--- a/NEWS Tue Sep 01 14:09:59 2009 +0200
+++ b/NEWS Tue Sep 01 14:10:38 2009 +0200
@@ -112,6 +112,9 @@
Suc_eq_add_numeral_1_left -> Suc_eq_plus1_left
Suc_plus1 -> Suc_eq_plus1
+* Moved theorems:
+Wellfounded.in_inv_image -> Relation.in_inv_image
+
* New sledgehammer option "Full Types" in Proof General settings menu.
Causes full type information to be output to the ATPs. This slows
ATPs down considerably but eliminates a source of unsound "proofs"
--- a/src/HOL/MicroJava/J/TypeRel.thy Tue Sep 01 14:09:59 2009 +0200
+++ b/src/HOL/MicroJava/J/TypeRel.thy Tue Sep 01 14:10:38 2009 +0200
@@ -97,6 +97,14 @@
qed
qed
+text {* Code generator setup (FIXME!) *}
+
+consts_code
+ "wfrec" ("\<module>wfrec?")
+attach {*
+fun wfrec f x = f (wfrec f) x;
+*}
+
consts
method :: "'c prog \<times> cname => ( sig \<rightharpoonup> cname \<times> ty \<times> 'c)" (* ###curry *)
--- a/src/HOL/Recdef.thy Tue Sep 01 14:09:59 2009 +0200
+++ b/src/HOL/Recdef.thy Tue Sep 01 14:10:38 2009 +0200
@@ -19,6 +19,65 @@
("Tools/recdef.ML")
begin
+inductive
+ wfrec_rel :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => 'a => 'b => bool"
+ for R :: "('a * 'a) set"
+ and F :: "('a => 'b) => 'a => 'b"
+where
+ wfrecI: "ALL z. (z, x) : R --> wfrec_rel R F z (g z) ==>
+ wfrec_rel R F x (F g x)"
+
+constdefs
+ cut :: "('a => 'b) => ('a * 'a)set => 'a => 'a => 'b"
+ "cut f r x == (%y. if (y,x):r then f y else undefined)"
+
+ adm_wf :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => bool"
+ "adm_wf R F == ALL f g x.
+ (ALL z. (z, x) : R --> f z = g z) --> F f x = F g x"
+
+ wfrec :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => 'a => 'b"
+ [code del]: "wfrec R F == %x. THE y. wfrec_rel R (%f x. F (cut f R x) x) x y"
+
+subsection{*Well-Founded Recursion*}
+
+text{*cut*}
+
+lemma cuts_eq: "(cut f r x = cut g r x) = (ALL y. (y,x):r --> f(y)=g(y))"
+by (simp add: expand_fun_eq cut_def)
+
+lemma cut_apply: "(x,a):r ==> (cut f r a)(x) = f(x)"
+by (simp add: cut_def)
+
+text{*Inductive characterization of wfrec combinator; for details see:
+John Harrison, "Inductive definitions: automation and application"*}
+
+lemma wfrec_unique: "[| adm_wf R F; wf R |] ==> EX! y. wfrec_rel R F x y"
+apply (simp add: adm_wf_def)
+apply (erule_tac a=x in wf_induct)
+apply (rule ex1I)
+apply (rule_tac g = "%x. THE y. wfrec_rel R F x y" in wfrec_rel.wfrecI)
+apply (fast dest!: theI')
+apply (erule wfrec_rel.cases, simp)
+apply (erule allE, erule allE, erule allE, erule mp)
+apply (fast intro: the_equality [symmetric])
+done
+
+lemma adm_lemma: "adm_wf R (%f x. F (cut f R x) x)"
+apply (simp add: adm_wf_def)
+apply (intro strip)
+apply (rule cuts_eq [THEN iffD2, THEN subst], assumption)
+apply (rule refl)
+done
+
+lemma wfrec: "wf(r) ==> wfrec r H a = H (cut (wfrec r H) r a) a"
+apply (simp add: wfrec_def)
+apply (rule adm_lemma [THEN wfrec_unique, THEN the1_equality], assumption)
+apply (rule wfrec_rel.wfrecI)
+apply (intro strip)
+apply (erule adm_lemma [THEN wfrec_unique, THEN theI'])
+done
+
+
text{** This form avoids giant explosions in proofs. NOTE USE OF ==*}
lemma def_wfrec: "[| f==wfrec r H; wf(r) |] ==> f(a) = H (cut f r a) a"
apply auto
--- a/src/HOL/Relation.thy Tue Sep 01 14:09:59 2009 +0200
+++ b/src/HOL/Relation.thy Tue Sep 01 14:10:38 2009 +0200
@@ -599,6 +599,9 @@
apply blast
done
+lemma in_inv_image[simp]: "((x,y) : inv_image r f) = ((f x, f y) : r)"
+ by (auto simp:inv_image_def)
+
subsection {* Finiteness *}
--- a/src/HOL/Tools/TFL/rules.ML Tue Sep 01 14:09:59 2009 +0200
+++ b/src/HOL/Tools/TFL/rules.ML Tue Sep 01 14:10:38 2009 +0200
@@ -456,7 +456,7 @@
fun is_cong thm =
case (Thm.prop_of thm)
of (Const("==>",_)$(Const("Trueprop",_)$ _) $
- (Const("==",_) $ (Const (@{const_name "Wellfounded.cut"},_) $ f $ R $ a $ x) $ _)) => false
+ (Const("==",_) $ (Const (@{const_name "Recdef.cut"},_) $ f $ R $ a $ x) $ _)) => false
| _ => true;
@@ -659,7 +659,7 @@
end;
fun restricted t = isSome (S.find_term
- (fn (Const(@{const_name "Wellfounded.cut"},_)) =>true | _ => false)
+ (fn (Const(@{const_name "Recdef.cut"},_)) =>true | _ => false)
t)
fun CONTEXT_REWRITE_RULE (func, G, cut_lemma, congs) th =
--- a/src/HOL/Wellfounded.thy Tue Sep 01 14:09:59 2009 +0200
+++ b/src/HOL/Wellfounded.thy Tue Sep 01 14:10:38 2009 +0200
@@ -13,14 +13,6 @@
subsection {* Basic Definitions *}
-inductive
- wfrec_rel :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => 'a => 'b => bool"
- for R :: "('a * 'a) set"
- and F :: "('a => 'b) => 'a => 'b"
-where
- wfrecI: "ALL z. (z, x) : R --> wfrec_rel R F z (g z) ==>
- wfrec_rel R F x (F g x)"
-
constdefs
wf :: "('a * 'a)set => bool"
"wf(r) == (!P. (!x. (!y. (y,x):r --> P(y)) --> P(x)) --> (!x. P(x)))"
@@ -31,16 +23,6 @@
acyclic :: "('a*'a)set => bool"
"acyclic r == !x. (x,x) ~: r^+"
- cut :: "('a => 'b) => ('a * 'a)set => 'a => 'a => 'b"
- "cut f r x == (%y. if (y,x):r then f y else undefined)"
-
- adm_wf :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => bool"
- "adm_wf R F == ALL f g x.
- (ALL z. (z, x) : R --> f z = g z) --> F f x = F g x"
-
- wfrec :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => 'a => 'b"
- [code del]: "wfrec R F == %x. THE y. wfrec_rel R (%f x. F (cut f R x) x) x y"
-
abbreviation acyclicP :: "('a => 'a => bool) => bool" where
"acyclicP r == acyclic {(x, y). r x y}"
@@ -425,54 +407,6 @@
by (blast intro: finite_acyclic_wf wf_acyclic)
-subsection{*Well-Founded Recursion*}
-
-text{*cut*}
-
-lemma cuts_eq: "(cut f r x = cut g r x) = (ALL y. (y,x):r --> f(y)=g(y))"
-by (simp add: expand_fun_eq cut_def)
-
-lemma cut_apply: "(x,a):r ==> (cut f r a)(x) = f(x)"
-by (simp add: cut_def)
-
-text{*Inductive characterization of wfrec combinator; for details see:
-John Harrison, "Inductive definitions: automation and application"*}
-
-lemma wfrec_unique: "[| adm_wf R F; wf R |] ==> EX! y. wfrec_rel R F x y"
-apply (simp add: adm_wf_def)
-apply (erule_tac a=x in wf_induct)
-apply (rule ex1I)
-apply (rule_tac g = "%x. THE y. wfrec_rel R F x y" in wfrec_rel.wfrecI)
-apply (fast dest!: theI')
-apply (erule wfrec_rel.cases, simp)
-apply (erule allE, erule allE, erule allE, erule mp)
-apply (fast intro: the_equality [symmetric])
-done
-
-lemma adm_lemma: "adm_wf R (%f x. F (cut f R x) x)"
-apply (simp add: adm_wf_def)
-apply (intro strip)
-apply (rule cuts_eq [THEN iffD2, THEN subst], assumption)
-apply (rule refl)
-done
-
-lemma wfrec: "wf(r) ==> wfrec r H a = H (cut (wfrec r H) r a) a"
-apply (simp add: wfrec_def)
-apply (rule adm_lemma [THEN wfrec_unique, THEN the1_equality], assumption)
-apply (rule wfrec_rel.wfrecI)
-apply (intro strip)
-apply (erule adm_lemma [THEN wfrec_unique, THEN theI'])
-done
-
-subsection {* Code generator setup *}
-
-consts_code
- "wfrec" ("\<module>wfrec?")
-attach {*
-fun wfrec f x = f (wfrec f) x;
-*}
-
-
subsection {* @{typ nat} is well-founded *}
lemma less_nat_rel: "op < = (\<lambda>m n. n = Suc m)^++"
@@ -696,9 +630,6 @@
apply blast
done
-lemma in_inv_image[simp]: "((x,y) : inv_image r f) = ((f x, f y) : r)"
- by (auto simp:inv_image_def)
-
text {* Measure Datatypes into @{typ nat} *}
definition measure :: "('a => nat) => ('a * 'a)set"
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/General/linear_set.scala Tue Sep 01 14:10:38 2009 +0200
@@ -0,0 +1,118 @@
+/* Title: Pure/General/linear_set.scala
+ Author: Makarius
+ Author: Fabian Immler TU Munich
+
+Sets with canonical linear order, or immutable linked-lists.
+*/
+package isabelle
+
+
+object Linear_Set
+{
+ private case class Rep[A](
+ val first_elem: Option[A], val last_elem: Option[A], val body: Map[A, A])
+
+ private def empty_rep[A] = Rep[A](None, None, Map())
+
+ private def make[A](first_elem: Option[A], last_elem: Option[A], body: Map[A, A]): Linear_Set[A] =
+ new Linear_Set[A] { override val rep = Rep(first_elem, last_elem, body) }
+
+
+ def empty[A]: Linear_Set[A] = new Linear_Set
+ def apply[A](elems: A*): Linear_Set[A] = empty[A] ++ elems
+
+ class Duplicate(s: String) extends Exception(s)
+ class Undefined(s: String) extends Exception(s)
+}
+
+
+class Linear_Set[A] extends scala.collection.immutable.Set[A]
+{
+ /* representation */
+
+ protected val rep = Linear_Set.empty_rep[A]
+
+
+ /* auxiliary operations */
+
+ def next(elem: A) = rep.body.get(elem)
+ def prev(elem: A) = rep.body.find(_._2 == elem).map(_._1) // slow
+
+ private def _insert_after(hook: Option[A], elem: A): Linear_Set[A] =
+ if (contains(elem)) throw new Linear_Set.Duplicate(elem.toString)
+ else hook match {
+ case Some(hook) =>
+ if (!contains(hook)) throw new Linear_Set.Undefined(hook.toString)
+ else if (rep.body.isDefinedAt(hook))
+ Linear_Set.make(rep.first_elem, rep.last_elem,
+ rep.body - hook + (hook -> elem) + (elem -> rep.body(hook)))
+ else Linear_Set.make(rep.first_elem, Some(elem), rep.body + (hook -> elem))
+ case None =>
+ if (isEmpty) Linear_Set.make(Some(elem), Some(elem), Map())
+ else Linear_Set.make(Some(elem), rep.last_elem, rep.body + (elem -> rep.first_elem.get))
+ }
+
+ def insert_after(hook: Option[A], elems: Seq[A]): Linear_Set[A] =
+ elems.reverse.foldLeft (this) ((ls, elem) => ls._insert_after(hook, elem))
+
+ def delete_after(elem: Option[A]): Linear_Set[A] =
+ elem match {
+ case Some(elem) =>
+ if (!contains(elem)) throw new Linear_Set.Undefined(elem.toString)
+ else if (!rep.body.isDefinedAt(elem)) throw new Linear_Set.Undefined(null)
+ else if (rep.body(elem) == rep.last_elem.get)
+ Linear_Set.make(rep.first_elem, Some(elem), rep.body - elem)
+ else Linear_Set.make(rep.first_elem, rep.last_elem,
+ rep.body - elem - rep.body(elem) + (elem -> rep.body(rep.body(elem))))
+ case None =>
+ if (isEmpty) throw new Linear_Set.Undefined(null)
+ else if (size == 1) empty
+ else Linear_Set.make(Some(rep.body(rep.first_elem.get)), rep.last_elem, rep.body - rep.first_elem.get)
+ }
+
+ def delete_between(from: Option[A], to: Option[A]): Linear_Set[A] = {
+ if(!rep.first_elem.isDefined) this
+ else {
+ val next =
+ if (from == rep.last_elem) None
+ else if (from == None) rep.first_elem
+ else from.map(rep.body(_))
+ if (next == to) this
+ else delete_after(from).delete_between(from, to)
+ }
+ }
+
+
+ /* Set methods */
+
+ override def stringPrefix = "Linear_Set"
+
+ def empty[B]: Linear_Set[B] = Linear_Set.empty
+
+ override def isEmpty: Boolean = !rep.last_elem.isDefined
+ def size: Int = if (isEmpty) 0 else rep.body.size + 1
+
+ def elements = new Iterator[A] {
+ private var next_elem = rep.first_elem
+ def hasNext = next_elem.isDefined
+ def next = {
+ val elem = next_elem.get
+ next_elem = if (rep.body.isDefinedAt(elem)) Some(rep.body(elem)) else None
+ elem
+ }
+ }
+
+ def contains(elem: A): Boolean =
+ !isEmpty && (rep.last_elem.get == elem || rep.body.isDefinedAt(elem))
+
+ def + (elem: A): Linear_Set[A] = _insert_after(rep.last_elem, elem)
+
+ override def + (elem1: A, elem2: A, elems: A*): Linear_Set[A] =
+ this + elem1 + elem2 ++ elems
+ override def ++ (elems: Iterable[A]): Linear_Set[A] = (this /: elems) ((s, elem) => s + elem)
+ override def ++ (elems: Iterator[A]): Linear_Set[A] = (this /: elems) ((s, elem) => s + elem)
+
+ def - (elem: A): Linear_Set[A] =
+ if (!contains(elem)) throw new Linear_Set.Undefined(elem.toString)
+ else delete_after(prev(elem))
+}
\ No newline at end of file
--- a/src/Pure/IsaMakefile Tue Sep 01 14:09:59 2009 +0200
+++ b/src/Pure/IsaMakefile Tue Sep 01 14:10:38 2009 +0200
@@ -117,14 +117,14 @@
## Scala material
-SCALA_FILES = General/event_bus.scala General/markup.scala \
- General/position.scala General/scan.scala General/swing_thread.scala \
- General/symbol.scala General/xml.scala General/yxml.scala \
- Isar/isar.scala Isar/isar_document.scala Isar/outer_keyword.scala \
- System/cygwin.scala System/gui_setup.scala \
+SCALA_FILES = General/event_bus.scala General/linear_set.scala \
+ General/markup.scala General/position.scala General/scan.scala \
+ General/swing_thread.scala General/symbol.scala General/xml.scala \
+ General/yxml.scala Isar/isar.scala Isar/isar_document.scala \
+ Isar/outer_keyword.scala System/cygwin.scala System/gui_setup.scala \
System/isabelle_process.scala System/isabelle_syntax.scala \
System/isabelle_system.scala System/platform.scala \
- Thy/completion.scala Thy/thy_header.scala \
+ Thy/completion.scala Thy/thy_header.scala
JAR_DIR = $(ISABELLE_HOME)/lib/classes
PURE_JAR = $(JAR_DIR)/Pure.jar