replaced a couple of constsdefs by definitions (also some old primrecs by modern ones)
authorhaftmann
Mon, 01 Mar 2010 13:40:23 +0100
changeset 35416 d8d7d1b785af
parent 35342 4dc65845eab3
child 35417 47ee18b6ae32
replaced a couple of constsdefs by definitions (also some old primrecs by modern ones)
doc-src/TutorialI/Advanced/Partial.thy
doc-src/TutorialI/CTL/CTL.thy
doc-src/TutorialI/Misc/Option2.thy
doc-src/TutorialI/Overview/LNCS/FP1.thy
doc-src/TutorialI/Overview/LNCS/Ordinal.thy
doc-src/TutorialI/Protocol/Message.thy
doc-src/TutorialI/Rules/Primes.thy
doc-src/TutorialI/Sets/Examples.thy
doc-src/ZF/If.thy
doc-src/ZF/ZF_examples.thy
src/FOL/IFOL.thy
src/FOL/ex/If.thy
src/FOLP/ex/If.thy
src/HOL/Algebra/AbelCoset.thy
src/HOL/Algebra/Bij.thy
src/HOL/Algebra/Coset.thy
src/HOL/Algebra/Divisibility.thy
src/HOL/Algebra/FiniteProduct.thy
src/HOL/Algebra/Group.thy
src/HOL/Algebra/IntRing.thy
src/HOL/Algebra/Ring.thy
src/HOL/Auth/CertifiedEmail.thy
src/HOL/Auth/Guard/Extensions.thy
src/HOL/Auth/Guard/Guard.thy
src/HOL/Auth/Guard/GuardK.thy
src/HOL/Auth/Guard/Guard_Public.thy
src/HOL/Auth/Guard/Guard_Shared.thy
src/HOL/Auth/Guard/Guard_Yahalom.thy
src/HOL/Auth/Guard/P1.thy
src/HOL/Auth/Guard/P2.thy
src/HOL/Auth/Guard/Proto.thy
src/HOL/Auth/KerberosIV.thy
src/HOL/Auth/KerberosIV_Gets.thy
src/HOL/Auth/KerberosV.thy
src/HOL/Auth/Message.thy
src/HOL/Auth/Smartcard/ShoupRubin.thy
src/HOL/Auth/Smartcard/ShoupRubinBella.thy
src/HOL/Auth/Smartcard/Smartcard.thy
src/HOL/Auth/TLS.thy
src/HOL/Auth/Yahalom.thy
src/HOL/Auth/ZhouGollmann.thy
src/HOL/Bali/AxCompl.thy
src/HOL/Bali/AxExample.thy
src/HOL/Bali/AxSem.thy
src/HOL/Bali/Basis.thy
src/HOL/Bali/Conform.thy
src/HOL/Bali/Decl.thy
src/HOL/Bali/DeclConcepts.thy
src/HOL/Bali/DefiniteAssignment.thy
src/HOL/Bali/Eval.thy
src/HOL/Bali/Example.thy
src/HOL/Bali/State.thy
src/HOL/Bali/Table.thy
src/HOL/Bali/Term.thy
src/HOL/Bali/Trans.thy
src/HOL/Bali/Type.thy
src/HOL/Bali/TypeRel.thy
src/HOL/Bali/TypeSafe.thy
src/HOL/Bali/WellForm.thy
src/HOL/Bali/WellType.thy
src/HOL/Decision_Procs/Cooper.thy
src/HOL/Decision_Procs/Ferrack.thy
src/HOL/Decision_Procs/MIR.thy
src/HOL/Decision_Procs/Parametric_Ferrante_Rackoff.thy
src/HOL/Decision_Procs/Reflected_Multivariate_Polynomial.thy
src/HOL/Finite_Set.thy
src/HOL/Fun.thy
src/HOL/HOL.thy
src/HOL/Hilbert_Choice.thy
src/HOL/Hoare/Arith2.thy
src/HOL/Hoare/Heap.thy
src/HOL/Hoare/Hoare_Logic.thy
src/HOL/Hoare/Hoare_Logic_Abort.thy
src/HOL/Hoare/Pointer_Examples.thy
src/HOL/Hoare/Pointers0.thy
src/HOL/Hoare/SepLogHeap.thy
src/HOL/Hoare/Separation.thy
src/HOL/Hoare_Parallel/Gar_Coll.thy
src/HOL/Hoare_Parallel/Graph.thy
src/HOL/Hoare_Parallel/Mul_Gar_Coll.thy
src/HOL/Hoare_Parallel/OG_Hoare.thy
src/HOL/Hoare_Parallel/OG_Tactics.thy
src/HOL/Hoare_Parallel/OG_Tran.thy
src/HOL/Hoare_Parallel/RG_Hoare.thy
src/HOL/Hoare_Parallel/RG_Tran.thy
src/HOL/IOA/Solve.thy
src/HOL/Import/HOL/HOL4Base.thy
src/HOL/Import/HOL/HOL4Prob.thy
src/HOL/Import/HOL/HOL4Real.thy
src/HOL/Import/HOL/HOL4Vec.thy
src/HOL/Import/HOL/HOL4Word32.thy
src/HOL/Import/HOL4Compat.thy
src/HOL/Import/HOLLight/HOLLight.thy
src/HOL/Import/HOLLightCompat.thy
src/HOL/Isar_Examples/Expr_Compiler.thy
src/HOL/Isar_Examples/Hoare.thy
src/HOL/Isar_Examples/Mutilated_Checkerboard.thy
src/HOL/Matrix/ComputeNumeral.thy
src/HOL/Matrix/Matrix.thy
src/HOL/Matrix/SparseMatrix.thy
src/HOL/Metis_Examples/BigO.thy
src/HOL/Metis_Examples/Message.thy
src/HOL/Metis_Examples/Tarski.thy
src/HOL/MicroJava/BV/Altern.thy
src/HOL/MicroJava/BV/BVExample.thy
src/HOL/MicroJava/BV/BVSpec.thy
src/HOL/MicroJava/BV/Correct.thy
src/HOL/MicroJava/BV/Effect.thy
src/HOL/MicroJava/BV/JType.thy
src/HOL/MicroJava/BV/JVM.thy
src/HOL/MicroJava/BV/JVMType.thy
src/HOL/MicroJava/BV/LBVJVM.thy
src/HOL/MicroJava/BV/Typing_Framework_JVM.thy
src/HOL/MicroJava/Comp/CorrComp.thy
src/HOL/MicroJava/Comp/CorrCompTp.thy
src/HOL/MicroJava/Comp/DefsComp.thy
src/HOL/MicroJava/Comp/Index.thy
src/HOL/MicroJava/Comp/TranslComp.thy
src/HOL/MicroJava/Comp/TranslCompTp.thy
src/HOL/MicroJava/Comp/TypeInf.thy
src/HOL/MicroJava/DFA/Err.thy
src/HOL/MicroJava/DFA/Kildall.thy
src/HOL/MicroJava/DFA/LBVComplete.thy
src/HOL/MicroJava/DFA/LBVSpec.thy
src/HOL/MicroJava/DFA/Listn.thy
src/HOL/MicroJava/DFA/Opt.thy
src/HOL/MicroJava/DFA/Product.thy
src/HOL/MicroJava/DFA/Semilat.thy
src/HOL/MicroJava/DFA/SemilatAlg.thy
src/HOL/MicroJava/DFA/Typing_Framework.thy
src/HOL/MicroJava/DFA/Typing_Framework_err.thy
src/HOL/MicroJava/J/Conform.thy
src/HOL/MicroJava/J/Decl.thy
src/HOL/MicroJava/J/Eval.thy
src/HOL/MicroJava/J/Exceptions.thy
src/HOL/MicroJava/J/JBasis.thy
src/HOL/MicroJava/J/JListExample.thy
src/HOL/MicroJava/J/State.thy
src/HOL/MicroJava/J/SystemClasses.thy
src/HOL/MicroJava/J/TypeRel.thy
src/HOL/MicroJava/J/WellForm.thy
src/HOL/MicroJava/J/WellType.thy
src/HOL/MicroJava/JVM/JVMDefensive.thy
src/HOL/MicroJava/JVM/JVMExceptions.thy
src/HOL/MicroJava/JVM/JVMExec.thy
src/HOL/MicroJava/JVM/JVMListExample.thy
src/HOL/MicroJava/JVM/JVMState.thy
src/HOL/Modelcheck/CTL.thy
src/HOL/Modelcheck/EindhovenExample.thy
src/HOL/Modelcheck/MuCalculus.thy
src/HOL/Modelcheck/MuckeExample1.thy
src/HOL/Modelcheck/MuckeExample2.thy
src/HOL/NanoJava/Decl.thy
src/HOL/NanoJava/Equivalence.thy
src/HOL/NanoJava/State.thy
src/HOL/NanoJava/TypeRel.thy
src/HOL/Nat.thy
src/HOL/Nitpick_Examples/Refute_Nits.thy
src/HOL/Nominal/Examples/Class.thy
src/HOL/Nominal/Examples/Fsub.thy
src/HOL/Nominal/Examples/LocalWeakening.thy
src/HOL/Nominal/Examples/SN.thy
src/HOL/Nominal/Nominal.thy
src/HOL/Number_Theory/MiscAlgebra.thy
src/HOL/Number_Theory/Residues.thy
src/HOL/Number_Theory/UniqueFactorization.thy
src/HOL/Recdef.thy
src/HOL/SET_Protocol/Message_SET.thy
src/HOL/SET_Protocol/Public_SET.thy
src/HOL/Set.thy
src/HOL/Statespace/StateFun.thy
src/HOL/UNITY/Comp.thy
src/HOL/UNITY/Comp/AllocImpl.thy
src/HOL/UNITY/Comp/Counter.thy
src/HOL/UNITY/Comp/Counterc.thy
src/HOL/UNITY/Comp/Priority.thy
src/HOL/UNITY/Comp/PriorityAux.thy
src/HOL/UNITY/Comp/Progress.thy
src/HOL/UNITY/Comp/TimerArray.thy
src/HOL/UNITY/Constrains.thy
src/HOL/UNITY/FP.thy
src/HOL/UNITY/Follows.thy
src/HOL/UNITY/Guar.thy
src/HOL/UNITY/Lift_prog.thy
src/HOL/UNITY/ListOrder.thy
src/HOL/UNITY/PPROD.thy
src/HOL/UNITY/ProgressSets.thy
src/HOL/UNITY/Project.thy
src/HOL/UNITY/Rename.thy
src/HOL/UNITY/Simple/Channel.thy
src/HOL/UNITY/Simple/Common.thy
src/HOL/UNITY/Simple/NSP_Bad.thy
src/HOL/UNITY/Simple/Reach.thy
src/HOL/UNITY/Simple/Reachability.thy
src/HOL/UNITY/Simple/Token.thy
src/HOL/UNITY/SubstAx.thy
src/HOL/UNITY/Transformers.thy
src/HOL/UNITY/UNITY.thy
src/HOL/UNITY/WFair.thy
src/HOL/Word/WordDefinition.thy
src/HOL/Word/WordGenLib.thy
src/HOL/ZF/Games.thy
src/HOL/ZF/HOLZF.thy
src/HOL/ZF/LProd.thy
src/HOL/ZF/MainZF.thy
src/HOL/ZF/Zet.thy
src/HOL/ex/Refute_Examples.thy
src/HOL/ex/Sudoku.thy
src/Sequents/LK0.thy
src/ZF/Sum.thy
--- a/doc-src/TutorialI/Advanced/Partial.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/doc-src/TutorialI/Advanced/Partial.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -34,7 +34,7 @@
 preconditions:
 *}
 
-constdefs subtract :: "nat \<Rightarrow> nat \<Rightarrow> nat"
+definition subtract :: "nat \<Rightarrow> nat \<Rightarrow> nat" where
 "n \<le> m \<Longrightarrow> subtract m n \<equiv> m - n"
 
 text{*
@@ -85,7 +85,7 @@
 Phrased differently, the relation
 *}
 
-constdefs step1 :: "('a \<Rightarrow> 'a) \<Rightarrow> ('a \<times> 'a)set"
+definition step1 :: "('a \<Rightarrow> 'a) \<Rightarrow> ('a \<times> 'a)set" where
   "step1 f \<equiv> {(y,x). y = f x \<and> y \<noteq> x}"
 
 text{*\noindent
@@ -160,7 +160,7 @@
 consider the following definition of function @{const find}:
 *}
 
-constdefs find2 :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a"
+definition find2 :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a" where
   "find2 f x \<equiv>
    fst(while (\<lambda>(x,x'). x' \<noteq> x) (\<lambda>(x,x'). (x',f x')) (x,f x))"
 
--- a/doc-src/TutorialI/CTL/CTL.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/doc-src/TutorialI/CTL/CTL.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -365,8 +365,7 @@
 *}
 
 (*<*)
-constdefs
- eufix :: "state set \<Rightarrow> state set \<Rightarrow> state set \<Rightarrow> state set"
+definition eufix :: "state set \<Rightarrow> state set \<Rightarrow> state set \<Rightarrow> state set" where
 "eufix A B T \<equiv> B \<union> A \<inter> (M\<inverse> `` T)"
 
 lemma "lfp(eufix A B) \<subseteq> eusem A B"
@@ -397,8 +396,7 @@
 done
 
 (*
-constdefs
- eusem :: "state set \<Rightarrow> state set \<Rightarrow> state set"
+definition eusem :: "state set \<Rightarrow> state set \<Rightarrow> state set" where
 "eusem A B \<equiv> {s. \<exists>p\<in>Paths s. \<exists>j. p j \<in> B \<and> (\<forall>i < j. p i \<in> A)}"
 
 axioms
@@ -414,8 +412,7 @@
 apply(blast intro: M_total[THEN someI_ex])
 done
 
-constdefs
- pcons :: "state \<Rightarrow> (nat \<Rightarrow> state) \<Rightarrow> (nat \<Rightarrow> state)"
+definition pcons :: "state \<Rightarrow> (nat \<Rightarrow> state) \<Rightarrow> (nat \<Rightarrow> state)" where
 "pcons s p == \<lambda>i. case i of 0 \<Rightarrow> s | Suc j \<Rightarrow> p j"
 
 lemma pcons_PathI: "[| (s,t) : M; p \<in> Paths t |] ==> pcons s p \<in> Paths s";
--- a/doc-src/TutorialI/Misc/Option2.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/doc-src/TutorialI/Misc/Option2.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -24,8 +24,7 @@
 *}
 (*<*)
 (*
-constdefs
- infplus :: "nat option \<Rightarrow> nat option \<Rightarrow> nat option"
+definition infplus :: "nat option \<Rightarrow> nat option \<Rightarrow> nat option" where
 "infplus x y \<equiv> case x of None \<Rightarrow> None
                | Some m \<Rightarrow> (case y of None \<Rightarrow> None | Some n \<Rightarrow> Some(m+n))"
 
--- a/doc-src/TutorialI/Overview/LNCS/FP1.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/doc-src/TutorialI/Overview/LNCS/FP1.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -62,7 +62,7 @@
 consts xor :: "bool \<Rightarrow> bool \<Rightarrow> bool"
 defs xor_def: "xor x y \<equiv> x \<and> \<not>y \<or> \<not>x \<and> y"
 
-constdefs nand :: "bool \<Rightarrow> bool \<Rightarrow> bool"
+definition nand :: "bool \<Rightarrow> bool \<Rightarrow> bool" where
          "nand x y \<equiv> \<not>(x \<and> y)"
 
 lemma "\<not> xor x x"
--- a/doc-src/TutorialI/Overview/LNCS/Ordinal.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/doc-src/TutorialI/Overview/LNCS/Ordinal.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -9,8 +9,7 @@
   "pred (Succ a) n = Some a"
   "pred (Limit f) n = Some (f n)"
 
-constdefs
-  OpLim :: "(nat \<Rightarrow> (ordinal \<Rightarrow> ordinal)) \<Rightarrow> (ordinal \<Rightarrow> ordinal)"
+definition OpLim :: "(nat \<Rightarrow> (ordinal \<Rightarrow> ordinal)) \<Rightarrow> (ordinal \<Rightarrow> ordinal)" where
   "OpLim F a \<equiv> Limit (\<lambda>n. F n a)"
   OpItw :: "(ordinal \<Rightarrow> ordinal) \<Rightarrow> (ordinal \<Rightarrow> ordinal)"    ("\<Squnion>")
   "\<Squnion>f \<equiv> OpLim (power f)"
@@ -29,8 +28,7 @@
   "\<nabla>f (Succ a) = f (Succ (\<nabla>f a))"
   "\<nabla>f (Limit h) = Limit (\<lambda>n. \<nabla>f (h n))"
 
-constdefs
-  deriv :: "(ordinal \<Rightarrow> ordinal) \<Rightarrow> (ordinal \<Rightarrow> ordinal)"
+definition deriv :: "(ordinal \<Rightarrow> ordinal) \<Rightarrow> (ordinal \<Rightarrow> ordinal)" where
   "deriv f \<equiv> \<nabla>(\<Squnion>f)"
 
 consts
@@ -40,8 +38,7 @@
   "veblen (Succ a) = \<nabla>(OpLim (power (veblen a)))"
   "veblen (Limit f) = \<nabla>(OpLim (\<lambda>n. veblen (f n)))"
 
-constdefs
-  veb :: "ordinal \<Rightarrow> ordinal"
+definition veb :: "ordinal \<Rightarrow> ordinal" where
   "veb a \<equiv> veblen a Zero"
   epsilon0 :: ordinal    ("\<epsilon>\<^sub>0")
   "\<epsilon>\<^sub>0 \<equiv> veb Zero"
--- a/doc-src/TutorialI/Protocol/Message.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/doc-src/TutorialI/Protocol/Message.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -46,8 +46,7 @@
 text{*The inverse of a symmetric key is itself; that of a public key
       is the private key and vice versa*}
 
-constdefs
-  symKeys :: "key set"
+definition symKeys :: "key set" where
   "symKeys == {K. invKey K = K}"
 (*>*)
 
@@ -92,8 +91,7 @@
   "{|x, y|}"      == "CONST MPair x y"
 
 
-constdefs
-  keysFor :: "msg set => key set"
+definition keysFor :: "msg set => key set" where
     --{*Keys useful to decrypt elements of a message set*}
   "keysFor H == invKey ` {K. \<exists>X. Crypt K X \<in> H}"
 
--- a/doc-src/TutorialI/Rules/Primes.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/doc-src/TutorialI/Rules/Primes.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -99,8 +99,7 @@
 
 (**** The material below was omitted from the book ****)
 
-constdefs
-  is_gcd  :: "[nat,nat,nat] \<Rightarrow> bool"        (*gcd as a relation*)
+definition is_gcd :: "[nat,nat,nat] \<Rightarrow> bool" where        (*gcd as a relation*)
     "is_gcd p m n == p dvd m  \<and>  p dvd n  \<and>
                      (ALL d. d dvd m \<and> d dvd n \<longrightarrow> d dvd p)"
 
--- a/doc-src/TutorialI/Sets/Examples.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/doc-src/TutorialI/Sets/Examples.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -156,8 +156,7 @@
 lemma "{x. P x \<longrightarrow> Q x} = -{x. P x} \<union> {x. Q x}"
 by blast
 
-constdefs
-  prime   :: "nat set"
+definition prime :: "nat set" where
     "prime == {p. 1<p & (ALL m. m dvd p --> m=1 | m=p)}"
 
 lemma "{p*q | p q. p\<in>prime \<and> q\<in>prime} = 
--- a/doc-src/ZF/If.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/doc-src/ZF/If.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -8,8 +8,7 @@
 
 theory If imports FOL begin
 
-constdefs
-  "if" :: "[o,o,o]=>o"
+definition "if" :: "[o,o,o]=>o" where
   "if(P,Q,R) == P&Q | ~P&R"
 
 lemma ifI:
--- a/doc-src/ZF/ZF_examples.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/doc-src/ZF/ZF_examples.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -64,7 +64,7 @@
      "t \<in> bt(A) ==> \<forall>k \<in> nat. n_nodes_aux(t)`k = n_nodes(t) #+ k"
   by (induct_tac t, simp_all) 
 
-constdefs  n_nodes_tail :: "i => i"
+definition n_nodes_tail :: "i => i" where
    "n_nodes_tail(t) == n_nodes_aux(t) ` 0"
 
 lemma "t \<in> bt(A) ==> n_nodes_tail(t) = n_nodes(t)"
--- a/src/FOL/IFOL.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/FOL/IFOL.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -760,8 +760,7 @@
 
 nonterminals letbinds letbind
 
-constdefs
-  Let :: "['a::{}, 'a => 'b] => ('b::{})"
+definition Let :: "['a::{}, 'a => 'b] => ('b::{})" where
     "Let(s, f) == f(s)"
 
 syntax
--- a/src/FOL/ex/If.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/FOL/ex/If.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -7,8 +7,7 @@
 
 theory If imports FOL begin
 
-constdefs
-  "if" :: "[o,o,o]=>o"
+definition "if" :: "[o,o,o]=>o" where
   "if(P,Q,R) == P&Q | ~P&R"
 
 lemma ifI:
--- a/src/FOLP/ex/If.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/FOLP/ex/If.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -4,8 +4,7 @@
 imports FOLP
 begin
 
-constdefs
-  "if" :: "[o,o,o]=>o"
+definition "if" :: "[o,o,o]=>o" where
   "if(P,Q,R) == P&Q | ~P&R"
 
 lemma ifI:
--- a/src/HOL/Algebra/AbelCoset.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Algebra/AbelCoset.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -38,15 +38,12 @@
                   ("racong\<index> _")
    "a_r_congruent G \<equiv> r_congruent \<lparr>carrier = carrier G, mult = add G, one = zero G\<rparr>"
 
-constdefs
-  A_FactGroup :: "[('a,'b) ring_scheme, 'a set] \<Rightarrow> ('a set) monoid"
-     (infixl "A'_Mod" 65)
+definition A_FactGroup :: "[('a,'b) ring_scheme, 'a set] \<Rightarrow> ('a set) monoid" (infixl "A'_Mod" 65) where
     --{*Actually defined for groups rather than monoids*}
   "A_FactGroup G H \<equiv> FactGroup \<lparr>carrier = carrier G, mult = add G, one = zero G\<rparr> H"
 
-constdefs
-  a_kernel :: "('a, 'm) ring_scheme \<Rightarrow> ('b, 'n) ring_scheme \<Rightarrow> 
-             ('a \<Rightarrow> 'b) \<Rightarrow> 'a set" 
+definition a_kernel :: "('a, 'm) ring_scheme \<Rightarrow> ('b, 'n) ring_scheme \<Rightarrow> 
+             ('a \<Rightarrow> 'b) \<Rightarrow> 'a set" where 
     --{*the kernel of a homomorphism (additive)*}
   "a_kernel G H h \<equiv> kernel \<lparr>carrier = carrier G, mult = add G, one = zero G\<rparr>
                               \<lparr>carrier = carrier H, mult = add H, one = zero H\<rparr> h"
--- a/src/HOL/Algebra/Bij.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Algebra/Bij.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -1,5 +1,4 @@
 (*  Title:      HOL/Algebra/Bij.thy
-    ID:         $Id$
     Author:     Florian Kammueller, with new proofs by L C Paulson
 *)
 
@@ -8,12 +7,11 @@
 
 section {* Bijections of a Set, Permutation and Automorphism Groups *}
 
-constdefs
-  Bij :: "'a set \<Rightarrow> ('a \<Rightarrow> 'a) set"
+definition Bij :: "'a set \<Rightarrow> ('a \<Rightarrow> 'a) set" where
     --{*Only extensional functions, since otherwise we get too many.*}
   "Bij S \<equiv> extensional S \<inter> {f. bij_betw f S S}"
 
-  BijGroup :: "'a set \<Rightarrow> ('a \<Rightarrow> 'a) monoid"
+definition BijGroup :: "'a set \<Rightarrow> ('a \<Rightarrow> 'a) monoid" where
   "BijGroup S \<equiv>
     \<lparr>carrier = Bij S,
      mult = \<lambda>g \<in> Bij S. \<lambda>f \<in> Bij S. compose S g f,
@@ -71,11 +69,10 @@
 done
 
 
-constdefs
-  auto :: "('a, 'b) monoid_scheme \<Rightarrow> ('a \<Rightarrow> 'a) set"
+definition auto :: "('a, 'b) monoid_scheme \<Rightarrow> ('a \<Rightarrow> 'a) set" where
   "auto G \<equiv> hom G G \<inter> Bij (carrier G)"
 
-  AutoGroup :: "('a, 'c) monoid_scheme \<Rightarrow> ('a \<Rightarrow> 'a) monoid"
+definition AutoGroup :: "('a, 'c) monoid_scheme \<Rightarrow> ('a \<Rightarrow> 'a) monoid" where
   "AutoGroup G \<equiv> BijGroup (carrier G) \<lparr>carrier := auto G\<rparr>"
 
 lemma (in group) id_in_auto: "(\<lambda>x \<in> carrier G. x) \<in> auto G"
--- a/src/HOL/Algebra/Coset.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Algebra/Coset.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -751,8 +751,7 @@
 
 subsection {*Order of a Group and Lagrange's Theorem*}
 
-constdefs
-  order :: "('a, 'b) monoid_scheme \<Rightarrow> nat"
+definition order :: "('a, 'b) monoid_scheme \<Rightarrow> nat" where
   "order S \<equiv> card (carrier S)"
 
 lemma (in group) rcosets_part_G:
@@ -822,9 +821,7 @@
 
 subsection {*Quotient Groups: Factorization of a Group*}
 
-constdefs
-  FactGroup :: "[('a,'b) monoid_scheme, 'a set] \<Rightarrow> ('a set) monoid"
-     (infixl "Mod" 65)
+definition FactGroup :: "[('a,'b) monoid_scheme, 'a set] \<Rightarrow> ('a set) monoid" (infixl "Mod" 65) where
     --{*Actually defined for groups rather than monoids*}
   "FactGroup G H \<equiv>
     \<lparr>carrier = rcosets\<^bsub>G\<^esub> H, mult = set_mult G, one = H\<rparr>"
@@ -890,9 +887,8 @@
 text{*The quotient by the kernel of a homomorphism is isomorphic to the 
   range of that homomorphism.*}
 
-constdefs
-  kernel :: "('a, 'm) monoid_scheme \<Rightarrow> ('b, 'n) monoid_scheme \<Rightarrow> 
-             ('a \<Rightarrow> 'b) \<Rightarrow> 'a set" 
+definition kernel :: "('a, 'm) monoid_scheme \<Rightarrow> ('b, 'n) monoid_scheme \<Rightarrow> 
+             ('a \<Rightarrow> 'b) \<Rightarrow> 'a set" where 
     --{*the kernel of a homomorphism*}
   "kernel G H h \<equiv> {x. x \<in> carrier G & h x = \<one>\<^bsub>H\<^esub>}"
 
--- a/src/HOL/Algebra/Divisibility.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Algebra/Divisibility.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -3630,8 +3630,7 @@
 
 text {* Number of factors for wellfoundedness *}
 
-constdefs
-  factorcount :: "_ \<Rightarrow> 'a \<Rightarrow> nat"
+definition factorcount :: "_ \<Rightarrow> 'a \<Rightarrow> nat" where
   "factorcount G a == THE c. (ALL as. set as \<subseteq> carrier G \<and> 
                                       wfactors G as a \<longrightarrow> c = length as)"
 
--- a/src/HOL/Algebra/FiniteProduct.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Algebra/FiniteProduct.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -26,8 +26,7 @@
 
 inductive_cases empty_foldSetDE [elim!]: "({}, x) \<in> foldSetD D f e"
 
-constdefs
-  foldD :: "['a set, 'b => 'a => 'a, 'a, 'b set] => 'a"
+definition foldD :: "['a set, 'b => 'a => 'a, 'a, 'b set] => 'a" where
   "foldD D f e A == THE x. (A, x) \<in> foldSetD D f e"
 
 lemma foldSetD_closed:
--- a/src/HOL/Algebra/Group.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Algebra/Group.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -478,8 +478,7 @@
 
 subsection {* Direct Products *}
 
-constdefs
-  DirProd :: "_ \<Rightarrow> _ \<Rightarrow> ('a \<times> 'b) monoid"  (infixr "\<times>\<times>" 80)
+definition DirProd :: "_ \<Rightarrow> _ \<Rightarrow> ('a \<times> 'b) monoid" (infixr "\<times>\<times>" 80) where
   "G \<times>\<times> H \<equiv> \<lparr>carrier = carrier G \<times> carrier H,
                 mult = (\<lambda>(g, h) (g', h'). (g \<otimes>\<^bsub>G\<^esub> g', h \<otimes>\<^bsub>H\<^esub> h')),
                 one = (\<one>\<^bsub>G\<^esub>, \<one>\<^bsub>H\<^esub>)\<rparr>"
@@ -545,8 +544,7 @@
   "[|h \<in> hom G H; i \<in> hom H I|] ==> compose (carrier G) i h \<in> hom G I"
 by (fastsimp simp add: hom_def compose_def)
 
-constdefs
-  iso :: "_ => _ => ('a => 'b) set"  (infixr "\<cong>" 60)
+definition iso :: "_ => _ => ('a => 'b) set" (infixr "\<cong>" 60) where
   "G \<cong> H == {h. h \<in> hom G H & bij_betw h (carrier G) (carrier H)}"
 
 lemma iso_refl: "(%x. x) \<in> G \<cong> G"
--- a/src/HOL/Algebra/IntRing.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Algebra/IntRing.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -22,8 +22,7 @@
 
 subsection {* @{text "\<Z>"}: The Set of Integers as Algebraic Structure *}
 
-constdefs
-  int_ring :: "int ring" ("\<Z>")
+definition int_ring :: "int ring" ("\<Z>") where
   "int_ring \<equiv> \<lparr>carrier = UNIV, mult = op *, one = 1, zero = 0, add = op +\<rparr>"
 
 lemma int_Zcarr [intro!, simp]:
@@ -324,8 +323,7 @@
 
 subsection {* Ideals and the Modulus *}
 
-constdefs
-   ZMod :: "int => int => int set"
+definition ZMod :: "int => int => int set" where
   "ZMod k r == (Idl\<^bsub>\<Z>\<^esub> {k}) +>\<^bsub>\<Z>\<^esub> r"
 
 lemmas ZMod_defs =
@@ -407,8 +405,7 @@
 
 subsection {* Factorization *}
 
-constdefs
-  ZFact :: "int \<Rightarrow> int set ring"
+definition ZFact :: "int \<Rightarrow> int set ring" where
   "ZFact k == \<Z> Quot (Idl\<^bsub>\<Z>\<^esub> {k})"
 
 lemmas ZFact_defs = ZFact_def FactRing_def
--- a/src/HOL/Algebra/Ring.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Algebra/Ring.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -198,8 +198,7 @@
   This definition makes it easy to lift lemmas from @{term finprod}.
 *}
 
-constdefs
-  finsum :: "[('b, 'm) ring_scheme, 'a => 'b, 'a set] => 'b"
+definition finsum :: "[('b, 'm) ring_scheme, 'a => 'b, 'a set] => 'b" where
   "finsum G f A == finprod (| carrier = carrier G,
      mult = add G, one = zero G |) f A"
 
--- a/src/HOL/Auth/CertifiedEmail.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/CertifiedEmail.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -25,8 +25,7 @@
   BothAuth :: nat
 
 text{*We formalize a fixed way of computing responses.  Could be better.*}
-constdefs
-  "response"    :: "agent => agent => nat => msg"
+definition "response" :: "agent => agent => nat => msg" where
    "response S R q == Hash {|Agent S, Key (shrK R), Nonce q|}"
 
 
--- a/src/HOL/Auth/Guard/Extensions.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Guard/Extensions.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -61,7 +61,7 @@
 
 subsubsection{*messages that are pairs*}
 
-constdefs is_MPair :: "msg => bool"
+definition is_MPair :: "msg => bool" where
 "is_MPair X == EX Y Z. X = {|Y,Z|}"
 
 declare is_MPair_def [simp]
@@ -96,7 +96,7 @@
 
 declare is_MPair_def [simp del]
 
-constdefs has_no_pair :: "msg set => bool"
+definition has_no_pair :: "msg set => bool" where
 "has_no_pair H == ALL X Y. {|X,Y|} ~:H"
 
 declare has_no_pair_def [simp]
@@ -117,7 +117,7 @@
 
 subsubsection{*lemmas on keysFor*}
 
-constdefs usekeys :: "msg set => key set"
+definition usekeys :: "msg set => key set" where
 "usekeys G == {K. EX Y. Crypt K Y:G}"
 
 lemma finite_keysFor [intro]: "finite G ==> finite (keysFor G)"
@@ -237,7 +237,7 @@
 
 subsubsection{*sets of keys*}
 
-constdefs keyset :: "msg set => bool"
+definition keyset :: "msg set => bool" where
 "keyset G == ALL X. X:G --> (EX K. X = Key K)"
 
 lemma keyset_in [dest]: "[| keyset G; X:G |] ==> EX K. X = Key K"
@@ -257,7 +257,7 @@
 
 subsubsection{*keys a priori necessary for decrypting the messages of G*}
 
-constdefs keysfor :: "msg set => msg set"
+definition keysfor :: "msg set => msg set" where
 "keysfor G == Key ` keysFor (parts G)"
 
 lemma keyset_keysfor [iff]: "keyset (keysfor G)"
@@ -295,7 +295,7 @@
 
 subsubsection{*general protocol properties*}
 
-constdefs is_Says :: "event => bool"
+definition is_Says :: "event => bool" where
 "is_Says ev == (EX A B X. ev = Says A B X)"
 
 lemma is_Says_Says [iff]: "is_Says (Says A B X)"
@@ -303,7 +303,7 @@
 
 (* one could also require that Gets occurs after Says
 but this is sufficient for our purpose *)
-constdefs Gets_correct :: "event list set => bool"
+definition Gets_correct :: "event list set => bool" where
 "Gets_correct p == ALL evs B X. evs:p --> Gets B X:set evs
 --> (EX A. Says A B X:set evs)"
 
@@ -312,7 +312,7 @@
 apply (simp add: Gets_correct_def)
 by (drule_tac x="Gets B X # evs" in spec, auto)
 
-constdefs one_step :: "event list set => bool"
+definition one_step :: "event list set => bool" where
 "one_step p == ALL evs ev. ev#evs:p --> evs:p"
 
 lemma one_step_Cons [dest]: "[| one_step p; ev#evs:p |] ==> evs:p"
@@ -324,7 +324,7 @@
 lemma trunc: "[| evs @ evs':p; one_step p |] ==> evs':p"
 by (induct evs, auto)
 
-constdefs has_only_Says :: "event list set => bool"
+definition has_only_Says :: "event list set => bool" where
 "has_only_Says p == ALL evs ev. evs:p --> ev:set evs
 --> (EX A B X. ev = Says A B X)"
 
@@ -450,7 +450,7 @@
       if A=A' then insert X (knows_max' A evs) else knows_max' A evs
   ))"
 
-constdefs knows_max :: "agent => event list => msg set"
+definition knows_max :: "agent => event list => msg set" where
 "knows_max A evs == knows_max' A evs Un initState A"
 
 abbreviation
@@ -512,7 +512,7 @@
     | Notes A X => parts {X} Un used' evs
   )"
 
-constdefs init :: "msg set"
+definition init :: "msg set" where
 "init == used []"
 
 lemma used_decomp: "used evs = init Un used' evs"
--- a/src/HOL/Auth/Guard/Guard.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Guard/Guard.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -76,7 +76,7 @@
 
 subsection{*guarded sets*}
 
-constdefs Guard :: "nat => key set => msg set => bool"
+definition Guard :: "nat => key set => msg set => bool" where
 "Guard n Ks H == ALL X. X:H --> X:guard n Ks"
 
 subsection{*basic facts about @{term Guard}*}
@@ -241,7 +241,7 @@
 
 subsection{*list corresponding to "decrypt"*}
 
-constdefs decrypt' :: "msg list => key => msg => msg list"
+definition decrypt' :: "msg list => key => msg => msg list" where
 "decrypt' l K Y == Y # remove l (Crypt K Y)"
 
 declare decrypt'_def [simp]
--- a/src/HOL/Auth/Guard/GuardK.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Guard/GuardK.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -85,7 +85,7 @@
 
 subsection{*guarded sets*}
 
-constdefs GuardK :: "nat => key set => msg set => bool"
+definition GuardK :: "nat => key set => msg set => bool" where
 "GuardK n Ks H == ALL X. X:H --> X:guardK n Ks"
 
 subsection{*basic facts about @{term GuardK}*}
@@ -239,7 +239,7 @@
 
 subsection{*list corresponding to "decrypt"*}
 
-constdefs decrypt' :: "msg list => key => msg => msg list"
+definition decrypt' :: "msg list => key => msg => msg list" where
 "decrypt' l K Y == Y # remove l (Crypt K Y)"
 
 declare decrypt'_def [simp]
--- a/src/HOL/Auth/Guard/Guard_Public.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Guard/Guard_Public.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -19,7 +19,7 @@
 
 subsubsection{*signature*}
 
-constdefs sign :: "agent => msg => msg"
+definition sign :: "agent => msg => msg" where
 "sign A X == {|Agent A, X, Crypt (priK A) (Hash X)|}"
 
 lemma sign_inj [iff]: "(sign A X = sign A' X') = (A=A' & X=X')"
@@ -27,7 +27,7 @@
 
 subsubsection{*agent associated to a key*}
 
-constdefs agt :: "key => agent"
+definition agt :: "key => agent" where
 "agt K == @A. K = priK A | K = pubK A"
 
 lemma agt_priK [simp]: "agt (priK A) = A"
@@ -57,7 +57,7 @@
 
 subsubsection{*sets of private keys*}
 
-constdefs priK_set :: "key set => bool"
+definition priK_set :: "key set => bool" where
 "priK_set Ks == ALL K. K:Ks --> (EX A. K = priK A)"
 
 lemma in_priK_set: "[| priK_set Ks; K:Ks |] ==> EX A. K = priK A"
@@ -71,7 +71,7 @@
 
 subsubsection{*sets of good keys*}
 
-constdefs good :: "key set => bool"
+definition good :: "key set => bool" where
 "good Ks == ALL K. K:Ks --> agt K ~:bad"
 
 lemma in_good: "[| good Ks; K:Ks |] ==> agt K ~:bad"
@@ -99,7 +99,7 @@
 
 subsubsection{*function giving a new nonce*}
 
-constdefs new :: "event list => nat"
+definition new :: "event list => nat" where
 "new evs == Suc (greatest evs)"
 
 lemma new_isnt_used [iff]: "Nonce (new evs) ~:used evs"
@@ -151,7 +151,7 @@
 
 subsubsection{*regular protocols*}
 
-constdefs regular :: "event list set => bool"
+definition regular :: "event list set => bool" where
 "regular p == ALL evs A. evs:p --> (Key (priK A):parts (spies evs)) = (A:bad)"
 
 lemma priK_parts_iff_bad [simp]: "[| evs:p; regular p |] ==>
--- a/src/HOL/Auth/Guard/Guard_Shared.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Guard/Guard_Shared.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -25,7 +25,7 @@
 
 subsubsection{*agent associated to a key*}
 
-constdefs agt :: "key => agent"
+definition agt :: "key => agent" where
 "agt K == @A. K = shrK A"
 
 lemma agt_shrK [simp]: "agt (shrK A) = A"
@@ -52,7 +52,7 @@
 
 subsubsection{*sets of symmetric keys*}
 
-constdefs shrK_set :: "key set => bool"
+definition shrK_set :: "key set => bool" where
 "shrK_set Ks == ALL K. K:Ks --> (EX A. K = shrK A)"
 
 lemma in_shrK_set: "[| shrK_set Ks; K:Ks |] ==> EX A. K = shrK A"
@@ -66,7 +66,7 @@
 
 subsubsection{*sets of good keys*}
 
-constdefs good :: "key set => bool"
+definition good :: "key set => bool" where
 "good Ks == ALL K. K:Ks --> agt K ~:bad"
 
 lemma in_good: "[| good Ks; K:Ks |] ==> agt K ~:bad"
@@ -154,7 +154,7 @@
 
 subsubsection{*regular protocols*}
 
-constdefs regular :: "event list set => bool"
+definition regular :: "event list set => bool" where
 "regular p == ALL evs A. evs:p --> (Key (shrK A):parts (spies evs)) = (A:bad)"
 
 lemma shrK_parts_iff_bad [simp]: "[| evs:p; regular p |] ==>
--- a/src/HOL/Auth/Guard/Guard_Yahalom.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Guard/Guard_Yahalom.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -198,7 +198,7 @@
 
 subsection{*guardedness of NB*}
 
-constdefs ya_keys :: "agent => agent => nat => nat => event list => key set"
+definition ya_keys :: "agent => agent => nat => nat => event list => key set" where
 "ya_keys A B NA NB evs == {shrK A,shrK B} Un {K. ya3 A B NA NB K:set evs}"
 
 lemma Guard_NB [rule_format]: "[| evs:ya; A ~:bad; B ~:bad |] ==>
--- a/src/HOL/Auth/Guard/P1.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Guard/P1.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -39,7 +39,7 @@
 subsubsection{*offer chaining:
 B chains his offer for A with the head offer of L for sending it to C*}
 
-constdefs chain :: "agent => nat => agent => msg => agent => msg"
+definition chain :: "agent => nat => agent => msg => agent => msg" where
 "chain B ofr A L C ==
 let m1= Crypt (pubK A) (Nonce ofr) in
 let m2= Hash {|head L, Agent C|} in
@@ -86,7 +86,7 @@
 
 subsubsection{*anchor of the offer list*}
 
-constdefs anchor :: "agent => nat => agent => msg"
+definition anchor :: "agent => nat => agent => msg" where
 "anchor A n B == chain A n A (cons nil nil) B"
 
 lemma anchor_inj [iff]: "(anchor A n B = anchor A' n' B')
@@ -107,7 +107,7 @@
 
 subsubsection{*request event*}
 
-constdefs reqm :: "agent => nat => nat => msg => agent => msg"
+definition reqm :: "agent => nat => nat => msg => agent => msg" where
 "reqm A r n I B == {|Agent A, Number r, cons (Agent A) (cons (Agent B) I),
 cons (anchor A n B) nil|}"
 
@@ -118,7 +118,7 @@
 lemma Nonce_in_reqm [iff]: "Nonce n:parts {reqm A r n I B}"
 by (auto simp: reqm_def)
 
-constdefs req :: "agent => nat => nat => msg => agent => event"
+definition req :: "agent => nat => nat => msg => agent => event" where
 "req A r n I B == Says A B (reqm A r n I B)"
 
 lemma req_inj [iff]: "(req A r n I B = req A' r' n' I' B')
@@ -127,8 +127,8 @@
 
 subsubsection{*propose event*}
 
-constdefs prom :: "agent => nat => agent => nat => msg => msg =>
-msg => agent => msg"
+definition prom :: "agent => nat => agent => nat => msg => msg =>
+msg => agent => msg" where
 "prom B ofr A r I L J C == {|Agent A, Number r,
 app (J, del (Agent B, I)), cons (chain B ofr A L C) L|}"
 
@@ -140,8 +140,8 @@
 lemma Nonce_in_prom [iff]: "Nonce ofr:parts {prom B ofr A r I L J C}"
 by (auto simp: prom_def)
 
-constdefs pro :: "agent => nat => agent => nat => msg => msg =>
-msg => agent => event"
+definition pro :: "agent => nat => agent => nat => msg => msg =>
+msg => agent => event" where
 "pro B ofr A r I L J C == Says B C (prom B ofr A r I L J C)"
 
 lemma pro_inj [dest]: "pro B ofr A r I L J C = pro B' ofr' A' r' I' L' J' C'
@@ -198,7 +198,7 @@
 
 subsubsection{*offers of an offer list*}
 
-constdefs offer_nonces :: "msg => msg set"
+definition offer_nonces :: "msg => msg set" where
 "offer_nonces L == {X. X:parts {L} & (EX n. X = Nonce n)}"
 
 subsubsection{*the originator can get the offers*}
@@ -252,7 +252,7 @@
 pro C (Suc ofr) A r I' L nil D
 # trace (B,Suc ofr,A,r,I'',tail L,K))"
 
-constdefs trace' :: "agent => nat => nat => msg => agent => nat => event list"
+definition trace' :: "agent => nat => nat => msg => agent => nat => event list" where
 "trace' A r n I B ofr == (
 let AI = cons (Agent A) I in
 let L = offer_list (A,n,B,AI,ofr) in
--- a/src/HOL/Auth/Guard/P2.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Guard/P2.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -26,7 +26,7 @@
 subsubsection{*offer chaining:
 B chains his offer for A with the head offer of L for sending it to C*}
 
-constdefs chain :: "agent => nat => agent => msg => agent => msg"
+definition chain :: "agent => nat => agent => msg => agent => msg" where
 "chain B ofr A L C ==
 let m1= sign B (Nonce ofr) in
 let m2= Hash {|head L, Agent C|} in
@@ -73,7 +73,7 @@
 
 subsubsection{*anchor of the offer list*}
 
-constdefs anchor :: "agent => nat => agent => msg"
+definition anchor :: "agent => nat => agent => msg" where
 "anchor A n B == chain A n A (cons nil nil) B"
 
 lemma anchor_inj [iff]:
@@ -88,7 +88,7 @@
 
 subsubsection{*request event*}
 
-constdefs reqm :: "agent => nat => nat => msg => agent => msg"
+definition reqm :: "agent => nat => nat => msg => agent => msg" where
 "reqm A r n I B == {|Agent A, Number r, cons (Agent A) (cons (Agent B) I),
 cons (anchor A n B) nil|}"
 
@@ -99,7 +99,7 @@
 lemma Nonce_in_reqm [iff]: "Nonce n:parts {reqm A r n I B}"
 by (auto simp: reqm_def)
 
-constdefs req :: "agent => nat => nat => msg => agent => event"
+definition req :: "agent => nat => nat => msg => agent => event" where
 "req A r n I B == Says A B (reqm A r n I B)"
 
 lemma req_inj [iff]: "(req A r n I B = req A' r' n' I' B')
@@ -108,8 +108,8 @@
 
 subsubsection{*propose event*}
 
-constdefs prom :: "agent => nat => agent => nat => msg => msg =>
-msg => agent => msg"
+definition prom :: "agent => nat => agent => nat => msg => msg =>
+msg => agent => msg" where
 "prom B ofr A r I L J C == {|Agent A, Number r,
 app (J, del (Agent B, I)), cons (chain B ofr A L C) L|}"
 
@@ -120,8 +120,8 @@
 lemma Nonce_in_prom [iff]: "Nonce ofr:parts {prom B ofr A r I L J C}"
 by (auto simp: prom_def)
 
-constdefs pro :: "agent => nat => agent => nat => msg => msg =>
-                  msg => agent => event"
+definition pro :: "agent => nat => agent => nat => msg => msg =>
+                  msg => agent => event" where
 "pro B ofr A r I L J C == Says B C (prom B ofr A r I L J C)"
 
 lemma pro_inj [dest]: "pro B ofr A r I L J C = pro B' ofr' A' r' I' L' J' C'
--- a/src/HOL/Auth/Guard/Proto.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Guard/Proto.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -23,7 +23,7 @@
 
 types proto = "rule set"
 
-constdefs wdef :: "proto => bool"
+definition wdef :: "proto => bool" where
 "wdef p == ALL R k. R:p --> Number k:parts {msg' R}
 --> Number k:parts (msg`(fst R))"
 
@@ -35,19 +35,17 @@
   nb    :: "nat => msg"
   key   :: "key => key"
 
-consts apm :: "subs => msg => msg"
-
-primrec
-"apm s (Agent A) = Agent (agent s A)"
-"apm s (Nonce n) = Nonce (nonce s n)"
-"apm s (Number n) = nb s n"
-"apm s (Key K) = Key (key s K)"
-"apm s (Hash X) = Hash (apm s X)"
-"apm s (Crypt K X) = (
+primrec apm :: "subs => msg => msg" where
+  "apm s (Agent A) = Agent (agent s A)"
+| "apm s (Nonce n) = Nonce (nonce s n)"
+| "apm s (Number n) = nb s n"
+| "apm s (Key K) = Key (key s K)"
+| "apm s (Hash X) = Hash (apm s X)"
+| "apm s (Crypt K X) = (
 if (EX A. K = pubK A) then Crypt (pubK (agent s (agt K))) (apm s X)
 else if (EX A. K = priK A) then Crypt (priK (agent s (agt K))) (apm s X)
 else Crypt (key s K) (apm s X))"
-"apm s {|X,Y|} = {|apm s X, apm s Y|}"
+| "apm s {|X,Y|} = {|apm s X, apm s Y|}"
 
 lemma apm_parts: "X:parts {Y} ==> apm s X:parts {apm s Y}"
 apply (erule parts.induct, simp_all, blast)
@@ -69,12 +67,10 @@
 apply (drule_tac Y="msg x" and s=s in apm_parts, simp)
 by (blast dest: parts_parts)
 
-consts ap :: "subs => event => event"
-
-primrec
-"ap s (Says A B X) = Says (agent s A) (agent s B) (apm s X)"
-"ap s (Gets A X) = Gets (agent s A) (apm s X)"
-"ap s (Notes A X) = Notes (agent s A) (apm s X)"
+primrec ap :: "subs => event => event" where
+  "ap s (Says A B X) = Says (agent s A) (agent s B) (apm s X)"
+| "ap s (Gets A X) = Gets (agent s A) (apm s X)"
+| "ap s (Notes A X) = Notes (agent s A) (apm s X)"
 
 abbreviation
   ap' :: "subs => rule => event" where
@@ -94,7 +90,7 @@
 
 subsection{*nonces generated by a rule*}
 
-constdefs newn :: "rule => nat set"
+definition newn :: "rule => nat set" where
 "newn R == {n. Nonce n:parts {msg (snd R)} & Nonce n ~:parts (msg`(fst R))}"
 
 lemma newn_parts: "n:newn R ==> Nonce (nonce s n):parts {apm' s R}"
@@ -102,7 +98,7 @@
 
 subsection{*traces generated by a protocol*}
 
-constdefs ok :: "event list => rule => subs => bool"
+definition ok :: "event list => rule => subs => bool" where
 "ok evs R s == ((ALL x. x:fst R --> ap s x:set evs)
 & (ALL n. n:newn R --> Nonce (nonce s n) ~:used evs))"
 
@@ -124,7 +120,7 @@
 apply (unfold one_step_def, clarify)
 by (ind_cases "ev # evs:tr p" for ev evs, auto)
 
-constdefs has_only_Says' :: "proto => bool"
+definition has_only_Says' :: "proto => bool" where
 "has_only_Says' p == ALL R. R:p --> is_Says (snd R)"
 
 lemma has_only_Says'D: "[| R:p; has_only_Says' p |]
@@ -165,8 +161,8 @@
 
 subsection{*introduction of a fresh guarded nonce*}
 
-constdefs fresh :: "proto => rule => subs => nat => key set => event list
-=> bool"
+definition fresh :: "proto => rule => subs => nat => key set => event list
+=> bool" where
 "fresh p R s n Ks evs == (EX evs1 evs2. evs = evs2 @ ap' s R # evs1
 & Nonce n ~:used evs1 & R:p & ok evs1 R s & Nonce n:parts {apm' s R}
 & apm' s R:guard n Ks)"
@@ -226,7 +222,7 @@
 
 subsection{*safe keys*}
 
-constdefs safe :: "key set => msg set => bool"
+definition safe :: "key set => msg set => bool" where
 "safe Ks G == ALL K. K:Ks --> Key K ~:analz G"
 
 lemma safeD [dest]: "[| safe Ks G; K:Ks |] ==> Key K ~:analz G"
@@ -240,7 +236,7 @@
 
 subsection{*guardedness preservation*}
 
-constdefs preserv :: "proto => keyfun => nat => key set => bool"
+definition preserv :: "proto => keyfun => nat => key set => bool" where
 "preserv p keys n Ks == (ALL evs R' s' R s. evs:tr p -->
 Guard n Ks (spies evs) --> safe Ks (spies evs) --> fresh p R' s' n Ks evs -->
 keys R' s' n evs <= Ks --> R:p --> ok evs R s --> apm' s R:guard n Ks)"
@@ -257,7 +253,7 @@
 
 subsection{*monotonic keyfun*}
 
-constdefs monoton :: "proto => keyfun => bool"
+definition monoton :: "proto => keyfun => bool" where
 "monoton p keys == ALL R' s' n ev evs. ev # evs:tr p -->
 keys R' s' n evs <= keys R' s' n (ev # evs)"
 
@@ -323,7 +319,7 @@
 
 subsection{*unicity*}
 
-constdefs uniq :: "proto => secfun => bool"
+definition uniq :: "proto => secfun => bool" where
 "uniq p secret == ALL evs R R' n n' Ks s s'. R:p --> R':p -->
 n:newn R --> n':newn R' --> nonce s n = nonce s' n' -->
 Nonce (nonce s n):parts {apm' s R} --> Nonce (nonce s n):parts {apm' s' R'} -->
@@ -340,13 +336,13 @@
 secret R n s Ks = secret R' n' s' Ks"
 by (unfold uniq_def, blast)
 
-constdefs ord :: "proto => (rule => rule => bool) => bool"
+definition ord :: "proto => (rule => rule => bool) => bool" where
 "ord p inff == ALL R R'. R:p --> R':p --> ~ inff R R' --> inff R' R"
 
 lemma ordD: "[| ord p inff; ~ inff R R'; R:p; R':p |] ==> inff R' R"
 by (unfold ord_def, blast)
 
-constdefs uniq' :: "proto => (rule => rule => bool) => secfun => bool"
+definition uniq' :: "proto => (rule => rule => bool) => secfun => bool" where
 "uniq' p inff secret == ALL evs R R' n n' Ks s s'. R:p --> R':p -->
 inff R R' --> n:newn R --> n':newn R' --> nonce s n = nonce s' n' -->
 Nonce (nonce s n):parts {apm' s R} --> Nonce (nonce s n):parts {apm' s' R'} -->
@@ -372,13 +368,12 @@
 
 subsection{*Needham-Schroeder-Lowe*}
 
-constdefs
-a :: agent "a == Friend 0"
-b :: agent "b == Friend 1"
-a' :: agent "a' == Friend 2"
-b' :: agent "b' == Friend 3"
-Na :: nat "Na == 0"
-Nb :: nat "Nb == 1"
+definition a :: agent where "a == Friend 0"
+definition b :: agent where "b == Friend 1"
+definition a' :: agent where "a' == Friend 2"
+definition b' :: agent where "b' == Friend 3"
+definition Na :: nat where "Na == 0"
+definition Nb :: nat where "Nb == 1"
 
 abbreviation
   ns1 :: rule where
@@ -408,19 +403,19 @@
   ns3b :: event where
   "ns3b == Says b' a (Crypt (pubK a) {|Nonce Na, Nonce Nb, Agent b|})"
 
-constdefs keys :: "keyfun"
+definition keys :: "keyfun" where
 "keys R' s' n evs == {priK' s' a, priK' s' b}"
 
 lemma "monoton ns keys"
 by (simp add: keys_def monoton_def)
 
-constdefs secret :: "secfun"
+definition secret :: "secfun" where
 "secret R n s Ks ==
 (if R=ns1 then apm s (Crypt (pubK b) {|Nonce Na, Agent a|})
 else if R=ns2 then apm s (Crypt (pubK a) {|Nonce Na, Nonce Nb, Agent b|})
 else Number 0)"
 
-constdefs inf :: "rule => rule => bool"
+definition inf :: "rule => rule => bool" where
 "inf R R' == (R=ns1 | (R=ns2 & R'~=ns1) | (R=ns3 & R'=ns3))"
 
 lemma inf_is_ord [iff]: "ord ns inf"
--- a/src/HOL/Auth/KerberosIV.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/KerberosIV.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -101,8 +101,7 @@
 
 
 (* Predicate formalising the association between authKeys and servKeys *)
-constdefs
-  AKcryptSK :: "[key, key, event list] => bool"
+definition AKcryptSK :: "[key, key, event list] => bool" where
   "AKcryptSK authK servK evs ==
      \<exists>A B Ts.
        Says Tgs A (Crypt authK
--- a/src/HOL/Auth/KerberosIV_Gets.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/KerberosIV_Gets.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -89,8 +89,7 @@
 
 
 (* Predicate formalising the association between authKeys and servKeys *)
-constdefs
-  AKcryptSK :: "[key, key, event list] => bool"
+definition AKcryptSK :: "[key, key, event list] => bool" where
   "AKcryptSK authK servK evs ==
      \<exists>A B Ts.
        Says Tgs A (Crypt authK
--- a/src/HOL/Auth/KerberosV.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/KerberosV.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -92,8 +92,7 @@
 
 
 (* Predicate formalising the association between authKeys and servKeys *)
-constdefs
-  AKcryptSK :: "[key, key, event list] => bool"
+definition AKcryptSK :: "[key, key, event list] => bool" where
   "AKcryptSK authK servK evs ==
      \<exists>A B tt.
        Says Tgs A \<lbrace>Crypt authK \<lbrace>Key servK, Agent B, tt\<rbrace>,
--- a/src/HOL/Auth/Message.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Message.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -32,8 +32,7 @@
 text{*The inverse of a symmetric key is itself; that of a public key
       is the private key and vice versa*}
 
-constdefs
-  symKeys :: "key set"
+definition symKeys :: "key set" where
   "symKeys == {K. invKey K = K}"
 
 datatype  --{*We allow any number of friendly agents*}
@@ -61,12 +60,11 @@
   "{|x, y|}"      == "CONST MPair x y"
 
 
-constdefs
-  HPair :: "[msg,msg] => msg"                       ("(4Hash[_] /_)" [0, 1000])
+definition HPair :: "[msg,msg] => msg" ("(4Hash[_] /_)" [0, 1000]) where
     --{*Message Y paired with a MAC computed with the help of X*}
     "Hash[X] Y == {| Hash{|X,Y|}, Y|}"
 
-  keysFor :: "msg set => key set"
+definition keysFor :: "msg set => key set" where
     --{*Keys useful to decrypt elements of a message set*}
   "keysFor H == invKey ` {K. \<exists>X. Crypt K X \<in> H}"
 
--- a/src/HOL/Auth/Smartcard/ShoupRubin.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Smartcard/ShoupRubin.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -1,5 +1,4 @@
-(*  ID:         $Id$
-    Author:     Giampaolo Bella, Catania University
+(*  Author:     Giampaolo Bella, Catania University
 *)
 
 header{*Original Shoup-Rubin protocol*}
@@ -29,9 +28,7 @@
     between each agent and his smartcard*)
    shouprubin_assumes_securemeans [iff]: "evs \<in> sr \<Longrightarrow> secureM"
 
-constdefs
-
-  Unique :: "[event, event list] => bool" ("Unique _ on _")
+definition Unique :: "[event, event list] => bool" ("Unique _ on _") where
    "Unique ev on evs == 
       ev \<notin> set (tl (dropWhile (% z. z \<noteq> ev) evs))"
 
--- a/src/HOL/Auth/Smartcard/ShoupRubinBella.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Smartcard/ShoupRubinBella.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -1,5 +1,4 @@
-(*  ID:         $Id$
-    Author:     Giampaolo Bella, Catania University
+(*  Author:     Giampaolo Bella, Catania University
 *)
 
 header{*Bella's modification of the Shoup-Rubin protocol*}
@@ -35,9 +34,7 @@
     between each agent and his smartcard*)
    shouprubin_assumes_securemeans [iff]: "evs \<in> srb \<Longrightarrow> secureM"
 
-constdefs
-
-  Unique :: "[event, event list] => bool" ("Unique _ on _")
+definition Unique :: "[event, event list] => bool" ("Unique _ on _") where
    "Unique ev on evs == 
       ev \<notin> set (tl (dropWhile (% z. z \<noteq> ev) evs))"
 
--- a/src/HOL/Auth/Smartcard/Smartcard.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Smartcard/Smartcard.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -43,15 +43,11 @@
   shrK_disj_pin [iff]:  "shrK P \<noteq> pin Q"
   crdK_disj_pin [iff]:   "crdK C \<noteq> pin P"
 
-constdefs
-  legalUse :: "card => bool" ("legalUse (_)")
+definition legalUse :: "card => bool" ("legalUse (_)") where
   "legalUse C == C \<notin> stolen"
 
-consts  
-  illegalUse :: "card  => bool"
-primrec
-  illegalUse_def: 
-  "illegalUse (Card A) = ( (Card A \<in> stolen \<and> A \<in> bad)  \<or>  Card A \<in> cloned )"
+primrec illegalUse :: "card  => bool" where
+  illegalUse_def: "illegalUse (Card A) = ( (Card A \<in> stolen \<and> A \<in> bad)  \<or>  Card A \<in> cloned )"
 
 
 text{*initState must be defined with care*}
--- a/src/HOL/Auth/TLS.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/TLS.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -43,8 +43,7 @@
 
 theory TLS imports Public Nat_Int_Bij begin
 
-constdefs
-  certificate      :: "[agent,key] => msg"
+definition certificate :: "[agent,key] => msg" where
     "certificate A KA == Crypt (priSK Server) {|Agent A, Key KA|}"
 
 text{*TLS apparently does not require separate keypairs for encryption and
--- a/src/HOL/Auth/Yahalom.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/Yahalom.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -74,8 +74,7 @@
           ==> Notes Spy {|Nonce NA, Nonce NB, Key K|} # evso \<in> yahalom"
 
 
-constdefs 
-  KeyWithNonce :: "[key, nat, event list] => bool"
+definition KeyWithNonce :: "[key, nat, event list] => bool" where
   "KeyWithNonce K NB evs ==
      \<exists>A B na X. 
        Says Server A {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB|}, X|} 
--- a/src/HOL/Auth/ZhouGollmann.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Auth/ZhouGollmann.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -21,8 +21,7 @@
 abbreviation f_con :: nat where "f_con == 4"
 
 
-constdefs
-  broken :: "agent set"    
+definition broken :: "agent set" where    
     --{*the compromised honest agents; TTP is included as it's not allowed to
         use the protocol*}
    "broken == bad - {Spy}"
--- a/src/HOL/Bali/AxCompl.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/AxCompl.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -20,9 +20,7 @@
            
 section "set of not yet initialzed classes"
 
-constdefs
-
-  nyinitcls :: "prog \<Rightarrow> state \<Rightarrow> qtname set"
+definition nyinitcls :: "prog \<Rightarrow> state \<Rightarrow> qtname set" where
  "nyinitcls G s \<equiv> {C. is_class G C \<and> \<not> initd C s}"
 
 lemma nyinitcls_subset_class: "nyinitcls G s \<subseteq> {C. is_class G C}"
@@ -115,8 +113,7 @@
 
 section "init-le"
 
-constdefs
-  init_le :: "prog \<Rightarrow> nat \<Rightarrow> state \<Rightarrow> bool"            ("_\<turnstile>init\<le>_"  [51,51] 50)
+definition init_le :: "prog \<Rightarrow> nat \<Rightarrow> state \<Rightarrow> bool" ("_\<turnstile>init\<le>_"  [51,51] 50) where
  "G\<turnstile>init\<le>n \<equiv> \<lambda>s. card (nyinitcls G s) \<le> n"
   
 lemma init_le_def2 [simp]: "(G\<turnstile>init\<le>n) s = (card (nyinitcls G s)\<le>n)"
@@ -135,9 +132,7 @@
 
 section "Most General Triples and Formulas"
 
-constdefs
-
-  remember_init_state :: "state assn"                ("\<doteq>")
+definition remember_init_state :: "state assn" ("\<doteq>") where
   "\<doteq> \<equiv> \<lambda>Y s Z. s = Z"
 
 lemma remember_init_state_def2 [simp]: "\<doteq> Y = op ="
@@ -579,8 +574,7 @@
 unroll the loop in iterated evaluations of the expression and evaluations of
 the loop body. *}
 
-constdefs
- unroll:: "prog \<Rightarrow> label \<Rightarrow> expr \<Rightarrow> stmt \<Rightarrow> (state \<times>  state) set"
+definition unroll :: "prog \<Rightarrow> label \<Rightarrow> expr \<Rightarrow> stmt \<Rightarrow> (state \<times>  state) set" where
 
  "unroll G l e c \<equiv> {(s,t). \<exists> v s1 s2.
                              G\<turnstile>s \<midarrow>e-\<succ>v\<rightarrow> s1 \<and> the_Bool v \<and> normal s1 \<and>
--- a/src/HOL/Bali/AxExample.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/AxExample.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -8,8 +8,7 @@
 imports AxSem Example
 begin
 
-constdefs
-  arr_inv :: "st \<Rightarrow> bool"
+definition arr_inv :: "st \<Rightarrow> bool" where
  "arr_inv \<equiv> \<lambda>s. \<exists>obj a T el. globs s (Stat Base) = Some obj \<and>
                               values obj (Inl (arr, Base)) = Some (Addr a) \<and>
                               heap s a = Some \<lparr>tag=Arr T 2,values=el\<rparr>"
--- a/src/HOL/Bali/AxSem.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/AxSem.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -63,8 +63,7 @@
       "res"    <= (type) "AxSem.res"
       "a assn" <= (type) "vals \<Rightarrow> state \<Rightarrow> a \<Rightarrow> bool"
 
-constdefs
-  assn_imp   :: "'a assn \<Rightarrow> 'a assn \<Rightarrow> bool"             (infixr "\<Rightarrow>" 25)
+definition assn_imp :: "'a assn \<Rightarrow> 'a assn \<Rightarrow> bool" (infixr "\<Rightarrow>" 25) where
  "P \<Rightarrow> Q \<equiv> \<forall>Y s Z. P Y s Z \<longrightarrow> Q Y s Z"
   
 lemma assn_imp_def2 [iff]: "(P \<Rightarrow> Q) = (\<forall>Y s Z. P Y s Z \<longrightarrow> Q Y s Z)"
@@ -77,8 +76,7 @@
 
 subsection "peek-and"
 
-constdefs
-  peek_and   :: "'a assn \<Rightarrow> (state \<Rightarrow>  bool) \<Rightarrow> 'a assn" (infixl "\<and>." 13)
+definition peek_and :: "'a assn \<Rightarrow> (state \<Rightarrow>  bool) \<Rightarrow> 'a assn" (infixl "\<and>." 13) where
  "P \<and>. p \<equiv> \<lambda>Y s Z. P Y s Z \<and> p s"
 
 lemma peek_and_def2 [simp]: "peek_and P p Y s = (\<lambda>Z. (P Y s Z \<and> p s))"
@@ -117,8 +115,7 @@
 
 subsection "assn-supd"
 
-constdefs
-  assn_supd  :: "'a assn \<Rightarrow> (state \<Rightarrow> state) \<Rightarrow> 'a assn" (infixl ";." 13)
+definition assn_supd :: "'a assn \<Rightarrow> (state \<Rightarrow> state) \<Rightarrow> 'a assn" (infixl ";." 13) where
  "P ;. f \<equiv> \<lambda>Y s' Z. \<exists>s. P Y s Z \<and> s' = f s"
 
 lemma assn_supd_def2 [simp]: "assn_supd P f Y s' Z = (\<exists>s. P Y s Z \<and> s' = f s)"
@@ -128,8 +125,7 @@
 
 subsection "supd-assn"
 
-constdefs
-  supd_assn  :: "(state \<Rightarrow> state) \<Rightarrow> 'a assn \<Rightarrow> 'a assn" (infixr ".;" 13)
+definition supd_assn :: "(state \<Rightarrow> state) \<Rightarrow> 'a assn \<Rightarrow> 'a assn" (infixr ".;" 13) where
  "f .; P \<equiv> \<lambda>Y s. P Y (f s)"
 
 
@@ -148,8 +144,7 @@
 
 subsection "subst-res"
 
-constdefs
-  subst_res   :: "'a assn \<Rightarrow> res \<Rightarrow> 'a assn"              ("_\<leftarrow>_"  [60,61] 60)
+definition subst_res :: "'a assn \<Rightarrow> res \<Rightarrow> 'a assn" ("_\<leftarrow>_"  [60,61] 60) where
  "P\<leftarrow>w \<equiv> \<lambda>Y. P w"
 
 lemma subst_res_def2 [simp]: "(P\<leftarrow>w) Y = P w"
@@ -184,8 +179,7 @@
 
 subsection "subst-Bool"
 
-constdefs
-  subst_Bool  :: "'a assn \<Rightarrow> bool \<Rightarrow> 'a assn"             ("_\<leftarrow>=_" [60,61] 60)
+definition subst_Bool :: "'a assn \<Rightarrow> bool \<Rightarrow> 'a assn" ("_\<leftarrow>=_" [60,61] 60) where
  "P\<leftarrow>=b \<equiv> \<lambda>Y s Z. \<exists>v. P (Val v) s Z \<and> (normal s \<longrightarrow> the_Bool v=b)"
 
 lemma subst_Bool_def2 [simp]: 
@@ -200,8 +194,7 @@
 
 subsection "peek-res"
 
-constdefs
-  peek_res    :: "(res \<Rightarrow> 'a assn) \<Rightarrow> 'a assn"
+definition peek_res :: "(res \<Rightarrow> 'a assn) \<Rightarrow> 'a assn" where
  "peek_res Pf \<equiv> \<lambda>Y. Pf Y Y"
 
 syntax
@@ -229,8 +222,7 @@
 
 subsection "ign-res"
 
-constdefs
-  ign_res    ::  "        'a assn \<Rightarrow> 'a assn"            ("_\<down>" [1000] 1000)
+definition ign_res :: "        'a assn \<Rightarrow> 'a assn" ("_\<down>" [1000] 1000) where
   "P\<down>        \<equiv> \<lambda>Y s Z. \<exists>Y. P Y s Z"
 
 lemma ign_res_def2 [simp]: "P\<down> Y s Z = (\<exists>Y. P Y s Z)"
@@ -261,8 +253,7 @@
 
 subsection "peek-st"
 
-constdefs
-  peek_st    :: "(st \<Rightarrow> 'a assn) \<Rightarrow> 'a assn"
+definition peek_st :: "(st \<Rightarrow> 'a assn) \<Rightarrow> 'a assn" where
  "peek_st P \<equiv> \<lambda>Y s. P (store s) Y s"
 
 syntax
@@ -306,8 +297,7 @@
 
 subsection "ign-res-eq"
 
-constdefs
-  ign_res_eq :: "'a assn \<Rightarrow> res \<Rightarrow> 'a assn"               ("_\<down>=_"  [60,61] 60)
+definition ign_res_eq :: "'a assn \<Rightarrow> res \<Rightarrow> 'a assn" ("_\<down>=_"  [60,61] 60) where
  "P\<down>=w       \<equiv> \<lambda>Y:. P\<down> \<and>. (\<lambda>s. Y=w)"
 
 lemma ign_res_eq_def2 [simp]: "(P\<down>=w) Y s Z = ((\<exists>Y. P Y s Z) \<and> Y=w)"
@@ -337,8 +327,7 @@
 
 subsection "RefVar"
 
-constdefs
-  RefVar    :: "(state \<Rightarrow> vvar \<times> state) \<Rightarrow> 'a assn \<Rightarrow> 'a assn"(infixr "..;" 13)
+definition RefVar :: "(state \<Rightarrow> vvar \<times> state) \<Rightarrow> 'a assn \<Rightarrow> 'a assn" (infixr "..;" 13) where
  "vf ..; P \<equiv> \<lambda>Y s. let (v,s') = vf s in P (Var v) s'"
  
 lemma RefVar_def2 [simp]: "(vf ..; P) Y s =  
@@ -349,12 +338,11 @@
 
 subsection "allocation"
 
-constdefs
-  Alloc      :: "prog \<Rightarrow> obj_tag \<Rightarrow> 'a assn \<Rightarrow> 'a assn"
+definition Alloc :: "prog \<Rightarrow> obj_tag \<Rightarrow> 'a assn \<Rightarrow> 'a assn" where
  "Alloc G otag P \<equiv> \<lambda>Y s Z.
                    \<forall>s' a. G\<turnstile>s \<midarrow>halloc otag\<succ>a\<rightarrow> s'\<longrightarrow> P (Val (Addr a)) s' Z"
 
-  SXAlloc     :: "prog \<Rightarrow> 'a assn \<Rightarrow> 'a assn"
+definition SXAlloc     :: "prog \<Rightarrow> 'a assn \<Rightarrow> 'a assn" where
  "SXAlloc G P \<equiv> \<lambda>Y s Z. \<forall>s'. G\<turnstile>s \<midarrow>sxalloc\<rightarrow> s' \<longrightarrow> P Y s' Z"
 
 
@@ -372,8 +360,7 @@
 
 section "validity"
 
-constdefs
-  type_ok  :: "prog \<Rightarrow> term \<Rightarrow> state \<Rightarrow> bool"
+definition type_ok :: "prog \<Rightarrow> term \<Rightarrow> state \<Rightarrow> bool" where
  "type_ok G t s \<equiv> 
     \<exists>L T C A. (normal s \<longrightarrow> \<lparr>prg=G,cls=C,lcl=L\<rparr>\<turnstile>t\<Colon>T \<and> 
                             \<lparr>prg=G,cls=C,lcl=L\<rparr>\<turnstile>dom (locals (store s))\<guillemotright>t\<guillemotright>A )
@@ -419,10 +406,8 @@
 apply auto
 done
 
-constdefs
-  mtriples  :: "('c \<Rightarrow> 'sig \<Rightarrow> 'a assn) \<Rightarrow> ('c \<Rightarrow> 'sig \<Rightarrow> expr) \<Rightarrow> 
-                ('c \<Rightarrow> 'sig \<Rightarrow> 'a assn) \<Rightarrow> ('c \<times>  'sig) set \<Rightarrow> 'a triples"
-                                     ("{{(1_)}/ _-\<succ>/ {(1_)} | _}"[3,65,3,65]75)
+definition mtriples :: "('c \<Rightarrow> 'sig \<Rightarrow> 'a assn) \<Rightarrow> ('c \<Rightarrow> 'sig \<Rightarrow> expr) \<Rightarrow> 
+                ('c \<Rightarrow> 'sig \<Rightarrow> 'a assn) \<Rightarrow> ('c \<times>  'sig) set \<Rightarrow> 'a triples" ("{{(1_)}/ _-\<succ>/ {(1_)} | _}"[3,65,3,65]75) where
  "{{P} tf-\<succ> {Q} | ms} \<equiv> (\<lambda>(C,sig). {Normal(P C sig)} tf C sig-\<succ> {Q C sig})`ms"
   
 consts
@@ -641,8 +626,7 @@
 axioms 
 *)
 
-constdefs
- adapt_pre :: "'a assn \<Rightarrow> 'a assn \<Rightarrow> 'a assn \<Rightarrow> 'a assn"
+definition adapt_pre :: "'a assn \<Rightarrow> 'a assn \<Rightarrow> 'a assn \<Rightarrow> 'a assn" where
 "adapt_pre P Q Q'\<equiv>\<lambda>Y s Z. \<forall>Y' s'. \<exists>Z'. P Y s Z' \<and> (Q Y' s' Z' \<longrightarrow> Q' Y' s' Z)"
 
 
--- a/src/HOL/Bali/Basis.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/Basis.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -237,8 +237,7 @@
 
 text{* Deemed too special for theory Map. *}
 
-constdefs
-  chg_map :: "('b => 'b) => 'a => ('a ~=> 'b) => ('a ~=> 'b)"
+definition chg_map :: "('b => 'b) => 'a => ('a ~=> 'b) => ('a ~=> 'b)" where
  "chg_map f a m == case m a of None => m | Some b => m(a|->f b)"
 
 lemma chg_map_new[simp]: "m a = None   ==> chg_map f a m = m"
@@ -253,8 +252,7 @@
 
 section "unique association lists"
 
-constdefs
-  unique   :: "('a \<times> 'b) list \<Rightarrow> bool"
+definition unique :: "('a \<times> 'b) list \<Rightarrow> bool" where
  "unique \<equiv> distinct \<circ> map fst"
 
 lemma uniqueD [rule_format (no_asm)]: 
--- a/src/HOL/Bali/Conform.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/Conform.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -22,9 +22,7 @@
 section "extension of global store"
 
 
-constdefs
-
-  gext    :: "st \<Rightarrow> st \<Rightarrow> bool"                ("_\<le>|_"       [71,71]   70)
+definition gext :: "st \<Rightarrow> st \<Rightarrow> bool" ("_\<le>|_"       [71,71]   70) where
    "s\<le>|s' \<equiv> \<forall>r. \<forall>obj\<in>globs s r: \<exists>obj'\<in>globs s' r: tag obj'= tag obj"
 
 text {* For the the proof of type soundness we will need the 
@@ -98,9 +96,7 @@
 
 section "value conformance"
 
-constdefs
-
-  conf  :: "prog \<Rightarrow> st \<Rightarrow> val \<Rightarrow> ty \<Rightarrow> bool"    ("_,_\<turnstile>_\<Colon>\<preceq>_"   [71,71,71,71] 70)
+definition conf :: "prog \<Rightarrow> st \<Rightarrow> val \<Rightarrow> ty \<Rightarrow> bool" ("_,_\<turnstile>_\<Colon>\<preceq>_"   [71,71,71,71] 70) where
            "G,s\<turnstile>v\<Colon>\<preceq>T \<equiv> \<exists>T'\<in>typeof (\<lambda>a. Option.map obj_ty (heap s a)) v:G\<turnstile>T'\<preceq>T"
 
 lemma conf_cong [simp]: "G,set_locals l s\<turnstile>v\<Colon>\<preceq>T = G,s\<turnstile>v\<Colon>\<preceq>T"
@@ -181,10 +177,7 @@
 
 section "value list conformance"
 
-constdefs
-
-  lconf :: "prog \<Rightarrow> st \<Rightarrow> ('a, val) table \<Rightarrow> ('a, ty) table \<Rightarrow> bool"
-                                                ("_,_\<turnstile>_[\<Colon>\<preceq>]_" [71,71,71,71] 70)
+definition lconf :: "prog \<Rightarrow> st \<Rightarrow> ('a, val) table \<Rightarrow> ('a, ty) table \<Rightarrow> bool" ("_,_\<turnstile>_[\<Colon>\<preceq>]_" [71,71,71,71] 70) where
            "G,s\<turnstile>vs[\<Colon>\<preceq>]Ts \<equiv> \<forall>n. \<forall>T\<in>Ts n: \<exists>v\<in>vs n: G,s\<turnstile>v\<Colon>\<preceq>T"
 
 lemma lconfD: "\<lbrakk>G,s\<turnstile>vs[\<Colon>\<preceq>]Ts; Ts n = Some T\<rbrakk> \<Longrightarrow> G,s\<turnstile>(the (vs n))\<Colon>\<preceq>T"
@@ -267,10 +260,7 @@
 *}
 
   
-constdefs
-
-  wlconf :: "prog \<Rightarrow> st \<Rightarrow> ('a, val) table \<Rightarrow> ('a, ty) table \<Rightarrow> bool"
-                                          ("_,_\<turnstile>_[\<sim>\<Colon>\<preceq>]_" [71,71,71,71] 70)
+definition wlconf :: "prog \<Rightarrow> st \<Rightarrow> ('a, val) table \<Rightarrow> ('a, ty) table \<Rightarrow> bool" ("_,_\<turnstile>_[\<sim>\<Colon>\<preceq>]_" [71,71,71,71] 70) where
            "G,s\<turnstile>vs[\<sim>\<Colon>\<preceq>]Ts \<equiv> \<forall>n. \<forall>T\<in>Ts n: \<forall> v\<in>vs n: G,s\<turnstile>v\<Colon>\<preceq>T"
 
 lemma wlconfD: "\<lbrakk>G,s\<turnstile>vs[\<sim>\<Colon>\<preceq>]Ts; Ts n = Some T; vs n = Some v\<rbrakk> \<Longrightarrow> G,s\<turnstile>v\<Colon>\<preceq>T"
@@ -348,9 +338,7 @@
 
 section "object conformance"
 
-constdefs
-
-  oconf :: "prog \<Rightarrow> st \<Rightarrow> obj \<Rightarrow> oref \<Rightarrow> bool"  ("_,_\<turnstile>_\<Colon>\<preceq>\<surd>_"  [71,71,71,71] 70)
+definition oconf :: "prog \<Rightarrow> st \<Rightarrow> obj \<Rightarrow> oref \<Rightarrow> bool" ("_,_\<turnstile>_\<Colon>\<preceq>\<surd>_"  [71,71,71,71] 70) where
            "G,s\<turnstile>obj\<Colon>\<preceq>\<surd>r \<equiv> G,s\<turnstile>values obj[\<Colon>\<preceq>]var_tys G (tag obj) r \<and> 
                            (case r of 
                               Heap a \<Rightarrow> is_type G (obj_ty obj) 
@@ -385,9 +373,7 @@
 
 section "state conformance"
 
-constdefs
-
-  conforms :: "state \<Rightarrow> env' \<Rightarrow> bool"          (     "_\<Colon>\<preceq>_"   [71,71]      70)
+definition conforms :: "state \<Rightarrow> env' \<Rightarrow> bool"   ("_\<Colon>\<preceq>_"   [71,71]      70)  where
    "xs\<Colon>\<preceq>E \<equiv> let (G, L) = E; s = snd xs; l = locals s in
     (\<forall>r. \<forall>obj\<in>globs s r:           G,s\<turnstile>obj   \<Colon>\<preceq>\<surd>r) \<and>
                 \<spacespace>                   G,s\<turnstile>l    [\<sim>\<Colon>\<preceq>]L\<spacespace> \<and>
--- a/src/HOL/Bali/Decl.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/Decl.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -206,8 +206,7 @@
   "mdecl" <= (type) "sig \<times> methd"
 
 
-constdefs 
-  mhead::"methd \<Rightarrow> mhead"
+definition mhead :: "methd \<Rightarrow> mhead" where
   "mhead m \<equiv> \<lparr>access=access m, static=static m, pars=pars m, resT=resT m\<rparr>"
 
 lemma access_mhead [simp]:"access (mhead m) = access m"
@@ -275,7 +274,7 @@
 lemma memberid_pair_simp1: "memberid p  = memberid (snd p)"
 by (simp add: pair_memberid_def)
 
-constdefs is_field :: "qtname \<times> memberdecl \<Rightarrow> bool"
+definition is_field :: "qtname \<times> memberdecl \<Rightarrow> bool" where
 "is_field m \<equiv> \<exists> declC f. m=(declC,fdecl f)"
   
 lemma is_fieldD: "is_field m \<Longrightarrow> \<exists> declC f. m=(declC,fdecl f)"
@@ -284,7 +283,7 @@
 lemma is_fieldI: "is_field (C,fdecl f)"
 by (simp add: is_field_def)
 
-constdefs is_method :: "qtname \<times> memberdecl \<Rightarrow> bool"
+definition is_method :: "qtname \<times> memberdecl \<Rightarrow> bool" where
 "is_method membr \<equiv> \<exists> declC m. membr=(declC,mdecl m)"
   
 lemma is_methodD: "is_method membr \<Longrightarrow> \<exists> declC m. membr=(declC,mdecl m)"
@@ -315,8 +314,7 @@
                       isuperIfs::qtname list,\<dots>::'a\<rparr>"
   "idecl" <= (type) "qtname \<times> iface"
 
-constdefs
-  ibody :: "iface \<Rightarrow> ibody"
+definition ibody :: "iface \<Rightarrow> ibody" where
   "ibody i \<equiv> \<lparr>access=access i,imethods=imethods i\<rparr>"
 
 lemma access_ibody [simp]: "(access (ibody i)) = access i"
@@ -351,8 +349,7 @@
                       super::qtname,superIfs::qtname list,\<dots>::'a\<rparr>"
   "cdecl" <= (type) "qtname \<times> class"
 
-constdefs
-  cbody :: "class \<Rightarrow> cbody"
+definition cbody :: "class \<Rightarrow> cbody" where
   "cbody c \<equiv> \<lparr>access=access c, cfields=cfields c,methods=methods c,init=init c\<rparr>"
 
 lemma access_cbody [simp]:"access (cbody c) = access c"
@@ -394,7 +391,7 @@
 lemma SXcptC_inject [simp]: "(SXcptC xn = SXcptC xm) = (xn = xm)"
 by (simp add: SXcptC_def)
 
-constdefs standard_classes :: "cdecl list"
+definition standard_classes :: "cdecl list" where
          "standard_classes \<equiv> [ObjectC, SXcptC Throwable,
                 SXcptC NullPointer, SXcptC OutOfMemory, SXcptC ClassCast,
                 SXcptC NegArrSize , SXcptC IndOutBound, SXcptC ArrStore]"
@@ -470,7 +467,7 @@
   where "G|-C <:C D == (C,D) \<in>(subcls1 G)^+"
 
 notation (xsymbols)
-  subcls1_syntax  ("_\<turnstile>_\<prec>\<^sub>C\<^sub>1_"  [71,71,71] 70) and
+  subcls1_syntax  ("_\<turnstile>_\<prec>\<^sub>C1_"  [71,71,71] 70) and
   subclseq_syntax  ("_\<turnstile>_\<preceq>\<^sub>C _"  [71,71,71] 70) and
   subcls_syntax  ("_\<turnstile>_\<prec>\<^sub>C _"  [71,71,71] 70)
 
@@ -510,7 +507,7 @@
 "\<lbrakk>G\<turnstile>C \<prec>\<^sub>C D\<rbrakk> \<Longrightarrow> \<exists> c. class G C = Some c"
 by (auto simp add: subcls1_def dest: tranclD)
 
-lemma no_subcls1_Object:"G\<turnstile>Object\<prec>\<^sub>C\<^sub>1 D \<Longrightarrow> P"
+lemma no_subcls1_Object:"G\<turnstile>Object\<prec>\<^sub>C1 D \<Longrightarrow> P"
 by (auto simp add: subcls1_def)
 
 lemma no_subcls_Object: "G\<turnstile>Object\<prec>\<^sub>C D \<Longrightarrow> P"
@@ -520,14 +517,13 @@
 
 section "well-structured programs"
 
-constdefs
-  ws_idecl :: "prog \<Rightarrow> qtname \<Rightarrow> qtname list \<Rightarrow> bool"
+definition ws_idecl :: "prog \<Rightarrow> qtname \<Rightarrow> qtname list \<Rightarrow> bool" where
  "ws_idecl G I si \<equiv> \<forall>J\<in>set si.  is_iface G J   \<and> (J,I)\<notin>(subint1 G)^+"
   
-  ws_cdecl :: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
+definition ws_cdecl :: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool" where
  "ws_cdecl G C sc \<equiv> C\<noteq>Object \<longrightarrow> is_class G sc \<and> (sc,C)\<notin>(subcls1 G)^+"
   
-  ws_prog  :: "prog \<Rightarrow> bool"
+definition ws_prog  :: "prog \<Rightarrow> bool" where
  "ws_prog G \<equiv> (\<forall>(I,i)\<in>set (ifaces  G). ws_idecl G I (isuperIfs i)) \<and> 
               (\<forall>(C,c)\<in>set (classes G). ws_cdecl G C (super c))"
 
@@ -680,7 +676,7 @@
   then have "is_class G C \<Longrightarrow> P C"  
   proof (induct rule: subcls1_induct)
     fix C
-    assume   hyp:"\<forall> S. G\<turnstile>C \<prec>\<^sub>C\<^sub>1 S \<longrightarrow> is_class G S \<longrightarrow> P S"
+    assume   hyp:"\<forall> S. G\<turnstile>C \<prec>\<^sub>C1 S \<longrightarrow> is_class G S \<longrightarrow> P S"
        and iscls:"is_class G C"
     show "P C"
     proof (cases "C=Object")
@@ -715,7 +711,7 @@
   then have "\<And> c. class G C = Some c\<Longrightarrow> P C c"  
   proof (induct rule: subcls1_induct)
     fix C c
-    assume   hyp:"\<forall> S. G\<turnstile>C \<prec>\<^sub>C\<^sub>1 S \<longrightarrow> (\<forall> s. class G S = Some s \<longrightarrow> P S s)"
+    assume   hyp:"\<forall> S. G\<turnstile>C \<prec>\<^sub>C1 S \<longrightarrow> (\<forall> s. class G S = Some s \<longrightarrow> P S s)"
        and iscls:"class G C = Some c"
     show "P C c"
     proof (cases "C=Object")
@@ -725,7 +721,7 @@
       with ws iscls obtain sc where
         sc: "class G (super c) = Some sc"
         by (auto dest: ws_prog_cdeclD)
-      from iscls False have "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 (super c)" by (rule subcls1I)
+      from iscls False have "G\<turnstile>C \<prec>\<^sub>C1 (super c)" by (rule subcls1I)
       with False ws step hyp iscls sc
       show "P C c" 
         by (auto)  
@@ -808,8 +804,7 @@
 apply simp
 done
 
-constdefs
-imethds:: "prog \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables"
+definition imethds :: "prog \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables" where
   --{* methods of an interface, with overriding and inheritance, cf. 9.2 *}
 "imethds G I 
   \<equiv> iface_rec (G,I)  
--- a/src/HOL/Bali/DeclConcepts.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/DeclConcepts.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -8,8 +8,7 @@
 
 section "access control (cf. 6.6), overriding and hiding (cf. 8.4.6.1)"
 
-constdefs
-is_public :: "prog \<Rightarrow> qtname \<Rightarrow> bool"
+definition is_public :: "prog \<Rightarrow> qtname \<Rightarrow> bool" where
 "is_public G qn \<equiv> (case class G qn of
                      None       \<Rightarrow> (case iface G qn of
                                       None       \<Rightarrow> False
@@ -38,14 +37,16 @@
 
 declare accessible_in_RefT_simp [simp del]
 
-constdefs
-  is_acc_class :: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> bool"
+definition is_acc_class :: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> bool" where
     "is_acc_class G P C \<equiv> is_class G C \<and> G\<turnstile>(Class C) accessible_in P"
-  is_acc_iface :: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> bool"
+
+definition is_acc_iface :: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> bool" where
     "is_acc_iface G P I \<equiv> is_iface G I \<and> G\<turnstile>(Iface I) accessible_in P"
-  is_acc_type  :: "prog \<Rightarrow> pname \<Rightarrow> ty     \<Rightarrow> bool"
+
+definition is_acc_type  :: "prog \<Rightarrow> pname \<Rightarrow> ty     \<Rightarrow> bool" where
     "is_acc_type  G P T \<equiv> is_type G T  \<and> G\<turnstile>T accessible_in P"
-  is_acc_reftype  :: "prog \<Rightarrow> pname \<Rightarrow> ref_ty \<Rightarrow> bool"
+
+definition is_acc_reftype  :: "prog \<Rightarrow> pname \<Rightarrow> ref_ty \<Rightarrow> bool" where
   "is_acc_reftype  G P T \<equiv> isrtype G T  \<and> G\<turnstile>T accessible_in' P"
 
 lemma is_acc_classD:
@@ -336,8 +337,7 @@
 text {* Convert a qualified method declaration (qualified with its declaring 
 class) to a qualified member declaration:  @{text methdMembr}  *}
 
-constdefs
-methdMembr :: "(qtname \<times> mdecl) \<Rightarrow> (qtname \<times> memberdecl)"
+definition methdMembr :: "(qtname \<times> mdecl) \<Rightarrow> (qtname \<times> memberdecl)" where
  "methdMembr m \<equiv> (fst m,mdecl (snd m))"
 
 lemma methdMembr_simp[simp]: "methdMembr (c,m) = (c,mdecl m)"
@@ -355,8 +355,7 @@
 text {* Convert a qualified method (qualified with its declaring 
 class) to a qualified member declaration:  @{text method}  *}
 
-constdefs
-method :: "sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> memberdecl)" 
+definition method :: "sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> memberdecl)" where 
 "method sig m \<equiv> (declclass m, mdecl (sig, mthd m))"
 
 lemma method_simp[simp]: "method sig (C,m) = (C,mdecl (sig,m))"
@@ -377,8 +376,7 @@
 lemma memberid_method_simp[simp]:  "memberid (method sig m) = mid sig"
   by (simp add: method_def) 
 
-constdefs
-fieldm :: "vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> (qtname \<times> memberdecl)" 
+definition fieldm :: "vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> (qtname \<times> memberdecl)" where 
 "fieldm n f \<equiv> (declclass f, fdecl (n, fld f))"
 
 lemma fieldm_simp[simp]: "fieldm n (C,f) = (C,fdecl (n,f))"
@@ -402,7 +400,7 @@
 text {* Select the signature out of a qualified method declaration:
  @{text msig} *}
 
-constdefs msig:: "(qtname \<times> mdecl) \<Rightarrow> sig"
+definition msig :: "(qtname \<times> mdecl) \<Rightarrow> sig" where
 "msig m \<equiv> fst (snd m)"
 
 lemma msig_simp[simp]: "msig (c,(s,m)) = s"
@@ -411,7 +409,7 @@
 text {* Convert a qualified method (qualified with its declaring 
 class) to a qualified method declaration:  @{text qmdecl}  *}
 
-constdefs qmdecl :: "sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> mdecl)"
+definition qmdecl :: "sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> mdecl)" where
 "qmdecl sig m \<equiv> (declclass m, (sig,mthd m))"
 
 lemma qmdecl_simp[simp]: "qmdecl sig (C,m) = (C,(sig,m))"
@@ -504,10 +502,8 @@
       it is not accessible for inheritance at all.
 \end{itemize}
 *}
-constdefs
-inheritable_in:: 
- "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> pname \<Rightarrow> bool"
-                  ("_ \<turnstile> _ inheritable'_in _" [61,61,61] 60)
+definition inheritable_in :: "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> pname \<Rightarrow> bool" ("_ \<turnstile> _ inheritable'_in _" [61,61,61] 60) where
+                  
 "G\<turnstile>membr inheritable_in pack 
   \<equiv> (case (accmodi membr) of
        Private   \<Rightarrow> False
@@ -529,25 +525,21 @@
 
 subsubsection "declared-in/undeclared-in"
 
-constdefs cdeclaredmethd:: "prog \<Rightarrow> qtname \<Rightarrow> (sig,methd) table"
+definition cdeclaredmethd :: "prog \<Rightarrow> qtname \<Rightarrow> (sig,methd) table" where
 "cdeclaredmethd G C 
   \<equiv> (case class G C of
        None \<Rightarrow> \<lambda> sig. None
      | Some c \<Rightarrow> table_of (methods c)
     )"
 
-constdefs
-cdeclaredfield:: "prog \<Rightarrow> qtname \<Rightarrow> (vname,field) table"
+definition cdeclaredfield :: "prog \<Rightarrow> qtname \<Rightarrow> (vname,field) table" where
 "cdeclaredfield G C 
   \<equiv> (case class G C of
        None \<Rightarrow> \<lambda> sig. None
      | Some c \<Rightarrow> table_of (cfields c)
     )"
 
-
-constdefs
-declared_in:: "prog  \<Rightarrow> memberdecl \<Rightarrow> qtname \<Rightarrow> bool"
-                                 ("_\<turnstile> _ declared'_in _" [61,61,61] 60)
+definition declared_in :: "prog  \<Rightarrow> memberdecl \<Rightarrow> qtname \<Rightarrow> bool" ("_\<turnstile> _ declared'_in _" [61,61,61] 60) where
 "G\<turnstile>m declared_in C \<equiv> (case m of
                         fdecl (fn,f ) \<Rightarrow> cdeclaredfield G C fn  = Some f
                       | mdecl (sig,m) \<Rightarrow> cdeclaredmethd G C sig = Some m)"
@@ -567,10 +559,7 @@
 by (cases m) 
    (auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def)
 
-constdefs
-undeclared_in:: "prog  \<Rightarrow> memberid \<Rightarrow> qtname \<Rightarrow> bool"
-                                 ("_\<turnstile> _ undeclared'_in _" [61,61,61] 60)
-
+definition undeclared_in :: "prog  \<Rightarrow> memberid \<Rightarrow> qtname \<Rightarrow> bool" ("_\<turnstile> _ undeclared'_in _" [61,61,61] 60) where
 "G\<turnstile>m undeclared_in C \<equiv> (case m of
                             fid fn  \<Rightarrow> cdeclaredfield G C fn  = None
                           | mid sig \<Rightarrow> cdeclaredmethd G C sig = None)"
@@ -591,7 +580,7 @@
 
   Immediate: "\<lbrakk>G\<turnstile>mbr m declared_in C;declclass m = C\<rbrakk> \<Longrightarrow> G\<turnstile>m member_of C"
 | Inherited: "\<lbrakk>G\<turnstile>m inheritable_in (pid C); G\<turnstile>memberid m undeclared_in C; 
-               G\<turnstile>C \<prec>\<^sub>C\<^sub>1 S; G\<turnstile>(Class S) accessible_in (pid C);G\<turnstile>m member_of S 
+               G\<turnstile>C \<prec>\<^sub>C1 S; G\<turnstile>(Class S) accessible_in (pid C);G\<turnstile>m member_of S 
               \<rbrakk> \<Longrightarrow> G\<turnstile>m member_of C"
 text {* Note that in the case of an inherited member only the members of the
 direct superclass are concerned. If a member of a superclass of the direct
@@ -617,19 +606,16 @@
                            ("_ \<turnstile>Field _  _ member'_of _" [61,61,61] 60)
  where "G\<turnstile>Field n f member_of C == G\<turnstile>fieldm n f member_of C"
 
-constdefs
-inherits:: "prog \<Rightarrow> qtname \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> bool"
-                           ("_ \<turnstile> _ inherits _" [61,61,61] 60)
+definition inherits :: "prog \<Rightarrow> qtname \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> bool" ("_ \<turnstile> _ inherits _" [61,61,61] 60) where
 "G\<turnstile>C inherits m 
   \<equiv> G\<turnstile>m inheritable_in (pid C) \<and> G\<turnstile>memberid m undeclared_in C \<and> 
-    (\<exists> S. G\<turnstile>C \<prec>\<^sub>C\<^sub>1 S \<and> G\<turnstile>(Class S) accessible_in (pid C) \<and> G\<turnstile>m member_of S)"
+    (\<exists> S. G\<turnstile>C \<prec>\<^sub>C1 S \<and> G\<turnstile>(Class S) accessible_in (pid C) \<and> G\<turnstile>m member_of S)"
 
 lemma inherits_member: "G\<turnstile>C inherits m \<Longrightarrow> G\<turnstile>m member_of C"
 by (auto simp add: inherits_def intro: members.Inherited)
 
 
-constdefs member_in::"prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool"
-                           ("_ \<turnstile> _ member'_in _" [61,61,61] 60)
+definition member_in :: "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool" ("_ \<turnstile> _ member'_in _" [61,61,61] 60) where
 "G\<turnstile>m member_in C \<equiv> \<exists> provC. G\<turnstile> C \<preceq>\<^sub>C provC \<and> G \<turnstile> m member_of provC"
 text {* A member is in a class if it is member of the class or a superclass.
 If a member is in a class we can select this member. This additional notion
@@ -676,7 +662,7 @@
            G\<turnstile>Method new declared_in (declclass new);  
            G\<turnstile>Method old declared_in (declclass old); 
            G\<turnstile>Method old inheritable_in pid (declclass new);
-           G\<turnstile>(declclass new) \<prec>\<^sub>C\<^sub>1 superNew;
+           G\<turnstile>(declclass new) \<prec>\<^sub>C1 superNew;
            G \<turnstile>Method old member_of superNew
            \<rbrakk> \<Longrightarrow> G\<turnstile>new overrides\<^sub>S old"
 
@@ -716,9 +702,7 @@
 
 subsubsection "Hiding"
 
-constdefs hides::
-"prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool" 
-                                ("_\<turnstile> _ hides _" [61,61,61] 60)
+definition hides :: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool" ("_\<turnstile> _ hides _" [61,61,61] 60) where 
 "G\<turnstile>new hides old
   \<equiv> is_static new \<and> msig new = msig old \<and>
     G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
@@ -777,11 +761,7 @@
 by (auto simp add: hides_def)
 
 subsubsection "permits access" 
-constdefs 
-permits_acc:: 
- "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
-                   ("_ \<turnstile> _ in _ permits'_acc'_from _" [61,61,61,61] 60)
-
+definition permits_acc :: "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool" ("_ \<turnstile> _ in _ permits'_acc'_from _" [61,61,61,61] 60) where
 "G\<turnstile>membr in cls permits_acc_from accclass 
   \<equiv> (case (accmodi membr) of
        Private   \<Rightarrow> (declclass membr = accclass)
@@ -980,7 +960,7 @@
   next
     case (Inherited n C S)
     assume undecl: "G\<turnstile> memberid n undeclared_in C"
-    assume  super: "G\<turnstile>C\<prec>\<^sub>C\<^sub>1S"
+    assume  super: "G\<turnstile>C\<prec>\<^sub>C1S"
     assume    hyp: "\<lbrakk>G \<turnstile> m member_of S; memberid n = memberid m\<rbrakk> \<Longrightarrow> n = m"
     assume   eqid: "memberid n = memberid m"
     assume "G \<turnstile> m member_of C"
@@ -1011,7 +991,7 @@
        (auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def)
 next
   case (Inherited m C S)  
-  assume "G\<turnstile>C\<prec>\<^sub>C\<^sub>1S" and "is_class G S"
+  assume "G\<turnstile>C\<prec>\<^sub>C1S" and "is_class G S"
   then show "is_class G C"
     by - (rule subcls_is_class2,auto)
 qed
@@ -1043,7 +1023,7 @@
         intro: rtrancl_trans)
 
 lemma stat_override_declclasses_relation: 
-"\<lbrakk>G\<turnstile>(declclass new) \<prec>\<^sub>C\<^sub>1 superNew; G \<turnstile>Method old member_of superNew \<rbrakk>
+"\<lbrakk>G\<turnstile>(declclass new) \<prec>\<^sub>C1 superNew; G \<turnstile>Method old member_of superNew \<rbrakk>
 \<Longrightarrow> G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old)"
 apply (rule trancl_rtrancl_trancl)
 apply (erule r_into_trancl)
@@ -1257,7 +1237,7 @@
             "G\<turnstile> memberid m undeclared_in D"  
             "G \<turnstile> Class S accessible_in pid D" 
             "G \<turnstile> m member_of S"
-    assume super: "G\<turnstile>D\<prec>\<^sub>C\<^sub>1S"
+    assume super: "G\<turnstile>D\<prec>\<^sub>C1S"
     assume hyp: "\<lbrakk>G\<turnstile>S\<preceq>\<^sub>C C; G\<turnstile>C\<preceq>\<^sub>C declclass m\<rbrakk> \<Longrightarrow> G \<turnstile> m member_of C"
     assume subclseq_C_m: "G\<turnstile>C\<preceq>\<^sub>C declclass m"
     assume "G\<turnstile>D\<preceq>\<^sub>C C"
@@ -1399,24 +1379,21 @@
 translations 
   "fspec" <= (type) "vname \<times> qtname" 
 
-constdefs
-imethds:: "prog \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables"
+definition imethds :: "prog \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables" where
 "imethds G I 
   \<equiv> iface_rec (G,I)  
               (\<lambda>I i ts. (Un_tables ts) \<oplus>\<oplus> 
                         (Option.set \<circ> table_of (map (\<lambda>(s,m). (s,I,m)) (imethods i))))"
 text {* methods of an interface, with overriding and inheritance, cf. 9.2 *}
 
-constdefs
-accimethds:: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables"
+definition accimethds :: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables" where
 "accimethds G pack I
   \<equiv> if G\<turnstile>Iface I accessible_in pack 
        then imethds G I
        else \<lambda> k. {}"
 text {* only returns imethds if the interface is accessible *}
 
-constdefs
-methd:: "prog \<Rightarrow> qtname  \<Rightarrow> (sig,qtname \<times> methd) table"
+definition methd :: "prog \<Rightarrow> qtname  \<Rightarrow> (sig,qtname \<times> methd) table" where
 
 "methd G C 
  \<equiv> class_rec (G,C) empty
@@ -1431,8 +1408,7 @@
      Every new method with the same signature coalesces the
      method of a superclass. *}
 
-constdefs                      
-accmethd:: "prog \<Rightarrow> qtname \<Rightarrow> qtname  \<Rightarrow> (sig,qtname \<times> methd) table"
+definition accmethd :: "prog \<Rightarrow> qtname \<Rightarrow> qtname  \<Rightarrow> (sig,qtname \<times> methd) table" where
 "accmethd G S C 
  \<equiv> filter_tab (\<lambda>sig m. G\<turnstile>method sig m of C accessible_from S) 
               (methd G C)"
@@ -1446,8 +1422,7 @@
     So we must test accessibility of method @{term m} of class @{term C} 
     (not @{term "declclass m"}) *}
 
-constdefs 
-dynmethd:: "prog  \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table"
+definition dynmethd :: "prog  \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table" where
 "dynmethd G statC dynC  
   \<equiv> \<lambda> sig. 
      (if G\<turnstile>dynC \<preceq>\<^sub>C statC
@@ -1473,8 +1448,7 @@
         filters the new methods (to get only those methods which actually
         override the methods of the static class) *}
 
-constdefs 
-dynimethd:: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table"
+definition dynimethd :: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table" where
 "dynimethd G I dynC 
   \<equiv> \<lambda> sig. if imethds G I sig \<noteq> {}
                then methd G dynC sig
@@ -1493,8 +1467,7 @@
    down to the actual dynamic class.
  *}
 
-constdefs
-dynlookup::"prog  \<Rightarrow> ref_ty \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table"
+definition dynlookup :: "prog  \<Rightarrow> ref_ty \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table" where
 "dynlookup G statT dynC
   \<equiv> (case statT of
        NullT        \<Rightarrow> empty
@@ -1506,8 +1479,7 @@
     In a wellformd context statT will not be NullT and in case
     statT is an array type, dynC=Object *}
 
-constdefs
-fields:: "prog \<Rightarrow> qtname \<Rightarrow> ((vname \<times> qtname) \<times> field) list"
+definition fields :: "prog \<Rightarrow> qtname \<Rightarrow> ((vname \<times> qtname) \<times> field) list" where
 "fields G C 
   \<equiv> class_rec (G,C) [] (\<lambda>C c ts. map (\<lambda>(n,t). ((n,C),t)) (cfields c) @ ts)"
 text {* @{term "fields G C"} 
@@ -1515,8 +1487,7 @@
      (private, inherited and hidden ones) not only the accessible ones
      (an instance of a object allocates all these fields *}
 
-constdefs
-accfield:: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (vname, qtname  \<times>  field) table"
+definition accfield :: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (vname, qtname  \<times>  field) table" where
 "accfield G S C
   \<equiv> let field_tab = table_of((map (\<lambda>((n,d),f).(n,(d,f)))) (fields G C))
     in filter_tab (\<lambda>n (declC,f). G\<turnstile> (declC,fdecl (n,f)) of C accessible_from S)
@@ -1531,12 +1502,10 @@
    inheritance, too. So we must test accessibility of field @{term f} of class 
    @{term C} (not @{term "declclass f"}) *} 
 
-constdefs
-
-  is_methd :: "prog \<Rightarrow> qtname  \<Rightarrow> sig \<Rightarrow> bool"
+definition is_methd :: "prog \<Rightarrow> qtname  \<Rightarrow> sig \<Rightarrow> bool" where
  "is_methd G \<equiv> \<lambda>C sig. is_class G C \<and> methd G C sig \<noteq> None"
 
-constdefs efname:: "((vname \<times> qtname) \<times> field) \<Rightarrow> (vname \<times> qtname)"
+definition efname :: "((vname \<times> qtname) \<times> field) \<Rightarrow> (vname \<times> qtname)" where
 "efname \<equiv> fst"
 
 lemma efname_simp[simp]:"efname (n,f) = n"
@@ -2300,8 +2269,7 @@
 
 section "calculation of the superclasses of a class"
 
-constdefs 
- superclasses:: "prog \<Rightarrow> qtname \<Rightarrow> qtname set"
+definition superclasses :: "prog \<Rightarrow> qtname \<Rightarrow> qtname set" where
  "superclasses G C \<equiv> class_rec (G,C) {} 
                        (\<lambda> C c superclss. (if C=Object 
                                             then {} 
--- a/src/HOL/Bali/DefiniteAssignment.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/DefiniteAssignment.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -74,7 +74,7 @@
 "jumpNestingOkS jmps (FinA a c) = False"
 
 
-constdefs jumpNestingOk :: "jump set \<Rightarrow> term \<Rightarrow> bool"
+definition jumpNestingOk :: "jump set \<Rightarrow> term \<Rightarrow> bool" where
 "jumpNestingOk jmps t \<equiv> (case t of
                       In1 se \<Rightarrow> (case se of
                                    Inl e \<Rightarrow> True
@@ -156,7 +156,7 @@
 "assignsEs     [] = {}"
 "assignsEs (e#es) = assignsE e \<union> assignsEs es"
 
-constdefs assigns:: "term \<Rightarrow> lname set"
+definition assigns :: "term \<Rightarrow> lname set" where
 "assigns t \<equiv> (case t of
                 In1 se \<Rightarrow> (case se of
                              Inl e \<Rightarrow> assignsE e
@@ -429,20 +429,14 @@
 
 subsection {* Lifting set operations to range of tables (map to a set) *}
 
-constdefs 
- union_ts:: "('a,'b) tables \<Rightarrow> ('a,'b) tables \<Rightarrow> ('a,'b) tables"
-                    ("_ \<Rightarrow>\<union> _" [67,67] 65)
+definition union_ts :: "('a,'b) tables \<Rightarrow> ('a,'b) tables \<Rightarrow> ('a,'b) tables" ("_ \<Rightarrow>\<union> _" [67,67] 65) where
  "A \<Rightarrow>\<union> B \<equiv> \<lambda> k. A k \<union> B k"
 
-constdefs
- intersect_ts:: "('a,'b) tables \<Rightarrow> ('a,'b) tables \<Rightarrow> ('a,'b) tables"
-                    ("_ \<Rightarrow>\<inter>  _" [72,72] 71)
+definition intersect_ts :: "('a,'b) tables \<Rightarrow> ('a,'b) tables \<Rightarrow> ('a,'b) tables" ("_ \<Rightarrow>\<inter>  _" [72,72] 71) where
  "A \<Rightarrow>\<inter>  B \<equiv> \<lambda> k. A k \<inter> B k"
 
-constdefs
- all_union_ts:: "('a,'b) tables \<Rightarrow> 'b set \<Rightarrow> ('a,'b) tables" 
-                                                     (infixl "\<Rightarrow>\<union>\<^sub>\<forall>" 40)
-"A \<Rightarrow>\<union>\<^sub>\<forall> B \<equiv> \<lambda> k. A k \<union> B"
+definition all_union_ts :: "('a,'b) tables \<Rightarrow> 'b set \<Rightarrow> ('a,'b) tables" (infixl "\<Rightarrow>\<union>\<^sub>\<forall>" 40) where 
+ "A \<Rightarrow>\<union>\<^sub>\<forall> B \<equiv> \<lambda> k. A k \<union> B"
   
 subsubsection {* Binary union of tables *}
 
@@ -513,15 +507,15 @@
          brk :: "breakass" --{* Definetly assigned variables for 
                                 abrupt completion with a break *}
 
-constdefs rmlab :: "'a \<Rightarrow> ('a,'b) tables \<Rightarrow> ('a,'b) tables"
+definition rmlab :: "'a \<Rightarrow> ('a,'b) tables \<Rightarrow> ('a,'b) tables" where
 "rmlab k A \<equiv> \<lambda> x. if x=k then UNIV else A x"
  
 (*
-constdefs setbrk :: "breakass \<Rightarrow> assigned \<Rightarrow> breakass set"
+definition setbrk :: "breakass \<Rightarrow> assigned \<Rightarrow> breakass set" where
 "setbrk b A \<equiv> {b} \<union> {a| a. a\<in> brk A \<and> lab a \<noteq> lab b}"
 *)
 
-constdefs range_inter_ts :: "('a,'b) tables \<Rightarrow> 'b set" ("\<Rightarrow>\<Inter>_" 80)
+definition range_inter_ts :: "('a,'b) tables \<Rightarrow> 'b set" ("\<Rightarrow>\<Inter>_" 80) where 
  "\<Rightarrow>\<Inter>A \<equiv> {x |x. \<forall> k. x \<in> A k}"
 
 text {*
--- a/src/HOL/Bali/Eval.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/Eval.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -140,8 +140,7 @@
   lst_inj_vals  ("\<lfloor>_\<rfloor>\<^sub>l" 1000)
   where "\<lfloor>es\<rfloor>\<^sub>l == In3 es"
 
-constdefs
-  undefined3 :: "('al + 'ar, 'b, 'c) sum3 \<Rightarrow> vals"
+definition undefined3 :: "('al + 'ar, 'b, 'c) sum3 \<Rightarrow> vals" where
  "undefined3 \<equiv> sum3_case (In1 \<circ> sum_case (\<lambda>x. undefined) (\<lambda>x. Unit))
                      (\<lambda>x. In2 undefined) (\<lambda>x. In3 undefined)"
 
@@ -160,8 +159,7 @@
 
 section "exception throwing and catching"
 
-constdefs
-  throw :: "val \<Rightarrow> abopt \<Rightarrow> abopt"
+definition throw :: "val \<Rightarrow> abopt \<Rightarrow> abopt" where
  "throw a' x \<equiv> abrupt_if True (Some (Xcpt (Loc (the_Addr a')))) (np a' x)"
 
 lemma throw_def2: 
@@ -170,8 +168,7 @@
 apply (simp (no_asm))
 done
 
-constdefs
-  fits    :: "prog \<Rightarrow> st \<Rightarrow> val \<Rightarrow> ty \<Rightarrow> bool" ("_,_\<turnstile>_ fits _"[61,61,61,61]60)
+definition fits :: "prog \<Rightarrow> st \<Rightarrow> val \<Rightarrow> ty \<Rightarrow> bool" ("_,_\<turnstile>_ fits _"[61,61,61,61]60) where
  "G,s\<turnstile>a' fits T  \<equiv> (\<exists>rt. T=RefT rt) \<longrightarrow> a'=Null \<or> G\<turnstile>obj_ty(lookup_obj s a')\<preceq>T"
 
 lemma fits_Null [simp]: "G,s\<turnstile>Null fits T"
@@ -195,8 +192,7 @@
 apply iprover
 done
 
-constdefs
-  catch ::"prog \<Rightarrow> state \<Rightarrow> qtname \<Rightarrow> bool"      ("_,_\<turnstile>catch _"[61,61,61]60)
+definition catch :: "prog \<Rightarrow> state \<Rightarrow> qtname \<Rightarrow> bool" ("_,_\<turnstile>catch _"[61,61,61]60) where
  "G,s\<turnstile>catch C\<equiv>\<exists>xc. abrupt s=Some (Xcpt xc) \<and> 
                     G,store s\<turnstile>Addr (the_Loc xc) fits Class C"
 
@@ -221,8 +217,7 @@
 apply (simp (no_asm))
 done
 
-constdefs
-  new_xcpt_var :: "vname \<Rightarrow> state \<Rightarrow> state"
+definition new_xcpt_var :: "vname \<Rightarrow> state \<Rightarrow> state" where
  "new_xcpt_var vn \<equiv> 
      \<lambda>(x,s). Norm (lupd(VName vn\<mapsto>Addr (the_Loc (the_Xcpt (the x)))) s)"
 
@@ -237,9 +232,7 @@
 
 section "misc"
 
-constdefs
-
-  assign     :: "('a \<Rightarrow> state \<Rightarrow> state) \<Rightarrow> 'a \<Rightarrow> state \<Rightarrow> state"
+definition assign :: "('a \<Rightarrow> state \<Rightarrow> state) \<Rightarrow> 'a \<Rightarrow> state \<Rightarrow> state" where
  "assign f v \<equiv> \<lambda>(x,s). let (x',s') = (if x = None then f v else id) (x,s)
                    in  (x',if x' = None then s' else s)"
 
@@ -300,9 +293,7 @@
 done
 *)
 
-constdefs
-
-  init_comp_ty :: "ty \<Rightarrow> stmt"
+definition init_comp_ty :: "ty \<Rightarrow> stmt" where
  "init_comp_ty T \<equiv> if (\<exists>C. T = Class C) then Init (the_Class T) else Skip"
 
 lemma init_comp_ty_PrimT [simp]: "init_comp_ty (PrimT pt) = Skip"
@@ -310,9 +301,7 @@
 apply (simp (no_asm))
 done
 
-constdefs
-
- invocation_class  :: "inv_mode \<Rightarrow> st \<Rightarrow> val \<Rightarrow> ref_ty \<Rightarrow> qtname"
+definition invocation_class :: "inv_mode \<Rightarrow> st \<Rightarrow> val \<Rightarrow> ref_ty \<Rightarrow> qtname" where
  "invocation_class m s a' statT 
     \<equiv> (case m of
          Static \<Rightarrow> if (\<exists> statC. statT = ClassT statC) 
@@ -321,7 +310,7 @@
        | SuperM \<Rightarrow> the_Class (RefT statT)
        | IntVir \<Rightarrow> obj_class (lookup_obj s a'))"
 
-invocation_declclass::"prog \<Rightarrow> inv_mode \<Rightarrow> st \<Rightarrow> val \<Rightarrow> ref_ty \<Rightarrow> sig \<Rightarrow> qtname"
+definition invocation_declclass::"prog \<Rightarrow> inv_mode \<Rightarrow> st \<Rightarrow> val \<Rightarrow> ref_ty \<Rightarrow> sig \<Rightarrow> qtname" where
 "invocation_declclass G m s a' statT sig 
    \<equiv> declclass (the (dynlookup G statT 
                                 (invocation_class m s a' statT)
@@ -341,9 +330,8 @@
                                             else Object)"
 by (simp add: invocation_class_def)
 
-constdefs
-  init_lvars :: "prog \<Rightarrow> qtname \<Rightarrow> sig \<Rightarrow> inv_mode \<Rightarrow> val \<Rightarrow> val list \<Rightarrow>
-                   state \<Rightarrow> state"
+definition init_lvars :: "prog \<Rightarrow> qtname \<Rightarrow> sig \<Rightarrow> inv_mode \<Rightarrow> val \<Rightarrow> val list \<Rightarrow>
+                   state \<Rightarrow> state" where
  "init_lvars G C sig mode a' pvs 
    \<equiv> \<lambda> (x,s). 
       let m = mthd (the (methd G C sig));
@@ -376,8 +364,7 @@
 apply (simp (no_asm) add: Let_def)
 done
 
-constdefs
-  body :: "prog \<Rightarrow> qtname \<Rightarrow> sig \<Rightarrow> expr"
+definition body :: "prog \<Rightarrow> qtname \<Rightarrow> sig \<Rightarrow> expr" where
  "body G C sig \<equiv> let m = the (methd G C sig) 
                  in Body (declclass m) (stmt (mbody (mthd m)))"
 
@@ -390,12 +377,10 @@
 
 section "variables"
 
-constdefs
-
-  lvar :: "lname \<Rightarrow> st \<Rightarrow> vvar"
+definition lvar :: "lname \<Rightarrow> st \<Rightarrow> vvar" where
  "lvar vn s \<equiv> (the (locals s vn), \<lambda>v. supd (lupd(vn\<mapsto>v)))"
 
-  fvar :: "qtname \<Rightarrow> bool \<Rightarrow> vname \<Rightarrow> val \<Rightarrow> state \<Rightarrow> vvar \<times> state"
+definition fvar :: "qtname \<Rightarrow> bool \<Rightarrow> vname \<Rightarrow> val \<Rightarrow> state \<Rightarrow> vvar \<times> state" where
  "fvar C stat fn a' s 
     \<equiv> let (oref,xf) = if stat then (Stat C,id)
                               else (Heap (the_Addr a'),np a');
@@ -403,7 +388,7 @@
                   f = (\<lambda>v. supd (upd_gobj oref n v)) 
       in ((the (values (the (globs (store s) oref)) n),f),abupd xf s)"
 
-  avar :: "prog \<Rightarrow> val \<Rightarrow> val \<Rightarrow> state \<Rightarrow> vvar \<times> state"
+definition avar :: "prog \<Rightarrow> val \<Rightarrow> val \<Rightarrow> state \<Rightarrow> vvar \<times> state" where
  "avar G i' a' s 
     \<equiv> let   oref = Heap (the_Addr a'); 
                i = the_Intg i'; 
@@ -446,9 +431,7 @@
 apply (simp (no_asm) add: Let_def split_beta)
 done
 
-constdefs
-check_field_access::
-"prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> vname \<Rightarrow> bool \<Rightarrow> val \<Rightarrow> state \<Rightarrow> state"
+definition check_field_access :: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> vname \<Rightarrow> bool \<Rightarrow> val \<Rightarrow> state \<Rightarrow> state" where
 "check_field_access G accC statDeclC fn stat a' s
  \<equiv> let oref = if stat then Stat statDeclC
                       else Heap (the_Addr a');
@@ -461,9 +444,7 @@
                   AccessViolation)
         s"
 
-constdefs
-check_method_access:: 
-  "prog \<Rightarrow> qtname \<Rightarrow> ref_ty \<Rightarrow> inv_mode \<Rightarrow>  sig \<Rightarrow> val \<Rightarrow> state \<Rightarrow> state"
+definition check_method_access :: "prog \<Rightarrow> qtname \<Rightarrow> ref_ty \<Rightarrow> inv_mode \<Rightarrow>  sig \<Rightarrow> val \<Rightarrow> state \<Rightarrow> state" where
 "check_method_access G accC statT mode sig  a' s
  \<equiv> let invC = invocation_class mode (store s) a' statT;
        dynM = the (dynlookup G statT invC sig)
--- a/src/HOL/Bali/Example.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/Example.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -153,23 +153,18 @@
   
   foo    :: mname
 
-constdefs
-  
-  foo_sig   :: sig
- "foo_sig   \<equiv> \<lparr>name=foo,parTs=[Class Base]\<rparr>"
+definition foo_sig :: sig
+ where "foo_sig   \<equiv> \<lparr>name=foo,parTs=[Class Base]\<rparr>"
   
-  foo_mhead :: mhead
- "foo_mhead \<equiv> \<lparr>access=Public,static=False,pars=[z],resT=Class Base\<rparr>"
+definition foo_mhead :: mhead
+ where "foo_mhead \<equiv> \<lparr>access=Public,static=False,pars=[z],resT=Class Base\<rparr>"
 
-constdefs
-  
-  Base_foo :: mdecl
- "Base_foo \<equiv> (foo_sig, \<lparr>access=Public,static=False,pars=[z],resT=Class Base,
+definition Base_foo :: mdecl
+ where "Base_foo \<equiv> (foo_sig, \<lparr>access=Public,static=False,pars=[z],resT=Class Base,
                         mbody=\<lparr>lcls=[],stmt=Return (!!z)\<rparr>\<rparr>)"
 
-constdefs
-  Ext_foo  :: mdecl
- "Ext_foo  \<equiv> (foo_sig, 
+definition Ext_foo :: mdecl
+ where "Ext_foo  \<equiv> (foo_sig, 
               \<lparr>access=Public,static=False,pars=[z],resT=Class Ext,
                mbody=\<lparr>lcls=[]
                      ,stmt=Expr({Ext,Ext,False}Cast (Class Ext) (!!z)..vee := 
@@ -177,12 +172,10 @@
                                 Return (Lit Null)\<rparr>
               \<rparr>)"
 
-constdefs
-  
-arr_viewed_from :: "qtname \<Rightarrow> qtname \<Rightarrow> var"
+definition arr_viewed_from :: "qtname \<Rightarrow> qtname \<Rightarrow> var" where
 "arr_viewed_from accC C \<equiv> {accC,Base,True}StatRef (ClassT C)..arr"
 
-BaseCl :: "class"
+definition BaseCl :: "class" where
 "BaseCl \<equiv> \<lparr>access=Public,
            cfields=[(arr, \<lparr>access=Public,static=True ,type=PrimT Boolean.[]\<rparr>),
                     (vee, \<lparr>access=Public,static=False,type=Iface HasFoo    \<rparr>)],
@@ -192,7 +185,7 @@
            super=Object,
            superIfs=[HasFoo]\<rparr>"
   
-ExtCl  :: "class"
+definition ExtCl  :: "class" where
 "ExtCl  \<equiv> \<lparr>access=Public,
            cfields=[(vee, \<lparr>access=Public,static=False,type= PrimT Integer\<rparr>)], 
            methods=[Ext_foo],
@@ -200,7 +193,7 @@
            super=Base,
            superIfs=[]\<rparr>"
 
-MainCl :: "class"
+definition MainCl :: "class" where
 "MainCl \<equiv> \<lparr>access=Public,
            cfields=[], 
            methods=[], 
@@ -209,16 +202,14 @@
            superIfs=[]\<rparr>"
 (* The "main" method is modeled seperately (see tprg) *)
 
-constdefs
-  
-  HasFooInt :: iface
- "HasFooInt \<equiv> \<lparr>access=Public,imethods=[(foo_sig, foo_mhead)],isuperIfs=[]\<rparr>"
+definition HasFooInt :: iface
+ where "HasFooInt \<equiv> \<lparr>access=Public,imethods=[(foo_sig, foo_mhead)],isuperIfs=[]\<rparr>"
 
-  Ifaces ::"idecl list"
- "Ifaces \<equiv> [(HasFoo,HasFooInt)]"
+definition Ifaces ::"idecl list"
+ where "Ifaces \<equiv> [(HasFoo,HasFooInt)]"
 
- "Classes" ::"cdecl list"
- "Classes \<equiv> [(Base,BaseCl),(Ext,ExtCl),(Main,MainCl)]@standard_classes"
+definition "Classes" ::"cdecl list"
+ where "Classes \<equiv> [(Base,BaseCl),(Ext,ExtCl),(Main,MainCl)]@standard_classes"
 
 lemmas table_classes_defs = 
      Classes_def standard_classes_def ObjectC_def SXcptC_def
@@ -273,8 +264,7 @@
   tprg :: prog where
   "tprg == \<lparr>ifaces=Ifaces,classes=Classes\<rparr>"
 
-constdefs
-  test    :: "(ty)list \<Rightarrow> stmt"
+definition test :: "(ty)list \<Rightarrow> stmt" where
  "test pTs \<equiv> e:==NewC Ext;; 
            \<spacespace> Try Expr({Main,ClassT Base,IntVir}!!e\<cdot>foo({pTs}[Lit Null]))
            \<spacespace> Catch((SXcpt NullPointer) z)
--- a/src/HOL/Bali/State.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/State.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -38,9 +38,7 @@
   "obj"   <= (type) "\<lparr>tag::obj_tag, values::vn \<Rightarrow> val option\<rparr>"
   "obj"   <= (type) "\<lparr>tag::obj_tag, values::vn \<Rightarrow> val option,\<dots>::'a\<rparr>"
 
-constdefs
-  
-  the_Arr :: "obj option \<Rightarrow> ty \<times> int \<times> (vn, val) table"
+definition the_Arr :: "obj option \<Rightarrow> ty \<times> int \<times> (vn, val) table" where
  "the_Arr obj \<equiv> SOME (T,k,t). obj = Some \<lparr>tag=Arr T k,values=t\<rparr>"
 
 lemma the_Arr_Arr [simp]: "the_Arr (Some \<lparr>tag=Arr T k,values=cs\<rparr>) = (T,k,cs)"
@@ -52,9 +50,7 @@
 apply (auto simp add: the_Arr_def)
 done
 
-constdefs
-
-  upd_obj       :: "vn \<Rightarrow> val \<Rightarrow> obj \<Rightarrow> obj" 
+definition upd_obj :: "vn \<Rightarrow> val \<Rightarrow> obj \<Rightarrow> obj" where 
  "upd_obj n v \<equiv> \<lambda> obj . obj \<lparr>values:=(values obj)(n\<mapsto>v)\<rparr>"
 
 lemma upd_obj_def2 [simp]: 
@@ -62,8 +58,7 @@
 apply (auto simp: upd_obj_def)
 done
 
-constdefs
-  obj_ty        :: "obj \<Rightarrow> ty"
+definition obj_ty :: "obj \<Rightarrow> ty" where
  "obj_ty obj    \<equiv> case tag obj of 
                     CInst C \<Rightarrow> Class C 
                   | Arr T k \<Rightarrow> T.[]"
@@ -102,9 +97,7 @@
 apply (auto split add: obj_tag.split_asm)
 done
 
-constdefs
-
-  obj_class :: "obj \<Rightarrow> qtname"
+definition obj_class :: "obj \<Rightarrow> qtname" where
  "obj_class obj \<equiv> case tag obj of 
                     CInst C \<Rightarrow> C 
                   | Arr T k \<Rightarrow> Object"
@@ -143,9 +136,7 @@
   "Stat" => "CONST Inr"
   "oref" <= (type) "loc + qtname"
 
-constdefs
-  fields_table::
-    "prog \<Rightarrow> qtname \<Rightarrow> (fspec \<Rightarrow> field \<Rightarrow> bool)  \<Rightarrow> (fspec, ty) table"
+definition fields_table :: "prog \<Rightarrow> qtname \<Rightarrow> (fspec \<Rightarrow> field \<Rightarrow> bool)  \<Rightarrow> (fspec, ty) table" where
  "fields_table G C P 
     \<equiv> Option.map type \<circ> table_of (filter (split P) (DeclConcepts.fields G C))"
 
@@ -182,14 +173,13 @@
 apply simp
 done
 
-constdefs
-  in_bounds :: "int \<Rightarrow> int \<Rightarrow> bool"            ("(_/ in'_bounds _)" [50, 51] 50)
+definition in_bounds :: "int \<Rightarrow> int \<Rightarrow> bool" ("(_/ in'_bounds _)" [50, 51] 50) where
  "i in_bounds k \<equiv> 0 \<le> i \<and> i < k"
 
-  arr_comps :: "'a \<Rightarrow> int \<Rightarrow> int \<Rightarrow> 'a option"
+definition arr_comps :: "'a \<Rightarrow> int \<Rightarrow> int \<Rightarrow> 'a option" where
  "arr_comps T k \<equiv> \<lambda>i. if i in_bounds k then Some T else None"
   
-  var_tys       :: "prog \<Rightarrow> obj_tag \<Rightarrow> oref \<Rightarrow> (vn, ty) table"
+definition var_tys       :: "prog \<Rightarrow> obj_tag \<Rightarrow> oref \<Rightarrow> (vn, ty) table" where
 "var_tys G oi r 
   \<equiv> case r of 
       Heap a \<Rightarrow> (case oi of 
@@ -232,15 +222,13 @@
 
 subsection "access"
 
-constdefs
-
-  globs  :: "st \<Rightarrow> globs"
+definition globs :: "st \<Rightarrow> globs" where
  "globs  \<equiv> st_case (\<lambda>g l. g)"
   
-  locals :: "st \<Rightarrow> locals"
+definition locals :: "st \<Rightarrow> locals" where
  "locals \<equiv> st_case (\<lambda>g l. l)"
 
-  heap   :: "st \<Rightarrow> heap"
+definition heap   :: "st \<Rightarrow> heap" where
  "heap s \<equiv> globs s \<circ> Heap"
 
 
@@ -262,8 +250,7 @@
 
 subsection "memory allocation"
 
-constdefs
-  new_Addr     :: "heap \<Rightarrow> loc option"
+definition new_Addr :: "heap \<Rightarrow> loc option" where
  "new_Addr h   \<equiv> if (\<forall>a. h a \<noteq> None) then None else Some (SOME a. h a = None)"
 
 lemma new_AddrD: "new_Addr h = Some a \<Longrightarrow> h a = None"
@@ -303,20 +290,19 @@
 
 subsection "update"
 
-constdefs
-  gupd       :: "oref  \<Rightarrow> obj \<Rightarrow> st \<Rightarrow> st"        ("gupd'(_\<mapsto>_')"[10,10]1000)
+definition gupd :: "oref  \<Rightarrow> obj \<Rightarrow> st \<Rightarrow> st" ("gupd'(_\<mapsto>_')"[10,10]1000) where
  "gupd r obj  \<equiv> st_case (\<lambda>g l. st (g(r\<mapsto>obj)) l)"
 
-  lupd       :: "lname \<Rightarrow> val \<Rightarrow> st \<Rightarrow> st"        ("lupd'(_\<mapsto>_')"[10,10]1000)
+definition lupd       :: "lname \<Rightarrow> val \<Rightarrow> st \<Rightarrow> st" ("lupd'(_\<mapsto>_')"[10,10]1000) where
  "lupd vn v   \<equiv> st_case (\<lambda>g l. st g (l(vn\<mapsto>v)))"
 
-  upd_gobj   :: "oref \<Rightarrow> vn \<Rightarrow> val \<Rightarrow> st \<Rightarrow> st"
+definition upd_gobj   :: "oref \<Rightarrow> vn \<Rightarrow> val \<Rightarrow> st \<Rightarrow> st" where
  "upd_gobj r n v \<equiv> st_case (\<lambda>g l. st (chg_map (upd_obj n v) r g) l)"
 
-  set_locals  :: "locals \<Rightarrow> st \<Rightarrow> st"
+definition set_locals  :: "locals \<Rightarrow> st \<Rightarrow> st" where
  "set_locals l \<equiv> st_case (\<lambda>g l'. st g l)"
 
-  init_obj    :: "prog \<Rightarrow> obj_tag \<Rightarrow> oref \<Rightarrow> st \<Rightarrow> st"
+definition init_obj    :: "prog \<Rightarrow> obj_tag \<Rightarrow> oref \<Rightarrow> st \<Rightarrow> st" where
  "init_obj G oi r \<equiv> gupd(r\<mapsto>\<lparr>tag=oi, values=init_vals (var_tys G oi r)\<rparr>)"
 
 abbreviation
@@ -476,8 +462,7 @@
 
         
 
-constdefs
-  abrupt_if    :: "bool \<Rightarrow> abopt \<Rightarrow> abopt \<Rightarrow> abopt"
+definition abrupt_if :: "bool \<Rightarrow> abopt \<Rightarrow> abopt \<Rightarrow> abopt" where
  "abrupt_if c x' x \<equiv> if c \<and> (x = None) then x' else x"
 
 lemma abrupt_if_True_None [simp]: "abrupt_if True x None = x"
@@ -557,8 +542,7 @@
 apply auto
 done
 
-constdefs
-   absorb :: "jump \<Rightarrow> abopt \<Rightarrow> abopt"
+definition absorb :: "jump \<Rightarrow> abopt \<Rightarrow> abopt" where
   "absorb j a \<equiv> if a=Some (Jump j) then None else a"
 
 lemma absorb_SomeD [dest!]: "absorb j a = Some x \<Longrightarrow> a = Some x"
@@ -611,9 +595,7 @@
 apply clarsimp
 done
 
-constdefs
-
-  normal     :: "state \<Rightarrow> bool"
+definition normal :: "state \<Rightarrow> bool" where
  "normal \<equiv> \<lambda>s. abrupt s = None"
 
 lemma normal_def2 [simp]: "normal s = (abrupt s = None)"
@@ -621,8 +603,7 @@
 apply (simp (no_asm))
 done
 
-constdefs
-  heap_free :: "nat \<Rightarrow> state \<Rightarrow> bool"
+definition heap_free :: "nat \<Rightarrow> state \<Rightarrow> bool" where
  "heap_free n \<equiv> \<lambda>s. atleast_free (heap (store s)) n"
 
 lemma heap_free_def2 [simp]: "heap_free n s = atleast_free (heap (store s)) n"
@@ -632,12 +613,10 @@
 
 subsection "update"
 
-constdefs
- 
-  abupd     :: "(abopt \<Rightarrow> abopt) \<Rightarrow> state \<Rightarrow> state"
+definition abupd :: "(abopt \<Rightarrow> abopt) \<Rightarrow> state \<Rightarrow> state" where
  "abupd f \<equiv> prod_fun f id"
 
-  supd     :: "(st \<Rightarrow> st) \<Rightarrow> state \<Rightarrow> state" 
+definition supd     :: "(st \<Rightarrow> st) \<Rightarrow> state \<Rightarrow> state" where
  "supd \<equiv> prod_fun id"
   
 lemma abupd_def2 [simp]: "abupd f (x,s) = (f x,s)"
@@ -692,12 +671,10 @@
 
 section "initialisation test"
 
-constdefs
-
-  inited   :: "qtname \<Rightarrow> globs \<Rightarrow> bool"
+definition inited :: "qtname \<Rightarrow> globs \<Rightarrow> bool" where
  "inited C g \<equiv> g (Stat C) \<noteq> None"
 
-  initd    :: "qtname \<Rightarrow> state \<Rightarrow> bool"
+definition initd    :: "qtname \<Rightarrow> state \<Rightarrow> bool" where
  "initd C \<equiv> inited C \<circ> globs \<circ> store"
 
 lemma not_inited_empty [simp]: "\<not>inited C empty"
@@ -731,7 +708,7 @@
 done
 
 section {* @{text error_free} *}
-constdefs error_free:: "state \<Rightarrow> bool"
+definition error_free :: "state \<Rightarrow> bool" where
 "error_free s \<equiv> \<not> (\<exists> err. abrupt s = Some (Error err))"
 
 lemma error_free_Norm [simp,intro]: "error_free (Norm s)"
--- a/src/HOL/Bali/Table.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/Table.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -53,9 +53,7 @@
 by (simp add: map_add_def)
 
 section {* Conditional Override *}
-constdefs
-cond_override:: 
-  "('b \<Rightarrow>'b \<Rightarrow> bool) \<Rightarrow> ('a, 'b)table \<Rightarrow> ('a, 'b)table \<Rightarrow> ('a, 'b) table"
+definition cond_override :: "('b \<Rightarrow>'b \<Rightarrow> bool) \<Rightarrow> ('a, 'b)table \<Rightarrow> ('a, 'b)table \<Rightarrow> ('a, 'b) table" where
 
 --{* when merging tables old and new, only override an entry of table old when  
    the condition cond holds *}
@@ -100,8 +98,7 @@
 
 section {* Filter on Tables *}
 
-constdefs
-filter_tab:: "('a \<Rightarrow> 'b \<Rightarrow> bool) \<Rightarrow> ('a, 'b) table \<Rightarrow> ('a, 'b) table"
+definition filter_tab :: "('a \<Rightarrow> 'b \<Rightarrow> bool) \<Rightarrow> ('a, 'b) table \<Rightarrow> ('a, 'b) table" where
 "filter_tab c t \<equiv> \<lambda> k. (case t k of 
                            None   \<Rightarrow> None
                          | Some x \<Rightarrow> if c k x then Some x else None)"
--- a/src/HOL/Bali/Term.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/Term.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -261,9 +261,7 @@
   StatRef :: "ref_ty \<Rightarrow> expr"
   where "StatRef rt == Cast (RefT rt) (Lit Null)"
   
-constdefs
-
-  is_stmt :: "term \<Rightarrow> bool"
+definition is_stmt :: "term \<Rightarrow> bool" where
  "is_stmt t \<equiv> \<exists>c. t=In1r c"
 
 ML {* bind_thms ("is_stmt_rews", sum3_instantiate @{context} @{thm is_stmt_def}) *}
@@ -467,7 +465,7 @@
 "eval_binop CondAnd v1 v2 = Bool ((the_Bool v1) \<and> (the_Bool v2))"
 "eval_binop CondOr  v1 v2 = Bool ((the_Bool v1) \<or> (the_Bool v2))"
 
-constdefs need_second_arg :: "binop \<Rightarrow> val \<Rightarrow> bool"
+definition need_second_arg :: "binop \<Rightarrow> val \<Rightarrow> bool" where
 "need_second_arg binop v1 \<equiv> \<not> ((binop=CondAnd \<and>  \<not> the_Bool v1) \<or>
                                (binop=CondOr  \<and> the_Bool v1))"
 text {* @{term CondAnd} and @{term CondOr} only evalulate the second argument
--- a/src/HOL/Bali/Trans.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/Trans.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -9,7 +9,7 @@
 
 theory Trans imports Evaln begin
 
-constdefs groundVar:: "var \<Rightarrow> bool"
+definition groundVar :: "var \<Rightarrow> bool" where
 "groundVar v \<equiv> (case v of
                    LVar ln \<Rightarrow> True
                  | {accC,statDeclC,stat}e..fn \<Rightarrow> \<exists> a. e=Lit a
@@ -34,7 +34,7 @@
     done
 qed
 
-constdefs groundExprs:: "expr list \<Rightarrow> bool"
+definition groundExprs :: "expr list \<Rightarrow> bool" where
 "groundExprs es \<equiv> list_all (\<lambda> e. \<exists> v. e=Lit v) es"
   
 consts the_val:: "expr \<Rightarrow> val"
--- a/src/HOL/Bali/Type.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/Type.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -41,8 +41,7 @@
 abbreviation Array :: "ty \<Rightarrow> ty"  ("_.[]" [90] 90)
   where "T.[] == RefT (ArrayT T)"
 
-constdefs
-  the_Class :: "ty \<Rightarrow> qtname"
+definition the_Class :: "ty \<Rightarrow> qtname" where
  "the_Class T \<equiv> SOME C. T = Class C" (** primrec not possible here **)
  
 lemma the_Class_eq [simp]: "the_Class (Class C)= C"
--- a/src/HOL/Bali/TypeRel.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/TypeRel.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -65,7 +65,7 @@
 done
 
 lemma subcls1I1:
- "\<lbrakk>class G C = Some c; C \<noteq> Object;D=super c\<rbrakk> \<Longrightarrow> G\<turnstile>C\<prec>\<^sub>C\<^sub>1 D"
+ "\<lbrakk>class G C = Some c; C \<noteq> Object;D=super c\<rbrakk> \<Longrightarrow> G\<turnstile>C\<prec>\<^sub>C1 D"
 apply (auto dest: subcls1I)
 done
 
@@ -126,7 +126,7 @@
 done
 
 lemma single_inheritance: 
-"\<lbrakk>G\<turnstile>A \<prec>\<^sub>C\<^sub>1 B; G\<turnstile>A \<prec>\<^sub>C\<^sub>1 C\<rbrakk> \<Longrightarrow> B = C"
+"\<lbrakk>G\<turnstile>A \<prec>\<^sub>C1 B; G\<turnstile>A \<prec>\<^sub>C1 C\<rbrakk> \<Longrightarrow> B = C"
 by (auto simp add: subcls1_def)
   
 lemma subcls_compareable:
@@ -134,11 +134,11 @@
  \<rbrakk> \<Longrightarrow> G\<turnstile>X \<preceq>\<^sub>C Y \<or> G\<turnstile>Y \<preceq>\<^sub>C X"
 by (rule triangle_lemma)  (auto intro: single_inheritance) 
 
-lemma subcls1_irrefl: "\<lbrakk>G\<turnstile>C \<prec>\<^sub>C\<^sub>1 D; ws_prog G \<rbrakk>
+lemma subcls1_irrefl: "\<lbrakk>G\<turnstile>C \<prec>\<^sub>C1 D; ws_prog G \<rbrakk>
  \<Longrightarrow> C \<noteq> D"
 proof 
   assume ws: "ws_prog G" and
-    subcls1: "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 D" and
+    subcls1: "G\<turnstile>C \<prec>\<^sub>C1 D" and
      eq_C_D: "C=D"
   from subcls1 obtain c 
     where
@@ -167,7 +167,7 @@
   then show ?thesis
   proof (induct rule: converse_trancl_induct)
     fix C
-    assume subcls1_C_D: "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 D"
+    assume subcls1_C_D: "G\<turnstile>C \<prec>\<^sub>C1 D"
     then obtain c  where
         "C\<noteq>Object" and
         "class G C = Some c" and
@@ -178,7 +178,7 @@
       by (auto dest: ws_prog_cdeclD)
   next
     fix C Z
-    assume subcls1_C_Z: "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 Z" and
+    assume subcls1_C_Z: "G\<turnstile>C \<prec>\<^sub>C1 Z" and
             subcls_Z_D: "G\<turnstile>Z \<prec>\<^sub>C D" and
            nsubcls_D_Z: "\<not> G\<turnstile>D \<prec>\<^sub>C Z"
     show "\<not> G\<turnstile>D \<prec>\<^sub>C C"
@@ -213,13 +213,13 @@
   then show ?thesis
   proof (induct rule: converse_trancl_induct)
     fix C
-    assume "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 D"
+    assume "G\<turnstile>C \<prec>\<^sub>C1 D"
     with ws 
     show "C\<noteq>D" 
       by (blast dest: subcls1_irrefl)
   next
     fix C Z
-    assume subcls1_C_Z: "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 Z" and
+    assume subcls1_C_Z: "G\<turnstile>C \<prec>\<^sub>C1 Z" and
             subcls_Z_D: "G\<turnstile>Z \<prec>\<^sub>C D" and
                neq_Z_D: "Z \<noteq> D"
     show "C\<noteq>D"
@@ -298,7 +298,7 @@
   assume       clsC: "class G C = Some c"
   assume subcls_C_C: "G\<turnstile>C \<prec>\<^sub>C D"
   then obtain S where 
-                  "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 S" and
+                  "G\<turnstile>C \<prec>\<^sub>C1 S" and
     subclseq_S_D: "G\<turnstile>S \<preceq>\<^sub>C D"
     by (blast dest: tranclD)
   with clsC 
@@ -341,9 +341,9 @@
 where
   direct:         "G\<turnstile>C\<leadsto>1J     \<spacespace>\<spacespace>     \<Longrightarrow> G\<turnstile>C\<leadsto>J"
 | subint:        "\<lbrakk>G\<turnstile>C\<leadsto>1I; G\<turnstile>I\<preceq>I J\<rbrakk>  \<Longrightarrow> G\<turnstile>C\<leadsto>J"
-| subcls1:       "\<lbrakk>G\<turnstile>C\<prec>\<^sub>C\<^sub>1D; G\<turnstile>D\<leadsto>J \<rbrakk>  \<Longrightarrow> G\<turnstile>C\<leadsto>J"
+| subcls1:       "\<lbrakk>G\<turnstile>C\<prec>\<^sub>C1D; G\<turnstile>D\<leadsto>J \<rbrakk>  \<Longrightarrow> G\<turnstile>C\<leadsto>J"
 
-lemma implmtD: "G\<turnstile>C\<leadsto>J \<Longrightarrow> (\<exists>I. G\<turnstile>C\<leadsto>1I \<and> G\<turnstile>I\<preceq>I J) \<or> (\<exists>D. G\<turnstile>C\<prec>\<^sub>C\<^sub>1D \<and> G\<turnstile>D\<leadsto>J)" 
+lemma implmtD: "G\<turnstile>C\<leadsto>J \<Longrightarrow> (\<exists>I. G\<turnstile>C\<leadsto>1I \<and> G\<turnstile>I\<preceq>I J) \<or> (\<exists>D. G\<turnstile>C\<prec>\<^sub>C1D \<and> G\<turnstile>D\<leadsto>J)" 
 apply (erule implmt.induct)
 apply fast+
 done
@@ -568,8 +568,7 @@
 apply (fast dest: widen_Class_Class widen_Class_Iface)
 done
 
-constdefs
-  widens :: "prog \<Rightarrow> [ty list, ty list] \<Rightarrow> bool" ("_\<turnstile>_[\<preceq>]_" [71,71,71] 70)
+definition widens :: "prog \<Rightarrow> [ty list, ty list] \<Rightarrow> bool" ("_\<turnstile>_[\<preceq>]_" [71,71,71] 70) where
  "G\<turnstile>Ts[\<preceq>]Ts' \<equiv> list_all2 (\<lambda>T T'. G\<turnstile>T\<preceq>T') Ts Ts'"
 
 lemma widens_Nil [simp]: "G\<turnstile>[][\<preceq>][]"
--- a/src/HOL/Bali/TypeSafe.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/TypeSafe.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -95,17 +95,13 @@
 
 section "result conformance"
 
-constdefs
-  assign_conforms :: "st \<Rightarrow> (val \<Rightarrow> state \<Rightarrow> state) \<Rightarrow> ty \<Rightarrow> env' \<Rightarrow> bool"
-          ("_\<le>|_\<preceq>_\<Colon>\<preceq>_"                                        [71,71,71,71] 70)
+definition assign_conforms :: "st \<Rightarrow> (val \<Rightarrow> state \<Rightarrow> state) \<Rightarrow> ty \<Rightarrow> env' \<Rightarrow> bool" ("_\<le>|_\<preceq>_\<Colon>\<preceq>_" [71,71,71,71] 70) where
 "s\<le>|f\<preceq>T\<Colon>\<preceq>E \<equiv>
  (\<forall>s' w. Norm s'\<Colon>\<preceq>E \<longrightarrow> fst E,s'\<turnstile>w\<Colon>\<preceq>T \<longrightarrow> s\<le>|s' \<longrightarrow> assign f w (Norm s')\<Colon>\<preceq>E) \<and>
  (\<forall>s' w. error_free s' \<longrightarrow> (error_free (assign f w s')))"      
 
 
-constdefs
-  rconf :: "prog \<Rightarrow> lenv \<Rightarrow> st \<Rightarrow> term \<Rightarrow> vals \<Rightarrow> tys \<Rightarrow> bool"
-          ("_,_,_\<turnstile>_\<succ>_\<Colon>\<preceq>_"                               [71,71,71,71,71,71] 70)
+definition rconf :: "prog \<Rightarrow> lenv \<Rightarrow> st \<Rightarrow> term \<Rightarrow> vals \<Rightarrow> tys \<Rightarrow> bool" ("_,_,_\<turnstile>_\<succ>_\<Colon>\<preceq>_" [71,71,71,71,71,71] 70) where
   "G,L,s\<turnstile>t\<succ>v\<Colon>\<preceq>T 
     \<equiv> case T of
         Inl T  \<Rightarrow> if (\<exists> var. t=In2 var)
@@ -330,11 +326,8 @@
 
 declare fun_upd_apply [simp del]
 
-
-constdefs
-  DynT_prop::"[prog,inv_mode,qtname,ref_ty] \<Rightarrow> bool" 
-                                              ("_\<turnstile>_\<rightarrow>_\<preceq>_"[71,71,71,71]70)
- "G\<turnstile>mode\<rightarrow>D\<preceq>t \<equiv> mode = IntVir \<longrightarrow> is_class G D \<and> 
+definition DynT_prop :: "[prog,inv_mode,qtname,ref_ty] \<Rightarrow> bool" ("_\<turnstile>_\<rightarrow>_\<preceq>_"[71,71,71,71]70) where
+  "G\<turnstile>mode\<rightarrow>D\<preceq>t \<equiv> mode = IntVir \<longrightarrow> is_class G D \<and> 
                      (if (\<exists>T. t=ArrayT T) then D=Object else G\<turnstile>Class D\<preceq>RefT t)"
 
 lemma DynT_propI: 
--- a/src/HOL/Bali/WellForm.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/WellForm.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -31,8 +31,7 @@
 text  {* well-formed field declaration (common part for classes and interfaces),
         cf. 8.3 and (9.3) *}
 
-constdefs
-  wf_fdecl :: "prog \<Rightarrow> pname \<Rightarrow> fdecl \<Rightarrow> bool"
+definition wf_fdecl :: "prog \<Rightarrow> pname \<Rightarrow> fdecl \<Rightarrow> bool" where
  "wf_fdecl G P \<equiv> \<lambda>(fn,f). is_acc_type G P (type f)"
 
 lemma wf_fdecl_def2: "\<And>fd. wf_fdecl G P fd = is_acc_type G P (type (snd fd))"
@@ -55,8 +54,7 @@
 \item the parameter names are unique
 \end{itemize} 
 *}
-constdefs
-  wf_mhead :: "prog \<Rightarrow> pname \<Rightarrow> sig \<Rightarrow> mhead \<Rightarrow> bool"
+definition wf_mhead :: "prog \<Rightarrow> pname \<Rightarrow> sig \<Rightarrow> mhead \<Rightarrow> bool" where
  "wf_mhead G P \<equiv> \<lambda> sig mh. length (parTs sig) = length (pars mh) \<and>
                             \<spacespace> ( \<forall>T\<in>set (parTs sig). is_acc_type G P T) \<and> 
                             is_acc_type G P (resTy mh) \<and>
@@ -78,7 +76,7 @@
 \end{itemize}
 *}
 
-constdefs callee_lcl:: "qtname \<Rightarrow> sig \<Rightarrow> methd \<Rightarrow> lenv"
+definition callee_lcl :: "qtname \<Rightarrow> sig \<Rightarrow> methd \<Rightarrow> lenv" where
 "callee_lcl C sig m 
  \<equiv> \<lambda> k. (case k of
             EName e 
@@ -88,12 +86,11 @@
                 | Res \<Rightarrow> Some (resTy m))
           | This \<Rightarrow> if is_static m then None else Some (Class C))"
 
-constdefs parameters :: "methd \<Rightarrow> lname set"
+definition parameters :: "methd \<Rightarrow> lname set" where
 "parameters m \<equiv>  set (map (EName \<circ> VNam) (pars m)) 
                   \<union> (if (static m) then {} else {This})"
 
-constdefs
-  wf_mdecl :: "prog \<Rightarrow> qtname \<Rightarrow> mdecl \<Rightarrow> bool"
+definition wf_mdecl :: "prog \<Rightarrow> qtname \<Rightarrow> mdecl \<Rightarrow> bool" where
  "wf_mdecl G C \<equiv> 
       \<lambda>(sig,m).
           wf_mhead G (pid C) sig (mhead m) \<and> 
@@ -219,8 +216,7 @@
       superinterfaces widens to each of the corresponding result types
 \end{itemize}
 *}
-constdefs
-  wf_idecl :: "prog  \<Rightarrow> idecl \<Rightarrow> bool"
+definition wf_idecl :: "prog  \<Rightarrow> idecl \<Rightarrow> bool" where
  "wf_idecl G \<equiv> 
     \<lambda>(I,i). 
         ws_idecl G I (isuperIfs i) \<and> 
@@ -321,8 +317,7 @@
 \end{itemize}
 *}
 (* to Table *)
-constdefs entails:: "('a,'b) table \<Rightarrow> ('b \<Rightarrow> bool) \<Rightarrow> bool"
-                                 ("_ entails _" 20)
+definition entails :: "('a,'b) table \<Rightarrow> ('b \<Rightarrow> bool) \<Rightarrow> bool" ("_ entails _" 20) where
 "t entails P \<equiv> \<forall>k. \<forall> x \<in> t k: P x"
 
 lemma entailsD:
@@ -332,8 +327,7 @@
 lemma empty_entails[simp]: "empty entails P"
 by (simp add: entails_def)
 
-constdefs
- wf_cdecl :: "prog \<Rightarrow> cdecl \<Rightarrow> bool"
+definition wf_cdecl :: "prog \<Rightarrow> cdecl \<Rightarrow> bool" where
 "wf_cdecl G \<equiv> 
    \<lambda>(C,c).
       \<not>is_iface G C \<and>
@@ -361,8 +355,7 @@
             ))"
 
 (*
-constdefs
- wf_cdecl :: "prog \<Rightarrow> cdecl \<Rightarrow> bool"
+definition wf_cdecl :: "prog \<Rightarrow> cdecl \<Rightarrow> bool" where
 "wf_cdecl G \<equiv> 
    \<lambda>(C,c).
       \<not>is_iface G C \<and>
@@ -518,8 +511,7 @@
 \item all defined classes are wellformed
 \end{itemize}
 *}
-constdefs
-  wf_prog  :: "prog \<Rightarrow> bool"
+definition wf_prog :: "prog \<Rightarrow> bool" where
  "wf_prog G \<equiv> let is = ifaces G; cs = classes G in
                  ObjectC \<in> set cs \<and> 
                 (\<forall> m\<in>set Object_mdecls. accmodi m \<noteq> Package) \<and>
@@ -919,7 +911,7 @@
      inheritable: "G \<turnstile>Method old inheritable_in pid C" and
          subclsC: "G\<turnstile>C\<prec>\<^sub>C declclass old"
     from cls_C neq_C_Obj  
-    have super: "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 super c" 
+    have super: "G\<turnstile>C \<prec>\<^sub>C1 super c" 
       by (rule subcls1I)
     from wf cls_C neq_C_Obj
     have accessible_super: "G\<turnstile>(Class (super c)) accessible_in (pid C)" 
@@ -1385,7 +1377,7 @@
       moreover note wf False cls_C  
       ultimately have "G\<turnstile>super c \<preceq>\<^sub>C declclass m"  
         by (auto intro: Hyp [rule_format])
-      moreover from cls_C False have  "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 super c" by (rule subcls1I)
+      moreover from cls_C False have  "G\<turnstile>C \<prec>\<^sub>C1 super c" by (rule subcls1I)
       ultimately show ?thesis by - (rule rtrancl_into_rtrancl2)
     next
       case Some
@@ -1539,7 +1531,7 @@
     by (auto intro: method_declared_inI)
   note trancl_rtrancl_tranc = trancl_rtrancl_trancl [trans] (* ### in Basis *)
   from clsC neq_C_Obj
-  have subcls1_C_super: "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 super c"
+  have subcls1_C_super: "G\<turnstile>C \<prec>\<^sub>C1 super c"
     by (rule subcls1I)
   then have "G\<turnstile>C \<prec>\<^sub>C super c" ..
   also from old wf is_cls_super
@@ -1609,7 +1601,7 @@
       by (auto dest: ws_prog_cdeclD)
     from clsC wf neq_C_Obj 
     have superAccessible: "G\<turnstile>(Class (super c)) accessible_in (pid C)" and
-         subcls1_C_super: "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 super c"
+         subcls1_C_super: "G\<turnstile>C \<prec>\<^sub>C1 super c"
       by (auto dest: wf_prog_cdecl wf_cdecl_supD is_acc_classD
               intro: subcls1I)
     show "\<exists>new. ?Constraint C new old"
--- a/src/HOL/Bali/WellType.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Bali/WellType.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -53,11 +53,10 @@
   emhead = "ref_ty \<times> mhead"
 
 --{* Some mnemotic selectors for emhead *}
-constdefs 
-  "declrefT" :: "emhead \<Rightarrow> ref_ty"
+definition "declrefT" :: "emhead \<Rightarrow> ref_ty" where
   "declrefT \<equiv> fst"
 
-  "mhd"     :: "emhead \<Rightarrow> mhead"
+definition "mhd"     :: "emhead \<Rightarrow> mhead" where
   "mhd \<equiv> snd"
 
 lemma declrefT_simp[simp]:"declrefT (r,m) = r"
@@ -138,11 +137,10 @@
 done
 
 
-constdefs
-  empty_dt :: "dyn_ty"
+definition empty_dt :: "dyn_ty" where
  "empty_dt \<equiv> \<lambda>a. None"
 
-  invmode :: "('a::type)member_scheme \<Rightarrow> expr \<Rightarrow> inv_mode"
+definition invmode :: "('a::type)member_scheme \<Rightarrow> expr \<Rightarrow> inv_mode" where
 "invmode m e \<equiv> if is_static m 
                   then Static 
                   else if e=Super then SuperM else IntVir"
--- a/src/HOL/Decision_Procs/Cooper.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Decision_Procs/Cooper.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -293,10 +293,10 @@
 by (induct p, simp_all)
 
 
-constdefs djf:: "('a \<Rightarrow> fm) \<Rightarrow> 'a \<Rightarrow> fm \<Rightarrow> fm"
+definition djf :: "('a \<Rightarrow> fm) \<Rightarrow> 'a \<Rightarrow> fm \<Rightarrow> fm" where
   "djf f p q \<equiv> (if q=T then T else if q=F then f p else 
   (let fp = f p in case fp of T \<Rightarrow> T | F \<Rightarrow> q | _ \<Rightarrow> Or (f p) q))"
-constdefs evaldjf:: "('a \<Rightarrow> fm) \<Rightarrow> 'a list \<Rightarrow> fm"
+definition evaldjf :: "('a \<Rightarrow> fm) \<Rightarrow> 'a list \<Rightarrow> fm" where
   "evaldjf f ps \<equiv> foldr (djf f) ps F"
 
 lemma djf_Or: "Ifm bbs bs (djf f p q) = Ifm bbs bs (Or (f p) q)"
@@ -340,7 +340,7 @@
   thus ?thesis by (simp only: list_all_iff)
 qed
 
-constdefs DJ :: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm"
+definition DJ :: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm" where
   "DJ f p \<equiv> evaldjf f (disjuncts p)"
 
 lemma DJ: assumes fdj: "\<forall> p q. f (Or p q) = Or (f p) (f q)"
@@ -395,7 +395,7 @@
   "lex_ns ([], ms) = True"
   "lex_ns (ns, []) = False"
   "lex_ns (n#ns, m#ms) = (n<m \<or> ((n = m) \<and> lex_ns (ns,ms))) "
-constdefs lex_bnd :: "num \<Rightarrow> num \<Rightarrow> bool"
+definition lex_bnd :: "num \<Rightarrow> num \<Rightarrow> bool" where
   "lex_bnd t s \<equiv> lex_ns (bnds t, bnds s)"
 
 consts
@@ -455,10 +455,10 @@
 lemma nummul_nb: "\<And> i. numbound0 t \<Longrightarrow> numbound0 (nummul i t)"
 by (induct t rule: nummul.induct, auto simp add: numadd_nb)
 
-constdefs numneg :: "num \<Rightarrow> num"
+definition numneg :: "num \<Rightarrow> num" where
   "numneg t \<equiv> nummul (- 1) t"
 
-constdefs numsub :: "num \<Rightarrow> num \<Rightarrow> num"
+definition numsub :: "num \<Rightarrow> num \<Rightarrow> num" where
   "numsub s t \<equiv> (if s = t then C 0 else numadd (s, numneg t))"
 
 lemma numneg: "Inum bs (numneg t) = Inum bs (Neg t)"
@@ -505,7 +505,7 @@
 lemma not_bn: "bound0 p \<Longrightarrow> bound0 (not p)"
 by (cases p, auto)
 
-constdefs conj :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition conj :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "conj p q \<equiv> (if (p = F \<or> q=F) then F else if p=T then q else if q=T then p else And p q)"
 lemma conj: "Ifm bbs bs (conj p q) = Ifm bbs bs (And p q)"
 by (cases "p=F \<or> q=F",simp_all add: conj_def) (cases p,simp_all)
@@ -515,7 +515,7 @@
 lemma conj_nb: "\<lbrakk>bound0 p ; bound0 q\<rbrakk> \<Longrightarrow> bound0 (conj p q)"
 using conj_def by auto 
 
-constdefs disj :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition disj :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "disj p q \<equiv> (if (p = T \<or> q=T) then T else if p=F then q else if q=F then p else Or p q)"
 
 lemma disj: "Ifm bbs bs (disj p q) = Ifm bbs bs (Or p q)"
@@ -525,7 +525,7 @@
 lemma disj_nb: "\<lbrakk>bound0 p ; bound0 q\<rbrakk> \<Longrightarrow> bound0 (disj p q)"
 using disj_def by auto 
 
-constdefs   imp :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition imp :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "imp p q \<equiv> (if (p = F \<or> q=T) then T else if p=T then q else if q=F then not p else Imp p q)"
 lemma imp: "Ifm bbs bs (imp p q) = Ifm bbs bs (Imp p q)"
 by (cases "p=F \<or> q=T",simp_all add: imp_def,cases p) (simp_all add: not)
@@ -534,7 +534,7 @@
 lemma imp_nb: "\<lbrakk>bound0 p ; bound0 q\<rbrakk> \<Longrightarrow> bound0 (imp p q)"
 using imp_def by (cases "p=F \<or> q=T",simp_all add: imp_def,cases p) simp_all
 
-constdefs   iff :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition iff :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "iff p q \<equiv> (if (p = q) then T else if (p = not q \<or> not p = q) then F else 
        if p=F then not q else if q=F then not p else if p=T then q else if q=T then p else 
   Iff p q)"
@@ -1749,7 +1749,7 @@
   shows "(\<exists> x. Ifm bbs (x#bs) p) = ((\<exists> j\<in> {1 .. d}. Ifm bbs (j#bs) (minusinf p)) \<or> (\<exists> j\<in> {1.. d}. \<exists> b\<in> (Inum (i#bs)) ` set (\<beta> p). Ifm bbs ((b+j)#bs) p))"
   using cp_thm[OF lp up dd dp,where i="i"] by auto
 
-constdefs unit:: "fm \<Rightarrow> fm \<times> num list \<times> int"
+definition unit :: "fm \<Rightarrow> fm \<times> num list \<times> int" where
   "unit p \<equiv> (let p' = zlfm p ; l = \<zeta> p' ; q = And (Dvd l (CN 0 1 (C 0))) (a\<beta> p' l); d = \<delta> q;
              B = remdups (map simpnum (\<beta> q)) ; a = remdups (map simpnum (\<alpha> q))
              in if length B \<le> length a then (q,B,d) else (mirror q, a,d))"
@@ -1814,7 +1814,7 @@
 qed
     (* Cooper's Algorithm *)
 
-constdefs cooper :: "fm \<Rightarrow> fm"
+definition cooper :: "fm \<Rightarrow> fm" where
   "cooper p \<equiv> 
   (let (q,B,d) = unit p; js = iupt 1 d;
        mq = simpfm (minusinf q);
--- a/src/HOL/Decision_Procs/Ferrack.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Decision_Procs/Ferrack.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -169,26 +169,26 @@
 lemma not[simp]: "Ifm bs (not p) = Ifm bs (NOT p)"
 by (cases p) auto
 
-constdefs conj :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition conj :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "conj p q \<equiv> (if (p = F \<or> q=F) then F else if p=T then q else if q=T then p else 
    if p = q then p else And p q)"
 lemma conj[simp]: "Ifm bs (conj p q) = Ifm bs (And p q)"
 by (cases "p=F \<or> q=F",simp_all add: conj_def) (cases p,simp_all)
 
-constdefs disj :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition disj :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "disj p q \<equiv> (if (p = T \<or> q=T) then T else if p=F then q else if q=F then p 
        else if p=q then p else Or p q)"
 
 lemma disj[simp]: "Ifm bs (disj p q) = Ifm bs (Or p q)"
 by (cases "p=T \<or> q=T",simp_all add: disj_def) (cases p,simp_all)
 
-constdefs  imp :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition imp :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "imp p q \<equiv> (if (p = F \<or> q=T \<or> p=q) then T else if p=T then q else if q=F then not p 
     else Imp p q)"
 lemma imp[simp]: "Ifm bs (imp p q) = Ifm bs (Imp p q)"
 by (cases "p=F \<or> q=T",simp_all add: imp_def) 
 
-constdefs   iff :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition iff :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "iff p q \<equiv> (if (p = q) then T else if (p = NOT q \<or> NOT p = q) then F else 
        if p=F then not q else if q=F then not p else if p=T then q else if q=T then p else 
   Iff p q)"
@@ -369,10 +369,10 @@
 lemma bound0_qf: "bound0 p \<Longrightarrow> qfree p"
 by (induct p, simp_all)
 
-constdefs djf:: "('a \<Rightarrow> fm) \<Rightarrow> 'a \<Rightarrow> fm \<Rightarrow> fm"
+definition djf :: "('a \<Rightarrow> fm) \<Rightarrow> 'a \<Rightarrow> fm \<Rightarrow> fm" where
   "djf f p q \<equiv> (if q=T then T else if q=F then f p else 
   (let fp = f p in case fp of T \<Rightarrow> T | F \<Rightarrow> q | _ \<Rightarrow> Or (f p) q))"
-constdefs evaldjf:: "('a \<Rightarrow> fm) \<Rightarrow> 'a list \<Rightarrow> fm"
+definition evaldjf :: "('a \<Rightarrow> fm) \<Rightarrow> 'a list \<Rightarrow> fm" where
   "evaldjf f ps \<equiv> foldr (djf f) ps F"
 
 lemma djf_Or: "Ifm bs (djf f p q) = Ifm bs (Or (f p) q)"
@@ -423,7 +423,7 @@
   thus ?thesis by (simp only: list_all_iff)
 qed
 
-constdefs DJ :: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm"
+definition DJ :: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm" where
   "DJ f p \<equiv> evaldjf f (disjuncts p)"
 
 lemma DJ: assumes fdj: "\<forall> p q. Ifm bs (f (Or p q)) = Ifm bs (Or (f p) (f q))"
@@ -653,10 +653,10 @@
 lemma nummul_nb[simp]: "\<And> i. numbound0 t \<Longrightarrow> numbound0 (nummul t i)"
 by (induct t rule: nummul.induct, auto )
 
-constdefs numneg :: "num \<Rightarrow> num"
+definition numneg :: "num \<Rightarrow> num" where
   "numneg t \<equiv> nummul t (- 1)"
 
-constdefs numsub :: "num \<Rightarrow> num \<Rightarrow> num"
+definition numsub :: "num \<Rightarrow> num \<Rightarrow> num" where
   "numsub s t \<equiv> (if s = t then C 0 else numadd (s,numneg t))"
 
 lemma numneg[simp]: "Inum bs (numneg t) = Inum bs (Neg t)"
@@ -724,7 +724,7 @@
   from maxcoeff_nz[OF nz th] show ?thesis .
 qed
 
-constdefs simp_num_pair:: "(num \<times> int) \<Rightarrow> num \<times> int"
+definition simp_num_pair :: "(num \<times> int) \<Rightarrow> num \<times> int" where
   "simp_num_pair \<equiv> (\<lambda> (t,n). (if n = 0 then (C 0, 0) else
    (let t' = simpnum t ; g = numgcd t' in 
       if g > 1 then (let g' = gcd n g in 
@@ -1779,7 +1779,7 @@
 
 
     (* Implement the right hand side of Ferrante and Rackoff's Theorem. *)
-constdefs ferrack:: "fm \<Rightarrow> fm"
+definition ferrack :: "fm \<Rightarrow> fm" where
   "ferrack p \<equiv> (let p' = rlfm (simpfm p); mp = minusinf p'; pp = plusinf p'
                 in if (mp = T \<or> pp = T) then T else 
                    (let U = remdps(map simp_num_pair 
--- a/src/HOL/Decision_Procs/MIR.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Decision_Procs/MIR.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -566,7 +566,7 @@
   thus ?thesis by (simp only: list_all_iff)
 qed
 
-constdefs DJ :: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm"
+definition DJ :: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm" where
   "DJ f p \<equiv> evaldjf f (disjuncts p)"
 
 lemma DJ: assumes fdj: "\<forall> p q. f (Or p q) = Or (f p) (f q)"
@@ -623,7 +623,7 @@
   "lex_ns ([], ms) = True"
   "lex_ns (ns, []) = False"
   "lex_ns (n#ns, m#ms) = (n<m \<or> ((n = m) \<and> lex_ns (ns,ms))) "
-constdefs lex_bnd :: "num \<Rightarrow> num \<Rightarrow> bool"
+definition lex_bnd :: "num \<Rightarrow> num \<Rightarrow> bool" where
   "lex_bnd t s \<equiv> lex_ns (bnds t, bnds s)"
 
 consts 
@@ -873,10 +873,10 @@
 lemma nummul_nb[simp]: "\<And> i. numbound0 t \<Longrightarrow> numbound0 (nummul t i)"
 by (induct t rule: nummul.induct, auto)
 
-constdefs numneg :: "num \<Rightarrow> num"
+definition numneg :: "num \<Rightarrow> num" where
   "numneg t \<equiv> nummul t (- 1)"
 
-constdefs numsub :: "num \<Rightarrow> num \<Rightarrow> num"
+definition numsub :: "num \<Rightarrow> num \<Rightarrow> num" where
   "numsub s t \<equiv> (if s = t then C 0 else numadd (s,numneg t))"
 
 lemma numneg[simp]: "Inum bs (numneg t) = Inum bs (Neg t)"
@@ -1038,7 +1038,7 @@
   from maxcoeff_nz[OF nz th] show ?thesis .
 qed
 
-constdefs simp_num_pair:: "(num \<times> int) \<Rightarrow> num \<times> int"
+definition simp_num_pair :: "(num \<times> int) \<Rightarrow> num \<times> int" where
   "simp_num_pair \<equiv> (\<lambda> (t,n). (if n = 0 then (C 0, 0) else
    (let t' = simpnum t ; g = numgcd t' in 
       if g > 1 then (let g' = gcd n g in 
@@ -1137,7 +1137,7 @@
 lemma not_nb[simp]: "bound0 p \<Longrightarrow> bound0 (not p)"
 by (induct p, auto)
 
-constdefs conj :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition conj :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "conj p q \<equiv> (if (p = F \<or> q=F) then F else if p=T then q else if q=T then p else 
    if p = q then p else And p q)"
 lemma conj[simp]: "Ifm bs (conj p q) = Ifm bs (And p q)"
@@ -1148,7 +1148,7 @@
 lemma conj_nb[simp]: "\<lbrakk>bound0 p ; bound0 q\<rbrakk> \<Longrightarrow> bound0 (conj p q)"
 using conj_def by auto 
 
-constdefs disj :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition disj :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "disj p q \<equiv> (if (p = T \<or> q=T) then T else if p=F then q else if q=F then p 
        else if p=q then p else Or p q)"
 
@@ -1159,7 +1159,7 @@
 lemma disj_nb[simp]: "\<lbrakk>bound0 p ; bound0 q\<rbrakk> \<Longrightarrow> bound0 (disj p q)"
 using disj_def by auto 
 
-constdefs   imp :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition imp :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "imp p q \<equiv> (if (p = F \<or> q=T \<or> p=q) then T else if p=T then q else if q=F then not p 
     else Imp p q)"
 lemma imp[simp]: "Ifm bs (imp p q) = Ifm bs (Imp p q)"
@@ -1169,7 +1169,7 @@
 lemma imp_nb[simp]: "\<lbrakk>bound0 p ; bound0 q\<rbrakk> \<Longrightarrow> bound0 (imp p q)"
 using imp_def by (cases "p=F \<or> q=T \<or> p=q",simp_all add: imp_def) 
 
-constdefs   iff :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition iff :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "iff p q \<equiv> (if (p = q) then T else if (p = not q \<or> not p = q) then F else 
        if p=F then not q else if q=F then not p else if p=T then q else if q=T then p else 
   Iff p q)"
@@ -1216,7 +1216,7 @@
   thus "real d rdvd real c * t" using d rdvd_mult[OF gnz, where n="d div g" and x="real (c div g) * t"] real_of_int_div[OF gnz gd] real_of_int_div[OF gnz gc] by simp
 qed
 
-constdefs simpdvd:: "int \<Rightarrow> num \<Rightarrow> (int \<times> num)"
+definition simpdvd :: "int \<Rightarrow> num \<Rightarrow> (int \<times> num)" where
   "simpdvd d t \<equiv> 
    (let g = numgcd t in 
       if g > 1 then (let g' = gcd d g in 
@@ -1479,7 +1479,7 @@
 
   (* Generic quantifier elimination *)
 
-constdefs list_conj :: "fm list \<Rightarrow> fm"
+definition list_conj :: "fm list \<Rightarrow> fm" where
   "list_conj ps \<equiv> foldr conj ps T"
 lemma list_conj: "Ifm bs (list_conj ps) = (\<forall>p\<in> set ps. Ifm bs p)"
   by (induct ps, auto simp add: list_conj_def)
@@ -1487,7 +1487,7 @@
   by (induct ps, auto simp add: list_conj_def)
 lemma list_conj_nb: " \<forall>p\<in> set ps. bound0 p \<Longrightarrow> bound0 (list_conj ps)"
   by (induct ps, auto simp add: list_conj_def)
-constdefs CJNB:: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm"
+definition CJNB :: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm" where
   "CJNB f p \<equiv> (let cjs = conjuncts p ; (yes,no) = List.partition bound0 cjs
                    in conj (decr (list_conj yes)) (f (list_conj no)))"
 
@@ -2954,7 +2954,7 @@
                                             else (NDvd (i*k) (CN 0 c (Mul k e))))"
   "a\<rho> p = (\<lambda> k. p)"
 
-constdefs \<sigma> :: "fm \<Rightarrow> int \<Rightarrow> num \<Rightarrow> fm"
+definition \<sigma> :: "fm \<Rightarrow> int \<Rightarrow> num \<Rightarrow> fm" where
   "\<sigma> p k t \<equiv> And (Dvd k t) (\<sigma>\<rho> p (t,k))"
 
 lemma \<sigma>\<rho>:
@@ -3517,7 +3517,7 @@
   "isrlfm (Ge  (CN 0 c e)) = (c>0 \<and> numbound0 e)"
   "isrlfm p = (isatom p \<and> (bound0 p))"
 
-constdefs fp :: "fm \<Rightarrow> int \<Rightarrow> num \<Rightarrow> int \<Rightarrow> fm"
+definition fp :: "fm \<Rightarrow> int \<Rightarrow> num \<Rightarrow> int \<Rightarrow> fm" where
   "fp p n s j \<equiv> (if n > 0 then 
             (And p (And (Ge (CN 0 n (Sub s (Add (Floor s) (C j)))))
                         (Lt (CN 0 n (Sub s (Add (Floor s) (C (j+1))))))))
@@ -3836,7 +3836,7 @@
 
     (* Linearize a formula where Bound 0 ranges over [0,1) *)
 
-constdefs rsplit :: "(int \<Rightarrow> num \<Rightarrow> fm) \<Rightarrow> num \<Rightarrow> fm"
+definition rsplit :: "(int \<Rightarrow> num \<Rightarrow> fm) \<Rightarrow> num \<Rightarrow> fm" where
   "rsplit f a \<equiv> foldr disj (map (\<lambda> (\<phi>, n, s). conj \<phi> (f n s)) (rsplit0 a)) F"
 
 lemma foldr_disj_map: "Ifm bs (foldr disj (map f xs) F) = (\<exists> x \<in> set xs. Ifm bs (f x))"
@@ -5103,7 +5103,7 @@
 
     (* Implement the right hand sides of Cooper's theorem and Ferrante and Rackoff. *)
 
-constdefs ferrack01:: "fm \<Rightarrow> fm"
+definition ferrack01 :: "fm \<Rightarrow> fm" where
   "ferrack01 p \<equiv> (let p' = rlfm(And (And (Ge(CN 0 1 (C 0))) (Lt (CN 0 1 (C (- 1))))) p);
                     U = remdups(map simp_num_pair 
                      (map (\<lambda> ((t,n),(s,m)). (Add (Mul m t) (Mul n s) , 2*n*m))
@@ -5350,7 +5350,7 @@
   shows "(\<exists> (x::int). Ifm (real x#bs) p) = ((\<exists> j\<in> {1 .. d}. Ifm (real j#bs) (minusinf p)) \<or> (\<exists> j\<in> {1.. d}. \<exists> b\<in> (Inum (real i#bs)) ` set (\<beta> p). Ifm ((b+real j)#bs) p))"
   using cp_thm[OF lp up dd dp] by auto
 
-constdefs unit:: "fm \<Rightarrow> fm \<times> num list \<times> int"
+definition unit :: "fm \<Rightarrow> fm \<times> num list \<times> int" where
   "unit p \<equiv> (let p' = zlfm p ; l = \<zeta> p' ; q = And (Dvd l (CN 0 1 (C 0))) (a\<beta> p' l); d = \<delta> q;
              B = remdups (map simpnum (\<beta> q)) ; a = remdups (map simpnum (\<alpha> q))
              in if length B \<le> length a then (q,B,d) else (mirror q, a,d))"
@@ -5417,7 +5417,7 @@
 qed
     (* Cooper's Algorithm *)
 
-constdefs cooper :: "fm \<Rightarrow> fm"
+definition cooper :: "fm \<Rightarrow> fm" where
   "cooper p \<equiv> 
   (let (q,B,d) = unit p; js = iupt (1,d);
        mq = simpfm (minusinf q);
@@ -5561,7 +5561,7 @@
   shows "(\<exists> (x::int). Ifm (real x#bs) p) = ((\<exists> j\<in> {1 .. \<delta> p}. Ifm (real j#bs) (minusinf p)) \<or> (\<exists> (e,c) \<in> R. \<exists> j\<in> {1.. c*(\<delta> p)}. Ifm (a#bs) (\<sigma> p c (Add e (C j)))))"
   using rl_thm[OF lp] \<rho>_cong[OF iszlfm_gen[OF lp, rule_format, where y="a"] R] by simp 
 
-constdefs chooset:: "fm \<Rightarrow> fm \<times> ((num\<times>int) list) \<times> int"
+definition chooset :: "fm \<Rightarrow> fm \<times> ((num\<times>int) list) \<times> int" where
   "chooset p \<equiv> (let q = zlfm p ; d = \<delta> q;
              B = remdups (map (\<lambda> (t,k). (simpnum t,k)) (\<rho> q)) ; 
              a = remdups (map (\<lambda> (t,k). (simpnum t,k)) (\<alpha>\<rho> q))
@@ -5621,7 +5621,7 @@
   ultimately show ?thes by blast
 qed
 
-constdefs stage:: "fm \<Rightarrow> int \<Rightarrow> (num \<times> int) \<Rightarrow> fm"
+definition stage :: "fm \<Rightarrow> int \<Rightarrow> (num \<times> int) \<Rightarrow> fm" where
   "stage p d \<equiv> (\<lambda> (e,c). evaldjf (\<lambda> j. simpfm (\<sigma> p c (Add e (C j)))) (iupt (1,c*d)))"
 lemma stage:
   shows "Ifm bs (stage p d (e,c)) = (\<exists> j\<in>{1 .. c*d}. Ifm bs (\<sigma> p c (Add e (C j))))"
@@ -5641,7 +5641,7 @@
   from evaldjf_bound0[OF th] show ?thesis by (unfold stage_def split_def) simp
 qed
 
-constdefs redlove:: "fm \<Rightarrow> fm"
+definition redlove :: "fm \<Rightarrow> fm" where
   "redlove p \<equiv> 
   (let (q,B,d) = chooset p;
        mq = simpfm (minusinf q);
--- a/src/HOL/Decision_Procs/Parametric_Ferrante_Rackoff.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Decision_Procs/Parametric_Ferrante_Rackoff.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -273,10 +273,10 @@
   assumes "SORT_CONSTRAINT('a::{ring_char_0,division_by_zero, field})"
   shows "allpolys isnpoly t \<Longrightarrow> isnpoly c \<Longrightarrow> allpolys isnpoly (tmmul t c)" by (induct t rule: tmmul.induct, simp_all add: Let_def polymul_norm)
 
-constdefs tmneg :: "tm \<Rightarrow> tm"
+definition tmneg :: "tm \<Rightarrow> tm" where
   "tmneg t \<equiv> tmmul t (C (- 1,1))"
 
-constdefs tmsub :: "tm \<Rightarrow> tm \<Rightarrow> tm"
+definition tmsub :: "tm \<Rightarrow> tm \<Rightarrow> tm" where
   "tmsub s t \<equiv> (if s = t then CP 0\<^sub>p else tmadd (s,tmneg t))"
 
 lemma tmneg[simp]: "Itm vs bs (tmneg t) = Itm vs bs (Neg t)"
@@ -477,26 +477,26 @@
 lemma not[simp]: "Ifm vs bs (not p) = Ifm vs bs (NOT p)"
 by (induct p rule: not.induct) auto
 
-constdefs conj :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition conj :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "conj p q \<equiv> (if (p = F \<or> q=F) then F else if p=T then q else if q=T then p else 
    if p = q then p else And p q)"
 lemma conj[simp]: "Ifm vs bs (conj p q) = Ifm vs bs (And p q)"
 by (cases "p=F \<or> q=F",simp_all add: conj_def) (cases p,simp_all)
 
-constdefs disj :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition disj :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "disj p q \<equiv> (if (p = T \<or> q=T) then T else if p=F then q else if q=F then p 
        else if p=q then p else Or p q)"
 
 lemma disj[simp]: "Ifm vs bs (disj p q) = Ifm vs bs (Or p q)"
 by (cases "p=T \<or> q=T",simp_all add: disj_def) (cases p,simp_all)
 
-constdefs  imp :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition imp :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "imp p q \<equiv> (if (p = F \<or> q=T \<or> p=q) then T else if p=T then q else if q=F then not p 
     else Imp p q)"
 lemma imp[simp]: "Ifm vs bs (imp p q) = Ifm vs bs (Imp p q)"
 by (cases "p=F \<or> q=T",simp_all add: imp_def) 
 
-constdefs   iff :: "fm \<Rightarrow> fm \<Rightarrow> fm"
+definition iff :: "fm \<Rightarrow> fm \<Rightarrow> fm" where
   "iff p q \<equiv> (if (p = q) then T else if (p = NOT q \<or> NOT p = q) then F else 
        if p=F then not q else if q=F then not p else if p=T then q else if q=T then p else 
   Iff p q)"
@@ -776,10 +776,10 @@
 lemma bound0_qf: "bound0 p \<Longrightarrow> qfree p"
 by (induct p, simp_all)
 
-constdefs djf:: "('a \<Rightarrow> fm) \<Rightarrow> 'a \<Rightarrow> fm \<Rightarrow> fm"
+definition djf :: "('a \<Rightarrow> fm) \<Rightarrow> 'a \<Rightarrow> fm \<Rightarrow> fm" where
   "djf f p q \<equiv> (if q=T then T else if q=F then f p else 
   (let fp = f p in case fp of T \<Rightarrow> T | F \<Rightarrow> q | _ \<Rightarrow> Or (f p) q))"
-constdefs evaldjf:: "('a \<Rightarrow> fm) \<Rightarrow> 'a list \<Rightarrow> fm"
+definition evaldjf :: "('a \<Rightarrow> fm) \<Rightarrow> 'a list \<Rightarrow> fm" where
   "evaldjf f ps \<equiv> foldr (djf f) ps F"
 
 lemma djf_Or: "Ifm vs bs (djf f p q) = Ifm vs bs (Or (f p) q)"
@@ -823,7 +823,7 @@
   thus ?thesis by (simp only: list_all_iff)
 qed
 
-constdefs DJ :: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm"
+definition DJ :: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm" where
   "DJ f p \<equiv> evaldjf f (disjuncts p)"
 
 lemma DJ: assumes fdj: "\<forall> p q. Ifm vs bs (f (Or p q)) = Ifm vs bs (Or (f p) (f q))"
@@ -869,10 +869,10 @@
   "conjuncts T = []"
   "conjuncts p = [p]"
 
-constdefs list_conj :: "fm list \<Rightarrow> fm"
+definition list_conj :: "fm list \<Rightarrow> fm" where
   "list_conj ps \<equiv> foldr conj ps T"
 
-constdefs CJNB:: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm"
+definition CJNB :: "(fm \<Rightarrow> fm) \<Rightarrow> fm \<Rightarrow> fm" where
   "CJNB f p \<equiv> (let cjs = conjuncts p ; (yes,no) = partition bound0 cjs
                    in conj (decr0 (list_conj yes)) (f (list_conj no)))"
 
@@ -1158,7 +1158,7 @@
   "conjs p = [p]"
 lemma conjs_ci: "(\<forall> q \<in> set (conjs p). Ifm vs bs q) = Ifm vs bs p"
 by (induct p rule: conjs.induct, auto)
-constdefs list_disj :: "fm list \<Rightarrow> fm"
+definition list_disj :: "fm list \<Rightarrow> fm" where
   "list_disj ps \<equiv> foldr disj ps F"
 
 lemma list_conj: "Ifm vs bs (list_conj ps) = (\<forall>p\<in> set ps. Ifm vs bs p)"
--- a/src/HOL/Decision_Procs/Reflected_Multivariate_Polynomial.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Decision_Procs/Reflected_Multivariate_Polynomial.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -188,12 +188,12 @@
 | "poly_cmul y (CN c n p) = CN (poly_cmul y c) n (poly_cmul y p)"
 | "poly_cmul y p = C y *\<^sub>p p"
 
-constdefs monic:: "poly \<Rightarrow> (poly \<times> bool)"
+definition monic :: "poly \<Rightarrow> (poly \<times> bool)" where
   "monic p \<equiv> (let h = headconst p in if h = 0\<^sub>N then (p,False) else ((C (Ninv h)) *\<^sub>p p, 0>\<^sub>N h))"
 
 subsection{* Pseudo-division *}
 
-constdefs shift1:: "poly \<Rightarrow> poly"
+definition shift1 :: "poly \<Rightarrow> poly" where
   "shift1 p \<equiv> CN 0\<^sub>p 0 p"
 consts funpow :: "nat \<Rightarrow> ('a \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a"
 
@@ -212,7 +212,7 @@
   by pat_completeness auto
 
 
-constdefs polydivide:: "poly \<Rightarrow> poly \<Rightarrow> (nat \<times> poly)"
+definition polydivide :: "poly \<Rightarrow> poly \<Rightarrow> (nat \<times> poly)" where
   "polydivide s p \<equiv> polydivide_aux (head p,degree p,p,0, s)"
 
 fun poly_deriv_aux :: "nat \<Rightarrow> poly \<Rightarrow> poly" where
@@ -262,7 +262,7 @@
 lemma isnpolyh_mono: "\<lbrakk>n' \<le> n ; isnpolyh p n\<rbrakk> \<Longrightarrow> isnpolyh p n'"
 by (induct p rule: isnpolyh.induct, auto)
 
-constdefs isnpoly:: "poly \<Rightarrow> bool"
+definition isnpoly :: "poly \<Rightarrow> bool" where
   "isnpoly p \<equiv> isnpolyh p 0"
 
 text{* polyadd preserves normal forms *}
--- a/src/HOL/Finite_Set.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Finite_Set.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -2528,8 +2528,7 @@
   fold1Set_insertI [intro]:
    "\<lbrakk> fold_graph f a A x; a \<notin> A \<rbrakk> \<Longrightarrow> fold1Set f (insert a A) x"
 
-constdefs
-  fold1 :: "('a => 'a => 'a) => 'a set => 'a"
+definition fold1 :: "('a => 'a => 'a) => 'a set => 'a" where
   "fold1 f A == THE x. fold1Set f A x"
 
 lemma fold1Set_nonempty:
--- a/src/HOL/Fun.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Fun.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -119,8 +119,9 @@
 
 subsection {* Injectivity and Surjectivity *}
 
-constdefs
-  inj_on :: "['a => 'b, 'a set] => bool"  -- "injective"
+definition
+  inj_on :: "['a => 'b, 'a set] => bool" where
+  -- "injective"
   "inj_on f A == ! x:A. ! y:A. f(x)=f(y) --> x=y"
 
 text{*A common special case: functions injective over the entire domain type.*}
@@ -132,11 +133,14 @@
   bij_betw :: "('a => 'b) => 'a set => 'b set => bool" where -- "bijective"
   [code del]: "bij_betw f A B \<longleftrightarrow> inj_on f A & f ` A = B"
 
-constdefs
-  surj :: "('a => 'b) => bool"                   (*surjective*)
+definition
+  surj :: "('a => 'b) => bool" where
+  -- "surjective"
   "surj f == ! y. ? x. y=f(x)"
 
-  bij :: "('a => 'b) => bool"                    (*bijective*)
+definition
+  bij :: "('a => 'b) => bool" where
+  -- "bijective"
   "bij f == inj f & surj f"
 
 lemma injI:
@@ -377,8 +381,8 @@
 
 subsection{*Function Updating*}
 
-constdefs
-  fun_upd :: "('a => 'b) => 'a => 'b => ('a => 'b)"
+definition
+  fun_upd :: "('a => 'b) => 'a => 'b => ('a => 'b)" where
   "fun_upd f a b == % x. if x=a then b else f x"
 
 nonterminals
--- a/src/HOL/HOL.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/HOL.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -1118,8 +1118,7 @@
   its premise.
 *}
 
-constdefs
-  simp_implies :: "[prop, prop] => prop"  (infixr "=simp=>" 1)
+definition simp_implies :: "[prop, prop] => prop"  (infixr "=simp=>" 1) where
   [code del]: "simp_implies \<equiv> op ==>"
 
 lemma simp_impliesI:
@@ -1392,13 +1391,23 @@
 )
 *}
 
-constdefs
-  induct_forall where "induct_forall P == \<forall>x. P x"
-  induct_implies where "induct_implies A B == A \<longrightarrow> B"
-  induct_equal where "induct_equal x y == x = y"
-  induct_conj where "induct_conj A B == A \<and> B"
-  induct_true where "induct_true == True"
-  induct_false where "induct_false == False"
+definition induct_forall where
+  "induct_forall P == \<forall>x. P x"
+
+definition induct_implies where
+  "induct_implies A B == A \<longrightarrow> B"
+
+definition induct_equal where
+  "induct_equal x y == x = y"
+
+definition induct_conj where
+  "induct_conj A B == A \<and> B"
+
+definition induct_true where
+  "induct_true == True"
+
+definition induct_false where
+  "induct_false == False"
 
 lemma induct_forall_eq: "(!!x. P x) == Trueprop (induct_forall (\<lambda>x. P x))"
   by (unfold atomize_all induct_forall_def)
--- a/src/HOL/Hilbert_Choice.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hilbert_Choice.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -307,8 +307,8 @@
 
 subsection {* Least value operator *}
 
-constdefs
-  LeastM :: "['a => 'b::ord, 'a => bool] => 'a"
+definition
+  LeastM :: "['a => 'b::ord, 'a => bool] => 'a" where
   "LeastM m P == SOME x. P x & (\<forall>y. P y --> m x <= m y)"
 
 syntax
@@ -360,11 +360,12 @@
 
 subsection {* Greatest value operator *}
 
-constdefs
-  GreatestM :: "['a => 'b::ord, 'a => bool] => 'a"
+definition
+  GreatestM :: "['a => 'b::ord, 'a => bool] => 'a" where
   "GreatestM m P == SOME x. P x & (\<forall>y. P y --> m y <= m x)"
 
-  Greatest :: "('a::ord => bool) => 'a"    (binder "GREATEST " 10)
+definition
+  Greatest :: "('a::ord => bool) => 'a" (binder "GREATEST " 10) where
   "Greatest == GreatestM (%x. x)"
 
 syntax
--- a/src/HOL/Hoare/Arith2.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare/Arith2.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -1,5 +1,4 @@
 (*  Title:      HOL/Hoare/Arith2.thy
-    ID:         $Id$
     Author:     Norbert Galm
     Copyright   1995 TUM
 
@@ -10,11 +9,10 @@
 imports Main
 begin
 
-constdefs
-  "cd"    :: "[nat, nat, nat] => bool"
+definition "cd" :: "[nat, nat, nat] => bool" where
   "cd x m n  == x dvd m & x dvd n"
 
-  gcd     :: "[nat, nat] => nat"
+definition gcd     :: "[nat, nat] => nat" where
   "gcd m n     == @x.(cd x m n) & (!y.(cd y m n) --> y<=x)"
 
 consts fac     :: "nat => nat"
--- a/src/HOL/Hoare/Heap.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare/Heap.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -1,5 +1,4 @@
 (*  Title:      HOL/Hoare/Heap.thy
-    ID:         $Id$
     Author:     Tobias Nipkow
     Copyright   2002 TUM
 
@@ -19,19 +18,17 @@
 lemma not_Ref_eq [iff]: "(ALL y. x ~= Ref y) = (x = Null)"
   by (induct x) auto
 
-consts addr :: "'a ref \<Rightarrow> 'a"
-primrec "addr(Ref a) = a"
+primrec addr :: "'a ref \<Rightarrow> 'a" where
+  "addr (Ref a) = a"
 
 
 section "The heap"
 
 subsection "Paths in the heap"
 
-consts
- Path :: "('a \<Rightarrow> 'a ref) \<Rightarrow> 'a ref \<Rightarrow> 'a list \<Rightarrow> 'a ref \<Rightarrow> bool"
-primrec
-"Path h x [] y = (x = y)"
-"Path h x (a#as) y = (x = Ref a \<and> Path h (h a) as y)"
+primrec Path :: "('a \<Rightarrow> 'a ref) \<Rightarrow> 'a ref \<Rightarrow> 'a list \<Rightarrow> 'a ref \<Rightarrow> bool" where
+  "Path h x [] y \<longleftrightarrow> x = y"
+| "Path h x (a#as) y \<longleftrightarrow> x = Ref a \<and> Path h (h a) as y"
 
 lemma [iff]: "Path h Null xs y = (xs = [] \<and> y = Null)"
 apply(case_tac xs)
@@ -60,8 +57,7 @@
 
 subsection "Non-repeating paths"
 
-constdefs
-  distPath :: "('a \<Rightarrow> 'a ref) \<Rightarrow> 'a ref \<Rightarrow> 'a list \<Rightarrow> 'a ref \<Rightarrow> bool"
+definition distPath :: "('a \<Rightarrow> 'a ref) \<Rightarrow> 'a ref \<Rightarrow> 'a list \<Rightarrow> 'a ref \<Rightarrow> bool" where
   "distPath h x as y   \<equiv>   Path h x as y  \<and>  distinct as"
 
 text{* The term @{term"distPath h x as y"} expresses the fact that a
@@ -86,8 +82,7 @@
 
 subsubsection "Relational abstraction"
 
-constdefs
- List :: "('a \<Rightarrow> 'a ref) \<Rightarrow> 'a ref \<Rightarrow> 'a list \<Rightarrow> bool"
+definition List :: "('a \<Rightarrow> 'a ref) \<Rightarrow> 'a ref \<Rightarrow> 'a list \<Rightarrow> bool" where
 "List h x as == Path h x as Null"
 
 lemma [simp]: "List h x [] = (x = Null)"
@@ -138,10 +133,10 @@
 
 subsection "Functional abstraction"
 
-constdefs
- islist :: "('a \<Rightarrow> 'a ref) \<Rightarrow> 'a ref \<Rightarrow> bool"
+definition islist :: "('a \<Rightarrow> 'a ref) \<Rightarrow> 'a ref \<Rightarrow> bool" where
 "islist h p == \<exists>as. List h p as"
- list :: "('a \<Rightarrow> 'a ref) \<Rightarrow> 'a ref \<Rightarrow> 'a list"
+
+definition list :: "('a \<Rightarrow> 'a ref) \<Rightarrow> 'a ref \<Rightarrow> 'a list" where
 "list h p == SOME as. List h p as"
 
 lemma List_conv_islist_list: "List h p as = (islist h p \<and> as = list h p)"
--- a/src/HOL/Hoare/Hoare_Logic.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare/Hoare_Logic.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -40,7 +40,7 @@
                                       (s ~: b --> Sem c2 s s'))"
 "Sem(While b x c) s s' = (? n. iter n b (Sem c) s s')"
 
-constdefs Valid :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> 'a bexp \<Rightarrow> bool"
+definition Valid :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> 'a bexp \<Rightarrow> bool" where
   "Valid p c q == !s s'. Sem c s s' --> s : p --> s' : q"
 
 
--- a/src/HOL/Hoare/Hoare_Logic_Abort.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare/Hoare_Logic_Abort.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -42,7 +42,7 @@
 "Sem(While b x c) s s' =
  (if s = None then s' = None else \<exists>n. iter n b (Sem c) s s')"
 
-constdefs Valid :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> 'a bexp \<Rightarrow> bool"
+definition Valid :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> 'a bexp \<Rightarrow> bool" where
   "Valid p c q == \<forall>s s'. Sem c s s' \<longrightarrow> s : Some ` p \<longrightarrow> s' : Some ` q"
 
 
--- a/src/HOL/Hoare/Pointer_Examples.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare/Pointer_Examples.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -216,10 +216,10 @@
 
 text"This is still a bit rough, especially the proof."
 
-constdefs
- cor :: "bool \<Rightarrow> bool \<Rightarrow> bool"
+definition cor :: "bool \<Rightarrow> bool \<Rightarrow> bool" where
 "cor P Q == if P then True else Q"
- cand :: "bool \<Rightarrow> bool \<Rightarrow> bool"
+
+definition cand :: "bool \<Rightarrow> bool \<Rightarrow> bool" where
 "cand P Q == if P then Q else False"
 
 consts merge :: "'a list * 'a list * ('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> 'a list"
@@ -481,7 +481,7 @@
 
 subsection "Storage allocation"
 
-constdefs new :: "'a set \<Rightarrow> 'a"
+definition new :: "'a set \<Rightarrow> 'a" where
 "new A == SOME a. a \<notin> A"
 
 
--- a/src/HOL/Hoare/Pointers0.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare/Pointers0.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -73,8 +73,7 @@
 
 subsubsection "Relational abstraction"
 
-constdefs
- List :: "('a::ref \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a list \<Rightarrow> bool"
+definition List :: "('a::ref \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a list \<Rightarrow> bool" where
 "List h x as == Path h x as Null"
 
 lemma [simp]: "List h x [] = (x = Null)"
@@ -122,10 +121,10 @@
 
 subsection "Functional abstraction"
 
-constdefs
- islist :: "('a::ref \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> bool"
+definition islist :: "('a::ref \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> bool" where
 "islist h p == \<exists>as. List h p as"
- list :: "('a::ref \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a list"
+
+definition list :: "('a::ref \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a list" where
 "list h p == SOME as. List h p as"
 
 lemma List_conv_islist_list: "List h p as = (islist h p \<and> as = list h p)"
@@ -407,7 +406,7 @@
 
 subsection "Storage allocation"
 
-constdefs new :: "'a set \<Rightarrow> 'a::ref"
+definition new :: "'a set \<Rightarrow> 'a::ref" where
 "new A == SOME a. a \<notin> A & a \<noteq> Null"
 
 
--- a/src/HOL/Hoare/SepLogHeap.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare/SepLogHeap.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -41,8 +41,7 @@
 
 subsection "Lists on the heap"
 
-constdefs
- List :: "heap \<Rightarrow> nat \<Rightarrow> nat list \<Rightarrow> bool"
+definition List :: "heap \<Rightarrow> nat \<Rightarrow> nat list \<Rightarrow> bool" where
 "List h x as == Path h x as 0"
 
 lemma [simp]: "List h x [] = (x = 0)"
--- a/src/HOL/Hoare/Separation.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare/Separation.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -16,20 +16,19 @@
 
 text{* The semantic definition of a few connectives: *}
 
-constdefs
- ortho:: "heap \<Rightarrow> heap \<Rightarrow> bool" (infix "\<bottom>" 55)
+definition ortho :: "heap \<Rightarrow> heap \<Rightarrow> bool" (infix "\<bottom>" 55) where
 "h1 \<bottom> h2 == dom h1 \<inter> dom h2 = {}"
 
- is_empty :: "heap \<Rightarrow> bool"
+definition is_empty :: "heap \<Rightarrow> bool" where
 "is_empty h == h = empty"
 
- singl:: "heap \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> bool"
+definition singl:: "heap \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> bool" where
 "singl h x y == dom h = {x} & h x = Some y"
 
- star:: "(heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> bool)"
+definition star:: "(heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> bool)" where
 "star P Q == \<lambda>h. \<exists>h1 h2. h = h1++h2 \<and> h1 \<bottom> h2 \<and> P h1 \<and> Q h2"
 
- wand:: "(heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> bool)"
+definition wand:: "(heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> bool)" where
 "wand P Q == \<lambda>h. \<forall>h'. h' \<bottom> h \<and> P h' \<longrightarrow> Q(h++h')"
 
 text{*This is what assertions look like without any syntactic sugar: *}
--- a/src/HOL/Hoare_Parallel/Gar_Coll.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare_Parallel/Gar_Coll.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -31,8 +31,7 @@
 under which the selected edge @{text "R"} and node @{text "T"} are
 valid: *}
 
-constdefs
-  Mut_init :: "gar_coll_state \<Rightarrow> bool"
+definition Mut_init :: "gar_coll_state \<Rightarrow> bool" where
   "Mut_init \<equiv> \<guillemotleft> T \<in> Reach \<acute>E \<and> R < length \<acute>E \<and> T < length \<acute>M \<guillemotright>"
 
 text {* \noindent For the mutator we
@@ -40,14 +39,13 @@
 @{text "\<acute>z"} is set to false if the mutator has already redirected an
 edge but has not yet colored the new target.   *}
 
-constdefs
-  Redirect_Edge :: "gar_coll_state ann_com"
+definition Redirect_Edge :: "gar_coll_state ann_com" where
   "Redirect_Edge \<equiv> .{\<acute>Mut_init \<and> \<acute>z}. \<langle>\<acute>E:=\<acute>E[R:=(fst(\<acute>E!R), T)],, \<acute>z:= (\<not>\<acute>z)\<rangle>"
 
-  Color_Target :: "gar_coll_state ann_com"
+definition Color_Target :: "gar_coll_state ann_com" where
   "Color_Target \<equiv> .{\<acute>Mut_init \<and> \<not>\<acute>z}. \<langle>\<acute>M:=\<acute>M[T:=Black],, \<acute>z:= (\<not>\<acute>z)\<rangle>"
 
-  Mutator :: "gar_coll_state ann_com"
+definition Mutator :: "gar_coll_state ann_com" where
   "Mutator \<equiv>
   .{\<acute>Mut_init \<and> \<acute>z}. 
   WHILE True INV .{\<acute>Mut_init \<and> \<acute>z}. 
@@ -88,22 +86,20 @@
 
 consts  M_init :: nodes
 
-constdefs
-  Proper_M_init :: "gar_coll_state \<Rightarrow> bool"
+definition Proper_M_init :: "gar_coll_state \<Rightarrow> bool" where
   "Proper_M_init \<equiv>  \<guillemotleft> Blacks M_init=Roots \<and> length M_init=length \<acute>M \<guillemotright>"
  
-  Proper :: "gar_coll_state \<Rightarrow> bool"
+definition Proper :: "gar_coll_state \<Rightarrow> bool" where
   "Proper \<equiv> \<guillemotleft> Proper_Roots \<acute>M \<and> Proper_Edges(\<acute>M, \<acute>E) \<and> \<acute>Proper_M_init \<guillemotright>"
 
-  Safe :: "gar_coll_state \<Rightarrow> bool"
+definition Safe :: "gar_coll_state \<Rightarrow> bool" where
   "Safe \<equiv> \<guillemotleft> Reach \<acute>E \<subseteq> Blacks \<acute>M \<guillemotright>"
 
 lemmas collector_defs = Proper_M_init_def Proper_def Safe_def
 
 subsubsection {* Blackening the roots *}
 
-constdefs
-  Blacken_Roots :: " gar_coll_state ann_com"
+definition Blacken_Roots :: " gar_coll_state ann_com" where
   "Blacken_Roots \<equiv> 
   .{\<acute>Proper}.
   \<acute>ind:=0;;
@@ -133,13 +129,11 @@
 
 subsubsection {* Propagating black *}
 
-constdefs
-  PBInv :: "gar_coll_state \<Rightarrow> nat \<Rightarrow> bool"
+definition PBInv :: "gar_coll_state \<Rightarrow> nat \<Rightarrow> bool" where
   "PBInv \<equiv> \<guillemotleft> \<lambda>ind. \<acute>obc < Blacks \<acute>M \<or> (\<forall>i <ind. \<not>BtoW (\<acute>E!i, \<acute>M) \<or>
    (\<not>\<acute>z \<and> i=R \<and> (snd(\<acute>E!R)) = T \<and> (\<exists>r. ind \<le> r \<and> r < length \<acute>E \<and> BtoW(\<acute>E!r,\<acute>M))))\<guillemotright>"
 
-constdefs  
-  Propagate_Black_aux :: "gar_coll_state ann_com"
+definition Propagate_Black_aux :: "gar_coll_state ann_com" where
   "Propagate_Black_aux \<equiv>
   .{\<acute>Proper \<and> Roots\<subseteq>Blacks \<acute>M \<and> \<acute>obc\<subseteq>Blacks \<acute>M \<and> \<acute>bc\<subseteq>Blacks \<acute>M}.
   \<acute>ind:=0;;
@@ -214,14 +208,12 @@
 
 subsubsection {* Refining propagating black *}
 
-constdefs
-  Auxk :: "gar_coll_state \<Rightarrow> bool"
+definition Auxk :: "gar_coll_state \<Rightarrow> bool" where
   "Auxk \<equiv> \<guillemotleft>\<acute>k<length \<acute>M \<and> (\<acute>M!\<acute>k\<noteq>Black \<or> \<not>BtoW(\<acute>E!\<acute>ind, \<acute>M) \<or> 
           \<acute>obc<Blacks \<acute>M \<or> (\<not>\<acute>z \<and> \<acute>ind=R \<and> snd(\<acute>E!R)=T  
           \<and> (\<exists>r. \<acute>ind<r \<and> r<length \<acute>E \<and> BtoW(\<acute>E!r, \<acute>M))))\<guillemotright>"
 
-constdefs  
-  Propagate_Black :: " gar_coll_state ann_com"
+definition Propagate_Black :: " gar_coll_state ann_com" where
   "Propagate_Black \<equiv>
   .{\<acute>Proper \<and> Roots\<subseteq>Blacks \<acute>M \<and> \<acute>obc\<subseteq>Blacks \<acute>M \<and> \<acute>bc\<subseteq>Blacks \<acute>M}.
   \<acute>ind:=0;;
@@ -328,12 +320,10 @@
 
 subsubsection {* Counting black nodes *}
 
-constdefs
-  CountInv :: "gar_coll_state \<Rightarrow> nat \<Rightarrow> bool"
+definition CountInv :: "gar_coll_state \<Rightarrow> nat \<Rightarrow> bool" where
   "CountInv \<equiv> \<guillemotleft> \<lambda>ind. {i. i<ind \<and> \<acute>Ma!i=Black}\<subseteq>\<acute>bc \<guillemotright>"
 
-constdefs
-  Count :: " gar_coll_state ann_com"
+definition Count :: " gar_coll_state ann_com" where
   "Count \<equiv>
   .{\<acute>Proper \<and> Roots\<subseteq>Blacks \<acute>M 
     \<and> \<acute>obc\<subseteq>Blacks \<acute>Ma \<and> Blacks \<acute>Ma\<subseteq>Blacks \<acute>M \<and> \<acute>bc\<subseteq>Blacks \<acute>M 
@@ -398,12 +388,10 @@
   Append_to_free2: "i \<notin> Reach e 
      \<Longrightarrow> n \<in> Reach (Append_to_free(i, e)) = ( n = i \<or> n \<in> Reach e)"
 
-constdefs
-  AppendInv :: "gar_coll_state \<Rightarrow> nat \<Rightarrow> bool"
+definition AppendInv :: "gar_coll_state \<Rightarrow> nat \<Rightarrow> bool" where
   "AppendInv \<equiv> \<guillemotleft>\<lambda>ind. \<forall>i<length \<acute>M. ind\<le>i \<longrightarrow> i\<in>Reach \<acute>E \<longrightarrow> \<acute>M!i=Black\<guillemotright>"
 
-constdefs
-  Append :: " gar_coll_state ann_com"
+definition Append :: " gar_coll_state ann_com" where
    "Append \<equiv>
   .{\<acute>Proper \<and> Roots\<subseteq>Blacks \<acute>M \<and> \<acute>Safe}.
   \<acute>ind:=0;;
@@ -444,8 +432,7 @@
 
 subsubsection {* Correctness of the Collector *}
 
-constdefs 
-  Collector :: " gar_coll_state ann_com"
+definition Collector :: " gar_coll_state ann_com" where
   "Collector \<equiv>
 .{\<acute>Proper}.  
  WHILE True INV .{\<acute>Proper}. 
--- a/src/HOL/Hoare_Parallel/Graph.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare_Parallel/Graph.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -13,20 +13,19 @@
 
 consts Roots :: "nat set"
 
-constdefs
-  Proper_Roots :: "nodes \<Rightarrow> bool"
+definition Proper_Roots :: "nodes \<Rightarrow> bool" where
   "Proper_Roots M \<equiv> Roots\<noteq>{} \<and> Roots \<subseteq> {i. i<length M}"
 
-  Proper_Edges :: "(nodes \<times> edges) \<Rightarrow> bool"
+definition Proper_Edges :: "(nodes \<times> edges) \<Rightarrow> bool" where
   "Proper_Edges \<equiv> (\<lambda>(M,E). \<forall>i<length E. fst(E!i)<length M \<and> snd(E!i)<length M)"
 
-  BtoW :: "(edge \<times> nodes) \<Rightarrow> bool"
+definition BtoW :: "(edge \<times> nodes) \<Rightarrow> bool" where
   "BtoW \<equiv> (\<lambda>(e,M). (M!fst e)=Black \<and> (M!snd e)\<noteq>Black)"
 
-  Blacks :: "nodes \<Rightarrow> nat set"
+definition Blacks :: "nodes \<Rightarrow> nat set" where
   "Blacks M \<equiv> {i. i<length M \<and> M!i=Black}"
 
-  Reach :: "edges \<Rightarrow> nat set"
+definition Reach :: "edges \<Rightarrow> nat set" where
   "Reach E \<equiv> {x. (\<exists>path. 1<length path \<and> path!(length path - 1)\<in>Roots \<and> x=path!0
               \<and> (\<forall>i<length path - 1. (\<exists>j<length E. E!j=(path!(i+1), path!i))))
               \<or> x\<in>Roots}"
--- a/src/HOL/Hoare_Parallel/Mul_Gar_Coll.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare_Parallel/Mul_Gar_Coll.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -26,24 +26,23 @@
 
 subsection {* The Mutators *}
 
-constdefs 
-  Mul_mut_init :: "mul_gar_coll_state \<Rightarrow> nat \<Rightarrow> bool"
+definition Mul_mut_init :: "mul_gar_coll_state \<Rightarrow> nat \<Rightarrow> bool" where
   "Mul_mut_init \<equiv> \<guillemotleft> \<lambda>n. n=length \<acute>Muts \<and> (\<forall>i<n. R (\<acute>Muts!i)<length \<acute>E 
                           \<and> T (\<acute>Muts!i)<length \<acute>M) \<guillemotright>"
 
-  Mul_Redirect_Edge  :: "nat \<Rightarrow> nat \<Rightarrow> mul_gar_coll_state ann_com"
+definition Mul_Redirect_Edge  :: "nat \<Rightarrow> nat \<Rightarrow> mul_gar_coll_state ann_com" where
   "Mul_Redirect_Edge j n \<equiv>
   .{\<acute>Mul_mut_init n \<and> Z (\<acute>Muts!j)}.
   \<langle>IF T(\<acute>Muts!j) \<in> Reach \<acute>E THEN  
   \<acute>E:= \<acute>E[R (\<acute>Muts!j):= (fst (\<acute>E!R(\<acute>Muts!j)), T (\<acute>Muts!j))] FI,, 
   \<acute>Muts:= \<acute>Muts[j:= (\<acute>Muts!j) \<lparr>Z:=False\<rparr>]\<rangle>"
 
-  Mul_Color_Target :: "nat \<Rightarrow> nat \<Rightarrow> mul_gar_coll_state ann_com"
+definition Mul_Color_Target :: "nat \<Rightarrow> nat \<Rightarrow> mul_gar_coll_state ann_com" where
   "Mul_Color_Target j n \<equiv>
   .{\<acute>Mul_mut_init n \<and> \<not> Z (\<acute>Muts!j)}. 
   \<langle>\<acute>M:=\<acute>M[T (\<acute>Muts!j):=Black],, \<acute>Muts:=\<acute>Muts[j:= (\<acute>Muts!j) \<lparr>Z:=True\<rparr>]\<rangle>"
 
-  Mul_Mutator :: "nat \<Rightarrow> nat \<Rightarrow>  mul_gar_coll_state ann_com"
+definition Mul_Mutator :: "nat \<Rightarrow> nat \<Rightarrow>  mul_gar_coll_state ann_com" where
   "Mul_Mutator j n \<equiv>
   .{\<acute>Mul_mut_init n \<and> Z (\<acute>Muts!j)}.  
   WHILE True  
@@ -156,28 +155,25 @@
 
 subsection {* The Collector *}
 
-constdefs
-  Queue :: "mul_gar_coll_state \<Rightarrow> nat"
+definition Queue :: "mul_gar_coll_state \<Rightarrow> nat" where
  "Queue \<equiv> \<guillemotleft> length (filter (\<lambda>i. \<not> Z i \<and> \<acute>M!(T i) \<noteq> Black) \<acute>Muts) \<guillemotright>"
 
 consts  M_init :: nodes
 
-constdefs
-  Proper_M_init :: "mul_gar_coll_state \<Rightarrow> bool"
+definition Proper_M_init :: "mul_gar_coll_state \<Rightarrow> bool" where
   "Proper_M_init \<equiv> \<guillemotleft> Blacks M_init=Roots \<and> length M_init=length \<acute>M \<guillemotright>"
 
-  Mul_Proper :: "mul_gar_coll_state \<Rightarrow> nat \<Rightarrow> bool"
+definition Mul_Proper :: "mul_gar_coll_state \<Rightarrow> nat \<Rightarrow> bool" where
   "Mul_Proper \<equiv> \<guillemotleft> \<lambda>n. Proper_Roots \<acute>M \<and> Proper_Edges (\<acute>M, \<acute>E) \<and> \<acute>Proper_M_init \<and> n=length \<acute>Muts \<guillemotright>"
 
-  Safe :: "mul_gar_coll_state \<Rightarrow> bool"
+definition Safe :: "mul_gar_coll_state \<Rightarrow> bool" where
   "Safe \<equiv> \<guillemotleft> Reach \<acute>E \<subseteq> Blacks \<acute>M \<guillemotright>"
 
 lemmas mul_collector_defs = Proper_M_init_def Mul_Proper_def Safe_def
 
 subsubsection {* Blackening Roots *}
 
-constdefs
-  Mul_Blacken_Roots :: "nat \<Rightarrow>  mul_gar_coll_state ann_com"
+definition Mul_Blacken_Roots :: "nat \<Rightarrow>  mul_gar_coll_state ann_com" where
   "Mul_Blacken_Roots n \<equiv>
   .{\<acute>Mul_Proper n}.
   \<acute>ind:=0;;
@@ -208,16 +204,14 @@
 
 subsubsection {* Propagating Black *} 
 
-constdefs
-  Mul_PBInv :: "mul_gar_coll_state \<Rightarrow> bool"
+definition Mul_PBInv :: "mul_gar_coll_state \<Rightarrow> bool" where
   "Mul_PBInv \<equiv>  \<guillemotleft>\<acute>Safe \<or> \<acute>obc\<subset>Blacks \<acute>M \<or> \<acute>l<\<acute>Queue 
                  \<or> (\<forall>i<\<acute>ind. \<not>BtoW(\<acute>E!i,\<acute>M)) \<and> \<acute>l\<le>\<acute>Queue\<guillemotright>"
 
-  Mul_Auxk :: "mul_gar_coll_state \<Rightarrow> bool"
+definition Mul_Auxk :: "mul_gar_coll_state \<Rightarrow> bool" where
   "Mul_Auxk \<equiv> \<guillemotleft>\<acute>l<\<acute>Queue \<or> \<acute>M!\<acute>k\<noteq>Black \<or> \<not>BtoW(\<acute>E!\<acute>ind, \<acute>M) \<or> \<acute>obc\<subset>Blacks \<acute>M\<guillemotright>"
 
-constdefs
-  Mul_Propagate_Black :: "nat \<Rightarrow>  mul_gar_coll_state ann_com"
+definition Mul_Propagate_Black :: "nat \<Rightarrow>  mul_gar_coll_state ann_com" where
   "Mul_Propagate_Black n \<equiv>
  .{\<acute>Mul_Proper n \<and> Roots\<subseteq>Blacks \<acute>M \<and> \<acute>obc\<subseteq>Blacks \<acute>M \<and> \<acute>bc\<subseteq>Blacks \<acute>M 
   \<and> (\<acute>Safe \<or> \<acute>l\<le>\<acute>Queue \<or> \<acute>obc\<subset>Blacks \<acute>M)}. 
@@ -296,11 +290,10 @@
 
 subsubsection {* Counting Black Nodes *}
 
-constdefs
-  Mul_CountInv :: "mul_gar_coll_state \<Rightarrow> nat \<Rightarrow> bool"
- "Mul_CountInv \<equiv> \<guillemotleft> \<lambda>ind. {i. i<ind \<and> \<acute>Ma!i=Black}\<subseteq>\<acute>bc \<guillemotright>"
+definition Mul_CountInv :: "mul_gar_coll_state \<Rightarrow> nat \<Rightarrow> bool" where
+  "Mul_CountInv \<equiv> \<guillemotleft> \<lambda>ind. {i. i<ind \<and> \<acute>Ma!i=Black}\<subseteq>\<acute>bc \<guillemotright>"
 
-  Mul_Count :: "nat \<Rightarrow>  mul_gar_coll_state ann_com"
+definition Mul_Count :: "nat \<Rightarrow>  mul_gar_coll_state ann_com" where
   "Mul_Count n \<equiv> 
   .{\<acute>Mul_Proper n \<and> Roots\<subseteq>Blacks \<acute>M 
     \<and> \<acute>obc\<subseteq>Blacks \<acute>Ma \<and> Blacks \<acute>Ma\<subseteq>Blacks \<acute>M \<and> \<acute>bc\<subseteq>Blacks \<acute>M 
@@ -396,11 +389,10 @@
   Append_to_free2: "i \<notin> Reach e 
            \<Longrightarrow> n \<in> Reach (Append_to_free(i, e)) = ( n = i \<or> n \<in> Reach e)"
 
-constdefs
-  Mul_AppendInv :: "mul_gar_coll_state \<Rightarrow> nat \<Rightarrow> bool"
+definition Mul_AppendInv :: "mul_gar_coll_state \<Rightarrow> nat \<Rightarrow> bool" where
   "Mul_AppendInv \<equiv> \<guillemotleft> \<lambda>ind. (\<forall>i. ind\<le>i \<longrightarrow> i<length \<acute>M \<longrightarrow> i\<in>Reach \<acute>E \<longrightarrow> \<acute>M!i=Black)\<guillemotright>"
 
-  Mul_Append :: "nat \<Rightarrow>  mul_gar_coll_state ann_com"
+definition Mul_Append :: "nat \<Rightarrow>  mul_gar_coll_state ann_com" where
   "Mul_Append n \<equiv> 
   .{\<acute>Mul_Proper n \<and> Roots\<subseteq>Blacks \<acute>M \<and> \<acute>Safe}.
   \<acute>ind:=0;;
@@ -438,8 +430,7 @@
 
 subsubsection {* Collector *}
 
-constdefs 
-  Mul_Collector :: "nat \<Rightarrow>  mul_gar_coll_state ann_com"
+definition Mul_Collector :: "nat \<Rightarrow>  mul_gar_coll_state ann_com" where
   "Mul_Collector n \<equiv>
 .{\<acute>Mul_Proper n}.  
 WHILE True INV .{\<acute>Mul_Proper n}. 
--- a/src/HOL/Hoare_Parallel/OG_Hoare.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare_Parallel/OG_Hoare.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -27,12 +27,12 @@
 consts post :: "'a ann_triple_op \<Rightarrow> 'a assn"
 primrec "post (c, q) = q"
 
-constdefs  interfree_aux :: "('a ann_com_op \<times> 'a assn \<times> 'a ann_com_op) \<Rightarrow> bool"
+definition interfree_aux :: "('a ann_com_op \<times> 'a assn \<times> 'a ann_com_op) \<Rightarrow> bool" where
   "interfree_aux \<equiv> \<lambda>(co, q, co'). co'= None \<or>  
                     (\<forall>(r,a) \<in> atomics (the co'). \<parallel>= (q \<inter> r) a q \<and>
                     (co = None \<or> (\<forall>p \<in> assertions (the co). \<parallel>= (p \<inter> r) a p)))"
 
-constdefs interfree :: "(('a ann_triple_op) list) \<Rightarrow> bool" 
+definition interfree :: "(('a ann_triple_op) list) \<Rightarrow> bool" where 
   "interfree Ts \<equiv> \<forall>i j. i < length Ts \<and> j < length Ts \<and> i \<noteq> j \<longrightarrow> 
                          interfree_aux (com (Ts!i), post (Ts!i), com (Ts!j)) "
 
--- a/src/HOL/Hoare_Parallel/OG_Tactics.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare_Parallel/OG_Tactics.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -171,8 +171,7 @@
   "\<parallel>- (q \<inter> (r \<inter> b)) a q \<Longrightarrow> interfree_aux (None, q, Some (AnnAwait r b a))"
 by(simp add: interfree_aux_def oghoare_sound)
 
-constdefs 
-  interfree_swap :: "('a ann_triple_op * ('a ann_triple_op) list) \<Rightarrow> bool"
+definition interfree_swap :: "('a ann_triple_op * ('a ann_triple_op) list) \<Rightarrow> bool" where
   "interfree_swap == \<lambda>(x, xs). \<forall>y\<in>set xs. interfree_aux (com x, post x, com y)
   \<and> interfree_aux(com y, post y, com x)"
 
@@ -208,7 +207,7 @@
   \<Longrightarrow> interfree (map (\<lambda>k. (c k, Q k)) [a..<b])"
 by(force simp add: interfree_def less_diff_conv)
 
-constdefs map_ann_hoare :: "(('a ann_com_op * 'a assn) list) \<Rightarrow> bool " ("[\<turnstile>] _" [0] 45)
+definition map_ann_hoare :: "(('a ann_com_op * 'a assn) list) \<Rightarrow> bool " ("[\<turnstile>] _" [0] 45) where
   "[\<turnstile>] Ts == (\<forall>i<length Ts. \<exists>c q. Ts!i=(Some c, q) \<and> \<turnstile> c q)"
 
 lemma MapAnnEmpty: "[\<turnstile>] []"
--- a/src/HOL/Hoare_Parallel/OG_Tran.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare_Parallel/OG_Tran.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -7,14 +7,13 @@
   'a ann_com_op = "('a ann_com) option"
   'a ann_triple_op = "('a ann_com_op \<times> 'a assn)"
   
-consts com :: "'a ann_triple_op \<Rightarrow> 'a ann_com_op"
-primrec "com (c, q) = c"
+primrec com :: "'a ann_triple_op \<Rightarrow> 'a ann_com_op" where
+  "com (c, q) = c"
 
-consts post :: "'a ann_triple_op \<Rightarrow> 'a assn"
-primrec "post (c, q) = q"
+primrec post :: "'a ann_triple_op \<Rightarrow> 'a assn" where
+  "post (c, q) = q"
 
-constdefs
-  All_None :: "'a ann_triple_op list \<Rightarrow> bool"
+definition All_None :: "'a ann_triple_op list \<Rightarrow> bool" where
   "All_None Ts \<equiv> \<forall>(c, q) \<in> set Ts. c = None"
 
 subsection {* The Transition Relation *}
@@ -88,26 +87,24 @@
 
 subsection {* Definition of Semantics *}
 
-constdefs
-  ann_sem :: "'a ann_com \<Rightarrow> 'a \<Rightarrow> 'a set"
+definition ann_sem :: "'a ann_com \<Rightarrow> 'a \<Rightarrow> 'a set" where
   "ann_sem c \<equiv> \<lambda>s. {t. (Some c, s) -*\<rightarrow> (None, t)}"
 
-  ann_SEM :: "'a ann_com \<Rightarrow> 'a set \<Rightarrow> 'a set"
+definition ann_SEM :: "'a ann_com \<Rightarrow> 'a set \<Rightarrow> 'a set" where
   "ann_SEM c S \<equiv> \<Union>ann_sem c ` S"  
 
-  sem :: "'a com \<Rightarrow> 'a \<Rightarrow> 'a set"
+definition sem :: "'a com \<Rightarrow> 'a \<Rightarrow> 'a set" where
   "sem c \<equiv> \<lambda>s. {t. \<exists>Ts. (c, s) -P*\<rightarrow> (Parallel Ts, t) \<and> All_None Ts}"
 
-  SEM :: "'a com \<Rightarrow> 'a set \<Rightarrow> 'a set"
+definition SEM :: "'a com \<Rightarrow> 'a set \<Rightarrow> 'a set" where
   "SEM c S \<equiv> \<Union>sem c ` S "
 
 abbreviation Omega :: "'a com"    ("\<Omega>" 63)
   where "\<Omega> \<equiv> While UNIV UNIV (Basic id)"
 
-consts fwhile :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> nat \<Rightarrow> 'a com"
-primrec 
-   "fwhile b c 0 = \<Omega>"
-   "fwhile b c (Suc n) = Cond b (Seq c (fwhile b c n)) (Basic id)"
+primrec fwhile :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> nat \<Rightarrow> 'a com" where
+    "fwhile b c 0 = \<Omega>"
+  | "fwhile b c (Suc n) = Cond b (Seq c (fwhile b c n)) (Basic id)"
 
 subsubsection {* Proofs *}
 
@@ -299,11 +296,10 @@
 
 section {* Validity of Correctness Formulas *}
 
-constdefs 
-  com_validity :: "'a assn \<Rightarrow> 'a com \<Rightarrow> 'a assn \<Rightarrow> bool"  ("(3\<parallel>= _// _//_)" [90,55,90] 50)
+definition com_validity :: "'a assn \<Rightarrow> 'a com \<Rightarrow> 'a assn \<Rightarrow> bool" ("(3\<parallel>= _// _//_)" [90,55,90] 50) where
   "\<parallel>= p c q \<equiv> SEM c p \<subseteq> q"
 
-  ann_com_validity :: "'a ann_com \<Rightarrow> 'a assn \<Rightarrow> bool"   ("\<Turnstile> _ _" [60,90] 45)
+definition ann_com_validity :: "'a ann_com \<Rightarrow> 'a assn \<Rightarrow> bool" ("\<Turnstile> _ _" [60,90] 45) where
   "\<Turnstile> c q \<equiv> ann_SEM c (pre c) \<subseteq> q"
 
 end
\ No newline at end of file
--- a/src/HOL/Hoare_Parallel/RG_Hoare.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare_Parallel/RG_Hoare.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -7,8 +7,7 @@
 declare Un_subset_iff [simp del] le_sup_iff [simp del]
 declare Cons_eq_map_conv [iff]
 
-constdefs
-  stable :: "'a set \<Rightarrow> ('a \<times> 'a) set \<Rightarrow> bool"  
+definition stable :: "'a set \<Rightarrow> ('a \<times> 'a) set \<Rightarrow> bool" where  
   "stable \<equiv> \<lambda>f g. (\<forall>x y. x \<in> f \<longrightarrow> (x, y) \<in> g \<longrightarrow> y \<in> f)" 
 
 inductive
@@ -39,16 +38,19 @@
              \<turnstile> P sat [pre', rely', guar', post'] \<rbrakk>
             \<Longrightarrow> \<turnstile> P sat [pre, rely, guar, post]"
 
-constdefs 
-  Pre :: "'a rgformula \<Rightarrow> 'a set"
+definition Pre :: "'a rgformula \<Rightarrow> 'a set" where
   "Pre x \<equiv> fst(snd x)"
-  Post :: "'a rgformula \<Rightarrow> 'a set"
+
+definition Post :: "'a rgformula \<Rightarrow> 'a set" where
   "Post x \<equiv> snd(snd(snd(snd x)))"
-  Rely :: "'a rgformula \<Rightarrow> ('a \<times> 'a) set"
+
+definition Rely :: "'a rgformula \<Rightarrow> ('a \<times> 'a) set" where
   "Rely x \<equiv> fst(snd(snd x))"
-  Guar :: "'a rgformula \<Rightarrow> ('a \<times> 'a) set"
+
+definition Guar :: "'a rgformula \<Rightarrow> ('a \<times> 'a) set" where
   "Guar x \<equiv> fst(snd(snd(snd x)))"
-  Com :: "'a rgformula \<Rightarrow> 'a com"
+
+definition Com :: "'a rgformula \<Rightarrow> 'a com" where
   "Com x \<equiv> fst x"
 
 subsection {* Proof System for Parallel Programs *}
@@ -1093,8 +1095,7 @@
 
 subsection {* Soundness of the System for Parallel Programs *}
 
-constdefs
-  ParallelCom :: "('a rgformula) list \<Rightarrow> 'a par_com"
+definition ParallelCom :: "('a rgformula) list \<Rightarrow> 'a par_com" where
   "ParallelCom Ps \<equiv> map (Some \<circ> fst) Ps" 
 
 lemma two: 
--- a/src/HOL/Hoare_Parallel/RG_Tran.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Hoare_Parallel/RG_Tran.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -81,8 +81,7 @@
 | CptnEnv: "(P, t)#xs \<in> cptn \<Longrightarrow> (P,s)#(P,t)#xs \<in> cptn"
 | CptnComp: "\<lbrakk>(P,s) -c\<rightarrow> (Q,t); (Q, t)#xs \<in> cptn \<rbrakk> \<Longrightarrow> (P,s)#(Q,t)#xs \<in> cptn"
 
-constdefs
-  cp :: "('a com) option \<Rightarrow> 'a \<Rightarrow> ('a confs) set"
+definition cp :: "('a com) option \<Rightarrow> 'a \<Rightarrow> ('a confs) set" where
   "cp P s \<equiv> {l. l!0=(P,s) \<and> l \<in> cptn}"  
 
 subsubsection {* Parallel computations *}
@@ -95,14 +94,12 @@
 | ParCptnEnv: "(P,t)#xs \<in> par_cptn \<Longrightarrow> (P,s)#(P,t)#xs \<in> par_cptn"
 | ParCptnComp: "\<lbrakk> (P,s) -pc\<rightarrow> (Q,t); (Q,t)#xs \<in> par_cptn \<rbrakk> \<Longrightarrow> (P,s)#(Q,t)#xs \<in> par_cptn"
 
-constdefs
-  par_cp :: "'a par_com \<Rightarrow> 'a \<Rightarrow> ('a par_confs) set"
+definition par_cp :: "'a par_com \<Rightarrow> 'a \<Rightarrow> ('a par_confs) set" where
   "par_cp P s \<equiv> {l. l!0=(P,s) \<and> l \<in> par_cptn}"  
 
 subsection{* Modular Definition of Computation *}
 
-constdefs 
-  lift :: "'a com \<Rightarrow> 'a conf \<Rightarrow> 'a conf"
+definition lift :: "'a com \<Rightarrow> 'a conf \<Rightarrow> 'a conf" where
   "lift Q \<equiv> \<lambda>(P, s). (if P=None then (Some Q,s) else (Some(Seq (the P) Q), s))"
 
 inductive_set cptn_mod :: "('a confs) set"
@@ -380,38 +377,36 @@
 
 types 'a rgformula = "'a com \<times> 'a set \<times> ('a \<times> 'a) set \<times> ('a \<times> 'a) set \<times> 'a set"
 
-constdefs
-  assum :: "('a set \<times> ('a \<times> 'a) set) \<Rightarrow> ('a confs) set"
+definition assum :: "('a set \<times> ('a \<times> 'a) set) \<Rightarrow> ('a confs) set" where
   "assum \<equiv> \<lambda>(pre, rely). {c. snd(c!0) \<in> pre \<and> (\<forall>i. Suc i<length c \<longrightarrow> 
                c!i -e\<rightarrow> c!(Suc i) \<longrightarrow> (snd(c!i), snd(c!Suc i)) \<in> rely)}"
 
-  comm :: "(('a \<times> 'a) set \<times> 'a set) \<Rightarrow> ('a confs) set"
+definition comm :: "(('a \<times> 'a) set \<times> 'a set) \<Rightarrow> ('a confs) set" where
   "comm \<equiv> \<lambda>(guar, post). {c. (\<forall>i. Suc i<length c \<longrightarrow> 
                c!i -c\<rightarrow> c!(Suc i) \<longrightarrow> (snd(c!i), snd(c!Suc i)) \<in> guar) \<and> 
                (fst (last c) = None \<longrightarrow> snd (last c) \<in> post)}"
 
-  com_validity :: "'a com \<Rightarrow> 'a set \<Rightarrow> ('a \<times> 'a) set \<Rightarrow> ('a \<times> 'a) set \<Rightarrow> 'a set \<Rightarrow> bool" 
-                 ("\<Turnstile> _ sat [_, _, _, _]" [60,0,0,0,0] 45)
+definition com_validity :: "'a com \<Rightarrow> 'a set \<Rightarrow> ('a \<times> 'a) set \<Rightarrow> ('a \<times> 'a) set \<Rightarrow> 'a set \<Rightarrow> bool" 
+                 ("\<Turnstile> _ sat [_, _, _, _]" [60,0,0,0,0] 45) where
   "\<Turnstile> P sat [pre, rely, guar, post] \<equiv> 
    \<forall>s. cp (Some P) s \<inter> assum(pre, rely) \<subseteq> comm(guar, post)"
 
 subsection {* Validity for Parallel Programs. *}
 
-constdefs
-  All_None :: "(('a com) option) list \<Rightarrow> bool"
+definition All_None :: "(('a com) option) list \<Rightarrow> bool" where
   "All_None xs \<equiv> \<forall>c\<in>set xs. c=None"
 
-  par_assum :: "('a set \<times> ('a \<times> 'a) set) \<Rightarrow> ('a par_confs) set"
+definition par_assum :: "('a set \<times> ('a \<times> 'a) set) \<Rightarrow> ('a par_confs) set" where
   "par_assum \<equiv> \<lambda>(pre, rely). {c. snd(c!0) \<in> pre \<and> (\<forall>i. Suc i<length c \<longrightarrow> 
              c!i -pe\<rightarrow> c!Suc i \<longrightarrow> (snd(c!i), snd(c!Suc i)) \<in> rely)}"
 
-  par_comm :: "(('a \<times> 'a) set \<times> 'a set) \<Rightarrow> ('a par_confs) set"
+definition par_comm :: "(('a \<times> 'a) set \<times> 'a set) \<Rightarrow> ('a par_confs) set" where
   "par_comm \<equiv> \<lambda>(guar, post). {c. (\<forall>i. Suc i<length c \<longrightarrow>   
         c!i -pc\<rightarrow> c!Suc i \<longrightarrow> (snd(c!i), snd(c!Suc i)) \<in> guar) \<and> 
          (All_None (fst (last c)) \<longrightarrow> snd( last c) \<in> post)}"
 
-  par_com_validity :: "'a  par_com \<Rightarrow> 'a set \<Rightarrow> ('a \<times> 'a) set \<Rightarrow> ('a \<times> 'a) set 
-\<Rightarrow> 'a set \<Rightarrow> bool"  ("\<Turnstile> _ SAT [_, _, _, _]" [60,0,0,0,0] 45)
+definition par_com_validity :: "'a  par_com \<Rightarrow> 'a set \<Rightarrow> ('a \<times> 'a) set \<Rightarrow> ('a \<times> 'a) set 
+\<Rightarrow> 'a set \<Rightarrow> bool"  ("\<Turnstile> _ SAT [_, _, _, _]" [60,0,0,0,0] 45) where
   "\<Turnstile> Ps SAT [pre, rely, guar, post] \<equiv> 
    \<forall>s. par_cp Ps s \<inter> par_assum(pre, rely) \<subseteq> par_comm(guar, post)"
 
@@ -419,23 +414,22 @@
 
 subsubsection {* Definition of the conjoin operator *}
 
-constdefs
-  same_length :: "'a par_confs \<Rightarrow> ('a confs) list \<Rightarrow> bool"
+definition same_length :: "'a par_confs \<Rightarrow> ('a confs) list \<Rightarrow> bool" where
   "same_length c clist \<equiv> (\<forall>i<length clist. length(clist!i)=length c)"
  
-  same_state :: "'a par_confs \<Rightarrow> ('a confs) list \<Rightarrow> bool"
+definition same_state :: "'a par_confs \<Rightarrow> ('a confs) list \<Rightarrow> bool" where
   "same_state c clist \<equiv> (\<forall>i <length clist. \<forall>j<length c. snd(c!j) = snd((clist!i)!j))"
 
-  same_program :: "'a par_confs \<Rightarrow> ('a confs) list \<Rightarrow> bool"
+definition same_program :: "'a par_confs \<Rightarrow> ('a confs) list \<Rightarrow> bool" where
   "same_program c clist \<equiv> (\<forall>j<length c. fst(c!j) = map (\<lambda>x. fst(nth x j)) clist)"
 
-  compat_label :: "'a par_confs \<Rightarrow> ('a confs) list \<Rightarrow> bool"
+definition compat_label :: "'a par_confs \<Rightarrow> ('a confs) list \<Rightarrow> bool" where
   "compat_label c clist \<equiv> (\<forall>j. Suc j<length c \<longrightarrow> 
          (c!j -pc\<rightarrow> c!Suc j \<and> (\<exists>i<length clist. (clist!i)!j -c\<rightarrow> (clist!i)! Suc j \<and> 
                        (\<forall>l<length clist. l\<noteq>i \<longrightarrow> (clist!l)!j -e\<rightarrow> (clist!l)! Suc j))) \<or> 
          (c!j -pe\<rightarrow> c!Suc j \<and> (\<forall>i<length clist. (clist!i)!j -e\<rightarrow> (clist!i)! Suc j)))"
 
-  conjoin :: "'a par_confs \<Rightarrow> ('a confs) list \<Rightarrow> bool"  ("_ \<propto> _" [65,65] 64)
+definition conjoin :: "'a par_confs \<Rightarrow> ('a confs) list \<Rightarrow> bool"  ("_ \<propto> _" [65,65] 64) where
   "c \<propto> clist \<equiv> (same_length c clist) \<and> (same_state c clist) \<and> (same_program c clist) \<and> (compat_label c clist)"
 
 subsubsection {* Some previous lemmas *}
--- a/src/HOL/IOA/Solve.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/IOA/Solve.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -10,9 +10,7 @@
 imports IOA
 begin
 
-constdefs
-
-  is_weak_pmap :: "['c => 'a, ('action,'c)ioa,('action,'a)ioa] => bool"
+definition is_weak_pmap :: "['c => 'a, ('action,'c)ioa,('action,'a)ioa] => bool" where
   "is_weak_pmap f C A ==
    (!s:starts_of(C). f(s):starts_of(A)) &
    (!s t a. reachable C s &
--- a/src/HOL/Import/HOL/HOL4Base.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Import/HOL/HOL4Base.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -4,22 +4,19 @@
 
 ;setup_theory bool
 
-constdefs
-  ARB :: "'a" 
+definition ARB :: "'a" where 
   "ARB == SOME x::'a::type. True"
 
 lemma ARB_DEF: "ARB = (SOME x::'a::type. True)"
   by (import bool ARB_DEF)
 
-constdefs
-  IN :: "'a => ('a => bool) => bool" 
+definition IN :: "'a => ('a => bool) => bool" where 
   "IN == %(x::'a::type) f::'a::type => bool. f x"
 
 lemma IN_DEF: "IN = (%(x::'a::type) f::'a::type => bool. f x)"
   by (import bool IN_DEF)
 
-constdefs
-  RES_FORALL :: "('a => bool) => ('a => bool) => bool" 
+definition RES_FORALL :: "('a => bool) => ('a => bool) => bool" where 
   "RES_FORALL ==
 %(p::'a::type => bool) m::'a::type => bool. ALL x::'a::type. IN x p --> m x"
 
@@ -28,8 +25,7 @@
     ALL x::'a::type. IN x p --> m x)"
   by (import bool RES_FORALL_DEF)
 
-constdefs
-  RES_EXISTS :: "('a => bool) => ('a => bool) => bool" 
+definition RES_EXISTS :: "('a => bool) => ('a => bool) => bool" where 
   "RES_EXISTS ==
 %(p::'a::type => bool) m::'a::type => bool. EX x::'a::type. IN x p & m x"
 
@@ -37,8 +33,7 @@
 (%(p::'a::type => bool) m::'a::type => bool. EX x::'a::type. IN x p & m x)"
   by (import bool RES_EXISTS_DEF)
 
-constdefs
-  RES_EXISTS_UNIQUE :: "('a => bool) => ('a => bool) => bool" 
+definition RES_EXISTS_UNIQUE :: "('a => bool) => ('a => bool) => bool" where 
   "RES_EXISTS_UNIQUE ==
 %(p::'a::type => bool) m::'a::type => bool.
    RES_EXISTS p m &
@@ -52,8 +47,7 @@
      (%x::'a::type. RES_FORALL p (%y::'a::type. m x & m y --> x = y)))"
   by (import bool RES_EXISTS_UNIQUE_DEF)
 
-constdefs
-  RES_SELECT :: "('a => bool) => ('a => bool) => 'a" 
+definition RES_SELECT :: "('a => bool) => ('a => bool) => 'a" where 
   "RES_SELECT ==
 %(p::'a::type => bool) m::'a::type => bool. SOME x::'a::type. IN x p & m x"
 
@@ -264,15 +258,13 @@
 
 ;setup_theory combin
 
-constdefs
-  K :: "'a => 'b => 'a" 
+definition K :: "'a => 'b => 'a" where 
   "K == %(x::'a::type) y::'b::type. x"
 
 lemma K_DEF: "K = (%(x::'a::type) y::'b::type. x)"
   by (import combin K_DEF)
 
-constdefs
-  S :: "('a => 'b => 'c) => ('a => 'b) => 'a => 'c" 
+definition S :: "('a => 'b => 'c) => ('a => 'b) => 'a => 'c" where 
   "S ==
 %(f::'a::type => 'b::type => 'c::type) (g::'a::type => 'b::type)
    x::'a::type. f x (g x)"
@@ -282,8 +274,7 @@
     x::'a::type. f x (g x))"
   by (import combin S_DEF)
 
-constdefs
-  I :: "'a => 'a" 
+definition I :: "'a => 'a" where 
   "(op ==::('a::type => 'a::type) => ('a::type => 'a::type) => prop)
  (I::'a::type => 'a::type)
  ((S::('a::type => ('a::type => 'a::type) => 'a::type)
@@ -299,16 +290,14 @@
    (K::'a::type => 'a::type => 'a::type))"
   by (import combin I_DEF)
 
-constdefs
-  C :: "('a => 'b => 'c) => 'b => 'a => 'c" 
+definition C :: "('a => 'b => 'c) => 'b => 'a => 'c" where 
   "C == %(f::'a::type => 'b::type => 'c::type) (x::'b::type) y::'a::type. f y x"
 
 lemma C_DEF: "C =
 (%(f::'a::type => 'b::type => 'c::type) (x::'b::type) y::'a::type. f y x)"
   by (import combin C_DEF)
 
-constdefs
-  W :: "('a => 'a => 'b) => 'a => 'b" 
+definition W :: "('a => 'a => 'b) => 'a => 'b" where 
   "W == %(f::'a::type => 'a::type => 'b::type) x::'a::type. f x x"
 
 lemma W_DEF: "W = (%(f::'a::type => 'a::type => 'b::type) x::'a::type. f x x)"
@@ -582,8 +571,7 @@
 
 ;setup_theory relation
 
-constdefs
-  TC :: "('a => 'a => bool) => 'a => 'a => bool" 
+definition TC :: "('a => 'a => bool) => 'a => 'a => bool" where 
   "TC ==
 %(R::'a::type => 'a::type => bool) (a::'a::type) b::'a::type.
    ALL P::'a::type => 'a::type => bool.
@@ -601,8 +589,7 @@
        P a b)"
   by (import relation TC_DEF)
 
-constdefs
-  RTC :: "('a => 'a => bool) => 'a => 'a => bool" 
+definition RTC :: "('a => 'a => bool) => 'a => 'a => bool" where 
   "RTC ==
 %(R::'a::type => 'a::type => bool) (a::'a::type) b::'a::type.
    ALL P::'a::type => 'a::type => bool.
@@ -644,8 +631,7 @@
    (ALL (x::'a::type) (y::'a::type) z::'a::type. R x y & R y z --> R x z)"
   by (import relation transitive_def)
 
-constdefs
-  pred_reflexive :: "('a => 'a => bool) => bool" 
+definition pred_reflexive :: "('a => 'a => bool) => bool" where 
   "pred_reflexive == %R::'a::type => 'a::type => bool. ALL x::'a::type. R x x"
 
 lemma reflexive_def: "ALL R::'a::type => 'a::type => bool.
@@ -788,8 +774,7 @@
    (ALL (x::'a::type) y::'a::type. RTC R x y --> RTC Q x y)"
   by (import relation RTC_MONOTONE)
 
-constdefs
-  WF :: "('a => 'a => bool) => bool" 
+definition WF :: "('a => 'a => bool) => bool" where 
   "WF ==
 %R::'a::type => 'a::type => bool.
    ALL B::'a::type => bool.
@@ -814,8 +799,7 @@
    WF x --> x xa xb --> xa ~= xb"
   by (import relation WF_NOT_REFL)
 
-constdefs
-  EMPTY_REL :: "'a => 'a => bool" 
+definition EMPTY_REL :: "'a => 'a => bool" where 
   "EMPTY_REL == %(x::'a::type) y::'a::type. False"
 
 lemma EMPTY_REL_DEF: "ALL (x::'a::type) y::'a::type. EMPTY_REL x y = False"
@@ -847,8 +831,7 @@
    WF R --> WF (relation.inv_image R f)"
   by (import relation WF_inv_image)
 
-constdefs
-  RESTRICT :: "('a => 'b) => ('a => 'a => bool) => 'a => 'a => 'b" 
+definition RESTRICT :: "('a => 'b) => ('a => 'a => bool) => 'a => 'a => 'b" where 
   "RESTRICT ==
 %(f::'a::type => 'b::type) (R::'a::type => 'a::type => bool) (x::'a::type)
    y::'a::type. if R y x then f y else ARB"
@@ -891,8 +874,7 @@
    the_fun R M x = Eps (approx R M x)"
   by (import relation the_fun_def)
 
-constdefs
-  WFREC :: "('a => 'a => bool) => (('a => 'b) => 'a => 'b) => 'a => 'b" 
+definition WFREC :: "('a => 'a => bool) => (('a => 'b) => 'a => 'b) => 'a => 'b" where 
   "WFREC ==
 %(R::'a::type => 'a::type => bool)
    (M::('a::type => 'b::type) => 'a::type => 'b::type) x::'a::type.
@@ -1052,8 +1034,7 @@
    split xb x = split f' xa"
   by (import pair pair_case_cong)
 
-constdefs
-  LEX :: "('a => 'a => bool) => ('b => 'b => bool) => 'a * 'b => 'a * 'b => bool" 
+definition LEX :: "('a => 'a => bool) => ('b => 'b => bool) => 'a * 'b => 'a * 'b => bool" where 
   "LEX ==
 %(R1::'a::type => 'a::type => bool) (R2::'b::type => 'b::type => bool)
    (s::'a::type, t::'b::type) (u::'a::type, v::'b::type).
@@ -1069,8 +1050,7 @@
    WF x & WF xa --> WF (LEX x xa)"
   by (import pair WF_LEX)
 
-constdefs
-  RPROD :: "('a => 'a => bool) => ('b => 'b => bool) => 'a * 'b => 'a * 'b => bool" 
+definition RPROD :: "('a => 'a => bool) => ('b => 'b => bool) => 'a * 'b => 'a * 'b => bool" where 
   "RPROD ==
 %(R1::'a::type => 'a::type => bool) (R2::'b::type => 'b::type => bool)
    (s::'a::type, t::'b::type) (u::'a::type, v::'b::type). R1 s u & R2 t v"
@@ -1113,8 +1093,7 @@
 lemma NOT_LESS_EQ: "ALL (m::nat) n::nat. m = n --> ~ m < n"
   by (import prim_rec NOT_LESS_EQ)
 
-constdefs
-  SIMP_REC_REL :: "(nat => 'a) => 'a => ('a => 'a) => nat => bool" 
+definition SIMP_REC_REL :: "(nat => 'a) => 'a => ('a => 'a) => nat => bool" where 
   "(op ==::((nat => 'a::type)
          => 'a::type => ('a::type => 'a::type) => nat => bool)
         => ((nat => 'a::type)
@@ -1187,8 +1166,7 @@
    (ALL m::nat. SIMP_REC x f (Suc m) = f (SIMP_REC x f m))"
   by (import prim_rec SIMP_REC_THM)
 
-constdefs
-  PRE :: "nat => nat" 
+definition PRE :: "nat => nat" where 
   "PRE == %m::nat. if m = 0 then 0 else SOME n::nat. m = Suc n"
 
 lemma PRE_DEF: "ALL m::nat. PRE m = (if m = 0 then 0 else SOME n::nat. m = Suc n)"
@@ -1197,8 +1175,7 @@
 lemma PRE: "PRE 0 = 0 & (ALL m::nat. PRE (Suc m) = m)"
   by (import prim_rec PRE)
 
-constdefs
-  PRIM_REC_FUN :: "'a => ('a => nat => 'a) => nat => nat => 'a" 
+definition PRIM_REC_FUN :: "'a => ('a => nat => 'a) => nat => nat => 'a" where 
   "PRIM_REC_FUN ==
 %(x::'a::type) f::'a::type => nat => 'a::type.
    SIMP_REC (%n::nat. x) (%(fun::nat => 'a::type) n::nat. f (fun (PRE n)) n)"
@@ -1214,8 +1191,7 @@
        PRIM_REC_FUN x f (Suc m) n = f (PRIM_REC_FUN x f m (PRE n)) n)"
   by (import prim_rec PRIM_REC_EQN)
 
-constdefs
-  PRIM_REC :: "'a => ('a => nat => 'a) => nat => 'a" 
+definition PRIM_REC :: "'a => ('a => nat => 'a) => nat => 'a" where 
   "PRIM_REC ==
 %(x::'a::type) (f::'a::type => nat => 'a::type) m::nat.
    PRIM_REC_FUN x f m (PRE m)"
@@ -1286,8 +1262,7 @@
 
 ;setup_theory arithmetic
 
-constdefs
-  nat_elim__magic :: "nat => nat" 
+definition nat_elim__magic :: "nat => nat" where 
   "nat_elim__magic == %n::nat. n"
 
 lemma nat_elim__magic: "ALL n::nat. nat_elim__magic n = n"
@@ -1746,22 +1721,19 @@
 
 ;setup_theory hrat
 
-constdefs
-  trat_1 :: "nat * nat" 
+definition trat_1 :: "nat * nat" where 
   "trat_1 == (0, 0)"
 
 lemma trat_1: "trat_1 = (0, 0)"
   by (import hrat trat_1)
 
-constdefs
-  trat_inv :: "nat * nat => nat * nat" 
+definition trat_inv :: "nat * nat => nat * nat" where 
   "trat_inv == %(x::nat, y::nat). (y, x)"
 
 lemma trat_inv: "ALL (x::nat) y::nat. trat_inv (x, y) = (y, x)"
   by (import hrat trat_inv)
 
-constdefs
-  trat_add :: "nat * nat => nat * nat => nat * nat" 
+definition trat_add :: "nat * nat => nat * nat => nat * nat" where 
   "trat_add ==
 %(x::nat, y::nat) (x'::nat, y'::nat).
    (PRE (Suc x * Suc y' + Suc x' * Suc y), PRE (Suc y * Suc y'))"
@@ -1771,8 +1743,7 @@
    (PRE (Suc x * Suc y' + Suc x' * Suc y), PRE (Suc y * Suc y'))"
   by (import hrat trat_add)
 
-constdefs
-  trat_mul :: "nat * nat => nat * nat => nat * nat" 
+definition trat_mul :: "nat * nat => nat * nat => nat * nat" where 
   "trat_mul ==
 %(x::nat, y::nat) (x'::nat, y'::nat).
    (PRE (Suc x * Suc x'), PRE (Suc y * Suc y'))"
@@ -1788,8 +1759,7 @@
 (ALL n::nat. trat_sucint (Suc n) = trat_add (trat_sucint n) trat_1)"
   by (import hrat trat_sucint)
 
-constdefs
-  trat_eq :: "nat * nat => nat * nat => bool" 
+definition trat_eq :: "nat * nat => nat * nat => bool" where 
   "trat_eq ==
 %(x::nat, y::nat) (x'::nat, y'::nat). Suc x * Suc y' = Suc x' * Suc y"
 
@@ -1901,23 +1871,20 @@
     (EX x::nat * nat. r = trat_eq x) = (dest_hrat (mk_hrat r) = r))"
   by (import hrat hrat_tybij)
 
-constdefs
-  hrat_1 :: "hrat" 
+definition hrat_1 :: "hrat" where 
   "hrat_1 == mk_hrat (trat_eq trat_1)"
 
 lemma hrat_1: "hrat_1 = mk_hrat (trat_eq trat_1)"
   by (import hrat hrat_1)
 
-constdefs
-  hrat_inv :: "hrat => hrat" 
+definition hrat_inv :: "hrat => hrat" where 
   "hrat_inv == %T1::hrat. mk_hrat (trat_eq (trat_inv (Eps (dest_hrat T1))))"
 
 lemma hrat_inv: "ALL T1::hrat.
    hrat_inv T1 = mk_hrat (trat_eq (trat_inv (Eps (dest_hrat T1))))"
   by (import hrat hrat_inv)
 
-constdefs
-  hrat_add :: "hrat => hrat => hrat" 
+definition hrat_add :: "hrat => hrat => hrat" where 
   "hrat_add ==
 %(T1::hrat) T2::hrat.
    mk_hrat (trat_eq (trat_add (Eps (dest_hrat T1)) (Eps (dest_hrat T2))))"
@@ -1927,8 +1894,7 @@
    mk_hrat (trat_eq (trat_add (Eps (dest_hrat T1)) (Eps (dest_hrat T2))))"
   by (import hrat hrat_add)
 
-constdefs
-  hrat_mul :: "hrat => hrat => hrat" 
+definition hrat_mul :: "hrat => hrat => hrat" where 
   "hrat_mul ==
 %(T1::hrat) T2::hrat.
    mk_hrat (trat_eq (trat_mul (Eps (dest_hrat T1)) (Eps (dest_hrat T2))))"
@@ -1938,8 +1904,7 @@
    mk_hrat (trat_eq (trat_mul (Eps (dest_hrat T1)) (Eps (dest_hrat T2))))"
   by (import hrat hrat_mul)
 
-constdefs
-  hrat_sucint :: "nat => hrat" 
+definition hrat_sucint :: "nat => hrat" where 
   "hrat_sucint == %T1::nat. mk_hrat (trat_eq (trat_sucint T1))"
 
 lemma hrat_sucint: "ALL T1::nat. hrat_sucint T1 = mk_hrat (trat_eq (trat_sucint T1))"
@@ -1987,8 +1952,7 @@
 
 ;setup_theory hreal
 
-constdefs
-  hrat_lt :: "hrat => hrat => bool" 
+definition hrat_lt :: "hrat => hrat => bool" where 
   "hrat_lt == %(x::hrat) y::hrat. EX d::hrat. y = hrat_add x d"
 
 lemma hrat_lt: "ALL (x::hrat) y::hrat. hrat_lt x y = (EX d::hrat. y = hrat_add x d)"
@@ -2096,8 +2060,7 @@
    hrat_lt x y --> (EX xa::hrat. hrat_lt x xa & hrat_lt xa y)"
   by (import hreal HRAT_MEAN)
 
-constdefs
-  isacut :: "(hrat => bool) => bool" 
+definition isacut :: "(hrat => bool) => bool" where 
   "isacut ==
 %C::hrat => bool.
    Ex C &
@@ -2113,8 +2076,7 @@
     (ALL x::hrat. C x --> (EX y::hrat. C y & hrat_lt x y)))"
   by (import hreal isacut)
 
-constdefs
-  cut_of_hrat :: "hrat => hrat => bool" 
+definition cut_of_hrat :: "hrat => hrat => bool" where 
   "cut_of_hrat == %(x::hrat) y::hrat. hrat_lt y x"
 
 lemma cut_of_hrat: "ALL x::hrat. cut_of_hrat x = (%y::hrat. hrat_lt y x)"
@@ -2173,15 +2135,13 @@
    (EX x::hrat. hreal.cut X x & ~ hreal.cut X (hrat_mul u x))"
   by (import hreal CUT_NEARTOP_MUL)
 
-constdefs
-  hreal_1 :: "hreal" 
+definition hreal_1 :: "hreal" where 
   "hreal_1 == hreal (cut_of_hrat hrat_1)"
 
 lemma hreal_1: "hreal_1 = hreal (cut_of_hrat hrat_1)"
   by (import hreal hreal_1)
 
-constdefs
-  hreal_add :: "hreal => hreal => hreal" 
+definition hreal_add :: "hreal => hreal => hreal" where 
   "hreal_add ==
 %(X::hreal) Y::hreal.
    hreal
@@ -2197,8 +2157,7 @@
            w = hrat_add x y & hreal.cut X x & hreal.cut Y y)"
   by (import hreal hreal_add)
 
-constdefs
-  hreal_mul :: "hreal => hreal => hreal" 
+definition hreal_mul :: "hreal => hreal => hreal" where 
   "hreal_mul ==
 %(X::hreal) Y::hreal.
    hreal
@@ -2214,8 +2173,7 @@
            w = hrat_mul x y & hreal.cut X x & hreal.cut Y y)"
   by (import hreal hreal_mul)
 
-constdefs
-  hreal_inv :: "hreal => hreal" 
+definition hreal_inv :: "hreal => hreal" where 
   "hreal_inv ==
 %X::hreal.
    hreal
@@ -2233,8 +2191,7 @@
            (ALL x::hrat. hreal.cut X x --> hrat_lt (hrat_mul w x) d))"
   by (import hreal hreal_inv)
 
-constdefs
-  hreal_sup :: "(hreal => bool) => hreal" 
+definition hreal_sup :: "(hreal => bool) => hreal" where 
   "hreal_sup ==
 %P::hreal => bool. hreal (%w::hrat. EX X::hreal. P X & hreal.cut X w)"
 
@@ -2242,8 +2199,7 @@
    hreal_sup P = hreal (%w::hrat. EX X::hreal. P X & hreal.cut X w)"
   by (import hreal hreal_sup)
 
-constdefs
-  hreal_lt :: "hreal => hreal => bool" 
+definition hreal_lt :: "hreal => hreal => bool" where 
   "hreal_lt ==
 %(X::hreal) Y::hreal.
    X ~= Y & (ALL x::hrat. hreal.cut X x --> hreal.cut Y x)"
@@ -2301,8 +2257,7 @@
 lemma HREAL_NOZERO: "ALL (X::hreal) Y::hreal. hreal_add X Y ~= X"
   by (import hreal HREAL_NOZERO)
 
-constdefs
-  hreal_sub :: "hreal => hreal => hreal" 
+definition hreal_sub :: "hreal => hreal => hreal" where 
   "hreal_sub ==
 %(Y::hreal) X::hreal.
    hreal
@@ -2358,15 +2313,13 @@
 (ALL x::nat. Suc (NUMERAL_BIT2 x) = NUMERAL_BIT1 (Suc x))"
   by (import numeral numeral_suc)
 
-constdefs
-  iZ :: "nat => nat" 
+definition iZ :: "nat => nat" where 
   "iZ == %x::nat. x"
 
 lemma iZ: "ALL x::nat. iZ x = x"
   by (import numeral iZ)
 
-constdefs
-  iiSUC :: "nat => nat" 
+definition iiSUC :: "nat => nat" where 
   "iiSUC == %n::nat. Suc (Suc n)"
 
 lemma iiSUC: "ALL n::nat. iiSUC n = Suc (Suc n)"
@@ -2699,8 +2652,7 @@
     iBIT_cases (NUMERAL_BIT2 n) zf bf1 bf2 = bf2 n)"
   by (import numeral iBIT_cases)
 
-constdefs
-  iDUB :: "nat => nat" 
+definition iDUB :: "nat => nat" where 
   "iDUB == %x::nat. x + x"
 
 lemma iDUB: "ALL x::nat. iDUB x = x + x"
@@ -2771,8 +2723,7 @@
    NUMERAL_BIT2 x * xa = iDUB (iZ (x * xa + xa))"
   by (import numeral numeral_mult)
 
-constdefs
-  iSQR :: "nat => nat" 
+definition iSQR :: "nat => nat" where 
   "iSQR == %x::nat. x * x"
 
 lemma iSQR: "ALL x::nat. iSQR x = x * x"
@@ -2809,8 +2760,7 @@
        ALL (xa::'A::type) y::'B::type. x (P xa y) = xa & Y (P xa y) = y)"
   by (import ind_type INJ_INVERSE2)
 
-constdefs
-  NUMPAIR :: "nat => nat => nat" 
+definition NUMPAIR :: "nat => nat => nat" where 
   "NUMPAIR == %(x::nat) y::nat. 2 ^ x * (2 * y + 1)"
 
 lemma NUMPAIR: "ALL (x::nat) y::nat. NUMPAIR x y = 2 ^ x * (2 * y + 1)"
@@ -2831,8 +2781,7 @@
 specification (NUMFST NUMSND) NUMPAIR_DEST: "ALL (x::nat) y::nat. NUMFST (NUMPAIR x y) = x & NUMSND (NUMPAIR x y) = y"
   by (import ind_type NUMPAIR_DEST)
 
-constdefs
-  NUMSUM :: "bool => nat => nat" 
+definition NUMSUM :: "bool => nat => nat" where 
   "NUMSUM == %(b::bool) x::nat. if b then Suc (2 * x) else 2 * x"
 
 lemma NUMSUM: "ALL (b::bool) x::nat. NUMSUM b x = (if b then Suc (2 * x) else 2 * x)"
@@ -2849,8 +2798,7 @@
 specification (NUMLEFT NUMRIGHT) NUMSUM_DEST: "ALL (x::bool) y::nat. NUMLEFT (NUMSUM x y) = x & NUMRIGHT (NUMSUM x y) = y"
   by (import ind_type NUMSUM_DEST)
 
-constdefs
-  INJN :: "nat => nat => 'a => bool" 
+definition INJN :: "nat => nat => 'a => bool" where 
   "INJN == %(m::nat) (n::nat) a::'a::type. n = m"
 
 lemma INJN: "ALL m::nat. INJN m = (%(n::nat) a::'a::type. n = m)"
@@ -2859,8 +2807,7 @@
 lemma INJN_INJ: "ALL (n1::nat) n2::nat. (INJN n1 = INJN n2) = (n1 = n2)"
   by (import ind_type INJN_INJ)
 
-constdefs
-  INJA :: "'a => nat => 'a => bool" 
+definition INJA :: "'a => nat => 'a => bool" where 
   "INJA == %(a::'a::type) (n::nat) b::'a::type. b = a"
 
 lemma INJA: "ALL a::'a::type. INJA a = (%(n::nat) b::'a::type. b = a)"
@@ -2869,8 +2816,7 @@
 lemma INJA_INJ: "ALL (a1::'a::type) a2::'a::type. (INJA a1 = INJA a2) = (a1 = a2)"
   by (import ind_type INJA_INJ)
 
-constdefs
-  INJF :: "(nat => nat => 'a => bool) => nat => 'a => bool" 
+definition INJF :: "(nat => nat => 'a => bool) => nat => 'a => bool" where 
   "INJF == %(f::nat => nat => 'a::type => bool) n::nat. f (NUMFST n) (NUMSND n)"
 
 lemma INJF: "ALL f::nat => nat => 'a::type => bool.
@@ -2881,8 +2827,7 @@
    (INJF f1 = INJF f2) = (f1 = f2)"
   by (import ind_type INJF_INJ)
 
-constdefs
-  INJP :: "(nat => 'a => bool) => (nat => 'a => bool) => nat => 'a => bool" 
+definition INJP :: "(nat => 'a => bool) => (nat => 'a => bool) => nat => 'a => bool" where 
   "INJP ==
 %(f1::nat => 'a::type => bool) (f2::nat => 'a::type => bool) (n::nat)
    a::'a::type. if NUMLEFT n then f1 (NUMRIGHT n) a else f2 (NUMRIGHT n) a"
@@ -2898,8 +2843,7 @@
    (INJP f1 f2 = INJP f1' f2') = (f1 = f1' & f2 = f2')"
   by (import ind_type INJP_INJ)
 
-constdefs
-  ZCONSTR :: "nat => 'a => (nat => nat => 'a => bool) => nat => 'a => bool" 
+definition ZCONSTR :: "nat => 'a => (nat => nat => 'a => bool) => nat => 'a => bool" where 
   "ZCONSTR ==
 %(c::nat) (i::'a::type) r::nat => nat => 'a::type => bool.
    INJP (INJN (Suc c)) (INJP (INJA i) (INJF r))"
@@ -2908,8 +2852,7 @@
    ZCONSTR c i r = INJP (INJN (Suc c)) (INJP (INJA i) (INJF r))"
   by (import ind_type ZCONSTR)
 
-constdefs
-  ZBOT :: "nat => 'a => bool" 
+definition ZBOT :: "nat => 'a => bool" where 
   "ZBOT == INJP (INJN 0) (SOME z::nat => 'a::type => bool. True)"
 
 lemma ZBOT: "ZBOT = INJP (INJN 0) (SOME z::nat => 'a::type => bool. True)"
@@ -2919,8 +2862,7 @@
    ZCONSTR x xa xb ~= ZBOT"
   by (import ind_type ZCONSTR_ZBOT)
 
-constdefs
-  ZRECSPACE :: "(nat => 'a => bool) => bool" 
+definition ZRECSPACE :: "(nat => 'a => bool) => bool" where 
   "ZRECSPACE ==
 %a0::nat => 'a::type => bool.
    ALL ZRECSPACE'::(nat => 'a::type => bool) => bool.
@@ -2993,15 +2935,13 @@
 (ALL r::nat => 'a::type => bool. ZRECSPACE r = (dest_rec (mk_rec r) = r))"
   by (import ind_type recspace_repfns)
 
-constdefs
-  BOTTOM :: "'a recspace" 
+definition BOTTOM :: "'a recspace" where 
   "BOTTOM == mk_rec ZBOT"
 
 lemma BOTTOM: "BOTTOM = mk_rec ZBOT"
   by (import ind_type BOTTOM)
 
-constdefs
-  CONSTR :: "nat => 'a => (nat => 'a recspace) => 'a recspace" 
+definition CONSTR :: "nat => 'a => (nat => 'a recspace) => 'a recspace" where 
   "CONSTR ==
 %(c::nat) (i::'a::type) r::nat => 'a::type recspace.
    mk_rec (ZCONSTR c i (%n::nat. dest_rec (r n)))"
@@ -3049,15 +2989,13 @@
 (ALL (a::'a::type) (f::nat => 'a::type) n::nat. FCONS a f (Suc n) = f n)"
   by (import ind_type FCONS)
 
-constdefs
-  FNIL :: "nat => 'a" 
+definition FNIL :: "nat => 'a" where 
   "FNIL == %n::nat. SOME x::'a::type. True"
 
 lemma FNIL: "ALL n::nat. FNIL n = (SOME x::'a::type. True)"
   by (import ind_type FNIL)
 
-constdefs
-  ISO :: "('a => 'b) => ('b => 'a) => bool" 
+definition ISO :: "('a => 'b) => ('b => 'a) => bool" where 
   "ISO ==
 %(f::'a::type => 'b::type) g::'b::type => 'a::type.
    (ALL x::'b::type. f (g x) = x) & (ALL y::'a::type. g (f y) = y)"
@@ -3434,8 +3372,7 @@
    (EX x::'a::type. IN x s & (ALL y::'a::type. IN y s --> M x <= M y))"
   by (import pred_set SET_MINIMUM)
 
-constdefs
-  EMPTY :: "'a => bool" 
+definition EMPTY :: "'a => bool" where 
   "EMPTY == %x::'a::type. False"
 
 lemma EMPTY_DEF: "EMPTY = (%x::'a::type. False)"
@@ -3468,8 +3405,7 @@
 lemma EQ_UNIV: "(ALL x::'a::type. IN x (s::'a::type => bool)) = (s = pred_set.UNIV)"
   by (import pred_set EQ_UNIV)
 
-constdefs
-  SUBSET :: "('a => bool) => ('a => bool) => bool" 
+definition SUBSET :: "('a => bool) => ('a => bool) => bool" where 
   "SUBSET ==
 %(s::'a::type => bool) t::'a::type => bool.
    ALL x::'a::type. IN x s --> IN x t"
@@ -3501,8 +3437,7 @@
 lemma UNIV_SUBSET: "ALL x::'a::type => bool. SUBSET pred_set.UNIV x = (x = pred_set.UNIV)"
   by (import pred_set UNIV_SUBSET)
 
-constdefs
-  PSUBSET :: "('a => bool) => ('a => bool) => bool" 
+definition PSUBSET :: "('a => bool) => ('a => bool) => bool" where 
   "PSUBSET == %(s::'a::type => bool) t::'a::type => bool. SUBSET s t & s ~= t"
 
 lemma PSUBSET_DEF: "ALL (s::'a::type => bool) t::'a::type => bool.
@@ -3640,8 +3575,7 @@
    pred_set.INTER (pred_set.UNION x xa) (pred_set.UNION x xb)"
   by (import pred_set INTER_OVER_UNION)
 
-constdefs
-  DISJOINT :: "('a => bool) => ('a => bool) => bool" 
+definition DISJOINT :: "('a => bool) => ('a => bool) => bool" where 
   "DISJOINT ==
 %(s::'a::type => bool) t::'a::type => bool. pred_set.INTER s t = EMPTY"
 
@@ -3672,8 +3606,7 @@
    DISJOINT u (pred_set.UNION s t) = (DISJOINT s u & DISJOINT t u)"
   by (import pred_set DISJOINT_UNION_BOTH)
 
-constdefs
-  DIFF :: "('a => bool) => ('a => bool) => 'a => bool" 
+definition DIFF :: "('a => bool) => ('a => bool) => 'a => bool" where 
   "DIFF ==
 %(s::'a::type => bool) t::'a::type => bool.
    GSPEC (%x::'a::type. (x, IN x s & ~ IN x t))"
@@ -3702,8 +3635,7 @@
 lemma DIFF_EQ_EMPTY: "ALL x::'a::type => bool. DIFF x x = EMPTY"
   by (import pred_set DIFF_EQ_EMPTY)
 
-constdefs
-  INSERT :: "'a => ('a => bool) => 'a => bool" 
+definition INSERT :: "'a => ('a => bool) => 'a => bool" where 
   "INSERT ==
 %(x::'a::type) s::'a::type => bool.
    GSPEC (%y::'a::type. (y, y = x | IN y s))"
@@ -3778,8 +3710,7 @@
    DIFF (INSERT x s) t = (if IN x t then DIFF s t else INSERT x (DIFF s t))"
   by (import pred_set INSERT_DIFF)
 
-constdefs
-  DELETE :: "('a => bool) => 'a => 'a => bool" 
+definition DELETE :: "('a => bool) => 'a => 'a => bool" where 
   "DELETE == %(s::'a::type => bool) x::'a::type. DIFF s (INSERT x EMPTY)"
 
 lemma DELETE_DEF: "ALL (s::'a::type => bool) x::'a::type. DELETE s x = DIFF s (INSERT x EMPTY)"
@@ -3852,8 +3783,7 @@
 specification (CHOICE) CHOICE_DEF: "ALL x::'a::type => bool. x ~= EMPTY --> IN (CHOICE x) x"
   by (import pred_set CHOICE_DEF)
 
-constdefs
-  REST :: "('a => bool) => 'a => bool" 
+definition REST :: "('a => bool) => 'a => bool" where 
   "REST == %s::'a::type => bool. DELETE s (CHOICE s)"
 
 lemma REST_DEF: "ALL s::'a::type => bool. REST s = DELETE s (CHOICE s)"
@@ -3871,8 +3801,7 @@
 lemma REST_PSUBSET: "ALL x::'a::type => bool. x ~= EMPTY --> PSUBSET (REST x) x"
   by (import pred_set REST_PSUBSET)
 
-constdefs
-  SING :: "('a => bool) => bool" 
+definition SING :: "('a => bool) => bool" where 
   "SING == %s::'a::type => bool. EX x::'a::type. s = INSERT x EMPTY"
 
 lemma SING_DEF: "ALL s::'a::type => bool. SING s = (EX x::'a::type. s = INSERT x EMPTY)"
@@ -3917,8 +3846,7 @@
 lemma SING_IFF_EMPTY_REST: "ALL x::'a::type => bool. SING x = (x ~= EMPTY & REST x = EMPTY)"
   by (import pred_set SING_IFF_EMPTY_REST)
 
-constdefs
-  IMAGE :: "('a => 'b) => ('a => bool) => 'b => bool" 
+definition IMAGE :: "('a => 'b) => ('a => bool) => 'b => bool" where 
   "IMAGE ==
 %(f::'a::type => 'b::type) s::'a::type => bool.
    GSPEC (%x::'a::type. (f x, IN x s))"
@@ -3971,8 +3899,7 @@
     (pred_set.INTER (IMAGE f s) (IMAGE f t))"
   by (import pred_set IMAGE_INTER)
 
-constdefs
-  INJ :: "('a => 'b) => ('a => bool) => ('b => bool) => bool" 
+definition INJ :: "('a => 'b) => ('a => bool) => ('b => bool) => bool" where 
   "INJ ==
 %(f::'a::type => 'b::type) (s::'a::type => bool) t::'b::type => bool.
    (ALL x::'a::type. IN x s --> IN (f x) t) &
@@ -3998,8 +3925,7 @@
    (ALL xa::'a::type => bool. INJ x xa EMPTY = (xa = EMPTY))"
   by (import pred_set INJ_EMPTY)
 
-constdefs
-  SURJ :: "('a => 'b) => ('a => bool) => ('b => bool) => bool" 
+definition SURJ :: "('a => 'b) => ('a => bool) => ('b => bool) => bool" where 
   "SURJ ==
 %(f::'a::type => 'b::type) (s::'a::type => bool) t::'b::type => bool.
    (ALL x::'a::type. IN x s --> IN (f x) t) &
@@ -4028,8 +3954,7 @@
    SURJ x xa xb = (IMAGE x xa = xb)"
   by (import pred_set IMAGE_SURJ)
 
-constdefs
-  BIJ :: "('a => 'b) => ('a => bool) => ('b => bool) => bool" 
+definition BIJ :: "('a => 'b) => ('a => bool) => ('b => bool) => bool" where 
   "BIJ ==
 %(f::'a::type => 'b::type) (s::'a::type => bool) t::'b::type => bool.
    INJ f s t & SURJ f s t"
@@ -4065,8 +3990,7 @@
    SURJ f s t --> (ALL x::'b::type. IN x t --> f (RINV f s x) = x)"
   by (import pred_set RINV_DEF)
 
-constdefs
-  FINITE :: "('a => bool) => bool" 
+definition FINITE :: "('a => bool) => bool" where 
   "FINITE ==
 %s::'a::type => bool.
    ALL P::('a::type => bool) => bool.
@@ -4219,8 +4143,7 @@
    (ALL x::'a::type => bool. FINITE x --> P x)"
   by (import pred_set FINITE_COMPLETE_INDUCTION)
 
-constdefs
-  INFINITE :: "('a => bool) => bool" 
+definition INFINITE :: "('a => bool) => bool" where 
   "INFINITE == %s::'a::type => bool. ~ FINITE s"
 
 lemma INFINITE_DEF: "ALL s::'a::type => bool. INFINITE s = (~ FINITE s)"
@@ -4320,8 +4243,7 @@
                                 (f n)))))))))"
   by (import pred_set FINITE_WEAK_ENUMERATE)
 
-constdefs
-  BIGUNION :: "(('a => bool) => bool) => 'a => bool" 
+definition BIGUNION :: "(('a => bool) => bool) => 'a => bool" where 
   "BIGUNION ==
 %P::('a::type => bool) => bool.
    GSPEC (%x::'a::type. (x, EX p::'a::type => bool. IN p P & IN x p))"
@@ -4367,8 +4289,7 @@
    FINITE (BIGUNION x)"
   by (import pred_set FINITE_BIGUNION)
 
-constdefs
-  BIGINTER :: "(('a => bool) => bool) => 'a => bool" 
+definition BIGINTER :: "(('a => bool) => bool) => 'a => bool" where 
   "BIGINTER ==
 %B::('a::type => bool) => bool.
    GSPEC (%x::'a::type. (x, ALL P::'a::type => bool. IN P B --> IN x P))"
@@ -4406,8 +4327,7 @@
    DISJOINT x (BIGINTER xb) & DISJOINT (BIGINTER xb) x"
   by (import pred_set DISJOINT_BIGINTER)
 
-constdefs
-  CROSS :: "('a => bool) => ('b => bool) => 'a * 'b => bool" 
+definition CROSS :: "('a => bool) => ('b => bool) => 'a * 'b => bool" where 
   "CROSS ==
 %(P::'a::type => bool) Q::'b::type => bool.
    GSPEC (%p::'a::type * 'b::type. (p, IN (fst p) P & IN (snd p) Q))"
@@ -4460,8 +4380,7 @@
    FINITE (CROSS P Q) = (P = EMPTY | Q = EMPTY | FINITE P & FINITE Q)"
   by (import pred_set FINITE_CROSS_EQ)
 
-constdefs
-  COMPL :: "('a => bool) => 'a => bool" 
+definition COMPL :: "('a => bool) => 'a => bool" where 
   "COMPL == DIFF pred_set.UNIV"
 
 lemma COMPL_DEF: "ALL P::'a::type => bool. COMPL P = DIFF pred_set.UNIV P"
@@ -4513,8 +4432,7 @@
 lemma CARD_COUNT: "ALL n::nat. CARD (count n) = n"
   by (import pred_set CARD_COUNT)
 
-constdefs
-  ITSET_tupled :: "('a => 'b => 'b) => ('a => bool) * 'b => 'b" 
+definition ITSET_tupled :: "('a => 'b => 'b) => ('a => bool) * 'b => 'b" where 
   "ITSET_tupled ==
 %f::'a::type => 'b::type => 'b::type.
    WFREC
@@ -4546,8 +4464,7 @@
         else ARB)"
   by (import pred_set ITSET_tupled_primitive_def)
 
-constdefs
-  ITSET :: "('a => 'b => 'b) => ('a => bool) => 'b => 'b" 
+definition ITSET :: "('a => 'b => 'b) => ('a => bool) => 'b => 'b" where 
   "ITSET ==
 %(f::'a::type => 'b::type => 'b::type) (x::'a::type => bool) x1::'b::type.
    ITSET_tupled f (x, x1)"
@@ -4578,8 +4495,7 @@
 
 ;setup_theory operator
 
-constdefs
-  ASSOC :: "('a => 'a => 'a) => bool" 
+definition ASSOC :: "('a => 'a => 'a) => bool" where 
   "ASSOC ==
 %f::'a::type => 'a::type => 'a::type.
    ALL (x::'a::type) (y::'a::type) z::'a::type. f x (f y z) = f (f x y) z"
@@ -4589,8 +4505,7 @@
    (ALL (x::'a::type) (y::'a::type) z::'a::type. f x (f y z) = f (f x y) z)"
   by (import operator ASSOC_DEF)
 
-constdefs
-  COMM :: "('a => 'a => 'b) => bool" 
+definition COMM :: "('a => 'a => 'b) => bool" where 
   "COMM ==
 %f::'a::type => 'a::type => 'b::type.
    ALL (x::'a::type) y::'a::type. f x y = f y x"
@@ -4599,8 +4514,7 @@
    COMM f = (ALL (x::'a::type) y::'a::type. f x y = f y x)"
   by (import operator COMM_DEF)
 
-constdefs
-  FCOMM :: "('a => 'b => 'a) => ('c => 'a => 'a) => bool" 
+definition FCOMM :: "('a => 'b => 'a) => ('c => 'a => 'a) => bool" where 
   "FCOMM ==
 %(f::'a::type => 'b::type => 'a::type) g::'c::type => 'a::type => 'a::type.
    ALL (x::'c::type) (y::'a::type) z::'b::type. g x (f y z) = f (g x y) z"
@@ -4611,8 +4525,7 @@
    (ALL (x::'c::type) (y::'a::type) z::'b::type. g x (f y z) = f (g x y) z)"
   by (import operator FCOMM_DEF)
 
-constdefs
-  RIGHT_ID :: "('a => 'b => 'a) => 'b => bool" 
+definition RIGHT_ID :: "('a => 'b => 'a) => 'b => bool" where 
   "RIGHT_ID ==
 %(f::'a::type => 'b::type => 'a::type) e::'b::type.
    ALL x::'a::type. f x e = x"
@@ -4621,8 +4534,7 @@
    RIGHT_ID f e = (ALL x::'a::type. f x e = x)"
   by (import operator RIGHT_ID_DEF)
 
-constdefs
-  LEFT_ID :: "('a => 'b => 'b) => 'a => bool" 
+definition LEFT_ID :: "('a => 'b => 'b) => 'a => bool" where 
   "LEFT_ID ==
 %(f::'a::type => 'b::type => 'b::type) e::'a::type.
    ALL x::'b::type. f e x = x"
@@ -4631,8 +4543,7 @@
    LEFT_ID f e = (ALL x::'b::type. f e x = x)"
   by (import operator LEFT_ID_DEF)
 
-constdefs
-  MONOID :: "('a => 'a => 'a) => 'a => bool" 
+definition MONOID :: "('a => 'a => 'a) => 'a => bool" where 
   "MONOID ==
 %(f::'a::type => 'a::type => 'a::type) e::'a::type.
    ASSOC f & RIGHT_ID f e & LEFT_ID f e"
@@ -4690,15 +4601,13 @@
 lemma IS_EL_DEF: "ALL (x::'a::type) l::'a::type list. x mem l = list_exists (op = x) l"
   by (import rich_list IS_EL_DEF)
 
-constdefs
-  AND_EL :: "bool list => bool" 
+definition AND_EL :: "bool list => bool" where 
   "AND_EL == list_all I"
 
 lemma AND_EL_DEF: "AND_EL = list_all I"
   by (import rich_list AND_EL_DEF)
 
-constdefs
-  OR_EL :: "bool list => bool" 
+definition OR_EL :: "bool list => bool" where 
   "OR_EL == list_exists I"
 
 lemma OR_EL_DEF: "OR_EL = list_exists I"
@@ -4816,16 +4725,14 @@
     (if P x then ([], x # l) else (x # fst (SPLITP P l), snd (SPLITP P l))))"
   by (import rich_list SPLITP)
 
-constdefs
-  PREFIX :: "('a => bool) => 'a list => 'a list" 
+definition PREFIX :: "('a => bool) => 'a list => 'a list" where 
   "PREFIX == %(P::'a::type => bool) l::'a::type list. fst (SPLITP (Not o P) l)"
 
 lemma PREFIX_DEF: "ALL (P::'a::type => bool) l::'a::type list.
    PREFIX P l = fst (SPLITP (Not o P) l)"
   by (import rich_list PREFIX_DEF)
 
-constdefs
-  SUFFIX :: "('a => bool) => 'a list => 'a list" 
+definition SUFFIX :: "('a => bool) => 'a list => 'a list" where 
   "SUFFIX ==
 %P::'a::type => bool.
    foldl (%(l'::'a::type list) x::'a::type. if P x then SNOC x l' else [])
@@ -4837,15 +4744,13 @@
     [] l"
   by (import rich_list SUFFIX_DEF)
 
-constdefs
-  UNZIP_FST :: "('a * 'b) list => 'a list" 
+definition UNZIP_FST :: "('a * 'b) list => 'a list" where 
   "UNZIP_FST == %l::('a::type * 'b::type) list. fst (unzip l)"
 
 lemma UNZIP_FST_DEF: "ALL l::('a::type * 'b::type) list. UNZIP_FST l = fst (unzip l)"
   by (import rich_list UNZIP_FST_DEF)
 
-constdefs
-  UNZIP_SND :: "('a * 'b) list => 'b list" 
+definition UNZIP_SND :: "('a * 'b) list => 'b list" where 
   "UNZIP_SND == %l::('a::type * 'b::type) list. snd (unzip l)"
 
 lemma UNZIP_SND_DEF: "ALL l::('a::type * 'b::type) list. UNZIP_SND l = snd (unzip l)"
@@ -5916,8 +5821,7 @@
 
 ;setup_theory state_transformer
 
-constdefs
-  UNIT :: "'b => 'a => 'b * 'a" 
+definition UNIT :: "'b => 'a => 'b * 'a" where 
   "(op ==::('b::type => 'a::type => 'b::type * 'a::type)
         => ('b::type => 'a::type => 'b::type * 'a::type) => prop)
  (UNIT::'b::type => 'a::type => 'b::type * 'a::type)
@@ -5926,8 +5830,7 @@
 lemma UNIT_DEF: "ALL x::'b::type. UNIT x = Pair x"
   by (import state_transformer UNIT_DEF)
 
-constdefs
-  BIND :: "('a => 'b * 'a) => ('b => 'a => 'c * 'a) => 'a => 'c * 'a" 
+definition BIND :: "('a => 'b * 'a) => ('b => 'a => 'c * 'a) => 'a => 'c * 'a" where 
   "(op ==::(('a::type => 'b::type * 'a::type)
          => ('b::type => 'a::type => 'c::type * 'a::type)
             => 'a::type => 'c::type * 'a::type)
@@ -5967,8 +5870,7 @@
              g)))"
   by (import state_transformer BIND_DEF)
 
-constdefs
-  MMAP :: "('c => 'b) => ('a => 'c * 'a) => 'a => 'b * 'a" 
+definition MMAP :: "('c => 'b) => ('a => 'c * 'a) => 'a => 'b * 'a" where 
   "MMAP ==
 %(f::'c::type => 'b::type) m::'a::type => 'c::type * 'a::type.
    BIND m (UNIT o f)"
@@ -5977,8 +5879,7 @@
    MMAP f m = BIND m (UNIT o f)"
   by (import state_transformer MMAP_DEF)
 
-constdefs
-  JOIN :: "('a => ('a => 'b * 'a) * 'a) => 'a => 'b * 'a" 
+definition JOIN :: "('a => ('a => 'b * 'a) * 'a) => 'a => 'b * 'a" where 
   "JOIN ==
 %z::'a::type => ('a::type => 'b::type * 'a::type) * 'a::type. BIND z I"
 
--- a/src/HOL/Import/HOL/HOL4Prob.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Import/HOL/HOL4Prob.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -373,8 +373,7 @@
    alg_twin x y = (EX l::bool list. x = SNOC True l & y = SNOC False l)"
   by (import prob_canon alg_twin_def)
 
-constdefs
-  alg_order_tupled :: "bool list * bool list => bool" 
+definition alg_order_tupled :: "bool list * bool list => bool" where 
   "(op ==::(bool list * bool list => bool)
         => (bool list * bool list => bool) => prop)
  (alg_order_tupled::bool list * bool list => bool)
@@ -1917,8 +1916,7 @@
    P 0 & (ALL v::nat. P (Suc v div 2) --> P (Suc v)) --> All P"
   by (import prob_uniform unif_bound_ind)
 
-constdefs
-  unif_tupled :: "nat * (nat => bool) => nat * (nat => bool)" 
+definition unif_tupled :: "nat * (nat => bool) => nat * (nat => bool)" where 
   "unif_tupled ==
 WFREC
  (SOME R::nat * (nat => bool) => nat * (nat => bool) => bool.
@@ -1963,8 +1961,7 @@
    (ALL v::nat. All (P v))"
   by (import prob_uniform unif_ind)
 
-constdefs
-  uniform_tupled :: "nat * nat * (nat => bool) => nat * (nat => bool)" 
+definition uniform_tupled :: "nat * nat * (nat => bool) => nat * (nat => bool)" where 
   "uniform_tupled ==
 WFREC
  (SOME R::nat * nat * (nat => bool) => nat * nat * (nat => bool) => bool.
--- a/src/HOL/Import/HOL/HOL4Real.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Import/HOL/HOL4Real.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -39,29 +39,25 @@
    hreal_lt (hreal_add x y) (hreal_add x z) = hreal_lt y z"
   by (import realax HREAL_LT_LADD)
 
-constdefs
-  treal_0 :: "hreal * hreal" 
+definition treal_0 :: "hreal * hreal" where 
   "treal_0 == (hreal_1, hreal_1)"
 
 lemma treal_0: "treal_0 = (hreal_1, hreal_1)"
   by (import realax treal_0)
 
-constdefs
-  treal_1 :: "hreal * hreal" 
+definition treal_1 :: "hreal * hreal" where 
   "treal_1 == (hreal_add hreal_1 hreal_1, hreal_1)"
 
 lemma treal_1: "treal_1 = (hreal_add hreal_1 hreal_1, hreal_1)"
   by (import realax treal_1)
 
-constdefs
-  treal_neg :: "hreal * hreal => hreal * hreal" 
+definition treal_neg :: "hreal * hreal => hreal * hreal" where 
   "treal_neg == %(x::hreal, y::hreal). (y, x)"
 
 lemma treal_neg: "ALL (x::hreal) y::hreal. treal_neg (x, y) = (y, x)"
   by (import realax treal_neg)
 
-constdefs
-  treal_add :: "hreal * hreal => hreal * hreal => hreal * hreal" 
+definition treal_add :: "hreal * hreal => hreal * hreal => hreal * hreal" where 
   "treal_add ==
 %(x1::hreal, y1::hreal) (x2::hreal, y2::hreal).
    (hreal_add x1 x2, hreal_add y1 y2)"
@@ -70,8 +66,7 @@
    treal_add (x1, y1) (x2, y2) = (hreal_add x1 x2, hreal_add y1 y2)"
   by (import realax treal_add)
 
-constdefs
-  treal_mul :: "hreal * hreal => hreal * hreal => hreal * hreal" 
+definition treal_mul :: "hreal * hreal => hreal * hreal => hreal * hreal" where 
   "treal_mul ==
 %(x1::hreal, y1::hreal) (x2::hreal, y2::hreal).
    (hreal_add (hreal_mul x1 x2) (hreal_mul y1 y2),
@@ -83,8 +78,7 @@
     hreal_add (hreal_mul x1 y2) (hreal_mul y1 x2))"
   by (import realax treal_mul)
 
-constdefs
-  treal_lt :: "hreal * hreal => hreal * hreal => bool" 
+definition treal_lt :: "hreal * hreal => hreal * hreal => bool" where 
   "treal_lt ==
 %(x1::hreal, y1::hreal) (x2::hreal, y2::hreal).
    hreal_lt (hreal_add x1 y2) (hreal_add x2 y1)"
@@ -93,8 +87,7 @@
    treal_lt (x1, y1) (x2, y2) = hreal_lt (hreal_add x1 y2) (hreal_add x2 y1)"
   by (import realax treal_lt)
 
-constdefs
-  treal_inv :: "hreal * hreal => hreal * hreal" 
+definition treal_inv :: "hreal * hreal => hreal * hreal" where 
   "treal_inv ==
 %(x::hreal, y::hreal).
    if x = y then treal_0
@@ -110,8 +103,7 @@
          else (hreal_1, hreal_add (hreal_inv (hreal_sub y x)) hreal_1))"
   by (import realax treal_inv)
 
-constdefs
-  treal_eq :: "hreal * hreal => hreal * hreal => bool" 
+definition treal_eq :: "hreal * hreal => hreal * hreal => bool" where 
   "treal_eq ==
 %(x1::hreal, y1::hreal) (x2::hreal, y2::hreal).
    hreal_add x1 y2 = hreal_add x2 y1"
@@ -194,15 +186,13 @@
    treal_lt treal_0 (treal_mul x y)"
   by (import realax TREAL_LT_MUL)
 
-constdefs
-  treal_of_hreal :: "hreal => hreal * hreal" 
+definition treal_of_hreal :: "hreal => hreal * hreal" where 
   "treal_of_hreal == %x::hreal. (hreal_add x hreal_1, hreal_1)"
 
 lemma treal_of_hreal: "ALL x::hreal. treal_of_hreal x = (hreal_add x hreal_1, hreal_1)"
   by (import realax treal_of_hreal)
 
-constdefs
-  hreal_of_treal :: "hreal * hreal => hreal" 
+definition hreal_of_treal :: "hreal * hreal => hreal" where 
   "hreal_of_treal == %(x::hreal, y::hreal). SOME d::hreal. x = hreal_add y d"
 
 lemma hreal_of_treal: "ALL (x::hreal) y::hreal.
@@ -579,8 +569,7 @@
    (EX x::real. ALL y::real. (EX x::real. P x & y < x) = (y < x))"
   by (import real REAL_SUP_EXISTS)
 
-constdefs
-  sup :: "(real => bool) => real" 
+definition sup :: "(real => bool) => real" where 
   "sup ==
 %P::real => bool.
    SOME s::real. ALL y::real. (EX x::real. P x & y < x) = (y < s)"
@@ -781,8 +770,7 @@
 
 ;setup_theory topology
 
-constdefs
-  re_Union :: "(('a => bool) => bool) => 'a => bool" 
+definition re_Union :: "(('a => bool) => bool) => 'a => bool" where 
   "re_Union ==
 %(P::('a::type => bool) => bool) x::'a::type.
    EX s::'a::type => bool. P s & s x"
@@ -791,8 +779,7 @@
    re_Union P = (%x::'a::type. EX s::'a::type => bool. P s & s x)"
   by (import topology re_Union)
 
-constdefs
-  re_union :: "('a => bool) => ('a => bool) => 'a => bool" 
+definition re_union :: "('a => bool) => ('a => bool) => 'a => bool" where 
   "re_union ==
 %(P::'a::type => bool) (Q::'a::type => bool) x::'a::type. P x | Q x"
 
@@ -800,8 +787,7 @@
    re_union P Q = (%x::'a::type. P x | Q x)"
   by (import topology re_union)
 
-constdefs
-  re_intersect :: "('a => bool) => ('a => bool) => 'a => bool" 
+definition re_intersect :: "('a => bool) => ('a => bool) => 'a => bool" where 
   "re_intersect ==
 %(P::'a::type => bool) (Q::'a::type => bool) x::'a::type. P x & Q x"
 
@@ -809,22 +795,19 @@
    re_intersect P Q = (%x::'a::type. P x & Q x)"
   by (import topology re_intersect)
 
-constdefs
-  re_null :: "'a => bool" 
+definition re_null :: "'a => bool" where 
   "re_null == %x::'a::type. False"
 
 lemma re_null: "re_null = (%x::'a::type. False)"
   by (import topology re_null)
 
-constdefs
-  re_universe :: "'a => bool" 
+definition re_universe :: "'a => bool" where 
   "re_universe == %x::'a::type. True"
 
 lemma re_universe: "re_universe = (%x::'a::type. True)"
   by (import topology re_universe)
 
-constdefs
-  re_subset :: "('a => bool) => ('a => bool) => bool" 
+definition re_subset :: "('a => bool) => ('a => bool) => bool" where 
   "re_subset ==
 %(P::'a::type => bool) Q::'a::type => bool. ALL x::'a::type. P x --> Q x"
 
@@ -832,8 +815,7 @@
    re_subset P Q = (ALL x::'a::type. P x --> Q x)"
   by (import topology re_subset)
 
-constdefs
-  re_compl :: "('a => bool) => 'a => bool" 
+definition re_compl :: "('a => bool) => 'a => bool" where 
   "re_compl == %(P::'a::type => bool) x::'a::type. ~ P x"
 
 lemma re_compl: "ALL P::'a::type => bool. re_compl P = (%x::'a::type. ~ P x)"
@@ -853,8 +835,7 @@
    re_subset P Q & re_subset Q R --> re_subset P R"
   by (import topology SUBSET_TRANS)
 
-constdefs
-  istopology :: "(('a => bool) => bool) => bool" 
+definition istopology :: "(('a => bool) => bool) => bool" where 
   "istopology ==
 %L::('a::type => bool) => bool.
    L re_null &
@@ -900,8 +881,7 @@
    re_subset xa (open x) --> open x (re_Union xa)"
   by (import topology TOPOLOGY_UNION)
 
-constdefs
-  neigh :: "'a topology => ('a => bool) * 'a => bool" 
+definition neigh :: "'a topology => ('a => bool) * 'a => bool" where 
   "neigh ==
 %(top::'a::type topology) (N::'a::type => bool, x::'a::type).
    EX P::'a::type => bool. open top P & re_subset P N & P x"
@@ -932,16 +912,14 @@
        S' x --> (EX N::'a::type => bool. neigh top (N, x) & re_subset N S'))"
   by (import topology OPEN_NEIGH)
 
-constdefs
-  closed :: "'a topology => ('a => bool) => bool" 
+definition closed :: "'a topology => ('a => bool) => bool" where 
   "closed == %(L::'a::type topology) S'::'a::type => bool. open L (re_compl S')"
 
 lemma closed: "ALL (L::'a::type topology) S'::'a::type => bool.
    closed L S' = open L (re_compl S')"
   by (import topology closed)
 
-constdefs
-  limpt :: "'a topology => 'a => ('a => bool) => bool" 
+definition limpt :: "'a topology => 'a => ('a => bool) => bool" where 
   "limpt ==
 %(top::'a::type topology) (x::'a::type) S'::'a::type => bool.
    ALL N::'a::type => bool.
@@ -957,8 +935,7 @@
    closed top S' = (ALL x::'a::type. limpt top x S' --> S' x)"
   by (import topology CLOSED_LIMPT)
 
-constdefs
-  ismet :: "('a * 'a => real) => bool" 
+definition ismet :: "('a * 'a => real) => bool" where 
   "ismet ==
 %m::'a::type * 'a::type => real.
    (ALL (x::'a::type) y::'a::type. (m (x, y) = 0) = (x = y)) &
@@ -1012,8 +989,7 @@
    x ~= y --> 0 < dist m (x, y)"
   by (import topology METRIC_NZ)
 
-constdefs
-  mtop :: "'a metric => 'a topology" 
+definition mtop :: "'a metric => 'a topology" where 
   "mtop ==
 %m::'a::type metric.
    topology
@@ -1042,8 +1018,7 @@
        S' xa --> (EX e>0. ALL y::'a::type. dist x (xa, y) < e --> S' y))"
   by (import topology MTOP_OPEN)
 
-constdefs
-  B :: "'a metric => 'a * real => 'a => bool" 
+definition B :: "'a metric => 'a * real => 'a => bool" where 
   "B ==
 %(m::'a::type metric) (x::'a::type, e::real) y::'a::type. dist m (x, y) < e"
 
@@ -1067,8 +1042,7 @@
 lemma ISMET_R1: "ismet (%(x::real, y::real). abs (y - x))"
   by (import topology ISMET_R1)
 
-constdefs
-  mr1 :: "real metric" 
+definition mr1 :: "real metric" where 
   "mr1 == metric (%(x::real, y::real). abs (y - x))"
 
 lemma mr1: "mr1 = metric (%(x::real, y::real). abs (y - x))"
@@ -1105,8 +1079,7 @@
 
 ;setup_theory nets
 
-constdefs
-  dorder :: "('a => 'a => bool) => bool" 
+definition dorder :: "('a => 'a => bool) => bool" where 
   "dorder ==
 %g::'a::type => 'a::type => bool.
    ALL (x::'a::type) y::'a::type.
@@ -1120,8 +1093,7 @@
        (EX z::'a::type. g z z & (ALL w::'a::type. g w z --> g w x & g w y)))"
   by (import nets dorder)
 
-constdefs
-  tends :: "('b => 'a) => 'a => 'a topology * ('b => 'b => bool) => bool" 
+definition tends :: "('b => 'a) => 'a => 'a topology * ('b => 'b => bool) => bool" where 
   "tends ==
 %(s::'b::type => 'a::type) (l::'a::type) (top::'a::type topology,
    g::'b::type => 'b::type => bool).
@@ -1137,8 +1109,7 @@
        (EX n::'b::type. g n n & (ALL m::'b::type. g m n --> N (s m))))"
   by (import nets tends)
 
-constdefs
-  bounded :: "'a metric * ('b => 'b => bool) => ('b => 'a) => bool" 
+definition bounded :: "'a metric * ('b => 'b => bool) => ('b => 'a) => bool" where 
   "bounded ==
 %(m::'a::type metric, g::'b::type => 'b::type => bool)
    f::'b::type => 'a::type.
@@ -1152,8 +1123,7 @@
        g N N & (ALL n::'b::type. g n N --> dist m (f n, x) < k))"
   by (import nets bounded)
 
-constdefs
-  tendsto :: "'a metric * 'a => 'a => 'a => bool" 
+definition tendsto :: "'a metric * 'a => 'a => 'a => bool" where 
   "tendsto ==
 %(m::'a::type metric, x::'a::type) (y::'a::type) z::'a::type.
    0 < dist m (x, y) & dist m (x, y) <= dist m (x, z)"
@@ -1366,15 +1336,13 @@
    hol4--> x x1 & hol4--> x x2 --> x1 = x2"
   by (import seq SEQ_UNIQ)
 
-constdefs
-  convergent :: "(nat => real) => bool" 
+definition convergent :: "(nat => real) => bool" where 
   "convergent == %f::nat => real. Ex (hol4--> f)"
 
 lemma convergent: "ALL f::nat => real. convergent f = Ex (hol4--> f)"
   by (import seq convergent)
 
-constdefs
-  cauchy :: "(nat => real) => bool" 
+definition cauchy :: "(nat => real) => bool" where 
   "cauchy ==
 %f::nat => real.
    ALL e>0.
@@ -1388,8 +1356,7 @@
           ALL (m::nat) n::nat. N <= m & N <= n --> abs (f m - f n) < e)"
   by (import seq cauchy)
 
-constdefs
-  lim :: "(nat => real) => real" 
+definition lim :: "(nat => real) => real" where 
   "lim == %f::nat => real. Eps (hol4--> f)"
 
 lemma lim: "ALL f::nat => real. lim f = Eps (hol4--> f)"
@@ -1398,8 +1365,7 @@
 lemma SEQ_LIM: "ALL f::nat => real. convergent f = hol4--> f (lim f)"
   by (import seq SEQ_LIM)
 
-constdefs
-  subseq :: "(nat => nat) => bool" 
+definition subseq :: "(nat => nat) => bool" where 
   "subseq == %f::nat => nat. ALL (m::nat) n::nat. m < n --> f m < f n"
 
 lemma subseq: "ALL f::nat => nat. subseq f = (ALL (m::nat) n::nat. m < n --> f m < f n)"
@@ -1541,23 +1507,20 @@
    (ALL (a::real) b::real. a <= b --> P (a, b))"
   by (import seq BOLZANO_LEMMA)
 
-constdefs
-  sums :: "(nat => real) => real => bool" 
+definition sums :: "(nat => real) => real => bool" where 
   "sums == %f::nat => real. hol4--> (%n::nat. real.sum (0, n) f)"
 
 lemma sums: "ALL (f::nat => real) s::real.
    sums f s = hol4--> (%n::nat. real.sum (0, n) f) s"
   by (import seq sums)
 
-constdefs
-  summable :: "(nat => real) => bool" 
+definition summable :: "(nat => real) => bool" where 
   "summable == %f::nat => real. Ex (sums f)"
 
 lemma summable: "ALL f::nat => real. summable f = Ex (sums f)"
   by (import seq summable)
 
-constdefs
-  suminf :: "(nat => real) => real" 
+definition suminf :: "(nat => real) => real" where 
   "suminf == %f::nat => real. Eps (sums f)"
 
 lemma suminf: "ALL f::nat => real. suminf f = Eps (sums f)"
@@ -1692,8 +1655,7 @@
 
 ;setup_theory lim
 
-constdefs
-  tends_real_real :: "(real => real) => real => real => bool" 
+definition tends_real_real :: "(real => real) => real => real => bool" where 
   "tends_real_real ==
 %(f::real => real) (l::real) x0::real.
    tends f l (mtop mr1, tendsto (mr1, x0))"
@@ -1763,8 +1725,7 @@
    tends_real_real f l x0"
   by (import lim LIM_TRANSFORM)
 
-constdefs
-  diffl :: "(real => real) => real => real => bool" 
+definition diffl :: "(real => real) => real => real => bool" where 
   "diffl ==
 %(f::real => real) (l::real) x::real.
    tends_real_real (%h::real. (f (x + h) - f x) / h) l 0"
@@ -1773,8 +1734,7 @@
    diffl f l x = tends_real_real (%h::real. (f (x + h) - f x) / h) l 0"
   by (import lim diffl)
 
-constdefs
-  contl :: "(real => real) => real => bool" 
+definition contl :: "(real => real) => real => bool" where 
   "contl ==
 %(f::real => real) x::real. tends_real_real (%h::real. f (x + h)) (f x) 0"
 
@@ -1782,8 +1742,7 @@
    contl f x = tends_real_real (%h::real. f (x + h)) (f x) 0"
   by (import lim contl)
 
-constdefs
-  differentiable :: "(real => real) => real => bool" 
+definition differentiable :: "(real => real) => real => bool" where 
   "differentiable == %(f::real => real) x::real. EX l::real. diffl f l x"
 
 lemma differentiable: "ALL (f::real => real) x::real.
@@ -2127,8 +2086,7 @@
    summable (%n::nat. f n * z ^ n)"
   by (import powser POWSER_INSIDE)
 
-constdefs
-  diffs :: "(nat => real) => nat => real" 
+definition diffs :: "(nat => real) => nat => real" where 
   "diffs == %(c::nat => real) n::nat. real (Suc n) * c (Suc n)"
 
 lemma diffs: "ALL c::nat => real. diffs c = (%n::nat. real (Suc n) * c (Suc n))"
@@ -2204,15 +2162,13 @@
 
 ;setup_theory transc
 
-constdefs
-  exp :: "real => real" 
+definition exp :: "real => real" where 
   "exp == %x::real. suminf (%n::nat. inverse (real (FACT n)) * x ^ n)"
 
 lemma exp: "ALL x::real. exp x = suminf (%n::nat. inverse (real (FACT n)) * x ^ n)"
   by (import transc exp)
 
-constdefs
-  cos :: "real => real" 
+definition cos :: "real => real" where 
   "cos ==
 %x::real.
    suminf
@@ -2226,8 +2182,7 @@
         (if EVEN n then (- 1) ^ (n div 2) / real (FACT n) else 0) * x ^ n)"
   by (import transc cos)
 
-constdefs
-  sin :: "real => real" 
+definition sin :: "real => real" where 
   "sin ==
 %x::real.
    suminf
@@ -2364,8 +2319,7 @@
 lemma EXP_TOTAL: "ALL y>0. EX x::real. exp x = y"
   by (import transc EXP_TOTAL)
 
-constdefs
-  ln :: "real => real" 
+definition ln :: "real => real" where 
   "ln == %x::real. SOME u::real. exp u = x"
 
 lemma ln: "ALL x::real. ln x = (SOME u::real. exp u = x)"
@@ -2410,16 +2364,14 @@
 lemma LN_POS: "ALL x>=1. 0 <= ln x"
   by (import transc LN_POS)
 
-constdefs
-  root :: "nat => real => real" 
+definition root :: "nat => real => real" where 
   "root == %(n::nat) x::real. SOME u::real. (0 < x --> 0 < u) & u ^ n = x"
 
 lemma root: "ALL (n::nat) x::real.
    root n x = (SOME u::real. (0 < x --> 0 < u) & u ^ n = x)"
   by (import transc root)
 
-constdefs
-  sqrt :: "real => real" 
+definition sqrt :: "real => real" where 
   "sqrt == root 2"
 
 lemma sqrt: "ALL x::real. sqrt x = root 2 x"
@@ -2584,8 +2536,7 @@
 lemma COS_ISZERO: "EX! x::real. 0 <= x & x <= 2 & cos x = 0"
   by (import transc COS_ISZERO)
 
-constdefs
-  pi :: "real" 
+definition pi :: "real" where 
   "pi == 2 * (SOME x::real. 0 <= x & x <= 2 & cos x = 0)"
 
 lemma pi: "pi = 2 * (SOME x::real. 0 <= x & x <= 2 & cos x = 0)"
@@ -2689,8 +2640,7 @@
     (EX n::nat. EVEN n & x = - (real n * (pi / 2))))"
   by (import transc SIN_ZERO)
 
-constdefs
-  tan :: "real => real" 
+definition tan :: "real => real" where 
   "tan == %x::real. sin x / cos x"
 
 lemma tan: "ALL x::real. tan x = sin x / cos x"
@@ -2736,23 +2686,20 @@
 lemma TAN_TOTAL: "ALL y::real. EX! x::real. - (pi / 2) < x & x < pi / 2 & tan x = y"
   by (import transc TAN_TOTAL)
 
-constdefs
-  asn :: "real => real" 
+definition asn :: "real => real" where 
   "asn == %y::real. SOME x::real. - (pi / 2) <= x & x <= pi / 2 & sin x = y"
 
 lemma asn: "ALL y::real.
    asn y = (SOME x::real. - (pi / 2) <= x & x <= pi / 2 & sin x = y)"
   by (import transc asn)
 
-constdefs
-  acs :: "real => real" 
+definition acs :: "real => real" where 
   "acs == %y::real. SOME x::real. 0 <= x & x <= pi & cos x = y"
 
 lemma acs: "ALL y::real. acs y = (SOME x::real. 0 <= x & x <= pi & cos x = y)"
   by (import transc acs)
 
-constdefs
-  atn :: "real => real" 
+definition atn :: "real => real" where 
   "atn == %y::real. SOME x::real. - (pi / 2) < x & x < pi / 2 & tan x = y"
 
 lemma atn: "ALL y::real. atn y = (SOME x::real. - (pi / 2) < x & x < pi / 2 & tan x = y)"
@@ -2845,8 +2792,7 @@
 lemma DIFF_ATN: "ALL x::real. diffl atn (inverse (1 + x ^ 2)) x"
   by (import transc DIFF_ATN)
 
-constdefs
-  division :: "real * real => (nat => real) => bool" 
+definition division :: "real * real => (nat => real) => bool" where 
   "(op ==::(real * real => (nat => real) => bool)
         => (real * real => (nat => real) => bool) => prop)
  (division::real * real => (nat => real) => bool)
@@ -2898,8 +2844,7 @@
                                   b)))))))))"
   by (import transc division)
 
-constdefs
-  dsize :: "(nat => real) => nat" 
+definition dsize :: "(nat => real) => nat" where 
   "(op ==::((nat => real) => nat) => ((nat => real) => nat) => prop)
  (dsize::(nat => real) => nat)
  (%D::nat => real.
@@ -2937,8 +2882,7 @@
                     ((op =::real => real => bool) (D n) (D N)))))))"
   by (import transc dsize)
 
-constdefs
-  tdiv :: "real * real => (nat => real) * (nat => real) => bool" 
+definition tdiv :: "real * real => (nat => real) * (nat => real) => bool" where 
   "tdiv ==
 %(a::real, b::real) (D::nat => real, p::nat => real).
    division (a, b) D & (ALL n::nat. D n <= p n & p n <= D (Suc n))"
@@ -2948,16 +2892,14 @@
    (division (a, b) D & (ALL n::nat. D n <= p n & p n <= D (Suc n)))"
   by (import transc tdiv)
 
-constdefs
-  gauge :: "(real => bool) => (real => real) => bool" 
+definition gauge :: "(real => bool) => (real => real) => bool" where 
   "gauge == %(E::real => bool) g::real => real. ALL x::real. E x --> 0 < g x"
 
 lemma gauge: "ALL (E::real => bool) g::real => real.
    gauge E g = (ALL x::real. E x --> 0 < g x)"
   by (import transc gauge)
 
-constdefs
-  fine :: "(real => real) => (nat => real) * (nat => real) => bool" 
+definition fine :: "(real => real) => (nat => real) * (nat => real) => bool" where 
   "(op ==::((real => real) => (nat => real) * (nat => real) => bool)
         => ((real => real) => (nat => real) * (nat => real) => bool)
            => prop)
@@ -3000,8 +2942,7 @@
                          (g (p n))))))))"
   by (import transc fine)
 
-constdefs
-  rsum :: "(nat => real) * (nat => real) => (real => real) => real" 
+definition rsum :: "(nat => real) * (nat => real) => (real => real) => real" where 
   "rsum ==
 %(D::nat => real, p::nat => real) f::real => real.
    real.sum (0, dsize D) (%n::nat. f (p n) * (D (Suc n) - D n))"
@@ -3011,8 +2952,7 @@
    real.sum (0, dsize D) (%n::nat. f (p n) * (D (Suc n) - D n))"
   by (import transc rsum)
 
-constdefs
-  Dint :: "real * real => (real => real) => real => bool" 
+definition Dint :: "real * real => (real => real) => real => bool" where 
   "Dint ==
 %(a::real, b::real) (f::real => real) k::real.
    ALL e>0.
@@ -3313,8 +3253,7 @@
     poly_diff_aux n (h # t) = real n * h # poly_diff_aux (Suc n) t)"
   by (import poly poly_diff_aux_def)
 
-constdefs
-  diff :: "real list => real list" 
+definition diff :: "real list => real list" where 
   "diff == %l::real list. if l = [] then [] else poly_diff_aux 1 (tl l)"
 
 lemma poly_diff_def: "ALL l::real list. diff l = (if l = [] then [] else poly_diff_aux 1 (tl l))"
@@ -3622,8 +3561,7 @@
    poly p = poly q --> poly (diff p) = poly (diff q)"
   by (import poly POLY_DIFF_WELLDEF)
 
-constdefs
-  poly_divides :: "real list => real list => bool" 
+definition poly_divides :: "real list => real list => bool" where 
   "poly_divides ==
 %(p1::real list) p2::real list.
    EX q::real list. poly p2 = poly (poly_mul p1 q)"
@@ -3681,8 +3619,7 @@
        ~ poly_divides (poly_exp [- a, 1] (Suc n)) p)"
   by (import poly POLY_ORDER)
 
-constdefs
-  poly_order :: "real => real list => nat" 
+definition poly_order :: "real => real list => nat" where 
   "poly_order ==
 %(a::real) p::real list.
    SOME n::nat.
@@ -3754,8 +3691,7 @@
    (ALL a::real. poly_order a q = (if poly_order a p = 0 then 0 else 1))"
   by (import poly POLY_SQUAREFREE_DECOMP_ORDER)
 
-constdefs
-  rsquarefree :: "real list => bool" 
+definition rsquarefree :: "real list => bool" where 
   "rsquarefree ==
 %p::real list.
    poly p ~= poly [] &
@@ -3798,8 +3734,7 @@
 lemma POLY_NORMALIZE: "ALL t::real list. poly (normalize t) = poly t"
   by (import poly POLY_NORMALIZE)
 
-constdefs
-  degree :: "real list => nat" 
+definition degree :: "real list => nat" where 
   "degree == %p::real list. PRE (length (normalize p))"
 
 lemma degree: "ALL p::real list. degree p = PRE (length (normalize p))"
--- a/src/HOL/Import/HOL/HOL4Vec.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Import/HOL/HOL4Vec.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -164,8 +164,7 @@
 lemma word_base0_def: "word_base0 = (%a::'a::type list. mk_word (CONSTR 0 a (%n::nat. BOTTOM)))"
   by (import word_base word_base0_def)
 
-constdefs
-  WORD :: "'a list => 'a word" 
+definition WORD :: "'a list => 'a word" where 
   "WORD == word_base0"
 
 lemma WORD: "WORD = word_base0"
@@ -680,8 +679,7 @@
 
 ;setup_theory word_num
 
-constdefs
-  LVAL :: "('a => nat) => nat => 'a list => nat" 
+definition LVAL :: "('a => nat) => nat => 'a list => nat" where 
   "LVAL ==
 %(f::'a::type => nat) b::nat. foldl (%(e::nat) x::'a::type. b * e + f x) 0"
 
@@ -756,8 +754,7 @@
     SNOC (frep (m mod b)) (NLIST n frep b (m div b)))"
   by (import word_num NLIST_DEF)
 
-constdefs
-  NWORD :: "nat => (nat => 'a) => nat => nat => 'a word" 
+definition NWORD :: "nat => (nat => 'a) => nat => nat => 'a word" where 
   "NWORD ==
 %(n::nat) (frep::nat => 'a::type) (b::nat) m::nat. WORD (NLIST n frep b m)"
 
@@ -1076,8 +1073,7 @@
    EXISTSABIT P (WCAT (w1, w2)) = (EXISTSABIT P w1 | EXISTSABIT P w2)"
   by (import word_bitop EXISTSABIT_WCAT)
 
-constdefs
-  SHR :: "bool => 'a => 'a word => 'a word * 'a" 
+definition SHR :: "bool => 'a => 'a word => 'a word * 'a" where 
   "SHR ==
 %(f::bool) (b::'a::type) w::'a::type word.
    (WCAT
@@ -1093,8 +1089,7 @@
     bit 0 w)"
   by (import word_bitop SHR_DEF)
 
-constdefs
-  SHL :: "bool => 'a word => 'a => 'a * 'a word" 
+definition SHL :: "bool => 'a word => 'a => 'a * 'a word" where 
   "SHL ==
 %(f::bool) (w::'a::type word) b::'a::type.
    (bit (PRE (WORDLEN w)) w,
@@ -1196,8 +1191,7 @@
 
 ;setup_theory bword_num
 
-constdefs
-  BV :: "bool => nat" 
+definition BV :: "bool => nat" where 
   "BV == %b::bool. if b then Suc 0 else 0"
 
 lemma BV_DEF: "ALL b::bool. BV b = (if b then Suc 0 else 0)"
@@ -1248,15 +1242,13 @@
              BNVAL (WCAT (w1, w2)) = BNVAL w1 * 2 ^ m + BNVAL w2))"
   by (import bword_num BNVAL_WCAT)
 
-constdefs
-  VB :: "nat => bool" 
+definition VB :: "nat => bool" where 
   "VB == %n::nat. n mod 2 ~= 0"
 
 lemma VB_DEF: "ALL n::nat. VB n = (n mod 2 ~= 0)"
   by (import bword_num VB_DEF)
 
-constdefs
-  NBWORD :: "nat => nat => bool word" 
+definition NBWORD :: "nat => nat => bool word" where 
   "NBWORD == %(n::nat) m::nat. WORD (NLIST n VB 2 m)"
 
 lemma NBWORD_DEF: "ALL (n::nat) m::nat. NBWORD n m = WORD (NLIST n VB 2 m)"
--- a/src/HOL/Import/HOL/HOL4Word32.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Import/HOL/HOL4Word32.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -68,8 +68,7 @@
    BITS h l n = MOD_2EXP (Suc h - l) (DIV_2EXP l n)"
   by (import bits BITS_def)
 
-constdefs
-  bit :: "nat => nat => bool" 
+definition bit :: "nat => nat => bool" where 
   "bit == %(b::nat) n::nat. BITS b b n = 1"
 
 lemma BIT_def: "ALL (b::nat) n::nat. bit b n = (BITS b b n = 1)"
@@ -840,15 +839,13 @@
 lemma w_T_def: "w_T = mk_word32 (EQUIV COMP0)"
   by (import word32 w_T_def)
 
-constdefs
-  word_suc :: "word32 => word32" 
+definition word_suc :: "word32 => word32" where 
   "word_suc == %T1::word32. mk_word32 (EQUIV (Suc (Eps (dest_word32 T1))))"
 
 lemma word_suc: "ALL T1::word32. word_suc T1 = mk_word32 (EQUIV (Suc (Eps (dest_word32 T1))))"
   by (import word32 word_suc)
 
-constdefs
-  word_add :: "word32 => word32 => word32" 
+definition word_add :: "word32 => word32 => word32" where 
   "word_add ==
 %(T1::word32) T2::word32.
    mk_word32 (EQUIV (Eps (dest_word32 T1) + Eps (dest_word32 T2)))"
@@ -858,8 +855,7 @@
    mk_word32 (EQUIV (Eps (dest_word32 T1) + Eps (dest_word32 T2)))"
   by (import word32 word_add)
 
-constdefs
-  word_mul :: "word32 => word32 => word32" 
+definition word_mul :: "word32 => word32 => word32" where 
   "word_mul ==
 %(T1::word32) T2::word32.
    mk_word32 (EQUIV (Eps (dest_word32 T1) * Eps (dest_word32 T2)))"
@@ -869,8 +865,7 @@
    mk_word32 (EQUIV (Eps (dest_word32 T1) * Eps (dest_word32 T2)))"
   by (import word32 word_mul)
 
-constdefs
-  word_1comp :: "word32 => word32" 
+definition word_1comp :: "word32 => word32" where 
   "word_1comp ==
 %T1::word32. mk_word32 (EQUIV (ONE_COMP (Eps (dest_word32 T1))))"
 
@@ -878,8 +873,7 @@
    word_1comp T1 = mk_word32 (EQUIV (ONE_COMP (Eps (dest_word32 T1))))"
   by (import word32 word_1comp)
 
-constdefs
-  word_2comp :: "word32 => word32" 
+definition word_2comp :: "word32 => word32" where 
   "word_2comp ==
 %T1::word32. mk_word32 (EQUIV (TWO_COMP (Eps (dest_word32 T1))))"
 
@@ -887,24 +881,21 @@
    word_2comp T1 = mk_word32 (EQUIV (TWO_COMP (Eps (dest_word32 T1))))"
   by (import word32 word_2comp)
 
-constdefs
-  word_lsr1 :: "word32 => word32" 
+definition word_lsr1 :: "word32 => word32" where 
   "word_lsr1 == %T1::word32. mk_word32 (EQUIV (LSR_ONE (Eps (dest_word32 T1))))"
 
 lemma word_lsr1: "ALL T1::word32.
    word_lsr1 T1 = mk_word32 (EQUIV (LSR_ONE (Eps (dest_word32 T1))))"
   by (import word32 word_lsr1)
 
-constdefs
-  word_asr1 :: "word32 => word32" 
+definition word_asr1 :: "word32 => word32" where 
   "word_asr1 == %T1::word32. mk_word32 (EQUIV (ASR_ONE (Eps (dest_word32 T1))))"
 
 lemma word_asr1: "ALL T1::word32.
    word_asr1 T1 = mk_word32 (EQUIV (ASR_ONE (Eps (dest_word32 T1))))"
   by (import word32 word_asr1)
 
-constdefs
-  word_ror1 :: "word32 => word32" 
+definition word_ror1 :: "word32 => word32" where 
   "word_ror1 == %T1::word32. mk_word32 (EQUIV (ROR_ONE (Eps (dest_word32 T1))))"
 
 lemma word_ror1: "ALL T1::word32.
@@ -940,8 +931,7 @@
 lemma MSB_def: "ALL T1::word32. MSB T1 = MSBn (Eps (dest_word32 T1))"
   by (import word32 MSB_def)
 
-constdefs
-  bitwise_or :: "word32 => word32 => word32" 
+definition bitwise_or :: "word32 => word32 => word32" where 
   "bitwise_or ==
 %(T1::word32) T2::word32.
    mk_word32 (EQUIV (OR (Eps (dest_word32 T1)) (Eps (dest_word32 T2))))"
@@ -951,8 +941,7 @@
    mk_word32 (EQUIV (OR (Eps (dest_word32 T1)) (Eps (dest_word32 T2))))"
   by (import word32 bitwise_or)
 
-constdefs
-  bitwise_eor :: "word32 => word32 => word32" 
+definition bitwise_eor :: "word32 => word32 => word32" where 
   "bitwise_eor ==
 %(T1::word32) T2::word32.
    mk_word32 (EQUIV (EOR (Eps (dest_word32 T1)) (Eps (dest_word32 T2))))"
@@ -962,8 +951,7 @@
    mk_word32 (EQUIV (EOR (Eps (dest_word32 T1)) (Eps (dest_word32 T2))))"
   by (import word32 bitwise_eor)
 
-constdefs
-  bitwise_and :: "word32 => word32 => word32" 
+definition bitwise_and :: "word32 => word32 => word32" where 
   "bitwise_and ==
 %(T1::word32) T2::word32.
    mk_word32 (EQUIV (AND (Eps (dest_word32 T1)) (Eps (dest_word32 T2))))"
@@ -1154,36 +1142,31 @@
 lemma ADD_TWO_COMP2: "ALL x::word32. word_add (word_2comp x) x = w_0"
   by (import word32 ADD_TWO_COMP2)
 
-constdefs
-  word_sub :: "word32 => word32 => word32" 
+definition word_sub :: "word32 => word32 => word32" where 
   "word_sub == %(a::word32) b::word32. word_add a (word_2comp b)"
 
 lemma word_sub: "ALL (a::word32) b::word32. word_sub a b = word_add a (word_2comp b)"
   by (import word32 word_sub)
 
-constdefs
-  word_lsl :: "word32 => nat => word32" 
+definition word_lsl :: "word32 => nat => word32" where 
   "word_lsl == %(a::word32) n::nat. word_mul a (n2w (2 ^ n))"
 
 lemma word_lsl: "ALL (a::word32) n::nat. word_lsl a n = word_mul a (n2w (2 ^ n))"
   by (import word32 word_lsl)
 
-constdefs
-  word_lsr :: "word32 => nat => word32" 
+definition word_lsr :: "word32 => nat => word32" where 
   "word_lsr == %(a::word32) n::nat. (word_lsr1 ^^ n) a"
 
 lemma word_lsr: "ALL (a::word32) n::nat. word_lsr a n = (word_lsr1 ^^ n) a"
   by (import word32 word_lsr)
 
-constdefs
-  word_asr :: "word32 => nat => word32" 
+definition word_asr :: "word32 => nat => word32" where 
   "word_asr == %(a::word32) n::nat. (word_asr1 ^^ n) a"
 
 lemma word_asr: "ALL (a::word32) n::nat. word_asr a n = (word_asr1 ^^ n) a"
   by (import word32 word_asr)
 
-constdefs
-  word_ror :: "word32 => nat => word32" 
+definition word_ror :: "word32 => nat => word32" where 
   "word_ror == %(a::word32) n::nat. (word_ror1 ^^ n) a"
 
 lemma word_ror: "ALL (a::word32) n::nat. word_ror a n = (word_ror1 ^^ n) a"
--- a/src/HOL/Import/HOL4Compat.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Import/HOL4Compat.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -15,8 +15,7 @@
 lemma COND_DEF:"(If b t f) = (@x. ((b = True) --> (x = t)) & ((b = False) --> (x = f)))"
   by auto
 
-constdefs
-  LET :: "['a \<Rightarrow> 'b,'a] \<Rightarrow> 'b"
+definition LET :: "['a \<Rightarrow> 'b,'a] \<Rightarrow> 'b" where
   "LET f s == f s"
 
 lemma [hol4rew]: "LET f s = Let s f"
@@ -119,10 +118,10 @@
 lemma LESS_OR_EQ: "m <= (n::nat) = (m < n | m = n)"
   by auto
 
-constdefs
-  nat_gt :: "nat => nat => bool"
+definition nat_gt :: "nat => nat => bool" where
   "nat_gt == %m n. n < m"
-  nat_ge :: "nat => nat => bool"
+
+definition nat_ge :: "nat => nat => bool" where
   "nat_ge == %m n. nat_gt m n | m = n"
 
 lemma [hol4rew]: "nat_gt m n = (n < m)"
@@ -200,8 +199,7 @@
   qed
 qed;
 
-constdefs
-  FUNPOW :: "('a => 'a) => nat => 'a => 'a"
+definition FUNPOW :: "('a => 'a) => nat => 'a => 'a" where
   "FUNPOW f n == f ^^ n"
 
 lemma FUNPOW: "(ALL f x. (f ^^ 0) x = x) &
@@ -229,14 +227,16 @@
 lemma DIVISION: "(0::nat) < n --> (!k. (k = k div n * n + k mod n) & k mod n < n)"
   by simp
 
-constdefs
-  ALT_ZERO :: nat
+definition ALT_ZERO :: nat where 
   "ALT_ZERO == 0"
-  NUMERAL_BIT1 :: "nat \<Rightarrow> nat"
+
+definition NUMERAL_BIT1 :: "nat \<Rightarrow> nat" where 
   "NUMERAL_BIT1 n == n + (n + Suc 0)"
-  NUMERAL_BIT2 :: "nat \<Rightarrow> nat"
+
+definition NUMERAL_BIT2 :: "nat \<Rightarrow> nat" where 
   "NUMERAL_BIT2 n == n + (n + Suc (Suc 0))"
-  NUMERAL :: "nat \<Rightarrow> nat"
+
+definition NUMERAL :: "nat \<Rightarrow> nat" where 
   "NUMERAL x == x"
 
 lemma [hol4rew]: "NUMERAL ALT_ZERO = 0"
@@ -329,8 +329,7 @@
 lemma NULL_DEF: "(null [] = True) & (!h t. null (h # t) = False)"
   by simp
 
-constdefs
-  sum :: "nat list \<Rightarrow> nat"
+definition sum :: "nat list \<Rightarrow> nat" where
   "sum l == foldr (op +) l 0"
 
 lemma SUM: "(sum [] = 0) & (!h t. sum (h#t) = h + sum t)"
@@ -359,8 +358,7 @@
   (ALL n x. replicate (Suc n) x = x # replicate n x)"
   by simp
 
-constdefs
-  FOLDR :: "[['a,'b]\<Rightarrow>'b,'b,'a list] \<Rightarrow> 'b"
+definition FOLDR :: "[['a,'b]\<Rightarrow>'b,'b,'a list] \<Rightarrow> 'b" where
   "FOLDR f e l == foldr f l e"
 
 lemma [hol4rew]: "FOLDR f e l = foldr f l e"
@@ -418,8 +416,7 @@
 lemma list_CASES: "(l = []) | (? t h. l = h#t)"
   by (induct l,auto)
 
-constdefs
-  ZIP :: "'a list * 'b list \<Rightarrow> ('a * 'b) list"
+definition ZIP :: "'a list * 'b list \<Rightarrow> ('a * 'b) list" where
   "ZIP == %(a,b). zip a b"
 
 lemma ZIP: "(zip [] [] = []) &
@@ -514,8 +511,7 @@
 lemma pow: "(!x::real. x ^ 0 = 1) & (!x::real. ALL n. x ^ (Suc n) = x * x ^ n)"
   by simp
 
-constdefs
-  real_gt :: "real => real => bool" 
+definition real_gt :: "real => real => bool" where 
   "real_gt == %x y. y < x"
 
 lemma [hol4rew]: "real_gt x y = (y < x)"
@@ -524,8 +520,7 @@
 lemma real_gt: "ALL x (y::real). (y < x) = (y < x)"
   by simp
 
-constdefs
-  real_ge :: "real => real => bool"
+definition real_ge :: "real => real => bool" where
   "real_ge x y == y <= x"
 
 lemma [hol4rew]: "real_ge x y = (y <= x)"
--- a/src/HOL/Import/HOLLight/HOLLight.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Import/HOLLight/HOLLight.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -95,8 +95,7 @@
 lemma EXCLUDED_MIDDLE: "ALL t::bool. t | ~ t"
   by (import hollight EXCLUDED_MIDDLE)
 
-constdefs
-  COND :: "bool => 'A => 'A => 'A" 
+definition COND :: "bool => 'A => 'A => 'A" where 
   "COND ==
 %(t::bool) (t1::'A::type) t2::'A::type.
    SOME x::'A::type. (t = True --> x = t1) & (t = False --> x = t2)"
@@ -173,15 +172,13 @@
 (b & P x True | ~ b & P y False)"
   by (import hollight th_cond)
 
-constdefs
-  LET_END :: "'A => 'A" 
+definition LET_END :: "'A => 'A" where 
   "LET_END == %t::'A::type. t"
 
 lemma DEF_LET_END: "LET_END = (%t::'A::type. t)"
   by (import hollight DEF_LET_END)
 
-constdefs
-  GABS :: "('A => bool) => 'A" 
+definition GABS :: "('A => bool) => 'A" where 
   "(op ==::(('A::type => bool) => 'A::type)
         => (('A::type => bool) => 'A::type) => prop)
  (GABS::('A::type => bool) => 'A::type)
@@ -193,8 +190,7 @@
  (Eps::('A::type => bool) => 'A::type)"
   by (import hollight DEF_GABS)
 
-constdefs
-  GEQ :: "'A => 'A => bool" 
+definition GEQ :: "'A => 'A => bool" where 
   "(op ==::('A::type => 'A::type => bool)
         => ('A::type => 'A::type => bool) => prop)
  (GEQ::'A::type => 'A::type => bool) (op =::'A::type => 'A::type => bool)"
@@ -208,8 +204,7 @@
    x = Pair_Rep a b"
   by (import hollight PAIR_EXISTS_THM)
 
-constdefs
-  CURRY :: "('A * 'B => 'C) => 'A => 'B => 'C" 
+definition CURRY :: "('A * 'B => 'C) => 'A => 'B => 'C" where 
   "CURRY ==
 %(u::'A::type * 'B::type => 'C::type) (ua::'A::type) ub::'B::type.
    u (ua, ub)"
@@ -219,8 +214,7 @@
     u (ua, ub))"
   by (import hollight DEF_CURRY)
 
-constdefs
-  UNCURRY :: "('A => 'B => 'C) => 'A * 'B => 'C" 
+definition UNCURRY :: "('A => 'B => 'C) => 'A * 'B => 'C" where 
   "UNCURRY ==
 %(u::'A::type => 'B::type => 'C::type) ua::'A::type * 'B::type.
    u (fst ua) (snd ua)"
@@ -230,8 +224,7 @@
     u (fst ua) (snd ua))"
   by (import hollight DEF_UNCURRY)
 
-constdefs
-  PASSOC :: "(('A * 'B) * 'C => 'D) => 'A * 'B * 'C => 'D" 
+definition PASSOC :: "(('A * 'B) * 'C => 'D) => 'A * 'B * 'C => 'D" where 
   "PASSOC ==
 %(u::('A::type * 'B::type) * 'C::type => 'D::type)
    ua::'A::type * 'B::type * 'C::type.
@@ -291,8 +284,7 @@
    (m * n = NUMERAL_BIT1 0) = (m = NUMERAL_BIT1 0 & n = NUMERAL_BIT1 0)"
   by (import hollight MULT_EQ_1)
 
-constdefs
-  EXP :: "nat => nat => nat" 
+definition EXP :: "nat => nat => nat" where 
   "EXP ==
 SOME EXP::nat => nat => nat.
    (ALL m::nat. EXP m 0 = NUMERAL_BIT1 0) &
@@ -549,8 +541,7 @@
    (EX m::nat. P m & (ALL x::nat. P x --> <= x m))"
   by (import hollight num_MAX)
 
-constdefs
-  EVEN :: "nat => bool" 
+definition EVEN :: "nat => bool" where 
   "EVEN ==
 SOME EVEN::nat => bool.
    EVEN 0 = True & (ALL n::nat. EVEN (Suc n) = (~ EVEN n))"
@@ -560,8 +551,7 @@
     EVEN 0 = True & (ALL n::nat. EVEN (Suc n) = (~ EVEN n)))"
   by (import hollight DEF_EVEN)
 
-constdefs
-  ODD :: "nat => bool" 
+definition ODD :: "nat => bool" where 
   "ODD ==
 SOME ODD::nat => bool. ODD 0 = False & (ALL n::nat. ODD (Suc n) = (~ ODD n))"
 
@@ -641,8 +631,7 @@
 lemma SUC_SUB1: "ALL x::nat. Suc x - NUMERAL_BIT1 0 = x"
   by (import hollight SUC_SUB1)
 
-constdefs
-  FACT :: "nat => nat" 
+definition FACT :: "nat => nat" where 
   "FACT ==
 SOME FACT::nat => nat.
    FACT 0 = NUMERAL_BIT1 0 & (ALL n::nat. FACT (Suc n) = Suc n * FACT n)"
@@ -669,8 +658,7 @@
       COND (n = 0) (x = 0 & xa = 0) (m = x * n + xa & < xa n)"
   by (import hollight DIVMOD_EXIST_0)
 
-constdefs
-  DIV :: "nat => nat => nat" 
+definition DIV :: "nat => nat => nat" where 
   "DIV ==
 SOME q::nat => nat => nat.
    EX r::nat => nat => nat.
@@ -686,8 +674,7 @@
            (m = q m n * n + r m n & < (r m n) n))"
   by (import hollight DEF_DIV)
 
-constdefs
-  MOD :: "nat => nat => nat" 
+definition MOD :: "nat => nat => nat" where 
   "MOD ==
 SOME r::nat => nat => nat.
    ALL (m::nat) n::nat.
@@ -877,8 +864,7 @@
  n ~= 0 & (ALL (q::nat) r::nat. m = q * n + r & < r n --> P q r))"
   by (import hollight DIVMOD_ELIM_THM)
 
-constdefs
-  eqeq :: "'q_9910 => 'q_9909 => ('q_9910 => 'q_9909 => bool) => bool" 
+definition eqeq :: "'q_9910 => 'q_9909 => ('q_9910 => 'q_9909 => bool) => bool" where 
   "eqeq ==
 %(u::'q_9910::type) (ua::'q_9909::type)
    ub::'q_9910::type => 'q_9909::type => bool. ub u ua"
@@ -888,8 +874,7 @@
     ub::'q_9910::type => 'q_9909::type => bool. ub u ua)"
   by (import hollight DEF__equal__equal_)
 
-constdefs
-  mod_nat :: "nat => nat => nat => bool" 
+definition mod_nat :: "nat => nat => nat => bool" where 
   "mod_nat ==
 %(u::nat) (ua::nat) ub::nat. EX (q1::nat) q2::nat. ua + u * q1 = ub + u * q2"
 
@@ -898,8 +883,7 @@
     EX (q1::nat) q2::nat. ua + u * q1 = ub + u * q2)"
   by (import hollight DEF_mod_nat)
 
-constdefs
-  minimal :: "(nat => bool) => nat" 
+definition minimal :: "(nat => bool) => nat" where 
   "minimal == %u::nat => bool. SOME n::nat. u n & (ALL m::nat. < m n --> ~ u m)"
 
 lemma DEF_minimal: "minimal =
@@ -910,8 +894,7 @@
    Ex P = (P (minimal P) & (ALL x::nat. < x (minimal P) --> ~ P x))"
   by (import hollight MINIMAL)
 
-constdefs
-  WF :: "('A => 'A => bool) => bool" 
+definition WF :: "('A => 'A => bool) => bool" where 
   "WF ==
 %u::'A::type => 'A::type => bool.
    ALL P::'A::type => bool.
@@ -1605,8 +1588,7 @@
        ALL (xa::'A::type) y::'B::type. x (P xa y) = xa & Y (P xa y) = y)"
   by (import hollight INJ_INVERSE2)
 
-constdefs
-  NUMPAIR :: "nat => nat => nat" 
+definition NUMPAIR :: "nat => nat => nat" where 
   "NUMPAIR ==
 %(u::nat) ua::nat.
    EXP (NUMERAL_BIT0 (NUMERAL_BIT1 0)) u *
@@ -1626,8 +1608,7 @@
    (NUMPAIR x1 y1 = NUMPAIR x2 y2) = (x1 = x2 & y1 = y2)"
   by (import hollight NUMPAIR_INJ)
 
-constdefs
-  NUMFST :: "nat => nat" 
+definition NUMFST :: "nat => nat" where 
   "NUMFST ==
 SOME X::nat => nat.
    EX Y::nat => nat.
@@ -1639,8 +1620,7 @@
        ALL (x::nat) y::nat. X (NUMPAIR x y) = x & Y (NUMPAIR x y) = y)"
   by (import hollight DEF_NUMFST)
 
-constdefs
-  NUMSND :: "nat => nat" 
+definition NUMSND :: "nat => nat" where 
   "NUMSND ==
 SOME Y::nat => nat.
    ALL (x::nat) y::nat. NUMFST (NUMPAIR x y) = x & Y (NUMPAIR x y) = y"
@@ -1650,8 +1630,7 @@
     ALL (x::nat) y::nat. NUMFST (NUMPAIR x y) = x & Y (NUMPAIR x y) = y)"
   by (import hollight DEF_NUMSND)
 
-constdefs
-  NUMSUM :: "bool => nat => nat" 
+definition NUMSUM :: "bool => nat => nat" where 
   "NUMSUM ==
 %(u::bool) ua::nat.
    COND u (Suc (NUMERAL_BIT0 (NUMERAL_BIT1 0) * ua))
@@ -1667,8 +1646,7 @@
    (NUMSUM b1 x1 = NUMSUM b2 x2) = (b1 = b2 & x1 = x2)"
   by (import hollight NUMSUM_INJ)
 
-constdefs
-  NUMLEFT :: "nat => bool" 
+definition NUMLEFT :: "nat => bool" where 
   "NUMLEFT ==
 SOME X::nat => bool.
    EX Y::nat => nat.
@@ -1680,8 +1658,7 @@
        ALL (x::bool) y::nat. X (NUMSUM x y) = x & Y (NUMSUM x y) = y)"
   by (import hollight DEF_NUMLEFT)
 
-constdefs
-  NUMRIGHT :: "nat => nat" 
+definition NUMRIGHT :: "nat => nat" where 
   "NUMRIGHT ==
 SOME Y::nat => nat.
    ALL (x::bool) y::nat. NUMLEFT (NUMSUM x y) = x & Y (NUMSUM x y) = y"
@@ -1691,8 +1668,7 @@
     ALL (x::bool) y::nat. NUMLEFT (NUMSUM x y) = x & Y (NUMSUM x y) = y)"
   by (import hollight DEF_NUMRIGHT)
 
-constdefs
-  INJN :: "nat => nat => 'A => bool" 
+definition INJN :: "nat => nat => 'A => bool" where 
   "INJN == %(u::nat) (n::nat) a::'A::type. n = u"
 
 lemma DEF_INJN: "INJN = (%(u::nat) (n::nat) a::'A::type. n = u)"
@@ -1710,8 +1686,7 @@
            ((op =::nat => nat => bool) n1 n2)))"
   by (import hollight INJN_INJ)
 
-constdefs
-  INJA :: "'A => nat => 'A => bool" 
+definition INJA :: "'A => nat => 'A => bool" where 
   "INJA == %(u::'A::type) (n::nat) b::'A::type. b = u"
 
 lemma DEF_INJA: "INJA = (%(u::'A::type) (n::nat) b::'A::type. b = u)"
@@ -1720,8 +1695,7 @@
 lemma INJA_INJ: "ALL (a1::'A::type) a2::'A::type. (INJA a1 = INJA a2) = (a1 = a2)"
   by (import hollight INJA_INJ)
 
-constdefs
-  INJF :: "(nat => nat => 'A => bool) => nat => 'A => bool" 
+definition INJF :: "(nat => nat => 'A => bool) => nat => 'A => bool" where 
   "INJF == %(u::nat => nat => 'A::type => bool) n::nat. u (NUMFST n) (NUMSND n)"
 
 lemma DEF_INJF: "INJF =
@@ -1732,8 +1706,7 @@
    (INJF f1 = INJF f2) = (f1 = f2)"
   by (import hollight INJF_INJ)
 
-constdefs
-  INJP :: "(nat => 'A => bool) => (nat => 'A => bool) => nat => 'A => bool" 
+definition INJP :: "(nat => 'A => bool) => (nat => 'A => bool) => nat => 'A => bool" where 
   "INJP ==
 %(u::nat => 'A::type => bool) (ua::nat => 'A::type => bool) (n::nat)
    a::'A::type. COND (NUMLEFT n) (u (NUMRIGHT n) a) (ua (NUMRIGHT n) a)"
@@ -1748,8 +1721,7 @@
    (INJP f1 f2 = INJP f1' f2') = (f1 = f1' & f2 = f2')"
   by (import hollight INJP_INJ)
 
-constdefs
-  ZCONSTR :: "nat => 'A => (nat => nat => 'A => bool) => nat => 'A => bool" 
+definition ZCONSTR :: "nat => 'A => (nat => nat => 'A => bool) => nat => 'A => bool" where 
   "ZCONSTR ==
 %(u::nat) (ua::'A::type) ub::nat => nat => 'A::type => bool.
    INJP (INJN (Suc u)) (INJP (INJA ua) (INJF ub))"
@@ -1759,8 +1731,7 @@
     INJP (INJN (Suc u)) (INJP (INJA ua) (INJF ub)))"
   by (import hollight DEF_ZCONSTR)
 
-constdefs
-  ZBOT :: "nat => 'A => bool" 
+definition ZBOT :: "nat => 'A => bool" where 
   "ZBOT == INJP (INJN 0) (SOME z::nat => 'A::type => bool. True)"
 
 lemma DEF_ZBOT: "ZBOT = INJP (INJN 0) (SOME z::nat => 'A::type => bool. True)"
@@ -1770,8 +1741,7 @@
    ZCONSTR x xa xb ~= ZBOT"
   by (import hollight ZCONSTR_ZBOT)
 
-constdefs
-  ZRECSPACE :: "(nat => 'A => bool) => bool" 
+definition ZRECSPACE :: "(nat => 'A => bool) => bool" where 
   "ZRECSPACE ==
 %a::nat => 'A::type => bool.
    ALL ZRECSPACE'::(nat => 'A::type => bool) => bool.
@@ -1809,8 +1779,7 @@
   [where a="a :: 'A recspace" and r=r ,
    OF type_definition_recspace]
 
-constdefs
-  BOTTOM :: "'A recspace" 
+definition BOTTOM :: "'A recspace" where 
   "(op ==::'A::type recspace => 'A::type recspace => prop)
  (BOTTOM::'A::type recspace)
  ((_mk_rec::(nat => 'A::type => bool) => 'A::type recspace)
@@ -1822,8 +1791,7 @@
    (ZBOT::nat => 'A::type => bool))"
   by (import hollight DEF_BOTTOM)
 
-constdefs
-  CONSTR :: "nat => 'A => (nat => 'A recspace) => 'A recspace" 
+definition CONSTR :: "nat => 'A => (nat => 'A recspace) => 'A recspace" where 
   "(op ==::(nat => 'A::type => (nat => 'A::type recspace) => 'A::type recspace)
         => (nat
             => 'A::type => (nat => 'A::type recspace) => 'A::type recspace)
@@ -1900,8 +1868,7 @@
          f (CONSTR c i r) = Fn c i r (%n::nat. f (r n))"
   by (import hollight CONSTR_REC)
 
-constdefs
-  FCONS :: "'A => (nat => 'A) => nat => 'A" 
+definition FCONS :: "'A => (nat => 'A) => nat => 'A" where 
   "FCONS ==
 SOME FCONS::'A::type => (nat => 'A::type) => nat => 'A::type.
    (ALL (a::'A::type) f::nat => 'A::type. FCONS a f 0 = a) &
@@ -1917,8 +1884,7 @@
 lemma FCONS_UNDO: "ALL f::nat => 'A::type. f = FCONS (f 0) (f o Suc)"
   by (import hollight FCONS_UNDO)
 
-constdefs
-  FNIL :: "nat => 'A" 
+definition FNIL :: "nat => 'A" where 
   "FNIL == %u::nat. SOME x::'A::type. True"
 
 lemma DEF_FNIL: "FNIL = (%u::nat. SOME x::'A::type. True)"
@@ -1995,8 +1961,7 @@
   [where a="a :: 'A hollight.option" and r=r ,
    OF type_definition_option]
 
-constdefs
-  NONE :: "'A hollight.option" 
+definition NONE :: "'A hollight.option" where 
   "(op ==::'A::type hollight.option => 'A::type hollight.option => prop)
  (NONE::'A::type hollight.option)
  ((_mk_option::'A::type recspace => 'A::type hollight.option)
@@ -2093,8 +2058,7 @@
   [where a="a :: 'A hollight.list" and r=r ,
    OF type_definition_list]
 
-constdefs
-  NIL :: "'A hollight.list" 
+definition NIL :: "'A hollight.list" where 
   "(op ==::'A::type hollight.list => 'A::type hollight.list => prop)
  (NIL::'A::type hollight.list)
  ((_mk_list::'A::type recspace => 'A::type hollight.list)
@@ -2114,8 +2078,7 @@
      (%n::nat. BOTTOM::'A::type recspace)))"
   by (import hollight DEF_NIL)
 
-constdefs
-  CONS :: "'A => 'A hollight.list => 'A hollight.list" 
+definition CONS :: "'A => 'A hollight.list => 'A hollight.list" where 
   "(op ==::('A::type => 'A::type hollight.list => 'A::type hollight.list)
         => ('A::type => 'A::type hollight.list => 'A::type hollight.list)
            => prop)
@@ -2160,8 +2123,7 @@
    EX x::bool => 'A::type. x False = a & x True = b"
   by (import hollight bool_RECURSION)
 
-constdefs
-  ISO :: "('A => 'B) => ('B => 'A) => bool" 
+definition ISO :: "('A => 'B) => ('B => 'A) => bool" where 
   "ISO ==
 %(u::'A::type => 'B::type) ua::'B::type => 'A::type.
    (ALL x::'B::type. u (ua x) = x) & (ALL y::'A::type. ua (u y) = y)"
@@ -2244,15 +2206,13 @@
      (%n::nat. BOTTOM::bool recspace)))"
   by (import hollight DEF__10303)
 
-constdefs
-  two_1 :: "N_2" 
+definition two_1 :: "N_2" where 
   "two_1 == _10302"
 
 lemma DEF_two_1: "two_1 = _10302"
   by (import hollight DEF_two_1)
 
-constdefs
-  two_2 :: "N_2" 
+definition two_2 :: "N_2" where 
   "two_2 == _10303"
 
 lemma DEF_two_2: "two_2 = _10303"
@@ -2337,22 +2297,19 @@
      (%n::nat. BOTTOM::bool recspace)))"
   by (import hollight DEF__10328)
 
-constdefs
-  three_1 :: "N_3" 
+definition three_1 :: "N_3" where 
   "three_1 == _10326"
 
 lemma DEF_three_1: "three_1 = _10326"
   by (import hollight DEF_three_1)
 
-constdefs
-  three_2 :: "N_3" 
+definition three_2 :: "N_3" where 
   "three_2 == _10327"
 
 lemma DEF_three_2: "three_2 = _10327"
   by (import hollight DEF_three_2)
 
-constdefs
-  three_3 :: "N_3" 
+definition three_3 :: "N_3" where 
   "three_3 == _10328"
 
 lemma DEF_three_3: "three_3 = _10328"
@@ -2365,8 +2322,7 @@
    All P"
   by (import hollight list_INDUCT)
 
-constdefs
-  HD :: "'A hollight.list => 'A" 
+definition HD :: "'A hollight.list => 'A" where 
   "HD ==
 SOME HD::'A::type hollight.list => 'A::type.
    ALL (t::'A::type hollight.list) h::'A::type. HD (CONS h t) = h"
@@ -2376,8 +2332,7 @@
     ALL (t::'A::type hollight.list) h::'A::type. HD (CONS h t) = h)"
   by (import hollight DEF_HD)
 
-constdefs
-  TL :: "'A hollight.list => 'A hollight.list" 
+definition TL :: "'A hollight.list => 'A hollight.list" where 
   "TL ==
 SOME TL::'A::type hollight.list => 'A::type hollight.list.
    ALL (h::'A::type) t::'A::type hollight.list. TL (CONS h t) = t"
@@ -2387,8 +2342,7 @@
     ALL (h::'A::type) t::'A::type hollight.list. TL (CONS h t) = t)"
   by (import hollight DEF_TL)
 
-constdefs
-  APPEND :: "'A hollight.list => 'A hollight.list => 'A hollight.list" 
+definition APPEND :: "'A hollight.list => 'A hollight.list => 'A hollight.list" where 
   "APPEND ==
 SOME APPEND::'A::type hollight.list
              => 'A::type hollight.list => 'A::type hollight.list.
@@ -2405,8 +2359,7 @@
         APPEND (CONS h t) l = CONS h (APPEND t l)))"
   by (import hollight DEF_APPEND)
 
-constdefs
-  REVERSE :: "'A hollight.list => 'A hollight.list" 
+definition REVERSE :: "'A hollight.list => 'A hollight.list" where 
   "REVERSE ==
 SOME REVERSE::'A::type hollight.list => 'A::type hollight.list.
    REVERSE NIL = NIL &
@@ -2420,8 +2373,7 @@
         REVERSE (CONS x l) = APPEND (REVERSE l) (CONS x NIL)))"
   by (import hollight DEF_REVERSE)
 
-constdefs
-  LENGTH :: "'A hollight.list => nat" 
+definition LENGTH :: "'A hollight.list => nat" where 
   "LENGTH ==
 SOME LENGTH::'A::type hollight.list => nat.
    LENGTH NIL = 0 &
@@ -2435,8 +2387,7 @@
         LENGTH (CONS h t) = Suc (LENGTH t)))"
   by (import hollight DEF_LENGTH)
 
-constdefs
-  MAP :: "('A => 'B) => 'A hollight.list => 'B hollight.list" 
+definition MAP :: "('A => 'B) => 'A hollight.list => 'B hollight.list" where 
   "MAP ==
 SOME MAP::('A::type => 'B::type)
           => 'A::type hollight.list => 'B::type hollight.list.
@@ -2452,8 +2403,7 @@
         MAP f (CONS h t) = CONS (f h) (MAP f t)))"
   by (import hollight DEF_MAP)
 
-constdefs
-  LAST :: "'A hollight.list => 'A" 
+definition LAST :: "'A hollight.list => 'A" where 
   "LAST ==
 SOME LAST::'A::type hollight.list => 'A::type.
    ALL (h::'A::type) t::'A::type hollight.list.
@@ -2465,8 +2415,7 @@
        LAST (CONS h t) = COND (t = NIL) h (LAST t))"
   by (import hollight DEF_LAST)
 
-constdefs
-  REPLICATE :: "nat => 'q_16860 => 'q_16860 hollight.list" 
+definition REPLICATE :: "nat => 'q_16860 => 'q_16860 hollight.list" where 
   "REPLICATE ==
 SOME REPLICATE::nat => 'q_16860::type => 'q_16860::type hollight.list.
    (ALL x::'q_16860::type. REPLICATE 0 x = NIL) &
@@ -2480,8 +2429,7 @@
         REPLICATE (Suc n) x = CONS x (REPLICATE n x)))"
   by (import hollight DEF_REPLICATE)
 
-constdefs
-  NULL :: "'q_16875 hollight.list => bool" 
+definition NULL :: "'q_16875 hollight.list => bool" where 
   "NULL ==
 SOME NULL::'q_16875::type hollight.list => bool.
    NULL NIL = True &
@@ -2495,8 +2443,7 @@
         NULL (CONS h t) = False))"
   by (import hollight DEF_NULL)
 
-constdefs
-  ALL_list :: "('q_16895 => bool) => 'q_16895 hollight.list => bool" 
+definition ALL_list :: "('q_16895 => bool) => 'q_16895 hollight.list => bool" where 
   "ALL_list ==
 SOME u::('q_16895::type => bool) => 'q_16895::type hollight.list => bool.
    (ALL P::'q_16895::type => bool. u P NIL = True) &
@@ -2527,9 +2474,8 @@
         t::'q_16916::type hollight.list. u P (CONS h t) = (P h | u P t)))"
   by (import hollight DEF_EX)
 
-constdefs
-  ITLIST :: "('q_16939 => 'q_16938 => 'q_16938)
-=> 'q_16939 hollight.list => 'q_16938 => 'q_16938" 
+definition ITLIST :: "('q_16939 => 'q_16938 => 'q_16938)
+=> 'q_16939 hollight.list => 'q_16938 => 'q_16938" where 
   "ITLIST ==
 SOME ITLIST::('q_16939::type => 'q_16938::type => 'q_16938::type)
              => 'q_16939::type hollight.list
@@ -2553,8 +2499,7 @@
         ITLIST f (CONS h t) b = f h (ITLIST f t b)))"
   by (import hollight DEF_ITLIST)
 
-constdefs
-  MEM :: "'q_16964 => 'q_16964 hollight.list => bool" 
+definition MEM :: "'q_16964 => 'q_16964 hollight.list => bool" where 
   "MEM ==
 SOME MEM::'q_16964::type => 'q_16964::type hollight.list => bool.
    (ALL x::'q_16964::type. MEM x NIL = False) &
@@ -2570,9 +2515,8 @@
         MEM x (CONS h t) = (x = h | MEM x t)))"
   by (import hollight DEF_MEM)
 
-constdefs
-  ALL2 :: "('q_16997 => 'q_17004 => bool)
-=> 'q_16997 hollight.list => 'q_17004 hollight.list => bool" 
+definition ALL2 :: "('q_16997 => 'q_17004 => bool)
+=> 'q_16997 hollight.list => 'q_17004 hollight.list => bool" where 
   "ALL2 ==
 SOME ALL2::('q_16997::type => 'q_17004::type => bool)
            => 'q_16997::type hollight.list
@@ -2604,10 +2548,9 @@
 ALL2 P (CONS h1 t1) (CONS h2 t2) = (P h1 h2 & ALL2 P t1 t2)"
   by (import hollight ALL2)
 
-constdefs
-  MAP2 :: "('q_17089 => 'q_17096 => 'q_17086)
+definition MAP2 :: "('q_17089 => 'q_17096 => 'q_17086)
 => 'q_17089 hollight.list
-   => 'q_17096 hollight.list => 'q_17086 hollight.list" 
+   => 'q_17096 hollight.list => 'q_17086 hollight.list" where 
   "MAP2 ==
 SOME MAP2::('q_17089::type => 'q_17096::type => 'q_17086::type)
            => 'q_17089::type hollight.list
@@ -2639,8 +2582,7 @@
 CONS (f h1 h2) (MAP2 f t1 t2)"
   by (import hollight MAP2)
 
-constdefs
-  EL :: "nat => 'q_17157 hollight.list => 'q_17157" 
+definition EL :: "nat => 'q_17157 hollight.list => 'q_17157" where 
   "EL ==
 SOME EL::nat => 'q_17157::type hollight.list => 'q_17157::type.
    (ALL l::'q_17157::type hollight.list. EL 0 l = HD l) &
@@ -2654,8 +2596,7 @@
         EL (Suc n) l = EL n (TL l)))"
   by (import hollight DEF_EL)
 
-constdefs
-  FILTER :: "('q_17182 => bool) => 'q_17182 hollight.list => 'q_17182 hollight.list" 
+definition FILTER :: "('q_17182 => bool) => 'q_17182 hollight.list => 'q_17182 hollight.list" where 
   "FILTER ==
 SOME FILTER::('q_17182::type => bool)
              => 'q_17182::type hollight.list
@@ -2676,8 +2617,7 @@
         COND (P h) (CONS h (FILTER P t)) (FILTER P t)))"
   by (import hollight DEF_FILTER)
 
-constdefs
-  ASSOC :: "'q_17211 => ('q_17211 * 'q_17205) hollight.list => 'q_17205" 
+definition ASSOC :: "'q_17211 => ('q_17211 * 'q_17205) hollight.list => 'q_17205" where 
   "ASSOC ==
 SOME ASSOC::'q_17211::type
             => ('q_17211::type * 'q_17205::type) hollight.list
@@ -2695,9 +2635,8 @@
        ASSOC a (CONS h t) = COND (fst h = a) (snd h) (ASSOC a t))"
   by (import hollight DEF_ASSOC)
 
-constdefs
-  ITLIST2 :: "('q_17235 => 'q_17243 => 'q_17233 => 'q_17233)
-=> 'q_17235 hollight.list => 'q_17243 hollight.list => 'q_17233 => 'q_17233" 
+definition ITLIST2 :: "('q_17235 => 'q_17243 => 'q_17233 => 'q_17233)
+=> 'q_17235 hollight.list => 'q_17243 hollight.list => 'q_17233 => 'q_17233" where 
   "ITLIST2 ==
 SOME ITLIST2::('q_17235::type
                => 'q_17243::type => 'q_17233::type => 'q_17233::type)
@@ -3041,8 +2980,7 @@
 ALL2 Q l l'"
   by (import hollight MONO_ALL2)
 
-constdefs
-  dist :: "nat * nat => nat" 
+definition dist :: "nat * nat => nat" where 
   "dist == %u::nat * nat. fst u - snd u + (snd u - fst u)"
 
 lemma DEF_dist: "dist = (%u::nat * nat. fst u - snd u + (snd u - fst u))"
@@ -3133,8 +3071,7 @@
    (EX (x::nat) N::nat. ALL i::nat. <= N i --> <= (P i) (Q i + x))"
   by (import hollight BOUNDS_IGNORE)
 
-constdefs
-  is_nadd :: "(nat => nat) => bool" 
+definition is_nadd :: "(nat => nat) => bool" where 
   "is_nadd ==
 %u::nat => nat.
    EX B::nat.
@@ -3211,8 +3148,7 @@
           (A * n + B)"
   by (import hollight NADD_ALTMUL)
 
-constdefs
-  nadd_eq :: "nadd => nadd => bool" 
+definition nadd_eq :: "nadd => nadd => bool" where 
   "nadd_eq ==
 %(u::nadd) ua::nadd.
    EX B::nat. ALL n::nat. <= (dist (dest_nadd u n, dest_nadd ua n)) B"
@@ -3231,8 +3167,7 @@
 lemma NADD_EQ_TRANS: "ALL (x::nadd) (y::nadd) z::nadd. nadd_eq x y & nadd_eq y z --> nadd_eq x z"
   by (import hollight NADD_EQ_TRANS)
 
-constdefs
-  nadd_of_num :: "nat => nadd" 
+definition nadd_of_num :: "nat => nadd" where 
   "nadd_of_num == %u::nat. mk_nadd (op * u)"
 
 lemma DEF_nadd_of_num: "nadd_of_num = (%u::nat. mk_nadd (op * u))"
@@ -3247,8 +3182,7 @@
 lemma NADD_OF_NUM_EQ: "ALL (m::nat) n::nat. nadd_eq (nadd_of_num m) (nadd_of_num n) = (m = n)"
   by (import hollight NADD_OF_NUM_EQ)
 
-constdefs
-  nadd_le :: "nadd => nadd => bool" 
+definition nadd_le :: "nadd => nadd => bool" where 
   "nadd_le ==
 %(u::nadd) ua::nadd.
    EX B::nat. ALL n::nat. <= (dest_nadd u n) (dest_nadd ua n + B)"
@@ -3289,8 +3223,7 @@
 lemma NADD_OF_NUM_LE: "ALL (m::nat) n::nat. nadd_le (nadd_of_num m) (nadd_of_num n) = <= m n"
   by (import hollight NADD_OF_NUM_LE)
 
-constdefs
-  nadd_add :: "nadd => nadd => nadd" 
+definition nadd_add :: "nadd => nadd => nadd" where 
   "nadd_add ==
 %(u::nadd) ua::nadd. mk_nadd (%n::nat. dest_nadd u n + dest_nadd ua n)"
 
@@ -3332,8 +3265,7 @@
     (nadd_of_num (x + xa))"
   by (import hollight NADD_OF_NUM_ADD)
 
-constdefs
-  nadd_mul :: "nadd => nadd => nadd" 
+definition nadd_mul :: "nadd => nadd => nadd" where 
   "nadd_mul ==
 %(u::nadd) ua::nadd. mk_nadd (%n::nat. dest_nadd u (dest_nadd ua n))"
 
@@ -3438,8 +3370,7 @@
    (EX (A::nat) N::nat. ALL n::nat. <= N n --> <= n (A * dest_nadd x n))"
   by (import hollight NADD_LBOUND)
 
-constdefs
-  nadd_rinv :: "nadd => nat => nat" 
+definition nadd_rinv :: "nadd => nat => nat" where 
   "nadd_rinv == %(u::nadd) n::nat. DIV (n * n) (dest_nadd u n)"
 
 lemma DEF_nadd_rinv: "nadd_rinv = (%(u::nadd) n::nat. DIV (n * n) (dest_nadd u n))"
@@ -3528,8 +3459,7 @@
           <= (dist (m * nadd_rinv x n, n * nadd_rinv x m)) (B * (m + n)))"
   by (import hollight NADD_MUL_LINV_LEMMA8)
 
-constdefs
-  nadd_inv :: "nadd => nadd" 
+definition nadd_inv :: "nadd => nadd" where 
   "nadd_inv ==
 %u::nadd.
    COND (nadd_eq u (nadd_of_num 0)) (nadd_of_num 0) (mk_nadd (nadd_rinv u))"
@@ -3570,15 +3500,13 @@
   [where a="a :: hreal" and r=r ,
    OF type_definition_hreal]
 
-constdefs
-  hreal_of_num :: "nat => hreal" 
+definition hreal_of_num :: "nat => hreal" where 
   "hreal_of_num == %m::nat. mk_hreal (nadd_eq (nadd_of_num m))"
 
 lemma DEF_hreal_of_num: "hreal_of_num = (%m::nat. mk_hreal (nadd_eq (nadd_of_num m)))"
   by (import hollight DEF_hreal_of_num)
 
-constdefs
-  hreal_add :: "hreal => hreal => hreal" 
+definition hreal_add :: "hreal => hreal => hreal" where 
   "hreal_add ==
 %(x::hreal) y::hreal.
    mk_hreal
@@ -3594,8 +3522,7 @@
             nadd_eq (nadd_add xa ya) u & dest_hreal x xa & dest_hreal y ya))"
   by (import hollight DEF_hreal_add)
 
-constdefs
-  hreal_mul :: "hreal => hreal => hreal" 
+definition hreal_mul :: "hreal => hreal => hreal" where 
   "hreal_mul ==
 %(x::hreal) y::hreal.
    mk_hreal
@@ -3611,8 +3538,7 @@
             nadd_eq (nadd_mul xa ya) u & dest_hreal x xa & dest_hreal y ya))"
   by (import hollight DEF_hreal_mul)
 
-constdefs
-  hreal_le :: "hreal => hreal => bool" 
+definition hreal_le :: "hreal => hreal => bool" where 
   "hreal_le ==
 %(x::hreal) y::hreal.
    SOME u::bool.
@@ -3626,8 +3552,7 @@
           nadd_le xa ya = u & dest_hreal x xa & dest_hreal y ya)"
   by (import hollight DEF_hreal_le)
 
-constdefs
-  hreal_inv :: "hreal => hreal" 
+definition hreal_inv :: "hreal => hreal" where 
   "hreal_inv ==
 %x::hreal.
    mk_hreal
@@ -3685,22 +3610,19 @@
    hreal_le a b --> hreal_le (hreal_mul a c) (hreal_mul b c)"
   by (import hollight HREAL_LE_MUL_RCANCEL_IMP)
 
-constdefs
-  treal_of_num :: "nat => hreal * hreal" 
+definition treal_of_num :: "nat => hreal * hreal" where 
   "treal_of_num == %u::nat. (hreal_of_num u, hreal_of_num 0)"
 
 lemma DEF_treal_of_num: "treal_of_num = (%u::nat. (hreal_of_num u, hreal_of_num 0))"
   by (import hollight DEF_treal_of_num)
 
-constdefs
-  treal_neg :: "hreal * hreal => hreal * hreal" 
+definition treal_neg :: "hreal * hreal => hreal * hreal" where 
   "treal_neg == %u::hreal * hreal. (snd u, fst u)"
 
 lemma DEF_treal_neg: "treal_neg = (%u::hreal * hreal. (snd u, fst u))"
   by (import hollight DEF_treal_neg)
 
-constdefs
-  treal_add :: "hreal * hreal => hreal * hreal => hreal * hreal" 
+definition treal_add :: "hreal * hreal => hreal * hreal => hreal * hreal" where 
   "treal_add ==
 %(u::hreal * hreal) ua::hreal * hreal.
    (hreal_add (fst u) (fst ua), hreal_add (snd u) (snd ua))"
@@ -3710,8 +3632,7 @@
     (hreal_add (fst u) (fst ua), hreal_add (snd u) (snd ua)))"
   by (import hollight DEF_treal_add)
 
-constdefs
-  treal_mul :: "hreal * hreal => hreal * hreal => hreal * hreal" 
+definition treal_mul :: "hreal * hreal => hreal * hreal => hreal * hreal" where 
   "treal_mul ==
 %(u::hreal * hreal) ua::hreal * hreal.
    (hreal_add (hreal_mul (fst u) (fst ua)) (hreal_mul (snd u) (snd ua)),
@@ -3723,8 +3644,7 @@
      hreal_add (hreal_mul (fst u) (snd ua)) (hreal_mul (snd u) (fst ua))))"
   by (import hollight DEF_treal_mul)
 
-constdefs
-  treal_le :: "hreal * hreal => hreal * hreal => bool" 
+definition treal_le :: "hreal * hreal => hreal * hreal => bool" where 
   "treal_le ==
 %(u::hreal * hreal) ua::hreal * hreal.
    hreal_le (hreal_add (fst u) (snd ua)) (hreal_add (fst ua) (snd u))"
@@ -3734,8 +3654,7 @@
     hreal_le (hreal_add (fst u) (snd ua)) (hreal_add (fst ua) (snd u)))"
   by (import hollight DEF_treal_le)
 
-constdefs
-  treal_inv :: "hreal * hreal => hreal * hreal" 
+definition treal_inv :: "hreal * hreal => hreal * hreal" where 
   "treal_inv ==
 %u::hreal * hreal.
    COND (fst u = snd u) (hreal_of_num 0, hreal_of_num 0)
@@ -3755,8 +3674,7 @@
         hreal_inv (SOME d::hreal. snd u = hreal_add (fst u) d))))"
   by (import hollight DEF_treal_inv)
 
-constdefs
-  treal_eq :: "hreal * hreal => hreal * hreal => bool" 
+definition treal_eq :: "hreal * hreal => hreal * hreal => bool" where 
   "treal_eq ==
 %(u::hreal * hreal) ua::hreal * hreal.
    hreal_add (fst u) (snd ua) = hreal_add (fst ua) (snd u)"
@@ -3916,15 +3834,13 @@
   [where a="a :: hollight.real" and r=r ,
    OF type_definition_real]
 
-constdefs
-  real_of_num :: "nat => hollight.real" 
+definition real_of_num :: "nat => hollight.real" where 
   "real_of_num == %m::nat. mk_real (treal_eq (treal_of_num m))"
 
 lemma DEF_real_of_num: "real_of_num = (%m::nat. mk_real (treal_eq (treal_of_num m)))"
   by (import hollight DEF_real_of_num)
 
-constdefs
-  real_neg :: "hollight.real => hollight.real" 
+definition real_neg :: "hollight.real => hollight.real" where 
   "real_neg ==
 %x1::hollight.real.
    mk_real
@@ -3940,8 +3856,7 @@
             treal_eq (treal_neg x1a) u & dest_real x1 x1a))"
   by (import hollight DEF_real_neg)
 
-constdefs
-  real_add :: "hollight.real => hollight.real => hollight.real" 
+definition real_add :: "hollight.real => hollight.real => hollight.real" where 
   "real_add ==
 %(x1::hollight.real) y1::hollight.real.
    mk_real
@@ -3959,8 +3874,7 @@
             dest_real x1 x1a & dest_real y1 y1a))"
   by (import hollight DEF_real_add)
 
-constdefs
-  real_mul :: "hollight.real => hollight.real => hollight.real" 
+definition real_mul :: "hollight.real => hollight.real => hollight.real" where 
   "real_mul ==
 %(x1::hollight.real) y1::hollight.real.
    mk_real
@@ -3978,8 +3892,7 @@
             dest_real x1 x1a & dest_real y1 y1a))"
   by (import hollight DEF_real_mul)
 
-constdefs
-  real_le :: "hollight.real => hollight.real => bool" 
+definition real_le :: "hollight.real => hollight.real => bool" where 
   "real_le ==
 %(x1::hollight.real) y1::hollight.real.
    SOME u::bool.
@@ -3993,8 +3906,7 @@
           treal_le x1a y1a = u & dest_real x1 x1a & dest_real y1 y1a)"
   by (import hollight DEF_real_le)
 
-constdefs
-  real_inv :: "hollight.real => hollight.real" 
+definition real_inv :: "hollight.real => hollight.real" where 
   "real_inv ==
 %x::hollight.real.
    mk_real
@@ -4008,15 +3920,13 @@
          EX xa::hreal * hreal. treal_eq (treal_inv xa) u & dest_real x xa))"
   by (import hollight DEF_real_inv)
 
-constdefs
-  real_sub :: "hollight.real => hollight.real => hollight.real" 
+definition real_sub :: "hollight.real => hollight.real => hollight.real" where 
   "real_sub == %(u::hollight.real) ua::hollight.real. real_add u (real_neg ua)"
 
 lemma DEF_real_sub: "real_sub = (%(u::hollight.real) ua::hollight.real. real_add u (real_neg ua))"
   by (import hollight DEF_real_sub)
 
-constdefs
-  real_lt :: "hollight.real => hollight.real => bool" 
+definition real_lt :: "hollight.real => hollight.real => bool" where 
   "real_lt == %(u::hollight.real) ua::hollight.real. ~ real_le ua u"
 
 lemma DEF_real_lt: "real_lt = (%(u::hollight.real) ua::hollight.real. ~ real_le ua u)"
@@ -4040,8 +3950,7 @@
 lemma DEF_real_gt: "hollight.real_gt = (%(u::hollight.real) ua::hollight.real. real_lt ua u)"
   by (import hollight DEF_real_gt)
 
-constdefs
-  real_abs :: "hollight.real => hollight.real" 
+definition real_abs :: "hollight.real => hollight.real" where 
   "real_abs ==
 %u::hollight.real. COND (real_le (real_of_num 0) u) u (real_neg u)"
 
@@ -4049,8 +3958,7 @@
 (%u::hollight.real. COND (real_le (real_of_num 0) u) u (real_neg u))"
   by (import hollight DEF_real_abs)
 
-constdefs
-  real_pow :: "hollight.real => nat => hollight.real" 
+definition real_pow :: "hollight.real => nat => hollight.real" where 
   "real_pow ==
 SOME real_pow::hollight.real => nat => hollight.real.
    (ALL x::hollight.real. real_pow x 0 = real_of_num (NUMERAL_BIT1 0)) &
@@ -4064,22 +3972,19 @@
         real_pow x (Suc n) = real_mul x (real_pow x n)))"
   by (import hollight DEF_real_pow)
 
-constdefs
-  real_div :: "hollight.real => hollight.real => hollight.real" 
+definition real_div :: "hollight.real => hollight.real => hollight.real" where 
   "real_div == %(u::hollight.real) ua::hollight.real. real_mul u (real_inv ua)"
 
 lemma DEF_real_div: "real_div = (%(u::hollight.real) ua::hollight.real. real_mul u (real_inv ua))"
   by (import hollight DEF_real_div)
 
-constdefs
-  real_max :: "hollight.real => hollight.real => hollight.real" 
+definition real_max :: "hollight.real => hollight.real => hollight.real" where 
   "real_max == %(u::hollight.real) ua::hollight.real. COND (real_le u ua) ua u"
 
 lemma DEF_real_max: "real_max = (%(u::hollight.real) ua::hollight.real. COND (real_le u ua) ua u)"
   by (import hollight DEF_real_max)
 
-constdefs
-  real_min :: "hollight.real => hollight.real => hollight.real" 
+definition real_min :: "hollight.real => hollight.real => hollight.real" where 
   "real_min == %(u::hollight.real) ua::hollight.real. COND (real_le u ua) u ua"
 
 lemma DEF_real_min: "real_min = (%(u::hollight.real) ua::hollight.real. COND (real_le u ua) u ua)"
@@ -5212,8 +5117,7 @@
 (ALL x::hollight.real. All (P x))"
   by (import hollight REAL_WLOG_LT)
 
-constdefs
-  mod_real :: "hollight.real => hollight.real => hollight.real => bool" 
+definition mod_real :: "hollight.real => hollight.real => hollight.real => bool" where 
   "mod_real ==
 %(u::hollight.real) (ua::hollight.real) ub::hollight.real.
    EX q::hollight.real. real_sub ua ub = real_mul q u"
@@ -5223,8 +5127,7 @@
     EX q::hollight.real. real_sub ua ub = real_mul q u)"
   by (import hollight DEF_mod_real)
 
-constdefs
-  DECIMAL :: "nat => nat => hollight.real" 
+definition DECIMAL :: "nat => nat => hollight.real" where 
   "DECIMAL == %(u::nat) ua::nat. real_div (real_of_num u) (real_of_num ua)"
 
 lemma DEF_DECIMAL: "DECIMAL = (%(u::nat) ua::nat. real_div (real_of_num u) (real_of_num ua))"
@@ -5267,8 +5170,7 @@
 (real_mul x1 y2 = real_mul x2 y1)"
   by (import hollight RAT_LEMMA5)
 
-constdefs
-  is_int :: "hollight.real => bool" 
+definition is_int :: "hollight.real => bool" where 
   "is_int ==
 %u::hollight.real.
    EX n::nat. u = real_of_num n | u = real_neg (real_of_num n)"
@@ -5297,8 +5199,7 @@
       dest_int x = real_of_num n | dest_int x = real_neg (real_of_num n)"
   by (import hollight dest_int_rep)
 
-constdefs
-  int_le :: "hollight.int => hollight.int => bool" 
+definition int_le :: "hollight.int => hollight.int => bool" where 
   "int_le ==
 %(u::hollight.int) ua::hollight.int. real_le (dest_int u) (dest_int ua)"
 
@@ -5306,8 +5207,7 @@
 (%(u::hollight.int) ua::hollight.int. real_le (dest_int u) (dest_int ua))"
   by (import hollight DEF_int_le)
 
-constdefs
-  int_lt :: "hollight.int => hollight.int => bool" 
+definition int_lt :: "hollight.int => hollight.int => bool" where 
   "int_lt ==
 %(u::hollight.int) ua::hollight.int. real_lt (dest_int u) (dest_int ua)"
 
@@ -5315,8 +5215,7 @@
 (%(u::hollight.int) ua::hollight.int. real_lt (dest_int u) (dest_int ua))"
   by (import hollight DEF_int_lt)
 
-constdefs
-  int_ge :: "hollight.int => hollight.int => bool" 
+definition int_ge :: "hollight.int => hollight.int => bool" where 
   "int_ge ==
 %(u::hollight.int) ua::hollight.int.
    hollight.real_ge (dest_int u) (dest_int ua)"
@@ -5326,8 +5225,7 @@
     hollight.real_ge (dest_int u) (dest_int ua))"
   by (import hollight DEF_int_ge)
 
-constdefs
-  int_gt :: "hollight.int => hollight.int => bool" 
+definition int_gt :: "hollight.int => hollight.int => bool" where 
   "int_gt ==
 %(u::hollight.int) ua::hollight.int.
    hollight.real_gt (dest_int u) (dest_int ua)"
@@ -5337,8 +5235,7 @@
     hollight.real_gt (dest_int u) (dest_int ua))"
   by (import hollight DEF_int_gt)
 
-constdefs
-  int_of_num :: "nat => hollight.int" 
+definition int_of_num :: "nat => hollight.int" where 
   "int_of_num == %u::nat. mk_int (real_of_num u)"
 
 lemma DEF_int_of_num: "int_of_num = (%u::nat. mk_int (real_of_num u))"
@@ -5347,8 +5244,7 @@
 lemma int_of_num_th: "ALL x::nat. dest_int (int_of_num x) = real_of_num x"
   by (import hollight int_of_num_th)
 
-constdefs
-  int_neg :: "hollight.int => hollight.int" 
+definition int_neg :: "hollight.int => hollight.int" where 
   "int_neg == %u::hollight.int. mk_int (real_neg (dest_int u))"
 
 lemma DEF_int_neg: "int_neg = (%u::hollight.int. mk_int (real_neg (dest_int u)))"
@@ -5357,8 +5253,7 @@
 lemma int_neg_th: "ALL x::hollight.int. dest_int (int_neg x) = real_neg (dest_int x)"
   by (import hollight int_neg_th)
 
-constdefs
-  int_add :: "hollight.int => hollight.int => hollight.int" 
+definition int_add :: "hollight.int => hollight.int => hollight.int" where 
   "int_add ==
 %(u::hollight.int) ua::hollight.int.
    mk_int (real_add (dest_int u) (dest_int ua))"
@@ -5372,8 +5267,7 @@
    dest_int (int_add x xa) = real_add (dest_int x) (dest_int xa)"
   by (import hollight int_add_th)
 
-constdefs
-  int_sub :: "hollight.int => hollight.int => hollight.int" 
+definition int_sub :: "hollight.int => hollight.int => hollight.int" where 
   "int_sub ==
 %(u::hollight.int) ua::hollight.int.
    mk_int (real_sub (dest_int u) (dest_int ua))"
@@ -5387,8 +5281,7 @@
    dest_int (int_sub x xa) = real_sub (dest_int x) (dest_int xa)"
   by (import hollight int_sub_th)
 
-constdefs
-  int_mul :: "hollight.int => hollight.int => hollight.int" 
+definition int_mul :: "hollight.int => hollight.int => hollight.int" where 
   "int_mul ==
 %(u::hollight.int) ua::hollight.int.
    mk_int (real_mul (dest_int u) (dest_int ua))"
@@ -5402,8 +5295,7 @@
    dest_int (int_mul x y) = real_mul (dest_int x) (dest_int y)"
   by (import hollight int_mul_th)
 
-constdefs
-  int_abs :: "hollight.int => hollight.int" 
+definition int_abs :: "hollight.int => hollight.int" where 
   "int_abs == %u::hollight.int. mk_int (real_abs (dest_int u))"
 
 lemma DEF_int_abs: "int_abs = (%u::hollight.int. mk_int (real_abs (dest_int u)))"
@@ -5412,8 +5304,7 @@
 lemma int_abs_th: "ALL x::hollight.int. dest_int (int_abs x) = real_abs (dest_int x)"
   by (import hollight int_abs_th)
 
-constdefs
-  int_max :: "hollight.int => hollight.int => hollight.int" 
+definition int_max :: "hollight.int => hollight.int => hollight.int" where 
   "int_max ==
 %(u::hollight.int) ua::hollight.int.
    mk_int (real_max (dest_int u) (dest_int ua))"
@@ -5427,8 +5318,7 @@
    dest_int (int_max x y) = real_max (dest_int x) (dest_int y)"
   by (import hollight int_max_th)
 
-constdefs
-  int_min :: "hollight.int => hollight.int => hollight.int" 
+definition int_min :: "hollight.int => hollight.int => hollight.int" where 
   "int_min ==
 %(u::hollight.int) ua::hollight.int.
    mk_int (real_min (dest_int u) (dest_int ua))"
@@ -5442,8 +5332,7 @@
    dest_int (int_min x y) = real_min (dest_int x) (dest_int y)"
   by (import hollight int_min_th)
 
-constdefs
-  int_pow :: "hollight.int => nat => hollight.int" 
+definition int_pow :: "hollight.int => nat => hollight.int" where 
   "int_pow == %(u::hollight.int) ua::nat. mk_int (real_pow (dest_int u) ua)"
 
 lemma DEF_int_pow: "int_pow = (%(u::hollight.int) ua::nat. mk_int (real_pow (dest_int u) ua))"
@@ -5496,8 +5385,7 @@
    d ~= int_of_num 0 --> (EX c::hollight.int. int_lt x (int_mul c d))"
   by (import hollight INT_ARCH)
 
-constdefs
-  mod_int :: "hollight.int => hollight.int => hollight.int => bool" 
+definition mod_int :: "hollight.int => hollight.int => hollight.int => bool" where 
   "mod_int ==
 %(u::hollight.int) (ua::hollight.int) ub::hollight.int.
    EX q::hollight.int. int_sub ua ub = int_mul q u"
@@ -5507,8 +5395,7 @@
     EX q::hollight.int. int_sub ua ub = int_mul q u)"
   by (import hollight DEF_mod_int)
 
-constdefs
-  IN :: "'A => ('A => bool) => bool" 
+definition IN :: "'A => ('A => bool) => bool" where 
   "IN == %(u::'A::type) ua::'A::type => bool. ua u"
 
 lemma DEF_IN: "IN = (%(u::'A::type) ua::'A::type => bool. ua u)"
@@ -5518,15 +5405,13 @@
    (x = xa) = (ALL xb::'A::type. IN xb x = IN xb xa)"
   by (import hollight EXTENSION)
 
-constdefs
-  GSPEC :: "('A => bool) => 'A => bool" 
+definition GSPEC :: "('A => bool) => 'A => bool" where 
   "GSPEC == %u::'A::type => bool. u"
 
 lemma DEF_GSPEC: "GSPEC = (%u::'A::type => bool. u)"
   by (import hollight DEF_GSPEC)
 
-constdefs
-  SETSPEC :: "'q_37056 => bool => 'q_37056 => bool" 
+definition SETSPEC :: "'q_37056 => bool => 'q_37056 => bool" where 
   "SETSPEC == %(u::'q_37056::type) (ua::bool) ub::'q_37056::type. ua & u = ub"
 
 lemma DEF_SETSPEC: "SETSPEC = (%(u::'q_37056::type) (ua::bool) ub::'q_37056::type. ua & u = ub)"
@@ -5548,15 +5433,13 @@
 (ALL (p::'q_37194::type => bool) x::'q_37194::type. IN x p = p x)"
   by (import hollight IN_ELIM_THM)
 
-constdefs
-  EMPTY :: "'A => bool" 
+definition EMPTY :: "'A => bool" where 
   "EMPTY == %x::'A::type. False"
 
 lemma DEF_EMPTY: "EMPTY = (%x::'A::type. False)"
   by (import hollight DEF_EMPTY)
 
-constdefs
-  INSERT :: "'A => ('A => bool) => 'A => bool" 
+definition INSERT :: "'A => ('A => bool) => 'A => bool" where 
   "INSERT == %(u::'A::type) (ua::'A::type => bool) y::'A::type. IN y ua | y = u"
 
 lemma DEF_INSERT: "INSERT =
@@ -5585,8 +5468,7 @@
     GSPEC (%ub::'A::type. EX x::'A::type. SETSPEC ub (IN x u | IN x ua) x))"
   by (import hollight DEF_UNION)
 
-constdefs
-  UNIONS :: "(('A => bool) => bool) => 'A => bool" 
+definition UNIONS :: "(('A => bool) => bool) => 'A => bool" where 
   "UNIONS ==
 %u::('A::type => bool) => bool.
    GSPEC
@@ -5615,8 +5497,7 @@
     GSPEC (%ub::'A::type. EX x::'A::type. SETSPEC ub (IN x u & IN x ua) x))"
   by (import hollight DEF_INTER)
 
-constdefs
-  INTERS :: "(('A => bool) => bool) => 'A => bool" 
+definition INTERS :: "(('A => bool) => bool) => 'A => bool" where 
   "INTERS ==
 %u::('A::type => bool) => bool.
    GSPEC
@@ -5632,8 +5513,7 @@
             SETSPEC ua (ALL ua::'A::type => bool. IN ua u --> IN x ua) x))"
   by (import hollight DEF_INTERS)
 
-constdefs
-  DIFF :: "('A => bool) => ('A => bool) => 'A => bool" 
+definition DIFF :: "('A => bool) => ('A => bool) => 'A => bool" where 
   "DIFF ==
 %(u::'A::type => bool) ua::'A::type => bool.
    GSPEC (%ub::'A::type. EX x::'A::type. SETSPEC ub (IN x u & ~ IN x ua) x)"
@@ -5648,8 +5528,7 @@
 GSPEC (%u::'A::type. EX y::'A::type. SETSPEC u (IN y s | y = x) y)"
   by (import hollight INSERT)
 
-constdefs
-  DELETE :: "('A => bool) => 'A => 'A => bool" 
+definition DELETE :: "('A => bool) => 'A => 'A => bool" where 
   "DELETE ==
 %(u::'A::type => bool) ua::'A::type.
    GSPEC (%ub::'A::type. EX y::'A::type. SETSPEC ub (IN y u & y ~= ua) y)"
@@ -5659,8 +5538,7 @@
     GSPEC (%ub::'A::type. EX y::'A::type. SETSPEC ub (IN y u & y ~= ua) y))"
   by (import hollight DEF_DELETE)
 
-constdefs
-  SUBSET :: "('A => bool) => ('A => bool) => bool" 
+definition SUBSET :: "('A => bool) => ('A => bool) => bool" where 
   "SUBSET ==
 %(u::'A::type => bool) ua::'A::type => bool.
    ALL x::'A::type. IN x u --> IN x ua"
@@ -5670,8 +5548,7 @@
     ALL x::'A::type. IN x u --> IN x ua)"
   by (import hollight DEF_SUBSET)
 
-constdefs
-  PSUBSET :: "('A => bool) => ('A => bool) => bool" 
+definition PSUBSET :: "('A => bool) => ('A => bool) => bool" where 
   "PSUBSET ==
 %(u::'A::type => bool) ua::'A::type => bool. SUBSET u ua & u ~= ua"
 
@@ -5679,8 +5556,7 @@
 (%(u::'A::type => bool) ua::'A::type => bool. SUBSET u ua & u ~= ua)"
   by (import hollight DEF_PSUBSET)
 
-constdefs
-  DISJOINT :: "('A => bool) => ('A => bool) => bool" 
+definition DISJOINT :: "('A => bool) => ('A => bool) => bool" where 
   "DISJOINT ==
 %(u::'A::type => bool) ua::'A::type => bool. hollight.INTER u ua = EMPTY"
 
@@ -5688,15 +5564,13 @@
 (%(u::'A::type => bool) ua::'A::type => bool. hollight.INTER u ua = EMPTY)"
   by (import hollight DEF_DISJOINT)
 
-constdefs
-  SING :: "('A => bool) => bool" 
+definition SING :: "('A => bool) => bool" where 
   "SING == %u::'A::type => bool. EX x::'A::type. u = INSERT x EMPTY"
 
 lemma DEF_SING: "SING = (%u::'A::type => bool. EX x::'A::type. u = INSERT x EMPTY)"
   by (import hollight DEF_SING)
 
-constdefs
-  FINITE :: "('A => bool) => bool" 
+definition FINITE :: "('A => bool) => bool" where 
   "FINITE ==
 %a::'A::type => bool.
    ALL FINITE'::('A::type => bool) => bool.
@@ -5718,15 +5592,13 @@
        FINITE' a)"
   by (import hollight DEF_FINITE)
 
-constdefs
-  INFINITE :: "('A => bool) => bool" 
+definition INFINITE :: "('A => bool) => bool" where 
   "INFINITE == %u::'A::type => bool. ~ FINITE u"
 
 lemma DEF_INFINITE: "INFINITE = (%u::'A::type => bool. ~ FINITE u)"
   by (import hollight DEF_INFINITE)
 
-constdefs
-  IMAGE :: "('A => 'B) => ('A => bool) => 'B => bool" 
+definition IMAGE :: "('A => 'B) => ('A => bool) => 'B => bool" where 
   "IMAGE ==
 %(u::'A::type => 'B::type) ua::'A::type => bool.
    GSPEC
@@ -5740,8 +5612,7 @@
          EX y::'B::type. SETSPEC ub (EX x::'A::type. IN x ua & y = u x) y))"
   by (import hollight DEF_IMAGE)
 
-constdefs
-  INJ :: "('A => 'B) => ('A => bool) => ('B => bool) => bool" 
+definition INJ :: "('A => 'B) => ('A => bool) => ('B => bool) => bool" where 
   "INJ ==
 %(u::'A::type => 'B::type) (ua::'A::type => bool) ub::'B::type => bool.
    (ALL x::'A::type. IN x ua --> IN (u x) ub) &
@@ -5754,8 +5625,7 @@
         IN x ua & IN y ua & u x = u y --> x = y))"
   by (import hollight DEF_INJ)
 
-constdefs
-  SURJ :: "('A => 'B) => ('A => bool) => ('B => bool) => bool" 
+definition SURJ :: "('A => 'B) => ('A => bool) => ('B => bool) => bool" where 
   "SURJ ==
 %(u::'A::type => 'B::type) (ua::'A::type => bool) ub::'B::type => bool.
    (ALL x::'A::type. IN x ua --> IN (u x) ub) &
@@ -5767,8 +5637,7 @@
     (ALL x::'B::type. IN x ub --> (EX y::'A::type. IN y ua & u y = x)))"
   by (import hollight DEF_SURJ)
 
-constdefs
-  BIJ :: "('A => 'B) => ('A => bool) => ('B => bool) => bool" 
+definition BIJ :: "('A => 'B) => ('A => bool) => ('B => bool) => bool" where 
   "BIJ ==
 %(u::'A::type => 'B::type) (ua::'A::type => bool) ub::'B::type => bool.
    INJ u ua ub & SURJ u ua ub"
@@ -5778,22 +5647,19 @@
     INJ u ua ub & SURJ u ua ub)"
   by (import hollight DEF_BIJ)
 
-constdefs
-  CHOICE :: "('A => bool) => 'A" 
+definition CHOICE :: "('A => bool) => 'A" where 
   "CHOICE == %u::'A::type => bool. SOME x::'A::type. IN x u"
 
 lemma DEF_CHOICE: "CHOICE = (%u::'A::type => bool. SOME x::'A::type. IN x u)"
   by (import hollight DEF_CHOICE)
 
-constdefs
-  REST :: "('A => bool) => 'A => bool" 
+definition REST :: "('A => bool) => 'A => bool" where 
   "REST == %u::'A::type => bool. DELETE u (CHOICE u)"
 
 lemma DEF_REST: "REST = (%u::'A::type => bool. DELETE u (CHOICE u))"
   by (import hollight DEF_REST)
 
-constdefs
-  CARD_GE :: "('q_37693 => bool) => ('q_37690 => bool) => bool" 
+definition CARD_GE :: "('q_37693 => bool) => ('q_37690 => bool) => bool" where 
   "CARD_GE ==
 %(u::'q_37693::type => bool) ua::'q_37690::type => bool.
    EX f::'q_37693::type => 'q_37690::type.
@@ -5807,8 +5673,7 @@
           IN y ua --> (EX x::'q_37693::type. IN x u & y = f x))"
   by (import hollight DEF_CARD_GE)
 
-constdefs
-  CARD_LE :: "('q_37702 => bool) => ('q_37701 => bool) => bool" 
+definition CARD_LE :: "('q_37702 => bool) => ('q_37701 => bool) => bool" where 
   "CARD_LE ==
 %(u::'q_37702::type => bool) ua::'q_37701::type => bool. CARD_GE ua u"
 
@@ -5816,8 +5681,7 @@
 (%(u::'q_37702::type => bool) ua::'q_37701::type => bool. CARD_GE ua u)"
   by (import hollight DEF_CARD_LE)
 
-constdefs
-  CARD_EQ :: "('q_37712 => bool) => ('q_37713 => bool) => bool" 
+definition CARD_EQ :: "('q_37712 => bool) => ('q_37713 => bool) => bool" where 
   "CARD_EQ ==
 %(u::'q_37712::type => bool) ua::'q_37713::type => bool.
    CARD_LE u ua & CARD_LE ua u"
@@ -5827,8 +5691,7 @@
     CARD_LE u ua & CARD_LE ua u)"
   by (import hollight DEF_CARD_EQ)
 
-constdefs
-  CARD_GT :: "('q_37727 => bool) => ('q_37728 => bool) => bool" 
+definition CARD_GT :: "('q_37727 => bool) => ('q_37728 => bool) => bool" where 
   "CARD_GT ==
 %(u::'q_37727::type => bool) ua::'q_37728::type => bool.
    CARD_GE u ua & ~ CARD_GE ua u"
@@ -5838,8 +5701,7 @@
     CARD_GE u ua & ~ CARD_GE ua u)"
   by (import hollight DEF_CARD_GT)
 
-constdefs
-  CARD_LT :: "('q_37743 => bool) => ('q_37744 => bool) => bool" 
+definition CARD_LT :: "('q_37743 => bool) => ('q_37744 => bool) => bool" where 
   "CARD_LT ==
 %(u::'q_37743::type => bool) ua::'q_37744::type => bool.
    CARD_LE u ua & ~ CARD_LE ua u"
@@ -5849,8 +5711,7 @@
     CARD_LE u ua & ~ CARD_LE ua u)"
   by (import hollight DEF_CARD_LT)
 
-constdefs
-  COUNTABLE :: "('q_37757 => bool) => bool" 
+definition COUNTABLE :: "('q_37757 => bool) => bool" where 
   "(op ==::(('q_37757::type => bool) => bool)
         => (('q_37757::type => bool) => bool) => prop)
  (COUNTABLE::('q_37757::type => bool) => bool)
@@ -6470,9 +6331,8 @@
    FINITE s --> FINITE (DIFF s t)"
   by (import hollight FINITE_DIFF)
 
-constdefs
-  FINREC :: "('q_41824 => 'q_41823 => 'q_41823)
-=> 'q_41823 => ('q_41824 => bool) => 'q_41823 => nat => bool" 
+definition FINREC :: "('q_41824 => 'q_41823 => 'q_41823)
+=> 'q_41823 => ('q_41824 => bool) => 'q_41823 => nat => bool" where 
   "FINREC ==
 SOME FINREC::('q_41824::type => 'q_41823::type => 'q_41823::type)
              => 'q_41823::type
@@ -6558,9 +6418,8 @@
            FINITE s --> g (INSERT x s) = COND (IN x s) (g s) (f x (g s))))"
   by (import hollight SET_RECURSION_LEMMA)
 
-constdefs
-  ITSET :: "('q_42525 => 'q_42524 => 'q_42524)
-=> ('q_42525 => bool) => 'q_42524 => 'q_42524" 
+definition ITSET :: "('q_42525 => 'q_42524 => 'q_42524)
+=> ('q_42525 => bool) => 'q_42524 => 'q_42524" where 
   "ITSET ==
 %(u::'q_42525::type => 'q_42524::type => 'q_42524::type)
    (ua::'q_42525::type => bool) ub::'q_42524::type.
@@ -6630,8 +6489,7 @@
           EX x::'A::type. SETSPEC u (IN x s & (P::'A::type => bool) x) x))"
   by (import hollight FINITE_RESTRICT)
 
-constdefs
-  CARD :: "('q_42918 => bool) => nat" 
+definition CARD :: "('q_42918 => bool) => nat" where 
   "CARD == %u::'q_42918::type => bool. ITSET (%x::'q_42918::type. Suc) u 0"
 
 lemma DEF_CARD: "CARD = (%u::'q_42918::type => bool. ITSET (%x::'q_42918::type. Suc) u 0)"
@@ -6674,8 +6532,7 @@
    CARD s + CARD t = CARD u"
   by (import hollight CARD_UNION_EQ)
 
-constdefs
-  HAS_SIZE :: "('q_43199 => bool) => nat => bool" 
+definition HAS_SIZE :: "('q_43199 => bool) => nat => bool" where 
   "HAS_SIZE == %(u::'q_43199::type => bool) ua::nat. FINITE u & CARD u = ua"
 
 lemma DEF_HAS_SIZE: "HAS_SIZE = (%(u::'q_43199::type => bool) ua::nat. FINITE u & CARD u = ua)"
@@ -6944,8 +6801,7 @@
        (ALL xa::'A::type. IN xa x --> (EX! m::nat. < m n & f m = xa)))"
   by (import hollight HAS_SIZE_INDEX)
 
-constdefs
-  set_of_list :: "'q_45968 hollight.list => 'q_45968 => bool" 
+definition set_of_list :: "'q_45968 hollight.list => 'q_45968 => bool" where 
   "set_of_list ==
 SOME set_of_list::'q_45968::type hollight.list => 'q_45968::type => bool.
    set_of_list NIL = EMPTY &
@@ -6959,8 +6815,7 @@
         set_of_list (CONS h t) = INSERT h (set_of_list t)))"
   by (import hollight DEF_set_of_list)
 
-constdefs
-  list_of_set :: "('q_45986 => bool) => 'q_45986 hollight.list" 
+definition list_of_set :: "('q_45986 => bool) => 'q_45986 hollight.list" where 
   "list_of_set ==
 %u::'q_45986::type => bool.
    SOME l::'q_45986::type hollight.list.
@@ -6999,8 +6854,7 @@
    hollight.UNION (set_of_list x) (set_of_list xa)"
   by (import hollight SET_OF_LIST_APPEND)
 
-constdefs
-  pairwise :: "('q_46198 => 'q_46198 => bool) => ('q_46198 => bool) => bool" 
+definition pairwise :: "('q_46198 => 'q_46198 => bool) => ('q_46198 => bool) => bool" where 
   "pairwise ==
 %(u::'q_46198::type => 'q_46198::type => bool) ua::'q_46198::type => bool.
    ALL (x::'q_46198::type) y::'q_46198::type.
@@ -7012,8 +6866,7 @@
        IN x ua & IN y ua & x ~= y --> u x y)"
   by (import hollight DEF_pairwise)
 
-constdefs
-  PAIRWISE :: "('q_46220 => 'q_46220 => bool) => 'q_46220 hollight.list => bool" 
+definition PAIRWISE :: "('q_46220 => 'q_46220 => bool) => 'q_46220 hollight.list => bool" where 
   "PAIRWISE ==
 SOME PAIRWISE::('q_46220::type => 'q_46220::type => bool)
                => 'q_46220::type hollight.list => bool.
@@ -7075,8 +6928,7 @@
        (EMPTY::'A::type => bool))))"
   by (import hollight FINITE_IMAGE_IMAGE)
 
-constdefs
-  dimindex :: "('A => bool) => nat" 
+definition dimindex :: "('A => bool) => nat" where 
   "(op ==::(('A::type => bool) => nat) => (('A::type => bool) => nat) => prop)
  (dimindex::('A::type => bool) => nat)
  (%u::'A::type => bool.
@@ -7125,8 +6977,7 @@
    dimindex s = dimindex t"
   by (import hollight DIMINDEX_FINITE_IMAGE)
 
-constdefs
-  finite_index :: "nat => 'A" 
+definition finite_index :: "nat => 'A" where 
   "(op ==::(nat => 'A::type) => (nat => 'A::type) => prop)
  (finite_index::nat => 'A::type)
  ((Eps::((nat => 'A::type) => bool) => nat => 'A::type)
@@ -7287,8 +7138,7 @@
                       xa))))))"
   by (import hollight CART_EQ)
 
-constdefs
-  lambda :: "(nat => 'A) => ('A, 'B) cart" 
+definition lambda :: "(nat => 'A) => ('A, 'B) cart" where 
   "(op ==::((nat => 'A::type) => ('A::type, 'B::type) cart)
         => ((nat => 'A::type) => ('A::type, 'B::type) cart) => prop)
  (lambda::(nat => 'A::type) => ('A::type, 'B::type) cart)
@@ -7388,8 +7238,7 @@
   [where a="a :: ('A, 'B) finite_sum" and r=r ,
    OF type_definition_finite_sum]
 
-constdefs
-  pastecart :: "('A, 'M) cart => ('A, 'N) cart => ('A, ('M, 'N) finite_sum) cart" 
+definition pastecart :: "('A, 'M) cart => ('A, 'N) cart => ('A, ('M, 'N) finite_sum) cart" where 
   "(op ==::(('A::type, 'M::type) cart
          => ('A::type, 'N::type) cart
             => ('A::type, ('M::type, 'N::type) finite_sum) cart)
@@ -7439,8 +7288,7 @@
                  (hollight.UNIV::'M::type => bool))))))"
   by (import hollight DEF_pastecart)
 
-constdefs
-  fstcart :: "('A, ('M, 'N) finite_sum) cart => ('A, 'M) cart" 
+definition fstcart :: "('A, ('M, 'N) finite_sum) cart => ('A, 'M) cart" where 
   "fstcart ==
 %u::('A::type, ('M::type, 'N::type) finite_sum) cart. lambda ($ u)"
 
@@ -7448,8 +7296,7 @@
 (%u::('A::type, ('M::type, 'N::type) finite_sum) cart. lambda ($ u))"
   by (import hollight DEF_fstcart)
 
-constdefs
-  sndcart :: "('A, ('M, 'N) finite_sum) cart => ('A, 'N) cart" 
+definition sndcart :: "('A, ('M, 'N) finite_sum) cart => ('A, 'N) cart" where 
   "(op ==::(('A::type, ('M::type, 'N::type) finite_sum) cart
          => ('A::type, 'N::type) cart)
         => (('A::type, ('M::type, 'N::type) finite_sum) cart
@@ -7616,8 +7463,7 @@
    (EX xb::'q_48070::type => 'q_48091::type. x = xb o xa)"
   by (import hollight FUNCTION_FACTORS_LEFT)
 
-constdefs
-  dotdot :: "nat => nat => nat => bool" 
+definition dotdot :: "nat => nat => nat => bool" where 
   "dotdot ==
 %(u::nat) ua::nat.
    GSPEC (%ub::nat. EX x::nat. SETSPEC ub (<= u x & <= x ua) x)"
@@ -7718,8 +7564,7 @@
    SUBSET (dotdot m n) (dotdot p q) = (< n m | <= p m & <= n q)"
   by (import hollight SUBSET_NUMSEG)
 
-constdefs
-  neutral :: "('q_48985 => 'q_48985 => 'q_48985) => 'q_48985" 
+definition neutral :: "('q_48985 => 'q_48985 => 'q_48985) => 'q_48985" where 
   "neutral ==
 %u::'q_48985::type => 'q_48985::type => 'q_48985::type.
    SOME x::'q_48985::type. ALL y::'q_48985::type. u x y = y & u y x = y"
@@ -7729,8 +7574,7 @@
     SOME x::'q_48985::type. ALL y::'q_48985::type. u x y = y & u y x = y)"
   by (import hollight DEF_neutral)
 
-constdefs
-  monoidal :: "('A => 'A => 'A) => bool" 
+definition monoidal :: "('A => 'A => 'A) => bool" where 
   "monoidal ==
 %u::'A::type => 'A::type => 'A::type.
    (ALL (x::'A::type) y::'A::type. u x y = u y x) &
@@ -7746,8 +7590,7 @@
     (ALL x::'A::type. u (neutral u) x = x))"
   by (import hollight DEF_monoidal)
 
-constdefs
-  support :: "('B => 'B => 'B) => ('A => 'B) => ('A => bool) => 'A => bool" 
+definition support :: "('B => 'B => 'B) => ('A => 'B) => ('A => bool) => 'A => bool" where 
   "support ==
 %(u::'B::type => 'B::type => 'B::type) (ua::'A::type => 'B::type)
    ub::'A::type => bool.
@@ -7763,9 +7606,8 @@
          EX x::'A::type. SETSPEC uc (IN x ub & ua x ~= neutral u) x))"
   by (import hollight DEF_support)
 
-constdefs
-  iterate :: "('q_49090 => 'q_49090 => 'q_49090)
-=> ('A => bool) => ('A => 'q_49090) => 'q_49090" 
+definition iterate :: "('q_49090 => 'q_49090 => 'q_49090)
+=> ('A => bool) => ('A => 'q_49090) => 'q_49090" where 
   "iterate ==
 %(u::'q_49090::type => 'q_49090::type => 'q_49090::type)
    (ua::'A::type => bool) ub::'A::type => 'q_49090::type.
@@ -8017,8 +7859,7 @@
        iterate u_4247 s f = iterate u_4247 t g)"
   by (import hollight ITERATE_EQ_GENERAL)
 
-constdefs
-  nsum :: "('q_51017 => bool) => ('q_51017 => nat) => nat" 
+definition nsum :: "('q_51017 => bool) => ('q_51017 => nat) => nat" where 
   "(op ==::(('q_51017::type => bool) => ('q_51017::type => nat) => nat)
         => (('q_51017::type => bool) => ('q_51017::type => nat) => nat)
            => prop)
@@ -8965,9 +8806,8 @@
    hollight.sum x xb = hollight.sum xa xc"
   by (import hollight SUM_EQ_GENERAL)
 
-constdefs
-  CASEWISE :: "(('q_57926 => 'q_57930) * ('q_57931 => 'q_57926 => 'q_57890)) hollight.list
-=> 'q_57931 => 'q_57930 => 'q_57890" 
+definition CASEWISE :: "(('q_57926 => 'q_57930) * ('q_57931 => 'q_57926 => 'q_57890)) hollight.list
+=> 'q_57931 => 'q_57930 => 'q_57890" where 
   "CASEWISE ==
 SOME CASEWISE::(('q_57926::type => 'q_57930::type) *
                 ('q_57931::type
@@ -9084,11 +8924,10 @@
     x"
   by (import hollight CASEWISE_WORKS)
 
-constdefs
-  admissible :: "('q_58228 => 'q_58221 => bool)
+definition admissible :: "('q_58228 => 'q_58221 => bool)
 => (('q_58228 => 'q_58224) => 'q_58234 => bool)
    => ('q_58234 => 'q_58221)
-      => (('q_58228 => 'q_58224) => 'q_58234 => 'q_58229) => bool" 
+      => (('q_58228 => 'q_58224) => 'q_58234 => 'q_58229) => bool" where 
   "admissible ==
 %(u::'q_58228::type => 'q_58221::type => bool)
    (ua::('q_58228::type => 'q_58224::type) => 'q_58234::type => bool)
@@ -9114,10 +8953,9 @@
        uc f a = uc g a)"
   by (import hollight DEF_admissible)
 
-constdefs
-  tailadmissible :: "('A => 'A => bool)
+definition tailadmissible :: "('A => 'A => bool)
 => (('A => 'B) => 'P => bool)
-   => ('P => 'A) => (('A => 'B) => 'P => 'B) => bool" 
+   => ('P => 'A) => (('A => 'B) => 'P => 'B) => bool" where 
   "tailadmissible ==
 %(u::'A::type => 'A::type => bool)
    (ua::('A::type => 'B::type) => 'P::type => bool)
@@ -9151,11 +8989,10 @@
            ua f a --> uc f a = COND (P f a) (f (G f a)) (H f a)))"
   by (import hollight DEF_tailadmissible)
 
-constdefs
-  superadmissible :: "('q_58378 => 'q_58378 => bool)
+definition superadmissible :: "('q_58378 => 'q_58378 => bool)
 => (('q_58378 => 'q_58380) => 'q_58386 => bool)
    => ('q_58386 => 'q_58378)
-      => (('q_58378 => 'q_58380) => 'q_58386 => 'q_58380) => bool" 
+      => (('q_58378 => 'q_58380) => 'q_58386 => 'q_58380) => bool" where 
   "superadmissible ==
 %(u::'q_58378::type => 'q_58378::type => bool)
    (ua::('q_58378::type => 'q_58380::type) => 'q_58386::type => bool)
--- a/src/HOL/Import/HOLLightCompat.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Import/HOLLightCompat.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -30,8 +30,7 @@
     by simp
 qed
 
-constdefs
-   Pred :: "nat \<Rightarrow> nat"
+definition Pred :: "nat \<Rightarrow> nat" where
    "Pred n \<equiv> n - (Suc 0)"
 
 lemma Pred_altdef: "Pred = (SOME PRE. PRE 0 = 0 & (ALL n. PRE (Suc n) = n))"
@@ -84,8 +83,7 @@
   apply auto
   done
 
-constdefs
-  NUMERAL_BIT0 :: "nat \<Rightarrow> nat"
+definition NUMERAL_BIT0 :: "nat \<Rightarrow> nat" where
   "NUMERAL_BIT0 n \<equiv> n + n"
 
 lemma NUMERAL_BIT1_altdef: "NUMERAL_BIT1 n = Suc (n + n)"
--- a/src/HOL/Isar_Examples/Expr_Compiler.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Isar_Examples/Expr_Compiler.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -85,8 +85,7 @@
     | Apply f => exec instrs (f (hd stack) (hd (tl stack))
                    # (tl (tl stack))) env)"
 
-constdefs
-  execute :: "(('adr, 'val) instr) list => ('adr => 'val) => 'val"
+definition execute :: "(('adr, 'val) instr) list => ('adr => 'val) => 'val" where
   "execute instrs env == hd (exec instrs [] env)"
 
 
--- a/src/HOL/Isar_Examples/Hoare.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Isar_Examples/Hoare.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -55,14 +55,10 @@
     (if s : b then Sem c1 s s' else Sem c2 s s')"
   "Sem (While b x c) s s' = (EX n. iter n b (Sem c) s s')"
 
-constdefs
-  Valid :: "'a bexp => 'a com => 'a bexp => bool"
-    ("(3|- _/ (2_)/ _)" [100, 55, 100] 50)
+definition Valid :: "'a bexp => 'a com => 'a bexp => bool" ("(3|- _/ (2_)/ _)" [100, 55, 100] 50) where
   "|- P c Q == ALL s s'. Sem c s s' --> s : P --> s' : Q"
 
-syntax (xsymbols)
-  Valid :: "'a bexp => 'a com => 'a bexp => bool"
-    ("(3\<turnstile> _/ (2_)/ _)" [100, 55, 100] 50)
+notation (xsymbols) Valid ("(3\<turnstile> _/ (2_)/ _)" [100, 55, 100] 50)
 
 lemma ValidI [intro?]:
     "(!!s s'. Sem c s s' ==> s : P ==> s' : Q) ==> |- P c Q"
--- a/src/HOL/Isar_Examples/Mutilated_Checkerboard.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Isar_Examples/Mutilated_Checkerboard.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -60,8 +60,7 @@
 
 subsection {* Basic properties of ``below'' *}
 
-constdefs
-  below :: "nat => nat set"
+definition below :: "nat => nat set" where
   "below n == {i. i < n}"
 
 lemma below_less_iff [iff]: "(i: below k) = (i < k)"
@@ -84,8 +83,7 @@
 
 subsection {* Basic properties of ``evnodd'' *}
 
-constdefs
-  evnodd :: "(nat * nat) set => nat => (nat * nat) set"
+definition evnodd :: "(nat * nat) set => nat => (nat * nat) set" where
   "evnodd A b == A Int {(i, j). (i + j) mod 2 = b}"
 
 lemma evnodd_iff:
@@ -247,8 +245,7 @@
 
 subsection {* Main theorem *}
 
-constdefs
-  mutilated_board :: "nat => nat => (nat * nat) set"
+definition mutilated_board :: "nat => nat => (nat * nat) set" where
   "mutilated_board m n ==
     below (2 * (m + 1)) <*> below (2 * (n + 1))
       - {(0, 0)} - {(2 * m + 1, 2 * n + 1)}"
--- a/src/HOL/Matrix/ComputeNumeral.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Matrix/ComputeNumeral.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -20,7 +20,7 @@
 lemmas bitiszero = iszero1 iszero2 iszero3 iszero4
 
 (* lezero for bit strings *)
-constdefs
+definition
   "lezero x == (x \<le> 0)"
 lemma lezero1: "lezero Int.Pls = True" unfolding Int.Pls_def lezero_def by auto
 lemma lezero2: "lezero Int.Min = True" unfolding Int.Min_def lezero_def by auto
@@ -60,7 +60,7 @@
 
 lemmas bitarith = bitnorm bitiszero bitneg bitlezero biteq bitless bitle bitsucc bitpred bituminus bitadd bitmul 
 
-constdefs 
+definition
   "nat_norm_number_of (x::nat) == x"
 
 lemma nat_norm_number_of: "nat_norm_number_of (number_of w) = (if lezero w then 0 else number_of w)"
--- a/src/HOL/Matrix/Matrix.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Matrix/Matrix.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -24,10 +24,10 @@
 apply (rule Abs_matrix_induct)
 by (simp add: Abs_matrix_inverse matrix_def)
 
-constdefs
-  nrows :: "('a::zero) matrix \<Rightarrow> nat"
+definition nrows :: "('a::zero) matrix \<Rightarrow> nat" where
   "nrows A == if nonzero_positions(Rep_matrix A) = {} then 0 else Suc(Max ((image fst) (nonzero_positions (Rep_matrix A))))"
-  ncols :: "('a::zero) matrix \<Rightarrow> nat"
+
+definition ncols :: "('a::zero) matrix \<Rightarrow> nat" where
   "ncols A == if nonzero_positions(Rep_matrix A) = {} then 0 else Suc(Max ((image snd) (nonzero_positions (Rep_matrix A))))"
 
 lemma nrows:
@@ -50,10 +50,10 @@
   thus "Rep_matrix A m n = 0" by (simp add: nonzero_positions_def image_Collect)
 qed
 
-constdefs
-  transpose_infmatrix :: "'a infmatrix \<Rightarrow> 'a infmatrix"
+definition transpose_infmatrix :: "'a infmatrix \<Rightarrow> 'a infmatrix" where
   "transpose_infmatrix A j i == A i j"
-  transpose_matrix :: "('a::zero) matrix \<Rightarrow> 'a matrix"
+
+definition transpose_matrix :: "('a::zero) matrix \<Rightarrow> 'a matrix" where
   "transpose_matrix == Abs_matrix o transpose_infmatrix o Rep_matrix"
 
 declare transpose_infmatrix_def[simp]
@@ -256,14 +256,16 @@
   ultimately show "finite ?u" by (rule finite_subset)
 qed
 
-constdefs
-  apply_infmatrix :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a infmatrix \<Rightarrow> 'b infmatrix"
+definition apply_infmatrix :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a infmatrix \<Rightarrow> 'b infmatrix" where
   "apply_infmatrix f == % A. (% j i. f (A j i))"
-  apply_matrix :: "('a \<Rightarrow> 'b) \<Rightarrow> ('a::zero) matrix \<Rightarrow> ('b::zero) matrix"
+
+definition apply_matrix :: "('a \<Rightarrow> 'b) \<Rightarrow> ('a::zero) matrix \<Rightarrow> ('b::zero) matrix" where
   "apply_matrix f == % A. Abs_matrix (apply_infmatrix f (Rep_matrix A))"
-  combine_infmatrix :: "('a \<Rightarrow> 'b \<Rightarrow> 'c) \<Rightarrow> 'a infmatrix \<Rightarrow> 'b infmatrix \<Rightarrow> 'c infmatrix"
+
+definition combine_infmatrix :: "('a \<Rightarrow> 'b \<Rightarrow> 'c) \<Rightarrow> 'a infmatrix \<Rightarrow> 'b infmatrix \<Rightarrow> 'c infmatrix" where
   "combine_infmatrix f == % A B. (% j i. f (A j i) (B j i))"
-  combine_matrix :: "('a \<Rightarrow> 'b \<Rightarrow> 'c) \<Rightarrow> ('a::zero) matrix \<Rightarrow> ('b::zero) matrix \<Rightarrow> ('c::zero) matrix"
+
+definition combine_matrix :: "('a \<Rightarrow> 'b \<Rightarrow> 'c) \<Rightarrow> ('a::zero) matrix \<Rightarrow> ('b::zero) matrix \<Rightarrow> ('c::zero) matrix" where
   "combine_matrix f == % A B. Abs_matrix (combine_infmatrix f (Rep_matrix A) (Rep_matrix B))"
 
 lemma expand_apply_infmatrix[simp]: "apply_infmatrix f A j i = f (A j i)"
@@ -272,10 +274,10 @@
 lemma expand_combine_infmatrix[simp]: "combine_infmatrix f A B j i = f (A j i) (B j i)"
 by (simp add: combine_infmatrix_def)
 
-constdefs
-commutative :: "('a \<Rightarrow> 'a \<Rightarrow> 'b) \<Rightarrow> bool"
+definition commutative :: "('a \<Rightarrow> 'a \<Rightarrow> 'b) \<Rightarrow> bool" where
 "commutative f == ! x y. f x y = f y x"
-associative :: "('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> bool"
+
+definition associative :: "('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> bool" where
 "associative f == ! x y z. f (f x y) z = f x (f y z)"
 
 text{*
@@ -356,12 +358,13 @@
 lemma combine_ncols: "f 0 0 = 0 \<Longrightarrow> ncols A <= q \<Longrightarrow> ncols B <= q \<Longrightarrow> ncols(combine_matrix f A B) <= q"
   by (simp add: ncols_le)
 
-constdefs
-  zero_r_neutral :: "('a \<Rightarrow> 'b::zero \<Rightarrow> 'a) \<Rightarrow> bool"
+definition zero_r_neutral :: "('a \<Rightarrow> 'b::zero \<Rightarrow> 'a) \<Rightarrow> bool" where
   "zero_r_neutral f == ! a. f a 0 = a"
-  zero_l_neutral :: "('a::zero \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> bool"
+
+definition zero_l_neutral :: "('a::zero \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> bool" where
   "zero_l_neutral f == ! a. f 0 a = a"
-  zero_closed :: "(('a::zero) \<Rightarrow> ('b::zero) \<Rightarrow> ('c::zero)) \<Rightarrow> bool"
+
+definition zero_closed :: "(('a::zero) \<Rightarrow> ('b::zero) \<Rightarrow> ('c::zero)) \<Rightarrow> bool" where
   "zero_closed f == (!x. f x 0 = 0) & (!y. f 0 y = 0)"
 
 consts foldseq :: "('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> (nat \<Rightarrow> 'a) \<Rightarrow> nat \<Rightarrow> 'a"
@@ -648,10 +651,10 @@
   then show ?concl by simp
 qed
 
-constdefs
-  mult_matrix_n :: "nat \<Rightarrow> (('a::zero) \<Rightarrow> ('b::zero) \<Rightarrow> ('c::zero)) \<Rightarrow> ('c \<Rightarrow> 'c \<Rightarrow> 'c) \<Rightarrow> 'a matrix \<Rightarrow> 'b matrix \<Rightarrow> 'c matrix"
+definition mult_matrix_n :: "nat \<Rightarrow> (('a::zero) \<Rightarrow> ('b::zero) \<Rightarrow> ('c::zero)) \<Rightarrow> ('c \<Rightarrow> 'c \<Rightarrow> 'c) \<Rightarrow> 'a matrix \<Rightarrow> 'b matrix \<Rightarrow> 'c matrix" where
   "mult_matrix_n n fmul fadd A B == Abs_matrix(% j i. foldseq fadd (% k. fmul (Rep_matrix A j k) (Rep_matrix B k i)) n)"
-  mult_matrix :: "(('a::zero) \<Rightarrow> ('b::zero) \<Rightarrow> ('c::zero)) \<Rightarrow> ('c \<Rightarrow> 'c \<Rightarrow> 'c) \<Rightarrow> 'a matrix \<Rightarrow> 'b matrix \<Rightarrow> 'c matrix"
+
+definition mult_matrix :: "(('a::zero) \<Rightarrow> ('b::zero) \<Rightarrow> ('c::zero)) \<Rightarrow> ('c \<Rightarrow> 'c \<Rightarrow> 'c) \<Rightarrow> 'a matrix \<Rightarrow> 'b matrix \<Rightarrow> 'c matrix" where
   "mult_matrix fmul fadd A B == mult_matrix_n (max (ncols A) (nrows B)) fmul fadd A B"
 
 lemma mult_matrix_n:
@@ -673,12 +676,13 @@
   finally show "mult_matrix_n n fmul fadd A B = mult_matrix_n m fmul fadd A B" by simp
 qed
 
-constdefs
-  r_distributive :: "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> ('b \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> bool"
+definition r_distributive :: "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> ('b \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> bool" where
   "r_distributive fmul fadd == ! a u v. fmul a (fadd u v) = fadd (fmul a u) (fmul a v)"
-  l_distributive :: "('a \<Rightarrow> 'b \<Rightarrow> 'a) \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> bool"
+
+definition l_distributive :: "('a \<Rightarrow> 'b \<Rightarrow> 'a) \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> bool" where
   "l_distributive fmul fadd == ! a u v. fmul (fadd u v) a = fadd (fmul u a) (fmul v a)"
-  distributive :: "('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> bool"
+
+definition distributive :: "('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> bool" where
   "distributive fmul fadd == l_distributive fmul fadd & r_distributive fmul fadd"
 
 lemma max1: "!! a x y. (a::nat) <= x \<Longrightarrow> a <= max x y" by (arith)
@@ -835,20 +839,22 @@
   apply (simp add: apply_matrix_def apply_infmatrix_def)
   by (simp add: zero_matrix_def)
 
-constdefs
-  singleton_matrix :: "nat \<Rightarrow> nat \<Rightarrow> ('a::zero) \<Rightarrow> 'a matrix"
+definition singleton_matrix :: "nat \<Rightarrow> nat \<Rightarrow> ('a::zero) \<Rightarrow> 'a matrix" where
   "singleton_matrix j i a == Abs_matrix(% m n. if j = m & i = n then a else 0)"
-  move_matrix :: "('a::zero) matrix \<Rightarrow> int \<Rightarrow> int \<Rightarrow> 'a matrix"
+
+definition move_matrix :: "('a::zero) matrix \<Rightarrow> int \<Rightarrow> int \<Rightarrow> 'a matrix" where
   "move_matrix A y x == Abs_matrix(% j i. if (neg ((int j)-y)) | (neg ((int i)-x)) then 0 else Rep_matrix A (nat ((int j)-y)) (nat ((int i)-x)))"
-  take_rows :: "('a::zero) matrix \<Rightarrow> nat \<Rightarrow> 'a matrix"
+
+definition take_rows :: "('a::zero) matrix \<Rightarrow> nat \<Rightarrow> 'a matrix" where
   "take_rows A r == Abs_matrix(% j i. if (j < r) then (Rep_matrix A j i) else 0)"
-  take_columns :: "('a::zero) matrix \<Rightarrow> nat \<Rightarrow> 'a matrix"
+
+definition take_columns :: "('a::zero) matrix \<Rightarrow> nat \<Rightarrow> 'a matrix" where
   "take_columns A c == Abs_matrix(% j i. if (i < c) then (Rep_matrix A j i) else 0)"
 
-constdefs
-  column_of_matrix :: "('a::zero) matrix \<Rightarrow> nat \<Rightarrow> 'a matrix"
+definition column_of_matrix :: "('a::zero) matrix \<Rightarrow> nat \<Rightarrow> 'a matrix" where
   "column_of_matrix A n == take_columns (move_matrix A 0 (- int n)) 1"
-  row_of_matrix :: "('a::zero) matrix \<Rightarrow> nat \<Rightarrow> 'a matrix"
+
+definition row_of_matrix :: "('a::zero) matrix \<Rightarrow> nat \<Rightarrow> 'a matrix" where
   "row_of_matrix A m == take_rows (move_matrix A (- int m) 0) 1"
 
 lemma Rep_singleton_matrix[simp]: "Rep_matrix (singleton_matrix j i e) m n = (if j = m & i = n then e else 0)"
@@ -1042,10 +1048,10 @@
   with contraprems show "False" by simp
 qed
 
-constdefs
-  foldmatrix :: "('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> ('a infmatrix) \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> 'a"
+definition foldmatrix :: "('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> ('a infmatrix) \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> 'a" where
   "foldmatrix f g A m n == foldseq_transposed g (% j. foldseq f (A j) n) m"
-  foldmatrix_transposed :: "('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> ('a infmatrix) \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> 'a"
+
+definition foldmatrix_transposed :: "('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> 'a) \<Rightarrow> ('a infmatrix) \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> 'a" where
   "foldmatrix_transposed f g A m n == foldseq g (% j. foldseq_transposed f (A j) n) m"
 
 lemma foldmatrix_transpose:
@@ -1691,12 +1697,13 @@
 lemma transpose_matrix_minus: "transpose_matrix (-(A::('a::group_add) matrix)) = - transpose_matrix (A::'a matrix)"
 by (simp add: minus_matrix_def transpose_apply_matrix)
 
-constdefs 
-  right_inverse_matrix :: "('a::{ring_1}) matrix \<Rightarrow> 'a matrix \<Rightarrow> bool"
+definition right_inverse_matrix :: "('a::{ring_1}) matrix \<Rightarrow> 'a matrix \<Rightarrow> bool" where
   "right_inverse_matrix A X == (A * X = one_matrix (max (nrows A) (ncols X))) \<and> nrows X \<le> ncols A" 
-  left_inverse_matrix :: "('a::{ring_1}) matrix \<Rightarrow> 'a matrix \<Rightarrow> bool"
+
+definition left_inverse_matrix :: "('a::{ring_1}) matrix \<Rightarrow> 'a matrix \<Rightarrow> bool" where
   "left_inverse_matrix A X == (X * A = one_matrix (max(nrows X) (ncols A))) \<and> ncols X \<le> nrows A" 
-  inverse_matrix :: "('a::{ring_1}) matrix \<Rightarrow> 'a matrix \<Rightarrow> bool"
+
+definition inverse_matrix :: "('a::{ring_1}) matrix \<Rightarrow> 'a matrix \<Rightarrow> bool" where
   "inverse_matrix A X == (right_inverse_matrix A X) \<and> (left_inverse_matrix A X)"
 
 lemma right_inverse_matrix_dim: "right_inverse_matrix A X \<Longrightarrow> nrows A = ncols X"
@@ -1781,8 +1788,7 @@
 lemma move_matrix_mult: "move_matrix ((A::('a::semiring_0) matrix)*B) j i = (move_matrix A j 0) * (move_matrix B 0 i)"
 by (simp add: move_matrix_ortho[of "A*B"] move_matrix_col_mult move_matrix_row_mult)
 
-constdefs
-  scalar_mult :: "('a::ring) \<Rightarrow> 'a matrix \<Rightarrow> 'a matrix"
+definition scalar_mult :: "('a::ring) \<Rightarrow> 'a matrix \<Rightarrow> 'a matrix" where
   "scalar_mult a m == apply_matrix (op * a) m"
 
 lemma scalar_mult_zero[simp]: "scalar_mult y 0 = 0" 
--- a/src/HOL/Matrix/SparseMatrix.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Matrix/SparseMatrix.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -552,8 +552,7 @@
   else if j < i then (le_spvec [] b & le_spmat ((i,a)#as) bs)
   else (le_spvec a b & le_spmat as bs))"
 
-constdefs
-  disj_matrices :: "('a::zero) matrix \<Rightarrow> 'a matrix \<Rightarrow> bool"
+definition disj_matrices :: "('a::zero) matrix \<Rightarrow> 'a matrix \<Rightarrow> bool" where
   "disj_matrices A B == (! j i. (Rep_matrix A j i \<noteq> 0) \<longrightarrow> (Rep_matrix B j i = 0)) & (! j i. (Rep_matrix B j i \<noteq> 0) \<longrightarrow> (Rep_matrix A j i = 0))"  
 
 declare [[simp_depth_limit = 6]]
@@ -802,8 +801,7 @@
   apply (simp_all add: sorted_spvec_abs_spvec)
   done
 
-constdefs
-  diff_spmat :: "('a::lattice_ring) spmat \<Rightarrow> 'a spmat \<Rightarrow> 'a spmat"
+definition diff_spmat :: "('a::lattice_ring) spmat \<Rightarrow> 'a spmat \<Rightarrow> 'a spmat" where
   "diff_spmat A B == add_spmat A (minus_spmat B)"
 
 lemma sorted_spmat_diff_spmat: "sorted_spmat A \<Longrightarrow> sorted_spmat B \<Longrightarrow> sorted_spmat (diff_spmat A B)"
@@ -815,8 +813,7 @@
 lemma sparse_row_diff_spmat: "sparse_row_matrix (diff_spmat A B ) = (sparse_row_matrix A) - (sparse_row_matrix B)"
   by (simp add: diff_spmat_def sparse_row_add_spmat sparse_row_matrix_minus)
 
-constdefs
-  sorted_sparse_matrix :: "'a spmat \<Rightarrow> bool"
+definition sorted_sparse_matrix :: "'a spmat \<Rightarrow> bool" where
   "sorted_sparse_matrix A == (sorted_spvec A) & (sorted_spmat A)"
 
 lemma sorted_sparse_matrix_imp_spvec: "sorted_sparse_matrix A \<Longrightarrow> sorted_spvec A"
@@ -1014,8 +1011,7 @@
   apply (simp_all add: sorted_nprt_spvec)
   done
 
-constdefs
-  mult_est_spmat :: "('a::lattice_ring) spmat \<Rightarrow> 'a spmat \<Rightarrow> 'a spmat \<Rightarrow> 'a spmat \<Rightarrow> 'a spmat"
+definition mult_est_spmat :: "('a::lattice_ring) spmat \<Rightarrow> 'a spmat \<Rightarrow> 'a spmat \<Rightarrow> 'a spmat \<Rightarrow> 'a spmat" where
   "mult_est_spmat r1 r2 s1 s2 == 
   add_spmat (mult_spmat (pprt_spmat s2) (pprt_spmat r2)) (add_spmat (mult_spmat (pprt_spmat s1) (nprt_spmat r2)) 
   (add_spmat (mult_spmat (nprt_spmat s2) (pprt_spmat r1)) (mult_spmat (nprt_spmat s1) (nprt_spmat r1))))"  
--- a/src/HOL/Metis_Examples/BigO.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Metis_Examples/BigO.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -1099,9 +1099,7 @@
 
 subsection {* Less than or equal to *}
 
-constdefs 
-  lesso :: "('a => 'b::linordered_idom) => ('a => 'b) => ('a => 'b)"
-      (infixl "<o" 70)
+definition lesso :: "('a => 'b::linordered_idom) => ('a => 'b) => ('a => 'b)" (infixl "<o" 70) where
   "f <o g == (%x. max (f x - g x) 0)"
 
 lemma bigo_lesseq1: "f =o O(h) ==> ALL x. abs (g x) <= abs (f x) ==>
--- a/src/HOL/Metis_Examples/Message.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Metis_Examples/Message.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -26,8 +26,7 @@
 text{*The inverse of a symmetric key is itself; that of a public key
       is the private key and vice versa*}
 
-constdefs
-  symKeys :: "key set"
+definition symKeys :: "key set" where
   "symKeys == {K. invKey K = K}"
 
 datatype  --{*We allow any number of friendly agents*}
@@ -55,12 +54,11 @@
   "{|x, y|}"      == "CONST MPair x y"
 
 
-constdefs
-  HPair :: "[msg,msg] => msg"                       ("(4Hash[_] /_)" [0, 1000])
+definition HPair :: "[msg,msg] => msg" ("(4Hash[_] /_)" [0, 1000]) where
     --{*Message Y paired with a MAC computed with the help of X*}
     "Hash[X] Y == {| Hash{|X,Y|}, Y|}"
 
-  keysFor :: "msg set => key set"
+definition keysFor :: "msg set => key set" where
     --{*Keys useful to decrypt elements of a message set*}
   "keysFor H == invKey ` {K. \<exists>X. Crypt K X \<in> H}"
 
--- a/src/HOL/Metis_Examples/Tarski.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/Metis_Examples/Tarski.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -20,59 +20,56 @@
   pset  :: "'a set"
   order :: "('a * 'a) set"
 
-constdefs
-  monotone :: "['a => 'a, 'a set, ('a *'a)set] => bool"
+definition monotone :: "['a => 'a, 'a set, ('a *'a)set] => bool" where
   "monotone f A r == \<forall>x\<in>A. \<forall>y\<in>A. (x, y): r --> ((f x), (f y)) : r"
 
-  least :: "['a => bool, 'a potype] => 'a"
+definition least :: "['a => bool, 'a potype] => 'a" where
   "least P po == @ x. x: pset po & P x &
                        (\<forall>y \<in> pset po. P y --> (x,y): order po)"
 
-  greatest :: "['a => bool, 'a potype] => 'a"
+definition greatest :: "['a => bool, 'a potype] => 'a" where
   "greatest P po == @ x. x: pset po & P x &
                           (\<forall>y \<in> pset po. P y --> (y,x): order po)"
 
-  lub  :: "['a set, 'a potype] => 'a"
+definition lub  :: "['a set, 'a potype] => 'a" where
   "lub S po == least (%x. \<forall>y\<in>S. (y,x): order po) po"
 
-  glb  :: "['a set, 'a potype] => 'a"
+definition glb  :: "['a set, 'a potype] => 'a" where
   "glb S po == greatest (%x. \<forall>y\<in>S. (x,y): order po) po"
 
-  isLub :: "['a set, 'a potype, 'a] => bool"
+definition isLub :: "['a set, 'a potype, 'a] => bool" where
   "isLub S po == %L. (L: pset po & (\<forall>y\<in>S. (y,L): order po) &
                    (\<forall>z\<in>pset po. (\<forall>y\<in>S. (y,z): order po) --> (L,z): order po))"
 
-  isGlb :: "['a set, 'a potype, 'a] => bool"
+definition isGlb :: "['a set, 'a potype, 'a] => bool" where
   "isGlb S po == %G. (G: pset po & (\<forall>y\<in>S. (G,y): order po) &
                  (\<forall>z \<in> pset po. (\<forall>y\<in>S. (z,y): order po) --> (z,G): order po))"
 
-  "fix"    :: "[('a => 'a), 'a set] => 'a set"
+definition "fix"    :: "[('a => 'a), 'a set] => 'a set" where
   "fix f A  == {x. x: A & f x = x}"
 
-  interval :: "[('a*'a) set,'a, 'a ] => 'a set"
+definition interval :: "[('a*'a) set,'a, 'a ] => 'a set" where
   "interval r a b == {x. (a,x): r & (x,b): r}"
 
-constdefs
-  Bot :: "'a potype => 'a"
+definition Bot :: "'a potype => 'a" where
   "Bot po == least (%x. True) po"
 
-  Top :: "'a potype => 'a"
+definition Top :: "'a potype => 'a" where
   "Top po == greatest (%x. True) po"
 
-  PartialOrder :: "('a potype) set"
+definition PartialOrder :: "('a potype) set" where
   "PartialOrder == {P. refl_on (pset P) (order P) & antisym (order P) &
                        trans (order P)}"
 
-  CompleteLattice :: "('a potype) set"
+definition CompleteLattice :: "('a potype) set" where
   "CompleteLattice == {cl. cl: PartialOrder &
                         (\<forall>S. S \<subseteq> pset cl --> (\<exists>L. isLub S cl L)) &
                         (\<forall>S. S \<subseteq> pset cl --> (\<exists>G. isGlb S cl G))}"
 
-  induced :: "['a set, ('a * 'a) set] => ('a *'a)set"
+definition induced :: "['a set, ('a * 'a) set] => ('a *'a)set" where
   "induced A r == {(a,b). a : A & b: A & (a,b): r}"
 
-constdefs
-  sublattice :: "('a potype * 'a set)set"
+definition sublattice :: "('a potype * 'a set)set" where
   "sublattice ==
       SIGMA cl: CompleteLattice.
           {S. S \<subseteq> pset cl &
@@ -82,8 +79,7 @@
   sublattice_syntax :: "['a set, 'a potype] => bool" ("_ <<= _" [51, 50] 50)
   where "S <<= cl \<equiv> S : sublattice `` {cl}"
 
-constdefs
-  dual :: "'a potype => 'a potype"
+definition dual :: "'a potype => 'a potype" where
   "dual po == (| pset = pset po, order = converse (order po) |)"
 
 locale PO =
--- a/src/HOL/MicroJava/BV/Altern.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/MicroJava/BV/Altern.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -8,19 +8,18 @@
 imports BVSpec
 begin
 
-constdefs
-  check_type :: "jvm_prog \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> JVMType.state \<Rightarrow> bool"
+definition check_type :: "jvm_prog \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> JVMType.state \<Rightarrow> bool" where
   "check_type G mxs mxr s \<equiv> s \<in> states G mxs mxr"
 
-  wt_instr_altern :: "[instr,jvm_prog,ty,method_type,nat,nat,p_count,
-                exception_table,p_count] \<Rightarrow> bool"
+definition wt_instr_altern :: "[instr,jvm_prog,ty,method_type,nat,nat,p_count,
+                exception_table,p_count] \<Rightarrow> bool" where
   "wt_instr_altern i G rT phi mxs mxr max_pc et pc \<equiv>
   app i G mxs rT pc et (phi!pc) \<and>
   check_type G mxs mxr (OK (phi!pc)) \<and>
   (\<forall>(pc',s') \<in> set (eff i G pc et (phi!pc)). pc' < max_pc \<and> G \<turnstile> s' <=' phi!pc')"
 
-  wt_method_altern :: "[jvm_prog,cname,ty list,ty,nat,nat,instr list,
-                 exception_table,method_type] \<Rightarrow> bool"
+definition wt_method_altern :: "[jvm_prog,cname,ty list,ty,nat,nat,instr list,
+                 exception_table,method_type] \<Rightarrow> bool" where
   "wt_method_altern G C pTs rT mxs mxl ins et phi \<equiv>
   let max_pc = length ins in
   0 < max_pc \<and> 
--- a/src/HOL/MicroJava/BV/BVExample.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/MicroJava/BV/BVExample.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -167,8 +167,7 @@
 
   @{prop [display] "P n"} 
 *}
-constdefs 
-  intervall :: "nat \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> bool" ("_ \<in> [_, _')")
+definition intervall :: "nat \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> bool" ("_ \<in> [_, _')") where
   "x \<in> [a, b) \<equiv> a \<le> x \<and> x < b"
 
 lemma pc_0: "x < n \<Longrightarrow> (x \<in> [0, n) \<Longrightarrow> P x) \<Longrightarrow> P x"
@@ -238,8 +237,7 @@
 lemmas eff_simps [simp] = eff_def norm_eff_def xcpt_eff_def
 declare appInvoke [simp del]
 
-constdefs
-  phi_append :: method_type ("\<phi>\<^sub>a")
+definition phi_append :: method_type ("\<phi>\<^sub>a") where
   "\<phi>\<^sub>a \<equiv> map (\<lambda>(x,y). Some (x, map OK y)) [ 
    (                                    [], [Class list_name, Class list_name]),
    (                     [Class list_name], [Class list_name, Class list_name]),
@@ -301,8 +299,7 @@
 abbreviation Ctest :: ty
   where "Ctest == Class test_name"
 
-constdefs
-  phi_makelist :: method_type ("\<phi>\<^sub>m")
+definition phi_makelist :: method_type ("\<phi>\<^sub>m") where
   "\<phi>\<^sub>m \<equiv> map (\<lambda>(x,y). Some (x, y)) [ 
     (                                   [], [OK Ctest, Err     , Err     ]),
     (                              [Clist], [OK Ctest, Err     , Err     ]),
@@ -376,8 +373,7 @@
   done
 
 text {* The whole program is welltyped: *}
-constdefs 
-  Phi :: prog_type ("\<Phi>")
+definition Phi :: prog_type ("\<Phi>") where
   "\<Phi> C sg \<equiv> if C = test_name \<and> sg = (makelist_name, []) then \<phi>\<^sub>m else          
              if C = list_name \<and> sg = (append_name, [Class list_name]) then \<phi>\<^sub>a else []"
 
--- a/src/HOL/MicroJava/BV/Correct.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/MicroJava/BV/Correct.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -9,47 +9,40 @@
 imports BVSpec "../JVM/JVMExec"
 begin
 
-constdefs
-  approx_val :: "[jvm_prog,aheap,val,ty err] \<Rightarrow> bool"
+definition approx_val :: "[jvm_prog,aheap,val,ty err] \<Rightarrow> bool" where
   "approx_val G h v any == case any of Err \<Rightarrow> True | OK T \<Rightarrow> G,h\<turnstile>v::\<preceq>T"
 
-  approx_loc :: "[jvm_prog,aheap,val list,locvars_type] \<Rightarrow> bool"
+definition approx_loc :: "[jvm_prog,aheap,val list,locvars_type] \<Rightarrow> bool" where
   "approx_loc G hp loc LT == list_all2 (approx_val G hp) loc LT"
 
-  approx_stk :: "[jvm_prog,aheap,opstack,opstack_type] \<Rightarrow> bool"
+definition approx_stk :: "[jvm_prog,aheap,opstack,opstack_type] \<Rightarrow> bool" where
   "approx_stk G hp stk ST == approx_loc G hp stk (map OK ST)"
 
-  correct_frame  :: "[jvm_prog,aheap,state_type,nat,bytecode] \<Rightarrow> frame \<Rightarrow> bool"
+definition correct_frame  :: "[jvm_prog,aheap,state_type,nat,bytecode] \<Rightarrow> frame \<Rightarrow> bool" where
   "correct_frame G hp == \<lambda>(ST,LT) maxl ins (stk,loc,C,sig,pc).
                          approx_stk G hp stk ST  \<and> approx_loc G hp loc LT \<and> 
                          pc < length ins \<and> length loc=length(snd sig)+maxl+1"
 
-
-consts
- correct_frames  :: "[jvm_prog,aheap,prog_type,ty,sig,frame list] \<Rightarrow> bool"
-primrec
-"correct_frames G hp phi rT0 sig0 [] = True"
+primrec correct_frames  :: "[jvm_prog,aheap,prog_type,ty,sig,frame list] \<Rightarrow> bool" where
+  "correct_frames G hp phi rT0 sig0 [] = True"
+| "correct_frames G hp phi rT0 sig0 (f#frs) =
+    (let (stk,loc,C,sig,pc) = f in
+    (\<exists>ST LT rT maxs maxl ins et.
+      phi C sig ! pc = Some (ST,LT) \<and> is_class G C \<and> 
+      method (G,C) sig = Some(C,rT,(maxs,maxl,ins,et)) \<and>
+    (\<exists>C' mn pTs. ins!pc = (Invoke C' mn pTs) \<and> 
+           (mn,pTs) = sig0 \<and> 
+           (\<exists>apTs D ST' LT'.
+           (phi C sig)!pc = Some ((rev apTs) @ (Class D) # ST', LT') \<and>
+           length apTs = length pTs \<and>
+           (\<exists>D' rT' maxs' maxl' ins' et'.
+             method (G,D) sig0 = Some(D',rT',(maxs',maxl',ins',et')) \<and>
+             G \<turnstile> rT0 \<preceq> rT') \<and>
+     correct_frame G hp (ST, LT) maxl ins f \<and> 
+     correct_frames G hp phi rT sig frs))))"
 
-"correct_frames G hp phi rT0 sig0 (f#frs) =
-  (let (stk,loc,C,sig,pc) = f in
-  (\<exists>ST LT rT maxs maxl ins et.
-    phi C sig ! pc = Some (ST,LT) \<and> is_class G C \<and> 
-    method (G,C) sig = Some(C,rT,(maxs,maxl,ins,et)) \<and>
-  (\<exists>C' mn pTs. ins!pc = (Invoke C' mn pTs) \<and> 
-         (mn,pTs) = sig0 \<and> 
-         (\<exists>apTs D ST' LT'.
-         (phi C sig)!pc = Some ((rev apTs) @ (Class D) # ST', LT') \<and>
-         length apTs = length pTs \<and>
-         (\<exists>D' rT' maxs' maxl' ins' et'.
-           method (G,D) sig0 = Some(D',rT',(maxs',maxl',ins',et')) \<and>
-           G \<turnstile> rT0 \<preceq> rT') \<and>
-   correct_frame G hp (ST, LT) maxl ins f \<and> 
-   correct_frames G hp phi rT sig frs))))"
-
-
-constdefs
- correct_state :: "[jvm_prog,prog_type,jvm_state] \<Rightarrow> bool"
-                  ("_,_ |-JVM _ [ok]"  [51,51] 50)
+definition correct_state :: "[jvm_prog,prog_type,jvm_state] \<Rightarrow> bool"
+                  ("_,_ |-JVM _ [ok]"  [51,51] 50) where
 "correct_state G phi == \<lambda>(xp,hp,frs).
    case xp of
      None \<Rightarrow> (case frs of
--- a/src/HOL/MicroJava/BV/Effect.thy	Wed Feb 24 11:55:52 2010 +0100
+++ b/src/HOL/MicroJava/BV/Effect.thy	Mon Mar 01 13:40:23 2010 +0100
@@ -13,27 +13,25 @@
   succ_type = "(p_count \<times> state_type option) list"
 
 text {* Program counter of successor instructions: *}
-consts
-  succs :: "instr \<Rightarrow> p_count \<Rightarrow> p_count list"
-primrec 
+primrec succs :: "instr \<Rightarrow> p_count \<Rightarrow> p_count list" where
   "succs (Load idx) pc         = [pc+1]"
-  "succs (Store idx) pc        = [pc+1]"
-  "succs (LitPush v) pc        = [pc+1]"
-  "succs (Getfield F C) pc     = [pc+1]"
-  "succs (Putfield F C) pc     = [pc+1]"
-  "succs (New C) pc            = [pc+1]"
-  "succs (Checkcast C) pc      = [pc+1]"
-  "succs Pop pc                = [pc+1]"
-  "succs Dup pc                = [pc+1]"
-  "succs Dup_x1 pc             = [pc+1]"
-  "succs Dup_x2 pc             = [pc+1]"
-  "succs Swap pc               = [pc+1]"
-  "succs IAdd pc               = [pc+1]"
-  "succs (Ifcmpeq b) pc        = [pc+1, nat (int pc + b)]"
-  "succs (Goto b) pc           = [nat (int pc + b)]"
-  "succs Return pc             = [pc]"  
-  "succs (Invoke C mn fpTs) pc = [pc+1]"
-  "succs Throw pc              = [pc]"
+| "succs (Store idx) pc        = [pc+1]"
+| "succs (LitPush v) pc        = [pc+1]"
+| "succs (Getfield F C) pc     = [pc+1]"
+| "succs (Putfield F C) pc     = [pc+1]"
+| "succs (New C) pc            = [pc+1]"
+| "succs (Checkcast C) pc      = [pc+1]"
+| "succs Pop pc                = [pc+1]"
+| "succs Dup pc                = [pc+1]"
+| "succs Dup_x1 pc             = [pc+1]"
+| "succs Dup_x2 pc             = [pc+1]"
+| "succs Swap pc               = [pc+1]"
+| "succs IAdd pc               = [pc+1]"
+| "succs (Ifcmpeq b) pc        = [pc+1, nat (int pc + b)]"
+| "succs (Goto b) pc           = [nat (int pc + b)]"
+| "succs Return pc             = [pc]"  
+| "succs (Invoke C mn fpTs) pc = [pc+1]"
+| "succs Throw pc              = [pc]"
 
 text "Effect of instruction on the state type:"
 consts 
@@ -63,21 +61,16 @@
 "eff' (Invoke C mn fpTs, G, (ST,LT))    = (let ST' = drop (length fpTs) ST 
   in  (fst (snd (the (method (G,C) (mn,fpTs))))#(tl ST'),LT))" 
 
-
-consts
-  match_any :: "jvm_prog \<Rightarrow> p_count \<Rightarrow> exception_table \<Rightarrow> cname list"
-primrec
+primrec match_any :: "jvm_prog \<Rightarrow> p_count \<Rightarrow> exception_table \<Rightarrow> cname list" where
   "match_any G pc [] = []"
-  "match_any G pc (e#es) = (let (start_pc, end_pc, handler_pc, catch_type) = e;
+| "match_any G pc (e#es) = (let (start_pc, end_pc, handler_pc, catch_type) = e;
                                 es' = match_any G pc es 
                             in 
                             if start_pc <= pc \<and> pc < end_pc then catch_type#es' else es')"
 
-consts
-  match :: "jvm_prog \<Rightarrow> xcpt \<Rightarrow> p_count \<Rightarrow> exception_table \<Rightarrow> cname list"
-primrec
+primrec match :: "jvm_prog \<Rightarrow> xcpt \<Rightarrow> p_count \<Rightarrow> exception_table \<Rightarrow> cname list" where
   "match G X pc [] = []"
-  "match G X pc (e#es) = 
+| "match G X pc (e#es) = 
   (if match_exception_entry G (Xcpt X) pc e then [Xcpt X] else match G X pc es)"
 
 lemma match_some_entry:
@@ -96,23 +89,21 @@
   "xcpt_names (i, G, pc, et)            = []" 
 
 
-constdefs
-  xcpt_eff :: "instr \<Rightarrow> jvm_prog \<Rightarrow> p_count \<Rightarrow> state