# HG changeset patch
# User wenzelm
# Date 1415736859 -3600
# Node ID 51890cb80b305359491a21d536a76f2212e53ef9
# Parent  2f65dcd32a5910d92dee4882a26a39ebafba358f# Parent  162a4c2e97bc222b21c0281f4e3a6d0800ac27db
merged

diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/CCL.thy
--- a/src/CCL/CCL.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/CCL.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -27,18 +27,18 @@
 
 consts
   (*** Evaluation Judgement ***)
-  Eval      ::       "[i,i]=>prop"          (infixl "--->" 20)
+  Eval      ::       "[i,i]\<Rightarrow>prop"          (infixl "--->" 20)
 
   (*** Bisimulations for pre-order and equality ***)
-  po          ::       "['a,'a]=>o"           (infixl "[=" 50)
+  po          ::       "['a,'a]\<Rightarrow>o"           (infixl "[=" 50)
 
   (*** Term Formers ***)
   true        ::       "i"
   false       ::       "i"
-  pair        ::       "[i,i]=>i"             ("(1<_,/_>)")
-  lambda      ::       "(i=>i)=>i"            (binder "lam " 55)
-  "case"      ::       "[i,i,i,[i,i]=>i,(i=>i)=>i]=>i"
-  "apply"     ::       "[i,i]=>i"             (infixl "`" 56)
+  pair        ::       "[i,i]\<Rightarrow>i"             ("(1<_,/_>)")
+  lambda      ::       "(i\<Rightarrow>i)\<Rightarrow>i"            (binder "lam " 55)
+  "case"      ::       "[i,i,i,[i,i]\<Rightarrow>i,(i\<Rightarrow>i)\<Rightarrow>i]\<Rightarrow>i"
+  "apply"     ::       "[i,i]\<Rightarrow>i"             (infixl "`" 56)
   bot         ::       "i"
 
   (******* EVALUATION SEMANTICS *******)
@@ -53,23 +53,23 @@
   pairV:       "<a,b> ---> <a,b>" and
   lamV:        "\<And>b. lam x. b(x) ---> lam x. b(x)" and
 
-  caseVtrue:   "[| t ---> true;  d ---> c |] ==> case(t,d,e,f,g) ---> c" and
-  caseVfalse:  "[| t ---> false;  e ---> c |] ==> case(t,d,e,f,g) ---> c" and
-  caseVpair:   "[| t ---> <a,b>;  f(a,b) ---> c |] ==> case(t,d,e,f,g) ---> c" and
-  caseVlam:    "\<And>b. [| t ---> lam x. b(x);  g(b) ---> c |] ==> case(t,d,e,f,g) ---> c"
+  caseVtrue:   "\<lbrakk>t ---> true; d ---> c\<rbrakk> \<Longrightarrow> case(t,d,e,f,g) ---> c" and
+  caseVfalse:  "\<lbrakk>t ---> false; e ---> c\<rbrakk> \<Longrightarrow> case(t,d,e,f,g) ---> c" and
+  caseVpair:   "\<lbrakk>t ---> <a,b>; f(a,b) ---> c\<rbrakk> \<Longrightarrow> case(t,d,e,f,g) ---> c" and
+  caseVlam:    "\<And>b. \<lbrakk>t ---> lam x. b(x); g(b) ---> c\<rbrakk> \<Longrightarrow> case(t,d,e,f,g) ---> c"
 
   (*** Properties of evaluation: note that "t ---> c" impies that c is canonical ***)
 
 axiomatization where
-  canonical:  "[| t ---> c; c==true ==> u--->v;
-                          c==false ==> u--->v;
-                    !!a b. c==<a,b> ==> u--->v;
-                      !!f. c==lam x. f(x) ==> u--->v |] ==>
+  canonical:  "\<lbrakk>t ---> c; c==true \<Longrightarrow> u--->v;
+                          c==false \<Longrightarrow> u--->v;
+                    \<And>a b. c==<a,b> \<Longrightarrow> u--->v;
+                      \<And>f. c==lam x. f(x) \<Longrightarrow> u--->v\<rbrakk> \<Longrightarrow>
              u--->v"
 
   (* Should be derivable - but probably a bitch! *)
 axiomatization where
-  substitute: "[| a==a'; t(a)--->c(a) |] ==> t(a')--->c(a')"
+  substitute: "\<lbrakk>a==a'; t(a)--->c(a)\<rbrakk> \<Longrightarrow> t(a')--->c(a')"
 
   (************** LOGIC ***************)
 
@@ -77,26 +77,26 @@
 
 axiomatization where
   bot_def:         "bot == (lam x. x`x)`(lam x. x`x)" and
-  apply_def:     "f ` t == case(f,bot,bot,%x y. bot,%u. u(t))"
+  apply_def:     "f ` t == case(f, bot, bot, \<lambda>x y. bot, \<lambda>u. u(t))"
 
-definition "fix" :: "(i=>i)=>i"
+definition "fix" :: "(i\<Rightarrow>i)\<Rightarrow>i"
   where "fix(f) == (lam x. f(x`x))`(lam x. f(x`x))"
 
   (*  The pre-order ([=) is defined as a simulation, and behavioural equivalence (=) *)
   (*  as a bisimulation.  They can both be expressed as (bi)simulations up to        *)
   (*  behavioural equivalence (ie the relations PO and EQ defined below).            *)
 
-definition SIM :: "[i,i,i set]=>o"
+definition SIM :: "[i,i,i set]\<Rightarrow>o"
   where
-  "SIM(t,t',R) ==  (t=true & t'=true) | (t=false & t'=false) |
-                  (EX a a' b b'. t=<a,b> & t'=<a',b'> & <a,a'> : R & <b,b'> : R) |
-                  (EX f f'. t=lam x. f(x) & t'=lam x. f'(x) & (ALL x.<f(x),f'(x)> : R))"
+  "SIM(t,t',R) ==  (t=true \<and> t'=true) | (t=false \<and> t'=false) |
+                  (\<exists>a a' b b'. t=<a,b> \<and> t'=<a',b'> \<and> <a,a'> : R \<and> <b,b'> : R) |
+                  (\<exists>f f'. t=lam x. f(x) \<and> t'=lam x. f'(x) \<and> (ALL x.<f(x),f'(x)> : R))"
 
-definition POgen :: "i set => i set"
-  where "POgen(R) == {p. EX t t'. p=<t,t'> & (t = bot | SIM(t,t',R))}"
+definition POgen :: "i set \<Rightarrow> i set"
+  where "POgen(R) == {p. \<exists>t t'. p=<t,t'> \<and> (t = bot | SIM(t,t',R))}"
 
-definition EQgen :: "i set => i set"
-  where "EQgen(R) == {p. EX t t'. p=<t,t'> & (t = bot & t' = bot | SIM(t,t',R))}"
+definition EQgen :: "i set \<Rightarrow> i set"
+  where "EQgen(R) == {p. \<exists>t t'. p=<t,t'> \<and> (t = bot \<and> t' = bot | SIM(t,t',R))}"
 
 definition PO :: "i set"
   where "PO == gfp(POgen)"
@@ -111,23 +111,23 @@
 
 axiomatization where
   po_refl:        "a [= a" and
-  po_trans:       "[| a [= b;  b [= c |] ==> a [= c" and
-  po_cong:        "a [= b ==> f(a) [= f(b)" and
+  po_trans:       "\<lbrakk>a [= b;  b [= c\<rbrakk> \<Longrightarrow> a [= c" and
+  po_cong:        "a [= b \<Longrightarrow> f(a) [= f(b)" and
 
   (* Extend definition of [= to program fragments of higher type *)
-  po_abstractn:   "(!!x. f(x) [= g(x)) ==> (%x. f(x)) [= (%x. g(x))"
+  po_abstractn:   "(\<And>x. f(x) [= g(x)) \<Longrightarrow> (\<lambda>x. f(x)) [= (\<lambda>x. g(x))"
 
   (** Equality - equivalence axioms inherited from FOL.thy   **)
   (**          - congruence of "=" is axiomatised implicitly **)
 
 axiomatization where
-  eq_iff:         "t = t' <-> t [= t' & t' [= t"
+  eq_iff:         "t = t' \<longleftrightarrow> t [= t' \<and> t' [= t"
 
   (** Properties of canonical values given by greatest fixed point definitions **)
 
 axiomatization where
-  PO_iff:         "t [= t' <-> <t,t'> : PO" and
-  EQ_iff:         "t =  t' <-> <t,t'> : EQ"
+  PO_iff:         "t [= t' \<longleftrightarrow> <t,t'> : PO" and
+  EQ_iff:         "t =  t' \<longleftrightarrow> <t,t'> : EQ"
 
   (** Behaviour of non-canonical terms (ie case) given by the following beta-rules **)
 
@@ -140,19 +140,19 @@
 
   (** The theory is non-trivial **)
 axiomatization where
-  distinctness:   "~ lam x. b(x) = bot"
+  distinctness:   "\<not> lam x. b(x) = bot"
 
   (*** Definitions of Termination and Divergence ***)
 
-definition Dvg :: "i => o"
+definition Dvg :: "i \<Rightarrow> o"
   where "Dvg(t) == t = bot"
 
-definition Trm :: "i => o"
-  where "Trm(t) == ~ Dvg(t)"
+definition Trm :: "i \<Rightarrow> o"
+  where "Trm(t) == \<not> Dvg(t)"
 
 text {*
 Would be interesting to build a similar theory for a typed programming language:
-    ie.     true :: bool,      fix :: ('a=>'a)=>'a  etc......
+    ie.     true :: bool,      fix :: ('a\<Rightarrow>'a)\<Rightarrow>'a  etc......
 
 This is starting to look like LCF.
 What are the advantages of this approach?
@@ -169,14 +169,14 @@
 subsection {* Congruence Rules *}
 
 (*similar to AP_THM in Gordon's HOL*)
-lemma fun_cong: "(f::'a=>'b) = g ==> f(x)=g(x)"
+lemma fun_cong: "(f::'a\<Rightarrow>'b) = g \<Longrightarrow> f(x)=g(x)"
   by simp
 
 (*similar to AP_TERM in Gordon's HOL and FOL's subst_context*)
-lemma arg_cong: "x=y ==> f(x)=f(y)"
+lemma arg_cong: "x=y \<Longrightarrow> f(x)=f(y)"
   by simp
 
-lemma abstractn: "(!!x. f(x) = g(x)) ==> f = g"
+lemma abstractn: "(\<And>x. f(x) = g(x)) \<Longrightarrow> f = g"
   apply (simp add: eq_iff)
   apply (blast intro: po_abstractn)
   done
@@ -186,16 +186,16 @@
 
 subsection {* Termination and Divergence *}
 
-lemma Trm_iff: "Trm(t) <-> ~ t = bot"
+lemma Trm_iff: "Trm(t) \<longleftrightarrow> \<not> t = bot"
   by (simp add: Trm_def Dvg_def)
 
-lemma Dvg_iff: "Dvg(t) <-> t = bot"
+lemma Dvg_iff: "Dvg(t) \<longleftrightarrow> t = bot"
   by (simp add: Trm_def Dvg_def)
 
 
 subsection {* Constructors are injective *}
 
-lemma eq_lemma: "[| x=a;  y=b;  x=y |] ==> a=b"
+lemma eq_lemma: "\<lbrakk>x=a; y=b; x=y\<rbrakk> \<Longrightarrow> a=b"
   by simp
 
 ML {*
@@ -215,8 +215,8 @@
 *}
 
 lemma ccl_injs:
-  "<a,b> = <a',b'> <-> (a=a' & b=b')"
-  "!!b b'. (lam x. b(x) = lam x. b'(x)) <-> ((ALL z. b(z)=b'(z)))"
+  "<a,b> = <a',b'> \<longleftrightarrow> (a=a' \<and> b=b')"
+  "\<And>b b'. (lam x. b(x) = lam x. b'(x)) \<longleftrightarrow> ((ALL z. b(z)=b'(z)))"
   by (inj_rl caseBs)
 
 
@@ -226,11 +226,10 @@
 
 subsection {* Constructors are distinct *}
 
-lemma lem: "t=t' ==> case(t,b,c,d,e) = case(t',b,c,d,e)"
+lemma lem: "t=t' \<Longrightarrow> case(t,b,c,d,e) = case(t',b,c,d,e)"
   by simp
 
 ML {*
-
 local
   fun pairs_of f x [] = []
     | pairs_of f x (y::ys) = (f x y) :: (f y x) :: (pairs_of f x ys)
@@ -247,7 +246,7 @@
            val arity = length (binder_types T)
        in sy ^ (arg_str arity name "") end
 
-  fun mk_thm_str thy a b = "~ " ^ (saturate thy a "a") ^ " = " ^ (saturate thy b "b")
+  fun mk_thm_str thy a b = "\<not> " ^ (saturate thy a "a") ^ " = " ^ (saturate thy b "b")
 
   val lemma = @{thm lem};
   val eq_lemma = @{thm eq_lemma};
@@ -259,18 +258,16 @@
   fun mk_lemmas rls = maps mk_lemma (mk_combs pair rls)
   fun mk_dstnct_rls thy xs = mk_combs (mk_thm_str thy) xs
 end
-
 *}
 
 ML {*
-
 val caseB_lemmas = mk_lemmas @{thms caseBs}
 
 val ccl_dstncts =
   let
     fun mk_raw_dstnct_thm rls s =
       Goal.prove_global @{theory} [] [] (Syntax.read_prop_global @{theory} s)
-        (fn _=> rtac @{thm notI} 1 THEN eresolve_tac rls 1)
+        (fn _ => rtac @{thm notI} 1 THEN eresolve_tac rls 1)
   in map (mk_raw_dstnct_thm caseB_lemmas)
     (mk_dstnct_rls @{theory} ["bot","true","false","pair","lambda"]) end
 
@@ -307,33 +304,33 @@
 
 subsection {* Facts from gfp Definition of @{text "[="} and @{text "="} *}
 
-lemma XHlemma1: "[| A=B;  a:B <-> P |] ==> a:A <-> P"
+lemma XHlemma1: "\<lbrakk>A=B; a:B \<longleftrightarrow> P\<rbrakk> \<Longrightarrow> a:A \<longleftrightarrow> P"
   by simp
 
-lemma XHlemma2: "(P(t,t') <-> Q) ==> (<t,t'> : {p. EX t t'. p=<t,t'> &  P(t,t')} <-> Q)"
+lemma XHlemma2: "(P(t,t') \<longleftrightarrow> Q) \<Longrightarrow> (<t,t'> : {p. \<exists>t t'. p=<t,t'> \<and>  P(t,t')} \<longleftrightarrow> Q)"
   by blast
 
 
 subsection {* Pre-Order *}
 
-lemma POgen_mono: "mono(%X. POgen(X))"
+lemma POgen_mono: "mono(\<lambda>X. POgen(X))"
   apply (unfold POgen_def SIM_def)
   apply (rule monoI)
   apply blast
   done
 
 lemma POgenXH: 
-  "<t,t'> : POgen(R) <-> t= bot | (t=true & t'=true)  | (t=false & t'=false) |  
-           (EX a a' b b'. t=<a,b> &  t'=<a',b'>  & <a,a'> : R & <b,b'> : R) |  
-           (EX f f'. t=lam x. f(x) &  t'=lam x. f'(x) & (ALL x. <f(x),f'(x)> : R))"
+  "<t,t'> : POgen(R) \<longleftrightarrow> t= bot | (t=true \<and> t'=true)  | (t=false \<and> t'=false) |  
+           (EX a a' b b'. t=<a,b> \<and> t'=<a',b'>  \<and> <a,a'> : R \<and> <b,b'> : R) |  
+           (EX f f'. t=lam x. f(x) \<and> t'=lam x. f'(x) \<and> (ALL x. <f(x),f'(x)> : R))"
   apply (unfold POgen_def SIM_def)
   apply (rule iff_refl [THEN XHlemma2])
   done
 
 lemma poXH: 
-  "t [= t' <-> t=bot | (t=true & t'=true) | (t=false & t'=false) |  
-                 (EX a a' b b'. t=<a,b> &  t'=<a',b'>  & a [= a' & b [= b') |  
-                 (EX f f'. t=lam x. f(x) &  t'=lam x. f'(x) & (ALL x. f(x) [= f'(x)))"
+  "t [= t' \<longleftrightarrow> t=bot | (t=true \<and> t'=true) | (t=false \<and> t'=false) |  
+                 (EX a a' b b'. t=<a,b> \<and> t'=<a',b'>  \<and> a [= a' \<and> b [= b') |  
+                 (EX f f'. t=lam x. f(x) \<and> t'=lam x. f'(x) \<and> (ALL x. f(x) [= f'(x)))"
   apply (simp add: PO_iff del: ex_simps)
   apply (rule POgen_mono
     [THEN PO_def [THEN def_gfp_Tarski], THEN XHlemma1, unfolded POgen_def SIM_def])
@@ -345,17 +342,17 @@
   apply simp
   done
 
-lemma bot_poleast: "a [= bot ==> a=bot"
+lemma bot_poleast: "a [= bot \<Longrightarrow> a=bot"
   apply (drule poXH [THEN iffD1])
   apply simp
   done
 
-lemma po_pair: "<a,b> [= <a',b'> <->  a [= a' & b [= b'"
+lemma po_pair: "<a,b> [= <a',b'> \<longleftrightarrow>  a [= a' \<and> b [= b'"
   apply (rule poXH [THEN iff_trans])
   apply simp
   done
 
-lemma po_lam: "lam x. f(x) [= lam x. f'(x) <-> (ALL x. f(x) [= f'(x))"
+lemma po_lam: "lam x. f(x) [= lam x. f'(x) \<longleftrightarrow> (ALL x. f(x) [= f'(x))"
   apply (rule poXH [THEN iff_trans])
   apply fastforce
   done
@@ -366,41 +363,41 @@
   assumes 1: "t [= t'"
     and 2: "a [= a'"
     and 3: "b [= b'"
-    and 4: "!!x y. c(x,y) [= c'(x,y)"
-    and 5: "!!u. d(u) [= d'(u)"
+    and 4: "\<And>x y. c(x,y) [= c'(x,y)"
+    and 5: "\<And>u. d(u) [= d'(u)"
   shows "case(t,a,b,c,d) [= case(t',a',b',c',d')"
   apply (rule 1 [THEN po_cong, THEN po_trans])
   apply (rule 2 [THEN po_cong, THEN po_trans])
   apply (rule 3 [THEN po_cong, THEN po_trans])
   apply (rule 4 [THEN po_abstractn, THEN po_abstractn, THEN po_cong, THEN po_trans])
-  apply (rule_tac f1 = "%d. case (t',a',b',c',d)" in
+  apply (rule_tac f1 = "\<lambda>d. case (t',a',b',c',d)" in
     5 [THEN po_abstractn, THEN po_cong, THEN po_trans])
   apply (rule po_refl)
   done
 
-lemma apply_pocong: "[| f [= f';  a [= a' |] ==> f ` a [= f' ` a'"
+lemma apply_pocong: "\<lbrakk>f [= f'; a [= a'\<rbrakk> \<Longrightarrow> f ` a [= f' ` a'"
   unfolding ccl_data_defs
   apply (rule case_pocong, (rule po_refl | assumption)+)
   apply (erule po_cong)
   done
 
-lemma npo_lam_bot: "~ lam x. b(x) [= bot"
+lemma npo_lam_bot: "\<not> lam x. b(x) [= bot"
   apply (rule notI)
   apply (drule bot_poleast)
   apply (erule distinctness [THEN notE])
   done
 
-lemma po_lemma: "[| x=a;  y=b;  x[=y |] ==> a[=b"
+lemma po_lemma: "\<lbrakk>x=a; y=b; x[=y\<rbrakk> \<Longrightarrow> a[=b"
   by simp
 
-lemma npo_pair_lam: "~ <a,b> [= lam x. f(x)"
+lemma npo_pair_lam: "\<not> <a,b> [= lam x. f(x)"
   apply (rule notI)
   apply (rule npo_lam_bot [THEN notE])
   apply (erule case_pocong [THEN caseBlam [THEN caseBpair [THEN po_lemma]]])
   apply (rule po_refl npo_lam_bot)+
   done
 
-lemma npo_lam_pair: "~ lam x. f(x) [= <a,b>"
+lemma npo_lam_pair: "\<not> lam x. f(x) [= <a,b>"
   apply (rule notI)
   apply (rule npo_lam_bot [THEN notE])
   apply (erule case_pocong [THEN caseBpair [THEN caseBlam [THEN po_lemma]]])
@@ -408,29 +405,25 @@
   done
 
 lemma npo_rls1:
-  "~ true [= false"
-  "~ false [= true"
-  "~ true [= <a,b>"
-  "~ <a,b> [= true"
-  "~ true [= lam x. f(x)"
-  "~ lam x. f(x) [= true"
-  "~ false [= <a,b>"
-  "~ <a,b> [= false"
-  "~ false [= lam x. f(x)"
-  "~ lam x. f(x) [= false"
-  by (tactic {*
-    REPEAT (rtac @{thm notI} 1 THEN
-      dtac @{thm case_pocong} 1 THEN
-      etac @{thm rev_mp} 5 THEN
-      ALLGOALS (simp_tac @{context}) THEN
-      REPEAT (resolve_tac [@{thm po_refl}, @{thm npo_lam_bot}] 1)) *})
+  "\<not> true [= false"
+  "\<not> false [= true"
+  "\<not> true [= <a,b>"
+  "\<not> <a,b> [= true"
+  "\<not> true [= lam x. f(x)"
+  "\<not> lam x. f(x) [= true"
+  "\<not> false [= <a,b>"
+  "\<not> <a,b> [= false"
+  "\<not> false [= lam x. f(x)"
+  "\<not> lam x. f(x) [= false"
+  by (rule notI, drule case_pocong, erule_tac [5] rev_mp, simp_all,
+    (rule po_refl npo_lam_bot)+)+
 
 lemmas npo_rls = npo_pair_lam npo_lam_pair npo_rls1
 
 
 subsection {* Coinduction for @{text "[="} *}
 
-lemma po_coinduct: "[|  <t,u> : R;  R <= POgen(R) |] ==> t [= u"
+lemma po_coinduct: "\<lbrakk><t,u> : R; R <= POgen(R)\<rbrakk> \<Longrightarrow> t [= u"
   apply (rule PO_def [THEN def_coinduct, THEN PO_iff [THEN iffD2]])
    apply assumption+
   done
@@ -438,26 +431,29 @@
 
 subsection {* Equality *}
 
-lemma EQgen_mono: "mono(%X. EQgen(X))"
+lemma EQgen_mono: "mono(\<lambda>X. EQgen(X))"
   apply (unfold EQgen_def SIM_def)
   apply (rule monoI)
   apply blast
   done
 
 lemma EQgenXH: 
-  "<t,t'> : EQgen(R) <-> (t=bot & t'=bot)  | (t=true & t'=true)  |  
-                                             (t=false & t'=false) |  
-                 (EX a a' b b'. t=<a,b> &  t'=<a',b'>  & <a,a'> : R & <b,b'> : R) |  
-                 (EX f f'. t=lam x. f(x) &  t'=lam x. f'(x) & (ALL x.<f(x),f'(x)> : R))"
+  "<t,t'> : EQgen(R) \<longleftrightarrow> (t=bot \<and> t'=bot)  | (t=true \<and> t'=true)  |  
+                                             (t=false \<and> t'=false) |  
+                 (EX a a' b b'. t=<a,b> \<and> t'=<a',b'>  \<and> <a,a'> : R \<and> <b,b'> : R) |  
+                 (EX f f'. t=lam x. f(x) \<and> t'=lam x. f'(x) \<and> (ALL x.<f(x),f'(x)> : R))"
   apply (unfold EQgen_def SIM_def)
   apply (rule iff_refl [THEN XHlemma2])
   done
 
 lemma eqXH: 
-  "t=t' <-> (t=bot & t'=bot)  | (t=true & t'=true)  | (t=false & t'=false) |  
-                     (EX a a' b b'. t=<a,b> &  t'=<a',b'>  & a=a' & b=b') |  
-                     (EX f f'. t=lam x. f(x) &  t'=lam x. f'(x) & (ALL x. f(x)=f'(x)))"
-  apply (subgoal_tac "<t,t'> : EQ <-> (t=bot & t'=bot) | (t=true & t'=true) | (t=false & t'=false) | (EX a a' b b'. t=<a,b> & t'=<a',b'> & <a,a'> : EQ & <b,b'> : EQ) | (EX f f'. t=lam x. f (x) & t'=lam x. f' (x) & (ALL x. <f (x) ,f' (x) > : EQ))")
+  "t=t' \<longleftrightarrow> (t=bot \<and> t'=bot)  | (t=true \<and> t'=true)  | (t=false \<and> t'=false) |  
+                     (EX a a' b b'. t=<a,b> \<and> t'=<a',b'>  \<and> a=a' \<and> b=b') |  
+                     (EX f f'. t=lam x. f(x) \<and> t'=lam x. f'(x) \<and> (ALL x. f(x)=f'(x)))"
+  apply (subgoal_tac "<t,t'> : EQ \<longleftrightarrow>
+    (t=bot \<and> t'=bot) | (t=true \<and> t'=true) | (t=false \<and> t'=false) |
+    (EX a a' b b'. t=<a,b> \<and> t'=<a',b'> \<and> <a,a'> : EQ \<and> <b,b'> : EQ) |
+    (EX f f'. t=lam x. f (x) \<and> t'=lam x. f' (x) \<and> (ALL x. <f (x) ,f' (x) > : EQ))")
   apply (erule rev_mp)
   apply (simp add: EQ_iff [THEN iff_sym])
   apply (rule EQgen_mono [THEN EQ_def [THEN def_gfp_Tarski], THEN XHlemma1,
@@ -465,26 +461,26 @@
   apply (rule iff_refl [THEN XHlemma2])
   done
 
-lemma eq_coinduct: "[|  <t,u> : R;  R <= EQgen(R) |] ==> t = u"
+lemma eq_coinduct: "\<lbrakk><t,u> : R; R <= EQgen(R)\<rbrakk> \<Longrightarrow> t = u"
   apply (rule EQ_def [THEN def_coinduct, THEN EQ_iff [THEN iffD2]])
    apply assumption+
   done
 
 lemma eq_coinduct3:
-  "[|  <t,u> : R;  R <= EQgen(lfp(%x. EQgen(x) Un R Un EQ)) |] ==> t = u"
+  "\<lbrakk><t,u> : R;  R <= EQgen(lfp(\<lambda>x. EQgen(x) Un R Un EQ))\<rbrakk> \<Longrightarrow> t = u"
   apply (rule EQ_def [THEN def_coinduct3, THEN EQ_iff [THEN iffD2]])
   apply (rule EQgen_mono | assumption)+
   done
 
-ML {*
-  fun eq_coinduct_tac ctxt s i = res_inst_tac ctxt [(("R", 0), s)] @{thm eq_coinduct} i
-  fun eq_coinduct3_tac ctxt s i = res_inst_tac ctxt [(("R", 0), s)] @{thm eq_coinduct3} i
+method_setup eq_coinduct3 = {*
+  Scan.lift Args.name_inner_syntax >> (fn s => fn ctxt =>
+    SIMPLE_METHOD' (res_inst_tac ctxt [(("R", 0), s)] @{thm eq_coinduct3}))
 *}
 
 
 subsection {* Untyped Case Analysis and Other Facts *}
 
-lemma cond_eta: "(EX f. t=lam x. f(x)) ==> t = lam x.(t ` x)"
+lemma cond_eta: "(EX f. t=lam x. f(x)) \<Longrightarrow> t = lam x.(t ` x)"
   by (auto simp: apply_def)
 
 lemma exhaustion: "(t=bot) | (t=true) | (t=false) | (EX a b. t=<a,b>) | (EX f. t=lam x. f(x))"
@@ -493,7 +489,7 @@
   done
 
 lemma term_case:
-  "[| P(bot);  P(true);  P(false);  !!x y. P(<x,y>);  !!b. P(lam x. b(x)) |] ==> P(t)"
+  "\<lbrakk>P(bot); P(true); P(false); \<And>x y. P(<x,y>); \<And>b. P(lam x. b(x))\<rbrakk> \<Longrightarrow> P(t)"
   using exhaustion [of t] by blast
 
 end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/Fix.thy
--- a/src/CCL/Fix.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/Fix.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -9,20 +9,20 @@
 imports Type
 begin
 
-definition idgen :: "i => i"
-  where "idgen(f) == lam t. case(t,true,false,%x y.<f`x, f`y>,%u. lam x. f ` u(x))"
+definition idgen :: "i \<Rightarrow> i"
+  where "idgen(f) == lam t. case(t,true,false, \<lambda>x y.<f`x, f`y>, \<lambda>u. lam x. f ` u(x))"
 
-axiomatization INCL :: "[i=>o]=>o" where
-  INCL_def: "INCL(%x. P(x)) == (ALL f.(ALL n:Nat. P(f^n`bot)) --> P(fix(f)))" and
-  po_INCL: "INCL(%x. a(x) [= b(x))" and
-  INCL_subst: "INCL(P) ==> INCL(%x. P((g::i=>i)(x)))"
+axiomatization INCL :: "[i\<Rightarrow>o]\<Rightarrow>o" where
+  INCL_def: "INCL(\<lambda>x. P(x)) == (ALL f.(ALL n:Nat. P(f^n`bot)) \<longrightarrow> P(fix(f)))" and
+  po_INCL: "INCL(\<lambda>x. a(x) [= b(x))" and
+  INCL_subst: "INCL(P) \<Longrightarrow> INCL(\<lambda>x. P((g::i\<Rightarrow>i)(x)))"
 
 
 subsection {* Fixed Point Induction *}
 
 lemma fix_ind:
   assumes base: "P(bot)"
-    and step: "!!x. P(x) ==> P(f(x))"
+    and step: "\<And>x. P(x) \<Longrightarrow> P(f(x))"
     and incl: "INCL(P)"
   shows "P(fix(f))"
   apply (rule incl [unfolded INCL_def, rule_format])
@@ -35,22 +35,22 @@
 
 subsection {* Inclusive Predicates *}
 
-lemma inclXH: "INCL(P) <-> (ALL f. (ALL n:Nat. P(f ^ n ` bot)) --> P(fix(f)))"
+lemma inclXH: "INCL(P) \<longleftrightarrow> (ALL f. (ALL n:Nat. P(f ^ n ` bot)) \<longrightarrow> P(fix(f)))"
   by (simp add: INCL_def)
 
-lemma inclI: "[| !!f. ALL n:Nat. P(f^n`bot) ==> P(fix(f)) |] ==> INCL(%x. P(x))"
+lemma inclI: "\<lbrakk>\<And>f. ALL n:Nat. P(f^n`bot) \<Longrightarrow> P(fix(f))\<rbrakk> \<Longrightarrow> INCL(\<lambda>x. P(x))"
   unfolding inclXH by blast
 
-lemma inclD: "[| INCL(P);  !!n. n:Nat ==> P(f^n`bot) |] ==> P(fix(f))"
+lemma inclD: "\<lbrakk>INCL(P); \<And>n. n:Nat \<Longrightarrow> P(f^n`bot)\<rbrakk> \<Longrightarrow> P(fix(f))"
   unfolding inclXH by blast
 
-lemma inclE: "[| INCL(P);  (ALL n:Nat. P(f^n`bot))-->P(fix(f)) ==> R |] ==> R"
+lemma inclE: "\<lbrakk>INCL(P); (ALL n:Nat. P(f^n`bot)) \<longrightarrow> P(fix(f)) \<Longrightarrow> R\<rbrakk> \<Longrightarrow> R"
   by (blast dest: inclD)
 
 
 subsection {* Lemmas for Inclusive Predicates *}
 
-lemma npo_INCL: "INCL(%x.~ a(x) [= t)"
+lemma npo_INCL: "INCL(\<lambda>x. \<not> a(x) [= t)"
   apply (rule inclI)
   apply (drule bspec)
    apply (rule zeroT)
@@ -62,16 +62,16 @@
   apply (rule po_cong, rule po_bot)
   done
 
-lemma conj_INCL: "[| INCL(P);  INCL(Q) |] ==> INCL(%x. P(x) & Q(x))"
+lemma conj_INCL: "\<lbrakk>INCL(P); INCL(Q)\<rbrakk> \<Longrightarrow> INCL(\<lambda>x. P(x) \<and> Q(x))"
   by (blast intro!: inclI dest!: inclD)
 
-lemma all_INCL: "[| !!a. INCL(P(a)) |] ==> INCL(%x. ALL a. P(a,x))"
+lemma all_INCL: "(\<And>a. INCL(P(a))) \<Longrightarrow> INCL(\<lambda>x. ALL a. P(a,x))"
   by (blast intro!: inclI dest!: inclD)
 
-lemma ball_INCL: "[| !!a. a:A ==> INCL(P(a)) |] ==> INCL(%x. ALL a:A. P(a,x))"
+lemma ball_INCL: "(\<And>a. a:A \<Longrightarrow> INCL(P(a))) \<Longrightarrow> INCL(\<lambda>x. ALL a:A. P(a,x))"
   by (blast intro!: inclI dest!: inclD)
 
-lemma eq_INCL: "INCL(%x. a(x) = (b(x)::'a::prog))"
+lemma eq_INCL: "INCL(\<lambda>x. a(x) = (b(x)::'a::prog))"
   apply (simp add: eq_iff)
   apply (rule conj_INCL po_INCL)+
   done
@@ -93,7 +93,7 @@
 
 (* All fixed points are lam-expressions *)
 
-schematic_lemma idgenfp_lam: "idgen(d) = d ==> d = lam x. ?f(x)"
+schematic_lemma idgenfp_lam: "idgen(d) = d \<Longrightarrow> d = lam x. ?f(x)"
   apply (unfold idgen_def)
   apply (erule ssubst)
   apply (rule refl)
@@ -101,15 +101,15 @@
 
 (* Lemmas for rewriting fixed points of idgen *)
 
-lemma l_lemma: "[| a = b;  a ` t = u |] ==> b ` t = u"
+lemma l_lemma: "\<lbrakk>a = b; a ` t = u\<rbrakk> \<Longrightarrow> b ` t = u"
   by (simp add: idgen_def)
 
 lemma idgen_lemmas:
-  "idgen(d) = d ==> d ` bot = bot"
-  "idgen(d) = d ==> d ` true = true"
-  "idgen(d) = d ==> d ` false = false"
-  "idgen(d) = d ==> d ` <a,b> = <d ` a,d ` b>"
-  "idgen(d) = d ==> d ` (lam x. f(x)) = lam x. d ` f(x)"
+  "idgen(d) = d \<Longrightarrow> d ` bot = bot"
+  "idgen(d) = d \<Longrightarrow> d ` true = true"
+  "idgen(d) = d \<Longrightarrow> d ` false = false"
+  "idgen(d) = d \<Longrightarrow> d ` <a,b> = <d ` a,d ` b>"
+  "idgen(d) = d \<Longrightarrow> d ` (lam x. f(x)) = lam x. d ` f(x)"
   by (erule l_lemma, simp add: idgen_def)+
 
 
@@ -117,7 +117,7 @@
   of idgen and hence are they same *)
 
 lemma po_eta:
-  "[| ALL x. t ` x [= u ` x;  EX f. t=lam x. f(x);  EX f. u=lam x. f(x) |] ==> t [= u"
+  "\<lbrakk>ALL x. t ` x [= u ` x; EX f. t=lam x. f(x); EX f. u=lam x. f(x)\<rbrakk> \<Longrightarrow> t [= u"
   apply (drule cond_eta)+
   apply (erule ssubst)
   apply (erule ssubst)
@@ -125,15 +125,15 @@
   apply simp
   done
 
-schematic_lemma po_eta_lemma: "idgen(d) = d ==> d = lam x. ?f(x)"
+schematic_lemma po_eta_lemma: "idgen(d) = d \<Longrightarrow> d = lam x. ?f(x)"
   apply (unfold idgen_def)
   apply (erule sym)
   done
 
 lemma lemma1:
-  "idgen(d) = d ==>
-    {p. EX a b. p=<a,b> & (EX t. a=fix(idgen) ` t & b = d ` t)} <=
-      POgen({p. EX a b. p=<a,b> & (EX t. a=fix(idgen) ` t  & b = d ` t)})"
+  "idgen(d) = d \<Longrightarrow>
+    {p. EX a b. p=<a,b> \<and> (EX t. a=fix(idgen) ` t \<and> b = d ` t)} <=
+      POgen({p. EX a b. p=<a,b> \<and> (EX t. a=fix(idgen) ` t  \<and> b = d ` t)})"
   apply clarify
   apply (rule_tac t = t in term_case)
       apply (simp_all add: POgenXH idgen_lemmas idgen_lemmas [OF fix_idgenfp])
@@ -141,22 +141,22 @@
   apply fast
   done
 
-lemma fix_least_idgen: "idgen(d) = d ==> fix(idgen) [= d"
+lemma fix_least_idgen: "idgen(d) = d \<Longrightarrow> fix(idgen) [= d"
   apply (rule allI [THEN po_eta])
     apply (rule lemma1 [THEN [2] po_coinduct])
      apply (blast intro: po_eta_lemma fix_idgenfp)+
   done
 
 lemma lemma2:
-  "idgen(d) = d ==>
-    {p. EX a b. p=<a,b> & b = d ` a} <= POgen({p. EX a b. p=<a,b> & b = d ` a})"
+  "idgen(d) = d \<Longrightarrow>
+    {p. EX a b. p=<a,b> \<and> b = d ` a} <= POgen({p. EX a b. p=<a,b> \<and> b = d ` a})"
   apply clarify
   apply (rule_tac t = a in term_case)
       apply (simp_all add: POgenXH idgen_lemmas)
   apply fast
   done
 
-lemma id_least_idgen: "idgen(d) = d ==> lam x. x [= d"
+lemma id_least_idgen: "idgen(d) = d \<Longrightarrow> lam x. x [= d"
   apply (rule allI [THEN po_eta])
     apply (rule lemma2 [THEN [2] po_coinduct])
      apply simp
@@ -170,15 +170,15 @@
 
 (********)
 
-lemma id_apply: "f = lam x. x ==> f`t = t"
+lemma id_apply: "f = lam x. x \<Longrightarrow> f`t = t"
   apply (erule ssubst)
   apply (rule applyB)
   done
 
 lemma term_ind:
   assumes 1: "P(bot)" and 2: "P(true)" and 3: "P(false)"
-    and 4: "!!x y.[| P(x);  P(y) |] ==> P(<x,y>)"
-    and 5: "!!u.(!!x. P(u(x))) ==> P(lam x. u(x))"
+    and 4: "\<And>x y. \<lbrakk>P(x); P(y)\<rbrakk> \<Longrightarrow> P(<x,y>)"
+    and 5: "\<And>u.(\<And>x. P(u(x))) \<Longrightarrow> P(lam x. u(x))"
     and 6: "INCL(P)"
   shows "P(t)"
   apply (rule reachability [THEN id_apply, THEN subst])
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/Gfp.thy
--- a/src/CCL/Gfp.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/Gfp.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -10,37 +10,35 @@
 begin
 
 definition
-  gfp :: "['a set=>'a set] => 'a set" where -- "greatest fixed point"
+  gfp :: "['a set\<Rightarrow>'a set] \<Rightarrow> 'a set" where -- "greatest fixed point"
   "gfp(f) == Union({u. u <= f(u)})"
 
 (* gfp(f) is the least upper bound of {u. u <= f(u)} *)
 
-lemma gfp_upperbound: "[| A <= f(A) |] ==> A <= gfp(f)"
+lemma gfp_upperbound: "A <= f(A) \<Longrightarrow> A <= gfp(f)"
   unfolding gfp_def by blast
 
-lemma gfp_least: "[| !!u. u <= f(u) ==> u<=A |] ==> gfp(f) <= A"
+lemma gfp_least: "(\<And>u. u <= f(u) \<Longrightarrow> u <= A) \<Longrightarrow> gfp(f) <= A"
   unfolding gfp_def by blast
 
-lemma gfp_lemma2: "mono(f) ==> gfp(f) <= f(gfp(f))"
+lemma gfp_lemma2: "mono(f) \<Longrightarrow> gfp(f) <= f(gfp(f))"
   by (rule gfp_least, rule subset_trans, assumption, erule monoD,
     rule gfp_upperbound, assumption)
 
-lemma gfp_lemma3: "mono(f) ==> f(gfp(f)) <= gfp(f)"
+lemma gfp_lemma3: "mono(f) \<Longrightarrow> f(gfp(f)) <= gfp(f)"
   by (rule gfp_upperbound, frule monoD, rule gfp_lemma2, assumption+)
 
-lemma gfp_Tarski: "mono(f) ==> gfp(f) = f(gfp(f))"
+lemma gfp_Tarski: "mono(f) \<Longrightarrow> gfp(f) = f(gfp(f))"
   by (rule equalityI gfp_lemma2 gfp_lemma3 | assumption)+
 
 
 (*** Coinduction rules for greatest fixed points ***)
 
 (*weak version*)
-lemma coinduct: "[| a: A;  A <= f(A) |] ==> a : gfp(f)"
+lemma coinduct: "\<lbrakk>a: A;  A <= f(A)\<rbrakk> \<Longrightarrow> a : gfp(f)"
   by (blast dest: gfp_upperbound)
 
-lemma coinduct2_lemma:
-  "[| A <= f(A) Un gfp(f);  mono(f) |] ==>   
-    A Un gfp(f) <= f(A Un gfp(f))"
+lemma coinduct2_lemma: "\<lbrakk>A <= f(A) Un gfp(f); mono(f)\<rbrakk> \<Longrightarrow> A Un gfp(f) <= f(A Un gfp(f))"
   apply (rule subset_trans)
    prefer 2
    apply (erule mono_Un)
@@ -50,8 +48,7 @@
   done
 
 (*strong version, thanks to Martin Coen*)
-lemma coinduct2:
-  "[| a: A;  A <= f(A) Un gfp(f);  mono(f) |] ==> a : gfp(f)"
+lemma coinduct2: "\<lbrakk>a: A; A <= f(A) Un gfp(f); mono(f)\<rbrakk> \<Longrightarrow> a : gfp(f)"
   apply (rule coinduct)
    prefer 2
    apply (erule coinduct2_lemma, assumption)
@@ -62,13 +59,13 @@
          - instead of the condition  A <= f(A)
                            consider  A <= (f(A) Un f(f(A)) ...) Un gfp(A) ***)
 
-lemma coinduct3_mono_lemma: "mono(f) ==> mono(%x. f(x) Un A Un B)"
+lemma coinduct3_mono_lemma: "mono(f) \<Longrightarrow> mono(\<lambda>x. f(x) Un A Un B)"
   by (rule monoI) (blast dest: monoD)
 
 lemma coinduct3_lemma:
-  assumes prem: "A <= f(lfp(%x. f(x) Un A Un gfp(f)))"
+  assumes prem: "A <= f(lfp(\<lambda>x. f(x) Un A Un gfp(f)))"
     and mono: "mono(f)"
-  shows "lfp(%x. f(x) Un A Un gfp(f)) <= f(lfp(%x. f(x) Un A Un gfp(f)))"
+  shows "lfp(\<lambda>x. f(x) Un A Un gfp(f)) <= f(lfp(\<lambda>x. f(x) Un A Un gfp(f)))"
   apply (rule subset_trans)
    apply (rule mono [THEN coinduct3_mono_lemma, THEN lfp_lemma3])
   apply (rule Un_least [THEN Un_least])
@@ -82,7 +79,7 @@
 
 lemma coinduct3:
   assumes 1: "a:A"
-    and 2: "A <= f(lfp(%x. f(x) Un A Un gfp(f)))"
+    and 2: "A <= f(lfp(\<lambda>x. f(x) Un A Un gfp(f)))"
     and 3: "mono(f)"
   shows "a : gfp(f)"
   apply (rule coinduct)
@@ -95,25 +92,25 @@
 
 subsection {* Definition forms of @{text "gfp_Tarski"}, to control unfolding *}
 
-lemma def_gfp_Tarski: "[| h==gfp(f);  mono(f) |] ==> h = f(h)"
+lemma def_gfp_Tarski: "\<lbrakk>h == gfp(f); mono(f)\<rbrakk> \<Longrightarrow> h = f(h)"
   apply unfold
   apply (erule gfp_Tarski)
   done
 
-lemma def_coinduct: "[| h==gfp(f);  a:A;  A <= f(A) |] ==> a: h"
+lemma def_coinduct: "\<lbrakk>h == gfp(f); a:A; A <= f(A)\<rbrakk> \<Longrightarrow> a: h"
   apply unfold
   apply (erule coinduct)
   apply assumption
   done
 
-lemma def_coinduct2: "[| h==gfp(f);  a:A;  A <= f(A) Un h; mono(f) |] ==> a: h"
+lemma def_coinduct2: "\<lbrakk>h == gfp(f); a:A; A <= f(A) Un h; mono(f)\<rbrakk> \<Longrightarrow> a: h"
   apply unfold
   apply (erule coinduct2)
    apply assumption
   apply assumption
   done
 
-lemma def_coinduct3: "[| h==gfp(f);  a:A;  A <= f(lfp(%x. f(x) Un A Un h)); mono(f) |] ==> a: h"
+lemma def_coinduct3: "\<lbrakk>h == gfp(f); a:A; A <= f(lfp(\<lambda>x. f(x) Un A Un h)); mono(f)\<rbrakk> \<Longrightarrow> a: h"
   apply unfold
   apply (erule coinduct3)
    apply assumption
@@ -121,7 +118,7 @@
   done
 
 (*Monotonicity of gfp!*)
-lemma gfp_mono: "[| mono(f);  !!Z. f(Z)<=g(Z) |] ==> gfp(f) <= gfp(g)"
+lemma gfp_mono: "\<lbrakk>mono(f); \<And>Z. f(Z) <= g(Z)\<rbrakk> \<Longrightarrow> gfp(f) <= gfp(g)"
   apply (rule gfp_upperbound)
   apply (rule subset_trans)
    apply (rule gfp_lemma2)
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/Hered.thy
--- a/src/CCL/Hered.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/Hered.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -15,10 +15,10 @@
   is.  Not so useful for functions!
 *}
 
-definition HTTgen :: "i set => i set" where
+definition HTTgen :: "i set \<Rightarrow> i set" where
   "HTTgen(R) ==
-    {t. t=true | t=false | (EX a b. t= <a, b> & a : R & b : R) |
-      (EX f. t = lam x. f(x) & (ALL x. f(x) : R))}"
+    {t. t=true | t=false | (EX a b. t= <a, b> \<and> a : R \<and> b : R) |
+      (EX f. t = lam x. f(x) \<and> (ALL x. f(x) : R))}"
 
 definition HTT :: "i set"
   where "HTT == gfp(HTTgen)"
@@ -26,22 +26,22 @@
 
 subsection {* Hereditary Termination *}
 
-lemma HTTgen_mono: "mono(%X. HTTgen(X))"
+lemma HTTgen_mono: "mono(\<lambda>X. HTTgen(X))"
   apply (unfold HTTgen_def)
   apply (rule monoI)
   apply blast
   done
 
 lemma HTTgenXH: 
-  "t : HTTgen(A) <-> t=true | t=false | (EX a b. t=<a,b> & a : A & b : A) |  
-                                        (EX f. t=lam x. f(x) & (ALL x. f(x) : A))"
+  "t : HTTgen(A) \<longleftrightarrow> t=true | t=false | (EX a b. t=<a,b> \<and> a : A \<and> b : A) |  
+                                        (EX f. t=lam x. f(x) \<and> (ALL x. f(x) : A))"
   apply (unfold HTTgen_def)
   apply blast
   done
 
 lemma HTTXH: 
-  "t : HTT <-> t=true | t=false | (EX a b. t=<a,b> & a : HTT & b : HTT) |  
-                                   (EX f. t=lam x. f(x) & (ALL x. f(x) : HTT))"
+  "t : HTT \<longleftrightarrow> t=true | t=false | (EX a b. t=<a,b> \<and> a : HTT \<and> b : HTT) |  
+                                   (EX f. t=lam x. f(x) \<and> (ALL x. f(x) : HTT))"
   apply (rule HTTgen_mono [THEN HTT_def [THEN def_gfp_Tarski], THEN XHlemma1, unfolded HTTgen_def])
   apply blast
   done
@@ -49,7 +49,7 @@
 
 subsection {* Introduction Rules for HTT *}
 
-lemma HTT_bot: "~ bot : HTT"
+lemma HTT_bot: "\<not> bot : HTT"
   by (blast dest: HTTXH [THEN iffD1])
 
 lemma HTT_true: "true : HTT"
@@ -58,12 +58,12 @@
 lemma HTT_false: "false : HTT"
   by (blast intro: HTTXH [THEN iffD2])
 
-lemma HTT_pair: "<a,b> : HTT <->  a : HTT  & b : HTT"
+lemma HTT_pair: "<a,b> : HTT \<longleftrightarrow> a : HTT \<and> b : HTT"
   apply (rule HTTXH [THEN iff_trans])
   apply blast
   done
 
-lemma HTT_lam: "lam x. f(x) : HTT <-> (ALL x. f(x) : HTT)"
+lemma HTT_lam: "lam x. f(x) : HTT \<longleftrightarrow> (ALL x. f(x) : HTT)"
   apply (rule HTTXH [THEN iff_trans])
   apply auto
   done
@@ -72,12 +72,12 @@
 
 lemma HTT_rews2:
   "one : HTT"
-  "inl(a) : HTT <-> a : HTT"
-  "inr(b) : HTT <-> b : HTT"
+  "inl(a) : HTT \<longleftrightarrow> a : HTT"
+  "inr(b) : HTT \<longleftrightarrow> b : HTT"
   "zero : HTT"
-  "succ(n) : HTT <-> n : HTT"
+  "succ(n) : HTT \<longleftrightarrow> n : HTT"
   "[] : HTT"
-  "x$xs : HTT <-> x : HTT & xs : HTT"
+  "x$xs : HTT \<longleftrightarrow> x : HTT \<and> xs : HTT"
   by (simp_all add: data_defs HTT_rews1)
 
 lemmas HTT_rews = HTT_rews1 HTT_rews2
@@ -85,13 +85,12 @@
 
 subsection {* Coinduction for HTT *}
 
-lemma HTT_coinduct: "[|  t : R;  R <= HTTgen(R) |] ==> t : HTT"
+lemma HTT_coinduct: "\<lbrakk>t : R; R <= HTTgen(R)\<rbrakk> \<Longrightarrow> t : HTT"
   apply (erule HTT_def [THEN def_coinduct])
   apply assumption
   done
 
-lemma HTT_coinduct3:
-  "[|  t : R;   R <= HTTgen(lfp(%x. HTTgen(x) Un R Un HTT)) |] ==> t : HTT"
+lemma HTT_coinduct3: "\<lbrakk>t : R; R <= HTTgen(lfp(\<lambda>x. HTTgen(x) Un R Un HTT))\<rbrakk> \<Longrightarrow> t : HTT"
   apply (erule HTTgen_mono [THEN [3] HTT_def [THEN def_coinduct3]])
   apply assumption
   done
@@ -99,16 +98,16 @@
 lemma HTTgenIs:
   "true : HTTgen(R)"
   "false : HTTgen(R)"
-  "[| a : R;  b : R |] ==> <a,b> : HTTgen(R)"
-  "!!b. [| !!x. b(x) : R |] ==> lam x. b(x) : HTTgen(R)"
+  "\<lbrakk>a : R; b : R\<rbrakk> \<Longrightarrow> <a,b> : HTTgen(R)"
+  "\<And>b. (\<And>x. b(x) : R) \<Longrightarrow> lam x. b(x) : HTTgen(R)"
   "one : HTTgen(R)"
-  "a : lfp(%x. HTTgen(x) Un R Un HTT) ==> inl(a) : HTTgen(lfp(%x. HTTgen(x) Un R Un HTT))"
-  "b : lfp(%x. HTTgen(x) Un R Un HTT) ==> inr(b) : HTTgen(lfp(%x. HTTgen(x) Un R Un HTT))"
-  "zero : HTTgen(lfp(%x. HTTgen(x) Un R Un HTT))"
-  "n : lfp(%x. HTTgen(x) Un R Un HTT) ==> succ(n) : HTTgen(lfp(%x. HTTgen(x) Un R Un HTT))"
-  "[] : HTTgen(lfp(%x. HTTgen(x) Un R Un HTT))"
-  "[| h : lfp(%x. HTTgen(x) Un R Un HTT); t : lfp(%x. HTTgen(x) Un R Un HTT) |] ==>
-    h$t : HTTgen(lfp(%x. HTTgen(x) Un R Un HTT))"
+  "a : lfp(\<lambda>x. HTTgen(x) Un R Un HTT) \<Longrightarrow> inl(a) : HTTgen(lfp(\<lambda>x. HTTgen(x) Un R Un HTT))"
+  "b : lfp(\<lambda>x. HTTgen(x) Un R Un HTT) \<Longrightarrow> inr(b) : HTTgen(lfp(\<lambda>x. HTTgen(x) Un R Un HTT))"
+  "zero : HTTgen(lfp(\<lambda>x. HTTgen(x) Un R Un HTT))"
+  "n : lfp(\<lambda>x. HTTgen(x) Un R Un HTT) \<Longrightarrow> succ(n) : HTTgen(lfp(\<lambda>x. HTTgen(x) Un R Un HTT))"
+  "[] : HTTgen(lfp(\<lambda>x. HTTgen(x) Un R Un HTT))"
+  "\<lbrakk>h : lfp(\<lambda>x. HTTgen(x) Un R Un HTT); t : lfp(\<lambda>x. HTTgen(x) Un R Un HTT)\<rbrakk> \<Longrightarrow>
+    h$t : HTTgen(lfp(\<lambda>x. HTTgen(x) Un R Un HTT))"
   unfolding data_defs by (genIs HTTgenXH HTTgen_mono)+
 
 
@@ -120,10 +119,10 @@
 lemma BoolF: "Bool <= HTT"
   by (fastforce simp: subsetXH BoolXH iff: HTT_rews)
 
-lemma PlusF: "[| A <= HTT;  B <= HTT |] ==> A + B  <= HTT"
+lemma PlusF: "\<lbrakk>A <= HTT; B <= HTT\<rbrakk> \<Longrightarrow> A + B  <= HTT"
   by (fastforce simp: subsetXH PlusXH iff: HTT_rews)
 
-lemma SigmaF: "[| A <= HTT;  !!x. x:A ==> B(x) <= HTT |] ==> SUM x:A. B(x) <= HTT"
+lemma SigmaF: "\<lbrakk>A <= HTT; \<And>x. x:A \<Longrightarrow> B(x) <= HTT\<rbrakk> \<Longrightarrow> SUM x:A. B(x) <= HTT"
   by (fastforce simp: subsetXH SgXH HTT_rews)
 
 
@@ -144,7 +143,7 @@
   apply (fast intro: HTTgenIs elim!: HTTgen_mono [THEN ci3_RI] dest: NatXH [THEN iffD1])
   done
 
-lemma ListF: "A <= HTT ==> List(A) <= HTT"
+lemma ListF: "A <= HTT \<Longrightarrow> List(A) <= HTT"
   apply clarify
   apply (erule HTT_coinduct3)
   apply (fast intro!: HTTgenIs elim!: HTTgen_mono [THEN ci3_RI]
@@ -152,14 +151,14 @@
     dest: ListXH [THEN iffD1])
   done
 
-lemma ListsF: "A <= HTT ==> Lists(A) <= HTT"
+lemma ListsF: "A <= HTT \<Longrightarrow> Lists(A) <= HTT"
   apply clarify
   apply (erule HTT_coinduct3)
   apply (fast intro!: HTTgenIs elim!: HTTgen_mono [THEN ci3_RI]
     subsetD [THEN HTTgen_mono [THEN ci3_AI]] dest: ListsXH [THEN iffD1])
   done
 
-lemma IListsF: "A <= HTT ==> ILists(A) <= HTT"
+lemma IListsF: "A <= HTT \<Longrightarrow> ILists(A) <= HTT"
   apply clarify
   apply (erule HTT_coinduct3)
   apply (fast intro!: HTTgenIs elim!: HTTgen_mono [THEN ci3_RI]
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/Lfp.thy
--- a/src/CCL/Lfp.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/Lfp.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -10,24 +10,24 @@
 begin
 
 definition
-  lfp :: "['a set=>'a set] => 'a set" where -- "least fixed point"
+  lfp :: "['a set\<Rightarrow>'a set] \<Rightarrow> 'a set" where -- "least fixed point"
   "lfp(f) == Inter({u. f(u) <= u})"
 
 (* lfp(f) is the greatest lower bound of {u. f(u) <= u} *)
 
-lemma lfp_lowerbound: "[| f(A) <= A |] ==> lfp(f) <= A"
+lemma lfp_lowerbound: "f(A) <= A \<Longrightarrow> lfp(f) <= A"
   unfolding lfp_def by blast
 
-lemma lfp_greatest: "[| !!u. f(u) <= u ==> A<=u |] ==> A <= lfp(f)"
+lemma lfp_greatest: "(\<And>u. f(u) <= u \<Longrightarrow> A<=u) \<Longrightarrow> A <= lfp(f)"
   unfolding lfp_def by blast
 
-lemma lfp_lemma2: "mono(f) ==> f(lfp(f)) <= lfp(f)"
+lemma lfp_lemma2: "mono(f) \<Longrightarrow> f(lfp(f)) <= lfp(f)"
   by (rule lfp_greatest, rule subset_trans, drule monoD, rule lfp_lowerbound, assumption+)
 
-lemma lfp_lemma3: "mono(f) ==> lfp(f) <= f(lfp(f))"
+lemma lfp_lemma3: "mono(f) \<Longrightarrow> lfp(f) <= f(lfp(f))"
   by (rule lfp_lowerbound, frule monoD, drule lfp_lemma2, assumption+)
 
-lemma lfp_Tarski: "mono(f) ==> lfp(f) = f(lfp(f))"
+lemma lfp_Tarski: "mono(f) \<Longrightarrow> lfp(f) = f(lfp(f))"
   by (rule equalityI lfp_lemma2 lfp_lemma3 | assumption)+
 
 
@@ -36,7 +36,7 @@
 lemma induct:
   assumes lfp: "a: lfp(f)"
     and mono: "mono(f)"
-    and indhyp: "!!x. [| x: f(lfp(f) Int {x. P(x)}) |] ==> P(x)"
+    and indhyp: "\<And>x. \<lbrakk>x: f(lfp(f) Int {x. P(x)})\<rbrakk> \<Longrightarrow> P(x)"
   shows "P(a)"
   apply (rule_tac a = a in Int_lower2 [THEN subsetD, THEN CollectD])
   apply (rule lfp [THEN [2] lfp_lowerbound [THEN subsetD]])
@@ -46,16 +46,13 @@
 
 (** Definition forms of lfp_Tarski and induct, to control unfolding **)
 
-lemma def_lfp_Tarski: "[| h==lfp(f);  mono(f) |] ==> h = f(h)"
+lemma def_lfp_Tarski: "\<lbrakk>h == lfp(f); mono(f)\<rbrakk> \<Longrightarrow> h = f(h)"
   apply unfold
   apply (drule lfp_Tarski)
   apply assumption
   done
 
-lemma def_induct:
-  "[| A == lfp(f);  a:A;  mono(f);                     
-    !!x. [| x: f(A Int {x. P(x)}) |] ==> P(x)         
-  |] ==> P(a)"
+lemma def_induct: "\<lbrakk>A == lfp(f);  a:A;  mono(f); \<And>x. x: f(A Int {x. P(x)}) \<Longrightarrow> P(x)\<rbrakk> \<Longrightarrow> P(a)"
   apply (rule induct [of concl: P a])
     apply simp
    apply assumption
@@ -63,7 +60,7 @@
   done
 
 (*Monotonicity of lfp!*)
-lemma lfp_mono: "[| mono(g);  !!Z. f(Z)<=g(Z) |] ==> lfp(f) <= lfp(g)"
+lemma lfp_mono: "\<lbrakk>mono(g); \<And>Z. f(Z) <= g(Z)\<rbrakk> \<Longrightarrow> lfp(f) <= lfp(g)"
   apply (rule lfp_lowerbound)
   apply (rule subset_trans)
    apply (erule meta_spec)
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/ROOT
--- a/src/CCL/ROOT	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/ROOT	Tue Nov 11 21:14:19 2014 +0100
@@ -11,15 +11,13 @@
     evaluation to weak head-normal form.
   *}
   options [document = false]
-  theories Wfd Fix
+  theories
+    Wfd
+    Fix
 
-session "CCL-ex" in ex = CCL +
-  description {*
-    Author:     Martin Coen, Cambridge University Computer Laboratory
-    Copyright   1993  University of Cambridge
+    (* Examples for Classical Computational Logic *)
+    "ex/Nat"
+    "ex/List"
+    "ex/Stream"
+    "ex/Flag"
 
-    Examples for Classical Computational Logic.
-  *}
-  options [document = false]
-  theories Nat List Stream Flag
-
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/Set.thy
--- a/src/CCL/Set.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/Set.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -10,74 +10,74 @@
 instance set :: ("term") "term" ..
 
 consts
-  Collect       :: "['a => o] => 'a set"                    (*comprehension*)
-  Compl         :: "('a set) => 'a set"                     (*complement*)
-  Int           :: "['a set, 'a set] => 'a set"         (infixl "Int" 70)
-  Un            :: "['a set, 'a set] => 'a set"         (infixl "Un" 65)
-  Union         :: "(('a set)set) => 'a set"                (*...of a set*)
-  Inter         :: "(('a set)set) => 'a set"                (*...of a set*)
-  UNION         :: "['a set, 'a => 'b set] => 'b set"       (*general*)
-  INTER         :: "['a set, 'a => 'b set] => 'b set"       (*general*)
-  Ball          :: "['a set, 'a => o] => o"                 (*bounded quants*)
-  Bex           :: "['a set, 'a => o] => o"                 (*bounded quants*)
-  mono          :: "['a set => 'b set] => o"                (*monotonicity*)
-  mem           :: "['a, 'a set] => o"                  (infixl ":" 50) (*membership*)
-  subset        :: "['a set, 'a set] => o"              (infixl "<=" 50)
-  singleton     :: "'a => 'a set"                       ("{_}")
+  Collect       :: "['a \<Rightarrow> o] \<Rightarrow> 'a set"                    (*comprehension*)
+  Compl         :: "('a set) \<Rightarrow> 'a set"                     (*complement*)
+  Int           :: "['a set, 'a set] \<Rightarrow> 'a set"         (infixl "Int" 70)
+  Un            :: "['a set, 'a set] \<Rightarrow> 'a set"         (infixl "Un" 65)
+  Union         :: "(('a set)set) \<Rightarrow> 'a set"                (*...of a set*)
+  Inter         :: "(('a set)set) \<Rightarrow> 'a set"                (*...of a set*)
+  UNION         :: "['a set, 'a \<Rightarrow> 'b set] \<Rightarrow> 'b set"       (*general*)
+  INTER         :: "['a set, 'a \<Rightarrow> 'b set] \<Rightarrow> 'b set"       (*general*)
+  Ball          :: "['a set, 'a \<Rightarrow> o] \<Rightarrow> o"                 (*bounded quants*)
+  Bex           :: "['a set, 'a \<Rightarrow> o] \<Rightarrow> o"                 (*bounded quants*)
+  mono          :: "['a set \<Rightarrow> 'b set] \<Rightarrow> o"                (*monotonicity*)
+  mem           :: "['a, 'a set] \<Rightarrow> o"                  (infixl ":" 50) (*membership*)
+  subset        :: "['a set, 'a set] \<Rightarrow> o"              (infixl "<=" 50)
+  singleton     :: "'a \<Rightarrow> 'a set"                       ("{_}")
   empty         :: "'a set"                             ("{}")
 
 syntax
-  "_Coll"       :: "[idt, o] => 'a set"                 ("(1{_./ _})") (*collection*)
+  "_Coll"       :: "[idt, o] \<Rightarrow> 'a set"                 ("(1{_./ _})") (*collection*)
 
   (* Big Intersection / Union *)
 
-  "_INTER"      :: "[idt, 'a set, 'b set] => 'b set"    ("(INT _:_./ _)" [0, 0, 0] 10)
-  "_UNION"      :: "[idt, 'a set, 'b set] => 'b set"    ("(UN _:_./ _)" [0, 0, 0] 10)
+  "_INTER"      :: "[idt, 'a set, 'b set] \<Rightarrow> 'b set"    ("(INT _:_./ _)" [0, 0, 0] 10)
+  "_UNION"      :: "[idt, 'a set, 'b set] \<Rightarrow> 'b set"    ("(UN _:_./ _)" [0, 0, 0] 10)
 
   (* Bounded Quantifiers *)
 
-  "_Ball"       :: "[idt, 'a set, o] => o"              ("(ALL _:_./ _)" [0, 0, 0] 10)
-  "_Bex"        :: "[idt, 'a set, o] => o"              ("(EX _:_./ _)" [0, 0, 0] 10)
+  "_Ball"       :: "[idt, 'a set, o] \<Rightarrow> o"              ("(ALL _:_./ _)" [0, 0, 0] 10)
+  "_Bex"        :: "[idt, 'a set, o] \<Rightarrow> o"              ("(EX _:_./ _)" [0, 0, 0] 10)
 
 translations
-  "{x. P}"      == "CONST Collect(%x. P)"
-  "INT x:A. B"  == "CONST INTER(A, %x. B)"
-  "UN x:A. B"   == "CONST UNION(A, %x. B)"
-  "ALL x:A. P"  == "CONST Ball(A, %x. P)"
-  "EX x:A. P"   == "CONST Bex(A, %x. P)"
+  "{x. P}"      == "CONST Collect(\<lambda>x. P)"
+  "INT x:A. B"  == "CONST INTER(A, \<lambda>x. B)"
+  "UN x:A. B"   == "CONST UNION(A, \<lambda>x. B)"
+  "ALL x:A. P"  == "CONST Ball(A, \<lambda>x. P)"
+  "EX x:A. P"   == "CONST Bex(A, \<lambda>x. P)"
 
 axiomatization where
-  mem_Collect_iff: "(a : {x. P(x)}) <-> P(a)" and
-  set_extension: "A = B <-> (ALL x. x:A <-> x:B)"
+  mem_Collect_iff: "(a : {x. P(x)}) \<longleftrightarrow> P(a)" and
+  set_extension: "A = B \<longleftrightarrow> (ALL x. x:A \<longleftrightarrow> x:B)"
 
 defs
-  Ball_def:      "Ball(A, P)  == ALL x. x:A --> P(x)"
-  Bex_def:       "Bex(A, P)   == EX x. x:A & P(x)"
-  mono_def:      "mono(f)     == (ALL A B. A <= B --> f(A) <= f(B))"
+  Ball_def:      "Ball(A, P)  == ALL x. x:A \<longrightarrow> P(x)"
+  Bex_def:       "Bex(A, P)   == EX x. x:A \<and> P(x)"
+  mono_def:      "mono(f)     == (ALL A B. A <= B \<longrightarrow> f(A) <= f(B))"
   subset_def:    "A <= B      == ALL x:A. x:B"
   singleton_def: "{a}         == {x. x=a}"
   empty_def:     "{}          == {x. False}"
   Un_def:        "A Un B      == {x. x:A | x:B}"
-  Int_def:       "A Int B     == {x. x:A & x:B}"
-  Compl_def:     "Compl(A)    == {x. ~x:A}"
+  Int_def:       "A Int B     == {x. x:A \<and> x:B}"
+  Compl_def:     "Compl(A)    == {x. \<not>x:A}"
   INTER_def:     "INTER(A, B) == {y. ALL x:A. y: B(x)}"
   UNION_def:     "UNION(A, B) == {y. EX x:A. y: B(x)}"
   Inter_def:     "Inter(S)    == (INT x:S. x)"
   Union_def:     "Union(S)    == (UN x:S. x)"
 
 
-lemma CollectI: "[| P(a) |] ==> a : {x. P(x)}"
+lemma CollectI: "P(a) \<Longrightarrow> a : {x. P(x)}"
   apply (rule mem_Collect_iff [THEN iffD2])
   apply assumption
   done
 
-lemma CollectD: "[| a : {x. P(x)} |] ==> P(a)"
+lemma CollectD: "a : {x. P(x)} \<Longrightarrow> P(a)"
   apply (erule mem_Collect_iff [THEN iffD1])
   done
 
 lemmas CollectE = CollectD [elim_format]
 
-lemma set_ext: "[| !!x. x:A <-> x:B |] ==> A = B"
+lemma set_ext: "(\<And>x. x:A \<longleftrightarrow> x:B) \<Longrightarrow> A = B"
   apply (rule set_extension [THEN iffD2])
   apply simp
   done
@@ -85,80 +85,79 @@
 
 subsection {* Bounded quantifiers *}
 
-lemma ballI: "[| !!x. x:A ==> P(x) |] ==> ALL x:A. P(x)"
+lemma ballI: "(\<And>x. x:A \<Longrightarrow> P(x)) \<Longrightarrow> ALL x:A. P(x)"
   by (simp add: Ball_def)
 
-lemma bspec: "[| ALL x:A. P(x);  x:A |] ==> P(x)"
+lemma bspec: "\<lbrakk>ALL x:A. P(x); x:A\<rbrakk> \<Longrightarrow> P(x)"
   by (simp add: Ball_def)
 
-lemma ballE: "[| ALL x:A. P(x);  P(x) ==> Q;  ~ x:A ==> Q |] ==> Q"
+lemma ballE: "\<lbrakk>ALL x:A. P(x); P(x) \<Longrightarrow> Q; \<not> x:A \<Longrightarrow> Q\<rbrakk> \<Longrightarrow> Q"
   unfolding Ball_def by blast
 
-lemma bexI: "[| P(x);  x:A |] ==> EX x:A. P(x)"
+lemma bexI: "\<lbrakk>P(x); x:A\<rbrakk> \<Longrightarrow> EX x:A. P(x)"
   unfolding Bex_def by blast
 
-lemma bexCI: "[| EX x:A. ~P(x) ==> P(a);  a:A |] ==> EX x:A. P(x)"
+lemma bexCI: "\<lbrakk>EX x:A. \<not>P(x) \<Longrightarrow> P(a); a:A\<rbrakk> \<Longrightarrow> EX x:A. P(x)"
   unfolding Bex_def by blast
 
-lemma bexE: "[| EX x:A. P(x);  !!x. [| x:A; P(x) |] ==> Q  |] ==> Q"
+lemma bexE: "\<lbrakk>EX x:A. P(x); \<And>x. \<lbrakk>x:A; P(x)\<rbrakk> \<Longrightarrow> Q\<rbrakk> \<Longrightarrow> Q"
   unfolding Bex_def by blast
 
 (*Trival rewrite rule;   (! x:A.P)=P holds only if A is nonempty!*)
-lemma ball_rew: "(ALL x:A. True) <-> True"
+lemma ball_rew: "(ALL x:A. True) \<longleftrightarrow> True"
   by (blast intro: ballI)
 
 
 subsection {* Congruence rules *}
 
 lemma ball_cong:
-  "[| A=A';  !!x. x:A' ==> P(x) <-> P'(x) |] ==>
-    (ALL x:A. P(x)) <-> (ALL x:A'. P'(x))"
+  "\<lbrakk>A = A'; \<And>x. x:A' \<Longrightarrow> P(x) \<longleftrightarrow> P'(x)\<rbrakk> \<Longrightarrow>
+    (ALL x:A. P(x)) \<longleftrightarrow> (ALL x:A'. P'(x))"
   by (blast intro: ballI elim: ballE)
 
 lemma bex_cong:
-  "[| A=A';  !!x. x:A' ==> P(x) <-> P'(x) |] ==>
-    (EX x:A. P(x)) <-> (EX x:A'. P'(x))"
+  "\<lbrakk>A = A'; \<And>x. x:A' \<Longrightarrow> P(x) \<longleftrightarrow> P'(x)\<rbrakk> \<Longrightarrow>
+    (EX x:A. P(x)) \<longleftrightarrow> (EX x:A'. P'(x))"
   by (blast intro: bexI elim: bexE)
 
 
 subsection {* Rules for subsets *}
 
-lemma subsetI: "(!!x. x:A ==> x:B) ==> A <= B"
+lemma subsetI: "(\<And>x. x:A \<Longrightarrow> x:B) \<Longrightarrow> A <= B"
   unfolding subset_def by (blast intro: ballI)
 
 (*Rule in Modus Ponens style*)
-lemma subsetD: "[| A <= B;  c:A |] ==> c:B"
+lemma subsetD: "\<lbrakk>A <= B; c:A\<rbrakk> \<Longrightarrow> c:B"
   unfolding subset_def by (blast elim: ballE)
 
 (*Classical elimination rule*)
-lemma subsetCE: "[| A <= B;  ~(c:A) ==> P;  c:B ==> P |] ==> P"
+lemma subsetCE: "\<lbrakk>A <= B; \<not>(c:A) \<Longrightarrow> P; c:B \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
   by (blast dest: subsetD)
 
 lemma subset_refl: "A <= A"
   by (blast intro: subsetI)
 
-lemma subset_trans: "[| A<=B;  B<=C |] ==> A<=C"
+lemma subset_trans: "\<lbrakk>A <= B; B <= C\<rbrakk> \<Longrightarrow> A <= C"
   by (blast intro: subsetI dest: subsetD)
 
 
 subsection {* Rules for equality *}
 
 (*Anti-symmetry of the subset relation*)
-lemma subset_antisym: "[| A <= B;  B <= A |] ==> A = B"
+lemma subset_antisym: "\<lbrakk>A <= B; B <= A\<rbrakk> \<Longrightarrow> A = B"
   by (blast intro: set_ext dest: subsetD)
 
 lemmas equalityI = subset_antisym
 
 (* Equality rules from ZF set theory -- are they appropriate here? *)
-lemma equalityD1: "A = B ==> A<=B"
-  and equalityD2: "A = B ==> B<=A"
+lemma equalityD1: "A = B \<Longrightarrow> A<=B"
+  and equalityD2: "A = B \<Longrightarrow> B<=A"
   by (simp_all add: subset_refl)
 
-lemma equalityE: "[| A = B;  [| A<=B; B<=A |] ==> P |]  ==>  P"
+lemma equalityE: "\<lbrakk>A = B; \<lbrakk>A <= B; B <= A\<rbrakk> \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
   by (simp add: subset_refl)
 
-lemma equalityCE:
-    "[| A = B;  [| c:A; c:B |] ==> P;  [| ~ c:A; ~ c:B |] ==> P |]  ==>  P"
+lemma equalityCE: "\<lbrakk>A = B; \<lbrakk>c:A; c:B\<rbrakk> \<Longrightarrow> P; \<lbrakk>\<not> c:A; \<not> c:B\<rbrakk> \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
   by (blast elim: equalityE subsetCE)
 
 lemma trivial_set: "{x. x:A} = A"
@@ -167,40 +166,40 @@
 
 subsection {* Rules for binary union *}
 
-lemma UnI1: "c:A ==> c : A Un B"
-  and UnI2: "c:B ==> c : A Un B"
+lemma UnI1: "c:A \<Longrightarrow> c : A Un B"
+  and UnI2: "c:B \<Longrightarrow> c : A Un B"
   unfolding Un_def by (blast intro: CollectI)+
 
 (*Classical introduction rule: no commitment to A vs B*)
-lemma UnCI: "(~c:B ==> c:A) ==> c : A Un B"
+lemma UnCI: "(\<not>c:B \<Longrightarrow> c:A) \<Longrightarrow> c : A Un B"
   by (blast intro: UnI1 UnI2)
 
-lemma UnE: "[| c : A Un B;  c:A ==> P;  c:B ==> P |] ==> P"
+lemma UnE: "\<lbrakk>c : A Un B; c:A \<Longrightarrow> P; c:B \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
   unfolding Un_def by (blast dest: CollectD)
 
 
 subsection {* Rules for small intersection *}
 
-lemma IntI: "[| c:A;  c:B |] ==> c : A Int B"
+lemma IntI: "\<lbrakk>c:A; c:B\<rbrakk> \<Longrightarrow> c : A Int B"
   unfolding Int_def by (blast intro: CollectI)
 
-lemma IntD1: "c : A Int B ==> c:A"
-  and IntD2: "c : A Int B ==> c:B"
+lemma IntD1: "c : A Int B \<Longrightarrow> c:A"
+  and IntD2: "c : A Int B \<Longrightarrow> c:B"
   unfolding Int_def by (blast dest: CollectD)+
 
-lemma IntE: "[| c : A Int B;  [| c:A; c:B |] ==> P |] ==> P"
+lemma IntE: "\<lbrakk>c : A Int B; \<lbrakk>c:A; c:B\<rbrakk> \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
   by (blast dest: IntD1 IntD2)
 
 
 subsection {* Rules for set complement *}
 
-lemma ComplI: "[| c:A ==> False |] ==> c : Compl(A)"
+lemma ComplI: "(c:A \<Longrightarrow> False) \<Longrightarrow> c : Compl(A)"
   unfolding Compl_def by (blast intro: CollectI)
 
 (*This form, with negated conclusion, works well with the Classical prover.
   Negated assumptions behave like formulae on the right side of the notional
   turnstile...*)
-lemma ComplD: "[| c : Compl(A) |] ==> ~c:A"
+lemma ComplD: "c : Compl(A) \<Longrightarrow> \<not>c:A"
   unfolding Compl_def by (blast dest: CollectD)
 
 lemmas ComplE = ComplD [elim_format]
@@ -211,13 +210,13 @@
 lemma empty_eq: "{x. False} = {}"
   by (simp add: empty_def)
 
-lemma emptyD: "a : {} ==> P"
+lemma emptyD: "a : {} \<Longrightarrow> P"
   unfolding empty_def by (blast dest: CollectD)
 
 lemmas emptyE = emptyD [elim_format]
 
 lemma not_emptyD:
-  assumes "~ A={}"
+  assumes "\<not> A={}"
   shows "EX x. x:A"
 proof -
   have "\<not> (EX x. x:A) \<Longrightarrow> A = {}"
@@ -231,7 +230,7 @@
 lemma singletonI: "a : {a}"
   unfolding singleton_def by (blast intro: CollectI)
 
-lemma singletonD: "b : {a} ==> b=a"
+lemma singletonD: "b : {a} \<Longrightarrow> b=a"
   unfolding singleton_def by (blast dest: CollectD)
 
 lemmas singletonE = singletonD [elim_format]
@@ -240,58 +239,54 @@
 subsection {* Unions of families *}
 
 (*The order of the premises presupposes that A is rigid; b may be flexible*)
-lemma UN_I: "[| a:A;  b: B(a) |] ==> b: (UN x:A. B(x))"
+lemma UN_I: "\<lbrakk>a:A; b: B(a)\<rbrakk> \<Longrightarrow> b: (UN x:A. B(x))"
   unfolding UNION_def by (blast intro: bexI CollectI)
 
-lemma UN_E: "[| b : (UN x:A. B(x));  !!x.[| x:A;  b: B(x) |] ==> R |] ==> R"
+lemma UN_E: "\<lbrakk>b : (UN x:A. B(x)); \<And>x. \<lbrakk>x:A; b: B(x)\<rbrakk> \<Longrightarrow> R\<rbrakk> \<Longrightarrow> R"
   unfolding UNION_def by (blast dest: CollectD elim: bexE)
 
-lemma UN_cong:
-  "[| A=B;  !!x. x:B ==> C(x) = D(x) |] ==>
-    (UN x:A. C(x)) = (UN x:B. D(x))"
+lemma UN_cong: "\<lbrakk>A = B; \<And>x. x:B \<Longrightarrow> C(x) = D(x)\<rbrakk> \<Longrightarrow> (UN x:A. C(x)) = (UN x:B. D(x))"
   by (simp add: UNION_def cong: bex_cong)
 
 
 subsection {* Intersections of families *}
 
-lemma INT_I: "(!!x. x:A ==> b: B(x)) ==> b : (INT x:A. B(x))"
+lemma INT_I: "(\<And>x. x:A \<Longrightarrow> b: B(x)) \<Longrightarrow> b : (INT x:A. B(x))"
   unfolding INTER_def by (blast intro: CollectI ballI)
 
-lemma INT_D: "[| b : (INT x:A. B(x));  a:A |] ==> b: B(a)"
+lemma INT_D: "\<lbrakk>b : (INT x:A. B(x)); a:A\<rbrakk> \<Longrightarrow> b: B(a)"
   unfolding INTER_def by (blast dest: CollectD bspec)
 
 (*"Classical" elimination rule -- does not require proving X:C *)
-lemma INT_E: "[| b : (INT x:A. B(x));  b: B(a) ==> R;  ~ a:A ==> R |] ==> R"
+lemma INT_E: "\<lbrakk>b : (INT x:A. B(x)); b: B(a) \<Longrightarrow> R; \<not> a:A \<Longrightarrow> R\<rbrakk> \<Longrightarrow> R"
   unfolding INTER_def by (blast dest: CollectD bspec)
 
-lemma INT_cong:
-  "[| A=B;  !!x. x:B ==> C(x) = D(x) |] ==>
-    (INT x:A. C(x)) = (INT x:B. D(x))"
+lemma INT_cong: "\<lbrakk>A = B; \<And>x. x:B \<Longrightarrow> C(x) = D(x)\<rbrakk> \<Longrightarrow> (INT x:A. C(x)) = (INT x:B. D(x))"
   by (simp add: INTER_def cong: ball_cong)
 
 
 subsection {* Rules for Unions *}
 
 (*The order of the premises presupposes that C is rigid; A may be flexible*)
-lemma UnionI: "[| X:C;  A:X |] ==> A : Union(C)"
+lemma UnionI: "\<lbrakk>X:C; A:X\<rbrakk> \<Longrightarrow> A : Union(C)"
   unfolding Union_def by (blast intro: UN_I)
 
-lemma UnionE: "[| A : Union(C);  !!X.[| A:X;  X:C |] ==> R |] ==> R"
+lemma UnionE: "\<lbrakk>A : Union(C); \<And>X. \<lbrakk> A:X; X:C\<rbrakk> \<Longrightarrow> R\<rbrakk> \<Longrightarrow> R"
   unfolding Union_def by (blast elim: UN_E)
 
 
 subsection {* Rules for Inter *}
 
-lemma InterI: "[| !!X. X:C ==> A:X |] ==> A : Inter(C)"
+lemma InterI: "(\<And>X. X:C \<Longrightarrow> A:X) \<Longrightarrow> A : Inter(C)"
   unfolding Inter_def by (blast intro: INT_I)
 
 (*A "destruct" rule -- every X in C contains A as an element, but
   A:X can hold when X:C does not!  This rule is analogous to "spec". *)
-lemma InterD: "[| A : Inter(C);  X:C |] ==> A:X"
+lemma InterD: "\<lbrakk>A : Inter(C);  X:C\<rbrakk> \<Longrightarrow> A:X"
   unfolding Inter_def by (blast dest: INT_D)
 
 (*"Classical" elimination rule -- does not require proving X:C *)
-lemma InterE: "[| A : Inter(C);  A:X ==> R;  ~ X:C ==> R |] ==> R"
+lemma InterE: "\<lbrakk>A : Inter(C); A:X \<Longrightarrow> R; \<not> X:C \<Longrightarrow> R\<rbrakk> \<Longrightarrow> R"
   unfolding Inter_def by (blast elim: INT_E)
 
 
@@ -299,19 +294,19 @@
 
 subsection {* Big Union -- least upper bound of a set *}
 
-lemma Union_upper: "B:A ==> B <= Union(A)"
+lemma Union_upper: "B:A \<Longrightarrow> B <= Union(A)"
   by (blast intro: subsetI UnionI)
 
-lemma Union_least: "[| !!X. X:A ==> X<=C |] ==> Union(A) <= C"
+lemma Union_least: "(\<And>X. X:A \<Longrightarrow> X<=C) \<Longrightarrow> Union(A) <= C"
   by (blast intro: subsetI dest: subsetD elim: UnionE)
 
 
 subsection {* Big Intersection -- greatest lower bound of a set *}
 
-lemma Inter_lower: "B:A ==> Inter(A) <= B"
+lemma Inter_lower: "B:A \<Longrightarrow> Inter(A) <= B"
   by (blast intro: subsetI dest: InterD)
 
-lemma Inter_greatest: "[| !!X. X:A ==> C<=X |] ==> C <= Inter(A)"
+lemma Inter_greatest: "(\<And>X. X:A \<Longrightarrow> C<=X) \<Longrightarrow> C <= Inter(A)"
   by (blast intro: subsetI InterI dest: subsetD)
 
 
@@ -323,7 +318,7 @@
 lemma Un_upper2: "B <= A Un B"
   by (blast intro: subsetI UnI2)
 
-lemma Un_least: "[| A<=C;  B<=C |] ==> A Un B <= C"
+lemma Un_least: "\<lbrakk>A<=C; B<=C\<rbrakk> \<Longrightarrow> A Un B <= C"
   by (blast intro: subsetI elim: UnE dest: subsetD)
 
 
@@ -335,22 +330,22 @@
 lemma Int_lower2: "A Int B <= B"
   by (blast intro: subsetI elim: IntE)
 
-lemma Int_greatest: "[| C<=A;  C<=B |] ==> C <= A Int B"
+lemma Int_greatest: "\<lbrakk>C<=A; C<=B\<rbrakk> \<Longrightarrow> C <= A Int B"
   by (blast intro: subsetI IntI dest: subsetD)
 
 
 subsection {* Monotonicity *}
 
-lemma monoI: "[| !!A B. A <= B ==> f(A) <= f(B) |] ==> mono(f)"
+lemma monoI: "(\<And>A B. A <= B \<Longrightarrow> f(A) <= f(B)) \<Longrightarrow> mono(f)"
   unfolding mono_def by blast
 
-lemma monoD: "[| mono(f);  A <= B |] ==> f(A) <= f(B)"
+lemma monoD: "\<lbrakk>mono(f); A <= B\<rbrakk> \<Longrightarrow> f(A) <= f(B)"
   unfolding mono_def by blast
 
-lemma mono_Un: "mono(f) ==> f(A) Un f(B) <= f(A Un B)"
+lemma mono_Un: "mono(f) \<Longrightarrow> f(A) Un f(B) <= f(A Un B)"
   by (blast intro: Un_least dest: monoD intro: Un_upper1 Un_upper2)
 
-lemma mono_Int: "mono(f) ==> f(A Int B) <= f(A) Int f(B)"
+lemma mono_Int: "mono(f) \<Longrightarrow> f(A Int B) <= f(A) Int f(B)"
   by (blast intro: Int_greatest dest: monoD intro: Int_lower1 Int_lower2)
 
 
@@ -362,12 +357,12 @@
   and [elim] = ballE InterD InterE INT_D INT_E subsetD subsetCE
 
 lemma mem_rews:
-  "(a : A Un B)   <->  (a:A | a:B)"
-  "(a : A Int B)  <->  (a:A & a:B)"
-  "(a : Compl(B)) <->  (~a:B)"
-  "(a : {b})      <->  (a=b)"
-  "(a : {})       <->   False"
-  "(a : {x. P(x)}) <->  P(a)"
+  "(a : A Un B)   \<longleftrightarrow>  (a:A | a:B)"
+  "(a : A Int B)  \<longleftrightarrow>  (a:A \<and> a:B)"
+  "(a : Compl(B)) \<longleftrightarrow>  (\<not>a:B)"
+  "(a : {b})      \<longleftrightarrow>  (a=b)"
+  "(a : {})       \<longleftrightarrow>   False"
+  "(a : {x. P(x)}) \<longleftrightarrow>  P(a)"
   by blast+
 
 lemmas [simp] = trivial_set empty_eq mem_rews
@@ -390,7 +385,7 @@
 lemma Int_Un_distrib: "(A Un B) Int C  =  (A Int C) Un (B Int C)"
   by (blast intro: equalityI)
 
-lemma subset_Int_eq: "(A<=B) <-> (A Int B = A)"
+lemma subset_Int_eq: "(A<=B) \<longleftrightarrow> (A Int B = A)"
   by (blast intro: equalityI elim: equalityE)
 
 
@@ -412,7 +407,7 @@
     "(A Int B) Un (B Int C) Un (C Int A) = (A Un B) Int (B Un C) Int (C Un A)"
   by (blast intro: equalityI)
 
-lemma subset_Un_eq: "(A<=B) <-> (A Un B = B)"
+lemma subset_Un_eq: "(A<=B) \<longleftrightarrow> (A Un B = B)"
   by (blast intro: equalityI elim: equalityE)
 
 
@@ -440,7 +435,7 @@
   by (blast intro: equalityI)
 
 (*Halmos, Naive Set Theory, page 16.*)
-lemma Un_Int_assoc_eq: "((A Int B) Un C = A Int (B Un C)) <-> (C<=A)"
+lemma Un_Int_assoc_eq: "((A Int B) Un C = A Int (B Un C)) \<longleftrightarrow> (C<=A)"
   by (blast intro: equalityI elim: equalityE)
 
 
@@ -450,7 +445,7 @@
   by (blast intro: equalityI)
 
 lemma Union_disjoint:
-    "(Union(C) Int A = {x. False}) <-> (ALL B:C. B Int A = {x. False})"
+    "(Union(C) Int A = {x. False}) \<longleftrightarrow> (ALL B:C. B Int A = {x. False})"
   by (blast intro: equalityI elim: equalityE)
 
 lemma Inter_Un_distrib: "Inter(A Un B) = Inter(A) Int Inter(B)"
@@ -475,29 +470,25 @@
 
 section {* Monotonicity of various operations *}
 
-lemma Union_mono: "A<=B ==> Union(A) <= Union(B)"
+lemma Union_mono: "A<=B \<Longrightarrow> Union(A) <= Union(B)"
   by blast
 
-lemma Inter_anti_mono: "[| B<=A |] ==> Inter(A) <= Inter(B)"
+lemma Inter_anti_mono: "B <= A \<Longrightarrow> Inter(A) <= Inter(B)"
   by blast
 
-lemma UN_mono:
-  "[| A<=B;  !!x. x:A ==> f(x)<=g(x) |] ==>  
-    (UN x:A. f(x)) <= (UN x:B. g(x))"
+lemma UN_mono: "\<lbrakk>A <= B; \<And>x. x:A \<Longrightarrow> f(x)<=g(x)\<rbrakk> \<Longrightarrow> (UN x:A. f(x)) <= (UN x:B. g(x))"
   by blast
 
-lemma INT_anti_mono:
-  "[| B<=A;  !!x. x:A ==> f(x)<=g(x) |] ==>  
-    (INT x:A. f(x)) <= (INT x:A. g(x))"
+lemma INT_anti_mono: "\<lbrakk>B <= A; \<And>x. x:A \<Longrightarrow> f(x) <= g(x)\<rbrakk> \<Longrightarrow> (INT x:A. f(x)) <= (INT x:A. g(x))"
   by blast
 
-lemma Un_mono: "[| A<=C;  B<=D |] ==> A Un B <= C Un D"
+lemma Un_mono: "\<lbrakk>A <= C; B <= D\<rbrakk> \<Longrightarrow> A Un B <= C Un D"
   by blast
 
-lemma Int_mono: "[| A<=C;  B<=D |] ==> A Int B <= C Int D"
+lemma Int_mono: "\<lbrakk>A <= C; B <= D\<rbrakk> \<Longrightarrow> A Int B <= C Int D"
   by blast
 
-lemma Compl_anti_mono: "[| A<=B |] ==> Compl(B) <= Compl(A)"
+lemma Compl_anti_mono: "A <= B \<Longrightarrow> Compl(B) <= Compl(A)"
   by blast
 
 end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/Term.thy
--- a/src/CCL/Term.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/Term.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -13,43 +13,43 @@
 
   one        :: "i"
 
-  "if"       :: "[i,i,i]=>i"           ("(3if _/ then _/ else _)" [0,0,60] 60)
+  "if"       :: "[i,i,i]\<Rightarrow>i"           ("(3if _/ then _/ else _)" [0,0,60] 60)
 
-  inl        :: "i=>i"
-  inr        :: "i=>i"
-  when       :: "[i,i=>i,i=>i]=>i"
+  inl        :: "i\<Rightarrow>i"
+  inr        :: "i\<Rightarrow>i"
+  when       :: "[i,i\<Rightarrow>i,i\<Rightarrow>i]\<Rightarrow>i"
 
-  split      :: "[i,[i,i]=>i]=>i"
-  fst        :: "i=>i"
-  snd        :: "i=>i"
-  thd        :: "i=>i"
+  split      :: "[i,[i,i]\<Rightarrow>i]\<Rightarrow>i"
+  fst        :: "i\<Rightarrow>i"
+  snd        :: "i\<Rightarrow>i"
+  thd        :: "i\<Rightarrow>i"
 
   zero       :: "i"
-  succ       :: "i=>i"
-  ncase      :: "[i,i,i=>i]=>i"
-  nrec       :: "[i,i,[i,i]=>i]=>i"
+  succ       :: "i\<Rightarrow>i"
+  ncase      :: "[i,i,i\<Rightarrow>i]\<Rightarrow>i"
+  nrec       :: "[i,i,[i,i]\<Rightarrow>i]\<Rightarrow>i"
 
   nil        :: "i"                        ("([])")
-  cons       :: "[i,i]=>i"                 (infixr "$" 80)
-  lcase      :: "[i,i,[i,i]=>i]=>i"
-  lrec       :: "[i,i,[i,i,i]=>i]=>i"
+  cons       :: "[i,i]\<Rightarrow>i"                 (infixr "$" 80)
+  lcase      :: "[i,i,[i,i]\<Rightarrow>i]\<Rightarrow>i"
+  lrec       :: "[i,i,[i,i,i]\<Rightarrow>i]\<Rightarrow>i"
 
-  "let"      :: "[i,i=>i]=>i"
-  letrec     :: "[[i,i=>i]=>i,(i=>i)=>i]=>i"
-  letrec2    :: "[[i,i,i=>i=>i]=>i,(i=>i=>i)=>i]=>i"
-  letrec3    :: "[[i,i,i,i=>i=>i=>i]=>i,(i=>i=>i=>i)=>i]=>i"
+  "let"      :: "[i,i\<Rightarrow>i]\<Rightarrow>i"
+  letrec     :: "[[i,i\<Rightarrow>i]\<Rightarrow>i,(i\<Rightarrow>i)\<Rightarrow>i]\<Rightarrow>i"
+  letrec2    :: "[[i,i,i\<Rightarrow>i\<Rightarrow>i]\<Rightarrow>i,(i\<Rightarrow>i\<Rightarrow>i)\<Rightarrow>i]\<Rightarrow>i"
+  letrec3    :: "[[i,i,i,i\<Rightarrow>i\<Rightarrow>i\<Rightarrow>i]\<Rightarrow>i,(i\<Rightarrow>i\<Rightarrow>i\<Rightarrow>i)\<Rightarrow>i]\<Rightarrow>i"
 
 syntax
-  "_let"     :: "[id,i,i]=>i"             ("(3let _ be _/ in _)"
+  "_let"     :: "[id,i,i]\<Rightarrow>i"             ("(3let _ be _/ in _)"
                         [0,0,60] 60)
 
-  "_letrec"  :: "[id,id,i,i]=>i"         ("(3letrec _ _ be _/ in _)"
+  "_letrec"  :: "[id,id,i,i]\<Rightarrow>i"         ("(3letrec _ _ be _/ in _)"
                         [0,0,0,60] 60)
 
-  "_letrec2" :: "[id,id,id,i,i]=>i"     ("(3letrec _ _ _ be _/ in _)"
+  "_letrec2" :: "[id,id,id,i,i]\<Rightarrow>i"     ("(3letrec _ _ _ be _/ in _)"
                         [0,0,0,0,60] 60)
 
-  "_letrec3" :: "[id,id,id,id,i,i]=>i" ("(3letrec _ _ _ _ be _/ in _)"
+  "_letrec3" :: "[id,id,id,id,i,i]\<Rightarrow>i" ("(3letrec _ _ _ _ be _/ in _)"
                         [0,0,0,0,0,60] 60)
 
 ML {*
@@ -91,7 +91,6 @@
          val (x',a') = Syntax_Trans.variant_abs(x,T,a3)
      in Const(@{syntax_const "_letrec3"},dummyT) $ Free(f',SS) $ Free(x',T) $ Free(y',U) $ Free(z',V) $ a' $ b'
       end;
-
 *}
 
 parse_translation {*
@@ -109,40 +108,40 @@
 *}
 
 consts
-  napply     :: "[i=>i,i,i]=>i"            ("(_ ^ _ ` _)" [56,56,56] 56)
+  napply     :: "[i\<Rightarrow>i,i,i]\<Rightarrow>i"            ("(_ ^ _ ` _)" [56,56,56] 56)
 
 defs
   one_def:                    "one == true"
-  if_def:     "if b then t else u  == case(b,t,u,% x y. bot,%v. bot)"
+  if_def:     "if b then t else u  == case(b, t, u, \<lambda> x y. bot, \<lambda>v. bot)"
   inl_def:                 "inl(a) == <true,a>"
   inr_def:                 "inr(b) == <false,b>"
-  when_def:           "when(t,f,g) == split(t,%b x. if b then f(x) else g(x))"
-  split_def:           "split(t,f) == case(t,bot,bot,f,%u. bot)"
-  fst_def:                 "fst(t) == split(t,%x y. x)"
-  snd_def:                 "snd(t) == split(t,%x y. y)"
-  thd_def:                 "thd(t) == split(t,%x p. split(p,%y z. z))"
+  when_def:           "when(t,f,g) == split(t, \<lambda>b x. if b then f(x) else g(x))"
+  split_def:           "split(t,f) == case(t, bot, bot, f, \<lambda>u. bot)"
+  fst_def:                 "fst(t) == split(t, \<lambda>x y. x)"
+  snd_def:                 "snd(t) == split(t, \<lambda>x y. y)"
+  thd_def:                 "thd(t) == split(t, \<lambda>x p. split(p, \<lambda>y z. z))"
   zero_def:                  "zero == inl(one)"
   succ_def:               "succ(n) == inr(n)"
-  ncase_def:         "ncase(n,b,c) == when(n,%x. b,%y. c(y))"
-  nrec_def:          " nrec(n,b,c) == letrec g x be ncase(x,b,%y. c(y,g(y))) in g(n)"
+  ncase_def:         "ncase(n,b,c) == when(n, \<lambda>x. b, \<lambda>y. c(y))"
+  nrec_def:          " nrec(n,b,c) == letrec g x be ncase(x, b, \<lambda>y. c(y,g(y))) in g(n)"
   nil_def:                     "[] == inl(one)"
   cons_def:                   "h$t == inr(<h,t>)"
-  lcase_def:         "lcase(l,b,c) == when(l,%x. b,%y. split(y,c))"
-  lrec_def:           "lrec(l,b,c) == letrec g x be lcase(x,b,%h t. c(h,t,g(t))) in g(l)"
+  lcase_def:         "lcase(l,b,c) == when(l, \<lambda>x. b, \<lambda>y. split(y,c))"
+  lrec_def:           "lrec(l,b,c) == letrec g x be lcase(x, b, \<lambda>h t. c(h,t,g(t))) in g(l)"
 
-  let_def:  "let x be t in f(x) == case(t,f(true),f(false),%x y. f(<x,y>),%u. f(lam x. u(x)))"
+  let_def:  "let x be t in f(x) == case(t,f(true),f(false), \<lambda>x y. f(<x,y>), \<lambda>u. f(lam x. u(x)))"
   letrec_def:
-  "letrec g x be h(x,g) in b(g) == b(%x. fix(%f. lam x. h(x,%y. f`y))`x)"
+  "letrec g x be h(x,g) in b(g) == b(\<lambda>x. fix(\<lambda>f. lam x. h(x,\<lambda>y. f`y))`x)"
 
   letrec2_def:  "letrec g x y be h(x,y,g) in f(g)==
-               letrec g' p be split(p,%x y. h(x,y,%u v. g'(<u,v>)))
-                          in f(%x y. g'(<x,y>))"
+               letrec g' p be split(p,\<lambda>x y. h(x,y,\<lambda>u v. g'(<u,v>)))
+                          in f(\<lambda>x y. g'(<x,y>))"
 
   letrec3_def:  "letrec g x y z be h(x,y,z,g) in f(g) ==
-             letrec g' p be split(p,%x xs. split(xs,%y z. h(x,y,z,%u v w. g'(<u,<v,w>>))))
-                          in f(%x y z. g'(<x,<y,z>>))"
+             letrec g' p be split(p,\<lambda>x xs. split(xs,\<lambda>y z. h(x,y,z,\<lambda>u v w. g'(<u,<v,w>>))))
+                          in f(\<lambda>x y z. g'(<x,<y,z>>))"
 
-  napply_def: "f ^n` a == nrec(n,a,%x g. f(g))"
+  napply_def: "f ^n` a == nrec(n,a,\<lambda>x g. f(g))"
 
 
 lemmas simp_can_defs = one_def inl_def inr_def
@@ -159,7 +158,7 @@
 
 subsection {* Beta Rules, including strictness *}
 
-lemma letB: "~ t=bot ==> let x be t in f(x) = f(t)"
+lemma letB: "\<not> t=bot \<Longrightarrow> let x be t in f(x) = f(t)"
   apply (unfold let_def)
   apply (erule rev_mp)
   apply (rule_tac t = "t" in term_case)
@@ -194,7 +193,7 @@
   done
 
 lemma letrecB:
-    "letrec g x be h(x,g) in g(a) = h(a,%y. letrec g x be h(x,g) in g(y))"
+    "letrec g x be h(x,g) in g(a) = h(a,\<lambda>y. letrec g x be h(x,g) in g(y))"
   apply (unfold letrec_def)
   apply (rule fixB [THEN ssubst], rule applyB [THEN ssubst], rule refl)
   done
@@ -254,12 +253,12 @@
   unfolding data_defs by beta_rl+
 
 lemma letrec2B:
-  "letrec g x y be h(x,y,g) in g(p,q) = h(p,q,%u v. letrec g x y be h(x,y,g) in g(u,v))"
+  "letrec g x y be h(x,y,g) in g(p,q) = h(p,q,\<lambda>u v. letrec g x y be h(x,y,g) in g(u,v))"
   unfolding data_defs letrec2_def by beta_rl+
 
 lemma letrec3B:
   "letrec g x y z be h(x,y,z,g) in g(p,q,r) =
-    h(p,q,r,%u v w. letrec g x y z be h(x,y,z,g) in g(u,v,w))"
+    h(p,q,r,\<lambda>u v w. letrec g x y z be h(x,y,z,g) in g(u,v,w))"
   unfolding data_defs letrec3_def by beta_rl+
 
 lemma napplyBzero: "f^zero`a = a"
@@ -276,10 +275,10 @@
 subsection {* Constructors are injective *}
 
 lemma term_injs:
-  "(inl(a) = inl(a')) <-> (a=a')"
-  "(inr(a) = inr(a')) <-> (a=a')"
-  "(succ(a) = succ(a')) <-> (a=a')"
-  "(a$b = a'$b') <-> (a=a' & b=b')"
+  "(inl(a) = inl(a')) \<longleftrightarrow> (a=a')"
+  "(inr(a) = inr(a')) \<longleftrightarrow> (a=a')"
+  "(succ(a) = succ(a')) \<longleftrightarrow> (a=a')"
+  "(a$b = a'$b') \<longleftrightarrow> (a=a' \<and> b=b')"
   by (inj_rl applyB splitB whenBinl whenBinr ncaseBsucc lcaseBcons)
 
 
@@ -295,10 +294,10 @@
 subsection {* Rules for pre-order @{text "[="} *}
 
 lemma term_porews:
-  "inl(a) [= inl(a') <-> a [= a'"
-  "inr(b) [= inr(b') <-> b [= b'"
-  "succ(n) [= succ(n') <-> n [= n'"
-  "x$xs [= x'$xs' <-> x [= x'  & xs [= xs'"
+  "inl(a) [= inl(a') \<longleftrightarrow> a [= a'"
+  "inr(b) [= inr(b') \<longleftrightarrow> b [= b'"
+  "succ(n) [= succ(n') \<longleftrightarrow> n [= n'"
+  "x$xs [= x'$xs' \<longleftrightarrow> x [= x' \<and> xs [= xs'"
   by (simp_all add: data_defs ccl_porews)
 
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/Trancl.thy
--- a/src/CCL/Trancl.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/Trancl.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -9,29 +9,28 @@
 imports CCL
 begin
 
-definition trans :: "i set => o"  (*transitivity predicate*)
-  where "trans(r) == (ALL x y z. <x,y>:r --> <y,z>:r --> <x,z>:r)"
+definition trans :: "i set \<Rightarrow> o"  (*transitivity predicate*)
+  where "trans(r) == (ALL x y z. <x,y>:r \<longrightarrow> <y,z>:r \<longrightarrow> <x,z>:r)"
 
 definition id :: "i set"  (*the identity relation*)
   where "id == {p. EX x. p = <x,x>}"
 
-definition relcomp :: "[i set,i set] => i set"  (infixr "O" 60)  (*composition of relations*)
-  where "r O s == {xz. EX x y z. xz = <x,z> & <x,y>:s & <y,z>:r}"
+definition relcomp :: "[i set,i set] \<Rightarrow> i set"  (infixr "O" 60)  (*composition of relations*)
+  where "r O s == {xz. EX x y z. xz = <x,z> \<and> <x,y>:s \<and> <y,z>:r}"
 
-definition rtrancl :: "i set => i set"  ("(_^*)" [100] 100)
-  where "r^* == lfp(%s. id Un (r O s))"
+definition rtrancl :: "i set \<Rightarrow> i set"  ("(_^*)" [100] 100)
+  where "r^* == lfp(\<lambda>s. id Un (r O s))"
 
-definition trancl :: "i set => i set"  ("(_^+)" [100] 100)
+definition trancl :: "i set \<Rightarrow> i set"  ("(_^+)" [100] 100)
   where "r^+ == r O rtrancl(r)"
 
 
 subsection {* Natural deduction for @{text "trans(r)"} *}
 
-lemma transI:
-  "(!! x y z. [| <x,y>:r;  <y,z>:r |] ==> <x,z>:r) ==> trans(r)"
+lemma transI: "(\<And>x y z. \<lbrakk><x,y>:r; <y,z>:r\<rbrakk> \<Longrightarrow> <x,z>:r) \<Longrightarrow> trans(r)"
   unfolding trans_def by blast
 
-lemma transD: "[| trans(r);  <a,b>:r;  <b,c>:r |] ==> <a,c>:r"
+lemma transD: "\<lbrakk>trans(r); <a,b>:r; <b,c>:r\<rbrakk> \<Longrightarrow> <a,c>:r"
   unfolding trans_def by blast
 
 
@@ -44,8 +43,7 @@
   apply (rule refl)
   done
 
-lemma idE:
-    "[| p: id;  !!x.[| p = <x,x> |] ==> P |] ==>  P"
+lemma idE: "\<lbrakk>p: id;  \<And>x. p = <x,x> \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
   apply (unfold id_def)
   apply (erule CollectE)
   apply blast
@@ -54,20 +52,14 @@
 
 subsection {* Composition of two relations *}
 
-lemma compI: "[| <a,b>:s; <b,c>:r |] ==> <a,c> : r O s"
+lemma compI: "\<lbrakk><a,b>:s; <b,c>:r\<rbrakk> \<Longrightarrow> <a,c> : r O s"
   unfolding relcomp_def by blast
 
 (*proof requires higher-level assumptions or a delaying of hyp_subst_tac*)
-lemma compE:
-    "[| xz : r O s;
-        !!x y z. [| xz = <x,z>;  <x,y>:s;  <y,z>:r |] ==> P
-     |] ==> P"
+lemma compE: "\<lbrakk>xz : r O s; \<And>x y z. \<lbrakk>xz = <x,z>; <x,y>:s; <y,z>:r\<rbrakk> \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
   unfolding relcomp_def by blast
 
-lemma compEpair:
-  "[| <a,c> : r O s;
-      !!y. [| <a,y>:s;  <y,c>:r |] ==> P
-   |] ==> P"
+lemma compEpair: "\<lbrakk><a,c> : r O s; \<And>y. \<lbrakk><a,y>:s; <y,c>:r\<rbrakk> \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
   apply (erule compE)
   apply (simp add: pair_inject)
   done
@@ -76,13 +68,13 @@
   and [elim] = compE idE
   and [elim!] = pair_inject
 
-lemma comp_mono: "[| r'<=r; s'<=s |] ==> (r' O s') <= (r O s)"
+lemma comp_mono: "\<lbrakk>r'<=r; s'<=s\<rbrakk> \<Longrightarrow> (r' O s') <= (r O s)"
   by blast
 
 
 subsection {* The relation rtrancl *}
 
-lemma rtrancl_fun_mono: "mono(%s. id Un (r O s))"
+lemma rtrancl_fun_mono: "mono(\<lambda>s. id Un (r O s))"
   apply (rule monoI)
   apply (rule monoI subset_refl comp_mono Un_mono)+
   apply assumption
@@ -98,13 +90,13 @@
   done
 
 (*Closure under composition with r*)
-lemma rtrancl_into_rtrancl: "[| <a,b> : r^*;  <b,c> : r |] ==> <a,c> : r^*"
+lemma rtrancl_into_rtrancl: "\<lbrakk><a,b> : r^*; <b,c> : r\<rbrakk> \<Longrightarrow> <a,c> : r^*"
   apply (subst rtrancl_unfold)
   apply blast
   done
 
 (*rtrancl of r contains r*)
-lemma r_into_rtrancl: "[| <a,b> : r |] ==> <a,b> : r^*"
+lemma r_into_rtrancl: "<a,b> : r \<Longrightarrow> <a,b> : r^*"
   apply (rule rtrancl_refl [THEN rtrancl_into_rtrancl])
   apply assumption
   done
@@ -113,10 +105,10 @@
 subsection {* standard induction rule *}
 
 lemma rtrancl_full_induct:
-  "[| <a,b> : r^*;
-      !!x. P(<x,x>);
-      !!x y z.[| P(<x,y>); <x,y>: r^*; <y,z>: r |]  ==>  P(<x,z>) |]
-   ==>  P(<a,b>)"
+  "\<lbrakk><a,b> : r^*;
+      \<And>x. P(<x,x>);
+      \<And>x y z. \<lbrakk>P(<x,y>); <x,y>: r^*; <y,z>: r\<rbrakk>  \<Longrightarrow> P(<x,z>)\<rbrakk>
+   \<Longrightarrow>  P(<a,b>)"
   apply (erule def_induct [OF rtrancl_def])
    apply (rule rtrancl_fun_mono)
   apply blast
@@ -124,12 +116,12 @@
 
 (*nice induction rule*)
 lemma rtrancl_induct:
-  "[| <a,b> : r^*;
+  "\<lbrakk><a,b> : r^*;
       P(a);
-      !!y z.[| <a,y> : r^*;  <y,z> : r;  P(y) |] ==> P(z) |]
-    ==> P(b)"
+      \<And>y z. \<lbrakk><a,y> : r^*; <y,z> : r;  P(y)\<rbrakk> \<Longrightarrow> P(z) \<rbrakk>
+    \<Longrightarrow> P(b)"
 (*by induction on this formula*)
-  apply (subgoal_tac "ALL y. <a,b> = <a,y> --> P(y)")
+  apply (subgoal_tac "ALL y. <a,b> = <a,y> \<longrightarrow> P(y)")
 (*now solve first subgoal: this formula is sufficient*)
   apply blast
 (*now do the induction*)
@@ -147,10 +139,8 @@
 
 (*elimination of rtrancl -- by induction on a special formula*)
 lemma rtranclE:
-  "[| <a,b> : r^*;  (a = b) ==> P;
-      !!y.[| <a,y> : r^*; <y,b> : r |] ==> P |]
-   ==> P"
-  apply (subgoal_tac "a = b | (EX y. <a,y> : r^* & <y,b> : r)")
+  "\<lbrakk><a,b> : r^*; a = b \<Longrightarrow> P; \<And>y. \<lbrakk><a,y> : r^*; <y,b> : r\<rbrakk> \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
+  apply (subgoal_tac "a = b | (EX y. <a,y> : r^* \<and> <y,b> : r)")
    prefer 2
    apply (erule rtrancl_induct)
     apply blast
@@ -163,7 +153,7 @@
 
 subsubsection {* Conversions between trancl and rtrancl *}
 
-lemma trancl_into_rtrancl: "[| <a,b> : r^+ |] ==> <a,b> : r^*"
+lemma trancl_into_rtrancl: "<a,b> : r^+ \<Longrightarrow> <a,b> : r^*"
   apply (unfold trancl_def)
   apply (erule compEpair)
   apply (erule rtrancl_into_rtrancl)
@@ -171,15 +161,15 @@
   done
 
 (*r^+ contains r*)
-lemma r_into_trancl: "[| <a,b> : r |] ==> <a,b> : r^+"
+lemma r_into_trancl: "<a,b> : r \<Longrightarrow> <a,b> : r^+"
   unfolding trancl_def by (blast intro: rtrancl_refl)
 
 (*intro rule by definition: from rtrancl and r*)
-lemma rtrancl_into_trancl1: "[| <a,b> : r^*;  <b,c> : r |]   ==>  <a,c> : r^+"
+lemma rtrancl_into_trancl1: "\<lbrakk><a,b> : r^*; <b,c> : r\<rbrakk> \<Longrightarrow> <a,c> : r^+"
   unfolding trancl_def by blast
 
 (*intro rule from r and rtrancl*)
-lemma rtrancl_into_trancl2: "[| <a,b> : r;  <b,c> : r^* |]   ==>  <a,c> : r^+"
+lemma rtrancl_into_trancl2: "\<lbrakk><a,b> : r; <b,c> : r^*\<rbrakk> \<Longrightarrow> <a,c> : r^+"
   apply (erule rtranclE)
    apply (erule subst)
    apply (erule r_into_trancl)
@@ -189,11 +179,10 @@
 
 (*elimination of r^+ -- NOT an induction rule*)
 lemma tranclE:
-  "[| <a,b> : r^+;
-      <a,b> : r ==> P;
-      !!y.[| <a,y> : r^+;  <y,b> : r |] ==> P
-   |] ==> P"
-  apply (subgoal_tac "<a,b> : r | (EX y. <a,y> : r^+ & <y,b> : r)")
+  "\<lbrakk><a,b> : r^+;
+    <a,b> : r \<Longrightarrow> P;
+    \<And>y. \<lbrakk><a,y> : r^+; <y,b> : r\<rbrakk> \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
+  apply (subgoal_tac "<a,b> : r | (EX y. <a,y> : r^+ \<and> <y,b> : r)")
    apply blast
   apply (unfold trancl_def)
   apply (erule compEpair)
@@ -212,7 +201,7 @@
     apply assumption+
   done
 
-lemma trancl_into_trancl2: "[| <a,b> : r;  <b,c> : r^+ |]   ==>  <a,c> : r^+"
+lemma trancl_into_trancl2: "\<lbrakk><a,b> : r; <b,c> : r^+\<rbrakk> \<Longrightarrow> <a,c> : r^+"
   apply (rule r_into_trancl [THEN trans_trancl [THEN transD]])
    apply assumption+
   done
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/Type.thy
--- a/src/CCL/Type.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/Type.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -11,39 +11,39 @@
 
 consts
 
-  Subtype       :: "['a set, 'a => o] => 'a set"
+  Subtype       :: "['a set, 'a \<Rightarrow> o] \<Rightarrow> 'a set"
   Bool          :: "i set"
   Unit          :: "i set"
-  Plus           :: "[i set, i set] => i set"        (infixr "+" 55)
-  Pi            :: "[i set, i => i set] => i set"
-  Sigma         :: "[i set, i => i set] => i set"
+  Plus           :: "[i set, i set] \<Rightarrow> i set"        (infixr "+" 55)
+  Pi            :: "[i set, i \<Rightarrow> i set] \<Rightarrow> i set"
+  Sigma         :: "[i set, i \<Rightarrow> i set] \<Rightarrow> i set"
   Nat           :: "i set"
-  List          :: "i set => i set"
-  Lists         :: "i set => i set"
-  ILists        :: "i set => i set"
-  TAll          :: "(i set => i set) => i set"       (binder "TALL " 55)
-  TEx           :: "(i set => i set) => i set"       (binder "TEX " 55)
-  Lift          :: "i set => i set"                  ("(3[_])")
+  List          :: "i set \<Rightarrow> i set"
+  Lists         :: "i set \<Rightarrow> i set"
+  ILists        :: "i set \<Rightarrow> i set"
+  TAll          :: "(i set \<Rightarrow> i set) \<Rightarrow> i set"       (binder "TALL " 55)
+  TEx           :: "(i set \<Rightarrow> i set) \<Rightarrow> i set"       (binder "TEX " 55)
+  Lift          :: "i set \<Rightarrow> i set"                  ("(3[_])")
 
-  SPLIT         :: "[i, [i, i] => i set] => i set"
+  SPLIT         :: "[i, [i, i] \<Rightarrow> i set] \<Rightarrow> i set"
 
 syntax
-  "_Pi"         :: "[idt, i set, i set] => i set"    ("(3PROD _:_./ _)"
+  "_Pi"         :: "[idt, i set, i set] \<Rightarrow> i set"    ("(3PROD _:_./ _)"
                                 [0,0,60] 60)
 
-  "_Sigma"      :: "[idt, i set, i set] => i set"    ("(3SUM _:_./ _)"
+  "_Sigma"      :: "[idt, i set, i set] \<Rightarrow> i set"    ("(3SUM _:_./ _)"
                                 [0,0,60] 60)
 
-  "_arrow"      :: "[i set, i set] => i set"         ("(_ ->/ _)"  [54, 53] 53)
-  "_star"       :: "[i set, i set] => i set"         ("(_ */ _)" [56, 55] 55)
-  "_Subtype"    :: "[idt, 'a set, o] => 'a set"      ("(1{_: _ ./ _})")
+  "_arrow"      :: "[i set, i set] \<Rightarrow> i set"         ("(_ ->/ _)"  [54, 53] 53)
+  "_star"       :: "[i set, i set] \<Rightarrow> i set"         ("(_ */ _)" [56, 55] 55)
+  "_Subtype"    :: "[idt, 'a set, o] \<Rightarrow> 'a set"      ("(1{_: _ ./ _})")
 
 translations
-  "PROD x:A. B" => "CONST Pi(A, %x. B)"
-  "A -> B"      => "CONST Pi(A, %_. B)"
-  "SUM x:A. B"  => "CONST Sigma(A, %x. B)"
-  "A * B"       => "CONST Sigma(A, %_. B)"
-  "{x: A. B}"   == "CONST Subtype(A, %x. B)"
+  "PROD x:A. B" => "CONST Pi(A, \<lambda>x. B)"
+  "A -> B"      => "CONST Pi(A, \<lambda>_. B)"
+  "SUM x:A. B"  => "CONST Sigma(A, \<lambda>x. B)"
+  "A * B"       => "CONST Sigma(A, \<lambda>_. B)"
+  "{x: A. B}"   == "CONST Subtype(A, \<lambda>x. B)"
 
 print_translation {*
  [(@{const_syntax Pi},
@@ -53,23 +53,23 @@
 *}
 
 defs
-  Subtype_def: "{x:A. P(x)} == {x. x:A & P(x)}"
+  Subtype_def: "{x:A. P(x)} == {x. x:A \<and> P(x)}"
   Unit_def:          "Unit == {x. x=one}"
   Bool_def:          "Bool == {x. x=true | x=false}"
   Plus_def:           "A+B == {x. (EX a:A. x=inl(a)) | (EX b:B. x=inr(b))}"
-  Pi_def:         "Pi(A,B) == {x. EX b. x=lam x. b(x) & (ALL x:A. b(x):B(x))}"
+  Pi_def:         "Pi(A,B) == {x. EX b. x=lam x. b(x) \<and> (ALL x:A. b(x):B(x))}"
   Sigma_def:   "Sigma(A,B) == {x. EX a:A. EX b:B(a).x=<a,b>}"
-  Nat_def:            "Nat == lfp(% X. Unit + X)"
-  List_def:       "List(A) == lfp(% X. Unit + A*X)"
+  Nat_def:            "Nat == lfp(\<lambda>X. Unit + X)"
+  List_def:       "List(A) == lfp(\<lambda>X. Unit + A*X)"
 
-  Lists_def:     "Lists(A) == gfp(% X. Unit + A*X)"
-  ILists_def:   "ILists(A) == gfp(% X.{} + A*X)"
+  Lists_def:     "Lists(A) == gfp(\<lambda>X. Unit + A*X)"
+  ILists_def:   "ILists(A) == gfp(\<lambda>X.{} + A*X)"
 
   Tall_def:   "TALL X. B(X) == Inter({X. EX Y. X=B(Y)})"
   Tex_def:     "TEX X. B(X) == Union({X. EX Y. X=B(Y)})"
   Lift_def:           "[A] == A Un {bot}"
 
-  SPLIT_def:   "SPLIT(p,B) == Union({A. EX x y. p=<x,y> & A=B(x,y)})"
+  SPLIT_def:   "SPLIT(p,B) == Union({A. EX x y. p=<x,y> \<and> A=B(x,y)})"
 
 
 lemmas simp_type_defs =
@@ -78,31 +78,29 @@
   and simp_data_defs = one_def inl_def inr_def
   and ind_data_defs = zero_def succ_def nil_def cons_def
 
-lemma subsetXH: "A <= B <-> (ALL x. x:A --> x:B)"
+lemma subsetXH: "A <= B \<longleftrightarrow> (ALL x. x:A \<longrightarrow> x:B)"
   by blast
 
 
 subsection {* Exhaustion Rules *}
 
-lemma EmptyXH: "!!a. a : {} <-> False"
-  and SubtypeXH: "!!a A P. a : {x:A. P(x)} <-> (a:A & P(a))"
-  and UnitXH: "!!a. a : Unit          <-> a=one"
-  and BoolXH: "!!a. a : Bool          <-> a=true | a=false"
-  and PlusXH: "!!a A B. a : A+B           <-> (EX x:A. a=inl(x)) | (EX x:B. a=inr(x))"
-  and PiXH: "!!a A B. a : PROD x:A. B(x) <-> (EX b. a=lam x. b(x) & (ALL x:A. b(x):B(x)))"
-  and SgXH: "!!a A B. a : SUM x:A. B(x)  <-> (EX x:A. EX y:B(x).a=<x,y>)"
+lemma EmptyXH: "\<And>a. a : {} \<longleftrightarrow> False"
+  and SubtypeXH: "\<And>a A P. a : {x:A. P(x)} \<longleftrightarrow> (a:A \<and> P(a))"
+  and UnitXH: "\<And>a. a : Unit          \<longleftrightarrow> a=one"
+  and BoolXH: "\<And>a. a : Bool          \<longleftrightarrow> a=true | a=false"
+  and PlusXH: "\<And>a A B. a : A+B           \<longleftrightarrow> (EX x:A. a=inl(x)) | (EX x:B. a=inr(x))"
+  and PiXH: "\<And>a A B. a : PROD x:A. B(x) \<longleftrightarrow> (EX b. a=lam x. b(x) \<and> (ALL x:A. b(x):B(x)))"
+  and SgXH: "\<And>a A B. a : SUM x:A. B(x)  \<longleftrightarrow> (EX x:A. EX y:B(x).a=<x,y>)"
   unfolding simp_type_defs by blast+
 
 lemmas XHs = EmptyXH SubtypeXH UnitXH BoolXH PlusXH PiXH SgXH
 
-lemma LiftXH: "a : [A] <-> (a=bot | a:A)"
-  and TallXH: "a : TALL X. B(X) <-> (ALL X. a:B(X))"
-  and TexXH: "a : TEX X. B(X) <-> (EX X. a:B(X))"
+lemma LiftXH: "a : [A] \<longleftrightarrow> (a=bot | a:A)"
+  and TallXH: "a : TALL X. B(X) \<longleftrightarrow> (ALL X. a:B(X))"
+  and TexXH: "a : TEX X. B(X) \<longleftrightarrow> (EX X. a:B(X))"
   unfolding simp_type_defs by blast+
 
-ML {*
-ML_Thms.bind_thms ("case_rls", XH_to_Es @{thms XHs});
-*}
+ML {* ML_Thms.bind_thms ("case_rls", XH_to_Es @{thms XHs}) *}
 
 
 subsection {* Canonical Type Rules *}
@@ -110,10 +108,10 @@
 lemma oneT: "one : Unit"
   and trueT: "true : Bool"
   and falseT: "false : Bool"
-  and lamT: "!!b B. [| !!x. x:A ==> b(x):B(x) |] ==> lam x. b(x) : Pi(A,B)"
-  and pairT: "!!b B. [| a:A; b:B(a) |] ==> <a,b>:Sigma(A,B)"
-  and inlT: "a:A ==> inl(a) : A+B"
-  and inrT: "b:B ==> inr(b) : A+B"
+  and lamT: "\<And>b B. (\<And>x. x:A \<Longrightarrow> b(x):B(x)) \<Longrightarrow> lam x. b(x) : Pi(A,B)"
+  and pairT: "\<And>b B. \<lbrakk>a:A; b:B(a)\<rbrakk> \<Longrightarrow> <a,b>:Sigma(A,B)"
+  and inlT: "a:A \<Longrightarrow> inl(a) : A+B"
+  and inrT: "b:B \<Longrightarrow> inr(b) : A+B"
   by (blast intro: XHs [THEN iffD2])+
 
 lemmas canTs = oneT trueT falseT pairT lamT inlT inrT
@@ -121,7 +119,7 @@
 
 subsection {* Non-Canonical Type Rules *}
 
-lemma lem: "[| a:B(u);  u=v |] ==> a : B(v)"
+lemma lem: "\<lbrakk>a:B(u); u = v\<rbrakk> \<Longrightarrow> a : B(v)"
   by blast
 
 
@@ -139,22 +137,19 @@
   Scan.succeed (SIMPLE_METHOD' o mk_ncanT_tac @{thms case_rls} @{thms case_rls})
 *}
 
-lemma ifT:
-  "[| b:Bool; b=true ==> t:A(true); b=false ==> u:A(false) |] ==>
-    if b then t else u : A(b)"
+lemma ifT: "\<lbrakk>b:Bool; b=true \<Longrightarrow> t:A(true); b=false \<Longrightarrow> u:A(false)\<rbrakk> \<Longrightarrow> if b then t else u : A(b)"
   by ncanT
 
-lemma applyT: "[| f : Pi(A,B);  a:A |] ==> f ` a : B(a)"
+lemma applyT: "\<lbrakk>f : Pi(A,B); a:A\<rbrakk> \<Longrightarrow> f ` a : B(a)"
   by ncanT
 
-lemma splitT:
-  "[| p:Sigma(A,B); !!x y. [| x:A;  y:B(x); p=<x,y> |] ==> c(x,y):C(<x,y>) |]
-    ==> split(p,c):C(p)"
+lemma splitT: "\<lbrakk>p:Sigma(A,B); \<And>x y. \<lbrakk>x:A; y:B(x); p=<x,y>\<rbrakk> \<Longrightarrow> c(x,y):C(<x,y>)\<rbrakk> \<Longrightarrow> split(p,c):C(p)"
   by ncanT
 
 lemma whenT:
-  "[| p:A+B; !!x.[| x:A;  p=inl(x) |] ==> a(x):C(inl(x)); !!y.[| y:B;  p=inr(y) |]
-    ==> b(y):C(inr(y)) |] ==> when(p,a,b) : C(p)"
+  "\<lbrakk>p:A+B;
+    \<And>x. \<lbrakk>x:A; p=inl(x)\<rbrakk> \<Longrightarrow> a(x):C(inl(x));
+    \<And>y. \<lbrakk>y:B;  p=inr(y)\<rbrakk> \<Longrightarrow> b(y):C(inr(y))\<rbrakk> \<Longrightarrow> when(p,a,b) : C(p)"
   by ncanT
 
 lemmas ncanTs = ifT applyT splitT whenT
@@ -162,30 +157,30 @@
 
 subsection {* Subtypes *}
 
-lemma SubtypeD1: "a : Subtype(A, P) ==> a : A"
-  and SubtypeD2: "a : Subtype(A, P) ==> P(a)"
+lemma SubtypeD1: "a : Subtype(A, P) \<Longrightarrow> a : A"
+  and SubtypeD2: "a : Subtype(A, P) \<Longrightarrow> P(a)"
   by (simp_all add: SubtypeXH)
 
-lemma SubtypeI: "[| a:A;  P(a) |] ==> a : {x:A. P(x)}"
+lemma SubtypeI: "\<lbrakk>a:A; P(a)\<rbrakk> \<Longrightarrow> a : {x:A. P(x)}"
   by (simp add: SubtypeXH)
 
-lemma SubtypeE: "[| a : {x:A. P(x)};  [| a:A;  P(a) |] ==> Q |] ==> Q"
+lemma SubtypeE: "\<lbrakk>a : {x:A. P(x)}; \<lbrakk>a:A; P(a)\<rbrakk> \<Longrightarrow> Q\<rbrakk> \<Longrightarrow> Q"
   by (simp add: SubtypeXH)
 
 
 subsection {* Monotonicity *}
 
-lemma idM: "mono (%X. X)"
+lemma idM: "mono (\<lambda>X. X)"
   apply (rule monoI)
   apply assumption
   done
 
-lemma constM: "mono(%X. A)"
+lemma constM: "mono(\<lambda>X. A)"
   apply (rule monoI)
   apply (rule subset_refl)
   done
 
-lemma "mono(%X. A(X)) ==> mono(%X.[A(X)])"
+lemma "mono(\<lambda>X. A(X)) \<Longrightarrow> mono(\<lambda>X.[A(X)])"
   apply (rule subsetI [THEN monoI])
   apply (drule LiftXH [THEN iffD1])
   apply (erule disjE)
@@ -196,18 +191,16 @@
   done
 
 lemma SgM:
-  "[| mono(%X. A(X)); !!x X. x:A(X) ==> mono(%X. B(X,x)) |] ==>
-    mono(%X. Sigma(A(X),B(X)))"
+  "\<lbrakk>mono(\<lambda>X. A(X)); \<And>x X. x:A(X) \<Longrightarrow> mono(\<lambda>X. B(X,x))\<rbrakk> \<Longrightarrow>
+    mono(\<lambda>X. Sigma(A(X),B(X)))"
   by (blast intro!: subsetI [THEN monoI] canTs elim!: case_rls
     dest!: monoD [THEN subsetD])
 
-lemma PiM:
-  "[| !!x. x:A ==> mono(%X. B(X,x)) |] ==> mono(%X. Pi(A,B(X)))"
+lemma PiM: "(\<And>x. x:A \<Longrightarrow> mono(\<lambda>X. B(X,x))) \<Longrightarrow> mono(\<lambda>X. Pi(A,B(X)))"
   by (blast intro!: subsetI [THEN monoI] canTs elim!: case_rls
     dest!: monoD [THEN subsetD])
 
-lemma PlusM:
-    "[| mono(%X. A(X));  mono(%X. B(X)) |] ==> mono(%X. A(X)+B(X))"
+lemma PlusM: "\<lbrakk>mono(\<lambda>X. A(X)); mono(\<lambda>X. B(X))\<rbrakk> \<Longrightarrow> mono(\<lambda>X. A(X)+B(X))"
   by (blast intro!: subsetI [THEN monoI] canTs elim!: case_rls
     dest!: monoD [THEN subsetD])
 
@@ -216,7 +209,7 @@
 
 subsubsection {* Conversion Rules for Fixed Points via monotonicity and Tarski *}
 
-lemma NatM: "mono(%X. Unit+X)"
+lemma NatM: "mono(\<lambda>X. Unit+X)"
   apply (rule PlusM constM idM)+
   done
 
@@ -225,7 +218,7 @@
   apply (rule NatM)
   done
 
-lemma ListM: "mono(%X.(Unit+Sigma(A,%y. X)))"
+lemma ListM: "mono(\<lambda>X.(Unit+Sigma(A,\<lambda>y. X)))"
   apply (rule PlusM SgM constM idM)+
   done
 
@@ -239,7 +232,7 @@
   apply (rule ListM)
   done
 
-lemma IListsM: "mono(%X.({} + Sigma(A,%y. X)))"
+lemma IListsM: "mono(\<lambda>X.({} + Sigma(A,\<lambda>y. X)))"
   apply (rule PlusM SgM constM idM)+
   done
 
@@ -253,10 +246,10 @@
 
 subsection {* Exhaustion Rules *}
 
-lemma NatXH: "a : Nat <-> (a=zero | (EX x:Nat. a=succ(x)))"
-  and ListXH: "a : List(A) <-> (a=[] | (EX x:A. EX xs:List(A).a=x$xs))"
-  and ListsXH: "a : Lists(A) <-> (a=[] | (EX x:A. EX xs:Lists(A).a=x$xs))"
-  and IListsXH: "a : ILists(A) <-> (EX x:A. EX xs:ILists(A).a=x$xs)"
+lemma NatXH: "a : Nat \<longleftrightarrow> (a=zero | (EX x:Nat. a=succ(x)))"
+  and ListXH: "a : List(A) \<longleftrightarrow> (a=[] | (EX x:A. EX xs:List(A).a=x$xs))"
+  and ListsXH: "a : Lists(A) \<longleftrightarrow> (a=[] | (EX x:A. EX xs:Lists(A).a=x$xs))"
+  and IListsXH: "a : ILists(A) \<longleftrightarrow> (EX x:A. EX xs:ILists(A).a=x$xs)"
   unfolding ind_data_defs
   by (rule ind_type_eqs [THEN XHlemma1], blast intro!: canTs elim!: case_rls)+
 
@@ -268,9 +261,9 @@
 subsection {* Type Rules *}
 
 lemma zeroT: "zero : Nat"
-  and succT: "n:Nat ==> succ(n) : Nat"
+  and succT: "n:Nat \<Longrightarrow> succ(n) : Nat"
   and nilT: "[] : List(A)"
-  and consT: "[| h:A;  t:List(A) |] ==> h$t : List(A)"
+  and consT: "\<lbrakk>h:A; t:List(A)\<rbrakk> \<Longrightarrow> h$t : List(A)"
   by (blast intro: iXHs [THEN iffD2])+
 
 lemmas icanTs = zeroT succT nilT consT
@@ -280,14 +273,12 @@
   Scan.succeed (SIMPLE_METHOD' o mk_ncanT_tac @{thms icase_rls} @{thms case_rls})
 *}
 
-lemma ncaseT:
-  "[| n:Nat; n=zero ==> b:C(zero); !!x.[| x:Nat;  n=succ(x) |] ==> c(x):C(succ(x)) |]
-    ==> ncase(n,b,c) : C(n)"
+lemma ncaseT: "\<lbrakk>n:Nat; n=zero \<Longrightarrow> b:C(zero); \<And>x. \<lbrakk>x:Nat; n=succ(x)\<rbrakk> \<Longrightarrow> c(x):C(succ(x))\<rbrakk>
+    \<Longrightarrow> ncase(n,b,c) : C(n)"
   by incanT
 
-lemma lcaseT:
-  "[| l:List(A); l=[] ==> b:C([]); !!h t.[| h:A;  t:List(A); l=h$t |] ==>
-    c(h,t):C(h$t) |] ==> lcase(l,b,c) : C(l)"
+lemma lcaseT: "\<lbrakk>l:List(A); l = [] \<Longrightarrow> b:C([]); \<And>h t. \<lbrakk>h:A; t:List(A); l=h$t\<rbrakk> \<Longrightarrow> c(h,t):C(h$t)\<rbrakk>
+    \<Longrightarrow> lcase(l,b,c) : C(l)"
   by incanT
 
 lemmas incanTs = ncaseT lcaseT
@@ -297,14 +288,13 @@
 
 lemmas ind_Ms = NatM ListM
 
-lemma Nat_ind: "[| n:Nat; P(zero); !!x.[| x:Nat; P(x) |] ==> P(succ(x)) |] ==> P(n)"
+lemma Nat_ind: "\<lbrakk>n:Nat; P(zero); \<And>x. \<lbrakk>x:Nat; P(x)\<rbrakk> \<Longrightarrow> P(succ(x))\<rbrakk> \<Longrightarrow> P(n)"
   apply (unfold ind_data_defs)
   apply (erule def_induct [OF Nat_def _ NatM])
   apply (blast intro: canTs elim!: case_rls)
   done
 
-lemma List_ind:
-  "[| l:List(A); P([]); !!x xs.[| x:A;  xs:List(A); P(xs) |] ==> P(x$xs) |] ==> P(l)"
+lemma List_ind: "\<lbrakk>l:List(A); P([]); \<And>x xs. \<lbrakk>x:A; xs:List(A); P(xs)\<rbrakk> \<Longrightarrow> P(x$xs)\<rbrakk> \<Longrightarrow> P(l)"
   apply (unfold ind_data_defs)
   apply (erule def_induct [OF List_def _ ListM])
   apply (blast intro: canTs elim!: case_rls)
@@ -315,16 +305,12 @@
 
 subsection {* Primitive Recursive Rules *}
 
-lemma nrecT:
-  "[| n:Nat; b:C(zero);
-      !!x g.[| x:Nat; g:C(x) |] ==> c(x,g):C(succ(x)) |] ==>
-      nrec(n,b,c) : C(n)"
+lemma nrecT: "\<lbrakk>n:Nat; b:C(zero); \<And>x g. \<lbrakk>x:Nat; g:C(x)\<rbrakk> \<Longrightarrow> c(x,g):C(succ(x))\<rbrakk>
+    \<Longrightarrow> nrec(n,b,c) : C(n)"
   by (erule Nat_ind) auto
 
-lemma lrecT:
-  "[| l:List(A); b:C([]);
-      !!x xs g.[| x:A;  xs:List(A); g:C(xs) |] ==> c(x,xs,g):C(x$xs) |] ==>
-      lrec(l,b,c) : C(l)"
+lemma lrecT: "\<lbrakk>l:List(A); b:C([]); \<And>x xs g. \<lbrakk>x:A; xs:List(A); g:C(xs)\<rbrakk> \<Longrightarrow> c(x,xs,g):C(x$xs) \<rbrakk>
+    \<Longrightarrow> lrec(l,b,c) : C(l)"
   by (erule List_ind) auto
 
 lemmas precTs = nrecT lrecT
@@ -332,8 +318,7 @@
 
 subsection {* Theorem proving *}
 
-lemma SgE2:
-  "[| <a,b> : Sigma(A,B);  [| a:A;  b:B(a) |] ==> P |] ==> P"
+lemma SgE2: "\<lbrakk><a,b> : Sigma(A,B); \<lbrakk>a:A; b:B(a)\<rbrakk> \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P"
   unfolding SgXH by blast
 
 (* General theorem proving ignores non-canonical term-formers,             *)
@@ -348,7 +333,7 @@
 
 subsection {* Infinite Data Types *}
 
-lemma lfp_subset_gfp: "mono(f) ==> lfp(f) <= gfp(f)"
+lemma lfp_subset_gfp: "mono(f) \<Longrightarrow> lfp(f) <= gfp(f)"
   apply (rule lfp_lowerbound [THEN subset_trans])
    apply (erule gfp_lemma3)
   apply (rule subset_refl)
@@ -356,16 +341,14 @@
 
 lemma gfpI:
   assumes "a:A"
-    and "!!x X.[| x:A;  ALL y:A. t(y):X |] ==> t(x) : B(X)"
+    and "\<And>x X. \<lbrakk>x:A; ALL y:A. t(y):X\<rbrakk> \<Longrightarrow> t(x) : B(X)"
   shows "t(a) : gfp(B)"
   apply (rule coinduct)
-   apply (rule_tac P = "%x. EX y:A. x=t (y)" in CollectI)
+   apply (rule_tac P = "\<lambda>x. EX y:A. x=t (y)" in CollectI)
    apply (blast intro!: assms)+
   done
 
-lemma def_gfpI:
-  "[| C==gfp(B);  a:A;  !!x X.[| x:A;  ALL y:A. t(y):X |] ==> t(x) : B(X) |] ==>
-    t(a) : C"
+lemma def_gfpI: "\<lbrakk>C == gfp(B); a:A; \<And>x X. \<lbrakk>x:A; ALL y:A. t(y):X\<rbrakk> \<Longrightarrow> t(x) : B(X)\<rbrakk> \<Longrightarrow> t(a) : C"
   apply unfold
   apply (erule gfpI)
   apply blast
@@ -383,15 +366,15 @@
 subsection {* Lemmas and tactics for using the rule @{text
   "coinduct3"} on @{text "[="} and @{text "="} *}
 
-lemma lfpI: "[| mono(f);  a : f(lfp(f)) |] ==> a : lfp(f)"
+lemma lfpI: "\<lbrakk>mono(f); a : f(lfp(f))\<rbrakk> \<Longrightarrow> a : lfp(f)"
   apply (erule lfp_Tarski [THEN ssubst])
   apply assumption
   done
 
-lemma ssubst_single: "[| a=a';  a' : A |] ==> a : A"
+lemma ssubst_single: "\<lbrakk>a = a'; a' : A\<rbrakk> \<Longrightarrow> a : A"
   by simp
 
-lemma ssubst_pair: "[| a=a';  b=b';  <a',b'> : A |] ==> <a,b> : A"
+lemma ssubst_pair: "\<lbrakk>a = a'; b = b'; <a',b'> : A\<rbrakk> \<Longrightarrow> <a,b> : A"
   by simp
 
 
@@ -402,14 +385,14 @@
 
 method_setup coinduct3 = {* Scan.succeed (SIMPLE_METHOD' o coinduct3_tac) *}
 
-lemma ci3_RI: "[| mono(Agen);  a : R |] ==> a : lfp(%x. Agen(x) Un R Un A)"
+lemma ci3_RI: "\<lbrakk>mono(Agen); a : R\<rbrakk> \<Longrightarrow> a : lfp(\<lambda>x. Agen(x) Un R Un A)"
   by coinduct3
 
-lemma ci3_AgenI: "[| mono(Agen);  a : Agen(lfp(%x. Agen(x) Un R Un A)) |] ==>
-    a : lfp(%x. Agen(x) Un R Un A)"
+lemma ci3_AgenI: "\<lbrakk>mono(Agen); a : Agen(lfp(\<lambda>x. Agen(x) Un R Un A))\<rbrakk> \<Longrightarrow>
+    a : lfp(\<lambda>x. Agen(x) Un R Un A)"
   by coinduct3
 
-lemma ci3_AI: "[| mono(Agen);  a : A |] ==> a : lfp(%x. Agen(x) Un R Un A)"
+lemma ci3_AI: "\<lbrakk>mono(Agen); a : A\<rbrakk> \<Longrightarrow> a : lfp(\<lambda>x. Agen(x) Un R Un A)"
   by coinduct3
 
 ML {*
@@ -434,19 +417,19 @@
 lemma POgenIs:
   "<true,true> : POgen(R)"
   "<false,false> : POgen(R)"
-  "[| <a,a'> : R;  <b,b'> : R |] ==> <<a,b>,<a',b'>> : POgen(R)"
-  "!!b b'. [|!!x. <b(x),b'(x)> : R |] ==><lam x. b(x),lam x. b'(x)> : POgen(R)"
+  "\<lbrakk><a,a'> : R; <b,b'> : R\<rbrakk> \<Longrightarrow> <<a,b>,<a',b'>> : POgen(R)"
+  "\<And>b b'. (\<And>x. <b(x),b'(x)> : R) \<Longrightarrow> <lam x. b(x),lam x. b'(x)> : POgen(R)"
   "<one,one> : POgen(R)"
-  "<a,a'> : lfp(%x. POgen(x) Un R Un PO) ==>
-    <inl(a),inl(a')> : POgen(lfp(%x. POgen(x) Un R Un PO))"
-  "<b,b'> : lfp(%x. POgen(x) Un R Un PO) ==>
-    <inr(b),inr(b')> : POgen(lfp(%x. POgen(x) Un R Un PO))"
-  "<zero,zero> : POgen(lfp(%x. POgen(x) Un R Un PO))"
-  "<n,n'> : lfp(%x. POgen(x) Un R Un PO) ==>
-    <succ(n),succ(n')> : POgen(lfp(%x. POgen(x) Un R Un PO))"
-  "<[],[]> : POgen(lfp(%x. POgen(x) Un R Un PO))"
-  "[| <h,h'> : lfp(%x. POgen(x) Un R Un PO);  <t,t'> : lfp(%x. POgen(x) Un R Un PO) |]
-    ==> <h$t,h'$t'> : POgen(lfp(%x. POgen(x) Un R Un PO))"
+  "<a,a'> : lfp(\<lambda>x. POgen(x) Un R Un PO) \<Longrightarrow>
+    <inl(a),inl(a')> : POgen(lfp(\<lambda>x. POgen(x) Un R Un PO))"
+  "<b,b'> : lfp(\<lambda>x. POgen(x) Un R Un PO) \<Longrightarrow>
+    <inr(b),inr(b')> : POgen(lfp(\<lambda>x. POgen(x) Un R Un PO))"
+  "<zero,zero> : POgen(lfp(\<lambda>x. POgen(x) Un R Un PO))"
+  "<n,n'> : lfp(\<lambda>x. POgen(x) Un R Un PO) \<Longrightarrow>
+    <succ(n),succ(n')> : POgen(lfp(\<lambda>x. POgen(x) Un R Un PO))"
+  "<[],[]> : POgen(lfp(\<lambda>x. POgen(x) Un R Un PO))"
+  "\<lbrakk><h,h'> : lfp(\<lambda>x. POgen(x) Un R Un PO);  <t,t'> : lfp(\<lambda>x. POgen(x) Un R Un PO)\<rbrakk>
+    \<Longrightarrow> <h$t,h'$t'> : POgen(lfp(\<lambda>x. POgen(x) Un R Un PO))"
   unfolding data_defs by (genIs POgenXH POgen_mono)+
 
 ML {*
@@ -468,19 +451,19 @@
 lemma EQgenIs:
   "<true,true> : EQgen(R)"
   "<false,false> : EQgen(R)"
-  "[| <a,a'> : R;  <b,b'> : R |] ==> <<a,b>,<a',b'>> : EQgen(R)"
-  "!!b b'. [|!!x. <b(x),b'(x)> : R |] ==> <lam x. b(x),lam x. b'(x)> : EQgen(R)"
+  "\<lbrakk><a,a'> : R; <b,b'> : R\<rbrakk> \<Longrightarrow> <<a,b>,<a',b'>> : EQgen(R)"
+  "\<And>b b'. (\<And>x. <b(x),b'(x)> : R) \<Longrightarrow> <lam x. b(x),lam x. b'(x)> : EQgen(R)"
   "<one,one> : EQgen(R)"
-  "<a,a'> : lfp(%x. EQgen(x) Un R Un EQ) ==>
-    <inl(a),inl(a')> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))"
-  "<b,b'> : lfp(%x. EQgen(x) Un R Un EQ) ==>
-    <inr(b),inr(b')> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))"
-  "<zero,zero> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))"
-  "<n,n'> : lfp(%x. EQgen(x) Un R Un EQ) ==>
-    <succ(n),succ(n')> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))"
-  "<[],[]> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))"
-  "[| <h,h'> : lfp(%x. EQgen(x) Un R Un EQ); <t,t'> : lfp(%x. EQgen(x) Un R Un EQ) |]
-    ==> <h$t,h'$t'> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))"
+  "<a,a'> : lfp(\<lambda>x. EQgen(x) Un R Un EQ) \<Longrightarrow>
+    <inl(a),inl(a')> : EQgen(lfp(\<lambda>x. EQgen(x) Un R Un EQ))"
+  "<b,b'> : lfp(\<lambda>x. EQgen(x) Un R Un EQ) \<Longrightarrow>
+    <inr(b),inr(b')> : EQgen(lfp(\<lambda>x. EQgen(x) Un R Un EQ))"
+  "<zero,zero> : EQgen(lfp(\<lambda>x. EQgen(x) Un R Un EQ))"
+  "<n,n'> : lfp(\<lambda>x. EQgen(x) Un R Un EQ) \<Longrightarrow>
+    <succ(n),succ(n')> : EQgen(lfp(\<lambda>x. EQgen(x) Un R Un EQ))"
+  "<[],[]> : EQgen(lfp(\<lambda>x. EQgen(x) Un R Un EQ))"
+  "\<lbrakk><h,h'> : lfp(\<lambda>x. EQgen(x) Un R Un EQ); <t,t'> : lfp(\<lambda>x. EQgen(x) Un R Un EQ)\<rbrakk>
+    \<Longrightarrow> <h$t,h'$t'> : EQgen(lfp(\<lambda>x. EQgen(x) Un R Un EQ))"
   unfolding data_defs by (genIs EQgenXH EQgen_mono)+
 
 ML {*
@@ -502,4 +485,8 @@
     ALLGOALS EQgen_raw_tac) i
 *}
 
+method_setup EQgen = {*
+  Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD' (EQgen_tac ctxt ths))
+*}
+
 end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/Wfd.thy
--- a/src/CCL/Wfd.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/Wfd.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -9,56 +9,57 @@
 imports Trancl Type Hered
 begin
 
-definition Wfd :: "[i set] => o"
-  where "Wfd(R) == ALL P.(ALL x.(ALL y.<y,x> : R --> y:P) --> x:P) --> (ALL a. a:P)"
+definition Wfd :: "[i set] \<Rightarrow> o"
+  where "Wfd(R) == ALL P.(ALL x.(ALL y.<y,x> : R \<longrightarrow> y:P) \<longrightarrow> x:P) \<longrightarrow> (ALL a. a:P)"
 
-definition wf :: "[i set] => i set"
-  where "wf(R) == {x. x:R & Wfd(R)}"
+definition wf :: "[i set] \<Rightarrow> i set"
+  where "wf(R) == {x. x:R \<and> Wfd(R)}"
 
-definition wmap :: "[i=>i,i set] => i set"
-  where "wmap(f,R) == {p. EX x y. p=<x,y>  &  <f(x),f(y)> : R}"
+definition wmap :: "[i\<Rightarrow>i,i set] \<Rightarrow> i set"
+  where "wmap(f,R) == {p. EX x y. p=<x,y> \<and> <f(x),f(y)> : R}"
 
 definition lex :: "[i set,i set] => i set"      (infixl "**" 70)
-  where "ra**rb == {p. EX a a' b b'. p = <<a,b>,<a',b'>> & (<a,a'> : ra | (a=a' & <b,b'> : rb))}"
+  where "ra**rb == {p. EX a a' b b'. p = <<a,b>,<a',b'>> \<and> (<a,a'> : ra | (a=a' \<and> <b,b'> : rb))}"
 
 definition NatPR :: "i set"
   where "NatPR == {p. EX x:Nat. p=<x,succ(x)>}"
 
-definition ListPR :: "i set => i set"
+definition ListPR :: "i set \<Rightarrow> i set"
   where "ListPR(A) == {p. EX h:A. EX t:List(A). p=<t,h$t>}"
 
 
 lemma wfd_induct:
   assumes 1: "Wfd(R)"
-    and 2: "!!x.[| ALL y. <y,x>: R --> P(y) |] ==> P(x)"
+    and 2: "\<And>x. ALL y. <y,x>: R \<longrightarrow> P(y) \<Longrightarrow> P(x)"
   shows "P(a)"
   apply (rule 1 [unfolded Wfd_def, rule_format, THEN CollectD])
   using 2 apply blast
   done
 
 lemma wfd_strengthen_lemma:
-  assumes 1: "!!x y.<x,y> : R ==> Q(x)"
-    and 2: "ALL x. (ALL y. <y,x> : R --> y : P) --> x : P"
-    and 3: "!!x. Q(x) ==> x:P"
+  assumes 1: "\<And>x y.<x,y> : R \<Longrightarrow> Q(x)"
+    and 2: "ALL x. (ALL y. <y,x> : R \<longrightarrow> y : P) \<longrightarrow> x : P"
+    and 3: "\<And>x. Q(x) \<Longrightarrow> x:P"
   shows "a:P"
   apply (rule 2 [rule_format])
   using 1 3
   apply blast
   done
 
-ML {*
-  fun wfd_strengthen_tac ctxt s i =
-    res_inst_tac ctxt [(("Q", 0), s)] @{thm wfd_strengthen_lemma} i THEN assume_tac ctxt (i+1)
+method_setup wfd_strengthen = {*
+  Scan.lift Args.name_inner_syntax >> (fn s => fn ctxt =>
+    SIMPLE_METHOD' (fn i =>
+      res_inst_tac ctxt [(("Q", 0), s)] @{thm wfd_strengthen_lemma} i THEN assume_tac ctxt (i+1)))
 *}
 
-lemma wf_anti_sym: "[| Wfd(r);  <a,x>:r;  <x,a>:r |] ==> P"
-  apply (subgoal_tac "ALL x. <a,x>:r --> <x,a>:r --> P")
+lemma wf_anti_sym: "\<lbrakk>Wfd(r); <a,x>:r; <x,a>:r\<rbrakk> \<Longrightarrow> P"
+  apply (subgoal_tac "ALL x. <a,x>:r \<longrightarrow> <x,a>:r \<longrightarrow> P")
    apply blast
   apply (erule wfd_induct)
   apply blast
   done
 
-lemma wf_anti_refl: "[| Wfd(r);  <a,a>: r |] ==> P"
+lemma wf_anti_refl: "\<lbrakk>Wfd(r); <a,a>: r\<rbrakk> \<Longrightarrow> P"
   apply (rule wf_anti_sym)
   apply assumption+
   done
@@ -86,26 +87,26 @@
 subsection {* Lexicographic Ordering *}
 
 lemma lexXH:
-  "p : ra**rb <-> (EX a a' b b'. p = <<a,b>,<a',b'>> & (<a,a'> : ra | a=a' & <b,b'> : rb))"
+  "p : ra**rb \<longleftrightarrow> (EX a a' b b'. p = <<a,b>,<a',b'>> \<and> (<a,a'> : ra | a=a' \<and> <b,b'> : rb))"
   unfolding lex_def by blast
 
-lemma lexI1: "<a,a'> : ra ==> <<a,b>,<a',b'>> : ra**rb"
+lemma lexI1: "<a,a'> : ra \<Longrightarrow> <<a,b>,<a',b'>> : ra**rb"
   by (blast intro!: lexXH [THEN iffD2])
 
-lemma lexI2: "<b,b'> : rb ==> <<a,b>,<a,b'>> : ra**rb"
+lemma lexI2: "<b,b'> : rb \<Longrightarrow> <<a,b>,<a,b'>> : ra**rb"
   by (blast intro!: lexXH [THEN iffD2])
 
 lemma lexE:
   assumes 1: "p : ra**rb"
-    and 2: "!!a a' b b'.[| <a,a'> : ra; p=<<a,b>,<a',b'>> |] ==> R"
-    and 3: "!!a b b'.[| <b,b'> : rb;  p = <<a,b>,<a,b'>> |] ==> R"
+    and 2: "\<And>a a' b b'. \<lbrakk><a,a'> : ra; p=<<a,b>,<a',b'>>\<rbrakk> \<Longrightarrow> R"
+    and 3: "\<And>a b b'. \<lbrakk><b,b'> : rb; p = <<a,b>,<a,b'>>\<rbrakk> \<Longrightarrow> R"
   shows R
   apply (rule 1 [THEN lexXH [THEN iffD1], THEN exE])
   using 2 3
   apply blast
   done
 
-lemma lex_pair: "[| p : r**s;  !!a a' b b'. p = <<a,b>,<a',b'>> ==> P |] ==>P"
+lemma lex_pair: "\<lbrakk>p : r**s; \<And>a a' b b'. p = <<a,b>,<a',b'>> \<Longrightarrow> P\<rbrakk> \<Longrightarrow>P"
   apply (erule lexE)
    apply blast+
   done
@@ -116,7 +117,7 @@
   shows "Wfd(R**S)"
   apply (unfold Wfd_def)
   apply safe
-  apply (tactic {* wfd_strengthen_tac @{context} "%x. EX a b. x=<a,b>" 1 *})
+  apply (wfd_strengthen "\<lambda>x. EX a b. x=<a,b>")
    apply (blast elim!: lex_pair)
   apply (subgoal_tac "ALL a b.<a,b>:P")
    apply blast
@@ -128,13 +129,13 @@
 
 subsection {* Mapping *}
 
-lemma wmapXH: "p : wmap(f,r) <-> (EX x y. p=<x,y>  &  <f(x),f(y)> : r)"
+lemma wmapXH: "p : wmap(f,r) \<longleftrightarrow> (EX x y. p=<x,y> \<and> <f(x),f(y)> : r)"
   unfolding wmap_def by blast
 
-lemma wmapI: "<f(a),f(b)> : r ==> <a,b> : wmap(f,r)"
+lemma wmapI: "<f(a),f(b)> : r \<Longrightarrow> <a,b> : wmap(f,r)"
   by (blast intro!: wmapXH [THEN iffD2])
 
-lemma wmapE: "[| p : wmap(f,r);  !!a b.[| <f(a),f(b)> : r;  p=<a,b> |] ==> R |] ==> R"
+lemma wmapE: "\<lbrakk>p : wmap(f,r); \<And>a b. \<lbrakk><f(a),f(b)> : r; p=<a,b>\<rbrakk> \<Longrightarrow> R\<rbrakk> \<Longrightarrow> R"
   by (blast dest!: wmapXH [THEN iffD1])
 
 lemma wmap_wf:
@@ -142,7 +143,7 @@
   shows "Wfd(wmap(f,r))"
   apply (unfold Wfd_def)
   apply clarify
-  apply (subgoal_tac "ALL b. ALL a. f (a) =b-->a:P")
+  apply (subgoal_tac "ALL b. ALL a. f (a) = b \<longrightarrow> a:P")
    apply blast
   apply (rule 1 [THEN wfd_induct, THEN allI])
   apply clarify
@@ -156,17 +157,17 @@
 
 subsection {* Projections *}
 
-lemma wfstI: "<xa,ya> : r ==> <<xa,xb>,<ya,yb>> : wmap(fst,r)"
+lemma wfstI: "<xa,ya> : r \<Longrightarrow> <<xa,xb>,<ya,yb>> : wmap(fst,r)"
   apply (rule wmapI)
   apply simp
   done
 
-lemma wsndI: "<xb,yb> : r ==> <<xa,xb>,<ya,yb>> : wmap(snd,r)"
+lemma wsndI: "<xb,yb> : r \<Longrightarrow> <<xa,xb>,<ya,yb>> : wmap(snd,r)"
   apply (rule wmapI)
   apply simp
   done
 
-lemma wthdI: "<xc,yc> : r ==> <<xa,<xb,xc>>,<ya,<yb,yc>>> : wmap(thd,r)"
+lemma wthdI: "<xc,yc> : r \<Longrightarrow> <<xa,<xb,xc>>,<ya,<yb,yc>>> : wmap(thd,r)"
   apply (rule wmapI)
   apply simp
   done
@@ -174,7 +175,7 @@
 
 subsection {* Ground well-founded relations *}
 
-lemma wfI: "[| Wfd(r);  a : r |] ==> a : wf(r)"
+lemma wfI: "\<lbrakk>Wfd(r);  a : r\<rbrakk> \<Longrightarrow> a : wf(r)"
   unfolding wf_def by blast
 
 lemma Empty_wf: "Wfd({})"
@@ -187,22 +188,22 @@
   apply (rule Empty_wf)
   done
 
-lemma NatPRXH: "p : NatPR <-> (EX x:Nat. p=<x,succ(x)>)"
+lemma NatPRXH: "p : NatPR \<longleftrightarrow> (EX x:Nat. p=<x,succ(x)>)"
   unfolding NatPR_def by blast
 
-lemma ListPRXH: "p : ListPR(A) <-> (EX h:A. EX t:List(A).p=<t,h$t>)"
+lemma ListPRXH: "p : ListPR(A) \<longleftrightarrow> (EX h:A. EX t:List(A).p=<t,h$t>)"
   unfolding ListPR_def by blast
 
-lemma NatPRI: "x : Nat ==> <x,succ(x)> : NatPR"
+lemma NatPRI: "x : Nat \<Longrightarrow> <x,succ(x)> : NatPR"
   by (auto simp: NatPRXH)
 
-lemma ListPRI: "[| t : List(A); h : A |] ==> <t,h $ t> : ListPR(A)"
+lemma ListPRI: "\<lbrakk>t : List(A); h : A\<rbrakk> \<Longrightarrow> <t,h $ t> : ListPR(A)"
   by (auto simp: ListPRXH)
 
 lemma NatPR_wf: "Wfd(NatPR)"
   apply (unfold Wfd_def)
   apply clarify
-  apply (tactic {* wfd_strengthen_tac @{context} "%x. x:Nat" 1 *})
+  apply (wfd_strengthen "\<lambda>x. x:Nat")
    apply (fastforce iff: NatPRXH)
   apply (erule Nat_ind)
    apply (fastforce iff: NatPRXH)+
@@ -211,7 +212,7 @@
 lemma ListPR_wf: "Wfd(ListPR(A))"
   apply (unfold Wfd_def)
   apply clarify
-  apply (tactic {* wfd_strengthen_tac @{context} "%x. x:List (A)" 1 *})
+  apply (wfd_strengthen "\<lambda>x. x:List (A)")
    apply (fastforce iff: ListPRXH)
   apply (erule List_ind)
    apply (fastforce iff: ListPRXH)+
@@ -222,7 +223,7 @@
 
 lemma letrecT:
   assumes 1: "a : A"
-    and 2: "!!p g.[| p:A; ALL x:{x: A. <x,p>:wf(R)}. g(x) : D(x) |] ==> h(p,g) : D(p)"
+    and 2: "\<And>p g. \<lbrakk>p:A; ALL x:{x: A. <x,p>:wf(R)}. g(x) : D(x)\<rbrakk> \<Longrightarrow> h(p,g) : D(p)"
   shows "letrec g x be h(x,g) in g(a) : D(a)"
   apply (rule 1 [THEN rev_mp])
   apply (rule wf_wf [THEN wfd_induct])
@@ -241,8 +242,8 @@
 lemma letrec2T:
   assumes "a : A"
     and "b : B"
-    and "!!p q g.[| p:A; q:B;
-              ALL x:A. ALL y:{y: B. <<x,y>,<p,q>>:wf(R)}. g(x,y) : D(x,y) |] ==> 
+    and "\<And>p q g. \<lbrakk>p:A; q:B;
+              ALL x:A. ALL y:{y: B. <<x,y>,<p,q>>:wf(R)}. g(x,y) : D(x,y)\<rbrakk> \<Longrightarrow> 
                 h(p,q,g) : D(p,q)"
   shows "letrec g x y be h(x,y,g) in g(a,b) : D(a,b)"
   apply (unfold letrec2_def)
@@ -255,16 +256,16 @@
     erule bspec SubtypeE sym [THEN subst])+
   done
 
-lemma lem: "SPLIT(<a,<b,c>>,%x xs. SPLIT(xs,%y z. B(x,y,z))) = B(a,b,c)"
+lemma lem: "SPLIT(<a,<b,c>>,\<lambda>x xs. SPLIT(xs,\<lambda>y z. B(x,y,z))) = B(a,b,c)"
   by (simp add: SPLITB)
 
 lemma letrec3T:
   assumes "a : A"
     and "b : B"
     and "c : C"
-    and "!!p q r g.[| p:A; q:B; r:C;
-       ALL x:A. ALL y:B. ALL z:{z:C. <<x,<y,z>>,<p,<q,r>>> : wf(R)}.  
-                                                        g(x,y,z) : D(x,y,z) |] ==> 
+    and "\<And>p q r g. \<lbrakk>p:A; q:B; r:C;
+       ALL x:A. ALL y:B. ALL z:{z:C. <<x,<y,z>>,<p,<q,r>>> : wf(R)}.
+                                                        g(x,y,z) : D(x,y,z) \<rbrakk> \<Longrightarrow>
                 h(p,q,r,g) : D(p,q,r)"
   shows "letrec g x y z be h(x,y,z,g) in g(a,b,c) : D(a,b,c)"
   apply (unfold letrec3_def)
@@ -283,22 +284,19 @@
 subsection {* Type Checking for Recursive Calls *}
 
 lemma rcallT:
-  "[| ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x);  
-      g(a) : D(a) ==> g(a) : E;  a:A;  <a,p>:wf(R) |] ==>  
-  g(a) : E"
+  "\<lbrakk>ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x);  
+    g(a) : D(a) \<Longrightarrow> g(a) : E;  a:A;  <a,p>:wf(R)\<rbrakk> \<Longrightarrow> g(a) : E"
   by blast
 
 lemma rcall2T:
-  "[| ALL x:A. ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y);  
-      g(a,b) : D(a,b) ==> g(a,b) : E;  a:A;  b:B;  <<a,b>,<p,q>>:wf(R) |] ==>  
-  g(a,b) : E"
+  "\<lbrakk>ALL x:A. ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y);
+    g(a,b) : D(a,b) \<Longrightarrow> g(a,b) : E; a:A; b:B; <<a,b>,<p,q>>:wf(R)\<rbrakk> \<Longrightarrow> g(a,b) : E"
   by blast
 
 lemma rcall3T:
-  "[| ALL x:A. ALL y:B. ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}. g(x,y,z):D(x,y,z);  
-      g(a,b,c) : D(a,b,c) ==> g(a,b,c) : E;   
-      a:A;  b:B;  c:C;  <<a,<b,c>>,<p,<q,r>>> : wf(R) |] ==>  
-  g(a,b,c) : E"
+  "\<lbrakk>ALL x:A. ALL y:B. ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}. g(x,y,z):D(x,y,z);
+    g(a,b,c) : D(a,b,c) \<Longrightarrow> g(a,b,c) : E;
+    a:A; b:B; c:C; <<a,<b,c>>,<p,<q,r>>> : wf(R)\<rbrakk> \<Longrightarrow> g(a,b,c) : E"
   by blast
 
 lemmas rcallTs = rcallT rcall2T rcall3T
@@ -309,9 +307,9 @@
 lemma hyprcallT:
   assumes 1: "g(a) = b"
     and 2: "ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x)"
-    and 3: "ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x) ==> b=g(a) ==> g(a) : D(a) ==> P"
-    and 4: "ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x) ==> a:A"
-    and 5: "ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x) ==> <a,p>:wf(R)"
+    and 3: "ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x) \<Longrightarrow> b=g(a) \<Longrightarrow> g(a) : D(a) \<Longrightarrow> P"
+    and 4: "ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x) \<Longrightarrow> a:A"
+    and 5: "ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x) \<Longrightarrow> <a,p>:wf(R)"
   shows P
   apply (rule 3 [OF 2, OF 1 [symmetric]])
   apply (rule rcallT [OF 2])
@@ -323,7 +321,7 @@
 lemma hyprcall2T:
   assumes 1: "g(a,b) = c"
     and 2: "ALL x:A. ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y)"
-    and 3: "[| c=g(a,b);  g(a,b) : D(a,b) |] ==> P"
+    and 3: "\<lbrakk>c = g(a,b); g(a,b) : D(a,b)\<rbrakk> \<Longrightarrow> P"
     and 4: "a:A"
     and 5: "b:B"
     and 6: "<<a,b>,<p,q>>:wf(R)"
@@ -341,7 +339,7 @@
 lemma hyprcall3T:
   assumes 1: "g(a,b,c) = d"
     and 2: "ALL x:A. ALL y:B. ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}.g(x,y,z):D(x,y,z)"
-    and 3: "[| d=g(a,b,c);  g(a,b,c) : D(a,b,c) |] ==> P"
+    and 3: "\<lbrakk>d = g(a,b,c); g(a,b,c) : D(a,b,c)\<rbrakk> \<Longrightarrow> P"
     and 4: "a:A"
     and 5: "b:B"
     and 6: "c:C"
@@ -363,14 +361,12 @@
 
 subsection {* Rules to Remove Induction Hypotheses after Type Checking *}
 
-lemma rmIH1: "[| ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x); P |] ==> P" .
+lemma rmIH1: "\<lbrakk>ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x); P\<rbrakk> \<Longrightarrow> P" .
 
-lemma rmIH2: "[| ALL x:A. ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y); P |] ==> P" .
+lemma rmIH2: "\<lbrakk>ALL x:A. ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y); P\<rbrakk> \<Longrightarrow> P" .
   
 lemma rmIH3:
- "[| ALL x:A. ALL y:B. ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}.g(x,y,z):D(x,y,z);  
-     P |] ==>  
-     P" .
+ "\<lbrakk>ALL x:A. ALL y:B. ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}.g(x,y,z):D(x,y,z); P\<rbrakk> \<Longrightarrow> P" .
 
 lemmas rmIHs = rmIH1 rmIH2 rmIH3
 
@@ -381,27 +377,27 @@
 (*                                      correctly by applying SubtypeI *)
 
 lemma Subtype_canTs:
-  "!!a b A B P. a : {x:A. b:{y:B(a).P(<x,y>)}} ==> <a,b> : {x:Sigma(A,B).P(x)}"
-  "!!a A B P. a : {x:A. P(inl(x))} ==> inl(a) : {x:A+B. P(x)}"
-  "!!b A B P. b : {x:B. P(inr(x))} ==> inr(b) : {x:A+B. P(x)}"
-  "!!a P. a : {x:Nat. P(succ(x))} ==> succ(a) : {x:Nat. P(x)}"
-  "!!h t A P. h : {x:A. t : {y:List(A).P(x$y)}} ==> h$t : {x:List(A).P(x)}"
+  "\<And>a b A B P. a : {x:A. b:{y:B(a).P(<x,y>)}} \<Longrightarrow> <a,b> : {x:Sigma(A,B).P(x)}"
+  "\<And>a A B P. a : {x:A. P(inl(x))} \<Longrightarrow> inl(a) : {x:A+B. P(x)}"
+  "\<And>b A B P. b : {x:B. P(inr(x))} \<Longrightarrow> inr(b) : {x:A+B. P(x)}"
+  "\<And>a P. a : {x:Nat. P(succ(x))} \<Longrightarrow> succ(a) : {x:Nat. P(x)}"
+  "\<And>h t A P. h : {x:A. t : {y:List(A).P(x$y)}} \<Longrightarrow> h$t : {x:List(A).P(x)}"
   by (assumption | rule SubtypeI canTs icanTs | erule SubtypeE)+
 
-lemma letT: "[| f(t):B;  ~t=bot  |] ==> let x be t in f(x) : B"
+lemma letT: "\<lbrakk>f(t):B; \<not>t=bot\<rbrakk> \<Longrightarrow> let x be t in f(x) : B"
   apply (erule letB [THEN ssubst])
   apply assumption
   done
 
-lemma applyT2: "[| a:A;  f : Pi(A,B)  |] ==> f ` a  : B(a)"
+lemma applyT2: "\<lbrakk>a:A; f : Pi(A,B)\<rbrakk> \<Longrightarrow> f ` a  : B(a)"
   apply (erule applyT)
   apply assumption
   done
 
-lemma rcall_lemma1: "[| a:A;  a:A ==> P(a) |] ==> a : {x:A. P(x)}"
+lemma rcall_lemma1: "\<lbrakk>a:A; a:A \<Longrightarrow> P(a)\<rbrakk> \<Longrightarrow> a : {x:A. P(x)}"
   by blast
 
-lemma rcall_lemma2: "[| a:{x:A. Q(x)};  [| a:A; Q(a) |] ==> P(a) |] ==> a : {x:A. P(x)}"
+lemma rcall_lemma2: "\<lbrakk>a:{x:A. Q(x)}; \<lbrakk>a:A; Q(a)\<rbrakk> \<Longrightarrow> P(a)\<rbrakk> \<Longrightarrow> a : {x:A. P(x)}"
   by blast
 
 lemmas rcall_lemmas = asm_rl rcall_lemma1 SubtypeD1 rcall_lemma2
@@ -410,7 +406,6 @@
 subsection {* Typechecking *}
 
 ML {*
-
 local
 
 val type_rls =
@@ -443,9 +438,11 @@
   in try_IHs rnames end)
 
 fun is_rigid_prog t =
-     case (Logic.strip_assums_concl t) of
-        (Const(@{const_name Trueprop},_) $ (Const(@{const_name mem},_) $ a $ _)) => null (Term.add_vars a [])
-       | _ => false
+  (case (Logic.strip_assums_concl t) of
+    (Const(@{const_name Trueprop},_) $ (Const(@{const_name mem},_) $ a $ _)) =>
+      null (Term.add_vars a [])
+  | _ => false)
+
 in
 
 fun rcall_tac ctxt i =
@@ -460,11 +457,10 @@
   match_tac ctxt [@{thm SubtypeI}] i
 
 fun tc_step_tac ctxt prems = SUBGOAL (fn (Bi,i) =>
-          if is_rigid_prog Bi then raw_step_tac ctxt prems i else no_tac)
+    if is_rigid_prog Bi then raw_step_tac ctxt prems i else no_tac)
 
 fun typechk_tac ctxt rls i = SELECT_GOAL (REPEAT_FIRST (tc_step_tac ctxt rls)) i
 
-fun tac ctxt = typechk_tac ctxt [] 1
 
 (*** Clean up Correctness Condictions ***)
 
@@ -481,6 +477,18 @@
 end
 *}
 
+method_setup typechk = {*
+  Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD' (typechk_tac ctxt ths))
+*}
+
+method_setup clean_ccs = {*
+  Scan.succeed (SIMPLE_METHOD o clean_ccs_tac)
+*}
+
+method_setup gen_ccs = {*
+  Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD' (gen_ccs_tac ctxt ths))
+*}
+
 
 subsection {* Evaluation *}
 
@@ -517,7 +525,7 @@
       etac @{thm substitute} 1)) *})
   done
 
-lemma fixV: "f(fix(f)) ---> c ==> fix(f) ---> c"
+lemma fixV: "f(fix(f)) ---> c \<Longrightarrow> fix(f) ---> c"
   apply (unfold fix_def)
   apply (rule applyV)
    apply (rule lamV)
@@ -525,7 +533,7 @@
   done
 
 lemma letrecV:
-  "h(t,%y. letrec g x be h(x,g) in g(y)) ---> c ==>  
+  "h(t,\<lambda>y. letrec g x be h(x,g) in g(y)) ---> c \<Longrightarrow>  
                  letrec g x be h(x,g) in g(t) ---> c"
   apply (unfold letrec_def)
   apply (assumption | rule fixV applyV  lamV)+
@@ -536,51 +544,51 @@
 lemma V_rls [eval]:
   "true ---> true"
   "false ---> false"
-  "!!b c t u. [| b--->true;  t--->c |] ==> if b then t else u ---> c"
-  "!!b c t u. [| b--->false;  u--->c |] ==> if b then t else u ---> c"
-  "!!a b. <a,b> ---> <a,b>"
-  "!!a b c t h. [| t ---> <a,b>;  h(a,b) ---> c |] ==> split(t,h) ---> c"
+  "\<And>b c t u. \<lbrakk>b--->true; t--->c\<rbrakk> \<Longrightarrow> if b then t else u ---> c"
+  "\<And>b c t u. \<lbrakk>b--->false; u--->c\<rbrakk> \<Longrightarrow> if b then t else u ---> c"
+  "\<And>a b. <a,b> ---> <a,b>"
+  "\<And>a b c t h. \<lbrakk>t ---> <a,b>; h(a,b) ---> c\<rbrakk> \<Longrightarrow> split(t,h) ---> c"
   "zero ---> zero"
-  "!!n. succ(n) ---> succ(n)"
-  "!!c n t u. [| n ---> zero; t ---> c |] ==> ncase(n,t,u) ---> c"
-  "!!c n t u x. [| n ---> succ(x); u(x) ---> c |] ==> ncase(n,t,u) ---> c"
-  "!!c n t u. [| n ---> zero; t ---> c |] ==> nrec(n,t,u) ---> c"
-  "!!c n t u x. [| n--->succ(x); u(x,nrec(x,t,u))--->c |] ==> nrec(n,t,u)--->c"
+  "\<And>n. succ(n) ---> succ(n)"
+  "\<And>c n t u. \<lbrakk>n ---> zero; t ---> c\<rbrakk> \<Longrightarrow> ncase(n,t,u) ---> c"
+  "\<And>c n t u x. \<lbrakk>n ---> succ(x); u(x) ---> c\<rbrakk> \<Longrightarrow> ncase(n,t,u) ---> c"
+  "\<And>c n t u. \<lbrakk>n ---> zero; t ---> c\<rbrakk> \<Longrightarrow> nrec(n,t,u) ---> c"
+  "\<And>c n t u x. \<lbrakk>n--->succ(x); u(x,nrec(x,t,u))--->c\<rbrakk> \<Longrightarrow> nrec(n,t,u)--->c"
   "[] ---> []"
-  "!!h t. h$t ---> h$t"
-  "!!c l t u. [| l ---> []; t ---> c |] ==> lcase(l,t,u) ---> c"
-  "!!c l t u x xs. [| l ---> x$xs; u(x,xs) ---> c |] ==> lcase(l,t,u) ---> c"
-  "!!c l t u. [| l ---> []; t ---> c |] ==> lrec(l,t,u) ---> c"
-  "!!c l t u x xs. [| l--->x$xs; u(x,xs,lrec(xs,t,u))--->c |] ==> lrec(l,t,u)--->c"
+  "\<And>h t. h$t ---> h$t"
+  "\<And>c l t u. \<lbrakk>l ---> []; t ---> c\<rbrakk> \<Longrightarrow> lcase(l,t,u) ---> c"
+  "\<And>c l t u x xs. \<lbrakk>l ---> x$xs; u(x,xs) ---> c\<rbrakk> \<Longrightarrow> lcase(l,t,u) ---> c"
+  "\<And>c l t u. \<lbrakk>l ---> []; t ---> c\<rbrakk> \<Longrightarrow> lrec(l,t,u) ---> c"
+  "\<And>c l t u x xs. \<lbrakk>l--->x$xs; u(x,xs,lrec(xs,t,u))--->c\<rbrakk> \<Longrightarrow> lrec(l,t,u)--->c"
   unfolding data_defs by eval+
 
 
 subsection {* Factorial *}
 
 schematic_lemma
-  "letrec f n be ncase(n,succ(zero),%x. nrec(n,zero,%y g. nrec(f(x),g,%z h. succ(h))))  
+  "letrec f n be ncase(n,succ(zero),\<lambda>x. nrec(n,zero,\<lambda>y g. nrec(f(x),g,\<lambda>z h. succ(h))))  
    in f(succ(succ(zero))) ---> ?a"
   by eval
 
 schematic_lemma
-  "letrec f n be ncase(n,succ(zero),%x. nrec(n,zero,%y g. nrec(f(x),g,%z h. succ(h))))  
+  "letrec f n be ncase(n,succ(zero),\<lambda>x. nrec(n,zero,\<lambda>y g. nrec(f(x),g,\<lambda>z h. succ(h))))  
    in f(succ(succ(succ(zero)))) ---> ?a"
   by eval
 
 subsection {* Less Than Or Equal *}
 
 schematic_lemma
-  "letrec f p be split(p,%m n. ncase(m,true,%x. ncase(n,false,%y. f(<x,y>))))
+  "letrec f p be split(p,\<lambda>m n. ncase(m,true,\<lambda>x. ncase(n,false,\<lambda>y. f(<x,y>))))
    in f(<succ(zero), succ(zero)>) ---> ?a"
   by eval
 
 schematic_lemma
-  "letrec f p be split(p,%m n. ncase(m,true,%x. ncase(n,false,%y. f(<x,y>))))
+  "letrec f p be split(p,\<lambda>m n. ncase(m,true,\<lambda>x. ncase(n,false,\<lambda>y. f(<x,y>))))
    in f(<succ(zero), succ(succ(succ(succ(zero))))>) ---> ?a"
   by eval
 
 schematic_lemma
-  "letrec f p be split(p,%m n. ncase(m,true,%x. ncase(n,false,%y. f(<x,y>))))
+  "letrec f p be split(p,\<lambda>m n. ncase(m,true,\<lambda>x. ncase(n,false,\<lambda>y. f(<x,y>))))
    in f(<succ(succ(succ(succ(succ(zero))))), succ(succ(succ(succ(zero))))>) ---> ?a"
   by eval
 
@@ -588,12 +596,12 @@
 subsection {* Reverse *}
 
 schematic_lemma
-  "letrec id l be lcase(l,[],%x xs. x$id(xs))  
+  "letrec id l be lcase(l,[],\<lambda>x xs. x$id(xs))  
    in id(zero$succ(zero)$[]) ---> ?a"
   by eval
 
 schematic_lemma
-  "letrec rev l be lcase(l,[],%x xs. lrec(rev(xs),x$[],%y ys g. y$g))  
+  "letrec rev l be lcase(l,[],\<lambda>x xs. lrec(rev(xs),x$[],\<lambda>y ys g. y$g))  
    in rev(zero$succ(zero)$(succ((lam x. x)`succ(zero)))$([])) ---> ?a"
   by eval
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/ex/Flag.thy
--- a/src/CCL/ex/Flag.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/ex/Flag.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -22,32 +22,32 @@
 definition blue :: "i"
   where "blue == inr(inr(one))"
 
-definition ccase :: "[i,i,i,i]=>i"
-  where "ccase(c,r,w,b) == when(c,%x. r,%wb. when(wb,%x. w,%x. b))"
+definition ccase :: "[i,i,i,i]\<Rightarrow>i"
+  where "ccase(c,r,w,b) == when(c, \<lambda>x. r, \<lambda>wb. when(wb, \<lambda>x. w, \<lambda>x. b))"
 
 definition flag :: "i"
   where
     "flag == lam l. letrec
       flagx l be lcase(l,<[],<[],[]>>,
-                       %h t. split(flagx(t),%lr p. split(p,%lw lb.
+                       \<lambda>h t. split(flagx(t), \<lambda>lr p. split(p, \<lambda>lw lb.
                             ccase(h, <red$lr,<lw,lb>>,
                                      <lr,<white$lw,lb>>,
                                      <lr,<lw,blue$lb>>))))
       in flagx(l)"
 
-axiomatization Perm :: "i => i => o"
-definition Flag :: "i => i => o" where
+axiomatization Perm :: "i \<Rightarrow> i \<Rightarrow> o"
+definition Flag :: "i \<Rightarrow> i \<Rightarrow> o" where
   "Flag(l,x) == ALL lr:List(Colour).ALL lw:List(Colour).ALL lb:List(Colour).
-                x = <lr,<lw,lb>> -->
-              (ALL c:Colour.(c mem lr = true --> c=red) &
-                            (c mem lw = true --> c=white) &
-                            (c mem lb = true --> c=blue)) &
+                x = <lr,<lw,lb>> \<longrightarrow>
+              (ALL c:Colour.(c mem lr = true \<longrightarrow> c=red) \<and>
+                            (c mem lw = true \<longrightarrow> c=white) \<and>
+                            (c mem lb = true \<longrightarrow> c=blue)) \<and>
               Perm(l,lr @ lw @ lb)"
 
 
 lemmas flag_defs = Colour_def red_def white_def blue_def ccase_def
 
-lemma ColourXH: "a : Colour <-> (a=red | a=white | a=blue)"
+lemma ColourXH: "a : Colour \<longleftrightarrow> (a=red | a=white | a=blue)"
   unfolding simp_type_defs flag_defs by blast
 
 lemma redT: "red : Colour"
@@ -56,23 +56,21 @@
   unfolding ColourXH by blast+
 
 lemma ccaseT:
-  "[| c:Colour; c=red ==> r : C(red); c=white ==> w : C(white); c=blue ==> b : C(blue) |]
-    ==> ccase(c,r,w,b) : C(c)"
+  "\<lbrakk>c:Colour; c=red \<Longrightarrow> r : C(red); c=white \<Longrightarrow> w : C(white); c=blue \<Longrightarrow> b : C(blue)\<rbrakk>
+    \<Longrightarrow> ccase(c,r,w,b) : C(c)"
   unfolding flag_defs by ncanT
 
 lemma "flag : List(Colour)->List(Colour)*List(Colour)*List(Colour)"
   apply (unfold flag_def)
-  apply (tactic {* typechk_tac @{context}
-    [@{thm redT}, @{thm whiteT}, @{thm blueT}, @{thm ccaseT}] 1 *})
-  apply (tactic "clean_ccs_tac @{context}")
+  apply (typechk redT whiteT blueT ccaseT)
+  apply clean_ccs
   apply (erule ListPRI [THEN ListPR_wf [THEN wfI]])
   apply assumption
   done
 
 lemma "flag : PROD l:List(Colour).{x:List(Colour)*List(Colour)*List(Colour).Flag(x,l)}"
   apply (unfold flag_def)
-  apply (tactic {* gen_ccs_tac @{context}
-    [@{thm redT}, @{thm whiteT}, @{thm blueT}, @{thm ccaseT}] 1 *})
+  apply (gen_ccs redT whiteT blueT ccaseT)
   oops
 
 end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/ex/List.thy
--- a/src/CCL/ex/List.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/ex/List.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -9,110 +9,109 @@
 imports Nat
 begin
 
-definition map :: "[i=>i,i]=>i"
-  where "map(f,l) == lrec(l,[],%x xs g. f(x)$g)"
+definition map :: "[i\<Rightarrow>i,i]\<Rightarrow>i"
+  where "map(f,l) == lrec(l, [], \<lambda>x xs g. f(x)$g)"
 
-definition comp :: "[i=>i,i=>i]=>i=>i"  (infixr "\<circ>" 55)
-  where "f \<circ> g == (%x. f(g(x)))"
+definition comp :: "[i\<Rightarrow>i,i\<Rightarrow>i]\<Rightarrow>i\<Rightarrow>i"  (infixr "\<circ>" 55)
+  where "f \<circ> g == (\<lambda>x. f(g(x)))"
 
-definition append :: "[i,i]=>i"  (infixr "@" 55)
-  where "l @ m == lrec(l,m,%x xs g. x$g)"
+definition append :: "[i,i]\<Rightarrow>i"  (infixr "@" 55)
+  where "l @ m == lrec(l, m, \<lambda>x xs g. x$g)"
 
-axiomatization member :: "[i,i]=>i"  (infixr "mem" 55)  (* FIXME dangling eq *)
-  where member_ax: "a mem l == lrec(l,false,%h t g. if eq(a,h) then true else g)"
+axiomatization member :: "[i,i]\<Rightarrow>i"  (infixr "mem" 55)  (* FIXME dangling eq *)
+  where member_ax: "a mem l == lrec(l, false, \<lambda>h t g. if eq(a,h) then true else g)"
 
-definition filter :: "[i,i]=>i"
-  where "filter(f,l) == lrec(l,[],%x xs g. if f`x then x$g else g)"
+definition filter :: "[i,i]\<Rightarrow>i"
+  where "filter(f,l) == lrec(l, [], \<lambda>x xs g. if f`x then x$g else g)"
 
-definition flat :: "i=>i"
-  where "flat(l) == lrec(l,[],%h t g. h @ g)"
+definition flat :: "i\<Rightarrow>i"
+  where "flat(l) == lrec(l, [], \<lambda>h t g. h @ g)"
 
-definition partition :: "[i,i]=>i" where
-  "partition(f,l) == letrec part l a b be lcase(l,<a,b>,%x xs.
+definition partition :: "[i,i]\<Rightarrow>i" where
+  "partition(f,l) == letrec part l a b be lcase(l, <a,b>, \<lambda>x xs.
                             if f`x then part(xs,x$a,b) else part(xs,a,x$b))
                     in part(l,[],[])"
 
-definition insert :: "[i,i,i]=>i"
-  where "insert(f,a,l) == lrec(l,a$[],%h t g. if f`a`h then a$h$t else h$g)"
+definition insert :: "[i,i,i]\<Rightarrow>i"
+  where "insert(f,a,l) == lrec(l, a$[], \<lambda>h t g. if f`a`h then a$h$t else h$g)"
 
-definition isort :: "i=>i"
-  where "isort(f) == lam l. lrec(l,[],%h t g. insert(f,h,g))"
+definition isort :: "i\<Rightarrow>i"
+  where "isort(f) == lam l. lrec(l, [], \<lambda>h t g. insert(f,h,g))"
 
-definition qsort :: "i=>i" where
-  "qsort(f) == lam l. letrec qsortx l be lcase(l,[],%h t.
+definition qsort :: "i\<Rightarrow>i" where
+  "qsort(f) == lam l. letrec qsortx l be lcase(l, [], \<lambda>h t.
                                    let p be partition(f`h,t)
-                                   in split(p,%x y. qsortx(x) @ h$qsortx(y)))
+                                   in split(p, \<lambda>x y. qsortx(x) @ h$qsortx(y)))
                           in qsortx(l)"
 
 lemmas list_defs = map_def comp_def append_def filter_def flat_def
   insert_def isort_def partition_def qsort_def
 
 lemma listBs [simp]:
-  "!!f g. (f \<circ> g) = (%a. f(g(a)))"
-  "!!a f g. (f \<circ> g)(a) = f(g(a))"
-  "!!f. map(f,[]) = []"
-  "!!f x xs. map(f,x$xs) = f(x)$map(f,xs)"
-  "!!m. [] @ m = m"
-  "!!x xs m. x$xs @ m = x$(xs @ m)"
-  "!!f. filter(f,[]) = []"
-  "!!f x xs. filter(f,x$xs) = if f`x then x$filter(f,xs) else filter(f,xs)"
+  "\<And>f g. (f \<circ> g) = (\<lambda>a. f(g(a)))"
+  "\<And>a f g. (f \<circ> g)(a) = f(g(a))"
+  "\<And>f. map(f,[]) = []"
+  "\<And>f x xs. map(f,x$xs) = f(x)$map(f,xs)"
+  "\<And>m. [] @ m = m"
+  "\<And>x xs m. x$xs @ m = x$(xs @ m)"
+  "\<And>f. filter(f,[]) = []"
+  "\<And>f x xs. filter(f,x$xs) = if f`x then x$filter(f,xs) else filter(f,xs)"
   "flat([]) = []"
-  "!!x xs. flat(x$xs) = x @ flat(xs)"
-  "!!a f. insert(f,a,[]) = a$[]"
-  "!!a f xs. insert(f,a,x$xs) = if f`a`x then a$x$xs else x$insert(f,a,xs)"
+  "\<And>x xs. flat(x$xs) = x @ flat(xs)"
+  "\<And>a f. insert(f,a,[]) = a$[]"
+  "\<And>a f xs. insert(f,a,x$xs) = if f`a`x then a$x$xs else x$insert(f,a,xs)"
   by (simp_all add: list_defs)
 
-lemma nmapBnil: "n:Nat ==> map(f) ^ n ` [] = []"
+lemma nmapBnil: "n:Nat \<Longrightarrow> map(f) ^ n ` [] = []"
   apply (erule Nat_ind)
    apply simp_all
   done
 
-lemma nmapBcons: "n:Nat ==> map(f)^n`(x$xs) = (f^n`x)$(map(f)^n`xs)"
+lemma nmapBcons: "n:Nat \<Longrightarrow> map(f)^n`(x$xs) = (f^n`x)$(map(f)^n`xs)"
   apply (erule Nat_ind)
    apply simp_all
   done
 
 
-lemma mapT: "[| !!x. x:A==>f(x):B;  l : List(A) |] ==> map(f,l) : List(B)"
+lemma mapT: "\<lbrakk>\<And>x. x:A \<Longrightarrow> f(x):B; l : List(A)\<rbrakk> \<Longrightarrow> map(f,l) : List(B)"
   apply (unfold map_def)
-  apply (tactic "typechk_tac @{context} [] 1")
+  apply typechk
   apply blast
   done
 
-lemma appendT: "[| l : List(A);  m : List(A) |] ==> l @ m : List(A)"
+lemma appendT: "\<lbrakk>l : List(A); m : List(A)\<rbrakk> \<Longrightarrow> l @ m : List(A)"
   apply (unfold append_def)
-  apply (tactic "typechk_tac @{context} [] 1")
+  apply typechk
   done
 
 lemma appendTS:
-  "[| l : {l:List(A). m : {m:List(A).P(l @ m)}} |] ==> l @ m : {x:List(A). P(x)}"
+  "\<lbrakk>l : {l:List(A). m : {m:List(A).P(l @ m)}}\<rbrakk> \<Longrightarrow> l @ m : {x:List(A). P(x)}"
   by (blast intro!: appendT)
 
-lemma filterT: "[| f:A->Bool;   l : List(A) |] ==> filter(f,l) : List(A)"
+lemma filterT: "\<lbrakk>f:A->Bool; l : List(A)\<rbrakk> \<Longrightarrow> filter(f,l) : List(A)"
   apply (unfold filter_def)
-  apply (tactic "typechk_tac @{context} [] 1")
+  apply typechk
   done
 
-lemma flatT: "l : List(List(A)) ==> flat(l) : List(A)"
+lemma flatT: "l : List(List(A)) \<Longrightarrow> flat(l) : List(A)"
   apply (unfold flat_def)
-  apply (tactic {* typechk_tac @{context} @{thms appendT} 1 *})
+  apply (typechk appendT)
   done
 
-lemma insertT: "[|  f : A->A->Bool; a:A; l : List(A) |] ==> insert(f,a,l) : List(A)"
+lemma insertT: "\<lbrakk>f : A->A->Bool; a:A; l : List(A)\<rbrakk> \<Longrightarrow> insert(f,a,l) : List(A)"
   apply (unfold insert_def)
-  apply (tactic "typechk_tac @{context} [] 1")
+  apply typechk
   done
 
 lemma insertTS:
-  "[| f : {f:A->A->Bool. a : {a:A. l : {l:List(A).P(insert(f,a,l))}}} |] ==>  
+  "\<lbrakk>f : {f:A->A->Bool. a : {a:A. l : {l:List(A).P(insert(f,a,l))}}} \<rbrakk> \<Longrightarrow>
    insert(f,a,l)  : {x:List(A). P(x)}"
   by (blast intro!: insertT)
 
-lemma partitionT:
-  "[| f:A->Bool;  l : List(A) |] ==> partition(f,l) : List(A)*List(A)"
+lemma partitionT: "\<lbrakk>f:A->Bool; l : List(A)\<rbrakk> \<Longrightarrow> partition(f,l) : List(A)*List(A)"
   apply (unfold partition_def)
-  apply (tactic "typechk_tac @{context} [] 1")
-  apply (tactic "clean_ccs_tac @{context}")
+  apply typechk
+  apply clean_ccs
   apply (rule ListPRI [THEN wfstI, THEN ListPR_wf [THEN wmap_wf, THEN wfI]])
     apply assumption+
   apply (rule ListPRI [THEN wfstI, THEN ListPR_wf [THEN wmap_wf, THEN wfI]])
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/ex/Nat.thy
--- a/src/CCL/ex/Nat.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/ex/Nat.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -6,44 +6,44 @@
 section {* Programs defined over the natural numbers *}
 
 theory Nat
-imports Wfd
+imports "../Wfd"
 begin
 
-definition not :: "i=>i"
+definition not :: "i\<Rightarrow>i"
   where "not(b) == if b then false else true"
 
-definition add :: "[i,i]=>i"  (infixr "#+" 60)
-  where "a #+ b == nrec(a,b,%x g. succ(g))"
+definition add :: "[i,i]\<Rightarrow>i"  (infixr "#+" 60)
+  where "a #+ b == nrec(a, b, \<lambda>x g. succ(g))"
 
-definition mult :: "[i,i]=>i"  (infixr "#*" 60)
-  where "a #* b == nrec(a,zero,%x g. b #+ g)"
+definition mult :: "[i,i]\<Rightarrow>i"  (infixr "#*" 60)
+  where "a #* b == nrec(a, zero, \<lambda>x g. b #+ g)"
 
-definition sub :: "[i,i]=>i"  (infixr "#-" 60)
+definition sub :: "[i,i]\<Rightarrow>i"  (infixr "#-" 60)
   where
     "a #- b ==
-      letrec sub x y be ncase(y,x,%yy. ncase(x,zero,%xx. sub(xx,yy)))
+      letrec sub x y be ncase(y, x, \<lambda>yy. ncase(x, zero, \<lambda>xx. sub(xx,yy)))
       in sub(a,b)"
 
-definition le :: "[i,i]=>i"  (infixr "#<=" 60)
+definition le :: "[i,i]\<Rightarrow>i"  (infixr "#<=" 60)
   where
     "a #<= b ==
-      letrec le x y be ncase(x,true,%xx. ncase(y,false,%yy. le(xx,yy)))
+      letrec le x y be ncase(x, true, \<lambda>xx. ncase(y, false, \<lambda>yy. le(xx,yy)))
       in le(a,b)"
 
-definition lt :: "[i,i]=>i"  (infixr "#<" 60)
+definition lt :: "[i,i]\<Rightarrow>i"  (infixr "#<" 60)
   where "a #< b == not(b #<= a)"
 
-definition div :: "[i,i]=>i"  (infixr "##" 60)
+definition div :: "[i,i]\<Rightarrow>i"  (infixr "##" 60)
   where
     "a ## b ==
       letrec div x y be if x #< y then zero else succ(div(x#-y,y))
       in div(a,b)"
 
-definition ackermann :: "[i,i]=>i"
+definition ackermann :: "[i,i]\<Rightarrow>i"
   where
     "ackermann(a,b) ==
-      letrec ack n m be ncase(n,succ(m),%x.
-        ncase(m,ack(x,succ(zero)),%y. ack(x,ack(succ(x),y))))
+      letrec ack n m be ncase(n, succ(m), \<lambda>x.
+        ncase(m,ack(x,succ(zero)), \<lambda>y. ack(x,ack(succ(x),y))))
       in ack(a,b)"
 
 lemmas nat_defs = not_def add_def mult_def sub_def le_def lt_def ackermann_def napply_def
@@ -60,39 +60,39 @@
   by (simp_all add: nat_defs)
 
 
-lemma napply_f: "n:Nat ==> f^n`f(a) = f^succ(n)`a"
+lemma napply_f: "n:Nat \<Longrightarrow> f^n`f(a) = f^succ(n)`a"
   apply (erule Nat_ind)
    apply simp_all
   done
 
-lemma addT: "[| a:Nat;  b:Nat |] ==> a #+ b : Nat"
+lemma addT: "\<lbrakk>a:Nat; b:Nat\<rbrakk> \<Longrightarrow> a #+ b : Nat"
   apply (unfold add_def)
-  apply (tactic {* typechk_tac @{context} [] 1 *})
+  apply typechk
   done
 
-lemma multT: "[| a:Nat;  b:Nat |] ==> a #* b : Nat"
+lemma multT: "\<lbrakk>a:Nat; b:Nat\<rbrakk> \<Longrightarrow> a #* b : Nat"
   apply (unfold add_def mult_def)
-  apply (tactic {* typechk_tac @{context} [] 1 *})
+  apply typechk
   done
 
 (* Defined to return zero if a<b *)
-lemma subT: "[| a:Nat;  b:Nat |] ==> a #- b : Nat"
+lemma subT: "\<lbrakk>a:Nat; b:Nat\<rbrakk> \<Longrightarrow> a #- b : Nat"
   apply (unfold sub_def)
-  apply (tactic {* typechk_tac @{context} [] 1 *})
-  apply (tactic {* clean_ccs_tac @{context} *})
+  apply typechk
+  apply clean_ccs
   apply (erule NatPRI [THEN wfstI, THEN NatPR_wf [THEN wmap_wf, THEN wfI]])
   done
 
-lemma leT: "[| a:Nat;  b:Nat |] ==> a #<= b : Bool"
+lemma leT: "\<lbrakk>a:Nat; b:Nat\<rbrakk> \<Longrightarrow> a #<= b : Bool"
   apply (unfold le_def)
-  apply (tactic {* typechk_tac @{context} [] 1 *})
-  apply (tactic {* clean_ccs_tac @{context} *})
+  apply typechk
+  apply clean_ccs
   apply (erule NatPRI [THEN wfstI, THEN NatPR_wf [THEN wmap_wf, THEN wfI]])
   done
 
-lemma ltT: "[| a:Nat;  b:Nat |] ==> a #< b : Bool"
+lemma ltT: "\<lbrakk>a:Nat; b:Nat\<rbrakk> \<Longrightarrow> a #< b : Bool"
   apply (unfold not_def lt_def)
-  apply (tactic {* typechk_tac @{context} @{thms leT} 1 *})
+  apply (typechk leT)
   done
 
 
@@ -100,9 +100,9 @@
 
 lemmas relI = NatPR_wf [THEN NatPR_wf [THEN lex_wf, THEN wfI]]
 
-lemma "[| a:Nat;  b:Nat |] ==> ackermann(a,b) : Nat"
+lemma "\<lbrakk>a:Nat; b:Nat\<rbrakk> \<Longrightarrow> ackermann(a,b) : Nat"
   apply (unfold ackermann_def)
-  apply (tactic {* gen_ccs_tac @{context} [] 1 *})
+  apply gen_ccs
   apply (erule NatPRI [THEN lexI1 [THEN relI]] NatPRI [THEN lexI2 [THEN relI]])+
   done
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CCL/ex/Stream.thy
--- a/src/CCL/ex/Stream.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CCL/ex/Stream.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -9,10 +9,10 @@
 imports List
 begin
 
-definition iter1 :: "[i=>i,i]=>i"
+definition iter1 :: "[i\<Rightarrow>i,i]\<Rightarrow>i"
   where "iter1(f,a) == letrec iter x be x$iter(f(x)) in iter(a)"
 
-definition iter2 :: "[i=>i,i]=>i"
+definition iter2 :: "[i\<Rightarrow>i,i]\<Rightarrow>i"
   where "iter2(f,a) == letrec iter x be x$map(f,iter(x)) in iter(a)"
 
 (*
@@ -27,12 +27,11 @@
 lemma map_comp:
   assumes 1: "l:Lists(A)"
   shows "map(f \<circ> g,l) = map(f,map(g,l))"
-  apply (tactic {* eq_coinduct3_tac @{context}
-    "{p. EX x y. p=<x,y> & (EX l:Lists (A) .x=map (f \<circ> g,l) & y=map (f,map (g,l)))}" 1 *})
+  apply (eq_coinduct3 "{p. EX x y. p=<x,y> \<and> (EX l:Lists (A) .x=map (f \<circ> g,l) \<and> y=map (f,map (g,l)))}")
    apply (blast intro: 1)
   apply safe
   apply (drule ListsXH [THEN iffD1])
-  apply (tactic "EQgen_tac @{context} [] 1")
+  apply EQgen
    apply fastforce
   done
 
@@ -40,13 +39,12 @@
 
 lemma map_id:
   assumes 1: "l:Lists(A)"
-  shows "map(%x. x,l) = l"
-  apply (tactic {* eq_coinduct3_tac @{context}
-    "{p. EX x y. p=<x,y> & (EX l:Lists (A) .x=map (%x. x,l) & y=l) }" 1 *})
+  shows "map(\<lambda>x. x, l) = l"
+  apply (eq_coinduct3 "{p. EX x y. p=<x,y> \<and> (EX l:Lists (A) .x=map (\<lambda>x. x,l) \<and> y=l) }")
   apply (blast intro: 1)
   apply safe
   apply (drule ListsXH [THEN iffD1])
-  apply (tactic "EQgen_tac @{context} [] 1")
+  apply EQgen
   apply blast
   done
 
@@ -57,14 +55,14 @@
   assumes "l:Lists(A)"
     and "m:Lists(A)"
   shows "map(f,l@m) = map(f,l) @ map(f,m)"
-  apply (tactic {* eq_coinduct3_tac @{context}
-    "{p. EX x y. p=<x,y> & (EX l:Lists (A). EX m:Lists (A). x=map (f,l@m) & y=map (f,l) @ map (f,m))}" 1 *})
+  apply (eq_coinduct3
+    "{p. EX x y. p=<x,y> \<and> (EX l:Lists (A). EX m:Lists (A). x=map (f,l@m) \<and> y=map (f,l) @ map (f,m))}")
   apply (blast intro: assms)
   apply safe
   apply (drule ListsXH [THEN iffD1])
-  apply (tactic "EQgen_tac @{context} [] 1")
+  apply EQgen
   apply (drule ListsXH [THEN iffD1])
-  apply (tactic "EQgen_tac @{context} [] 1")
+  apply EQgen
   apply blast
   done
 
@@ -76,12 +74,12 @@
     and "l:Lists(A)"
     and "m:Lists(A)"
   shows "k @ l @ m = (k @ l) @ m"
-  apply (tactic {* eq_coinduct3_tac @{context}
-    "{p. EX x y. p=<x,y> & (EX k:Lists (A). EX l:Lists (A). EX m:Lists (A). x=k @ l @ m & y= (k @ l) @ m) }" 1*})
+  apply (eq_coinduct3
+    "{p. EX x y. p=<x,y> \<and> (EX k:Lists (A). EX l:Lists (A). EX m:Lists (A). x=k @ l @ m \<and> y= (k @ l) @ m) }")
   apply (blast intro: assms)
   apply safe
   apply (drule ListsXH [THEN iffD1])
-  apply (tactic "EQgen_tac @{context} [] 1")
+  apply EQgen
    prefer 2
    apply blast
   apply (tactic {* DEPTH_SOLVE (etac (XH_to_E @{thm ListsXH}) 1
@@ -94,12 +92,11 @@
 lemma ilist_append:
   assumes "l:ILists(A)"
   shows "l @ m = l"
-  apply (tactic {* eq_coinduct3_tac @{context}
-    "{p. EX x y. p=<x,y> & (EX l:ILists (A) .EX m. x=l@m & y=l)}" 1 *})
+  apply (eq_coinduct3 "{p. EX x y. p=<x,y> \<and> (EX l:ILists (A) .EX m. x=l@m \<and> y=l)}")
   apply (blast intro: assms)
   apply safe
   apply (drule IListsXH [THEN iffD1])
-  apply (tactic "EQgen_tac @{context} [] 1")
+  apply EQgen
   apply blast
   done
 
@@ -121,17 +118,17 @@
   done
 
 lemma iter2Blemma:
-  "n:Nat ==>  
+  "n:Nat \<Longrightarrow>  
     map(f) ^ n ` iter2(f,a) = (f ^ n ` a) $ (map(f) ^ n ` map(f,iter2(f,a)))"
-  apply (rule_tac P = "%x. ?lhs (x) = ?rhs" in iter2B [THEN ssubst])
+  apply (rule_tac P = "\<lambda>x. ?lhs (x) = ?rhs" in iter2B [THEN ssubst])
   apply (simp add: nmapBcons)
   done
 
 lemma iter1_iter2_eq: "iter1(f,a) = iter2(f,a)"
-  apply (tactic {* eq_coinduct3_tac @{context}
-    "{p. EX x y. p=<x,y> & (EX n:Nat. x=iter1 (f,f^n`a) & y=map (f) ^n`iter2 (f,a))}" 1*})
+  apply (eq_coinduct3
+    "{p. EX x y. p=<x,y> \<and> (EX n:Nat. x=iter1 (f,f^n`a) \<and> y=map (f) ^n`iter2 (f,a))}")
   apply (fast intro!: napplyBzero [symmetric] napplyBzero [symmetric, THEN arg_cong])
-  apply (tactic {* EQgen_tac @{context} [@{thm iter1B}, @{thm iter2Blemma}] 1 *})
+  apply (EQgen iter1B iter2Blemma)
   apply (subst napply_f, assumption)
   apply (rule_tac f1 = f in napplyBsucc [THEN subst])
   apply blast
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CTT/Arith.thy
--- a/src/CTT/Arith.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CTT/Arith.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -12,28 +12,28 @@
 subsection {* Arithmetic operators and their definitions *}
 
 definition
-  add :: "[i,i]=>i"   (infixr "#+" 65) where
-  "a#+b == rec(a, b, %u v. succ(v))"
+  add :: "[i,i]\<Rightarrow>i"   (infixr "#+" 65) where
+  "a#+b == rec(a, b, \<lambda>u v. succ(v))"
 
 definition
-  diff :: "[i,i]=>i"   (infixr "-" 65) where
-  "a-b == rec(b, a, %u v. rec(v, 0, %x y. x))"
+  diff :: "[i,i]\<Rightarrow>i"   (infixr "-" 65) where
+  "a-b == rec(b, a, \<lambda>u v. rec(v, 0, \<lambda>x y. x))"
 
 definition
-  absdiff :: "[i,i]=>i"   (infixr "|-|" 65) where
+  absdiff :: "[i,i]\<Rightarrow>i"   (infixr "|-|" 65) where
   "a|-|b == (a-b) #+ (b-a)"
 
 definition
-  mult :: "[i,i]=>i"   (infixr "#*" 70) where
-  "a#*b == rec(a, 0, %u v. b #+ v)"
+  mult :: "[i,i]\<Rightarrow>i"   (infixr "#*" 70) where
+  "a#*b == rec(a, 0, \<lambda>u v. b #+ v)"
 
 definition
-  mod :: "[i,i]=>i"   (infixr "mod" 70) where
+  mod :: "[i,i]\<Rightarrow>i"   (infixr "mod" 70) where
   "a mod b == rec(a, 0, %u v. rec(succ(v) |-| b, 0, %x y. succ(v)))"
 
 definition
-  div :: "[i,i]=>i"   (infixr "div" 70) where
-  "a div b == rec(a, 0, %u v. rec(succ(u) mod b, succ(v), %x y. v))"
+  div :: "[i,i]\<Rightarrow>i"   (infixr "div" 70) where
+  "a div b == rec(a, 0, \<lambda>u v. rec(succ(u) mod b, succ(v), \<lambda>x y. v))"
 
 
 notation (xsymbols)
@@ -52,27 +52,27 @@
 
 (*typing of add: short and long versions*)
 
-lemma add_typing: "[| a:N;  b:N |] ==> a #+ b : N"
+lemma add_typing: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> a #+ b : N"
 apply (unfold arith_defs)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
-lemma add_typingL: "[| a=c:N;  b=d:N |] ==> a #+ b = c #+ d : N"
+lemma add_typingL: "\<lbrakk>a = c:N; b = d:N\<rbrakk> \<Longrightarrow> a #+ b = c #+ d : N"
 apply (unfold arith_defs)
-apply (tactic "equal_tac @{context} []")
+apply equal
 done
 
 
 (*computation for add: 0 and successor cases*)
 
-lemma addC0: "b:N ==> 0 #+ b = b : N"
+lemma addC0: "b:N \<Longrightarrow> 0 #+ b = b : N"
 apply (unfold arith_defs)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
-lemma addC_succ: "[| a:N;  b:N |] ==> succ(a) #+ b = succ(a #+ b) : N"
+lemma addC_succ: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> succ(a) #+ b = succ(a #+ b) : N"
 apply (unfold arith_defs)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 
@@ -80,26 +80,26 @@
 
 (*typing of mult: short and long versions*)
 
-lemma mult_typing: "[| a:N;  b:N |] ==> a #* b : N"
+lemma mult_typing: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> a #* b : N"
 apply (unfold arith_defs)
-apply (tactic {* typechk_tac @{context} [@{thm add_typing}] *})
+apply (typechk add_typing)
 done
 
-lemma mult_typingL: "[| a=c:N;  b=d:N |] ==> a #* b = c #* d : N"
+lemma mult_typingL: "\<lbrakk>a = c:N; b = d:N\<rbrakk> \<Longrightarrow> a #* b = c #* d : N"
 apply (unfold arith_defs)
-apply (tactic {* equal_tac @{context} [@{thm add_typingL}] *})
+apply (equal add_typingL)
 done
 
 (*computation for mult: 0 and successor cases*)
 
-lemma multC0: "b:N ==> 0 #* b = 0 : N"
+lemma multC0: "b:N \<Longrightarrow> 0 #* b = 0 : N"
 apply (unfold arith_defs)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
-lemma multC_succ: "[| a:N;  b:N |] ==> succ(a) #* b = b #+ (a #* b) : N"
+lemma multC_succ: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> succ(a) #* b = b #+ (a #* b) : N"
 apply (unfold arith_defs)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 
@@ -107,40 +107,40 @@
 
 (*typing of difference*)
 
-lemma diff_typing: "[| a:N;  b:N |] ==> a - b : N"
+lemma diff_typing: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> a - b : N"
 apply (unfold arith_defs)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
-lemma diff_typingL: "[| a=c:N;  b=d:N |] ==> a - b = c - d : N"
+lemma diff_typingL: "\<lbrakk>a = c:N; b = d:N\<rbrakk> \<Longrightarrow> a - b = c - d : N"
 apply (unfold arith_defs)
-apply (tactic "equal_tac @{context} []")
+apply equal
 done
 
 
 (*computation for difference: 0 and successor cases*)
 
-lemma diffC0: "a:N ==> a - 0 = a : N"
+lemma diffC0: "a:N \<Longrightarrow> a - 0 = a : N"
 apply (unfold arith_defs)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
-(*Note: rec(a, 0, %z w.z) is pred(a). *)
+(*Note: rec(a, 0, \<lambda>z w.z) is pred(a). *)
 
-lemma diff_0_eq_0: "b:N ==> 0 - b = 0 : N"
+lemma diff_0_eq_0: "b:N \<Longrightarrow> 0 - b = 0 : N"
 apply (unfold arith_defs)
-apply (tactic {* NE_tac @{context} "b" 1 *})
-apply (tactic "hyp_rew_tac @{context} []")
+apply (NE b)
+apply hyp_rew
 done
 
 
 (*Essential to simplify FIRST!!  (Else we get a critical pair)
   succ(a) - succ(b) rewrites to   pred(succ(a) - b)  *)
-lemma diff_succ_succ: "[| a:N;  b:N |] ==> succ(a) - succ(b) = a - b : N"
+lemma diff_succ_succ: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> succ(a) - succ(b) = a - b : N"
 apply (unfold arith_defs)
-apply (tactic "hyp_rew_tac @{context} []")
-apply (tactic {* NE_tac @{context} "b" 1 *})
-apply (tactic "hyp_rew_tac @{context} []")
+apply hyp_rew
+apply (NE b)
+apply hyp_rew
 done
 
 
@@ -174,67 +174,77 @@
 local val congr_rls = @{thms congr_rls} in
 
 fun arith_rew_tac ctxt prems = make_rew_tac ctxt
-    (Arith_simp.norm_tac ctxt (congr_rls, prems))
+  (Arith_simp.norm_tac ctxt (congr_rls, prems))
 
 fun hyp_arith_rew_tac ctxt prems = make_rew_tac ctxt
-    (Arith_simp.cond_norm_tac ctxt (prove_cond_tac, congr_rls, prems))
+  (Arith_simp.cond_norm_tac ctxt (prove_cond_tac, congr_rls, prems))
 
 end
 *}
 
+method_setup arith_rew = {*
+  Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD (arith_rew_tac ctxt ths))
+*}
+
+method_setup hyp_arith_rew = {*
+  Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD (hyp_arith_rew_tac ctxt ths))
+*}
+
 
 subsection {* Addition *}
 
 (*Associative law for addition*)
-lemma add_assoc: "[| a:N;  b:N;  c:N |] ==> (a #+ b) #+ c = a #+ (b #+ c) : N"
-apply (tactic {* NE_tac @{context} "a" 1 *})
-apply (tactic "hyp_arith_rew_tac @{context} []")
+lemma add_assoc: "\<lbrakk>a:N; b:N; c:N\<rbrakk> \<Longrightarrow> (a #+ b) #+ c = a #+ (b #+ c) : N"
+apply (NE a)
+apply hyp_arith_rew
 done
 
 
 (*Commutative law for addition.  Can be proved using three inductions.
   Must simplify after first induction!  Orientation of rewrites is delicate*)
-lemma add_commute: "[| a:N;  b:N |] ==> a #+ b = b #+ a : N"
-apply (tactic {* NE_tac @{context} "a" 1 *})
-apply (tactic "hyp_arith_rew_tac @{context} []")
-apply (tactic {* NE_tac @{context} "b" 2 *})
+lemma add_commute: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> a #+ b = b #+ a : N"
+apply (NE a)
+apply hyp_arith_rew
 apply (rule sym_elem)
-apply (tactic {* NE_tac @{context} "b" 1 *})
-apply (tactic "hyp_arith_rew_tac @{context} []")
+prefer 2
+apply (NE b)
+prefer 4
+apply (NE b)
+apply hyp_arith_rew
 done
 
 
 subsection {* Multiplication *}
 
 (*right annihilation in product*)
-lemma mult_0_right: "a:N ==> a #* 0 = 0 : N"
-apply (tactic {* NE_tac @{context} "a" 1 *})
-apply (tactic "hyp_arith_rew_tac @{context} []")
+lemma mult_0_right: "a:N \<Longrightarrow> a #* 0 = 0 : N"
+apply (NE a)
+apply hyp_arith_rew
 done
 
 (*right successor law for multiplication*)
-lemma mult_succ_right: "[| a:N;  b:N |] ==> a #* succ(b) = a #+ (a #* b) : N"
-apply (tactic {* NE_tac @{context} "a" 1 *})
-apply (tactic {* hyp_arith_rew_tac @{context} [@{thm add_assoc} RS @{thm sym_elem}] *})
+lemma mult_succ_right: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> a #* succ(b) = a #+ (a #* b) : N"
+apply (NE a)
+apply (hyp_arith_rew add_assoc [THEN sym_elem])
 apply (assumption | rule add_commute mult_typingL add_typingL intrL_rls refl_elem)+
 done
 
 (*Commutative law for multiplication*)
-lemma mult_commute: "[| a:N;  b:N |] ==> a #* b = b #* a : N"
-apply (tactic {* NE_tac @{context} "a" 1 *})
-apply (tactic {* hyp_arith_rew_tac @{context} [@{thm mult_0_right}, @{thm mult_succ_right}] *})
+lemma mult_commute: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> a #* b = b #* a : N"
+apply (NE a)
+apply (hyp_arith_rew mult_0_right mult_succ_right)
 done
 
 (*addition distributes over multiplication*)
-lemma add_mult_distrib: "[| a:N;  b:N;  c:N |] ==> (a #+ b) #* c = (a #* c) #+ (b #* c) : N"
-apply (tactic {* NE_tac @{context} "a" 1 *})
-apply (tactic {* hyp_arith_rew_tac @{context} [@{thm add_assoc} RS @{thm sym_elem}] *})
+lemma add_mult_distrib: "\<lbrakk>a:N; b:N; c:N\<rbrakk> \<Longrightarrow> (a #+ b) #* c = (a #* c) #+ (b #* c) : N"
+apply (NE a)
+apply (hyp_arith_rew add_assoc [THEN sym_elem])
 done
 
 (*Associative law for multiplication*)
-lemma mult_assoc: "[| a:N;  b:N;  c:N |] ==> (a #* b) #* c = a #* (b #* c) : N"
-apply (tactic {* NE_tac @{context} "a" 1 *})
-apply (tactic {* hyp_arith_rew_tac @{context} [@{thm add_mult_distrib}] *})
+lemma mult_assoc: "\<lbrakk>a:N; b:N; c:N\<rbrakk> \<Longrightarrow> (a #* b) #* c = a #* (b #* c) : N"
+apply (NE a)
+apply (hyp_arith_rew add_mult_distrib)
 done
 
 
@@ -244,34 +254,36 @@
 Difference on natural numbers, without negative numbers
   a - b = 0  iff  a<=b    a - b = succ(c) iff a>b   *}
 
-lemma diff_self_eq_0: "a:N ==> a - a = 0 : N"
-apply (tactic {* NE_tac @{context} "a" 1 *})
-apply (tactic "hyp_arith_rew_tac @{context} []")
+lemma diff_self_eq_0: "a:N \<Longrightarrow> a - a = 0 : N"
+apply (NE a)
+apply hyp_arith_rew
 done
 
 
-lemma add_0_right: "[| c : N; 0 : N; c : N |] ==> c #+ 0 = c : N"
+lemma add_0_right: "\<lbrakk>c : N; 0 : N; c : N\<rbrakk> \<Longrightarrow> c #+ 0 = c : N"
   by (rule addC0 [THEN [3] add_commute [THEN trans_elem]])
 
 (*Addition is the inverse of subtraction: if b<=x then b#+(x-b) = x.
   An example of induction over a quantified formula (a product).
   Uses rewriting with a quantified, implicative inductive hypothesis.*)
 schematic_lemma add_diff_inverse_lemma:
-  "b:N ==> ?a : PROD x:N. Eq(N, b-x, 0) --> Eq(N, b #+ (x-b), x)"
-apply (tactic {* NE_tac @{context} "b" 1 *})
+  "b:N \<Longrightarrow> ?a : PROD x:N. Eq(N, b-x, 0) --> Eq(N, b #+ (x-b), x)"
+apply (NE b)
 (*strip one "universal quantifier" but not the "implication"*)
 apply (rule_tac [3] intr_rls)
 (*case analysis on x in
     (succ(u) <= x) --> (succ(u)#+(x-succ(u)) = x) *)
-apply (tactic {* NE_tac @{context} "x" 4 *}, tactic "assume_tac @{context} 4")
+prefer 4
+apply (NE x)
+apply assumption
 (*Prepare for simplification of types -- the antecedent succ(u)<=x *)
-apply (rule_tac [5] replace_type)
-apply (rule_tac [4] replace_type)
-apply (tactic "arith_rew_tac @{context} []")
+apply (rule_tac [2] replace_type)
+apply (rule_tac [1] replace_type)
+apply arith_rew
 (*Solves first 0 goal, simplifies others.  Two sugbgoals remain.
   Both follow by rewriting, (2) using quantified induction hyp*)
-apply (tactic "intr_tac @{context} []") (*strips remaining PRODs*)
-apply (tactic {* hyp_arith_rew_tac @{context} [@{thm add_0_right}] *})
+apply intr (*strips remaining PRODs*)
+apply (hyp_arith_rew add_0_right)
 apply assumption
 done
 
@@ -280,7 +292,7 @@
   Using ProdE does not work -- for ?B(?a) is ambiguous.
   Instead, add_diff_inverse_lemma states the desired induction scheme
     the use of RS below instantiates Vars in ProdE automatically. *)
-lemma add_diff_inverse: "[| a:N;  b:N;  b-a = 0 : N |] ==> b #+ (a-b) = a : N"
+lemma add_diff_inverse: "\<lbrakk>a:N; b:N; b - a = 0 : N\<rbrakk> \<Longrightarrow> b #+ (a-b) = a : N"
 apply (rule EqE)
 apply (rule add_diff_inverse_lemma [THEN ProdE, THEN ProdE])
 apply (assumption | rule EqI)+
@@ -291,82 +303,80 @@
 
 (*typing of absolute difference: short and long versions*)
 
-lemma absdiff_typing: "[| a:N;  b:N |] ==> a |-| b : N"
+lemma absdiff_typing: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> a |-| b : N"
 apply (unfold arith_defs)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
-lemma absdiff_typingL: "[| a=c:N;  b=d:N |] ==> a |-| b = c |-| d : N"
+lemma absdiff_typingL: "\<lbrakk>a = c:N; b = d:N\<rbrakk> \<Longrightarrow> a |-| b = c |-| d : N"
 apply (unfold arith_defs)
-apply (tactic "equal_tac @{context} []")
+apply equal
 done
 
-lemma absdiff_self_eq_0: "a:N ==> a |-| a = 0 : N"
+lemma absdiff_self_eq_0: "a:N \<Longrightarrow> a |-| a = 0 : N"
 apply (unfold absdiff_def)
-apply (tactic {* arith_rew_tac @{context} [@{thm diff_self_eq_0}] *})
+apply (arith_rew diff_self_eq_0)
 done
 
-lemma absdiffC0: "a:N ==> 0 |-| a = a : N"
+lemma absdiffC0: "a:N \<Longrightarrow> 0 |-| a = a : N"
 apply (unfold absdiff_def)
-apply (tactic "hyp_arith_rew_tac @{context} []")
+apply hyp_arith_rew
 done
 
 
-lemma absdiff_succ_succ: "[| a:N;  b:N |] ==> succ(a) |-| succ(b)  =  a |-| b : N"
+lemma absdiff_succ_succ: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> succ(a) |-| succ(b)  =  a |-| b : N"
 apply (unfold absdiff_def)
-apply (tactic "hyp_arith_rew_tac @{context} []")
+apply hyp_arith_rew
 done
 
 (*Note how easy using commutative laws can be?  ...not always... *)
-lemma absdiff_commute: "[| a:N;  b:N |] ==> a |-| b = b |-| a : N"
+lemma absdiff_commute: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> a |-| b = b |-| a : N"
 apply (unfold absdiff_def)
 apply (rule add_commute)
-apply (tactic {* typechk_tac @{context} [@{thm diff_typing}] *})
+apply (typechk diff_typing)
 done
 
 (*If a+b=0 then a=0.   Surprisingly tedious*)
-schematic_lemma add_eq0_lemma: "[| a:N;  b:N |] ==> ?c : PROD u: Eq(N,a#+b,0) .  Eq(N,a,0)"
-apply (tactic {* NE_tac @{context} "a" 1 *})
+schematic_lemma add_eq0_lemma: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> ?c : PROD u: Eq(N,a#+b,0) .  Eq(N,a,0)"
+apply (NE a)
 apply (rule_tac [3] replace_type)
-apply (tactic "arith_rew_tac @{context} []")
-apply (tactic "intr_tac @{context} []") (*strips remaining PRODs*)
+apply arith_rew
+apply intr (*strips remaining PRODs*)
 apply (rule_tac [2] zero_ne_succ [THEN FE])
 apply (erule_tac [3] EqE [THEN sym_elem])
-apply (tactic {* typechk_tac @{context} [@{thm add_typing}] *})
+apply (typechk add_typing)
 done
 
 (*Version of above with the premise  a+b=0.
   Again, resolution instantiates variables in ProdE *)
-lemma add_eq0: "[| a:N;  b:N;  a #+ b = 0 : N |] ==> a = 0 : N"
+lemma add_eq0: "\<lbrakk>a:N; b:N; a #+ b = 0 : N\<rbrakk> \<Longrightarrow> a = 0 : N"
 apply (rule EqE)
 apply (rule add_eq0_lemma [THEN ProdE])
 apply (rule_tac [3] EqI)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
 (*Here is a lemma to infer a-b=0 and b-a=0 from a|-|b=0, below. *)
 schematic_lemma absdiff_eq0_lem:
-    "[| a:N;  b:N;  a |-| b = 0 : N |] ==>
-     ?a : SUM v: Eq(N, a-b, 0) . Eq(N, b-a, 0)"
+  "\<lbrakk>a:N; b:N; a |-| b = 0 : N\<rbrakk> \<Longrightarrow> ?a : SUM v: Eq(N, a-b, 0) . Eq(N, b-a, 0)"
 apply (unfold absdiff_def)
-apply (tactic "intr_tac @{context} []")
-apply (tactic "eqintr_tac @{context}")
+apply intr
+apply eqintr
 apply (rule_tac [2] add_eq0)
 apply (rule add_eq0)
 apply (rule_tac [6] add_commute [THEN trans_elem])
-apply (tactic {* typechk_tac @{context} [@{thm diff_typing}] *})
+apply (typechk diff_typing)
 done
 
 (*if  a |-| b = 0  then  a = b
   proof: a-b=0 and b-a=0, so b = a+(b-a) = a+0 = a*)
-lemma absdiff_eq0: "[| a |-| b = 0 : N;  a:N;  b:N |] ==> a = b : N"
+lemma absdiff_eq0: "\<lbrakk>a |-| b = 0 : N; a:N; b:N\<rbrakk> \<Longrightarrow> a = b : N"
 apply (rule EqE)
 apply (rule absdiff_eq0_lem [THEN SumE])
-apply (tactic "TRYALL (assume_tac @{context})")
-apply (tactic "eqintr_tac @{context}")
+apply eqintr
 apply (rule add_diff_inverse [THEN sym_elem, THEN trans_elem])
-apply (rule_tac [3] EqE, tactic "assume_tac @{context} 3")
-apply (tactic {* hyp_arith_rew_tac @{context} [@{thm add_0_right}] *})
+apply (erule_tac [3] EqE)
+apply (hyp_arith_rew add_0_right)
 done
 
 
@@ -374,41 +384,41 @@
 
 (*typing of remainder: short and long versions*)
 
-lemma mod_typing: "[| a:N;  b:N |] ==> a mod b : N"
+lemma mod_typing: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> a mod b : N"
 apply (unfold mod_def)
-apply (tactic {* typechk_tac @{context} [@{thm absdiff_typing}] *})
+apply (typechk absdiff_typing)
 done
 
-lemma mod_typingL: "[| a=c:N;  b=d:N |] ==> a mod b = c mod d : N"
+lemma mod_typingL: "\<lbrakk>a = c:N; b = d:N\<rbrakk> \<Longrightarrow> a mod b = c mod d : N"
 apply (unfold mod_def)
-apply (tactic {* equal_tac @{context} [@{thm absdiff_typingL}] *})
+apply (equal absdiff_typingL)
 done
 
 
 (*computation for  mod : 0 and successor cases*)
 
-lemma modC0: "b:N ==> 0 mod b = 0 : N"
+lemma modC0: "b:N \<Longrightarrow> 0 mod b = 0 : N"
 apply (unfold mod_def)
-apply (tactic {* rew_tac @{context} [@{thm absdiff_typing}] *})
+apply (rew absdiff_typing)
 done
 
-lemma modC_succ:
-"[| a:N; b:N |] ==> succ(a) mod b = rec(succ(a mod b) |-| b, 0, %x y. succ(a mod b)) : N"
+lemma modC_succ: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow>
+  succ(a) mod b = rec(succ(a mod b) |-| b, 0, \<lambda>x y. succ(a mod b)) : N"
 apply (unfold mod_def)
-apply (tactic {* rew_tac @{context} [@{thm absdiff_typing}] *})
+apply (rew absdiff_typing)
 done
 
 
 (*typing of quotient: short and long versions*)
 
-lemma div_typing: "[| a:N;  b:N |] ==> a div b : N"
+lemma div_typing: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> a div b : N"
 apply (unfold div_def)
-apply (tactic {* typechk_tac @{context} [@{thm absdiff_typing}, @{thm mod_typing}] *})
+apply (typechk absdiff_typing mod_typing)
 done
 
-lemma div_typingL: "[| a=c:N;  b=d:N |] ==> a div b = c div d : N"
+lemma div_typingL: "\<lbrakk>a = c:N; b = d:N\<rbrakk> \<Longrightarrow> a div b = c div d : N"
 apply (unfold div_def)
-apply (tactic {* equal_tac @{context} [@{thm absdiff_typingL}, @{thm mod_typingL}] *})
+apply (equal absdiff_typingL mod_typingL)
 done
 
 lemmas div_typing_rls = mod_typing div_typing absdiff_typing
@@ -416,54 +426,51 @@
 
 (*computation for quotient: 0 and successor cases*)
 
-lemma divC0: "b:N ==> 0 div b = 0 : N"
+lemma divC0: "b:N \<Longrightarrow> 0 div b = 0 : N"
 apply (unfold div_def)
-apply (tactic {* rew_tac @{context} [@{thm mod_typing}, @{thm absdiff_typing}] *})
+apply (rew mod_typing absdiff_typing)
 done
 
-lemma divC_succ:
- "[| a:N;  b:N |] ==> succ(a) div b =
-     rec(succ(a) mod b, succ(a div b), %x y. a div b) : N"
+lemma divC_succ: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow>
+  succ(a) div b = rec(succ(a) mod b, succ(a div b), \<lambda>x y. a div b) : N"
 apply (unfold div_def)
-apply (tactic {* rew_tac @{context} [@{thm mod_typing}] *})
+apply (rew mod_typing)
 done
 
 
 (*Version of above with same condition as the  mod  one*)
-lemma divC_succ2: "[| a:N;  b:N |] ==>
-     succ(a) div b =rec(succ(a mod b) |-| b, succ(a div b), %x y. a div b) : N"
+lemma divC_succ2: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow>
+  succ(a) div b =rec(succ(a mod b) |-| b, succ(a div b), \<lambda>x y. a div b) : N"
 apply (rule divC_succ [THEN trans_elem])
-apply (tactic {* rew_tac @{context} (@{thms div_typing_rls} @ [@{thm modC_succ}]) *})
-apply (tactic {* NE_tac @{context} "succ (a mod b) |-|b" 1 *})
-apply (tactic {* rew_tac @{context} [@{thm mod_typing}, @{thm div_typing}, @{thm absdiff_typing}] *})
+apply (rew div_typing_rls modC_succ)
+apply (NE "succ (a mod b) |-|b")
+apply (rew mod_typing div_typing absdiff_typing)
 done
 
 (*for case analysis on whether a number is 0 or a successor*)
-lemma iszero_decidable: "a:N ==> rec(a, inl(eq), %ka kb. inr(<ka, eq>)) :
+lemma iszero_decidable: "a:N \<Longrightarrow> rec(a, inl(eq), \<lambda>ka kb. inr(<ka, eq>)) :
                       Eq(N,a,0) + (SUM x:N. Eq(N,a, succ(x)))"
-apply (tactic {* NE_tac @{context} "a" 1 *})
+apply (NE a)
 apply (rule_tac [3] PlusI_inr)
 apply (rule_tac [2] PlusI_inl)
-apply (tactic "eqintr_tac @{context}")
-apply (tactic "equal_tac @{context} []")
+apply eqintr
+apply equal
 done
 
 (*Main Result.  Holds when b is 0 since   a mod 0 = a     and    a div 0 = 0  *)
-lemma mod_div_equality: "[| a:N;  b:N |] ==> a mod b  #+  (a div b) #* b = a : N"
-apply (tactic {* NE_tac @{context} "a" 1 *})
-apply (tactic {* arith_rew_tac @{context} (@{thms div_typing_rls} @
-  [@{thm modC0}, @{thm modC_succ}, @{thm divC0}, @{thm divC_succ2}]) *})
+lemma mod_div_equality: "\<lbrakk>a:N; b:N\<rbrakk> \<Longrightarrow> a mod b #+ (a div b) #* b = a : N"
+apply (NE a)
+apply (arith_rew div_typing_rls modC0 modC_succ divC0 divC_succ2)
 apply (rule EqE)
 (*case analysis on   succ(u mod b)|-|b  *)
 apply (rule_tac a1 = "succ (u mod b) |-| b" in iszero_decidable [THEN PlusE])
 apply (erule_tac [3] SumE)
-apply (tactic {* hyp_arith_rew_tac @{context} (@{thms div_typing_rls} @
-  [@{thm modC0}, @{thm modC_succ}, @{thm divC0}, @{thm divC_succ2}]) *})
+apply (hyp_arith_rew div_typing_rls modC0 modC_succ divC0 divC_succ2)
 (*Replace one occurrence of  b  by succ(u mod b).  Clumsy!*)
 apply (rule add_typingL [THEN trans_elem])
 apply (erule EqE [THEN absdiff_eq0, THEN sym_elem])
 apply (rule_tac [3] refl_elem)
-apply (tactic {* hyp_arith_rew_tac @{context} @{thms div_typing_rls} *})
+apply (hyp_arith_rew div_typing_rls)
 done
 
 end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CTT/Bool.thy
--- a/src/CTT/Bool.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CTT/Bool.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -22,8 +22,8 @@
   "false == inr(tt)"
 
 definition
-  cond :: "[i,i,i]=>i" where
-  "cond(a,b,c) == when(a, %u. b, %u. c)"
+  cond :: "[i,i,i]\<Rightarrow>i" where
+  "cond(a,b,c) == when(a, \<lambda>u. b, \<lambda>u. c)"
 
 lemmas bool_defs = Bool_def true_def false_def cond_def
 
@@ -33,7 +33,7 @@
 (*formation rule*)
 lemma boolF: "Bool type"
 apply (unfold bool_defs)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
 
@@ -41,26 +41,24 @@
 
 lemma boolI_true: "true : Bool"
 apply (unfold bool_defs)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
 lemma boolI_false: "false : Bool"
 apply (unfold bool_defs)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
 (*elimination rule: typing of cond*)
-lemma boolE: 
-    "[| p:Bool;  a : C(true);  b : C(false) |] ==> cond(p,a,b) : C(p)"
+lemma boolE: "\<lbrakk>p:Bool; a : C(true); b : C(false)\<rbrakk> \<Longrightarrow> cond(p,a,b) : C(p)"
 apply (unfold bool_defs)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 apply (erule_tac [!] TE)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
-lemma boolEL: 
-    "[| p = q : Bool;  a = c : C(true);  b = d : C(false) |]  
-     ==> cond(p,a,b) = cond(q,c,d) : C(p)"
+lemma boolEL: "\<lbrakk>p = q : Bool; a = c : C(true); b = d : C(false)\<rbrakk>
+  \<Longrightarrow> cond(p,a,b) = cond(q,c,d) : C(p)"
 apply (unfold bool_defs)
 apply (rule PlusEL)
 apply (erule asm_rl refl_elem [THEN TEL])+
@@ -68,22 +66,20 @@
 
 (*computation rules for true, false*)
 
-lemma boolC_true: 
-    "[| a : C(true);  b : C(false) |] ==> cond(true,a,b) = a : C(true)"
+lemma boolC_true: "\<lbrakk>a : C(true); b : C(false)\<rbrakk> \<Longrightarrow> cond(true,a,b) = a : C(true)"
 apply (unfold bool_defs)
 apply (rule comp_rls)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 apply (erule_tac [!] TE)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
-lemma boolC_false: 
-    "[| a : C(true);  b : C(false) |] ==> cond(false,a,b) = b : C(false)"
+lemma boolC_false: "\<lbrakk>a : C(true); b : C(false)\<rbrakk> \<Longrightarrow> cond(false,a,b) = b : C(false)"
 apply (unfold bool_defs)
 apply (rule comp_rls)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 apply (erule_tac [!] TE)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
 end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CTT/CTT.thy
--- a/src/CTT/CTT.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CTT/CTT.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -20,56 +20,56 @@
   (*Types*)
   F         :: "t"
   T         :: "t"          (*F is empty, T contains one element*)
-  contr     :: "i=>i"
+  contr     :: "i\<Rightarrow>i"
   tt        :: "i"
   (*Natural numbers*)
   N         :: "t"
-  succ      :: "i=>i"
-  rec       :: "[i, i, [i,i]=>i] => i"
+  succ      :: "i\<Rightarrow>i"
+  rec       :: "[i, i, [i,i]\<Rightarrow>i] \<Rightarrow> i"
   (*Unions*)
-  inl       :: "i=>i"
-  inr       :: "i=>i"
-  when      :: "[i, i=>i, i=>i]=>i"
+  inl       :: "i\<Rightarrow>i"
+  inr       :: "i\<Rightarrow>i"
+  when      :: "[i, i\<Rightarrow>i, i\<Rightarrow>i]\<Rightarrow>i"
   (*General Sum and Binary Product*)
-  Sum       :: "[t, i=>t]=>t"
-  fst       :: "i=>i"
-  snd       :: "i=>i"
-  split     :: "[i, [i,i]=>i] =>i"
+  Sum       :: "[t, i\<Rightarrow>t]\<Rightarrow>t"
+  fst       :: "i\<Rightarrow>i"
+  snd       :: "i\<Rightarrow>i"
+  split     :: "[i, [i,i]\<Rightarrow>i] \<Rightarrow>i"
   (*General Product and Function Space*)
-  Prod      :: "[t, i=>t]=>t"
+  Prod      :: "[t, i\<Rightarrow>t]\<Rightarrow>t"
   (*Types*)
-  Plus      :: "[t,t]=>t"           (infixr "+" 40)
+  Plus      :: "[t,t]\<Rightarrow>t"           (infixr "+" 40)
   (*Equality type*)
-  Eq        :: "[t,i,i]=>t"
+  Eq        :: "[t,i,i]\<Rightarrow>t"
   eq        :: "i"
   (*Judgements*)
-  Type      :: "t => prop"          ("(_ type)" [10] 5)
-  Eqtype    :: "[t,t]=>prop"        ("(_ =/ _)" [10,10] 5)
-  Elem      :: "[i, t]=>prop"       ("(_ /: _)" [10,10] 5)
-  Eqelem    :: "[i,i,t]=>prop"      ("(_ =/ _ :/ _)" [10,10,10] 5)
-  Reduce    :: "[i,i]=>prop"        ("Reduce[_,_]")
+  Type      :: "t \<Rightarrow> prop"          ("(_ type)" [10] 5)
+  Eqtype    :: "[t,t]\<Rightarrow>prop"        ("(_ =/ _)" [10,10] 5)
+  Elem      :: "[i, t]\<Rightarrow>prop"       ("(_ /: _)" [10,10] 5)
+  Eqelem    :: "[i,i,t]\<Rightarrow>prop"      ("(_ =/ _ :/ _)" [10,10,10] 5)
+  Reduce    :: "[i,i]\<Rightarrow>prop"        ("Reduce[_,_]")
   (*Types*)
 
   (*Functions*)
-  lambda    :: "(i => i) => i"      (binder "lam " 10)
-  app       :: "[i,i]=>i"           (infixl "`" 60)
+  lambda    :: "(i \<Rightarrow> i) \<Rightarrow> i"      (binder "lam " 10)
+  app       :: "[i,i]\<Rightarrow>i"           (infixl "`" 60)
   (*Natural numbers*)
   Zero      :: "i"                  ("0")
   (*Pairing*)
-  pair      :: "[i,i]=>i"           ("(1<_,/_>)")
+  pair      :: "[i,i]\<Rightarrow>i"           ("(1<_,/_>)")
 
 syntax
-  "_PROD"   :: "[idt,t,t]=>t"       ("(3PROD _:_./ _)" 10)
-  "_SUM"    :: "[idt,t,t]=>t"       ("(3SUM _:_./ _)" 10)
+  "_PROD"   :: "[idt,t,t]\<Rightarrow>t"       ("(3PROD _:_./ _)" 10)
+  "_SUM"    :: "[idt,t,t]\<Rightarrow>t"       ("(3SUM _:_./ _)" 10)
 translations
-  "PROD x:A. B" == "CONST Prod(A, %x. B)"
-  "SUM x:A. B"  == "CONST Sum(A, %x. B)"
+  "PROD x:A. B" == "CONST Prod(A, \<lambda>x. B)"
+  "SUM x:A. B"  == "CONST Sum(A, \<lambda>x. B)"
 
 abbreviation
-  Arrow     :: "[t,t]=>t"  (infixr "-->" 30) where
+  Arrow     :: "[t,t]\<Rightarrow>t"  (infixr "-->" 30) where
   "A --> B == PROD _:A. B"
 abbreviation
-  Times     :: "[t,t]=>t"  (infixr "*" 50) where
+  Times     :: "[t,t]\<Rightarrow>t"  (infixr "*" 50) where
   "A * B == SUM _:A. B"
 
 notation (xsymbols)
@@ -86,12 +86,12 @@
   Times  (infixr "\<times>" 50)
 
 syntax (xsymbols)
-  "_PROD"   :: "[idt,t,t] => t"     ("(3\<Pi> _\<in>_./ _)"    10)
-  "_SUM"    :: "[idt,t,t] => t"     ("(3\<Sigma> _\<in>_./ _)" 10)
+  "_PROD"   :: "[idt,t,t] \<Rightarrow> t"     ("(3\<Pi> _\<in>_./ _)"    10)
+  "_SUM"    :: "[idt,t,t] \<Rightarrow> t"     ("(3\<Sigma> _\<in>_./ _)" 10)
 
 syntax (HTML output)
-  "_PROD"   :: "[idt,t,t] => t"     ("(3\<Pi> _\<in>_./ _)"    10)
-  "_SUM"    :: "[idt,t,t] => t"     ("(3\<Sigma> _\<in>_./ _)" 10)
+  "_PROD"   :: "[idt,t,t] \<Rightarrow> t"     ("(3\<Pi> _\<in>_./ _)"    10)
+  "_SUM"    :: "[idt,t,t] \<Rightarrow> t"     ("(3\<Sigma> _\<in>_./ _)" 10)
 
   (*Reduction: a weaker notion than equality;  a hack for simplification.
     Reduce[a,b] means either that  a=b:A  for some A or else that "a" and "b"
@@ -101,166 +101,158 @@
     No new theorems can be proved about the standard judgements.*)
 axiomatization where
   refl_red: "\<And>a. Reduce[a,a]" and
-  red_if_equal: "\<And>a b A. a = b : A ==> Reduce[a,b]" and
-  trans_red: "\<And>a b c A. [| a = b : A;  Reduce[b,c] |] ==> a = c : A" and
+  red_if_equal: "\<And>a b A. a = b : A \<Longrightarrow> Reduce[a,b]" and
+  trans_red: "\<And>a b c A. \<lbrakk>a = b : A; Reduce[b,c]\<rbrakk> \<Longrightarrow> a = c : A" and
 
   (*Reflexivity*)
 
-  refl_type: "\<And>A. A type ==> A = A" and
-  refl_elem: "\<And>a A. a : A ==> a = a : A" and
+  refl_type: "\<And>A. A type \<Longrightarrow> A = A" and
+  refl_elem: "\<And>a A. a : A \<Longrightarrow> a = a : A" and
 
   (*Symmetry*)
 
-  sym_type:  "\<And>A B. A = B ==> B = A" and
-  sym_elem:  "\<And>a b A. a = b : A ==> b = a : A" and
+  sym_type:  "\<And>A B. A = B \<Longrightarrow> B = A" and
+  sym_elem:  "\<And>a b A. a = b : A \<Longrightarrow> b = a : A" and
 
   (*Transitivity*)
 
-  trans_type:   "\<And>A B C. [| A = B;  B = C |] ==> A = C" and
-  trans_elem:   "\<And>a b c A. [| a = b : A;  b = c : A |] ==> a = c : A" and
+  trans_type:   "\<And>A B C. \<lbrakk>A = B; B = C\<rbrakk> \<Longrightarrow> A = C" and
+  trans_elem:   "\<And>a b c A. \<lbrakk>a = b : A; b = c : A\<rbrakk> \<Longrightarrow> a = c : A" and
 
-  equal_types:  "\<And>a A B. [| a : A;  A = B |] ==> a : B" and
-  equal_typesL: "\<And>a b A B. [| a = b : A;  A = B |] ==> a = b : B" and
+  equal_types:  "\<And>a A B. \<lbrakk>a : A; A = B\<rbrakk> \<Longrightarrow> a : B" and
+  equal_typesL: "\<And>a b A B. \<lbrakk>a = b : A; A = B\<rbrakk> \<Longrightarrow> a = b : B" and
 
   (*Substitution*)
 
-  subst_type:   "\<And>a A B. [| a : A;  !!z. z:A ==> B(z) type |] ==> B(a) type" and
-  subst_typeL:  "\<And>a c A B D. [| a = c : A;  !!z. z:A ==> B(z) = D(z) |] ==> B(a) = D(c)" and
+  subst_type:   "\<And>a A B. \<lbrakk>a : A; \<And>z. z:A \<Longrightarrow> B(z) type\<rbrakk> \<Longrightarrow> B(a) type" and
+  subst_typeL:  "\<And>a c A B D. \<lbrakk>a = c : A; \<And>z. z:A \<Longrightarrow> B(z) = D(z)\<rbrakk> \<Longrightarrow> B(a) = D(c)" and
 
-  subst_elem:   "\<And>a b A B. [| a : A;  !!z. z:A ==> b(z):B(z) |] ==> b(a):B(a)" and
+  subst_elem:   "\<And>a b A B. \<lbrakk>a : A; \<And>z. z:A \<Longrightarrow> b(z):B(z)\<rbrakk> \<Longrightarrow> b(a):B(a)" and
   subst_elemL:
-    "\<And>a b c d A B. [| a=c : A;  !!z. z:A ==> b(z)=d(z) : B(z) |] ==> b(a)=d(c) : B(a)" and
+    "\<And>a b c d A B. \<lbrakk>a = c : A; \<And>z. z:A \<Longrightarrow> b(z)=d(z) : B(z)\<rbrakk> \<Longrightarrow> b(a)=d(c) : B(a)" and
 
 
   (*The type N -- natural numbers*)
 
   NF: "N type" and
   NI0: "0 : N" and
-  NI_succ: "\<And>a. a : N ==> succ(a) : N" and
-  NI_succL:  "\<And>a b. a = b : N ==> succ(a) = succ(b) : N" and
+  NI_succ: "\<And>a. a : N \<Longrightarrow> succ(a) : N" and
+  NI_succL:  "\<And>a b. a = b : N \<Longrightarrow> succ(a) = succ(b) : N" and
 
   NE:
-   "\<And>p a b C. [| p: N;  a: C(0);  !!u v. [| u: N; v: C(u) |] ==> b(u,v): C(succ(u)) |]
-   ==> rec(p, a, %u v. b(u,v)) : C(p)" and
+   "\<And>p a b C. \<lbrakk>p: N; a: C(0); \<And>u v. \<lbrakk>u: N; v: C(u)\<rbrakk> \<Longrightarrow> b(u,v): C(succ(u))\<rbrakk>
+   \<Longrightarrow> rec(p, a, \<lambda>u v. b(u,v)) : C(p)" and
 
   NEL:
-   "\<And>p q a b c d C. [| p = q : N;  a = c : C(0);
-      !!u v. [| u: N; v: C(u) |] ==> b(u,v) = d(u,v): C(succ(u)) |]
-   ==> rec(p, a, %u v. b(u,v)) = rec(q,c,d) : C(p)" and
+   "\<And>p q a b c d C. \<lbrakk>p = q : N; a = c : C(0);
+      \<And>u v. \<lbrakk>u: N; v: C(u)\<rbrakk> \<Longrightarrow> b(u,v) = d(u,v): C(succ(u))\<rbrakk>
+   \<Longrightarrow> rec(p, a, \<lambda>u v. b(u,v)) = rec(q,c,d) : C(p)" and
 
   NC0:
-   "\<And>a b C. [| a: C(0);  !!u v. [| u: N; v: C(u) |] ==> b(u,v): C(succ(u)) |]
-   ==> rec(0, a, %u v. b(u,v)) = a : C(0)" and
+   "\<And>a b C. \<lbrakk>a: C(0); \<And>u v. \<lbrakk>u: N; v: C(u)\<rbrakk> \<Longrightarrow> b(u,v): C(succ(u))\<rbrakk>
+   \<Longrightarrow> rec(0, a, \<lambda>u v. b(u,v)) = a : C(0)" and
 
   NC_succ:
-   "\<And>p a b C. [| p: N;  a: C(0);
-       !!u v. [| u: N; v: C(u) |] ==> b(u,v): C(succ(u)) |] ==>
-   rec(succ(p), a, %u v. b(u,v)) = b(p, rec(p, a, %u v. b(u,v))) : C(succ(p))" and
+   "\<And>p a b C. \<lbrakk>p: N;  a: C(0); \<And>u v. \<lbrakk>u: N; v: C(u)\<rbrakk> \<Longrightarrow> b(u,v): C(succ(u))\<rbrakk> \<Longrightarrow>
+   rec(succ(p), a, \<lambda>u v. b(u,v)) = b(p, rec(p, a, \<lambda>u v. b(u,v))) : C(succ(p))" and
 
   (*The fourth Peano axiom.  See page 91 of Martin-Lof's book*)
-  zero_ne_succ:
-    "\<And>a. [| a: N;  0 = succ(a) : N |] ==> 0: F" and
+  zero_ne_succ: "\<And>a. \<lbrakk>a: N; 0 = succ(a) : N\<rbrakk> \<Longrightarrow> 0: F" and
 
 
   (*The Product of a family of types*)
 
-  ProdF:  "\<And>A B. [| A type; !!x. x:A ==> B(x) type |] ==> PROD x:A. B(x) type" and
+  ProdF: "\<And>A B. \<lbrakk>A type; \<And>x. x:A \<Longrightarrow> B(x) type\<rbrakk> \<Longrightarrow> PROD x:A. B(x) type" and
 
   ProdFL:
-   "\<And>A B C D. [| A = C;  !!x. x:A ==> B(x) = D(x) |] ==>
-   PROD x:A. B(x) = PROD x:C. D(x)" and
+    "\<And>A B C D. \<lbrakk>A = C; \<And>x. x:A \<Longrightarrow> B(x) = D(x)\<rbrakk> \<Longrightarrow> PROD x:A. B(x) = PROD x:C. D(x)" and
 
   ProdI:
-   "\<And>b A B. [| A type;  !!x. x:A ==> b(x):B(x)|] ==> lam x. b(x) : PROD x:A. B(x)" and
+    "\<And>b A B. \<lbrakk>A type; \<And>x. x:A \<Longrightarrow> b(x):B(x)\<rbrakk> \<Longrightarrow> lam x. b(x) : PROD x:A. B(x)" and
 
-  ProdIL:
-   "\<And>b c A B. [| A type;  !!x. x:A ==> b(x) = c(x) : B(x)|] ==>
-   lam x. b(x) = lam x. c(x) : PROD x:A. B(x)" and
+  ProdIL: "\<And>b c A B. \<lbrakk>A type; \<And>x. x:A \<Longrightarrow> b(x) = c(x) : B(x)\<rbrakk> \<Longrightarrow>
+    lam x. b(x) = lam x. c(x) : PROD x:A. B(x)" and
 
-  ProdE:  "\<And>p a A B. [| p : PROD x:A. B(x);  a : A |] ==> p`a : B(a)" and
-  ProdEL: "\<And>p q a b A B. [| p=q: PROD x:A. B(x);  a=b : A |] ==> p`a = q`b : B(a)" and
+  ProdE:  "\<And>p a A B. \<lbrakk>p : PROD x:A. B(x); a : A\<rbrakk> \<Longrightarrow> p`a : B(a)" and
+  ProdEL: "\<And>p q a b A B. \<lbrakk>p = q: PROD x:A. B(x); a = b : A\<rbrakk> \<Longrightarrow> p`a = q`b : B(a)" and
 
-  ProdC:
-   "\<And>a b A B. [| a : A;  !!x. x:A ==> b(x) : B(x)|] ==>
-   (lam x. b(x)) ` a = b(a) : B(a)" and
+  ProdC: "\<And>a b A B. \<lbrakk>a : A; \<And>x. x:A \<Longrightarrow> b(x) : B(x)\<rbrakk> \<Longrightarrow> (lam x. b(x)) ` a = b(a) : B(a)" and
 
-  ProdC2:
-   "\<And>p A B. p : PROD x:A. B(x) ==> (lam x. p`x) = p : PROD x:A. B(x)" and
+  ProdC2: "\<And>p A B. p : PROD x:A. B(x) \<Longrightarrow> (lam x. p`x) = p : PROD x:A. B(x)" and
 
 
   (*The Sum of a family of types*)
 
-  SumF:  "\<And>A B. [| A type;  !!x. x:A ==> B(x) type |] ==> SUM x:A. B(x) type" and
-  SumFL:
-    "\<And>A B C D. [| A = C;  !!x. x:A ==> B(x) = D(x) |] ==> SUM x:A. B(x) = SUM x:C. D(x)" and
+  SumF:  "\<And>A B. \<lbrakk>A type; \<And>x. x:A \<Longrightarrow> B(x) type\<rbrakk> \<Longrightarrow> SUM x:A. B(x) type" and
+  SumFL: "\<And>A B C D. \<lbrakk>A = C; \<And>x. x:A \<Longrightarrow> B(x) = D(x)\<rbrakk> \<Longrightarrow> SUM x:A. B(x) = SUM x:C. D(x)" and
 
-  SumI:  "\<And>a b A B. [| a : A;  b : B(a) |] ==> <a,b> : SUM x:A. B(x)" and
-  SumIL: "\<And>a b c d A B. [| a=c:A;  b=d:B(a) |] ==> <a,b> = <c,d> : SUM x:A. B(x)" and
+  SumI:  "\<And>a b A B. \<lbrakk>a : A; b : B(a)\<rbrakk> \<Longrightarrow> <a,b> : SUM x:A. B(x)" and
+  SumIL: "\<And>a b c d A B. \<lbrakk> a = c : A; b = d : B(a)\<rbrakk> \<Longrightarrow> <a,b> = <c,d> : SUM x:A. B(x)" and
 
-  SumE:
-    "\<And>p c A B C. [| p: SUM x:A. B(x);  !!x y. [| x:A; y:B(x) |] ==> c(x,y): C(<x,y>) |]
-    ==> split(p, %x y. c(x,y)) : C(p)" and
+  SumE: "\<And>p c A B C. \<lbrakk>p: SUM x:A. B(x); \<And>x y. \<lbrakk>x:A; y:B(x)\<rbrakk> \<Longrightarrow> c(x,y): C(<x,y>)\<rbrakk>
+    \<Longrightarrow> split(p, \<lambda>x y. c(x,y)) : C(p)" and
 
-  SumEL:
-    "\<And>p q c d A B C. [| p=q : SUM x:A. B(x);
-       !!x y. [| x:A; y:B(x) |] ==> c(x,y)=d(x,y): C(<x,y>)|]
-    ==> split(p, %x y. c(x,y)) = split(q, % x y. d(x,y)) : C(p)" and
+  SumEL: "\<And>p q c d A B C. \<lbrakk>p = q : SUM x:A. B(x);
+      \<And>x y. \<lbrakk>x:A; y:B(x)\<rbrakk> \<Longrightarrow> c(x,y)=d(x,y): C(<x,y>)\<rbrakk>
+    \<Longrightarrow> split(p, \<lambda>x y. c(x,y)) = split(q, \<lambda>x y. d(x,y)) : C(p)" and
 
-  SumC:
-    "\<And>a b c A B C. [| a: A;  b: B(a);  !!x y. [| x:A; y:B(x) |] ==> c(x,y): C(<x,y>) |]
-    ==> split(<a,b>, %x y. c(x,y)) = c(a,b) : C(<a,b>)" and
+  SumC: "\<And>a b c A B C. \<lbrakk>a: A;  b: B(a); \<And>x y. \<lbrakk>x:A; y:B(x)\<rbrakk> \<Longrightarrow> c(x,y): C(<x,y>)\<rbrakk>
+    \<Longrightarrow> split(<a,b>, \<lambda>x y. c(x,y)) = c(a,b) : C(<a,b>)" and
 
-  fst_def:   "\<And>a. fst(a) == split(a, %x y. x)" and
-  snd_def:   "\<And>a. snd(a) == split(a, %x y. y)" and
+  fst_def:   "\<And>a. fst(a) == split(a, \<lambda>x y. x)" and
+  snd_def:   "\<And>a. snd(a) == split(a, \<lambda>x y. y)" and
 
 
   (*The sum of two types*)
 
-  PlusF:   "\<And>A B. [| A type;  B type |] ==> A+B type" and
-  PlusFL:  "\<And>A B C D. [| A = C;  B = D |] ==> A+B = C+D" and
+  PlusF: "\<And>A B. \<lbrakk>A type; B type\<rbrakk> \<Longrightarrow> A+B type" and
+  PlusFL: "\<And>A B C D. \<lbrakk>A = C; B = D\<rbrakk> \<Longrightarrow> A+B = C+D" and
 
-  PlusI_inl:   "\<And>a A B. [| a : A;  B type |] ==> inl(a) : A+B" and
-  PlusI_inlL: "\<And>a c A B. [| a = c : A;  B type |] ==> inl(a) = inl(c) : A+B" and
+  PlusI_inl: "\<And>a A B. \<lbrakk>a : A; B type\<rbrakk> \<Longrightarrow> inl(a) : A+B" and
+  PlusI_inlL: "\<And>a c A B. \<lbrakk>a = c : A; B type\<rbrakk> \<Longrightarrow> inl(a) = inl(c) : A+B" and
 
-  PlusI_inr:   "\<And>b A B. [| A type;  b : B |] ==> inr(b) : A+B" and
-  PlusI_inrL: "\<And>b d A B. [| A type;  b = d : B |] ==> inr(b) = inr(d) : A+B" and
+  PlusI_inr: "\<And>b A B. \<lbrakk>A type; b : B\<rbrakk> \<Longrightarrow> inr(b) : A+B" and
+  PlusI_inrL: "\<And>b d A B. \<lbrakk>A type; b = d : B\<rbrakk> \<Longrightarrow> inr(b) = inr(d) : A+B" and
 
   PlusE:
-    "\<And>p c d A B C. [| p: A+B;  !!x. x:A ==> c(x): C(inl(x));
-                !!y. y:B ==> d(y): C(inr(y)) |]
-    ==> when(p, %x. c(x), %y. d(y)) : C(p)" and
+    "\<And>p c d A B C. \<lbrakk>p: A+B;
+      \<And>x. x:A \<Longrightarrow> c(x): C(inl(x));
+      \<And>y. y:B \<Longrightarrow> d(y): C(inr(y)) \<rbrakk> \<Longrightarrow> when(p, \<lambda>x. c(x), \<lambda>y. d(y)) : C(p)" and
 
   PlusEL:
-    "\<And>p q c d e f A B C. [| p = q : A+B;  !!x. x: A ==> c(x) = e(x) : C(inl(x));
-                     !!y. y: B ==> d(y) = f(y) : C(inr(y)) |]
-    ==> when(p, %x. c(x), %y. d(y)) = when(q, %x. e(x), %y. f(y)) : C(p)" and
+    "\<And>p q c d e f A B C. \<lbrakk>p = q : A+B;
+      \<And>x. x: A \<Longrightarrow> c(x) = e(x) : C(inl(x));
+      \<And>y. y: B \<Longrightarrow> d(y) = f(y) : C(inr(y))\<rbrakk>
+    \<Longrightarrow> when(p, \<lambda>x. c(x), \<lambda>y. d(y)) = when(q, \<lambda>x. e(x), \<lambda>y. f(y)) : C(p)" and
 
   PlusC_inl:
-    "\<And>a c d A C. [| a: A;  !!x. x:A ==> c(x): C(inl(x));
-              !!y. y:B ==> d(y): C(inr(y)) |]
-    ==> when(inl(a), %x. c(x), %y. d(y)) = c(a) : C(inl(a))" and
+    "\<And>a c d A C. \<lbrakk>a: A;
+      \<And>x. x:A \<Longrightarrow> c(x): C(inl(x));
+      \<And>y. y:B \<Longrightarrow> d(y): C(inr(y)) \<rbrakk>
+    \<Longrightarrow> when(inl(a), \<lambda>x. c(x), \<lambda>y. d(y)) = c(a) : C(inl(a))" and
 
   PlusC_inr:
-    "\<And>b c d A B C. [| b: B;  !!x. x:A ==> c(x): C(inl(x));
-              !!y. y:B ==> d(y): C(inr(y)) |]
-    ==> when(inr(b), %x. c(x), %y. d(y)) = d(b) : C(inr(b))" and
+    "\<And>b c d A B C. \<lbrakk>b: B;
+      \<And>x. x:A \<Longrightarrow> c(x): C(inl(x));
+      \<And>y. y:B \<Longrightarrow> d(y): C(inr(y))\<rbrakk>
+    \<Longrightarrow> when(inr(b), \<lambda>x. c(x), \<lambda>y. d(y)) = d(b) : C(inr(b))" and
 
 
   (*The type Eq*)
 
-  EqF:    "\<And>a b A. [| A type;  a : A;  b : A |] ==> Eq(A,a,b) type" and
-  EqFL: "\<And>a b c d A B. [| A=B;  a=c: A;  b=d : A |] ==> Eq(A,a,b) = Eq(B,c,d)" and
-  EqI: "\<And>a b A. a = b : A ==> eq : Eq(A,a,b)" and
-  EqE: "\<And>p a b A. p : Eq(A,a,b) ==> a = b : A" and
+  EqF: "\<And>a b A. \<lbrakk>A type; a : A; b : A\<rbrakk> \<Longrightarrow> Eq(A,a,b) type" and
+  EqFL: "\<And>a b c d A B. \<lbrakk>A = B; a = c : A; b = d : A\<rbrakk> \<Longrightarrow> Eq(A,a,b) = Eq(B,c,d)" and
+  EqI: "\<And>a b A. a = b : A \<Longrightarrow> eq : Eq(A,a,b)" and
+  EqE: "\<And>p a b A. p : Eq(A,a,b) \<Longrightarrow> a = b : A" and
 
   (*By equality of types, can prove C(p) from C(eq), an elimination rule*)
-  EqC: "\<And>p a b A. p : Eq(A,a,b) ==> p = eq : Eq(A,a,b)" and
+  EqC: "\<And>p a b A. p : Eq(A,a,b) \<Longrightarrow> p = eq : Eq(A,a,b)" and
 
   (*The type F*)
 
   FF: "F type" and
-  FE: "\<And>p C. [| p: F;  C type |] ==> contr(p) : C" and
-  FEL:  "\<And>p q C. [| p = q : F;  C type |] ==> contr(p) = contr(q) : C" and
+  FE: "\<And>p C. \<lbrakk>p: F; C type\<rbrakk> \<Longrightarrow> contr(p) : C" and
+  FEL: "\<And>p q C. \<lbrakk>p = q : F; C type\<rbrakk> \<Longrightarrow> contr(p) = contr(q) : C" and
 
   (*The type T
      Martin-Lof's book (page 68) discusses elimination and computation.
@@ -270,9 +262,9 @@
 
   TF: "T type" and
   TI: "tt : T" and
-  TE: "\<And>p c C. [| p : T;  c : C(tt) |] ==> c : C(p)" and
-  TEL: "\<And>p q c d C. [| p = q : T;  c = d : C(tt) |] ==> c = d : C(p)" and
-  TC: "\<And>p. p : T ==> p = tt : T"
+  TE: "\<And>p c C. \<lbrakk>p : T; c : C(tt)\<rbrakk> \<Longrightarrow> c : C(p)" and
+  TEL: "\<And>p q c d C. \<lbrakk>p = q : T; c = d : C(tt)\<rbrakk> \<Longrightarrow> c = d : C(p)" and
+  TC: "\<And>p. p : T \<Longrightarrow> p = tt : T"
 
 
 subsection "Tactics and derived rules for Constructive Type Theory"
@@ -302,7 +294,7 @@
 lemmas basic_defs = fst_def snd_def
 
 (*Compare with standard version: B is applied to UNSIMPLIFIED expression! *)
-lemma SumIL2: "[| c=a : A;  d=b : B(a) |] ==> <c,d> = <a,b> : Sum(A,B)"
+lemma SumIL2: "\<lbrakk>c = a : A; d = b : B(a)\<rbrakk> \<Longrightarrow> <c,d> = <a,b> : Sum(A,B)"
 apply (rule sym_elem)
 apply (rule SumIL)
 apply (rule_tac [!] sym_elem)
@@ -316,7 +308,7 @@
 lemma subst_prodE:
   assumes "p: Prod(A,B)"
     and "a: A"
-    and "!!z. z: B(a) ==> c(z): C(z)"
+    and "\<And>z. z: B(a) \<Longrightarrow> c(z): C(z)"
   shows "c(p`a): C(p`a)"
 apply (rule assms ProdE)+
 done
@@ -378,14 +370,18 @@
   REPEAT_FIRST (ASSUME ctxt (filt_resolve_tac (thms @ equal_rls) 3))
 
 end
+*}
 
-*}
+method_setup form = {* Scan.succeed (fn ctxt => SIMPLE_METHOD (form_tac ctxt)) *}
+method_setup typechk = {* Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD (typechk_tac ctxt ths)) *}
+method_setup intr = {* Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD (intr_tac ctxt ths)) *}
+method_setup equal = {* Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD (equal_tac ctxt ths)) *}
 
 
 subsection {* Simplification *}
 
 (*To simplify the type in a goal*)
-lemma replace_type: "[| B = A;  a : A |] ==> a : B"
+lemma replace_type: "\<lbrakk>B = A; a : A\<rbrakk> \<Longrightarrow> a : B"
 apply (rule equal_types)
 apply (rule_tac [2] sym_type)
 apply assumption+
@@ -394,7 +390,7 @@
 (*Simplify the parameter of a unary type operator.*)
 lemma subst_eqtyparg:
   assumes 1: "a=c : A"
-    and 2: "!!z. z:A ==> B(z) type"
+    and 2: "\<And>z. z:A \<Longrightarrow> B(z) type"
   shows "B(a)=B(c)"
 apply (rule subst_typeL)
 apply (rule_tac [2] refl_type)
@@ -460,12 +456,21 @@
 fun pc_tac ctxt thms = DEPTH_SOLVE_1 o (step_tac ctxt thms)
 *}
 
+method_setup eqintr = {* Scan.succeed (SIMPLE_METHOD o eqintr_tac) *}
+method_setup NE = {*
+  Scan.lift Args.name_inner_syntax >> (fn s => fn ctxt => SIMPLE_METHOD' (NE_tac ctxt s))
+*}
+method_setup pc = {* Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD' (pc_tac ctxt ths)) *}
+method_setup add_mp = {* Scan.succeed (SIMPLE_METHOD' o add_mp_tac) *}
+
 ML_file "rew.ML"
+method_setup rew = {* Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD (rew_tac ctxt ths)) *}
+method_setup hyp_rew = {* Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD (hyp_rew_tac ctxt ths)) *}
 
 
 subsection {* The elimination rules for fst/snd *}
 
-lemma SumE_fst: "p : Sum(A,B) ==> fst(p) : A"
+lemma SumE_fst: "p : Sum(A,B) \<Longrightarrow> fst(p) : A"
 apply (unfold basic_defs)
 apply (erule SumE)
 apply assumption
@@ -475,12 +480,12 @@
 lemma SumE_snd:
   assumes major: "p: Sum(A,B)"
     and "A type"
-    and "!!x. x:A ==> B(x) type"
+    and "\<And>x. x:A \<Longrightarrow> B(x) type"
   shows "snd(p) : B(fst(p))"
   apply (unfold basic_defs)
   apply (rule major [THEN SumE])
   apply (rule SumC [THEN subst_eqtyparg, THEN replace_type])
-  apply (tactic {* typechk_tac @{context} @{thms assms} *})
+  apply (typechk assms)
   done
 
 end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CTT/ROOT
--- a/src/CTT/ROOT	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CTT/ROOT	Tue Nov 11 21:14:19 2014 +0100
@@ -17,14 +17,11 @@
     1991)
   *}
   options [document = false]
-  theories Main
+  theories
+    Main
 
-session "CTT-ex" in ex = CTT +
-  description {*
-    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1991  University of Cambridge
-
-    Examples for Constructive Type Theory.
-  *}
-  options [document = false]
-  theories Typechecking Elimination Equality Synthesis
+    (* Examples for Constructive Type Theory *)
+    "ex/Typechecking"
+    "ex/Elimination"
+    "ex/Equality"
+    "ex/Synthesis"
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CTT/ex/Elimination.thy
--- a/src/CTT/ex/Elimination.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CTT/ex/Elimination.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -9,123 +9,123 @@
 section "Examples with elimination rules"
 
 theory Elimination
-imports CTT
+imports "../CTT"
 begin
 
 text "This finds the functions fst and snd!"
 
-schematic_lemma [folded basic_defs]: "A type ==> ?a : (A*A) --> A"
-apply (tactic {* pc_tac @{context} [] 1 *})
+schematic_lemma [folded basic_defs]: "A type \<Longrightarrow> ?a : (A*A) --> A"
+apply pc
 done
 
-schematic_lemma [folded basic_defs]: "A type ==> ?a : (A*A) --> A"
-apply (tactic {* pc_tac @{context} [] 1 *})
+schematic_lemma [folded basic_defs]: "A type \<Longrightarrow> ?a : (A*A) --> A"
+apply pc
 back
 done
 
 text "Double negation of the Excluded Middle"
-schematic_lemma "A type ==> ?a : ((A + (A-->F)) --> F) --> F"
-apply (tactic "intr_tac @{context} []")
+schematic_lemma "A type \<Longrightarrow> ?a : ((A + (A-->F)) --> F) --> F"
+apply intr
 apply (rule ProdE)
 apply assumption
-apply (tactic "pc_tac @{context} [] 1")
+apply pc
 done
 
-schematic_lemma "[| A type;  B type |] ==> ?a : (A*B) --> (B*A)"
-apply (tactic "pc_tac @{context} [] 1")
+schematic_lemma "\<lbrakk>A type; B type\<rbrakk> \<Longrightarrow> ?a : (A*B) \<longrightarrow> (B*A)"
+apply pc
 done
 (*The sequent version (ITT) could produce an interesting alternative
   by backtracking.  No longer.*)
 
 text "Binary sums and products"
-schematic_lemma "[| A type; B type; C type |] ==> ?a : (A+B --> C) --> (A-->C) * (B-->C)"
-apply (tactic "pc_tac @{context} [] 1")
+schematic_lemma "\<lbrakk>A type; B type; C type\<rbrakk> \<Longrightarrow> ?a : (A+B --> C) --> (A-->C) * (B-->C)"
+apply pc
 done
 
 (*A distributive law*)
-schematic_lemma "[| A type;  B type;  C type |] ==> ?a : A * (B+C)  -->  (A*B + A*C)"
-apply (tactic "pc_tac @{context} [] 1")
+schematic_lemma "\<lbrakk>A type; B type; C type\<rbrakk> \<Longrightarrow> ?a : A * (B+C)  -->  (A*B + A*C)"
+apply pc
 done
 
 (*more general version, same proof*)
 schematic_lemma
   assumes "A type"
-    and "!!x. x:A ==> B(x) type"
-    and "!!x. x:A ==> C(x) type"
+    and "\<And>x. x:A \<Longrightarrow> B(x) type"
+    and "\<And>x. x:A \<Longrightarrow> C(x) type"
   shows "?a : (SUM x:A. B(x) + C(x)) --> (SUM x:A. B(x)) + (SUM x:A. C(x))"
-apply (tactic {* pc_tac @{context} @{thms assms} 1 *})
+apply (pc assms)
 done
 
 text "Construction of the currying functional"
-schematic_lemma "[| A type;  B type;  C type |] ==> ?a : (A*B --> C) --> (A--> (B-->C))"
-apply (tactic "pc_tac @{context} [] 1")
+schematic_lemma "\<lbrakk>A type; B type; C type\<rbrakk> \<Longrightarrow> ?a : (A*B --> C) --> (A--> (B-->C))"
+apply pc
 done
 
 (*more general goal with same proof*)
 schematic_lemma
   assumes "A type"
-    and "!!x. x:A ==> B(x) type"
-    and "!!z. z: (SUM x:A. B(x)) ==> C(z) type"
+    and "\<And>x. x:A \<Longrightarrow> B(x) type"
+    and "\<And>z. z: (SUM x:A. B(x)) \<Longrightarrow> C(z) type"
   shows "?a : PROD f: (PROD z : (SUM x:A . B(x)) . C(z)).
                       (PROD x:A . PROD y:B(x) . C(<x,y>))"
-apply (tactic {* pc_tac @{context} @{thms assms} 1 *})
+apply (pc assms)
 done
 
 text "Martin-Lof (1984), page 48: axiom of sum-elimination (uncurry)"
-schematic_lemma "[| A type;  B type;  C type |] ==> ?a : (A --> (B-->C)) --> (A*B --> C)"
-apply (tactic "pc_tac @{context} [] 1")
+schematic_lemma "\<lbrakk>A type; B type; C type\<rbrakk> \<Longrightarrow> ?a : (A --> (B-->C)) --> (A*B --> C)"
+apply pc
 done
 
 (*more general goal with same proof*)
 schematic_lemma
   assumes "A type"
-    and "!!x. x:A ==> B(x) type"
-    and "!!z. z: (SUM x:A . B(x)) ==> C(z) type"
+    and "\<And>x. x:A \<Longrightarrow> B(x) type"
+    and "\<And>z. z: (SUM x:A . B(x)) \<Longrightarrow> C(z) type"
   shows "?a : (PROD x:A . PROD y:B(x) . C(<x,y>))
         --> (PROD z : (SUM x:A . B(x)) . C(z))"
-apply (tactic {* pc_tac @{context} @{thms assms} 1 *})
+apply (pc assms)
 done
 
 text "Function application"
-schematic_lemma "[| A type;  B type |] ==> ?a : ((A --> B) * A) --> B"
-apply (tactic "pc_tac @{context} [] 1")
+schematic_lemma "\<lbrakk>A type; B type\<rbrakk> \<Longrightarrow> ?a : ((A --> B) * A) --> B"
+apply pc
 done
 
 text "Basic test of quantifier reasoning"
 schematic_lemma
   assumes "A type"
     and "B type"
-    and "!!x y.[| x:A;  y:B |] ==> C(x,y) type"
+    and "\<And>x y. \<lbrakk>x:A; y:B\<rbrakk> \<Longrightarrow> C(x,y) type"
   shows
     "?a :     (SUM y:B . PROD x:A . C(x,y))
           --> (PROD x:A . SUM y:B . C(x,y))"
-apply (tactic {* pc_tac @{context} @{thms assms} 1 *})
+apply (pc assms)
 done
 
 text "Martin-Lof (1984) pages 36-7: the combinator S"
 schematic_lemma
   assumes "A type"
-    and "!!x. x:A ==> B(x) type"
-    and "!!x y.[| x:A; y:B(x) |] ==> C(x,y) type"
+    and "\<And>x. x:A \<Longrightarrow> B(x) type"
+    and "\<And>x y. \<lbrakk>x:A; y:B(x)\<rbrakk> \<Longrightarrow> C(x,y) type"
   shows "?a :    (PROD x:A. PROD y:B(x). C(x,y))
              --> (PROD f: (PROD x:A. B(x)). PROD x:A. C(x, f`x))"
-apply (tactic {* pc_tac @{context} @{thms assms} 1 *})
+apply (pc assms)
 done
 
 text "Martin-Lof (1984) page 58: the axiom of disjunction elimination"
 schematic_lemma
   assumes "A type"
     and "B type"
-    and "!!z. z: A+B ==> C(z) type"
+    and "\<And>z. z: A+B \<Longrightarrow> C(z) type"
   shows "?a : (PROD x:A. C(inl(x))) --> (PROD y:B. C(inr(y)))
           --> (PROD z: A+B. C(z))"
-apply (tactic {* pc_tac @{context} @{thms assms} 1 *})
+apply (pc assms)
 done
 
 (*towards AXIOM OF CHOICE*)
 schematic_lemma [folded basic_defs]:
-  "[| A type; B type; C type |] ==> ?a : (A --> B*C) --> (A-->B) * (A-->C)"
-apply (tactic "pc_tac @{context} [] 1")
+  "\<lbrakk>A type; B type; C type\<rbrakk> \<Longrightarrow> ?a : (A --> B*C) --> (A-->B) * (A-->C)"
+apply pc
 done
 
 
@@ -133,61 +133,64 @@
 text "AXIOM OF CHOICE!  Delicate use of elimination rules"
 schematic_lemma
   assumes "A type"
-    and "!!x. x:A ==> B(x) type"
-    and "!!x y.[| x:A;  y:B(x) |] ==> C(x,y) type"
+    and "\<And>x. x:A \<Longrightarrow> B(x) type"
+    and "\<And>x y. \<lbrakk>x:A; y:B(x)\<rbrakk> \<Longrightarrow> C(x,y) type"
   shows "?a : PROD h: (PROD x:A. SUM y:B(x). C(x,y)).
                          (SUM f: (PROD x:A. B(x)). PROD x:A. C(x, f`x))"
-apply (tactic {* intr_tac @{context} @{thms assms} *})
-apply (tactic "add_mp_tac @{context} 2")
-apply (tactic "add_mp_tac @{context} 1")
+apply (intr assms)
+prefer 2 apply add_mp
+prefer 2 apply add_mp
 apply (erule SumE_fst)
 apply (rule replace_type)
 apply (rule subst_eqtyparg)
 apply (rule comp_rls)
 apply (rule_tac [4] SumE_snd)
-apply (tactic {* typechk_tac @{context} (@{thm SumE_fst} :: @{thms assms}) *})
+apply (typechk SumE_fst assms)
 done
 
 text "Axiom of choice.  Proof without fst, snd.  Harder still!"
 schematic_lemma [folded basic_defs]:
   assumes "A type"
-    and "!!x. x:A ==> B(x) type"
-    and "!!x y.[| x:A;  y:B(x) |] ==> C(x,y) type"
+    and "\<And>x. x:A \<Longrightarrow> B(x) type"
+    and "\<And>x y. \<lbrakk>x:A; y:B(x)\<rbrakk> \<Longrightarrow> C(x,y) type"
   shows "?a : PROD h: (PROD x:A. SUM y:B(x). C(x,y)).
                          (SUM f: (PROD x:A. B(x)). PROD x:A. C(x, f`x))"
-apply (tactic {* intr_tac @{context} @{thms assms} *})
-(*Must not use add_mp_tac as subst_prodE hides the construction.*)
-apply (rule ProdE [THEN SumE], assumption)
-apply (tactic "TRYALL (assume_tac @{context})")
+apply (intr assms)
+(*Must not use add_mp as subst_prodE hides the construction.*)
+apply (rule ProdE [THEN SumE])
+apply assumption
+apply assumption
+apply assumption
 apply (rule replace_type)
 apply (rule subst_eqtyparg)
 apply (rule comp_rls)
 apply (erule_tac [4] ProdE [THEN SumE])
-apply (tactic {* typechk_tac @{context} @{thms assms} *})
+apply (typechk assms)
 apply (rule replace_type)
 apply (rule subst_eqtyparg)
 apply (rule comp_rls)
-apply (tactic {* typechk_tac @{context} @{thms assms} *})
+apply (typechk assms)
 apply assumption
 done
 
 text "Example of sequent_style deduction"
 (*When splitting z:A*B, the assumption C(z) is affected;  ?a becomes
-    lam u. split(u,%v w.split(v,%x y.lam z. <x,<y,z>>) ` w)     *)
+    lam u. split(u,\<lambda>v w.split(v,\<lambda>x y.lam z. <x,<y,z>>) ` w)     *)
 schematic_lemma
   assumes "A type"
     and "B type"
-    and "!!z. z:A*B ==> C(z) type"
+    and "\<And>z. z:A*B \<Longrightarrow> C(z) type"
   shows "?a : (SUM z:A*B. C(z)) --> (SUM u:A. SUM v:B. C(<u,v>))"
 apply (rule intr_rls)
 apply (tactic {* biresolve_tac safe_brls 2 *})
 (*Now must convert assumption C(z) into antecedent C(<kd,ke>) *)
 apply (rule_tac [2] a = "y" in ProdE)
-apply (tactic {* typechk_tac @{context} @{thms assms} *})
+apply (typechk assms)
 apply (rule SumE, assumption)
-apply (tactic "intr_tac @{context} []")
-apply (tactic "TRYALL (assume_tac @{context})")
-apply (tactic {* typechk_tac @{context} @{thms assms} *})
+apply intr
+defer 1
+apply assumption+
+apply (typechk assms)
 done
 
 end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CTT/ex/Equality.thy
--- a/src/CTT/ex/Equality.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CTT/ex/Equality.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -6,64 +6,63 @@
 section "Equality reasoning by rewriting"
 
 theory Equality
-imports CTT
+imports "../CTT"
 begin
 
-lemma split_eq: "p : Sum(A,B) ==> split(p,pair) = p : Sum(A,B)"
+lemma split_eq: "p : Sum(A,B) \<Longrightarrow> split(p,pair) = p : Sum(A,B)"
 apply (rule EqE)
 apply (rule elim_rls, assumption)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
-lemma when_eq: "[| A type;  B type;  p : A+B |] ==> when(p,inl,inr) = p : A + B"
+lemma when_eq: "\<lbrakk>A type; B type; p : A+B\<rbrakk> \<Longrightarrow> when(p,inl,inr) = p : A + B"
 apply (rule EqE)
 apply (rule elim_rls, assumption)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 (*in the "rec" formulation of addition, 0+n=n *)
-lemma "p:N ==> rec(p,0, %y z. succ(y)) = p : N"
+lemma "p:N \<Longrightarrow> rec(p,0, \<lambda>y z. succ(y)) = p : N"
 apply (rule EqE)
 apply (rule elim_rls, assumption)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 (*the harder version, n+0=n: recursive, uses induction hypothesis*)
-lemma "p:N ==> rec(p,0, %y z. succ(z)) = p : N"
+lemma "p:N \<Longrightarrow> rec(p,0, \<lambda>y z. succ(z)) = p : N"
 apply (rule EqE)
 apply (rule elim_rls, assumption)
-apply (tactic "hyp_rew_tac @{context} []")
+apply hyp_rew
 done
 
 (*Associativity of addition*)
-lemma "[| a:N;  b:N;  c:N |]
-      ==> rec(rec(a, b, %x y. succ(y)), c, %x y. succ(y)) =
-          rec(a, rec(b, c, %x y. succ(y)), %x y. succ(y)) : N"
-apply (tactic {* NE_tac @{context} "a" 1 *})
-apply (tactic "hyp_rew_tac @{context} []")
+lemma "\<lbrakk>a:N; b:N; c:N\<rbrakk>
+  \<Longrightarrow> rec(rec(a, b, \<lambda>x y. succ(y)), c, \<lambda>x y. succ(y)) =
+    rec(a, rec(b, c, \<lambda>x y. succ(y)), \<lambda>x y. succ(y)) : N"
+apply (NE a)
+apply hyp_rew
 done
 
 (*Martin-Lof (1984) page 62: pairing is surjective*)
-lemma "p : Sum(A,B) ==> <split(p,%x y. x), split(p,%x y. y)> = p : Sum(A,B)"
+lemma "p : Sum(A,B) \<Longrightarrow> <split(p,\<lambda>x y. x), split(p,\<lambda>x y. y)> = p : Sum(A,B)"
 apply (rule EqE)
 apply (rule elim_rls, assumption)
 apply (tactic {* DEPTH_SOLVE_1 (rew_tac @{context} []) *}) (*!!!!!!!*)
 done
 
-lemma "[| a : A;  b : B |] ==>
-     (lam u. split(u, %v w.<w,v>)) ` <a,b> = <b,a> : SUM x:B. A"
-apply (tactic "rew_tac @{context} []")
+lemma "\<lbrakk>a : A; b : B\<rbrakk> \<Longrightarrow> (lam u. split(u, \<lambda>v w.<w,v>)) ` <a,b> = <b,a> : SUM x:B. A"
+apply rew
 done
 
 (*a contrived, complicated simplication, requires sum-elimination also*)
-lemma "(lam f. lam x. f`(f`x)) ` (lam u. split(u, %v w.<w,v>)) =
+lemma "(lam f. lam x. f`(f`x)) ` (lam u. split(u, \<lambda>v w.<w,v>)) =
       lam x. x  :  PROD x:(SUM y:N. N). (SUM y:N. N)"
 apply (rule reduction_rls)
 apply (rule_tac [3] intrL_rls)
 apply (rule_tac [4] EqE)
-apply (rule_tac [4] SumE, tactic "assume_tac @{context} 4")
+apply (erule_tac [4] SumE)
 (*order of unifiers is essential here*)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CTT/ex/Synthesis.thy
--- a/src/CTT/ex/Synthesis.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CTT/ex/Synthesis.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -6,27 +6,27 @@
 section "Synthesis examples, using a crude form of narrowing"
 
 theory Synthesis
-imports Arith
+imports "../Arith"
 begin
 
 text "discovery of predecessor function"
 schematic_lemma "?a : SUM pred:?A . Eq(N, pred`0, 0)
                   *  (PROD n:N. Eq(N, pred ` succ(n), n))"
-apply (tactic "intr_tac @{context} []")
-apply (tactic "eqintr_tac @{context}")
+apply intr
+apply eqintr
 apply (rule_tac [3] reduction_rls)
 apply (rule_tac [5] comp_rls)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 text "the function fst as an element of a function type"
 schematic_lemma [folded basic_defs]:
-  "A type ==> ?a: SUM f:?B . PROD i:A. PROD j:A. Eq(A, f ` <i,j>, i)"
-apply (tactic "intr_tac @{context} []")
-apply (tactic "eqintr_tac @{context}")
+  "A type \<Longrightarrow> ?a: SUM f:?B . PROD i:A. PROD j:A. Eq(A, f ` <i,j>, i)"
+apply intr
+apply eqintr
 apply (rule_tac [2] reduction_rls)
 apply (rule_tac [4] comp_rls)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 txt "now put in A everywhere"
 apply assumption+
 done
@@ -36,10 +36,10 @@
   See following example.*)
 schematic_lemma "?a : PROD i:N. Eq(?A, ?b(inl(i)), <0    ,   i>)
                    * Eq(?A, ?b(inr(i)), <succ(0), i>)"
-apply (tactic "intr_tac @{context} []")
-apply (tactic "eqintr_tac @{context}")
+apply intr
+apply eqintr
 apply (rule comp_rls)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 (*Here we allow the type to depend on i.
@@ -55,13 +55,13 @@
 schematic_lemma [folded basic_defs]:
   "?a : PROD i:N. PROD j:N. Eq(?A, ?b(inl(<i,j>)), i)
                            *  Eq(?A, ?b(inr(<i,j>)), j)"
-apply (tactic "intr_tac @{context} []")
-apply (tactic "eqintr_tac @{context}")
+apply intr
+apply eqintr
 apply (rule PlusC_inl [THEN trans_elem])
 apply (rule_tac [4] comp_rls)
 apply (rule_tac [7] reduction_rls)
 apply (rule_tac [10] comp_rls)
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
 (*similar but allows the type to depend on i and j*)
@@ -79,10 +79,10 @@
 schematic_lemma [folded arith_defs]:
   "?c : PROD n:N. Eq(N, ?f(0,n), n)
                   *  (PROD m:N. Eq(N, ?f(succ(m), n), succ(?f(m,n))))"
-apply (tactic "intr_tac @{context} []")
-apply (tactic "eqintr_tac @{context}")
+apply intr
+apply eqintr
 apply (rule comp_rls)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 text "The addition function -- using explicit lambdas"
@@ -90,15 +90,15 @@
   "?c : SUM plus : ?A .
          PROD x:N. Eq(N, plus`0`x, x)
                 *  (PROD y:N. Eq(N, plus`succ(y)`x, succ(plus`y`x)))"
-apply (tactic "intr_tac @{context} []")
-apply (tactic "eqintr_tac @{context}")
+apply intr
+apply eqintr
 apply (tactic "resolve_tac [TSimp.split_eqn] 3")
 apply (tactic "SELECT_GOAL (rew_tac @{context} []) 4")
 apply (tactic "resolve_tac [TSimp.split_eqn] 3")
 apply (tactic "SELECT_GOAL (rew_tac @{context} []) 4")
 apply (rule_tac [3] p = "y" in NC_succ)
   (**  by (resolve_tac comp_rls 3);  caused excessive branching  **)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/CTT/ex/Typechecking.thy
--- a/src/CTT/ex/Typechecking.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/CTT/ex/Typechecking.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -6,7 +6,7 @@
 section "Easy examples: type checking and type deduction"
 
 theory Typechecking
-imports CTT
+imports "../CTT"
 begin
 
 subsection {* Single-step proofs: verifying that a type is well-formed *}
@@ -34,54 +34,54 @@
 subsection {* Multi-step proofs: Type inference *}
 
 lemma "PROD w:N. N + N type"
-apply (tactic "form_tac @{context}")
+apply form
 done
 
 schematic_lemma "<0, succ(0)> : ?A"
-apply (tactic "intr_tac @{context} []")
+apply intr
 done
 
 schematic_lemma "PROD w:N . Eq(?A,w,w) type"
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
 schematic_lemma "PROD x:N . PROD y:N . Eq(?A,x,y) type"
-apply (tactic "typechk_tac @{context} []")
+apply typechk
 done
 
 text "typechecking an application of fst"
-schematic_lemma "(lam u. split(u, %v w. v)) ` <0, succ(0)> : ?A"
-apply (tactic "typechk_tac @{context} []")
+schematic_lemma "(lam u. split(u, \<lambda>v w. v)) ` <0, succ(0)> : ?A"
+apply typechk
 done
 
 text "typechecking the predecessor function"
-schematic_lemma "lam n. rec(n, 0, %x y. x) : ?A"
-apply (tactic "typechk_tac @{context} []")
+schematic_lemma "lam n. rec(n, 0, \<lambda>x y. x) : ?A"
+apply typechk
 done
 
 text "typechecking the addition function"
-schematic_lemma "lam n. lam m. rec(n, m, %x y. succ(y)) : ?A"
-apply (tactic "typechk_tac @{context} []")
+schematic_lemma "lam n. lam m. rec(n, m, \<lambda>x y. succ(y)) : ?A"
+apply typechk
 done
 
 (*Proofs involving arbitrary types.
   For concreteness, every type variable left over is forced to be N*)
-ML {* val N_tac = TRYALL (rtac @{thm NF}) *}
+method_setup N = {* Scan.succeed (fn _ => SIMPLE_METHOD (TRYALL (resolve_tac @{thms NF}))) *}
 
 schematic_lemma "lam w. <w,w> : ?A"
-apply (tactic "typechk_tac @{context} []")
-apply (tactic N_tac)
+apply typechk
+apply N
 done
 
 schematic_lemma "lam x. lam y. x : ?A"
-apply (tactic "typechk_tac @{context} []")
-apply (tactic N_tac)
+apply typechk
+apply N
 done
 
 text "typechecking fst (as a function object)"
-schematic_lemma "lam i. split(i, %j k. j) : ?A"
-apply (tactic "typechk_tac @{context} []")
-apply (tactic N_tac)
+schematic_lemma "lam i. split(i, \<lambda>j k. j) : ?A"
+apply typechk
+apply N
 done
 
 end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Doc/antiquote_setup.ML
--- a/src/Doc/antiquote_setup.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Doc/antiquote_setup.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -90,7 +90,7 @@
         else txt1 ^ " : " ^ txt2;
       val txt' = if kind = "" then txt else kind ^ " " ^ txt;
 
-      val pos = #pos source1;
+      val (pos, _) = #range source1;
       val _ =
         ML_Context.eval_in (SOME ctxt) ML_Compiler.flags pos (ml (toks1, toks2))
           handle ERROR msg => error (msg ^ Position.here pos);
diff -r 2f65dcd32a59 -r 51890cb80b30 src/HOL/ex/Cartouche_Examples.thy
--- a/src/HOL/ex/Cartouche_Examples.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/HOL/ex/Cartouche_Examples.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -146,7 +146,8 @@
           ML_Lex.read Position.none "fn _ => (" @
           ML_Lex.read_source false source @
           ML_Lex.read Position.none ");";
-        val _ = ML_Context.eval_in (SOME context) ML_Compiler.flags (#pos source) toks;
+        val (pos, _) = #range source;
+        val _ = ML_Context.eval_in (SOME context) ML_Compiler.flags pos toks;
       in "" end);
 *}
 
@@ -213,7 +214,7 @@
   fun ml_tactic source ctxt =
     let
       val ctxt' = ctxt |> Context.proof_map
-        (ML_Context.expression (#pos source)
+        (ML_Context.expression (#range source)
           "fun tactic (ctxt : Proof.context) : tactic"
           "Context.map_proof (ML_Tactic.set tactic)" (ML_Lex.read_source false source));
     in Data.get ctxt' ctxt end;
diff -r 2f65dcd32a59 -r 51890cb80b30 src/LCF/LCF.thy
--- a/src/LCF/LCF.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/LCF/LCF.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -31,28 +31,28 @@
  UU     :: "'a"
  TT     :: "tr"
  FF     :: "tr"
- FIX    :: "('a => 'a) => 'a"
- FST    :: "'a*'b => 'a"
- SND    :: "'a*'b => 'b"
- INL    :: "'a => 'a+'b"
- INR    :: "'b => 'a+'b"
- WHEN   :: "['a=>'c, 'b=>'c, 'a+'b] => 'c"
- adm    :: "('a => o) => o"
+ FIX    :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a"
+ FST    :: "'a*'b \<Rightarrow> 'a"
+ SND    :: "'a*'b \<Rightarrow> 'b"
+ INL    :: "'a \<Rightarrow> 'a+'b"
+ INR    :: "'b \<Rightarrow> 'a+'b"
+ WHEN   :: "['a\<Rightarrow>'c, 'b\<Rightarrow>'c, 'a+'b] \<Rightarrow> 'c"
+ adm    :: "('a \<Rightarrow> o) \<Rightarrow> o"
  VOID   :: "void"               ("'(')")
- PAIR   :: "['a,'b] => 'a*'b"   ("(1<_,/_>)" [0,0] 100)
- COND   :: "[tr,'a,'a] => 'a"   ("(_ =>/ (_ |/ _))" [60,60,60] 60)
- less   :: "['a,'a] => o"       (infixl "<<" 50)
+ PAIR   :: "['a,'b] \<Rightarrow> 'a*'b"   ("(1<_,/_>)" [0,0] 100)
+ COND   :: "[tr,'a,'a] \<Rightarrow> 'a"   ("(_ \<Rightarrow>/ (_ |/ _))" [60,60,60] 60)
+ less   :: "['a,'a] \<Rightarrow> o"       (infixl "<<" 50)
 
 axiomatization where
   (** DOMAIN THEORY **)
 
-  eq_def:        "x=y == x << y & y << x" and
+  eq_def:        "x=y == x << y \<and> y << x" and
 
-  less_trans:    "[| x << y; y << z |] ==> x << z" and
+  less_trans:    "\<lbrakk>x << y; y << z\<rbrakk> \<Longrightarrow> x << z" and
 
-  less_ext:      "(ALL x. f(x) << g(x)) ==> f << g" and
+  less_ext:      "(\<forall>x. f(x) << g(x)) \<Longrightarrow> f << g" and
 
-  mono:          "[| f << g; x << y |] ==> f(x) << g(y)" and
+  mono:          "\<lbrakk>f << g; x << y\<rbrakk> \<Longrightarrow> f(x) << g(y)" and
 
   minimal:       "UU << x" and
 
@@ -61,16 +61,16 @@
 axiomatization where
   (** TR **)
 
-  tr_cases:      "p=UU | p=TT | p=FF" and
+  tr_cases:      "p=UU \<or> p=TT \<or> p=FF" and
 
-  not_TT_less_FF: "~ TT << FF" and
-  not_FF_less_TT: "~ FF << TT" and
-  not_TT_less_UU: "~ TT << UU" and
-  not_FF_less_UU: "~ FF << UU" and
+  not_TT_less_FF: "\<not> TT << FF" and
+  not_FF_less_TT: "\<not> FF << TT" and
+  not_TT_less_UU: "\<not> TT << UU" and
+  not_FF_less_UU: "\<not> FF << UU" and
 
-  COND_UU:       "UU => x | y  =  UU" and
-  COND_TT:       "TT => x | y  =  x" and
-  COND_FF:       "FF => x | y  =  y"
+  COND_UU:       "UU \<Rightarrow> x | y  =  UU" and
+  COND_TT:       "TT \<Rightarrow> x | y  =  x" and
+  COND_FF:       "FF \<Rightarrow> x | y  =  y"
 
 axiomatization where
   (** PAIRS **)
@@ -83,18 +83,18 @@
 axiomatization where
   (*** STRICT SUM ***)
 
-  INL_DEF: "~x=UU ==> ~INL(x)=UU" and
-  INR_DEF: "~x=UU ==> ~INR(x)=UU" and
+  INL_DEF: "\<not>x=UU \<Longrightarrow> \<not>INL(x)=UU" and
+  INR_DEF: "\<not>x=UU \<Longrightarrow> \<not>INR(x)=UU" and
 
   INL_STRICT: "INL(UU) = UU" and
   INR_STRICT: "INR(UU) = UU" and
 
   WHEN_UU:  "WHEN(f,g,UU) = UU" and
-  WHEN_INL: "~x=UU ==> WHEN(f,g,INL(x)) = f(x)" and
-  WHEN_INR: "~x=UU ==> WHEN(f,g,INR(x)) = g(x)" and
+  WHEN_INL: "\<not>x=UU \<Longrightarrow> WHEN(f,g,INL(x)) = f(x)" and
+  WHEN_INR: "\<not>x=UU \<Longrightarrow> WHEN(f,g,INR(x)) = g(x)" and
 
   SUM_EXHAUSTION:
-    "z = UU | (EX x. ~x=UU & z = INL(x)) | (EX y. ~y=UU & z = INR(y))"
+    "z = UU \<or> (\<exists>x. \<not>x=UU \<and> z = INL(x)) \<or> (\<exists>y. \<not>y=UU \<and> z = INR(y))"
 
 axiomatization where
   (** VOID **)
@@ -104,7 +104,7 @@
   (** INDUCTION **)
 
 axiomatization where
-  induct:        "[| adm(P); P(UU); ALL x. P(x) --> P(f(x)) |] ==> P(FIX(f))"
+  induct: "\<lbrakk>adm(P); P(UU); \<forall>x. P(x) \<longrightarrow> P(f(x))\<rbrakk> \<Longrightarrow> P(FIX(f))"
 
 axiomatization where
   (** Admissibility / Chain Completeness **)
@@ -112,20 +112,20 @@
      Note that "easiness" of types is not taken into account
      because it cannot be expressed schematically; flatness could be. *)
 
-  adm_less:      "\<And>t u. adm(%x. t(x) << u(x))" and
-  adm_not_less:  "\<And>t u. adm(%x.~ t(x) << u)" and
-  adm_not_free:  "\<And>A. adm(%x. A)" and
-  adm_subst:     "\<And>P t. adm(P) ==> adm(%x. P(t(x)))" and
-  adm_conj:      "\<And>P Q. [| adm(P); adm(Q) |] ==> adm(%x. P(x)&Q(x))" and
-  adm_disj:      "\<And>P Q. [| adm(P); adm(Q) |] ==> adm(%x. P(x)|Q(x))" and
-  adm_imp:       "\<And>P Q. [| adm(%x.~P(x)); adm(Q) |] ==> adm(%x. P(x)-->Q(x))" and
-  adm_all:       "\<And>P. (!!y. adm(P(y))) ==> adm(%x. ALL y. P(y,x))"
+  adm_less:      "\<And>t u. adm(\<lambda>x. t(x) << u(x))" and
+  adm_not_less:  "\<And>t u. adm(\<lambda>x.\<not> t(x) << u)" and
+  adm_not_free:  "\<And>A. adm(\<lambda>x. A)" and
+  adm_subst:     "\<And>P t. adm(P) \<Longrightarrow> adm(\<lambda>x. P(t(x)))" and
+  adm_conj:      "\<And>P Q. \<lbrakk>adm(P); adm(Q)\<rbrakk> \<Longrightarrow> adm(\<lambda>x. P(x)\<and>Q(x))" and
+  adm_disj:      "\<And>P Q. \<lbrakk>adm(P); adm(Q)\<rbrakk> \<Longrightarrow> adm(\<lambda>x. P(x)\<or>Q(x))" and
+  adm_imp:       "\<And>P Q. \<lbrakk>adm(\<lambda>x.\<not>P(x)); adm(Q)\<rbrakk> \<Longrightarrow> adm(\<lambda>x. P(x)\<longrightarrow>Q(x))" and
+  adm_all:       "\<And>P. (\<And>y. adm(P(y))) \<Longrightarrow> adm(\<lambda>x. \<forall>y. P(y,x))"
 
 
-lemma eq_imp_less1: "x = y ==> x << y"
+lemma eq_imp_less1: "x = y \<Longrightarrow> x << y"
   by (simp add: eq_def)
 
-lemma eq_imp_less2: "x = y ==> y << x"
+lemma eq_imp_less2: "x = y \<Longrightarrow> y << x"
   by (simp add: eq_def)
 
 lemma less_refl [simp]: "x << x"
@@ -133,37 +133,37 @@
   apply (rule refl)
   done
 
-lemma less_anti_sym: "[| x << y; y << x |] ==> x=y"
+lemma less_anti_sym: "\<lbrakk>x << y; y << x\<rbrakk> \<Longrightarrow> x=y"
   by (simp add: eq_def)
 
-lemma ext: "(!!x::'a::cpo. f(x)=(g(x)::'b::cpo)) ==> (%x. f(x))=(%x. g(x))"
+lemma ext: "(\<And>x::'a::cpo. f(x)=(g(x)::'b::cpo)) \<Longrightarrow> (\<lambda>x. f(x))=(\<lambda>x. g(x))"
   apply (rule less_anti_sym)
   apply (rule less_ext)
   apply simp
   apply simp
   done
 
-lemma cong: "[| f=g; x=y |] ==> f(x)=g(y)"
+lemma cong: "\<lbrakk>f = g; x = y\<rbrakk> \<Longrightarrow> f(x)=g(y)"
   by simp
 
-lemma less_ap_term: "x << y ==> f(x) << f(y)"
+lemma less_ap_term: "x << y \<Longrightarrow> f(x) << f(y)"
   by (rule less_refl [THEN mono])
 
-lemma less_ap_thm: "f << g ==> f(x) << g(x)"
+lemma less_ap_thm: "f << g \<Longrightarrow> f(x) << g(x)"
   by (rule less_refl [THEN [2] mono])
 
-lemma ap_term: "(x::'a::cpo) = y ==> (f(x)::'b::cpo) = f(y)"
+lemma ap_term: "(x::'a::cpo) = y \<Longrightarrow> (f(x)::'b::cpo) = f(y)"
   apply (rule cong [OF refl])
   apply simp
   done
 
-lemma ap_thm: "f = g ==> f(x) = g(x)"
+lemma ap_thm: "f = g \<Longrightarrow> f(x) = g(x)"
   apply (erule cong)
   apply (rule refl)
   done
 
 
-lemma UU_abs: "(%x::'a::cpo. UU) = UU"
+lemma UU_abs: "(\<lambda>x::'a::cpo. UU) = UU"
   apply (rule less_anti_sym)
   prefer 2
   apply (rule minimal)
@@ -175,28 +175,28 @@
 lemma UU_app: "UU(x) = UU"
   by (rule UU_abs [symmetric, THEN ap_thm])
 
-lemma less_UU: "x << UU ==> x=UU"
+lemma less_UU: "x << UU \<Longrightarrow> x=UU"
   apply (rule less_anti_sym)
   apply assumption
   apply (rule minimal)
   done
 
-lemma tr_induct: "[| P(UU); P(TT); P(FF) |] ==> ALL b. P(b)"
+lemma tr_induct: "\<lbrakk>P(UU); P(TT); P(FF)\<rbrakk> \<Longrightarrow> \<forall>b. P(b)"
   apply (rule allI)
   apply (rule mp)
   apply (rule_tac [2] p = b in tr_cases)
   apply blast
   done
 
-lemma Contrapos: "~ B ==> (A ==> B) ==> ~A"
+lemma Contrapos: "\<not> B \<Longrightarrow> (A \<Longrightarrow> B) \<Longrightarrow> \<not>A"
   by blast
 
-lemma not_less_imp_not_eq1: "~ x << y \<Longrightarrow> x \<noteq> y"
+lemma not_less_imp_not_eq1: "\<not> x << y \<Longrightarrow> x \<noteq> y"
   apply (erule Contrapos)
   apply simp
   done
 
-lemma not_less_imp_not_eq2: "~ y << x \<Longrightarrow> x \<noteq> y"
+lemma not_less_imp_not_eq2: "\<not> y << x \<Longrightarrow> x \<noteq> y"
   apply (erule Contrapos)
   apply simp
   done
@@ -216,7 +216,7 @@
 
 
 lemma COND_cases_iff [rule_format]:
-    "ALL b. P(b=>x|y) <-> (b=UU-->P(UU)) & (b=TT-->P(x)) & (b=FF-->P(y))"
+    "\<forall>b. P(b\<Rightarrow>x|y) \<longleftrightarrow> (b=UU\<longrightarrow>P(UU)) \<and> (b=TT\<longrightarrow>P(x)) \<and> (b=FF\<longrightarrow>P(y))"
   apply (insert not_UU_eq_TT not_UU_eq_FF not_TT_eq_UU
     not_TT_eq_FF not_FF_eq_UU not_FF_eq_TT)
   apply (rule tr_induct)
@@ -229,7 +229,7 @@
   done
 
 lemma COND_cases: 
-  "[| x = UU --> P(UU); x = TT --> P(xa); x = FF --> P(y) |] ==> P(x => xa | y)"
+  "\<lbrakk>x = UU \<longrightarrow> P(UU); x = TT \<longrightarrow> P(xa); x = FF \<longrightarrow> P(y)\<rbrakk> \<Longrightarrow> P(x \<Rightarrow> xa | y)"
   apply (rule COND_cases_iff [THEN iffD2])
   apply blast
   done
@@ -247,7 +247,7 @@
 
 subsection {* Ordered pairs and products *}
 
-lemma expand_all_PROD: "(ALL p. P(p)) <-> (ALL x y. P(<x,y>))"
+lemma expand_all_PROD: "(\<forall>p. P(p)) \<longleftrightarrow> (\<forall>x y. P(<x,y>))"
   apply (rule iffI)
   apply blast
   apply (rule allI)
@@ -255,7 +255,7 @@
   apply blast
   done
 
-lemma PROD_less: "(p::'a*'b) << q <-> FST(p) << FST(q) & SND(p) << SND(q)"
+lemma PROD_less: "(p::'a*'b) << q \<longleftrightarrow> FST(p) << FST(q) \<and> SND(p) << SND(q)"
   apply (rule iffI)
   apply (rule conjI)
   apply (erule less_ap_term)
@@ -266,17 +266,17 @@
   apply (rule mono, erule less_ap_term, assumption)
   done
 
-lemma PROD_eq: "p=q <-> FST(p)=FST(q) & SND(p)=SND(q)"
+lemma PROD_eq: "p=q \<longleftrightarrow> FST(p)=FST(q) \<and> SND(p)=SND(q)"
   apply (rule iffI)
   apply simp
   apply (unfold eq_def)
   apply (simp add: PROD_less)
   done
 
-lemma PAIR_less [simp]: "<a,b> << <c,d> <-> a<<c & b<<d"
+lemma PAIR_less [simp]: "<a,b> << <c,d> \<longleftrightarrow> a<<c \<and> b<<d"
   by (simp add: PROD_less)
 
-lemma PAIR_eq [simp]: "<a,b> = <c,d> <-> a=c & b=d"
+lemma PAIR_eq [simp]: "<a,b> = <c,d> \<longleftrightarrow> a=c \<and> b=d"
   by (simp add: PROD_eq)
 
 lemma UU_is_UU_UU [simp]: "<UU,UU> = UU"
@@ -295,20 +295,20 @@
 
 subsection {* Fixedpoint theory *}
 
-lemma adm_eq: "adm(%x. t(x)=(u(x)::'a::cpo))"
+lemma adm_eq: "adm(\<lambda>x. t(x)=(u(x)::'a::cpo))"
   apply (unfold eq_def)
   apply (rule adm_conj adm_less)+
   done
 
-lemma adm_not_not: "adm(P) ==> adm(%x.~~P(x))"
+lemma adm_not_not: "adm(P) \<Longrightarrow> adm(\<lambda>x. \<not> \<not> P(x))"
   by simp
 
-lemma not_eq_TT: "ALL p. ~p=TT <-> (p=FF | p=UU)"
-  and not_eq_FF: "ALL p. ~p=FF <-> (p=TT | p=UU)"
-  and not_eq_UU: "ALL p. ~p=UU <-> (p=TT | p=FF)"
+lemma not_eq_TT: "\<forall>p. \<not>p=TT \<longleftrightarrow> (p=FF \<or> p=UU)"
+  and not_eq_FF: "\<forall>p. \<not>p=FF \<longleftrightarrow> (p=TT \<or> p=UU)"
+  and not_eq_UU: "\<forall>p. \<not>p=UU \<longleftrightarrow> (p=TT \<or> p=FF)"
   by (rule tr_induct, simp_all)+
 
-lemma adm_not_eq_tr: "ALL p::tr. adm(%x. ~t(x)=p)"
+lemma adm_not_eq_tr: "\<forall>p::tr. adm(\<lambda>x. \<not>t(x)=p)"
   apply (rule tr_induct)
   apply (simp_all add: not_eq_TT not_eq_FF not_eq_UU)
   apply (rule adm_disj adm_eq)+
@@ -318,15 +318,15 @@
   adm_not_free adm_eq adm_less adm_not_less
   adm_not_eq_tr adm_conj adm_disj adm_imp adm_all
 
-
-ML {*
-  fun induct_tac ctxt v i =
-    res_inst_tac ctxt [(("f", 0), v)] @{thm induct} i THEN
-    REPEAT (resolve_tac @{thms adm_lemmas} i)
+method_setup induct = {*
+  Scan.lift Args.name_inner_syntax >> (fn v => fn ctxt =>
+    SIMPLE_METHOD' (fn i =>
+      res_inst_tac ctxt [(("f", 0), v)] @{thm induct} i THEN
+      REPEAT (resolve_tac @{thms adm_lemmas} i)))
 *}
 
-lemma least_FIX: "f(p) = p ==> FIX(f) << p"
-  apply (tactic {* induct_tac @{context} "f" 1 *})
+lemma least_FIX: "f(p) = p \<Longrightarrow> FIX(f) << p"
+  apply (induct f)
   apply (rule minimal)
   apply (intro strip)
   apply (erule subst)
@@ -335,7 +335,7 @@
 
 lemma lfp_is_FIX:
   assumes 1: "f(p) = p"
-    and 2: "ALL q. f(q)=q --> p << q"
+    and 2: "\<forall>q. f(q)=q \<longrightarrow> p << q"
   shows "p = FIX(f)"
   apply (rule less_anti_sym)
   apply (rule 2 [THEN spec, THEN mp])
@@ -345,7 +345,7 @@
   done
 
 
-lemma FIX_pair: "<FIX(f),FIX(g)> = FIX(%p.<f(FST(p)),g(SND(p))>)"
+lemma FIX_pair: "<FIX(f),FIX(g)> = FIX(\<lambda>p.<f(FST(p)),g(SND(p))>)"
   apply (rule lfp_is_FIX)
   apply (simp add: FIX_eq [of f] FIX_eq [of g])
   apply (intro strip)
@@ -357,20 +357,20 @@
   apply (erule subst, rule SND [symmetric])
   done
 
-lemma FIX1: "FIX(f) = FST(FIX(%p. <f(FST(p)),g(SND(p))>))"
+lemma FIX1: "FIX(f) = FST(FIX(\<lambda>p. <f(FST(p)),g(SND(p))>))"
   by (rule FIX_pair [unfolded PROD_eq FST SND, THEN conjunct1])
 
-lemma FIX2: "FIX(g) = SND(FIX(%p. <f(FST(p)),g(SND(p))>))"
+lemma FIX2: "FIX(g) = SND(FIX(\<lambda>p. <f(FST(p)),g(SND(p))>))"
   by (rule FIX_pair [unfolded PROD_eq FST SND, THEN conjunct2])
 
 lemma induct2:
-  assumes 1: "adm(%p. P(FST(p),SND(p)))"
+  assumes 1: "adm(\<lambda>p. P(FST(p),SND(p)))"
     and 2: "P(UU::'a,UU::'b)"
-    and 3: "ALL x y. P(x,y) --> P(f(x),g(y))"
+    and 3: "\<forall>x y. P(x,y) \<longrightarrow> P(f(x),g(y))"
   shows "P(FIX(f),FIX(g))"
   apply (rule FIX1 [THEN ssubst, of _ f g])
   apply (rule FIX2 [THEN ssubst, of _ f g])
-  apply (rule induct [where ?f = "%x. <f(FST(x)),g(SND(x))>"])
+  apply (rule induct [where ?f = "\<lambda>x. <f(FST(x)),g(SND(x))>"])
   apply (rule 1)
   apply simp
   apply (rule 2)
diff -r 2f65dcd32a59 -r 51890cb80b30 src/LCF/ROOT
--- a/src/LCF/ROOT	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/LCF/ROOT	Tue Nov 11 21:14:19 2014 +0100
@@ -11,19 +11,12 @@
     Logic and Computation: Interactive proof with Cambridge LCF (CUP, 1987)
   *}
   options [document = false]
-  theories LCF
-
-session "LCF-ex" in ex = LCF +
-  description {*
-    Author:     Tobias Nipkow
-    Copyright   1991  University of Cambridge
+  theories
+    LCF
 
-    Some examples from Lawrence Paulson's book Logic and Computation.
-  *}
-  options [document = false]
-  theories
-    Ex1
-    Ex2
-    Ex3
-    Ex4
+    (* Some examples from Lawrence Paulson's book Logic and Computation *)
+    "ex/Ex1"
+    "ex/Ex2"
+    "ex/Ex3"
+    "ex/Ex4"
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/LCF/ex/Ex1.thy
--- a/src/LCF/ex/Ex1.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/LCF/ex/Ex1.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -1,17 +1,17 @@
 section {*  Section 10.4 *}
 
 theory Ex1
-imports LCF
+imports "../LCF"
 begin
 
 axiomatization
-  P     :: "'a => tr" and
-  G     :: "'a => 'a" and
-  H     :: "'a => 'a" and
-  K     :: "('a => 'a) => ('a => 'a)"
+  P     :: "'a \<Rightarrow> tr" and
+  G     :: "'a \<Rightarrow> 'a" and
+  H     :: "'a \<Rightarrow> 'a" and
+  K     :: "('a \<Rightarrow> 'a) \<Rightarrow> ('a \<Rightarrow> 'a)"
 where
   P_strict:     "P(UU) = UU" and
-  K:            "K = (%h x. P(x) => x | h(h(G(x))))" and
+  K:            "K = (\<lambda>h x. P(x) \<Rightarrow> x | h(h(G(x))))" and
   H:            "H = FIX(K)"
 
 
@@ -27,8 +27,8 @@
   apply simp
   done
 
-lemma H_idemp_lemma: "ALL x. H(FIX(K,x)) = FIX(K,x)"
-  apply (tactic {* induct_tac @{context} "K" 1 *})
+lemma H_idemp_lemma: "\<forall>x. H(FIX(K,x)) = FIX(K,x)"
+  apply (induct K)
   apply simp
   apply (simp split: COND_cases_iff)
   apply (intro strip)
@@ -36,7 +36,7 @@
   apply simp
   done
 
-lemma H_idemp: "ALL x. H(H(x)) = H(x)"
+lemma H_idemp: "\<forall>x. H(H(x)) = H(x)"
   apply (rule H_idemp_lemma [folded H])
   done
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/LCF/ex/Ex2.thy
--- a/src/LCF/ex/Ex2.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/LCF/ex/Ex2.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -1,25 +1,25 @@
 section {* Example 3.8 *}
 
 theory Ex2
-imports LCF
+imports "../LCF"
 begin
 
 axiomatization
-  P     :: "'a => tr" and
-  F     :: "'b => 'b" and
-  G     :: "'a => 'a" and
-  H     :: "'a => 'b => 'b" and
-  K     :: "('a => 'b => 'b) => ('a => 'b => 'b)"
+  P     :: "'a \<Rightarrow> tr" and
+  F     :: "'b \<Rightarrow> 'b" and
+  G     :: "'a \<Rightarrow> 'a" and
+  H     :: "'a \<Rightarrow> 'b \<Rightarrow> 'b" and
+  K     :: "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'b \<Rightarrow> 'b)"
 where
   F_strict:     "F(UU) = UU" and
-  K:            "K = (%h x y. P(x) => y | F(h(G(x),y)))" and
+  K:            "K = (\<lambda>h x y. P(x) \<Rightarrow> y | F(h(G(x),y)))" and
   H:            "H = FIX(K)"
 
 declare F_strict [simp] K [simp]
 
-lemma example: "ALL x. F(H(x::'a,y::'b)) = H(x,F(y))"
+lemma example: "\<forall>x. F(H(x::'a,y::'b)) = H(x,F(y))"
   apply (simplesubst H)
-  apply (tactic {* induct_tac @{context} "K:: ('a=>'b=>'b) => ('a=>'b=>'b)" 1 *})
+  apply (induct "K:: ('a\<Rightarrow>'b\<Rightarrow>'b) \<Rightarrow> ('a\<Rightarrow>'b\<Rightarrow>'b)")
   apply simp
   apply (simp split: COND_cases_iff)
   done
diff -r 2f65dcd32a59 -r 51890cb80b30 src/LCF/ex/Ex3.thy
--- a/src/LCF/ex/Ex3.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/LCF/ex/Ex3.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -1,12 +1,12 @@
 section {* Addition with fixpoint of successor *}
 
 theory Ex3
-imports LCF
+imports "../LCF"
 begin
 
 axiomatization
-  s     :: "'a => 'a" and
-  p     :: "'a => 'a => 'a"
+  s     :: "'a \<Rightarrow> 'a" and
+  p     :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"
 where
   p_strict:     "p(UU) = UU" and
   p_s:          "p(s(x),y) = s(p(x,y))"
@@ -14,7 +14,7 @@
 declare p_strict [simp] p_s [simp]
 
 lemma example: "p(FIX(s),y) = FIX(s)"
-  apply (tactic {* induct_tac @{context} "s" 1 *})
+  apply (induct s)
   apply simp
   apply simp
   done
diff -r 2f65dcd32a59 -r 51890cb80b30 src/LCF/ex/Ex4.thy
--- a/src/LCF/ex/Ex4.thy	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/LCF/ex/Ex4.thy	Tue Nov 11 21:14:19 2014 +0100
@@ -2,15 +2,15 @@
 section {* Prefixpoints *}
 
 theory Ex4
-imports LCF
+imports "../LCF"
 begin
 
 lemma example:
-  assumes asms: "f(p) << p"  "!!q. f(q) << q ==> p << q"
+  assumes asms: "f(p) << p"  "\<And>q. f(q) << q \<Longrightarrow> p << q"
   shows "FIX(f)=p"
   apply (unfold eq_def)
   apply (rule conjI)
-  apply (tactic {* induct_tac @{context} "f" 1 *})
+  apply (induct f)
   apply (rule minimal)
   apply (intro strip)
   apply (rule less_trans)
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/General/position.ML
--- a/src/Pure/General/position.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/General/position.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -53,6 +53,8 @@
   val set_range: range -> T
   val reset_range: T -> T
   val range: T -> T -> range
+  val range_of_properties: Properties.T -> range
+  val properties_of_range: range -> Properties.T
   val thread_data: unit -> T
   val setmp_thread_data: T -> ('a -> 'b) -> 'a -> 'b
   val default: T -> bool * T
@@ -134,17 +136,16 @@
 
 (* markup properties *)
 
+fun get props name =
+  (case Properties.get props name of
+    NONE => 0
+  | SOME s => Markup.parse_int s);
+
 fun of_properties props =
-  let
-    fun get name =
-      (case Properties.get props name of
-        NONE => 0
-      | SOME s => Markup.parse_int s);
-  in
-    make {line = get Markup.lineN, offset = get Markup.offsetN,
-      end_offset = get Markup.end_offsetN, props = props}
-  end;
-
+  make {line = get props Markup.lineN,
+    offset = get props Markup.offsetN,
+    end_offset = get props Markup.end_offsetN,
+    props = props};
 
 fun value k i = if valid i then [(k, Markup.print_int i)] else [];
 
@@ -221,6 +222,19 @@
 
 fun range pos pos' = (set_range (pos, pos'), pos');
 
+fun range_of_properties props =
+  let
+    val pos = of_properties props;
+    val pos' =
+      make {line = get props Markup.end_lineN,
+        offset = get props Markup.end_offsetN,
+        end_offset = 0,
+        props = props};
+  in (pos, pos') end;
+
+fun properties_of_range (pos, pos') =
+  properties_of pos @ value Markup.end_lineN (the_default 0 (line_of pos'));
+
 
 (* thread data *)
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/General/symbol_pos.ML
--- a/src/Pure/General/symbol_pos.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/General/symbol_pos.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -39,7 +39,7 @@
   val implode: T list -> text
   val implode_range: Position.T -> Position.T -> T list -> text * Position.range
   val explode: text * Position.T -> T list
-  type source = {delimited: bool, text: text, pos: Position.T}
+  type source = {delimited: bool, text: text, range: Position.range}
   val source_explode: source -> T list
   val source_content: source -> string * Position.T
   val scan_ident: T list -> T list * T list
@@ -255,11 +255,11 @@
 
 (* full source information *)
 
-type source = {delimited: bool, text: text, pos: Position.T};
+type source = {delimited: bool, text: text, range: Position.range};
 
-fun source_explode {delimited = _, text, pos} = explode (text, pos);
+fun source_explode {delimited = _, text, range = (pos, _)} = explode (text, pos);
 
-fun source_content {delimited = _, text, pos} =
+fun source_content {delimited = _, text, range = (pos, _)} =
   let val syms = explode (text, pos) in (content syms, pos) end;
 
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/Isar/attrib.ML
--- a/src/Pure/Isar/attrib.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/Isar/attrib.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -206,13 +206,12 @@
 fun setup binding scan comment = define_global binding (attribute_syntax scan) comment #> snd;
 fun local_setup binding scan comment = define binding (attribute_syntax scan) comment #> snd;
 
-fun attribute_setup name source cmt =
-  (ML_Lex.read Position.none ("(" ^ ML_Syntax.make_binding name ^ ", ") @
-    ML_Lex.read_source false source @
-    ML_Lex.read Position.none (", " ^ ML_Syntax.print_string cmt ^ ")"))
-  |> ML_Context.expression (#pos source)
-    "val (name, scan, comment): binding * attribute context_parser * string"
-    "Context.map_proof (Attrib.local_setup name scan comment)"
+fun attribute_setup name source comment =
+  ML_Lex.read_source false source
+  |> ML_Context.expression (#range source)
+    "val parser: Thm.attribute context_parser"
+    ("Context.map_proof (Attrib.local_setup " ^ ML_Syntax.atomic (ML_Syntax.make_binding name) ^
+      " parser " ^ ML_Syntax.print_string comment ^ ")")
   |> Context.proof_map;
 
 
@@ -293,7 +292,7 @@
   in
     (case Token.read_no_commands keywords Parse.attribs syms of
       [raw_srcs] => check_attribs ctxt raw_srcs
-    | _ => error ("Malformed attributes" ^ Position.here (#pos source)))
+    | _ => error ("Malformed attributes" ^ Position.here (#1 (#range source))))
   end;
 
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/Isar/isar_cmd.ML
--- a/src/Pure/Isar/isar_cmd.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/Isar/isar_cmd.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -60,12 +60,14 @@
 
 fun global_setup source =
   ML_Lex.read_source false source
-  |> ML_Context.expression (#pos source) "val setup: theory -> theory" "Context.map_theory setup"
+  |> ML_Context.expression (#range source)
+    "val setup: theory -> theory" "Context.map_theory setup"
   |> Context.theory_map;
 
 fun local_setup source =
   ML_Lex.read_source false source
-  |> ML_Context.expression (#pos source) "val setup: local_theory -> local_theory" "Context.map_proof setup"
+  |> ML_Context.expression (#range source)
+    "val local_setup: local_theory -> local_theory" "Context.map_proof local_setup"
   |> Context.proof_map;
 
 
@@ -73,35 +75,35 @@
 
 fun parse_ast_translation source =
   ML_Lex.read_source false source
-  |> ML_Context.expression (#pos source)
+  |> ML_Context.expression (#range source)
     "val parse_ast_translation: (string * (Proof.context -> Ast.ast list -> Ast.ast)) list"
     "Context.map_theory (Sign.parse_ast_translation parse_ast_translation)"
   |> Context.theory_map;
 
 fun parse_translation source =
   ML_Lex.read_source false source
-  |> ML_Context.expression (#pos source)
+  |> ML_Context.expression (#range source)
     "val parse_translation: (string * (Proof.context -> term list -> term)) list"
     "Context.map_theory (Sign.parse_translation parse_translation)"
   |> Context.theory_map;
 
 fun print_translation source =
   ML_Lex.read_source false source
-  |> ML_Context.expression (#pos source)
+  |> ML_Context.expression (#range source)
     "val print_translation: (string * (Proof.context -> term list -> term)) list"
     "Context.map_theory (Sign.print_translation print_translation)"
   |> Context.theory_map;
 
 fun typed_print_translation source =
   ML_Lex.read_source false source
-  |> ML_Context.expression (#pos source)
+  |> ML_Context.expression (#range source)
     "val typed_print_translation: (string * (Proof.context -> typ -> term list -> term)) list"
     "Context.map_theory (Sign.typed_print_translation typed_print_translation)"
   |> Context.theory_map;
 
 fun print_ast_translation source =
   ML_Lex.read_source false source
-  |> ML_Context.expression (#pos source)
+  |> ML_Context.expression (#range source)
     "val print_ast_translation: (string * (Proof.context -> Ast.ast list -> Ast.ast)) list"
     "Context.map_theory (Sign.print_ast_translation print_ast_translation)"
   |> Context.theory_map;
@@ -139,7 +141,7 @@
         \end;\n");
   in
     Context.theory_map
-      (ML_Context.exec (fn () => ML_Context.eval ML_Compiler.flags (#pos source) ants))
+      (ML_Context.exec (fn () => ML_Context.eval ML_Compiler.flags (#1 (#range source)) ants))
   end;
 
 
@@ -158,7 +160,7 @@
 
 fun declaration {syntax, pervasive} source =
   ML_Lex.read_source false source
-  |> ML_Context.expression (#pos source)
+  |> ML_Context.expression (#range source)
     "val declaration: Morphism.declaration"
     ("Context.map_proof (Local_Theory.declaration {syntax = " ^ Bool.toString syntax ^ ", \
       \pervasive = " ^ Bool.toString pervasive ^ "} declaration)")
@@ -169,7 +171,7 @@
 
 fun simproc_setup name lhss source identifier =
   ML_Lex.read_source false source
-  |> ML_Context.expression (#pos source)
+  |> ML_Context.expression (#range source)
     "val proc: Morphism.morphism -> Proof.context -> cterm -> thm option"
     ("Context.map_proof (Simplifier.def_simproc_cmd {name = " ^ ML_Syntax.make_binding name ^ ", \
       \lhss = " ^ ML_Syntax.print_strings lhss ^ ", proc = proc, \
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/Isar/isar_syn.ML
--- a/src/Pure/Isar/isar_syn.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/Isar/isar_syn.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -232,7 +232,7 @@
     (Resources.provide_parse_files "SML_file" >> (fn files => Toplevel.theory (fn thy =>
         let
           val ([{lines, pos, ...}], thy') = files thy;
-          val source = {delimited = true, text = cat_lines lines, pos = pos};
+          val source = {delimited = true, text = cat_lines lines, range = (pos, pos)};
           val flags = {SML = true, exchange = false, redirect = true, verbose = true};
         in
           thy' |> Context.theory_map
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/Isar/method.ML
--- a/src/Pure/Isar/method.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/Isar/method.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -282,7 +282,7 @@
     Scan.lift (Args.text_declaration (fn source =>
       let
         val context' = context |>
-          ML_Context.expression (#pos source)
+          ML_Context.expression (#range source)
             "fun tactic (morphism: Morphism.morphism) (facts: thm list) : tactic"
             "Method.set_tactic tactic" (ML_Lex.read_source false source);
         val tac = the_tactic context';
@@ -377,13 +377,12 @@
 fun setup binding scan comment = define_global binding (method_syntax scan) comment #> snd;
 fun local_setup binding scan comment = define binding (method_syntax scan) comment #> snd;
 
-fun method_setup name source cmt =
-  (ML_Lex.read Position.none ("(" ^ ML_Syntax.make_binding name ^ ", ") @
-    ML_Lex.read_source false source @
-    ML_Lex.read Position.none (", " ^ ML_Syntax.print_string cmt ^ ")"))
-  |> ML_Context.expression (#pos source)
-    "val (name, scan, comment): binding * (Proof.context -> Proof.method) context_parser * string"
-    "Context.map_proof (Method.local_setup name scan comment)"
+fun method_setup name source comment =
+  ML_Lex.read_source false source
+  |> ML_Context.expression (#range source)
+    "val parser: (Proof.context -> Proof.method) context_parser"
+    ("Context.map_proof (Method.local_setup " ^ ML_Syntax.atomic (ML_Syntax.make_binding name) ^
+      " parser " ^ ML_Syntax.print_string comment ^ ")")
   |> Context.proof_map;
 
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/Isar/token.ML
--- a/src/Pure/Isar/token.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/Isar/token.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -268,8 +268,8 @@
       val tree = XML.Elem (Markup.token delimited (Position.properties_of pos), [XML.Text source]);
     in YXML.string_of tree end;
 
-fun source_position_of (Token ((source, (pos, _)), (kind, _), _)) =
-  {delimited = delimited_kind kind, text = source, pos = pos};
+fun source_position_of (Token ((source, range), (kind, _), _)) =
+  {delimited = delimited_kind kind, text = source, range = range};
 
 fun content_of (Token (_, (_, x), _)) = x;
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/ML/ml_antiquotations.ML
--- a/src/Pure/ML/ml_antiquotations.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/ML/ml_antiquotations.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -34,10 +34,10 @@
 
 val _ = Theory.setup
  (ML_Antiquotation.value @{binding source}
-    (Scan.lift Args.text_source_position >> (fn {delimited, text, pos} =>
+    (Scan.lift Args.text_source_position >> (fn {delimited, text, range} =>
       "{delimited = " ^ Bool.toString delimited ^
       ", text = " ^ ML_Syntax.print_string text ^
-      ", pos = " ^ ML_Syntax.print_position pos ^ "}")));
+      ", range = " ^ ML_Syntax.print_range range ^ "}")));
 
 
 (* formal entities *)
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/ML/ml_context.ML
--- a/src/Pure/ML/ml_context.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/ML/ml_context.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -25,8 +25,8 @@
   val eval_in: Proof.context option -> ML_Compiler.flags -> Position.T ->
     ML_Lex.token Antiquote.antiquote list -> unit
   val eval_source_in: Proof.context option -> ML_Compiler.flags -> Symbol_Pos.source -> unit
-  val expression: Position.T -> string -> string -> ML_Lex.token Antiquote.antiquote list ->
-    Context.generic -> Context.generic
+  val expression: Position.range -> string -> string ->
+    ML_Lex.token Antiquote.antiquote list -> Context.generic -> Context.generic
 end
 
 structure ML_Context: ML_CONTEXT =
@@ -173,7 +173,7 @@
   in eval flags pos (ML_Lex.read pos (File.read path)) end;
 
 fun eval_source flags source =
-  eval flags (#pos source) (ML_Lex.read_source (#SML flags) source);
+  eval flags (#1 (#range source)) (ML_Lex.read_source (#SML flags) source);
 
 fun eval_in ctxt flags pos ants =
   Context.setmp_thread_data (Option.map Context.Proof ctxt)
@@ -183,11 +183,16 @@
   Context.setmp_thread_data (Option.map Context.Proof ctxt)
     (fn () => eval_source flags source) ();
 
-fun expression pos bind body ants =
-  exec (fn () =>
-    eval ML_Compiler.flags pos
-     (ML_Lex.read Position.none ("Context.set_thread_data (SOME (let " ^ bind ^ " = ") @ ants @
-      ML_Lex.read Position.none (" in " ^ body ^ " end (ML_Context.the_generic_context ())));")));
+fun expression range bind body ants =
+  let
+    val hidden = ML_Lex.read Position.none;
+    val visible = ML_Lex.read_set_range range;
+  in
+    exec (fn () =>
+      eval ML_Compiler.flags (#1 range)
+       (hidden "Context.set_thread_data (SOME (let" @ visible bind @ hidden "=" @ ants @
+        hidden ("in " ^ body ^ " end (ML_Context.the_generic_context ())));")))
+  end;
 
 end;
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/ML/ml_file.ML
--- a/src/Pure/ML/ml_file.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/ML/ml_file.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -13,7 +13,7 @@
         let
           val [{src_path, lines, digest, pos}] = files (Context.theory_of gthy);
           val provide = Resources.provide (src_path, digest);
-          val source = {delimited = true, text = cat_lines lines, pos = pos};
+          val source = {delimited = true, text = cat_lines lines, range = (pos, pos)};
           val flags = {SML = false, exchange = false, redirect = true, verbose = true};
         in
           gthy
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/ML/ml_lex.ML
--- a/src/Pure/ML/ml_lex.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/ML/ml_lex.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -26,6 +26,7 @@
       Source.source) Source.source
   val tokenize: string -> token list
   val read: Position.T -> Symbol_Pos.text -> token Antiquote.antiquote list
+  val read_set_range: Position.range -> Symbol_Pos.text -> token Antiquote.antiquote list
   val read_source: bool -> Symbol_Pos.source -> token Antiquote.antiquote list
 end;
 
@@ -325,7 +326,11 @@
 
 val read = gen_read false;
 
-fun read_source SML {delimited, text, pos} =
+fun read_set_range range =
+  read Position.none
+  #> map (fn Antiquote.Text tok => Antiquote.Text (set_range range tok) | antiq => antiq);
+
+fun read_source SML ({delimited, text, range = (pos, _)}: Symbol_Pos.source) =
   let
     val language = if SML then Markup.language_SML else Markup.language_ML;
     val _ =
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/ML/ml_syntax.ML
--- a/src/Pure/ML/ml_syntax.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/ML/ml_syntax.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -20,6 +20,7 @@
   val print_strings: string list -> string
   val print_properties: Properties.T -> string
   val print_position: Position.T -> string
+  val print_range: Position.range -> string
   val make_binding: string * Position.T -> string
   val print_indexname: indexname -> string
   val print_class: class -> string
@@ -77,8 +78,15 @@
 val print_strings = print_list print_string;
 
 val print_properties = print_list (print_pair print_string print_string);
-fun print_position pos = "Position.of_properties " ^ print_properties (Position.properties_of pos);
-fun make_binding (name, pos) = "Binding.make " ^ print_pair print_string print_position (name, pos);
+
+fun print_position pos =
+  "Position.of_properties " ^ print_properties (Position.properties_of pos);
+
+fun print_range range =
+  "Position.range_of_properties " ^ print_properties (Position.properties_of_range range);
+
+fun make_binding (name, pos) =
+  "Binding.make " ^ print_pair print_string print_position (name, pos);
 
 val print_indexname = print_pair print_string print_int;
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/PIDE/markup.ML
--- a/src/Pure/PIDE/markup.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/PIDE/markup.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -47,6 +47,7 @@
   val completionN: string val completion: T
   val no_completionN: string val no_completion: T
   val lineN: string
+  val end_lineN: string
   val offsetN: string
   val end_offsetN: string
   val fileN: string
@@ -329,8 +330,11 @@
 (* position *)
 
 val lineN = "line";
+val end_lineN = "end_line";
+
 val offsetN = "offset";
 val end_offsetN = "end_offset";
+
 val fileN = "file";
 val idN = "id";
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/PIDE/markup.scala
--- a/src/Pure/PIDE/markup.scala	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/PIDE/markup.scala	Tue Nov 11 21:14:19 2014 +0100
@@ -100,6 +100,7 @@
   /* position */
 
   val LINE = "line"
+  val END_LINE = "line"
   val OFFSET = "offset"
   val END_OFFSET = "end_offset"
   val FILE = "file"
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/Syntax/syntax.ML
--- a/src/Pure/Syntax/syntax.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/Syntax/syntax.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -163,21 +163,21 @@
 
 local
 
-fun token_position (XML.Elem ((name, props), _)) =
+fun token_range (XML.Elem ((name, props), _)) =
       if name = Markup.tokenN
-      then (Markup.is_delimited props, Position.of_properties props)
-      else (false, Position.none)
-  | token_position (XML.Text _) = (false, Position.none);
+      then (Markup.is_delimited props, Position.range_of_properties props)
+      else (false, Position.no_range)
+  | token_range (XML.Text _) = (false, Position.no_range);
 
-fun token_source tree =
+fun token_source tree : Symbol_Pos.source =
   let
     val text = XML.content_of [tree];
-    val (delimited, pos) = token_position tree;
-  in {delimited = delimited, text = text, pos = pos} end;
+    val (delimited, range) = token_range tree;
+  in {delimited = delimited, text = text, range = range} end;
 
 in
 
-fun read_token_pos str = #2 (token_position (YXML.parse str handle Fail msg => error msg));
+fun read_token_pos str = #1 (#2 (token_range (YXML.parse str handle Fail msg => error msg)));
 
 fun read_token str = token_source (YXML.parse str handle Fail msg => error msg);
 
@@ -187,8 +187,9 @@
       let
         val source = token_source tree;
         val syms = Symbol_Pos.source_explode source;
-        val _ = Context_Position.report ctxt (#pos source) (markup (#delimited source));
-      in parse (syms, #pos source) end;
+        val (pos, _) = #range source;
+        val _ = Context_Position.report ctxt pos (markup (#delimited source));
+      in parse (syms, pos) end;
   in
     (case YXML.parse_body str handle Fail msg => error msg of
       body as [tree as XML.Elem ((name, _), _)] =>
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/Syntax/syntax_phases.ML
--- a/src/Pure/Syntax/syntax_phases.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/Syntax/syntax_phases.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -462,10 +462,11 @@
       | decode ps (Ast.Appl asts) = decode_appl ps asts;
 
     val source = Syntax.read_token str;
+    val (pos, _) = #range source;
     val syms = Symbol_Pos.source_explode source;
     val ast =
-      parse_asts ctxt true root (syms, #pos source)
-      |> uncurry (report_result ctxt (#pos source))
+      parse_asts ctxt true root (syms, pos)
+      |> uncurry (report_result ctxt pos)
       |> decode [];
     val _ = Context_Position.reports_text ctxt (! reports);
   in ast end;
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/Thy/latex.ML
--- a/src/Pure/Thy/latex.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/Thy/latex.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -132,7 +132,7 @@
       enclose "{\\isacharbackquoteopen}" "{\\isacharbackquoteclose}" (output_syms s)
     else if Token.is_kind Token.Verbatim tok then
       let
-        val {text, pos, ...} = Token.source_position_of tok;
+        val {text, range = (pos, _), ...} = Token.source_position_of tok;
         val ants = Antiquote.read (Symbol_Pos.explode (text, pos), pos);
         val out = implode (map output_syms_antiq ants);
       in enclose "{\\isacharverbatimopen}" "{\\isacharverbatimclose}" out end
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/Thy/thy_output.ML
--- a/src/Pure/Thy/thy_output.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/Thy/thy_output.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -195,10 +195,10 @@
     val _ = Position.reports (maps words ants);
   in implode (map expand ants) end;
 
-fun check_text {delimited, text, pos} state =
- (Position.report pos (Markup.language_document delimited);
+fun check_text {delimited, text, range} state =
+ (Position.report (fst range) (Markup.language_document delimited);
   if Toplevel.is_skipped_proof state then ()
-  else ignore (eval_antiquote state (text, pos)));
+  else ignore (eval_antiquote state (text, fst range)));
 
 
 
@@ -372,7 +372,7 @@
         Parse.position (Scan.one (Token.is_command andf is_markup mark o Token.content_of)) --
       Scan.repeat tag --
       Parse.!!!! ((improper -- locale -- improper) |-- Parse.document_source --| improper_end)
-      >> (fn (((tok, pos'), tags), {text, pos, ...}) =>
+      >> (fn (((tok, pos'), tags), {text, range = (pos, _), ...}) =>
         let val name = Token.content_of tok
         in (SOME (name, pos', tags), (mk (name, (text, pos)), (flag, d))) end));
 
@@ -385,7 +385,7 @@
 
     val cmt = Scan.peek (fn d =>
       Parse.$$$ "--" |-- Parse.!!!! (improper |-- Parse.document_source)
-      >> (fn {text, pos, ...} => (NONE, (MarkupToken ("cmt", (text, pos)), ("", d)))));
+      >> (fn {text, range = (pos, _), ...} => (NONE, (MarkupToken ("cmt", (text, pos)), ("", d)))));
 
     val other = Scan.peek (fn d =>
        Parse.not_eof >> (fn tok => (NONE, (BasicToken tok, ("", d)))));
@@ -482,7 +482,7 @@
 
 fun pretty_text_report ctxt source =
   let
-    val {delimited, pos, ...} = source;
+    val {delimited, range = (pos, _), ...} = source;
     val _ = Context_Position.report ctxt pos (Markup.language_text delimited);
     val (s, _) = Symbol_Pos.source_content source;
   in pretty_text ctxt s end;
@@ -664,7 +664,7 @@
 
 fun ml_text name ml = antiquotation name (Scan.lift Args.text_source_position)
   (fn {context = ctxt, ...} => fn source =>
-   (ML_Context.eval_in (SOME ctxt) ML_Compiler.flags (#pos source) (ml source);
+   (ML_Context.eval_in (SOME ctxt) ML_Compiler.flags (#1 (#range source)) (ml source);
     Symbol_Pos.source_content source |> #1
     |> verbatim_text ctxt));
 
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/Thy/thy_syntax.ML
--- a/src/Pure/Thy/thy_syntax.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/Thy/thy_syntax.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -26,7 +26,7 @@
 
 fun reports_of_token tok =
   let
-    val {text, pos, ...} = Token.source_position_of tok;
+    val {text, range = (pos, _), ...} = Token.source_position_of tok;
     val malformed_symbols =
       Symbol_Pos.explode (text, pos)
       |> map_filter (fn (sym, pos) =>
diff -r 2f65dcd32a59 -r 51890cb80b30 src/Pure/Tools/rail.ML
--- a/src/Pure/Tools/rail.ML	Tue Nov 11 19:38:45 2014 +0100
+++ b/src/Pure/Tools/rail.ML	Tue Nov 11 21:14:19 2014 +0100
@@ -283,7 +283,7 @@
 
 fun read ctxt (source: Symbol_Pos.source) =
   let
-    val {text, pos, ...} = source;
+    val {text, range = (pos, _), ...} = source;
     val _ = Context_Position.report ctxt pos Markup.language_rail;
     val toks = tokenize (Symbol_Pos.explode (text, pos));
     val _ = Context_Position.reports ctxt (maps reports_of_token toks);