/Wellfounded.thy	Tue Mar 10 22:50:19 2009 +0100
+++ b/src/HOL/Wellfounded.thy	Wed Mar 11 08:45:57 2009 +0100
@@ -960,4 +960,10 @@
 
 declare "prod.size" [noatp]
 
+lemma [code]:
+  "size (P :: 'a Predicate.pred) = 0" by (cases P) simp
+
+lemma [code]:
+  "pred_size f P = 0" by (cases P) simp
+
 end
diff -r 699afca33527 -r aad3cd70e25a src/HOL/ex/ApproximationEx.thy
--- a/src/HOL/ex/ApproximationEx.thy	Tue Mar 10 22:50:19 2009 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,52 +0,0 @@
-(*  Title:      HOL/ex/ApproximationEx.thy
-    Author:     Johannes Hoelzl <hoelzl@in.tum.de> 2009
-*)
-
-theory ApproximationEx
-imports "~~/src/HOL/Decision_Procs/Approximation"
-begin
-
-text {*
-
-Here are some examples how to use the approximation method.
-
-The parameter passed to the method specifies the precision used by the computations, it is specified
-as number of bits to calculate. When a variable is used it needs to be bounded by an interval. This
-interval is specified as a conjunction of the lower and upper bound. It must have the form
-@{text "\<lbrakk> l\<^isub>1 \<le> x\<^isub>1 \<and> x\<^isub>1 \<le> u\<^isub>1 ; \<dots> ; l\<^isub>n \<le> x\<^isub>n \<and> x\<^isub>n \<le> u\<^isub>n \<rbrakk> \<Longrightarrow> F"} where @{term F} is the formula, and
-@{text "x\<^isub>1, \<dots>, x\<^isub>n"} are the variables. The lower bounds @{text "l\<^isub>1, \<dots>, l\<^isub>n"} and the upper bounds
-@{text "u\<^isub>1, \<dots>, u\<^isub>n"} must either be integer numerals, floating point numbers or of the form
-@{term "m * pow2 e"} to specify a exact floating point value.
-
-*}
-
-section "Compute some transcendental values"
-
-lemma "\<bar> ln 2 - 544531980202654583340825686620847 / 785593587443817081832229725798400 \<bar> < inverse (2^51) "
-  by (approximation 80)
-
-lemma "\<bar> exp 1.626 - 5.083499996273 \<bar> < (inverse 10 ^ 10 :: real)"
-  by (approximation 80)
-
-lemma "\<bar> sqrt 2 - 1.4142135623730951 \<bar> < inverse 10 ^ 16"
-  by (approximation 80)
-   
-lemma "\<bar> pi - 3.1415926535897932385 \<bar> < inverse 10 ^ 18"
-  by (approximation 80)
-
-section "Use variable ranges"
-
-lemma "0.5 \<le> x \<and> x \<le> 4.5 \<Longrightarrow> \<bar> arctan x - 0.91 \<bar> < 0.455"
-  by (approximation 10)
-
-lemma "0.49 \<le> x \<and> x \<le> 4.49 \<Longrightarrow> \<bar> arctan x - 0.91 \<bar> < 0.455"
-  by (approximation 20)
-
-lemma "1 * pow2 -1 \<le> x \<and> x \<le> 9 * pow2 -1 \<Longrightarrow> \<bar> arctan x - 0.91 \<bar> < 0.455"
-  by (approximation 10)
-
-lemma "0 \<le> x \<and> x \<le> 1 \<Longrightarrow> 0 \<le> sin x"
-  by (approximation 10)
-
-end
-
diff -r 699afca33527 -r aad3cd70e25a src/HOL/ex/Dense_Linear_Order_Ex.thy
--- a/src/HOL/ex/Dense_Linear_Order_Ex.thy	Tue Mar 10 22:50:19 2009 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,153 +0,0 @@
-(* Author:     Amine Chaieb, TU Muenchen *)
-
-header {* Examples for Ferrante and Rackoff's quantifier elimination procedure *}
-
-theory Dense_Linear_Order_Ex
-imports "~~/src/HOL/Decision_Procs/Dense_Linear_Order" Main
-begin
-
-lemma
-  "\<exists>(y::'a::{ordered_field,recpower,number_ring, division_by_zero}) <2. x + 3* y < 0 \<and> x - y >0"
-  by ferrack
-
-lemma "~ (ALL x (y::'a::{ordered_field,recpower,number_ring, division_by_zero}). x < y --> 10*x < 11*y)"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. x < y --> (10*(x + 5*y + -1) < 60*y)"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. x ~= y --> x < y"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (x ~= y & 10*x ~= 9*y & 10*x < y) --> x < y"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (x ~= y & 5*x <= y) --> 500*x <= 100*y"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX (y::'a::{ordered_field,recpower,number_ring, division_by_zero}). 4*x + 3*y <= 0 & 4*x + 3*y >= -1)"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) < 0. (EX (y::'a::{ordered_field,recpower,number_ring, division_by_zero}) > 0. 7*x + y > 0 & x - y <= 9)"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (0 < x & x < 1) --> (ALL y > 1. x + y ~= 1)"
-  by ferrack
-
-lemma "EX x. (ALL (y::'a::{ordered_field,recpower,number_ring, division_by_zero}). y < 2 -->  2*(y - x) \<le> 0 )"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). x < 10 | x > 20 | (EX y. y>= 0 & y <= 10 & x+y = 20)"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. x + y < z --> y >= z --> x < 0"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. x + 7*y < 5* z & 5*y >= 7*z & x < 0"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. abs (x + y) <= z --> (abs z = z)"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. x + 7*y - 5* z < 0 & 5*y + 7*z + 3*x < 0"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. (abs (5*x+3*y+z) <= 5*x+3*y+z & abs (5*x+3*y+z) >= - (5*x+3*y+z)) | (abs (5*x+3*y+z) >= 5*x+3*y+z & abs (5*x+3*y+z) <= - (5*x+3*y+z))"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. x < y --> (EX z>0. x+z = y)"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. x < y --> (EX z>0. x+z = y)"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (EX z>0. abs (x - y) <= z )"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (ALL z<0. (z < x --> z <= y) & (z > y --> z >= x))"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (ALL z>=0. abs (3*x+7*y) <= 2*z + 1)"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (ALL z<0. (z < x --> z <= y) & (z > y --> z >= x))"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero})>0. (ALL y. (EX z. 13* abs z \<noteq> abs (12*y - x) & 5*x - 3*(abs y) <= 7*z))"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). abs (4*x + 17) < 4 & (ALL y . abs (x*34 - 34*y - 9) \<noteq> 0 \<longrightarrow> (EX z. 5*x - 3*abs y <= 7*z))"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y > abs (23*x - 9). (ALL z > abs (3*y - 19* abs x). x+z > 2*y))"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y< abs (3*x - 1). (ALL z >= (3*abs x - 1). abs (12*x - 13*y + 19*z) > abs (23*x) ))"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). abs x < 100 & (ALL y > x. (EX z<2*y - x. 5*x - 3*y <= 7*z))"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z w. 7*x<3*y --> 5*y < 7*z --> z < 2*w --> 7*(2*w-x) > 2*y"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z w. 5*x + 3*z - 17*w + abs (y - 8*x + z) <= 89"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z w. 5*x + 3*z - 17*w + 7* (y - 8*x + z) <= max y (7*z - x + w)"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z w. min (5*x + 3*z) (17*w) + 5* abs (y - 8*x + z) <= max y (7*z - x + w)"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. (EX w >= (x+y+z). w <= abs x + abs y + abs z)"
-  by ferrack
-
-lemma "~(ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y z w. 3* x + z*4 = 3*y & x + y < z & x> w & 3*x < w + y))"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (EX z w. abs (x-y) = (z-w) & z*1234 < 233*x & w ~= y)"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y z w. min (5*x + 3*z) (17*w) + 5* abs (y - 8*x + z) <= max y (7*z - x + w))"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z. (ALL w >= abs (x+y+z). w >= abs x + abs y + abs z)"
-  by ferrack
-
-lemma "EX z. (ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (EX w >= (x+y+z). w <= abs x + abs y + abs z))"
-  by ferrack
-
-lemma "EX z. (ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) < abs z. (EX y w. x< y & x < z & x> w & 3*x < w + y))"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y. (EX z. (ALL w. abs (x-y) = abs (z-w) --> z < x & w ~= y))"
-  by ferrack
-
-lemma "EX y. (ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX z w. min (5*x + 3*z) (17*w) + 5* abs (y - 8*x + z) <= max y (7*z - x + w)))"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) z. (ALL w >= 13*x - 4*z. (EX y. w >= abs x + abs y + z))"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (ALL y < x. (EX z > (x+y).
-  (ALL w. 5*w + 10*x - z >= y --> w + 7*x + 3*z >= 2*y)))"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (ALL y. (EX z > y.
-  (ALL w . w < 13 --> w + 10*x - z >= y --> 5*w + 7*x + 13*z >= 2*y)))"
-  by ferrack
-
-lemma "EX (x::'a::{ordered_field,recpower,number_ring, division_by_zero}) y z w. min (5*x + 3*z) (17*w) + 5* abs (y - 8*x + z) <= max y (7*z - x + w)"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y. (ALL z>19. y <= x + z & (EX w. abs (y - x) < w)))"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y. (ALL z>19. y <= x + z & (EX w. abs (x + z) < w - y)))"
-  by ferrack
-
-lemma "ALL (x::'a::{ordered_field,recpower,number_ring, division_by_zero}). (EX y. abs y ~= abs x & (ALL z> max x y. (EX w. w ~= y & w ~= z & 3*w - z >= x + y)))"
-  by ferrack
-
-end
diff -r 699afca33527 -r aad3cd70e25a src/HOL/ex/ExecutableContent.thy
--- a/src/HOL/ex/ExecutableContent.thy	Tue Mar 10 22:50:19 2009 +0100
+++ b/src/HOL/ex/ExecutableContent.thy	Wed Mar 11 08:45:57 2009 +0100
@@ -24,24 +24,6 @@
   "~~/src/HOL/ex/Records"
 begin
 
-lemma [code, code del]:
-  "(size :: 'a::size Predicate.pred => nat) = size" ..
-lemma [code, code del]:
-  "pred_size = pred_size" ..
-lemma [code, code del]:
-  "pred_case = pred_case" ..
-lemma [code, code del]:
-  "pred_rec = pred_rec" ..
-lemma [code, code del]:
-  "(Code_Eval.term_of \<Colon> 'a::{type, term_of} Predicate.pred \<Rightarrow> Code_Eval.term) = Code_Eval.term_of" ..
-lemma [code, code del]:
-  "(Code_Eval.term_of \<Colon> 'a::{type, term_of} Predicate.seq \<Rightarrow> Code_Eval.term) = Code_Eval.term_of" ..
-
-text {* However, some aren't executable *}
-
-declare pair_leq_def[code del]
-declare max_weak_def[code del]
-declare min_weak_def[code del]
-declare ms_weak_def[code del]
+declare min_weak_def [code del]
 
 end
diff -r 699afca33527 -r aad3cd70e25a src/HOL/ex/ROOT.ML
--- a/src/HOL/ex/ROOT.ML	Tue Mar 10 22:50:19 2009 +0100
+++ b/src/HOL/ex/ROOT.ML	Wed Mar 11 08:45:57 2009 +0100
@@ -60,7 +60,6 @@
   "Code_Antiq",
   "Termination",
   "Coherent",
-  "Dense_Linear_Order_Ex",
   "PresburgerEx",
   "ReflectionEx",
   "BinEx",