fixed dots;
authorwenzelm
Fri Oct 10 19:02:28 1997 +0200 (1997-10-10)
changeset 3842b55686a7b22c
parent 3841 22bbc1676768
child 3843 162f95673705
fixed dots;
src/HOL/Arith.ML
src/HOL/Finite.ML
src/HOL/Fun.ML
src/HOL/Gfp.ML
src/HOL/HOL.ML
src/HOL/HOL.thy
src/HOL/Hoare/Arith2.ML
src/HOL/Hoare/Arith2.thy
src/HOL/Hoare/Hoare.ML
src/HOL/Hoare/Hoare.thy
src/HOL/IMP/Hoare.ML
src/HOL/IMP/Hoare.thy
src/HOL/IMP/VC.ML
src/HOL/IMP/VC.thy
src/HOL/IOA/IOA.ML
src/HOL/IOA/IOA.thy
src/HOL/IOA/Solve.ML
src/HOL/Induct/LFilter.ML
src/HOL/Induct/LList.ML
src/HOL/Induct/LList.thy
src/HOL/Induct/PropLog.thy
src/HOL/Induct/SList.ML
src/HOL/Induct/SList.thy
src/HOL/Induct/Simult.ML
src/HOL/Induct/Term.ML
src/HOL/Lex/AutoChopper.ML
src/HOL/Lex/Prefix.ML
src/HOL/Lfp.ML
src/HOL/List.ML
src/HOL/List.thy
src/HOL/MiniML/Instance.ML
src/HOL/MiniML/Maybe.thy
src/HOL/MiniML/Type.ML
src/HOL/MiniML/Type.thy
src/HOL/MiniML/W.ML
src/HOL/Modelcheck/MuCalculus.thy
src/HOL/NatDef.ML
src/HOL/NatDef.thy
src/HOL/Prod.ML
src/HOL/Prod.thy
src/HOL/Quot/FRACT.ML
src/HOL/Quot/HQUOT.ML
src/HOL/Quot/HQUOT.thy
src/HOL/Quot/NPAIR.thy
src/HOL/Quot/PER.ML
src/HOL/Quot/PER0.thy
src/HOL/Set.ML
src/HOL/Set.thy
src/HOL/Subst/AList.thy
src/HOL/Subst/Subst.ML
src/HOL/Subst/Subst.thy
src/HOL/Sum.ML
src/HOL/Sum.thy
src/HOL/TLA/IntLemmas.ML
src/HOL/TLA/Intensional.ML
src/HOL/TLA/Stfun.ML
src/HOL/Univ.ML
src/HOL/W0/Maybe.thy
src/HOL/W0/Type.ML
src/HOL/W0/Type.thy
src/HOL/W0/W.ML
src/HOL/WF.thy
src/HOL/cladata.ML
src/HOL/datatype.ML
src/HOL/equalities.ML
src/HOL/ex/MT.ML
src/HOL/ex/MT.thy
src/HOL/ex/NatSum.ML
src/HOL/ex/Puzzle.ML
src/HOL/ex/Qsort.ML
src/HOL/ex/Recdef.thy
src/HOL/ex/Sorting.ML
src/HOL/ex/cla.ML
src/HOL/ex/meson.ML
src/HOL/ex/mesontest.ML
src/HOL/ex/set.ML
src/HOL/mono.ML
src/HOL/simpdata.ML
src/HOLCF/Cfun2.ML
src/HOLCF/Cfun3.ML
src/HOLCF/Cfun3.thy
src/HOLCF/Cont.ML
src/HOLCF/Cont.thy
src/HOLCF/Cprod2.ML
src/HOLCF/Cprod3.ML
src/HOLCF/Cprod3.thy
src/HOLCF/Discrete.ML
src/HOLCF/Fix.ML
src/HOLCF/Fix.thy
src/HOLCF/Fun2.ML
src/HOLCF/Fun3.ML
src/HOLCF/IMP/Denotational.thy
src/HOLCF/IOA/ABP/Correctness.ML
src/HOLCF/IOA/meta_theory/CompoExecs.ML
src/HOLCF/IOA/meta_theory/CompoExecs.thy
src/HOLCF/IOA/meta_theory/CompoScheds.ML
src/HOLCF/IOA/meta_theory/CompoScheds.thy
src/HOLCF/IOA/meta_theory/CompoTraces.ML
src/HOLCF/IOA/meta_theory/CompoTraces.thy
src/HOLCF/IOA/meta_theory/Deadlock.ML
src/HOLCF/IOA/meta_theory/Sequence.ML
src/HOLCF/IOA/meta_theory/Traces.ML
src/HOLCF/IOA/meta_theory/Traces.thy
src/HOLCF/Lift.ML
src/HOLCF/Lift2.ML
src/HOLCF/Lift3.ML
src/HOLCF/Pcpo.ML
src/HOLCF/Pcpo.thy
src/HOLCF/Porder.ML
src/HOLCF/Porder.thy
src/HOLCF/Porder0.ML
src/HOLCF/Sprod2.ML
src/HOLCF/Sprod3.ML
src/HOLCF/Sprod3.thy
src/HOLCF/Ssum0.thy
src/HOLCF/Ssum1.thy
src/HOLCF/Ssum2.ML
src/HOLCF/Ssum3.ML
src/HOLCF/Ssum3.thy
src/HOLCF/Tr.thy
src/HOLCF/Up1.thy
src/HOLCF/Up2.ML
src/HOLCF/Up3.ML
src/HOLCF/Up3.thy
src/HOLCF/ex/Dlist.ML
src/HOLCF/ex/Dnat.ML
src/HOLCF/ex/Focus_ex.ML
src/HOLCF/ex/Focus_ex.thy
src/HOLCF/ex/Hoare.ML
src/HOLCF/ex/Loop.ML
src/HOLCF/ex/Stream.ML
src/HOLCF/ex/loeckx.ML
     1.1 --- a/src/HOL/Arith.ML	Fri Oct 10 18:37:49 1997 +0200
     1.2 +++ b/src/HOL/Arith.ML	Fri Oct 10 19:02:28 1997 +0200
     1.3 @@ -255,7 +255,7 @@
     1.4  
     1.5  (*non-strict, in 1st argument*)
     1.6  goal Arith.thy "!!i j k::nat. i<=j ==> i + k <= j + k";
     1.7 -by (res_inst_tac [("f", "%j.j+k")] less_mono_imp_le_mono 1);
     1.8 +by (res_inst_tac [("f", "%j. j+k")] less_mono_imp_le_mono 1);
     1.9  by (etac add_less_mono1 1);
    1.10  by (assume_tac 1);
    1.11  qed "add_le_mono1";
     2.1 --- a/src/HOL/Finite.ML	Fri Oct 10 18:37:49 1997 +0200
     2.2 +++ b/src/HOL/Finite.ML	Fri Oct 10 19:02:28 1997 +0200
     2.3 @@ -215,8 +215,8 @@
     2.4  qed "finite_has_card";
     2.5  
     2.6  goal Finite.thy
     2.7 -  "!!A.[| x ~: A; insert x A = {f i|i.i<n} |] ==> \
     2.8 -\  ? m::nat. m<n & (? g. A = {g i|i.i<m})";
     2.9 +  "!!A.[| x ~: A; insert x A = {f i|i. i<n} |] ==> \
    2.10 +\  ? m::nat. m<n & (? g. A = {g i|i. i<m})";
    2.11  by (res_inst_tac [("n","n")] natE 1);
    2.12   by (hyp_subst_tac 1);
    2.13   by (Asm_full_simp_tac 1);
    2.14 @@ -277,11 +277,11 @@
    2.15  val lemma = result();
    2.16  
    2.17  goal Finite.thy "!!A. [| finite A; x ~: A |] ==> \
    2.18 -\ (LEAST n. ? f. insert x A = {f i|i.i<n}) = Suc(LEAST n. ? f. A={f i|i.i<n})";
    2.19 +\ (LEAST n. ? f. insert x A = {f i|i. i<n}) = Suc(LEAST n. ? f. A={f i|i. i<n})";
    2.20  by (rtac Least_equality 1);
    2.21   by (dtac finite_has_card 1);
    2.22   by (etac exE 1);
    2.23 - by (dres_inst_tac [("P","%n.? f. A={f i|i.i<n}")] LeastI 1);
    2.24 + by (dres_inst_tac [("P","%n.? f. A={f i|i. i<n}")] LeastI 1);
    2.25   by (etac exE 1);
    2.26   by (res_inst_tac
    2.27     [("x","%i. if i<(LEAST n. ? f. A={f i |i. i < n}) then f i else x")] exI 1);
     3.1 --- a/src/HOL/Fun.ML	Fri Oct 10 18:37:49 1997 +0200
     3.2 +++ b/src/HOL/Fun.ML	Fri Oct 10 19:02:28 1997 +0200
     3.3 @@ -46,7 +46,7 @@
     3.4  by (etac arg_cong 1);
     3.5  qed "inj_eq";
     3.6  
     3.7 -val [major] = goal Fun.thy "inj(f) ==> (@x.f(x)=f(y)) = y";
     3.8 +val [major] = goal Fun.thy "inj(f) ==> (@x. f(x)=f(y)) = y";
     3.9  by (rtac (major RS injD) 1);
    3.10  by (rtac selectI 1);
    3.11  by (rtac refl 1);
     4.1 --- a/src/HOL/Gfp.ML	Fri Oct 10 18:37:49 1997 +0200
     4.2 +++ b/src/HOL/Gfp.ML	Fri Oct 10 19:02:28 1997 +0200
     4.3 @@ -73,13 +73,13 @@
     4.4           - instead of the condition  X <= f(X)
     4.5                             consider  X <= (f(X) Un f(f(X)) ...) Un gfp(X) ***)
     4.6  
     4.7 -val [prem] = goal Gfp.thy "mono(f) ==> mono(%x.f(x) Un X Un B)";
     4.8 +val [prem] = goal Gfp.thy "mono(f) ==> mono(%x. f(x) Un X Un B)";
     4.9  by (REPEAT (ares_tac [subset_refl, monoI, Un_mono, prem RS monoD] 1));
    4.10  qed "coinduct3_mono_lemma";
    4.11  
    4.12  val [prem,mono] = goal Gfp.thy
    4.13 -    "[| X <= f(lfp(%x.f(x) Un X Un gfp(f)));  mono(f) |] ==> \
    4.14 -\    lfp(%x.f(x) Un X Un gfp(f)) <= f(lfp(%x.f(x) Un X Un gfp(f)))";
    4.15 +    "[| X <= f(lfp(%x. f(x) Un X Un gfp(f)));  mono(f) |] ==> \
    4.16 +\    lfp(%x. f(x) Un X Un gfp(f)) <= f(lfp(%x. f(x) Un X Un gfp(f)))";
    4.17  by (rtac subset_trans 1);
    4.18  by (rtac (mono RS coinduct3_mono_lemma RS lfp_lemma3) 1);
    4.19  by (rtac (Un_least RS Un_least) 1);
    4.20 @@ -92,7 +92,7 @@
    4.21  qed "coinduct3_lemma";
    4.22  
    4.23  val prems = goal Gfp.thy
    4.24 -    "[| mono(f);  a:X;  X <= f(lfp(%x.f(x) Un X Un gfp(f))) |] ==> a : gfp(f)";
    4.25 +    "[| mono(f);  a:X;  X <= f(lfp(%x. f(x) Un X Un gfp(f))) |] ==> a : gfp(f)";
    4.26  by (rtac (coinduct3_lemma RSN (2,weak_coinduct)) 1);
    4.27  by (resolve_tac (prems RL [coinduct3_mono_lemma RS lfp_Tarski RS ssubst]) 1);
    4.28  by (rtac (UnI2 RS UnI1) 1);
    4.29 @@ -123,7 +123,7 @@
    4.30  qed "def_Collect_coinduct";
    4.31  
    4.32  val rew::prems = goal Gfp.thy
    4.33 -    "[| A==gfp(f); mono(f);  a:X;  X <= f(lfp(%x.f(x) Un X Un A)) |] ==> a: A";
    4.34 +    "[| A==gfp(f); mono(f);  a:X;  X <= f(lfp(%x. f(x) Un X Un A)) |] ==> a: A";
    4.35  by (rewtac rew);
    4.36  by (REPEAT (ares_tac (map (rewrite_rule [rew]) prems @ [coinduct3]) 1));
    4.37  qed "def_coinduct3";
     5.1 --- a/src/HOL/HOL.ML	Fri Oct 10 18:37:49 1997 +0200
     5.2 +++ b/src/HOL/HOL.ML	Fri Oct 10 19:02:28 1997 +0200
     5.3 @@ -90,15 +90,15 @@
     5.4  qed_goalw "allI" HOL.thy [All_def] "(!!x::'a. P(x)) ==> !x. P(x)"
     5.5   (fn prems => [resolve_tac (prems RL [eqTrueI RS ext]) 1]);
     5.6  
     5.7 -qed_goalw "spec" HOL.thy [All_def] "! x::'a.P(x) ==> P(x)"
     5.8 +qed_goalw "spec" HOL.thy [All_def] "! x::'a. P(x) ==> P(x)"
     5.9   (fn prems => [rtac eqTrueE 1, resolve_tac (prems RL [fun_cong]) 1]);
    5.10  
    5.11 -qed_goal "allE" HOL.thy "[| !x.P(x);  P(x) ==> R |] ==> R"
    5.12 +qed_goal "allE" HOL.thy "[| !x. P(x);  P(x) ==> R |] ==> R"
    5.13   (fn major::prems=>
    5.14    [ (REPEAT (resolve_tac (prems @ [major RS spec]) 1)) ]);
    5.15  
    5.16  qed_goal "all_dupE" HOL.thy 
    5.17 -    "[| ! x.P(x);  [| P(x); ! x.P(x) |] ==> R |] ==> R"
    5.18 +    "[| ! x. P(x);  [| P(x); ! x. P(x) |] ==> R |] ==> R"
    5.19   (fn prems =>
    5.20    [ (REPEAT (resolve_tac (prems @ (prems RL [spec])) 1)) ]);
    5.21  
    5.22 @@ -155,11 +155,11 @@
    5.23  (** Existential quantifier **)
    5.24  section "?";
    5.25  
    5.26 -qed_goalw "exI" HOL.thy [Ex_def] "P(x) ==> ? x::'a.P(x)"
    5.27 +qed_goalw "exI" HOL.thy [Ex_def] "P(x) ==> ? x::'a. P(x)"
    5.28   (fn prems => [rtac selectI 1, resolve_tac prems 1]);
    5.29  
    5.30  qed_goalw "exE" HOL.thy [Ex_def]
    5.31 -  "[| ? x::'a.P(x); !!x. P(x) ==> Q |] ==> Q"
    5.32 +  "[| ? x::'a. P(x); !!x. P(x) ==> Q |] ==> Q"
    5.33    (fn prems => [REPEAT(resolve_tac prems 1)]);
    5.34  
    5.35  
    5.36 @@ -237,12 +237,12 @@
    5.37  
    5.38  (*Sometimes easier to use: the premises have no shared variables.  Safe!*)
    5.39  qed_goal "ex_ex1I" HOL.thy
    5.40 -    "[| ? x.P(x);  !!x y. [| P(x); P(y) |] ==> x=y |] ==> ?! x. P(x)"
    5.41 +    "[| ? x. P(x);  !!x y. [| P(x); P(y) |] ==> x=y |] ==> ?! x. P(x)"
    5.42   (fn [ex,eq] => [ (rtac (ex RS exE) 1),
    5.43                    (REPEAT (ares_tac [ex1I,eq] 1)) ]);
    5.44  
    5.45  qed_goalw "ex1E" HOL.thy [Ex1_def]
    5.46 -    "[| ?! x.P(x);  !!x. [| P(x);  ! y. P(y) --> y=x |] ==> R |] ==> R"
    5.47 +    "[| ?! x. P(x);  !!x. [| P(x);  ! y. P(y) --> y=x |] ==> R |] ==> R"
    5.48   (fn major::prems =>
    5.49    [rtac (major RS exE) 1, REPEAT (etac conjE 1 ORELSE ares_tac prems 1)]);
    5.50  
    5.51 @@ -252,23 +252,23 @@
    5.52  
    5.53  (*Easier to apply than selectI: conclusion has only one occurrence of P*)
    5.54  qed_goal "selectI2" HOL.thy
    5.55 -    "[| P(a);  !!x. P(x) ==> Q(x) |] ==> Q(@x.P(x))"
    5.56 +    "[| P(a);  !!x. P(x) ==> Q(x) |] ==> Q(@x. P(x))"
    5.57   (fn prems => [ resolve_tac prems 1, 
    5.58                  rtac selectI 1, 
    5.59                  resolve_tac prems 1 ]);
    5.60  
    5.61  (*Easier to apply than selectI2 if witness ?a comes from an EX-formula*)
    5.62  qed_goal "selectI2EX" HOL.thy
    5.63 -  "[| ? a.P a; !!x. P x ==> Q x |] ==> Q(Eps P)"
    5.64 +  "[| ? a. P a; !!x. P x ==> Q x |] ==> Q(Eps P)"
    5.65  (fn [major,minor] => [rtac (major RS exE) 1, etac selectI2 1, etac minor 1]);
    5.66  
    5.67  qed_goal "select_equality" HOL.thy
    5.68 -    "[| P(a);  !!x. P(x) ==> x=a |] ==> (@x.P(x)) = a"
    5.69 +    "[| P(a);  !!x. P(x) ==> x=a |] ==> (@x. P(x)) = a"
    5.70   (fn prems => [ rtac selectI2 1, 
    5.71                  REPEAT (ares_tac prems 1) ]);
    5.72  
    5.73  qed_goalw "select1_equality" HOL.thy [Ex1_def]
    5.74 -  "!!P. [| ?!x.P(x); P(a) |] ==> (@x.P(x)) = a"
    5.75 +  "!!P. [| ?!x. P(x); P(a) |] ==> (@x. P(x)) = a"
    5.76  (fn _ => [rtac select_equality 1, atac 1,
    5.77            etac exE 1, etac conjE 1,
    5.78            rtac allE 1, atac 1,
    5.79 @@ -313,7 +313,7 @@
    5.80      (REPEAT (DEPTH_SOLVE_1 
    5.81          (eresolve_tac ([asm_rl,impCE,notE]@prems) 1))) ]);
    5.82  
    5.83 -qed_goal "exCI" HOL.thy "(! x. ~P(x) ==> P(a)) ==> ? x.P(x)"
    5.84 +qed_goal "exCI" HOL.thy "(! x. ~P(x) ==> P(a)) ==> ? x. P(x)"
    5.85   (fn prems=>
    5.86    [ (rtac ccontr 1),
    5.87      (REPEAT (ares_tac (prems@[exI,allI,notI,notE]) 1))  ]);
     6.1 --- a/src/HOL/HOL.thy	Fri Oct 10 18:37:49 1997 +0200
     6.2 +++ b/src/HOL/HOL.thy	Fri Oct 10 19:02:28 1997 +0200
     6.3 @@ -106,7 +106,7 @@
     6.4  
     6.5  translations
     6.6    "x ~= y"      == "~ (x = y)"
     6.7 -  "@ x.b"       == "Eps (%x. b)"
     6.8 +  "@ x. b"      == "Eps (%x. b)"
     6.9    "ALL xs. P"   => "! xs. P"
    6.10    "EX xs. P"    => "? xs. P"
    6.11    "EX! xs. P"   => "?! xs. P"
    6.12 @@ -149,18 +149,18 @@
    6.13  
    6.14    refl          "t = (t::'a)"
    6.15    subst         "[| s = t; P(s) |] ==> P(t::'a)"
    6.16 -  ext           "(!!x::'a. (f(x)::'b) = g(x)) ==> (%x.f(x)) = (%x.g(x))"
    6.17 -  selectI       "P(x::'a) ==> P(@x.P(x))"
    6.18 +  ext           "(!!x::'a. (f x ::'b) = g x) ==> (%x. f x) = (%x. g x)"
    6.19 +  selectI       "P (x::'a) ==> P (@x. P x)"
    6.20  
    6.21    impI          "(P ==> Q) ==> P-->Q"
    6.22    mp            "[| P-->Q;  P |] ==> Q"
    6.23  
    6.24  defs
    6.25  
    6.26 -  True_def      "True      == ((%x::bool.x)=(%x.x))"
    6.27 -  All_def       "All(P)    == (P = (%x.True))"
    6.28 -  Ex_def        "Ex(P)     == P(@x.P(x))"
    6.29 -  False_def     "False     == (!P.P)"
    6.30 +  True_def      "True      == ((%x::bool. x) = (%x. x))"
    6.31 +  All_def       "All(P)    == (P = (%x. True))"
    6.32 +  Ex_def        "Ex(P)     == P(@x. P(x))"
    6.33 +  False_def     "False     == (!P. P)"
    6.34    not_def       "~ P       == P-->False"
    6.35    and_def       "P & Q     == !R. (P-->Q-->R) --> R"
    6.36    or_def        "P | Q     == !R. (P-->R) --> (Q-->R) --> R"
     7.1 --- a/src/HOL/Hoare/Arith2.ML	Fri Oct 10 18:37:49 1997 +0200
     7.2 +++ b/src/HOL/Hoare/Arith2.ML	Fri Oct 10 19:02:28 1997 +0200
     7.3 @@ -62,7 +62,7 @@
     7.4  
     7.5  val prems=goalw thy [gcd_def] "n<=m ==> gcd m n = gcd (m-n) n";
     7.6  by (cut_facts_tac prems 1);
     7.7 -by (subgoal_tac "n<=m ==> !x.cd x m n = cd x (m-n) n" 1);
     7.8 +by (subgoal_tac "n<=m ==> !x. cd x m n = cd x (m-n) n" 1);
     7.9  by (Asm_simp_tac 1);
    7.10  by (rtac allI 1);
    7.11  by (etac cd_diff_l 1);
    7.12 @@ -70,7 +70,7 @@
    7.13  
    7.14  val prems=goalw thy [gcd_def] "m<=n ==> gcd m n = gcd m (n-m)";
    7.15  by (cut_facts_tac prems 1);
    7.16 -by (subgoal_tac "m<=n ==> !x.cd x m n = cd x m (n-m)" 1);
    7.17 +by (subgoal_tac "m<=n ==> !x. cd x m n = cd x m (n-m)" 1);
    7.18  by (Asm_simp_tac 1);
    7.19  by (rtac allI 1);
    7.20  by (etac cd_diff_r 1);
     8.1 --- a/src/HOL/Hoare/Arith2.thy	Fri Oct 10 18:37:49 1997 +0200
     8.2 +++ b/src/HOL/Hoare/Arith2.thy	Fri Oct 10 19:02:28 1997 +0200
     8.3 @@ -16,7 +16,7 @@
     8.4    "gcd m n     == @x.(cd x m n) & (!y.(cd y m n) --> y<=x)"
     8.5  
     8.6    pow     :: [nat, nat] => nat                              (infixl 75)
     8.7 -  "m pow n     == nat_rec (Suc 0) (%u v.m*v) n"
     8.8 +  "m pow n     == nat_rec (Suc 0) (%u v. m*v) n"
     8.9  
    8.10    fac     :: nat => nat
    8.11    "fac m       == nat_rec (Suc 0) (%u v.(Suc u)*v) m"
     9.1 --- a/src/HOL/Hoare/Hoare.ML	Fri Oct 10 18:37:49 1997 +0200
     9.2 +++ b/src/HOL/Hoare/Hoare.ML	Fri Oct 10 19:02:28 1997 +0200
     9.3 @@ -11,20 +11,20 @@
     9.4  (*** Hoare rules ***)
     9.5  
     9.6  val SkipRule = prove_goalw thy [Spec_def,Skip_def]
     9.7 -  "(!!s.p(s) ==> q(s)) ==> Spec p Skip q"
     9.8 +  "(!!s. p(s) ==> q(s)) ==> Spec p Skip q"
     9.9    (fn prems => [fast_tac (!claset addIs prems) 1]);
    9.10  
    9.11  val AssignRule = prove_goalw thy [Spec_def,Assign_def]
    9.12 -  "(!!s. p s ==> q(%x.if x=v then e s else s x)) ==> Spec p (Assign v e) q"
    9.13 +  "(!!s. p s ==> q(%x. if x=v then e s else s x)) ==> Spec p (Assign v e) q"
    9.14    (fn prems => [fast_tac (!claset addIs prems) 1]);
    9.15  
    9.16  val SeqRule = prove_goalw thy [Spec_def,Seq_def]
    9.17 -  "[| Spec p c (%s.q s); Spec (%s.q s) c' r |] ==> Spec p (Seq c c') r"
    9.18 +  "[| Spec p c (%s. q s); Spec (%s. q s) c' r |] ==> Spec p (Seq c c') r"
    9.19    (fn prems => [cut_facts_tac prems 1, Fast_tac 1]);
    9.20  
    9.21  val IfRule = prove_goalw thy [Spec_def,Cond_def]
    9.22    "[| !!s. p s ==> (b s --> q s) & (~b s --> q' s); \
    9.23 -\     Spec (%s.q s) c r; Spec (%s.q' s) c' r |] \
    9.24 +\     Spec (%s. q s) c r; Spec (%s. q' s) c' r |] \
    9.25  \  ==> Spec p (Cond b c c') r"
    9.26    (fn [prem1,prem2,prem3] =>
    9.27       [REPEAT (rtac allI 1),
    9.28 @@ -39,7 +39,7 @@
    9.29                         fast_tac (!claset addIs [prem1]) 1]);
    9.30  
    9.31  val lemma = prove_goalw thy [Spec_def,While_def]
    9.32 -  "[| Spec (%s.I s & b s) c I; !!s. [| I s; ~b s |] ==> q s |] \
    9.33 +  "[| Spec (%s. I s & b s) c I; !!s. [| I s; ~b s |] ==> q s |] \
    9.34  \  ==> Spec I (While b I c) q"
    9.35    (fn [prem1,prem2] =>
    9.36       [REPEAT(rtac allI 1), rtac impI 1, etac exE 1, rtac mp 1, atac 2,
    9.37 @@ -134,7 +134,7 @@
    9.38  (* VarsElimTac: Taktik zum Eliminieren von bestimmten Programmvariablen aus dem Subgoal i
    9.39   - v::vl:(term) list  Liste der zu eliminierenden Programmvariablen
    9.40   - meta_spec:thm      Theorem, welches zur Entfernung der Variablen benutzt wird
    9.41 -		      z.B.: "(!!s x.PROP P(s,x)) ==> (!!s.PROP P(s,x(s)))"
    9.42 +		      z.B.: "(!!s x. PROP P(s,x)) ==> (!!s. PROP P(s,x(s)))"
    9.43   - namexAll:string    Name von    ^                                  (hier "x")
    9.44   - varx:term          Term zu                                      ^ (hier Var(("x",0),...))
    9.45   - varP:term          Term zu                                  ^     (hier Var(("P",0),...))
    9.46 @@ -144,25 +144,25 @@
    9.47        - eliminiere jede pvar durch Anwendung von comp_inst_ren_tac. Dazu:
    9.48        - Unbenennung in meta_spec: namexAll wird in den Namen der Prog.-Var. umbenannt
    9.49  	z.B.: fuer die Prog.-Var. mit Namen "a" ergibt sich
    9.50 -	      meta_spec zu "(!! s a.PROP P(s,a)) ==> (!! s.PROP P(s,x(s)))"
    9.51 +	      meta_spec zu "(!! s a. PROP P(s,a)) ==> (!! s. PROP P(s,x(s)))"
    9.52        - Instanziierungen in meta_spec:
    9.53 -	      varx wird mit "%s:(type_pvar) state.s(pvar)" instanziiert
    9.54 +	      varx wird mit "%s:(type_pvar) state. s(pvar)" instanziiert
    9.55  	      varP wird entsprechend instanziiert. Beispiel fuer Prog.-Var. "a":
    9.56 -	 - zu Subgoal "!!s.s(Suc(0)) = s(0) ==> s(0) = 1" bestimme Term ohne "!!s.":
    9.57 +	 - zu Subgoal "!!s. s(Suc(0)) = s(0) ==> s(0) = 1" bestimme Term ohne "!!s.":
    9.58  		trm0 = "s(Suc(0)) = s(0) ==> s(0) = 1" (s ist hier freie Variable)
    9.59  	 - substituiere alle Vorkommen von s(pvar) durch eine freie Var. xs:
    9.60  		trm1 = "s(Suc(0)) = xs ==> xs = 1"
    9.61  	 - abstrahiere ueber xs:
    9.62 -		trm2 = "%xs.s(Suc(0)) = xs ==> xs = 1"
    9.63 +		trm2 = "%xs. s(Suc(0)) = xs ==> xs = 1"
    9.64  	 - abstrahiere ueber restliche Vorkommen von s:
    9.65 -		trm3 = "%s xs.s(Suc(0)) = xs ==> xs = 1"
    9.66 +		trm3 = "%s xs. s(Suc(0)) = xs ==> xs = 1"
    9.67  	 - instanziiere varP mit trm3
    9.68  *)
    9.69  
    9.70  (* StateElimTac: tactic to eliminate all program variable from subgoal i
    9.71 -    - applies to subgoals of the form "!!s:('a) state.P(s)",
    9.72 +    - applies to subgoals of the form "!!s:('a) state. P(s)",
    9.73          i.e. the term  Const("all",_) $ Abs ("s",pvar --> 'a,_)
    9.74 -    -   meta_spec has the form "(!!s x.PROP P(s,x)) ==> (!!s.PROP P(s,x(s)))"
    9.75 +    -   meta_spec has the form "(!!s x. PROP P(s,x)) ==> (!!s. PROP P(s,x(s)))"
    9.76  *)
    9.77  
    9.78  val StateElimTac = SUBGOAL (fn (Bi,i) =>
    10.1 --- a/src/HOL/Hoare/Hoare.thy	Fri Oct 10 18:37:49 1997 +0200
    10.2 +++ b/src/HOL/Hoare/Hoare.thy	Fri Oct 10 19:02:28 1997 +0200
    10.3 @@ -34,7 +34,7 @@
    10.4    "Skip s s' == (s=s')"
    10.5  
    10.6    Assign        :: [pvar, 'a exp] => 'a com
    10.7 -  "Assign v e s s' == (s' = (%x.if x=v then e(s) else s(x)))"
    10.8 +  "Assign v e s s' == (s' = (%x. if x=v then e(s) else s(x)))"
    10.9  
   10.10    Seq           :: ['a com, 'a com] => 'a com
   10.11    "Seq c c' s s' == ? s''. c s s'' & c' s'' s'"
    11.1 --- a/src/HOL/IMP/Hoare.ML	Fri Oct 10 18:37:49 1997 +0200
    11.2 +++ b/src/HOL/IMP/Hoare.ML	Fri Oct 10 19:02:28 1997 +0200
    11.3 @@ -27,7 +27,7 @@
    11.4  by (Simp_tac 1);
    11.5  qed "wp_SKIP";
    11.6  
    11.7 -goalw Hoare.thy [wp_def] "wp (x:=a) Q = (%s.Q(s[a s/x]))";
    11.8 +goalw Hoare.thy [wp_def] "wp (x:=a) Q = (%s. Q(s[a s/x]))";
    11.9  by (Simp_tac 1);
   11.10  qed "wp_Ass";
   11.11  
   11.12 @@ -66,7 +66,7 @@
   11.13  
   11.14  goal thy
   11.15    "wp (WHILE b DO c) Q s = \
   11.16 -\  (s : gfp(%S.{s.if b s then wp c (%s.s:S) s else Q s}))";
   11.17 +\  (s : gfp(%S.{s. if b s then wp c (%s. s:S) s else Q s}))";
   11.18  by (simp_tac (!simpset setloop(split_tac[expand_if])) 1);
   11.19  by (rtac iffI 1);
   11.20   by (rtac weak_coinduct 1);
    12.1 --- a/src/HOL/IMP/Hoare.thy	Fri Oct 10 18:37:49 1997 +0200
    12.2 +++ b/src/HOL/IMP/Hoare.thy	Fri Oct 10 19:02:28 1997 +0200
    12.3 @@ -20,7 +20,7 @@
    12.4  inductive hoare
    12.5  intrs
    12.6    skip "|- {P}SKIP{P}"
    12.7 -  ass  "|- {%s.P(s[a s/x])} x:=a {P}"
    12.8 +  ass  "|- {%s. P(s[a s/x])} x:=a {P}"
    12.9    semi "[| |- {P}c{Q}; |- {Q}d{R} |] ==> |- {P} c;d {R}"
   12.10    If "[| |- {%s. P s & b s}c{Q}; |- {%s. P s & ~b s}d{Q} |] ==>
   12.11        |- {P} IF b THEN c ELSE d {Q}"
    13.1 --- a/src/HOL/IMP/VC.ML	Fri Oct 10 18:37:49 1997 +0200
    13.2 +++ b/src/HOL/IMP/VC.ML	Fri Oct 10 19:02:28 1997 +0200
    13.3 @@ -10,7 +10,7 @@
    13.4  
    13.5  AddIs hoare.intrs;
    13.6  
    13.7 -val lemma = prove_goal HOL.thy "!s.P s --> P s" (K[Fast_tac 1]);
    13.8 +val lemma = prove_goal HOL.thy "!s. P s --> P s" (K[Fast_tac 1]);
    13.9  
   13.10  goal VC.thy "!Q. (!s. vc c Q s) --> |- {awp c Q} astrip c {Q}";
   13.11  by (acom.induct_tac "c" 1);
    14.1 --- a/src/HOL/IMP/VC.thy	Fri Oct 10 18:37:49 1997 +0200
    14.2 +++ b/src/HOL/IMP/VC.thy	Fri Oct 10 19:02:28 1997 +0200
    14.3 @@ -23,14 +23,14 @@
    14.4  
    14.5  primrec awp acom
    14.6    "awp Askip Q = Q"
    14.7 -  "awp (Aass x a) Q = (%s.Q(s[a s/x]))"
    14.8 +  "awp (Aass x a) Q = (%s. Q(s[a s/x]))"
    14.9    "awp (Asemi c d) Q = awp c (awp d Q)"
   14.10    "awp (Aif b c d) Q = (%s. (b s-->awp c Q s) & (~b s-->awp d Q s))" 
   14.11    "awp (Awhile b I c) Q = I"
   14.12  
   14.13  primrec vc acom
   14.14 -  "vc Askip Q = (%s.True)"
   14.15 -  "vc (Aass x a) Q = (%s.True)"
   14.16 +  "vc Askip Q = (%s. True)"
   14.17 +  "vc (Aass x a) Q = (%s. True)"
   14.18    "vc (Asemi c d) Q = (%s. vc c (awp d Q) s & vc d Q s)"
   14.19    "vc (Aif b c d) Q = (%s. vc c Q s & vc d Q s)" 
   14.20    "vc (Awhile b I c) Q = (%s. (I s & ~b s --> Q s) &
   14.21 @@ -45,8 +45,8 @@
   14.22  
   14.23  (* simultaneous computation of vc and awp: *)
   14.24  primrec vcawp acom
   14.25 -  "vcawp Askip Q = (%s.True, Q)"
   14.26 -  "vcawp (Aass x a) Q = (%s.True, %s.Q(s[a s/x]))"
   14.27 +  "vcawp Askip Q = (%s. True, Q)"
   14.28 +  "vcawp (Aass x a) Q = (%s. True, %s. Q(s[a s/x]))"
   14.29    "vcawp (Asemi c d) Q = (let (vcd,wpd) = vcawp d Q;
   14.30                                (vcc,wpc) = vcawp c wpd
   14.31                            in (%s. vcc s & vcd s, wpc))"
    15.1 --- a/src/HOL/IOA/IOA.ML	Fri Oct 10 18:37:49 1997 +0200
    15.2 +++ b/src/HOL/IOA/IOA.ML	Fri Oct 10 19:02:28 1997 +0200
    15.3 @@ -47,7 +47,7 @@
    15.4  qed "mk_trace_thm";
    15.5  
    15.6  goalw IOA.thy [reachable_def] "!!A. s:starts_of(A) ==> reachable A s";
    15.7 -  by (res_inst_tac [("x","(%i.None,%i.s)")] bexI 1);
    15.8 +  by (res_inst_tac [("x","(%i. None,%i. s)")] bexI 1);
    15.9    by (Simp_tac 1);
   15.10    by (asm_simp_tac (!simpset addsimps exec_rws) 1);
   15.11  qed "reachable_0";
   15.12 @@ -56,9 +56,9 @@
   15.13  "!!A. [| reachable A s; (s,a,t) : trans_of(A) |] ==> reachable A t";
   15.14    by (asm_full_simp_tac (!simpset delsimps bex_simps) 1);
   15.15    by (safe_tac (!claset));
   15.16 -  by (res_inst_tac [("x","(%i.if i<n then fst ex i                    \
   15.17 +  by (res_inst_tac [("x","(%i. if i<n then fst ex i                    \
   15.18  \                            else (if i=n then Some a else None),    \
   15.19 -\                         %i.if i<Suc n then snd ex i else t)")] bexI 1);
   15.20 +\                         %i. if i<Suc n then snd ex i else t)")] bexI 1);
   15.21    by (res_inst_tac [("x","Suc(n)")] exI 1);
   15.22    by (Simp_tac 1);
   15.23    by (Asm_simp_tac 1);
    16.1 --- a/src/HOL/IOA/IOA.thy	Fri Oct 10 18:37:49 1997 +0200
    16.2 +++ b/src/HOL/IOA/IOA.thy	Fri Oct 10 19:02:28 1997 +0200
    16.3 @@ -104,13 +104,13 @@
    16.4  (* Restrict the trace to those members of the set s *)
    16.5  filter_oseq_def
    16.6    "filter_oseq p s ==                                                   
    16.7 -   (%i.case s(i)                                                       
    16.8 +   (%i. case s(i)                                                       
    16.9           of None => None                                               
   16.10            | Some(x) => if p x then Some x else None)"
   16.11  
   16.12  
   16.13  mk_trace_def
   16.14 -  "mk_trace(ioa) == filter_oseq(%a.a:externals(asig_of(ioa)))"
   16.15 +  "mk_trace(ioa) == filter_oseq(%a. a:externals(asig_of(ioa)))"
   16.16  
   16.17  
   16.18  (* Does an ioa have an execution with the given trace *)
    17.1 --- a/src/HOL/IOA/Solve.ML	Fri Oct 10 18:37:49 1997 +0200
    17.2 +++ b/src/HOL/IOA/Solve.ML	Fri Oct 10 19:02:28 1997 +0200
    17.3 @@ -22,7 +22,7 @@
    17.4    by (Asm_full_simp_tac 1);
    17.5  
    17.6    (* give execution of abstract automata *)
    17.7 -  by (res_inst_tac[("x","(mk_trace A (fst ex),%i.f(snd ex i))")] bexI 1);
    17.8 +  by (res_inst_tac[("x","(mk_trace A (fst ex),%i. f(snd ex i))")] bexI 1);
    17.9  
   17.10    (* Traces coincide *)
   17.11    by (asm_simp_tac (!simpset addsimps [mk_trace_def,filter_oseq_idemp])1);
   17.12 @@ -68,9 +68,9 @@
   17.13  by (asm_full_simp_tac (!simpset addsimps [reachable_def]) 1); 
   17.14  by (etac bexE 1);
   17.15  by (res_inst_tac [("x",
   17.16 -   "(filter_oseq (%a.a:actions(asig_of(C1))) \
   17.17 +   "(filter_oseq (%a. a:actions(asig_of(C1))) \
   17.18  \                (fst ex),                                                \
   17.19 -\    %i.fst (snd ex i))")]  bexI 1);
   17.20 +\    %i. fst (snd ex i))")]  bexI 1);
   17.21  (* fst(s) is in projected execution *)
   17.22   by (Simp_tac 1);
   17.23   by (Fast_tac 1);
   17.24 @@ -88,9 +88,9 @@
   17.25  by (asm_full_simp_tac (!simpset addsimps [reachable_def]) 1); 
   17.26  by (etac bexE 1);
   17.27  by (res_inst_tac [("x",
   17.28 -   "(filter_oseq (%a.a:actions(asig_of(C2)))\
   17.29 +   "(filter_oseq (%a. a:actions(asig_of(C2)))\
   17.30  \                (fst ex),                                                \
   17.31 -\    %i.snd (snd ex i))")]  bexI 1);
   17.32 +\    %i. snd (snd ex i))")]  bexI 1);
   17.33  (* fst(s) is in projected execution *)
   17.34   by (Simp_tac 1);
   17.35   by (Fast_tac 1);
    18.1 --- a/src/HOL/Induct/LFilter.ML	Fri Oct 10 18:37:49 1997 +0200
    18.2 +++ b/src/HOL/Induct/LFilter.ML	Fri Oct 10 19:02:28 1997 +0200
    18.3 @@ -178,7 +178,7 @@
    18.4  
    18.5  (*** lfilter: simple facts by coinduction ***)
    18.6  
    18.7 -goal thy "lfilter (%x.True) l = l";
    18.8 +goal thy "lfilter (%x. True) l = l";
    18.9  by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
   18.10  by (ALLGOALS Simp_tac);
   18.11  by (Blast_tac 1);
    19.1 --- a/src/HOL/Induct/LList.ML	Fri Oct 10 18:37:49 1997 +0200
    19.2 +++ b/src/HOL/Induct/LList.ML	Fri Oct 10 19:02:28 1997 +0200
    19.3 @@ -62,16 +62,16 @@
    19.4  (*** LList_corec satisfies the desired recurion equation ***)
    19.5  
    19.6  (*A continuity result?*)
    19.7 -goalw LList.thy [CONS_def] "CONS M (UN x.f(x)) = (UN x. CONS M (f x))";
    19.8 +goalw LList.thy [CONS_def] "CONS M (UN x. f(x)) = (UN x. CONS M (f x))";
    19.9  by (simp_tac (!simpset addsimps [In1_UN1, Scons_UN1_y]) 1);
   19.10  qed "CONS_UN1";
   19.11  
   19.12  (*UNUSED; obsolete?
   19.13 -goal Prod.thy "split p (%x y.UN z.f x y z) = (UN z. split p (%x y.f x y z))";
   19.14 +goal Prod.thy "split p (%x y. UN z. f x y z) = (UN z. split p (%x y. f x y z))";
   19.15  by (simp_tac (!simpset setloop (split_tac [expand_split])) 1);
   19.16  qed "split_UN1";
   19.17  
   19.18 -goal Sum.thy "sum_case s f (%y.UN z.g y z) = (UN z.sum_case s f (%y.g y z))";
   19.19 +goal Sum.thy "sum_case s f (%y. UN z. g y z) = (UN z. sum_case s f (%y. g y z))";
   19.20  by (simp_tac (!simpset setloop (split_tac [expand_sum_case])) 1);
   19.21  qed "sum_case2_UN1";
   19.22  *)
   19.23 @@ -87,7 +87,7 @@
   19.24  (** The directions of the equality are proved separately **)
   19.25  
   19.26  goalw LList.thy [LList_corec_def]
   19.27 -    "LList_corec a f <= sum_case (%u.NIL) \
   19.28 +    "LList_corec a f <= sum_case (%u. NIL) \
   19.29  \                          (split(%z w. CONS z (LList_corec w f))) (f a)";
   19.30  by (rtac UN1_least 1);
   19.31  by (res_inst_tac [("n","k")] natE 1);
   19.32 @@ -96,7 +96,7 @@
   19.33  qed "LList_corec_subset1";
   19.34  
   19.35  goalw LList.thy [LList_corec_def]
   19.36 -    "sum_case (%u.NIL) (split(%z w. CONS z (LList_corec w f))) (f a) <= \
   19.37 +    "sum_case (%u. NIL) (split(%z w. CONS z (LList_corec w f))) (f a) <= \
   19.38  \    LList_corec a f";
   19.39  by (simp_tac (!simpset addsimps [CONS_UN1]) 1);
   19.40  by (safe_tac (!claset));
   19.41 @@ -114,15 +114,15 @@
   19.42  (*definitional version of same*)
   19.43  val [rew] = goal LList.thy
   19.44      "[| !!x. h(x) == LList_corec x f |] ==>     \
   19.45 -\    h(a) = sum_case (%u.NIL) (split(%z w. CONS z (h w))) (f a)";
   19.46 +\    h(a) = sum_case (%u. NIL) (split(%z w. CONS z (h w))) (f a)";
   19.47  by (rewtac rew);
   19.48  by (rtac LList_corec 1);
   19.49  qed "def_LList_corec";
   19.50  
   19.51  (*A typical use of co-induction to show membership in the gfp. 
   19.52    Bisimulation is  range(%x. LList_corec x f) *)
   19.53 -goal LList.thy "LList_corec a f : llist({u.True})";
   19.54 -by (res_inst_tac [("X", "range(%x.LList_corec x ?g)")] llist_coinduct 1);
   19.55 +goal LList.thy "LList_corec a f : llist({u. True})";
   19.56 +by (res_inst_tac [("X", "range(%x. LList_corec x ?g)")] llist_coinduct 1);
   19.57  by (rtac rangeI 1);
   19.58  by (safe_tac (!claset));
   19.59  by (stac LList_corec 1);
   19.60 @@ -132,9 +132,9 @@
   19.61  
   19.62  (*Lemma for the proof of llist_corec*)
   19.63  goal LList.thy
   19.64 -   "LList_corec a (%z.sum_case Inl (split(%v w.Inr((Leaf(v),w)))) (f z)) : \
   19.65 +   "LList_corec a (%z. sum_case Inl (split(%v w. Inr((Leaf(v),w)))) (f z)) : \
   19.66  \   llist(range Leaf)";
   19.67 -by (res_inst_tac [("X", "range(%x.LList_corec x ?g)")] llist_coinduct 1);
   19.68 +by (res_inst_tac [("X", "range(%x. LList_corec x ?g)")] llist_coinduct 1);
   19.69  by (rtac rangeI 1);
   19.70  by (safe_tac (!claset));
   19.71  by (stac LList_corec 1);
   19.72 @@ -263,12 +263,12 @@
   19.73  
   19.74  (*abstract proof using a bisimulation*)
   19.75  val [prem1,prem2] = goal LList.thy
   19.76 - "[| !!x. h1(x) = sum_case (%u.NIL) (split(%z w. CONS z (h1 w))) (f x);  \
   19.77 -\    !!x. h2(x) = sum_case (%u.NIL) (split(%z w. CONS z (h2 w))) (f x) |]\
   19.78 + "[| !!x. h1(x) = sum_case (%u. NIL) (split(%z w. CONS z (h1 w))) (f x);  \
   19.79 +\    !!x. h2(x) = sum_case (%u. NIL) (split(%z w. CONS z (h2 w))) (f x) |]\
   19.80  \ ==> h1=h2";
   19.81  by (rtac ext 1);
   19.82  (*next step avoids an unknown (and flexflex pair) in simplification*)
   19.83 -by (res_inst_tac [("A", "{u.True}"),
   19.84 +by (res_inst_tac [("A", "{u. True}"),
   19.85                    ("r", "range(%u. (h1(u),h2(u)))")] LList_equalityI 1);
   19.86  by (rtac rangeI 1);
   19.87  by (safe_tac (!claset));
   19.88 @@ -280,8 +280,8 @@
   19.89  qed "LList_corec_unique";
   19.90  
   19.91  val [prem] = goal LList.thy
   19.92 - "[| !!x. h(x) = sum_case (%u.NIL) (split(%z w. CONS z (h w))) (f x) |] \
   19.93 -\ ==> h = (%x.LList_corec x f)";
   19.94 + "[| !!x. h(x) = sum_case (%u. NIL) (split(%z w. CONS z (h w))) (f x) |] \
   19.95 +\ ==> h = (%x. LList_corec x f)";
   19.96  by (rtac (LList_corec RS (prem RS LList_corec_unique)) 1);
   19.97  qed "equals_LList_corec";
   19.98  
   19.99 @@ -298,8 +298,8 @@
  19.100  qed "ntrunc_CONS";
  19.101  
  19.102  val [prem1,prem2] = goal LList.thy
  19.103 - "[| !!x. h1(x) = sum_case (%u.NIL) (split(%z w. CONS z (h1 w))) (f x);  \
  19.104 -\    !!x. h2(x) = sum_case (%u.NIL) (split(%z w. CONS z (h2 w))) (f x) |]\
  19.105 + "[| !!x. h1(x) = sum_case (%u. NIL) (split(%z w. CONS z (h1 w))) (f x);  \
  19.106 +\    !!x. h2(x) = sum_case (%u. NIL) (split(%z w. CONS z (h2 w))) (f x) |]\
  19.107  \ ==> h1=h2";
  19.108  by (rtac (ntrunc_equality RS ext) 1);
  19.109  by (rename_tac "x k" 1);
  19.110 @@ -338,14 +338,14 @@
  19.111  by (REPEAT (ares_tac [list_Fun_CONS_I, singletonI, UnI1] 1));
  19.112  qed "Lconst_type";
  19.113  
  19.114 -goal LList.thy "Lconst(M) = LList_corec M (%x.Inr((x,x)))";
  19.115 +goal LList.thy "Lconst(M) = LList_corec M (%x. Inr((x,x)))";
  19.116  by (rtac (equals_LList_corec RS fun_cong) 1);
  19.117  by (Simp_tac 1);
  19.118  by (rtac Lconst 1);
  19.119  qed "Lconst_eq_LList_corec";
  19.120  
  19.121  (*Thus we could have used gfp in the definition of Lconst*)
  19.122 -goal LList.thy "gfp(%N. CONS M N) = LList_corec M (%x.Inr((x,x)))";
  19.123 +goal LList.thy "gfp(%N. CONS M N) = LList_corec M (%x. Inr((x,x)))";
  19.124  by (rtac (equals_LList_corec RS fun_cong) 1);
  19.125  by (Simp_tac 1);
  19.126  by (rtac (Lconst_fun_mono RS gfp_Tarski) 1);
  19.127 @@ -485,7 +485,7 @@
  19.128                        rangeI RS LListD_Fun_CONS_I] 1));
  19.129  qed "Lmap_compose";
  19.130  
  19.131 -val [prem] = goal LList.thy "M: llist(A) ==> Lmap (%x.x) M = M";
  19.132 +val [prem] = goal LList.thy "M: llist(A) ==> Lmap (%x. x) M = M";
  19.133  by (rtac (prem RS imageI RS LList_equalityI) 1);
  19.134  by (safe_tac (!claset));
  19.135  by (etac llist.elim 1);
  19.136 @@ -547,7 +547,7 @@
  19.137  (*strong co-induction: bisimulation and case analysis on one variable*)
  19.138  goal LList.thy
  19.139      "!!M N. [| M: llist(A); N: llist(A) |] ==> Lappend M N: llist(A)";
  19.140 -by (res_inst_tac [("X", "(%u.Lappend u N)``llist(A)")] llist_coinduct 1);
  19.141 +by (res_inst_tac [("X", "(%u. Lappend u N)``llist(A)")] llist_coinduct 1);
  19.142  by (etac imageI 1);
  19.143  by (rtac subsetI 1);
  19.144  by (etac imageE 1);
  19.145 @@ -605,7 +605,7 @@
  19.146  (*definitional version of same*)
  19.147  val [rew] = goal LList.thy
  19.148      "[| !!x. h(x) == llist_corec x f |] ==>     \
  19.149 -\    h(a) = sum_case (%u.LNil) (split(%z w. LCons z (h w))) (f a)";
  19.150 +\    h(a) = sum_case (%u. LNil) (split(%z w. LCons z (h w))) (f a)";
  19.151  by (rewtac rew);
  19.152  by (rtac llist_corec 1);
  19.153  qed "def_llist_corec";
  19.154 @@ -740,7 +740,7 @@
  19.155  by (ALLGOALS Simp_tac);
  19.156  qed "lmap_compose";
  19.157  
  19.158 -goal LList.thy "lmap (%x.x) l = l";
  19.159 +goal LList.thy "lmap (%x. x) l = l";
  19.160  by (res_inst_tac [("l","l")] llist_fun_equalityI 1);
  19.161  by (ALLGOALS Simp_tac);
  19.162  qed "lmap_ident";
  19.163 @@ -793,8 +793,8 @@
  19.164      "(!!x. h(x) = LCons x (lmap f (h x))) ==> h = iterates(f)";
  19.165  by (rtac ext 1);
  19.166  by (res_inst_tac [("r", 
  19.167 -   "UN u. range(%n. (nat_rec (h u) (%m y.lmap f y) n, \
  19.168 -\                    nat_rec (iterates f u) (%m y.lmap f y) n))")] 
  19.169 +   "UN u. range(%n. (nat_rec (h u) (%m y. lmap f y) n, \
  19.170 +\                    nat_rec (iterates f u) (%m y. lmap f y) n))")] 
  19.171      llist_equalityI 1);
  19.172  by (REPEAT (resolve_tac [UN1_I, range_eqI, Pair_cong, nat_rec_0 RS sym] 1));
  19.173  by (safe_tac (!claset));
    20.1 --- a/src/HOL/Induct/LList.thy	Fri Oct 10 18:37:49 1997 +0200
    20.2 +++ b/src/HOL/Induct/LList.thy	Fri Oct 10 19:02:28 1997 +0200
    20.3 @@ -11,7 +11,7 @@
    20.4  bounds on the amount of lookahead required.
    20.5  
    20.6  Could try (but would it work for the gfp analogue of term?)
    20.7 -  LListD_Fun_def "LListD_Fun(A) == (%Z.diag({Numb(0)}) <++> diag(A) <**> Z)"
    20.8 +  LListD_Fun_def "LListD_Fun(A) == (%Z. diag({Numb(0)}) <++> diag(A) <**> Z)"
    20.9  
   20.10  A nice but complex example would be [ML for the Working Programmer, page 176]
   20.11    from(1) = enumerate (Lmap (Lmap(pack), makeqq(from(1),from(1))))
   20.12 @@ -74,7 +74,7 @@
   20.13              |] ==> (CONS a M, CONS b N) : LListD(r)"
   20.14  
   20.15  translations
   20.16 -  "case p of LNil => a | LCons x l => b" == "llist_case a (%x l.b) p"
   20.17 +  "case p of LNil => a | LCons x l => b" == "llist_case a (%x l. b) p"
   20.18  
   20.19  
   20.20  defs
   20.21 @@ -108,7 +108,7 @@
   20.22    llist_corec_def
   20.23     "llist_corec a f == 
   20.24         Abs_llist(LList_corec a 
   20.25 -                 (%z.case f z of Inl x    => Inl(x)
   20.26 +                 (%z. case f z of Inl x    => Inl(x)
   20.27                                 | Inr(v,w) => Inr(Leaf(v), w)))"
   20.28  
   20.29    llistD_Fun_def
    21.1 --- a/src/HOL/Induct/PropLog.thy	Fri Oct 10 18:37:49 1997 +0200
    21.2 +++ b/src/HOL/Induct/PropLog.thy	Fri Oct 10 19:02:28 1997 +0200
    21.3 @@ -33,14 +33,14 @@
    21.4    eval_def "tt[p] == eval2 p tt"
    21.5  
    21.6  primrec eval2 pl
    21.7 -  "eval2(false) = (%x.False)"
    21.8 -  "eval2(#v) = (%tt.v:tt)"
    21.9 -  "eval2(p->q) = (%tt.eval2 p tt-->eval2 q tt)"
   21.10 +  "eval2(false) = (%x. False)"
   21.11 +  "eval2(#v) = (%tt. v:tt)"
   21.12 +  "eval2(p->q) = (%tt. eval2 p tt-->eval2 q tt)"
   21.13  
   21.14  primrec hyps pl
   21.15    "hyps(false) = (%tt.{})"
   21.16    "hyps(#v) = (%tt.{if v:tt then #v else #v->false})"
   21.17 -  "hyps(p->q) = (%tt.hyps p tt Un hyps q tt)"
   21.18 +  "hyps(p->q) = (%tt. hyps p tt Un hyps q tt)"
   21.19  
   21.20  end
   21.21  
    22.1 --- a/src/HOL/Induct/SList.ML	Fri Oct 10 18:37:49 1997 +0200
    22.2 +++ b/src/HOL/Induct/SList.ML	Fri Oct 10 19:02:28 1997 +0200
    22.3 @@ -315,7 +315,7 @@
    22.4  by (ALLGOALS(asm_simp_tac (!simpset setloop (split_tac [expand_if]))));
    22.5  qed "mem_append2";
    22.6  
    22.7 -goal SList.thy "x mem [x:xs.P(x)] = (x mem xs & P(x))";
    22.8 +goal SList.thy "x mem [x:xs. P(x)] = (x mem xs & P(x))";
    22.9  by (list_ind_tac "xs" 1);
   22.10  by (ALLGOALS(asm_simp_tac (!simpset setloop (split_tac [expand_if]))));
   22.11  qed "mem_filter2";
   22.12 @@ -347,7 +347,7 @@
   22.13  
   22.14  (** Additional mapping lemmas **)
   22.15  
   22.16 -goal SList.thy "map (%x.x) xs = xs";
   22.17 +goal SList.thy "map (%x. x) xs = xs";
   22.18  by (list_ind_tac "xs" 1);
   22.19  by (ALLGOALS Asm_simp_tac);
   22.20  qed "map_ident2";
    23.1 --- a/src/HOL/Induct/SList.thy	Fri Oct 10 18:37:49 1997 +0200
    23.2 +++ b/src/HOL/Induct/SList.thy	Fri Oct 10 19:02:28 1997 +0200
    23.3 @@ -56,9 +56,9 @@
    23.4    "[x]"         == "x#[]"
    23.5    "[]"          == "Nil"
    23.6  
    23.7 -  "case xs of Nil => a | y#ys => b" == "list_case a (%y ys.b) xs"
    23.8 +  "case xs of Nil => a | y#ys => b" == "list_case a (%y ys. b) xs"
    23.9  
   23.10 -  "[x:xs . P]"  == "filter (%x.P) xs"
   23.11 +  "[x:xs . P]"  == "filter (%x. P) xs"
   23.12  
   23.13  defs
   23.14    (* Defining the Concrete Constructors *)
   23.15 @@ -82,7 +82,7 @@
   23.16    Nil_def       "Nil == Abs_list(NIL)"
   23.17    Cons_def      "x#xs == Abs_list(CONS (Leaf x) (Rep_list xs))"
   23.18  
   23.19 -  List_case_def "List_case c d == Case (%x.c) (Split d)"
   23.20 +  List_case_def "List_case c d == Case (%x. c) (Split d)"
   23.21  
   23.22    (* list Recursion -- the trancl is Essential; see list.ML *)
   23.23  
   23.24 @@ -99,11 +99,11 @@
   23.25    Rep_map_def "Rep_map f xs == list_rec xs NIL (%x l r. CONS (f x) r)"
   23.26    Abs_map_def "Abs_map g M == List_rec M Nil (%N L r. g(N)#r)"
   23.27  
   23.28 -  null_def      "null(xs)            == list_rec xs True (%x xs r.False)"
   23.29 -  hd_def        "hd(xs)              == list_rec xs arbitrary (%x xs r.x)"
   23.30 -  tl_def        "tl(xs)              == list_rec xs arbitrary (%x xs r.xs)"
   23.31 +  null_def      "null(xs)            == list_rec xs True (%x xs r. False)"
   23.32 +  hd_def        "hd(xs)              == list_rec xs arbitrary (%x xs r. x)"
   23.33 +  tl_def        "tl(xs)              == list_rec xs arbitrary (%x xs r. xs)"
   23.34    (* a total version of tl: *)
   23.35 -  ttl_def       "ttl(xs)             == list_rec xs [] (%x xs r.xs)"
   23.36 +  ttl_def       "ttl(xs)             == list_rec xs [] (%x xs r. xs)"
   23.37  
   23.38    set_def       "set xs              == list_rec xs {} (%x l r. insert x r)"
   23.39  
   23.40 @@ -114,6 +114,6 @@
   23.41    filter_def    "filter P xs         == 
   23.42                    list_rec xs [] (%x xs r. if P(x) then x#r else r)"
   23.43  
   23.44 -  list_case_def  "list_case a f xs == list_rec xs a (%x xs r.f x xs)"
   23.45 +  list_case_def  "list_case a f xs == list_rec xs a (%x xs r. f x xs)"
   23.46  
   23.47  end
    24.1 --- a/src/HOL/Induct/Simult.ML	Fri Oct 10 18:37:49 1997 +0200
    24.2 +++ b/src/HOL/Induct/Simult.ML	Fri Oct 10 19:02:28 1997 +0200
    24.3 @@ -87,8 +87,8 @@
    24.4  \       Q(Fnil);        \
    24.5  \       !!t ts. [| P(t);  Q(ts) |] ==> Q(Fcons t ts)    \
    24.6  \    |] ==> (! t. P(t)) & (! ts. Q(ts))";
    24.7 -by (res_inst_tac [("P1","%z.P(Abs_Tree(z))"),
    24.8 -                  ("Q1","%z.Q(Abs_Forest(z))")] 
    24.9 +by (res_inst_tac [("P1","%z. P(Abs_Tree(z))"),
   24.10 +                  ("Q1","%z. Q(Abs_Forest(z))")] 
   24.11      (Tree_Forest_induct RS conjE) 1);
   24.12  (*Instantiates ?A1 to range(Leaf). *)
   24.13  by (fast_tac (!claset addSEs [Rep_Tree_inverse RS subst, 
    25.1 --- a/src/HOL/Induct/Term.ML	Fri Oct 10 18:37:49 1997 +0200
    25.2 +++ b/src/HOL/Induct/Term.ML	Fri Oct 10 19:02:28 1997 +0200
    25.3 @@ -37,7 +37,7 @@
    25.4  (*Induction for the set term(A) *)
    25.5  val [major,minor] = goal Term.thy 
    25.6      "[| M: term(A);  \
    25.7 -\       !!x zs. [| x: A;  zs: list(term(A));  zs: list({x.R(x)}) \
    25.8 +\       !!x zs. [| x: A;  zs: list(term(A));  zs: list({x. R(x)}) \
    25.9  \               |] ==> R(x$zs)  \
   25.10  \    |] ==> R(M)";
   25.11  by (rtac (major RS term.induct) 1);
    26.1 --- a/src/HOL/Lex/AutoChopper.ML	Fri Oct 10 18:37:49 1997 +0200
    26.2 +++ b/src/HOL/Lex/AutoChopper.ML	Fri Oct 10 19:02:28 1997 +0200
    26.3 @@ -42,7 +42,7 @@
    26.4  bind_thm("no_acc", result() RS spec RS spec RS mp);
    26.5  
    26.6  
    26.7 -val [prem] = goal HOL.thy "? x.P(f(x)) ==> ? y.P(y)";
    26.8 +val [prem] = goal HOL.thy "? x. P(f(x)) ==> ? y. P(y)";
    26.9  by (cut_facts_tac [prem] 1);
   26.10  by (Fast_tac 1);
   26.11  val ex_special = result();
   26.12 @@ -108,9 +108,9 @@
   26.13   by (Asm_simp_tac 1);
   26.14   by (case_tac "acc_prefix A (next A st a) list" 1);
   26.15    by (strip_tac 1);
   26.16 -  by (res_inst_tac [("f","%k.a#k")] ex_special 1);
   26.17 +  by (res_inst_tac [("f","%k. a#k")] ex_special 1);
   26.18    by (Simp_tac 1);
   26.19 -  by (res_inst_tac [("t","%k.ys=r@a#k"),("s","%k.ys=(r@[a])@k")] subst 1);
   26.20 +  by (res_inst_tac [("t","%k. ys=r@a#k"),("s","%k. ys=(r@[a])@k")] subst 1);
   26.21     by (Simp_tac 1);
   26.22    by (Fast_tac 1);
   26.23   by (strip_tac 1);
   26.24 @@ -121,9 +121,9 @@
   26.25    by (Fast_tac 1);
   26.26   by (Simp_tac 1);
   26.27  by (strip_tac 1);
   26.28 -by (res_inst_tac [("f","%k.a#k")] ex_special 1);
   26.29 +by (res_inst_tac [("f","%k. a#k")] ex_special 1);
   26.30  by (Simp_tac 1);
   26.31 -by (res_inst_tac [("t","%k.ys=r@a#k"),("s","%k.ys=(r@[a])@k")] subst 1);
   26.32 +by (res_inst_tac [("t","%k. ys=r@a#k"),("s","%k. ys=(r@[a])@k")] subst 1);
   26.33   by (Simp_tac 1);
   26.34  by (Fast_tac 1);
   26.35  val step2_c = (result() repeat_RS spec) RS mp;
   26.36 @@ -172,7 +172,7 @@
   26.37  "! st erk r p ys yss zs. \
   26.38  \  acc xs st erk r p A = (ys#yss, zs) --> \
   26.39  \  (if acc_prefix A st xs  \
   26.40 -\   then ? g.ys=r@g & (!as. as<=xs & g<=as & g~=as --> ~fin A (nexts A st as))\
   26.41 +\   then ? g. ys=r@g & (!as. as<=xs & g<=as & g~=as --> ~fin A (nexts A st as))\
   26.42  \   else (erk~=[] & ys=erk) | (erk=[] & (ys#yss,zs)=p))";
   26.43  by (simp_tac (!simpset setloop (split_tac [expand_if])) 1);
   26.44  by (list.induct_tac "xs" 1);
   26.45 @@ -183,10 +183,10 @@
   26.46  by (case_tac "acc_prefix A (next A st a) list" 1);
   26.47   by (rtac conjI 1);
   26.48    by (strip_tac 1);
   26.49 -  by (res_inst_tac [("f","%k.a#k")] ex_special 1);
   26.50 -  by (res_inst_tac [("t","%k.ys=r@a#k"),("s","%k.ys=(r@[a])@k")] subst 1);
   26.51 +  by (res_inst_tac [("f","%k. a#k")] ex_special 1);
   26.52 +  by (res_inst_tac [("t","%k. ys=r@a#k"),("s","%k. ys=(r@[a])@k")] subst 1);
   26.53     by (Simp_tac 1);
   26.54 -  by (res_inst_tac [("P","%k.ys = (r@[a])@k & (!as. as<=list & k<=as & k ~= as --> ~ fin A (nexts A (next A st a) as))")] exE 1);
   26.55 +  by (res_inst_tac [("P","%k. ys = (r@[a])@k & (!as. as<=list & k<=as & k ~= as --> ~ fin A (nexts A (next A st a) as))")] exE 1);
   26.56     by (asm_simp_tac HOL_ss 1);
   26.57    by (res_inst_tac [("x","x")] exI 1);
   26.58    by (Asm_simp_tac 1);
   26.59 @@ -194,10 +194,10 @@
   26.60     by (Simp_tac 1);
   26.61    by (asm_simp_tac (!simpset addcongs[conj_cong]) 1);
   26.62   by (strip_tac 1);
   26.63 - by (res_inst_tac [("f","%k.a#k")] ex_special 1);
   26.64 - by (res_inst_tac [("t","%k.ys=r@a#k"),("s","%k.ys=(r@[a])@k")] subst 1);
   26.65 + by (res_inst_tac [("f","%k. a#k")] ex_special 1);
   26.66 + by (res_inst_tac [("t","%k. ys=r@a#k"),("s","%k. ys=(r@[a])@k")] subst 1);
   26.67    by (Simp_tac 1);
   26.68 - by (res_inst_tac [("P","%k.ys=(r@[a])@k & (!as. as<=list & k<=as & k~=as --> ~ fin A (nexts A (next A st a) as))")] exE 1);
   26.69 + by (res_inst_tac [("P","%k. ys=(r@[a])@k & (!as. as<=list & k<=as & k~=as --> ~ fin A (nexts A (next A st a) as))")] exE 1);
   26.70    by (asm_simp_tac HOL_ss 1);
   26.71   by (res_inst_tac [("x","x")] exI 1);
   26.72   by (Asm_simp_tac 1);
    27.1 --- a/src/HOL/Lex/Prefix.ML	Fri Oct 10 18:37:49 1997 +0200
    27.2 +++ b/src/HOL/Lex/Prefix.ML	Fri Oct 10 19:02:28 1997 +0200
    27.3 @@ -6,7 +6,7 @@
    27.4  
    27.5  open Prefix;
    27.6  
    27.7 -val [maj,min] = goal Prefix.thy "[| Q([]); !! y ys. Q(y#ys) |] ==> ! l.Q(l)";
    27.8 +val [maj,min] = goal Prefix.thy "[| Q([]); !! y ys. Q(y#ys) |] ==> ! l. Q(l)";
    27.9  by (rtac allI 1);
   27.10  by (list.induct_tac "l" 1);
   27.11  by (rtac maj 1);
    28.1 --- a/src/HOL/Lfp.ML	Fri Oct 10 18:37:49 1997 +0200
    28.2 +++ b/src/HOL/Lfp.ML	Fri Oct 10 19:02:28 1997 +0200
    28.3 @@ -41,7 +41,7 @@
    28.4  
    28.5  val [lfp,mono,indhyp] = goal Lfp.thy
    28.6      "[| a: lfp(f);  mono(f);                            \
    28.7 -\       !!x. [| x: f(lfp(f) Int {x.P(x)}) |] ==> P(x)   \
    28.8 +\       !!x. [| x: f(lfp(f) Int {x. P(x)}) |] ==> P(x)   \
    28.9  \    |] ==> P(a)";
   28.10  by (res_inst_tac [("a","a")] (Int_lower2 RS subsetD RS CollectD) 1);
   28.11  by (rtac (lfp RSN (2, lfp_lowerbound RS subsetD)) 1);
   28.12 @@ -66,7 +66,7 @@
   28.13  
   28.14  val rew::prems = goal Lfp.thy
   28.15      "[| A == lfp(f);  mono(f);   a:A;                   \
   28.16 -\       !!x. [| x: f(A Int {x.P(x)}) |] ==> P(x)        \
   28.17 +\       !!x. [| x: f(A Int {x. P(x)}) |] ==> P(x)        \
   28.18  \    |] ==> P(a)";
   28.19  by (EVERY1 [rtac induct,        (*backtracking to force correct induction*)
   28.20              REPEAT1 o (ares_tac (map (rewrite_rule [rew]) prems))]);
    29.1 --- a/src/HOL/List.ML	Fri Oct 10 18:37:49 1997 +0200
    29.2 +++ b/src/HOL/List.ML	Fri Oct 10 19:02:28 1997 +0200
    29.3 @@ -174,7 +174,7 @@
    29.4  by (ALLGOALS Asm_simp_tac);
    29.5  bind_thm("map_ext", impI RS (allI RS (result() RS mp)));
    29.6  
    29.7 -goal thy "map (%x.x) = (%xs.xs)";
    29.8 +goal thy "map (%x. x) = (%xs. xs)";
    29.9  by (rtac ext 1);
   29.10  by (induct_tac "xs" 1);
   29.11  by (ALLGOALS Asm_simp_tac);
   29.12 @@ -235,7 +235,7 @@
   29.13  qed "mem_append";
   29.14  Addsimps[mem_append];
   29.15  
   29.16 -goal thy "x mem [x:xs.P(x)] = (x mem xs & P(x))";
   29.17 +goal thy "x mem [x:xs. P(x)] = (x mem xs & P(x))";
   29.18  by (induct_tac "xs" 1);
   29.19  by (ALLGOALS (asm_simp_tac (!simpset setloop (split_tac [expand_if]))));
   29.20  qed "mem_filter";
   29.21 @@ -285,7 +285,7 @@
   29.22  
   29.23  section "list_all";
   29.24  
   29.25 -goal thy "list_all (%x.True) xs = True";
   29.26 +goal thy "list_all (%x. True) xs = True";
   29.27  by (induct_tac "xs" 1);
   29.28  by (ALLGOALS Asm_simp_tac);
   29.29  qed "list_all_True";
   29.30 @@ -599,7 +599,7 @@
   29.31  Addsimps [takeWhile_append1];
   29.32  
   29.33  goal thy
   29.34 -  "(!x:set xs.P(x)) --> takeWhile P (xs @ ys) = xs @ takeWhile P ys";
   29.35 +  "(!x:set xs. P(x)) --> takeWhile P (xs @ ys) = xs @ takeWhile P ys";
   29.36  by (induct_tac "xs" 1);
   29.37   by (Simp_tac 1);
   29.38  by (asm_full_simp_tac (!simpset setloop (split_tac[expand_if])) 1);
   29.39 @@ -616,7 +616,7 @@
   29.40  Addsimps [dropWhile_append1];
   29.41  
   29.42  goal thy
   29.43 -  "(!x:set xs.P(x)) --> dropWhile P (xs @ ys) = dropWhile P ys";
   29.44 +  "(!x:set xs. P(x)) --> dropWhile P (xs @ ys) = dropWhile P ys";
   29.45  by (induct_tac "xs" 1);
   29.46   by (Simp_tac 1);
   29.47  by (asm_full_simp_tac (!simpset setloop (split_tac[expand_if])) 1);
    30.1 --- a/src/HOL/List.thy	Fri Oct 10 18:37:49 1997 +0200
    30.2 +++ b/src/HOL/List.thy	Fri Oct 10 19:02:28 1997 +0200
    30.3 @@ -38,7 +38,7 @@
    30.4  translations
    30.5    "[x, xs]"     == "x#[xs]"
    30.6    "[x]"         == "x#[]"
    30.7 -  "[x:xs . P]"  == "filter (%x.P) xs"
    30.8 +  "[x:xs . P]"  == "filter (%x. P) xs"
    30.9  
   30.10  syntax (symbols)
   30.11    "@filter"   :: [idt, 'a list, bool] => 'a list          ("(1[_\\<in>_ ./ _])")
    31.1 --- a/src/HOL/MiniML/Instance.ML	Fri Oct 10 18:37:49 1997 +0200
    31.2 +++ b/src/HOL/MiniML/Instance.ML	Fri Oct 10 19:02:28 1997 +0200
    31.3 @@ -211,7 +211,7 @@
    31.4  
    31.5  goalw thy [le_type_scheme_def,is_bound_typ_instance] "sch <= BVar n";
    31.6  by (strip_tac 1);
    31.7 -by (res_inst_tac [("x","%a.t")]exI 1);
    31.8 +by (res_inst_tac [("x","%a. t")]exI 1);
    31.9  by (Simp_tac 1);
   31.10  qed "bound_typ_instance_BVar";
   31.11  AddIffs [bound_typ_instance_BVar];
    32.1 --- a/src/HOL/MiniML/Maybe.thy	Fri Oct 10 18:37:49 1997 +0200
    32.2 +++ b/src/HOL/MiniML/Maybe.thy	Fri Oct 10 19:02:28 1997 +0200
    32.3 @@ -13,6 +13,6 @@
    32.4    "option_bind m f == case m of None => None | Some r => f r"
    32.5  
    32.6  syntax "@option_bind" :: [pttrns,'a option,'b] => 'c ("(_ := _;//_)" 0)
    32.7 -translations "P := E; F" == "option_bind E (%P.F)"
    32.8 +translations "P := E; F" == "option_bind E (%P. F)"
    32.9  
   32.10  end
    33.1 --- a/src/HOL/MiniML/Type.ML	Fri Oct 10 18:37:49 1997 +0200
    33.2 +++ b/src/HOL/MiniML/Type.ML	Fri Oct 10 19:02:28 1997 +0200
    33.3 @@ -16,7 +16,7 @@
    33.4  by (Fast_tac 1);
    33.5  qed_spec_mp "mk_scheme_Fun";
    33.6  
    33.7 -goal thy "!t'.mk_scheme t = mk_scheme t' --> t=t'";
    33.8 +goal thy "!t'. mk_scheme t = mk_scheme t' --> t=t'";
    33.9  by (typ.induct_tac "t" 1);
   33.10   by (rtac allI 1);
   33.11   by (typ.induct_tac "t'" 1);
   33.12 @@ -110,14 +110,14 @@
   33.13  Addsimps[new_tv_id_subst];
   33.14  
   33.15  goal thy "new_tv n (sch::type_scheme) --> \
   33.16 -\              $(%k.if k<n then S k else S' k) sch = $S sch";
   33.17 +\              $(%k. if k<n then S k else S' k) sch = $S sch";
   33.18  by (type_scheme.induct_tac "sch" 1);
   33.19  by (ALLGOALS Asm_simp_tac);
   33.20  qed "new_if_subst_type_scheme";
   33.21  Addsimps [new_if_subst_type_scheme];
   33.22  
   33.23  goal thy "new_tv n (A::type_scheme list) --> \
   33.24 -\              $(%k.if k<n then S k else S' k) A = $S A";
   33.25 +\              $(%k. if k<n then S k else S' k) A = $S A";
   33.26  by (list.induct_tac "A" 1);
   33.27  by (ALLGOALS Asm_simp_tac);
   33.28  qed "new_if_subst_type_scheme_list";
   33.29 @@ -673,7 +673,7 @@
   33.30  
   33.31  (* application of id_subst does not change type expression *)
   33.32  goalw thy [id_subst_def]
   33.33 -  "$ id_subst = (%t::typ.t)";
   33.34 +  "$ id_subst = (%t::typ. t)";
   33.35  by (rtac ext 1);
   33.36  by (typ.induct_tac "t" 1);
   33.37  by (ALLGOALS Asm_simp_tac);
   33.38 @@ -681,7 +681,7 @@
   33.39  Addsimps [app_subst_id_te];
   33.40  
   33.41  goalw thy [id_subst_def]
   33.42 -  "$ id_subst = (%sch::type_scheme.sch)";
   33.43 +  "$ id_subst = (%sch::type_scheme. sch)";
   33.44  by (rtac ext 1);
   33.45  by (type_scheme.induct_tac "t" 1);
   33.46  by (ALLGOALS Asm_simp_tac);
   33.47 @@ -690,7 +690,7 @@
   33.48  
   33.49  (* application of id_subst does not change list of type expressions *)
   33.50  goalw thy [app_subst_list]
   33.51 -  "$ id_subst = (%A::type_scheme list.A)";
   33.52 +  "$ id_subst = (%A::type_scheme list. A)";
   33.53  by (rtac ext 1); 
   33.54  by (list.induct_tac "A" 1);
   33.55  by (ALLGOALS Asm_simp_tac);
    34.1 --- a/src/HOL/MiniML/Type.thy	Fri Oct 10 18:37:49 1997 +0200
    34.2 +++ b/src/HOL/MiniML/Type.thy	Fri Oct 10 19:02:28 1997 +0200
    34.3 @@ -112,7 +112,7 @@
    34.4  (* identity *)
    34.5  constdefs
    34.6          id_subst :: subst
    34.7 -        "id_subst == (%n.TVar n)"
    34.8 +        "id_subst == (%n. TVar n)"
    34.9  
   34.10  (* extension of substitution to type structures *)
   34.11  consts
    35.1 --- a/src/HOL/MiniML/W.ML	Fri Oct 10 18:37:49 1997 +0200
    35.2 +++ b/src/HOL/MiniML/W.ML	Fri Oct 10 19:02:28 1997 +0200
    35.3 @@ -485,7 +485,7 @@
    35.4  (* case Abs e *)
    35.5  by (strip_tac 1);
    35.6  by (eresolve_tac has_type_casesE 1);
    35.7 -by (eres_inst_tac [("x","%x.if x=n then t1 else (S' x)")] allE 1);
    35.8 +by (eres_inst_tac [("x","%x. if x=n then t1 else (S' x)")] allE 1);
    35.9  by (eres_inst_tac [("x","(FVar n)#A")] allE 1);
   35.10  by (eres_inst_tac [("x","t2")] allE 1);
   35.11  by (eres_inst_tac [("x","Suc n")] allE 1);
   35.12 @@ -515,9 +515,9 @@
   35.13          conjunct1,new_scheme_list_le,new_tv_subst_scheme_list]) 1);
   35.14  (** LEVEL 35 **)
   35.15  by (subgoal_tac
   35.16 -  "$ (%x.if x=ma then t' else (if x:(free_tv t - free_tv Sa) then R x \
   35.17 +  "$ (%x. if x=ma then t' else (if x:(free_tv t - free_tv Sa) then R x \
   35.18  \        else Ra x)) ($ Sa t) = \
   35.19 -\  $ (%x.if x=ma then t' else (if x:(free_tv t - free_tv Sa) then R x \
   35.20 +\  $ (%x. if x=ma then t' else (if x:(free_tv t - free_tv Sa) then R x \
   35.21  \        else Ra x)) (ta -> (TVar ma))" 1);
   35.22  by (res_inst_tac [("t","$ (%x. if x = ma then t' else \
   35.23  \   (if x:(free_tv t - free_tv Sa) then R x else Ra x)) ($ Sa t)"),
    36.1 --- a/src/HOL/Modelcheck/MuCalculus.thy	Fri Oct 10 18:37:49 1997 +0200
    36.2 +++ b/src/HOL/Modelcheck/MuCalculus.thy	Fri Oct 10 19:02:28 1997 +0200
    36.3 @@ -18,7 +18,7 @@
    36.4  
    36.5  defs 
    36.6  
    36.7 -Charfun_def      "Charfun     == (% A.% x.x:A)"
    36.8 +Charfun_def      "Charfun     == (% A.% x. x:A)"
    36.9  monoP_def        "monoP f     == mono(Collect o f o Charfun)"
   36.10  mu_def           "mu f        == Charfun(lfp(Collect o f o Charfun))"
   36.11  nu_def           "nu f        == Charfun(gfp(Collect o f o Charfun))"
    37.1 --- a/src/HOL/NatDef.ML	Fri Oct 10 18:37:49 1997 +0200
    37.2 +++ b/src/HOL/NatDef.ML	Fri Oct 10 19:02:28 1997 +0200
    37.3 @@ -585,14 +585,14 @@
    37.4  qed "Least_nat_def";
    37.5  
    37.6  val [prem1,prem2] = goalw thy [Least_nat_def]
    37.7 -    "[| P(k::nat);  !!x. x<k ==> ~P(x) |] ==> (LEAST x.P(x)) = k";
    37.8 +    "[| P(k::nat);  !!x. x<k ==> ~P(x) |] ==> (LEAST x. P(x)) = k";
    37.9  by (rtac select_equality 1);
   37.10  by (blast_tac (!claset addSIs [prem1,prem2]) 1);
   37.11  by (cut_facts_tac [less_linear] 1);
   37.12  by (blast_tac (!claset addSIs [prem1] addSDs [prem2]) 1);
   37.13  qed "Least_equality";
   37.14  
   37.15 -val [prem] = goal thy "P(k::nat) ==> P(LEAST x.P(x))";
   37.16 +val [prem] = goal thy "P(k::nat) ==> P(LEAST x. P(x))";
   37.17  by (rtac (prem RS rev_mp) 1);
   37.18  by (res_inst_tac [("n","k")] less_induct 1);
   37.19  by (rtac impI 1);
   37.20 @@ -604,7 +604,7 @@
   37.21  qed "LeastI";
   37.22  
   37.23  (*Proof is almost identical to the one above!*)
   37.24 -val [prem] = goal thy "P(k::nat) ==> (LEAST x.P(x)) <= k";
   37.25 +val [prem] = goal thy "P(k::nat) ==> (LEAST x. P(x)) <= k";
   37.26  by (rtac (prem RS rev_mp) 1);
   37.27  by (res_inst_tac [("n","k")] less_induct 1);
   37.28  by (rtac impI 1);
   37.29 @@ -615,7 +615,7 @@
   37.30  by (blast_tac (!claset addIs [less_imp_le,le_trans]) 1);
   37.31  qed "Least_le";
   37.32  
   37.33 -val [prem] = goal thy "k < (LEAST x.P(x)) ==> ~P(k::nat)";
   37.34 +val [prem] = goal thy "k < (LEAST x. P(x)) ==> ~P(k::nat)";
   37.35  by (rtac notI 1);
   37.36  by (etac (rewrite_rule [le_def] Least_le RS notE) 1);
   37.37  by (rtac prem 1);
    38.1 --- a/src/HOL/NatDef.thy	Fri Oct 10 18:37:49 1997 +0200
    38.2 +++ b/src/HOL/NatDef.thy	Fri Oct 10 19:02:28 1997 +0200
    38.3 @@ -56,7 +56,7 @@
    38.4  translations
    38.5     "1"  == "Suc 0"
    38.6     "2"  == "Suc 1"
    38.7 -  "case p of 0 => a | Suc y => b" == "nat_case a (%y.b) p"
    38.8 +  "case p of 0 => a | Suc y => b" == "nat_case a (%y. b) p"
    38.9  
   38.10  
   38.11  defs
    39.1 --- a/src/HOL/Prod.ML	Fri Oct 10 18:37:49 1997 +0200
    39.2 +++ b/src/HOL/Prod.ML	Fri Oct 10 19:02:28 1997 +0200
    39.3 @@ -88,7 +88,7 @@
    39.4  !!a b. ... = ?P(a,b)
    39.5  which cannot be solved by reflexivity.
    39.6     
    39.7 -val [prem] = goal Prod.thy "(!!x.PROP P x) ==> (!!a b. PROP P(a,b))";
    39.8 +val [prem] = goal Prod.thy "(!!x. PROP P x) ==> (!!a b. PROP P(a,b))";
    39.9  br prem 1;
   39.10  val lemma1 = result();
   39.11  
   39.12 @@ -226,7 +226,7 @@
   39.13  by (asm_simp_tac (!simpset addsimps [prod_fun,o_def]) 1);
   39.14  qed "prod_fun_compose";
   39.15  
   39.16 -goal Prod.thy "prod_fun (%x.x) (%y.y) = (%z.z)";
   39.17 +goal Prod.thy "prod_fun (%x. x) (%y. y) = (%z. z)";
   39.18  by (rtac ext 1);
   39.19  by (res_inst_tac [("p","z")] PairE 1);
   39.20  by (asm_simp_tac (!simpset addsimps [prod_fun]) 1);
    40.1 --- a/src/HOL/Prod.thy	Fri Oct 10 18:37:49 1997 +0200
    40.2 +++ b/src/HOL/Prod.thy	Fri Oct 10 19:02:28 1997 +0200
    40.3 @@ -52,17 +52,17 @@
    40.4    "@Times"      :: "['a set, 'a => 'b set] => ('a * 'b) set"    ("_ Times _" [81, 80] 80)
    40.5  
    40.6  translations
    40.7 -  "(x, y, z)"   == "(x, (y, z))"
    40.8 -  "(x, y)"      == "Pair x y"
    40.9 +  "(x, y, z)"    == "(x, (y, z))"
   40.10 +  "(x, y)"       == "Pair x y"
   40.11  
   40.12 -  "%(x,y,zs).b" == "split(%x (y,zs).b)"
   40.13 -  "%(x,y).b"    == "split(%x y.b)"
   40.14 +  "%(x,y,zs).b"  == "split(%x (y,zs).b)"
   40.15 +  "%(x,y).b"     == "split(%x y. b)"
   40.16    "_abs (Pair x y) t" => "%(x,y).t"
   40.17    (* The last rule accommodates tuples in `case C ... (x,y) ... => ...'
   40.18       The (x,y) is parsed as `Pair x y' because it is logic, not pttrn *)
   40.19  
   40.20 -  "SIGMA x:A.B" => "Sigma A (%x.B)"
   40.21 -  "A Times B"   => "Sigma A (_K B)"
   40.22 +  "SIGMA x:A. B" => "Sigma A (%x. B)"
   40.23 +  "A Times B"    => "Sigma A (_K B)"
   40.24  
   40.25  syntax (symbols)
   40.26    "@Sigma"      :: "[pttrn, 'a set, 'b set] => ('a * 'b) set"   ("(3\\<Sigma> _\\<in>_./ _)" 10)
    41.1 --- a/src/HOL/Quot/FRACT.ML	Fri Oct 10 18:37:49 1997 +0200
    41.2 +++ b/src/HOL/Quot/FRACT.ML	Fri Oct 10 19:02:28 1997 +0200
    41.3 @@ -7,7 +7,7 @@
    41.4  open FRACT;
    41.5  
    41.6  goalw thy [per_def,per_NP_def]
    41.7 -"(op ===)=(%x y.fst(rep_NP x)*snd(rep_NP y)=fst(rep_NP y)*snd(rep_NP x))";
    41.8 +"(op ===)=(%x y. fst(rep_NP x)*snd(rep_NP y)=fst(rep_NP y)*snd(rep_NP x))";
    41.9  fr refl;
   41.10  qed "inst_NP_per";
   41.11  
    42.1 --- a/src/HOL/Quot/HQUOT.ML	Fri Oct 10 18:37:49 1997 +0200
    42.2 +++ b/src/HOL/Quot/HQUOT.ML	Fri Oct 10 19:02:28 1997 +0200
    42.3 @@ -7,7 +7,7 @@
    42.4  open HQUOT;
    42.5  
    42.6  (* first prove some helpful lemmas *)
    42.7 -goalw thy [quot_def] "{y.y===x}:quot";
    42.8 +goalw thy [quot_def] "{y. y===x}:quot";
    42.9  by (Asm_simp_tac 1);
   42.10  by (fast_tac (set_cs addIs [per_sym]) 1);
   42.11  qed "per_class_rep_quot";
   42.12 @@ -20,7 +20,7 @@
   42.13  qed "quot_eq";
   42.14  
   42.15  (* prepare induction and exhaustiveness *)
   42.16 -val prems = goal thy "!s.s:quot --> P (Abs_quot s) ==> P x";
   42.17 +val prems = goal thy "!s. s:quot --> P (Abs_quot s) ==> P x";
   42.18  by (cut_facts_tac prems 1);
   42.19  by (rtac (Abs_quot_inverse RS subst) 1);
   42.20  by (rtac Rep_quot 1);
   42.21 @@ -28,7 +28,7 @@
   42.22  by (asm_full_simp_tac (HOL_ss addsimps [Rep_quot,Rep_quot_inverse]) 1);
   42.23  qed "all_q";
   42.24  
   42.25 -goal thy "? s.s:quot & x=Abs_quot s";
   42.26 +goal thy "? s. s:quot & x=Abs_quot s";
   42.27  by (res_inst_tac [("x","Rep_quot x")] exI 1);
   42.28  by (asm_full_simp_tac (HOL_ss addsimps [Rep_quot,Rep_quot_inverse]) 1);
   42.29  qed "exh_q";
   42.30 @@ -113,7 +113,7 @@
   42.31  qed "er_class_not";
   42.32  
   42.33  (* exhaustiveness and induction *)
   42.34 -goalw thy [peclass_def] "? s.x=<[s]>";
   42.35 +goalw thy [peclass_def] "? s. x=<[s]>";
   42.36  by (rtac all_q 1);
   42.37  by (strip_tac 1);
   42.38  by (asm_full_simp_tac (HOL_ss addsimps [mem_Collect_eq,quot_def]) 1);
   42.39 @@ -128,7 +128,7 @@
   42.40  by (fast_tac set_cs 1);
   42.41  qed "per_class_exh";
   42.42  
   42.43 -val prems = goal thy "!x.P<[x]> ==> P s";
   42.44 +val prems = goal thy "!x. P<[x]> ==> P s";
   42.45  by (cut_facts_tac (prems@[
   42.46  	read_instantiate[("x","s::'a::per quot")] per_class_exh]) 1);
   42.47  by (fast_tac set_cs 1);
   42.48 @@ -160,7 +160,7 @@
   42.49  qed "er_class_any_in";
   42.50  
   42.51  (* equivalent theorem for per would need !x.x:D *)
   42.52 -val prems = goal thy "!x::'a::per.x:D==><[any_in (q::'a::per quot)]> = q";
   42.53 +val prems = goal thy "!x::'a::per. x:D==><[any_in (q::'a::per quot)]> = q";
   42.54  by (cut_facts_tac prems 1);
   42.55  fr per_class_all;
   42.56  fr allI;
    43.1 --- a/src/HOL/Quot/HQUOT.thy	Fri Oct 10 18:37:49 1997 +0200
    43.2 +++ b/src/HOL/Quot/HQUOT.thy	Fri Oct 10 19:02:28 1997 +0200
    43.3 @@ -9,7 +9,7 @@
    43.4  
    43.5  HQUOT = PER +      
    43.6  
    43.7 -typedef 'a quot = "{s::'a::per set. ? r.!y.y:s=y===r}" (quotNE)
    43.8 +typedef 'a quot = "{s::'a::per set. ? r.!y. y:s=y===r}" (quotNE)
    43.9  
   43.10  (* constants for equivalence classes *)
   43.11  consts
   43.12 @@ -21,7 +21,7 @@
   43.13  translations    "<[x]>" == "peclass x"
   43.14  
   43.15  defs
   43.16 -        peclass_def     "<[x]> == Abs_quot {y.y===x}"
   43.17 +        peclass_def     "<[x]> == Abs_quot {y. y===x}"
   43.18          any_in_def      "any_in f == @x.<[x]>=f"
   43.19  end
   43.20  
    44.1 --- a/src/HOL/Quot/NPAIR.thy	Fri Oct 10 18:37:49 1997 +0200
    44.2 +++ b/src/HOL/Quot/NPAIR.thy	Fri Oct 10 19:02:28 1997 +0200
    44.3 @@ -18,7 +18,7 @@
    44.4  
    44.5  (* NPAIR (continued) *)
    44.6  defs	per_NP_def 
    44.7 -  "eqv ==(%x y.fst(rep_NP x)*snd(rep_NP y)=fst(rep_NP y)*snd(rep_NP x))"
    44.8 +  "eqv ==(%x y. fst(rep_NP x)*snd(rep_NP y)=fst(rep_NP y)*snd(rep_NP x))"
    44.9  
   44.10  (* for proves of this rule see [Slo97diss] *)
   44.11  rules
    45.1 --- a/src/HOL/Quot/PER.ML	Fri Oct 10 18:37:49 1997 +0200
    45.2 +++ b/src/HOL/Quot/PER.ML	Fri Oct 10 19:02:28 1997 +0200
    45.3 @@ -6,12 +6,12 @@
    45.4  *)
    45.5  open PER;
    45.6  
    45.7 -goalw thy [fun_per_def,per_def] "f===g=(!x y.x:D&y:D&x===y-->f x===g y)";
    45.8 +goalw thy [fun_per_def,per_def] "f===g=(!x y. x:D&y:D&x===y-->f x===g y)";
    45.9  by (rtac refl 1);
   45.10  qed "inst_fun_per";
   45.11  
   45.12  (* Witness that quot is not empty *)
   45.13 -goal thy "?z:{s.? r.!y.y:s=y===r}";
   45.14 +goal thy "?z:{s.? r.!y. y:s=y===r}";
   45.15  fr CollectI;
   45.16  by (res_inst_tac [("x","x")] exI 1);
   45.17  by (rtac allI 1);
    46.1 --- a/src/HOL/Quot/PER0.thy	Fri Oct 10 18:37:49 1997 +0200
    46.2 +++ b/src/HOL/Quot/PER0.thy	Fri Oct 10 19:02:28 1997 +0200
    46.3 @@ -27,9 +27,9 @@
    46.4          D         :: "'a::per set"
    46.5  defs
    46.6          per_def         "(op ===) == eqv"
    46.7 -        Dom             "D=={x.x===x}"
    46.8 +        Dom             "D=={x. x===x}"
    46.9  (* define ==== on and function type => *)
   46.10 -        fun_per_def     "eqv f g == !x y.x:D & y:D & x===y --> f x === g y"
   46.11 +        fun_per_def     "eqv f g == !x y. x:D & y:D & x===y --> f x === g y"
   46.12  
   46.13  syntax (symbols)
   46.14    "op ==="   :: "['a,'a::per] => bool"        (infixl "\\<sim>" 50)
    47.1 --- a/src/HOL/Set.ML	Fri Oct 10 18:37:49 1997 +0200
    47.2 +++ b/src/HOL/Set.ML	Fri Oct 10 19:02:28 1997 +0200
    47.3 @@ -13,11 +13,11 @@
    47.4  Addsimps [Collect_mem_eq];
    47.5  AddIffs  [mem_Collect_eq];
    47.6  
    47.7 -goal Set.thy "!!a. P(a) ==> a : {x.P(x)}";
    47.8 +goal Set.thy "!!a. P(a) ==> a : {x. P(x)}";
    47.9  by (Asm_simp_tac 1);
   47.10  qed "CollectI";
   47.11  
   47.12 -val prems = goal Set.thy "!!a. a : {x.P(x)} ==> P(a)";
   47.13 +val prems = goal Set.thy "!!a. a : {x. P(x)} ==> P(a)";
   47.14  by (Asm_full_simp_tac 1);
   47.15  qed "CollectD";
   47.16  
   47.17 @@ -67,7 +67,7 @@
   47.18  qed "bexI";
   47.19  
   47.20  qed_goal "bexCI" Set.thy 
   47.21 -   "[| ! x:A. ~P(x) ==> P(a);  a:A |] ==> ? x:A.P(x)"
   47.22 +   "[| ! x:A. ~P(x) ==> P(a);  a:A |] ==> ? x:A. P(x)"
   47.23   (fn prems=>
   47.24    [ (rtac classical 1),
   47.25      (REPEAT (ares_tac (prems@[bexI,ballI,notI,notE]) 1))  ]);
   47.26 @@ -82,12 +82,12 @@
   47.27  AddSEs [bexE];
   47.28  
   47.29  (*Trival rewrite rule*)
   47.30 -goal Set.thy "(! x:A.P) = ((? x. x:A) --> P)";
   47.31 +goal Set.thy "(! x:A. P) = ((? x. x:A) --> P)";
   47.32  by (simp_tac (!simpset addsimps [Ball_def]) 1);
   47.33  qed "ball_triv";
   47.34  
   47.35  (*Dual form for existentials*)
   47.36 -goal Set.thy "(? x:A.P) = ((? x. x:A) & P)";
   47.37 +goal Set.thy "(? x:A. P) = ((? x. x:A) & P)";
   47.38  by (simp_tac (!simpset addsimps [Bex_def]) 1);
   47.39  qed "bex_triv";
   47.40  
   47.41 @@ -113,7 +113,7 @@
   47.42  
   47.43  section "Subsets";
   47.44  
   47.45 -val prems = goalw Set.thy [subset_def] "(!!x.x:A ==> x:B) ==> A <= B";
   47.46 +val prems = goalw Set.thy [subset_def] "(!!x. x:A ==> x:B) ==> A <= B";
   47.47  by (REPEAT (ares_tac (prems @ [ballI]) 1));
   47.48  qed "subsetI";
   47.49  
   47.50 @@ -415,7 +415,7 @@
   47.51  AddSDs [singleton_inject];
   47.52  AddSEs [singletonE];
   47.53  
   47.54 -goal Set.thy "{x.x=a} = {a}";
   47.55 +goal Set.thy "{x. x=a} = {a}";
   47.56  by(Blast_tac 1);
   47.57  qed "singleton_conv";
   47.58  Addsimps [singleton_conv];
   47.59 @@ -606,7 +606,7 @@
   47.60  
   47.61  (*The eta-expansion gives variable-name preservation.*)
   47.62  val major::prems = goalw thy [image_def]
   47.63 -    "[| b : (%x.f(x))``A;  !!x.[| b=f(x);  x:A |] ==> P |] ==> P"; 
   47.64 +    "[| b : (%x. f(x))``A;  !!x.[| b=f(x);  x:A |] ==> P |] ==> P"; 
   47.65  by (rtac (major RS CollectD RS bexE) 1);
   47.66  by (REPEAT (ares_tac prems 1));
   47.67  qed "imageE";
   47.68 @@ -632,7 +632,7 @@
   47.69  bind_thm ("rangeI", UNIV_I RS imageI);
   47.70  
   47.71  val [major,minor] = goal thy 
   47.72 -    "[| b : range(%x.f(x));  !!x. b=f(x) ==> P |] ==> P"; 
   47.73 +    "[| b : range(%x. f(x));  !!x. b=f(x) ==> P |] ==> P"; 
   47.74  by (rtac (major RS imageE) 1);
   47.75  by (etac minor 1);
   47.76  qed "rangeE";
    48.1 --- a/src/HOL/Set.thy	Fri Oct 10 18:37:49 1997 +0200
    48.2 +++ b/src/HOL/Set.thy	Fri Oct 10 19:02:28 1997 +0200
    48.3 @@ -125,8 +125,8 @@
    48.4  
    48.5    (* Isomorphisms between Predicates and Sets *)
    48.6  
    48.7 -  mem_Collect_eq    "(a : {x.P(x)}) = P(a)"
    48.8 -  Collect_mem_eq    "{x.x:A} = A"
    48.9 +  mem_Collect_eq    "(a : {x. P(x)}) = P(a)"
   48.10 +  Collect_mem_eq    "{x. x:A} = A"
   48.11  
   48.12  
   48.13  defs
   48.14 @@ -136,18 +136,18 @@
   48.15    subset_def    "A <= B         == ! x:A. x:B"
   48.16    psubset_def   "A < B          == (A::'a set) <= B & ~ A=B"
   48.17    Compl_def     "Compl A        == {x. ~x:A}"
   48.18 -  Un_def        "A Un B         == {x.x:A | x:B}"
   48.19 -  Int_def       "A Int B        == {x.x:A & x:B}"
   48.20 +  Un_def        "A Un B         == {x. x:A | x:B}"
   48.21 +  Int_def       "A Int B        == {x. x:A & x:B}"
   48.22    set_diff_def  "A - B          == {x. x:A & ~x:B}"
   48.23    INTER_def     "INTER A B      == {y. ! x:A. y: B(x)}"
   48.24    UNION_def     "UNION A B      == {y. ? x:A. y: B(x)}"
   48.25 -  INTER1_def    "INTER1 B       == INTER {x.True} B"
   48.26 -  UNION1_def    "UNION1 B       == UNION {x.True} B"
   48.27 +  INTER1_def    "INTER1 B       == INTER {x. True} B"
   48.28 +  UNION1_def    "UNION1 B       == UNION {x. True} B"
   48.29    Inter_def     "Inter S        == (INT x:S. x)"
   48.30    Union_def     "Union S        == (UN x:S. x)"
   48.31    Pow_def       "Pow A          == {B. B <= A}"
   48.32    empty_def     "{}             == {x. False}"
   48.33 -  insert_def    "insert a B     == {x.x=a} Un B"
   48.34 +  insert_def    "insert a B     == {x. x=a} Un B"
   48.35    image_def     "f``A           == {y. ? x:A. y=f(x)}"
   48.36  
   48.37  end
    49.1 --- a/src/HOL/Subst/AList.thy	Fri Oct 10 18:37:49 1997 +0200
    49.2 +++ b/src/HOL/Subst/AList.thy	Fri Oct 10 19:02:28 1997 +0200
    49.3 @@ -17,6 +17,6 @@
    49.4  
    49.5    alist_rec_def "alist_rec al b c == list_rec b (split c) al"
    49.6  
    49.7 -  assoc_def   "assoc v d al == alist_rec al d (%x y xs g.if v=x then y else g)"
    49.8 +  assoc_def   "assoc v d al == alist_rec al d (%x y xs g. if v=x then y else g)"
    49.9  
   49.10  end
    50.1 --- a/src/HOL/Subst/Subst.ML	Fri Oct 10 18:37:49 1997 +0200
    50.2 +++ b/src/HOL/Subst/Subst.ML	Fri Oct 10 19:02:28 1997 +0200
    50.3 @@ -34,7 +34,7 @@
    50.4  qed_spec_mp "Var_not_occs";
    50.5  
    50.6  goal Subst.thy
    50.7 -    "(t <|r = t <|s) = (! v.v : vars_of(t) --> Var(v) <|r = Var(v) <|s)";
    50.8 +    "(t <|r = t <|s) = (! v. v : vars_of(t) --> Var(v) <|r = Var(v) <|s)";
    50.9  by (induct_tac "t" 1);
   50.10  by (ALLGOALS Asm_full_simp_tac);
   50.11  by (ALLGOALS Blast_tac);
   50.12 @@ -54,7 +54,7 @@
   50.13  
   50.14  (**** Equality between Substitutions ****)
   50.15  
   50.16 -goalw Subst.thy [subst_eq_def] "r =$= s = (! t.t <| r = t <| s)";
   50.17 +goalw Subst.thy [subst_eq_def] "r =$= s = (! t. t <| r = t <| s)";
   50.18  by (Simp_tac 1);
   50.19  qed "subst_eq_iff";
   50.20  
   50.21 @@ -150,7 +150,7 @@
   50.22  
   50.23  
   50.24  goalw Subst.thy [srange_def]  
   50.25 -   "v : srange(s) = (? w.w : sdom(s) & v : vars_of(Var(w) <| s))";
   50.26 +   "v : srange(s) = (? w. w : sdom(s) & v : vars_of(Var(w) <| s))";
   50.27  by (Blast_tac 1);
   50.28  qed "srange_iff";
   50.29  
   50.30 @@ -186,12 +186,12 @@
   50.31  qed_spec_mp "Var_intro";
   50.32  
   50.33  goal Subst.thy
   50.34 -    "v : srange(s) --> (? w.w : sdom(s) & v : vars_of(Var(w) <| s))";
   50.35 +    "v : srange(s) --> (? w. w : sdom(s) & v : vars_of(Var(w) <| s))";
   50.36  by (simp_tac (!simpset addsimps [srange_iff]) 1);
   50.37  qed_spec_mp "srangeD";
   50.38  
   50.39  goal Subst.thy
   50.40 -   "sdom(s) Int srange(s) = {} = (! t.sdom(s) Int vars_of(t <| s) = {})";
   50.41 +   "sdom(s) Int srange(s) = {} = (! t. sdom(s) Int vars_of(t <| s) = {})";
   50.42  by (simp_tac (!simpset addsimps [empty_iff_all_not]) 1);
   50.43  by (fast_tac (!claset addIs [Var_in_srange] addDs [srangeD]) 1);
   50.44  qed "dom_range_disjoint";
    51.1 --- a/src/HOL/Subst/Subst.thy	Fri Oct 10 18:37:49 1997 +0200
    51.2 +++ b/src/HOL/Subst/Subst.thy	Fri Oct 10 19:02:28 1997 +0200
    51.3 @@ -26,7 +26,7 @@
    51.4  
    51.5  defs 
    51.6  
    51.7 -  subst_eq_def  "r =$= s == ALL t.t <| r = t <| s"
    51.8 +  subst_eq_def  "r =$= s == ALL t. t <| r = t <| s"
    51.9  
   51.10    comp_def    "al <> bl == alist_rec al bl (%x y xs g. (x,y <| bl)#g)"
   51.11  
    52.1 --- a/src/HOL/Sum.ML	Fri Oct 10 18:37:49 1997 +0200
    52.2 +++ b/src/HOL/Sum.ML	Fri Oct 10 19:02:28 1997 +0200
    52.3 @@ -194,7 +194,7 @@
    52.4  by (etac IntD1 1);
    52.5  qed "PartD1";
    52.6  
    52.7 -goal Sum.thy "Part A (%x.x) = A";
    52.8 +goal Sum.thy "Part A (%x. x) = A";
    52.9  by (Blast_tac 1);
   52.10  qed "Part_id";
   52.11  
   52.12 @@ -203,6 +203,6 @@
   52.13  qed "Part_Int";
   52.14  
   52.15  (*For inductive definitions*)
   52.16 -goal Sum.thy "Part (A Int {x.P x}) h = (Part A h) Int {x.P x}";
   52.17 +goal Sum.thy "Part (A Int {x. P x}) h = (Part A h) Int {x. P x}";
   52.18  by (Blast_tac 1);
   52.19  qed "Part_Collect";
    53.1 --- a/src/HOL/Sum.thy	Fri Oct 10 18:37:49 1997 +0200
    53.2 +++ b/src/HOL/Sum.thy	Fri Oct 10 19:02:28 1997 +0200
    53.3 @@ -34,7 +34,7 @@
    53.4    Part          :: ['a set, 'b => 'a] => 'a set
    53.5  
    53.6  translations
    53.7 -  "case p of Inl x => a | Inr y => b" == "sum_case (%x.a) (%y.b) p"
    53.8 +  "case p of Inl x => a | Inr y => b" == "sum_case (%x. a) (%y. b) p"
    53.9  
   53.10  defs
   53.11    Inl_def       "Inl == (%a. Abs_Sum(Inl_Rep(a)))"
    54.1 --- a/src/HOL/TLA/IntLemmas.ML	Fri Oct 10 18:37:49 1997 +0200
    54.2 +++ b/src/HOL/TLA/IntLemmas.ML	Fri Oct 10 19:02:28 1997 +0200
    54.3 @@ -359,24 +359,24 @@
    54.4  
    54.5  
    54.6  qed_goal "allEW" Intensional.thy 
    54.7 -         "[| RALL x.P(x);  P(x) ==> R |] ==> R::('w::world) form"
    54.8 +         "[| RALL x. P(x);  P(x) ==> R |] ==> R::('w::world) form"
    54.9   (fn major::prems=>
   54.10    [ (REPEAT (resolve_tac (prems @ [major RS specW]) 1)) ]);
   54.11  
   54.12  qed_goal "all_dupEW" Intensional.thy 
   54.13 -    "[| RALL x.P(x);  [| P(x); RALL x.P(x) |] ==> R |] ==> R::('w::world) form"
   54.14 +    "[| RALL x. P(x);  [| P(x); RALL x. P(x) |] ==> R |] ==> R::('w::world) form"
   54.15   (fn prems =>
   54.16    [ (REPEAT (resolve_tac (prems @ (prems RL [specW])) 1)) ]);
   54.17  
   54.18  
   54.19 -qed_goal "exIW" Intensional.thy "P(x) ==> REX x.P(x)"
   54.20 +qed_goal "exIW" Intensional.thy "P(x) ==> REX x. P(x)"
   54.21    (fn [prem] => [rtac intI 1,
   54.22                   rewrite_goals_tac intensional_rews,
   54.23                   rtac exI 1,
   54.24                   rtac (prem RS intD) 1]);
   54.25  
   54.26  qed_goal "exEW" Intensional.thy 
   54.27 -  "[| w |= REX x.P(x); !!x. P(x) .-> Q |] ==> w |= Q"
   54.28 +  "[| w |= REX x. P(x); !!x. P(x) .-> Q |] ==> w |= Q"
   54.29    (fn [major,minor] => [rtac exE 1,
   54.30                          rtac (rewrite_rule intensional_rews major) 1,
   54.31                          etac rev_mpW 1,
   54.32 @@ -385,7 +385,7 @@
   54.33  (** Classical quantifier reasoning **)
   54.34  
   54.35  qed_goal "exCIW" Intensional.thy 
   54.36 -  "(w |= (RALL x. .~P(x)) .-> P(a)) ==> w |= REX x.P(x)"
   54.37 +  "(w |= (RALL x. .~P(x)) .-> P(a)) ==> w |= REX x. P(x)"
   54.38    (fn prems => [cut_facts_tac prems 1,
   54.39                  rewrite_goals_tac intensional_rews,
   54.40                  fast_tac HOL_cs 1]);
    55.1 --- a/src/HOL/TLA/Intensional.ML	Fri Oct 10 18:37:49 1997 +0200
    55.2 +++ b/src/HOL/TLA/Intensional.ML	Fri Oct 10 19:02:28 1997 +0200
    55.3 @@ -35,7 +35,7 @@
    55.4     "(P .| #True) .= #True", "(#True .| P) .= #True", 
    55.5     "(P .| #False) .= P", "(#False .| P) .= P", 
    55.6     "(P .| P) .= P", "(P .| .~P) .= #True", "(.~P .| P) .= #True",
    55.7 -   "(RALL x.P) .= P", "(REX x.P) .= P",
    55.8 +   "(RALL x. P) .= P", "(REX x. P) .= P",
    55.9     "(.~Q .-> .~P) .= (P .-> Q)",
   55.10     "(P.|Q .-> R) .= ((P.->R).&(Q.->R))" ];
   55.11  
    56.1 --- a/src/HOL/TLA/Stfun.ML	Fri Oct 10 18:37:49 1997 +0200
    56.2 +++ b/src/HOL/TLA/Stfun.ML	Fri Oct 10 19:02:28 1997 +0200
    56.3 @@ -8,7 +8,7 @@
    56.4  
    56.5  (* A stronger version of existential elimination (goal needn't be boolean) *)
    56.6  qed_goalw "exE_prop" HOL.thy [Ex_def]
    56.7 -  "[| ? x::'a.P(x); !!x. P(x) ==> PROP R |] ==> PROP R"
    56.8 +  "[| ? x::'a. P(x); !!x. P(x) ==> PROP R |] ==> PROP R"
    56.9    (fn prems => [REPEAT(resolve_tac prems 1)]);
   56.10  
   56.11  (* Might as well use that version in automated proofs *)
    57.1 --- a/src/HOL/Univ.ML	Fri Oct 10 18:37:49 1997 +0200
    57.2 +++ b/src/HOL/Univ.ML	Fri Oct 10 19:02:28 1997 +0200
    57.3 @@ -439,23 +439,23 @@
    57.4  
    57.5  (**** UN x. B(x) rules ****)
    57.6  
    57.7 -goalw Univ.thy [ntrunc_def] "ntrunc k (UN x.f(x)) = (UN x. ntrunc k (f x))";
    57.8 +goalw Univ.thy [ntrunc_def] "ntrunc k (UN x. f(x)) = (UN x. ntrunc k (f x))";
    57.9  by (Blast_tac 1);
   57.10  qed "ntrunc_UN1";
   57.11  
   57.12 -goalw Univ.thy [Scons_def] "(UN x.f(x)) $ M = (UN x. f(x) $ M)";
   57.13 +goalw Univ.thy [Scons_def] "(UN x. f(x)) $ M = (UN x. f(x) $ M)";
   57.14  by (Blast_tac 1);
   57.15  qed "Scons_UN1_x";
   57.16  
   57.17 -goalw Univ.thy [Scons_def] "M $ (UN x.f(x)) = (UN x. M $ f(x))";
   57.18 +goalw Univ.thy [Scons_def] "M $ (UN x. f(x)) = (UN x. M $ f(x))";
   57.19  by (Blast_tac 1);
   57.20  qed "Scons_UN1_y";
   57.21  
   57.22 -goalw Univ.thy [In0_def] "In0(UN x.f(x)) = (UN x. In0(f(x)))";
   57.23 +goalw Univ.thy [In0_def] "In0(UN x. f(x)) = (UN x. In0(f(x)))";
   57.24  by (rtac Scons_UN1_y 1);
   57.25  qed "In0_UN1";
   57.26  
   57.27 -goalw Univ.thy [In1_def] "In1(UN x.f(x)) = (UN x. In1(f(x)))";
   57.28 +goalw Univ.thy [In1_def] "In1(UN x. f(x)) = (UN x. In1(f(x)))";
   57.29  by (rtac Scons_UN1_y 1);
   57.30  qed "In1_UN1";
   57.31  
    58.1 --- a/src/HOL/W0/Maybe.thy	Fri Oct 10 18:37:49 1997 +0200
    58.2 +++ b/src/HOL/W0/Maybe.thy	Fri Oct 10 19:02:28 1997 +0200
    58.3 @@ -15,6 +15,6 @@
    58.4    "m bind f == case m of Ok r => f r | Fail => Fail"
    58.5  
    58.6  syntax "@bind" :: [patterns,'a maybe,'b] => 'c ("(_ := _;//_)" 0)
    58.7 -translations "P := E; F" == "E bind (%P.F)"
    58.8 +translations "P := E; F" == "E bind (%P. F)"
    58.9  
   58.10  end
    59.1 --- a/src/HOL/W0/Type.ML	Fri Oct 10 18:37:49 1997 +0200
    59.2 +++ b/src/HOL/W0/Type.ML	Fri Oct 10 19:02:28 1997 +0200
    59.3 @@ -15,7 +15,7 @@
    59.4  
    59.5  (* application of id_subst does not change type expression *)
    59.6  goalw thy [id_subst_def]
    59.7 -  "$ id_subst = (%t::typ.t)";
    59.8 +  "$ id_subst = (%t::typ. t)";
    59.9  by (rtac ext 1);
   59.10  by (typ.induct_tac "t" 1);
   59.11  by (ALLGOALS Asm_simp_tac);
   59.12 @@ -24,7 +24,7 @@
   59.13  
   59.14  (* application of id_subst does not change list of type expressions *)
   59.15  goalw thy [app_subst_list]
   59.16 -  "$ id_subst = (%ts::typ list.ts)";
   59.17 +  "$ id_subst = (%ts::typ list. ts)";
   59.18  by (rtac ext 1); 
   59.19  by (list.induct_tac "ts" 1);
   59.20  by (ALLGOALS Asm_simp_tac);
    60.1 --- a/src/HOL/W0/Type.thy	Fri Oct 10 18:37:49 1997 +0200
    60.2 +++ b/src/HOL/W0/Type.thy	Fri Oct 10 19:02:28 1997 +0200
    60.3 @@ -30,7 +30,7 @@
    60.4  (* identity *)
    60.5  constdefs
    60.6          id_subst :: subst
    60.7 -        "id_subst == (%n.TVar n)"
    60.8 +        "id_subst == (%n. TVar n)"
    60.9  
   60.10  (* extension of substitution to type structures *)
   60.11  consts
    61.1 --- a/src/HOL/W0/W.ML	Fri Oct 10 18:37:49 1997 +0200
    61.2 +++ b/src/HOL/W0/W.ML	Fri Oct 10 19:02:28 1997 +0200
    61.3 @@ -237,7 +237,7 @@
    61.4  (* case Abs e *)
    61.5  by (strip_tac 1);
    61.6  by (eresolve_tac has_type_casesE 1);
    61.7 -by (eres_inst_tac [("x","%x.if x=n then t1 else (s' x)")] allE 1);
    61.8 +by (eres_inst_tac [("x","%x. if x=n then t1 else (s' x)")] allE 1);
    61.9  by (eres_inst_tac [("x","(TVar n)#a")] allE 1);
   61.10  by (eres_inst_tac [("x","t2")] allE 1);
   61.11  by (eres_inst_tac [("x","Suc n")] allE 1);
   61.12 @@ -268,9 +268,9 @@
   61.13  
   61.14  (** LEVEL 35 **)
   61.15  by (subgoal_tac
   61.16 -  "$ (%x.if x=ma then t' else (if x:(free_tv t - free_tv sa) then r x \
   61.17 +  "$ (%x. if x=ma then t' else (if x:(free_tv t - free_tv sa) then r x \
   61.18  \        else ra x)) ($ sa t) = \
   61.19 -\  $ (%x.if x=ma then t' else (if x:(free_tv t - free_tv sa) then r x \
   61.20 +\  $ (%x. if x=ma then t' else (if x:(free_tv t - free_tv sa) then r x \
   61.21  \        else ra x)) (ta -> (TVar ma))" 1);
   61.22  by (res_inst_tac [("t","$ (%x. if x = ma then t' else \
   61.23  \   (if x:(free_tv t - free_tv sa) then r x else ra x)) ($ sa t)"),
    62.1 --- a/src/HOL/WF.thy	Fri Oct 10 18:37:49 1997 +0200
    62.2 +++ b/src/HOL/WF.thy	Fri Oct 10 19:02:28 1997 +0200
    62.3 @@ -10,7 +10,7 @@
    62.4  
    62.5  constdefs
    62.6    wf         :: "('a * 'a)set => bool"
    62.7 -  "wf(r) == (!P. (!x. (!y. (y,x):r --> P(y)) --> P(x)) --> (!x.P(x)))"
    62.8 +  "wf(r) == (!P. (!x. (!y. (y,x):r --> P(y)) --> P(x)) --> (!x. P(x)))"
    62.9  
   62.10    acyclic :: "('a*'a)set => bool"
   62.11    "acyclic r == !x. (x,x) ~: r^+"
    63.1 --- a/src/HOL/cladata.ML	Fri Oct 10 18:37:49 1997 +0200
    63.2 +++ b/src/HOL/cladata.ML	Fri Oct 10 19:02:28 1997 +0200
    63.3 @@ -68,7 +68,7 @@
    63.4  
    63.5  (*Better then ex1E for classical reasoner: needs no quantifier duplication!*)
    63.6  qed_goal "alt_ex1E" thy
    63.7 -    "[| ?! x.P(x);                                              \
    63.8 +    "[| ?! x. P(x);                                              \
    63.9  \       !!x. [| P(x);  ALL y y'. P(y) & P(y') --> y=y' |] ==> R  \
   63.10  \    |] ==> R"
   63.11   (fn major::prems =>
    64.1 --- a/src/HOL/datatype.ML	Fri Oct 10 18:37:49 1997 +0200
    64.2 +++ b/src/HOL/datatype.ML	Fri Oct 10 19:02:28 1997 +0200
    64.3 @@ -341,7 +341,7 @@
    64.4        fun t_inducting ((_, name, types, vns, _) :: cs) =
    64.5          let
    64.6            val h = if null types then " P(" ^ name ^ ")"
    64.7 -                  else " !!" ^ (space_implode " " vns) ^ "." ^
    64.8 +                  else " !!" ^ (space_implode " " vns) ^ ". " ^
    64.9                      (assumpt (types, vns, false)) ^
   64.10                      "P(" ^ C_exp name vns ^ ")";
   64.11            val rest = t_inducting cs;
    65.1 --- a/src/HOL/equalities.ML	Fri Oct 10 18:37:49 1997 +0200
    65.2 +++ b/src/HOL/equalities.ML	Fri Oct 10 19:02:28 1997 +0200
    65.3 @@ -12,7 +12,7 @@
    65.4  
    65.5  section "{}";
    65.6  
    65.7 -goal Set.thy "{x.False} = {}";
    65.8 +goal Set.thy "{x. False} = {}";
    65.9  by (Blast_tac 1);
   65.10  qed "Collect_False_empty";
   65.11  Addsimps [Collect_False_empty];
   65.12 @@ -118,7 +118,7 @@
   65.13  
   65.14  goalw Set.thy [image_def]
   65.15  "(%x. if P x then f x else g x) `` S                    \
   65.16 -\ = (f `` ({x.x:S & P x})) Un (g `` ({x.x:S & ~(P x)}))";
   65.17 +\ = (f `` ({x. x:S & P x})) Un (g `` ({x. x:S & ~(P x)}))";
   65.18  by (split_tac [expand_if] 1);
   65.19  by (Blast_tac 1);
   65.20  qed "if_image_distrib";
   65.21 @@ -421,11 +421,11 @@
   65.22  by (Blast_tac 1);
   65.23  qed "INT1_insert_distrib";
   65.24  
   65.25 -goal Set.thy "Union(range(f)) = (UN x.f(x))";
   65.26 +goal Set.thy "Union(range(f)) = (UN x. f(x))";
   65.27  by (Blast_tac 1);
   65.28  qed "Union_range_eq";
   65.29  
   65.30 -goal Set.thy "Inter(range(f)) = (INT x.f(x))";
   65.31 +goal Set.thy "Inter(range(f)) = (INT x. f(x))";
   65.32  by (Blast_tac 1);
   65.33  qed "Inter_range_eq";
   65.34  
   65.35 @@ -445,12 +445,12 @@
   65.36  by (Blast_tac 1);
   65.37  qed "INT_constant";
   65.38  
   65.39 -goal Set.thy "(UN x.B) = B";
   65.40 +goal Set.thy "(UN x. B) = B";
   65.41  by (Blast_tac 1);
   65.42  qed "UN1_constant";
   65.43  Addsimps[UN1_constant];
   65.44  
   65.45 -goal Set.thy "(INT x.B) = B";
   65.46 +goal Set.thy "(INT x. B) = B";
   65.47  by (Blast_tac 1);
   65.48  qed "INT1_constant";
   65.49  Addsimps[INT1_constant];
   65.50 @@ -524,11 +524,11 @@
   65.51  (** These are not added to the default simpset because (a) they duplicate the
   65.52      body and (b) there are no similar rules for Int. **)
   65.53  
   65.54 -goal Set.thy "(ALL x:A Un B.P x) = ((ALL x:A.P x) & (ALL x:B.P x))";
   65.55 +goal Set.thy "(ALL x:A Un B. P x) = ((ALL x:A. P x) & (ALL x:B. P x))";
   65.56  by (Blast_tac 1);
   65.57  qed "ball_Un";
   65.58  
   65.59 -goal Set.thy "(EX x:A Un B.P x) = ((EX x:A.P x) | (EX x:B.P x))";
   65.60 +goal Set.thy "(EX x:A Un B. P x) = ((EX x:A. P x) | (EX x:B. P x))";
   65.61  by (Blast_tac 1);
   65.62  qed "bex_Un";
   65.63  
   65.64 @@ -620,7 +620,7 @@
   65.65  by (Blast_tac 1);
   65.66  qed "set_eq_subset";
   65.67  
   65.68 -goal Set.thy "A <= B =  (! t.t:A --> t:B)";
   65.69 +goal Set.thy "A <= B =  (! t. t:A --> t:B)";
   65.70  by (Blast_tac 1);
   65.71  qed "subset_iff";
   65.72  
   65.73 @@ -647,32 +647,32 @@
   65.74  in
   65.75  val UN1_simps = map prover 
   65.76                  ["(UN x. insert a (B x)) = insert a (UN x. B x)",
   65.77 -                 "(UN x. A x Int B)  = ((UN x.A x) Int B)",
   65.78 -                 "(UN x. A Int B x)  = (A Int (UN x.B x))",
   65.79 -                 "(UN x. A x Un B)   = ((UN x.A x) Un B)",
   65.80 -                 "(UN x. A Un B x)   = (A Un (UN x.B x))",
   65.81 -                 "(UN x. A x - B)    = ((UN x.A x) - B)",
   65.82 -                 "(UN x. A - B x)    = (A - (INT x.B x))"];
   65.83 +                 "(UN x. A x Int B)  = ((UN x. A x) Int B)",
   65.84 +                 "(UN x. A Int B x)  = (A Int (UN x. B x))",
   65.85 +                 "(UN x. A x Un B)   = ((UN x. A x) Un B)",
   65.86 +                 "(UN x. A Un B x)   = (A Un (UN x. B x))",
   65.87 +                 "(UN x. A x - B)    = ((UN x. A x) - B)",
   65.88 +                 "(UN x. A - B x)    = (A - (INT x. B x))"];
   65.89  
   65.90  val INT1_simps = map prover
   65.91                  ["(INT x. insert a (B x)) = insert a (INT x. B x)",
   65.92 -                 "(INT x. A x Int B) = ((INT x.A x) Int B)",
   65.93 -                 "(INT x. A Int B x) = (A Int (INT x.B x))",
   65.94 -                 "(INT x. A x Un B)  = ((INT x.A x) Un B)",
   65.95 -                 "(INT x. A Un B x)  = (A Un (INT x.B x))",
   65.96 -                 "(INT x. A x - B)   = ((INT x.A x) - B)",
   65.97 -                 "(INT x. A - B x)   = (A - (UN x.B x))"];
   65.98 +                 "(INT x. A x Int B) = ((INT x. A x) Int B)",
   65.99 +                 "(INT x. A Int B x) = (A Int (INT x. B x))",
  65.100 +                 "(INT x. A x Un B)  = ((INT x. A x) Un B)",
  65.101 +                 "(INT x. A Un B x)  = (A Un (INT x. B x))",
  65.102 +                 "(INT x. A x - B)   = ((INT x. A x) - B)",
  65.103 +                 "(INT x. A - B x)   = (A - (UN x. B x))"];
  65.104  
  65.105  val UN_simps = map prover 
  65.106 -                ["(UN x:C. A x Int B)  = ((UN x:C.A x) Int B)",
  65.107 -                 "(UN x:C. A Int B x)  = (A Int (UN x:C.B x))",
  65.108 -                 "(UN x:C. A x - B)    = ((UN x:C.A x) - B)",
  65.109 -                 "(UN x:C. A - B x)    = (A - (INT x:C.B x))"];
  65.110 +                ["(UN x:C. A x Int B)  = ((UN x:C. A x) Int B)",
  65.111 +                 "(UN x:C. A Int B x)  = (A Int (UN x:C. B x))",
  65.112 +                 "(UN x:C. A x - B)    = ((UN x:C. A x) - B)",
  65.113 +                 "(UN x:C. A - B x)    = (A - (INT x:C. B x))"];
  65.114  
  65.115  val INT_simps = map prover
  65.116                  ["(INT x:C. insert a (B x)) = insert a (INT x:C. B x)",
  65.117 -                 "(INT x:C. A x Un B)  = ((INT x:C.A x) Un B)",
  65.118 -                 "(INT x:C. A Un B x)  = (A Un (INT x:C.B x))"];
  65.119 +                 "(INT x:C. A x Un B)  = ((INT x:C. A x) Un B)",
  65.120 +                 "(INT x:C. A Un B x)  = (A Un (INT x:C. B x))"];
  65.121  
  65.122  (*The missing laws for bounded Unions and Intersections are conditional
  65.123    on the index set's being non-empty.  Thus they are probably NOT worth 
    66.1 --- a/src/HOL/ex/MT.ML	Fri Oct 10 18:37:49 1997 +0200
    66.2 +++ b/src/HOL/ex/MT.ML	Fri Oct 10 19:02:28 1997 +0200
    66.3 @@ -66,7 +66,7 @@
    66.4  qed "lfp_elim2";
    66.5  
    66.6  val prems = goal MT.thy
    66.7 -  " [| x:lfp(f); mono(f); !!y. y:f(lfp(f) Int {x.P(x)}) ==> P(y) |] ==> \
    66.8 +  " [| x:lfp(f); mono(f); !!y. y:f(lfp(f) Int {x. P(x)}) ==> P(y) |] ==> \
    66.9  \   P(x)";
   66.10  by (cut_facts_tac prems 1);
   66.11  by (etac induct 1);
   66.12 @@ -446,7 +446,7 @@
   66.13  val prems = goal MT.thy 
   66.14    " te |- e ===> t ==> \
   66.15  \   ( e = fn x1 => e1 --> \
   66.16 -\     (? t1 t2.t=t_fun t1 t2 & te + {x1 |=> t1} |- e1 ===> t2) \
   66.17 +\     (? t1 t2. t=t_fun t1 t2 & te + {x1 |=> t1} |- e1 ===> t2) \
   66.18  \   )";
   66.19  by (elab_e_elim_tac prems);
   66.20  qed "elab_fn_elim_lem";
   66.21 @@ -538,11 +538,11 @@
   66.22  (* Elimination rule for hasty_rel *)
   66.23  
   66.24  val prems = goalw MT.thy [hasty_rel_def]
   66.25 -  " [| !! c t.c isof t ==> P((v_const(c),t)); \
   66.26 +  " [| !! c t. c isof t ==> P((v_const(c),t)); \
   66.27  \      !! te ev e t ve. \
   66.28  \        [| te |- fn ev => e ===> t; \
   66.29  \           ve_dom(ve) = te_dom(te); \
   66.30 -\           !ev1.ev1:ve_dom(ve) --> (ve_app ve ev1,te_app te ev1) : hasty_rel \
   66.31 +\           !ev1. ev1:ve_dom(ve) --> (ve_app ve ev1,te_app te ev1) : hasty_rel \
   66.32  \        |] ==> P((v_clos(<|ev,e,ve|>),t)); \
   66.33  \      (v,t) : hasty_rel \
   66.34  \   |] ==> P((v,t))";
   66.35 @@ -558,11 +558,11 @@
   66.36  
   66.37  val prems = goal MT.thy 
   66.38    " [| (v,t) : hasty_rel; \
   66.39 -\      !! c t.c isof t ==> P (v_const c) t; \
   66.40 +\      !! c t. c isof t ==> P (v_const c) t; \
   66.41  \      !! te ev e t ve. \
   66.42  \        [| te |- fn ev => e ===> t; \
   66.43  \           ve_dom(ve) = te_dom(te); \
   66.44 -\           !ev1.ev1:ve_dom(ve) --> (ve_app ve ev1,te_app te ev1) : hasty_rel \
   66.45 +\           !ev1. ev1:ve_dom(ve) --> (ve_app ve ev1,te_app te ev1) : hasty_rel \
   66.46  \        |] ==> P (v_clos <|ev,e,ve|>) t \
   66.47  \   |] ==> P v t";
   66.48  by (res_inst_tac [("P","P")] infsys_p2 1);
   66.49 @@ -602,7 +602,7 @@
   66.50  val prems = goalw MT.thy [hasty_env_def,hasty_def] 
   66.51    " v hasty t ==> \
   66.52  \   ! x e ve. \
   66.53 -\     v=v_clos(<|x,e,ve|>) --> (? te.te |- fn x => e ===> t & ve hastyenv te)";
   66.54 +\     v=v_clos(<|x,e,ve|>) --> (? te. te |- fn x => e ===> t & ve hastyenv te)";
   66.55  by (cut_facts_tac prems 1);
   66.56  by (rtac hasty_rel_elim 1);
   66.57  by (ALLGOALS (blast_tac (v_ext_cs HOL_cs)));
   66.58 @@ -610,7 +610,7 @@
   66.59  
   66.60  goal MT.thy 
   66.61    "!!t. v_clos(<|ev,e,ve|>) hasty t ==>  \
   66.62 -\       ? te.te |- fn ev => e ===> t & ve hastyenv te ";
   66.63 +\       ? te. te |- fn ev => e ===> t & ve hastyenv te ";
   66.64  by (dtac hasty_elim_clos_lem 1);
   66.65  by (Blast_tac 1);
   66.66  qed "hasty_elim_clos";
    67.1 --- a/src/HOL/ex/MT.thy	Fri Oct 10 18:37:49 1997 +0200
    67.2 +++ b/src/HOL/ex/MT.thy	Fri Oct 10 19:02:28 1997 +0200
    67.3 @@ -247,7 +247,7 @@
    67.4       ve_dom(ve) = te_dom(te) & 
    67.5       ( ! x. 
    67.6           x:ve_dom(ve) --> 
    67.7 -         (? c.ve_app ve x = v_const(c) & c isof te_app te x) 
    67.8 +         (? c. ve_app ve x = v_const(c) & c isof te_app te x) 
    67.9       ) 
   67.10     "
   67.11  
   67.12 @@ -263,7 +263,7 @@
   67.13             p = (v_clos(<|ev,e,ve|>),t) & 
   67.14             te |- fn ev => e ===> t & 
   67.15             ve_dom(ve) = te_dom(te) & 
   67.16 -           (! ev1.ev1:ve_dom(ve) --> (ve_app ve ev1,te_app te ev1) : r) 
   67.17 +           (! ev1. ev1:ve_dom(ve) --> (ve_app ve ev1,te_app te ev1) : r) 
   67.18         ) 
   67.19       } 
   67.20     "
    68.1 --- a/src/HOL/ex/NatSum.ML	Fri Oct 10 18:37:49 1997 +0200
    68.2 +++ b/src/HOL/ex/NatSum.ML	Fri Oct 10 19:02:28 1997 +0200
    68.3 @@ -11,7 +11,7 @@
    68.4  Addsimps [add_mult_distrib, add_mult_distrib2];
    68.5  
    68.6  (*The sum of the first n positive integers equals n(n+1)/2.*)
    68.7 -goal NatSum.thy "2*sum (%i.i) (Suc n) = n*Suc(n)";
    68.8 +goal NatSum.thy "2*sum (%i. i) (Suc n) = n*Suc(n)";
    68.9  by (Simp_tac 1);
   68.10  by (nat_ind_tac "n" 1);
   68.11  by (Simp_tac 1);
   68.12 @@ -19,7 +19,7 @@
   68.13  qed "sum_of_naturals";
   68.14  
   68.15  goal NatSum.thy
   68.16 -  "Suc(Suc(Suc(Suc 2)))*sum (%i.i*i) (Suc n) = n*Suc(n)*Suc(2*n)";
   68.17 +  "Suc(Suc(Suc(Suc 2)))*sum (%i. i*i) (Suc n) = n*Suc(n)*Suc(2*n)";
   68.18  by (Simp_tac 1);
   68.19  by (nat_ind_tac "n" 1);
   68.20  by (Simp_tac 1);
   68.21 @@ -27,7 +27,7 @@
   68.22  qed "sum_of_squares";
   68.23  
   68.24  goal NatSum.thy
   68.25 -  "Suc(Suc 2)*sum (%i.i*i*i) (Suc n) = n*n*Suc(n)*Suc(n)";
   68.26 +  "Suc(Suc 2)*sum (%i. i*i*i) (Suc n) = n*n*Suc(n)*Suc(n)";
   68.27  by (Simp_tac 1);
   68.28  by (nat_ind_tac "n" 1);
   68.29  by (Simp_tac 1);
   68.30 @@ -35,7 +35,7 @@
   68.31  qed "sum_of_cubes";
   68.32  
   68.33  (*The sum of the first n odd numbers equals n squared.*)
   68.34 -goal NatSum.thy "sum (%i.Suc(i+i)) n = n*n";
   68.35 +goal NatSum.thy "sum (%i. Suc(i+i)) n = n*n";
   68.36  by (nat_ind_tac "n" 1);
   68.37  by (Simp_tac 1);
   68.38  by (Asm_simp_tac 1);
    69.1 --- a/src/HOL/ex/Puzzle.ML	Fri Oct 10 18:37:49 1997 +0200
    69.2 +++ b/src/HOL/ex/Puzzle.ML	Fri Oct 10 19:02:28 1997 +0200
    69.3 @@ -9,7 +9,7 @@
    69.4  *)
    69.5  
    69.6  (*specialized form of induction needed below*)
    69.7 -val prems = goal Nat.thy "[| P(0); !!n. P(Suc(n)) |] ==> !n.P(n)";
    69.8 +val prems = goal Nat.thy "[| P(0); !!n. P(Suc(n)) |] ==> !n. P(n)";
    69.9  by (EVERY1 [rtac (nat_induct RS allI), resolve_tac prems, resolve_tac prems]);
   69.10  qed "nat_exh";
   69.11  
   69.12 @@ -35,7 +35,7 @@
   69.13  by (deepen_tac (!claset addIs [Puzzle.f_ax, le_less_trans, lemma1]) 0 1);
   69.14  qed "lemma2";
   69.15  
   69.16 -val prems = goal Puzzle.thy "(!!n.f(n) <= f(Suc(n))) ==> m<n --> f(m) <= f(n)";
   69.17 +val prems = goal Puzzle.thy "(!!n. f(n) <= f(Suc(n))) ==> m<n --> f(m) <= f(n)";
   69.18  by (res_inst_tac[("n","n")]nat_induct 1);
   69.19  by (Simp_tac 1);
   69.20  by (simp_tac (!simpset addsimps [less_Suc_eq]) 1);
    70.1 --- a/src/HOL/ex/Qsort.ML	Fri Oct 10 18:37:49 1997 +0200
    70.2 +++ b/src/HOL/ex/Qsort.ML	Fri Oct 10 19:02:28 1997 +0200
    70.3 @@ -35,7 +35,7 @@
    70.4  Addsimps [set_qsort];
    70.5  
    70.6  goal List.thy
    70.7 -  "(!x:set[x:xs.P(x)].Q(x)) = (!x:set xs. P(x)-->Q(x))";
    70.8 +  "(!x:set[x:xs. P(x)].Q(x)) = (!x:set xs. P(x)-->Q(x))";
    70.9  by (list.induct_tac "xs" 1);
   70.10  by (ALLGOALS(asm_simp_tac (!simpset setloop (split_tac [expand_if]))));
   70.11  qed"Ball_set_filter";
    71.1 --- a/src/HOL/ex/Recdef.thy	Fri Oct 10 18:37:49 1997 +0200
    71.2 +++ b/src/HOL/ex/Recdef.thy	Fri Oct 10 19:02:28 1997 +0200
    71.3 @@ -94,9 +94,9 @@
    71.4     TFL requires (%x.mapf x) instead of mapf.
    71.5  *)
    71.6  consts mapf :: nat => nat list
    71.7 -recdef mapf "measure(%m.m)"
    71.8 +recdef mapf "measure(%m. m)"
    71.9  congs "[map_cong]"
   71.10  "mapf 0 = []"
   71.11 -"mapf (Suc n) = concat(map (%x.mapf x) (replicate n n))"
   71.12 +"mapf (Suc n) = concat(map (%x. mapf x) (replicate n n))"
   71.13  
   71.14  end
    72.1 --- a/src/HOL/ex/Sorting.ML	Fri Oct 10 18:37:49 1997 +0200
    72.2 +++ b/src/HOL/ex/Sorting.ML	Fri Oct 10 19:02:28 1997 +0200
    72.3 @@ -6,12 +6,12 @@
    72.4  Some general lemmas
    72.5  *)
    72.6  
    72.7 -goal Sorting.thy "!x.mset (xs@ys) x = mset xs x + mset ys x";
    72.8 +goal Sorting.thy "!x. mset (xs@ys) x = mset xs x + mset ys x";
    72.9  by (list.induct_tac "xs" 1);
   72.10  by (ALLGOALS(asm_simp_tac (!simpset setloop (split_tac [expand_if]))));
   72.11  qed "mset_append";
   72.12  
   72.13 -goal Sorting.thy "!x. mset [x:xs. ~p(x)] x + mset [x:xs.p(x)] x = \
   72.14 +goal Sorting.thy "!x. mset [x:xs. ~p(x)] x + mset [x:xs. p(x)] x = \
   72.15  \                     mset xs x";
   72.16  by (list.induct_tac "xs" 1);
   72.17  by (ALLGOALS(asm_simp_tac (!simpset setloop (split_tac [expand_if]))));
   72.18 @@ -19,7 +19,7 @@
   72.19  
   72.20  Addsimps [mset_append, mset_compl_add];
   72.21  
   72.22 -goal Sorting.thy "set xs = {x.mset xs x ~= 0}";
   72.23 +goal Sorting.thy "set xs = {x. mset xs x ~= 0}";
   72.24  by (list.induct_tac "xs" 1);
   72.25  by (ALLGOALS(asm_simp_tac (!simpset setloop (split_tac [expand_if]))));
   72.26  by (Fast_tac 1);
    73.1 --- a/src/HOL/ex/cla.ML	Fri Oct 10 18:37:49 1997 +0200
    73.2 +++ b/src/HOL/ex/cla.ML	Fri Oct 10 19:02:28 1997 +0200
    73.3 @@ -129,15 +129,15 @@
    73.4  by (Blast_tac 1);
    73.5  result(); 
    73.6  
    73.7 -goal HOL.thy "(? x. P-->Q(x))  =  (P --> (? x.Q(x)))";
    73.8 +goal HOL.thy "(? x. P-->Q(x))  =  (P --> (? x. Q(x)))";
    73.9  by (Blast_tac 1);
   73.10  result(); 
   73.11  
   73.12 -goal HOL.thy "(? x.P(x)-->Q) = ((! x.P(x)) --> Q)";
   73.13 +goal HOL.thy "(? x. P(x)-->Q) = ((! x. P(x)) --> Q)";
   73.14  by (Blast_tac 1);
   73.15  result(); 
   73.16  
   73.17 -goal HOL.thy "((! x.P(x)) | Q)  =  (! x. P(x) | Q)";
   73.18 +goal HOL.thy "((! x. P(x)) | Q)  =  (! x. P(x) | Q)";
   73.19  by (Blast_tac 1);
   73.20  result(); 
   73.21  
   73.22 @@ -204,7 +204,7 @@
   73.23  
   73.24  writeln"Problem 24";
   73.25  goal HOL.thy "~(? x. S(x)&Q(x)) & (! x. P(x) --> Q(x)|R(x)) &  \
   73.26 -\    (~(? x.P(x)) --> (? x.Q(x))) & (! x. Q(x)|R(x) --> S(x))  \
   73.27 +\    (~(? x. P(x)) --> (? x. Q(x))) & (! x. Q(x)|R(x) --> S(x))  \
   73.28  \   --> (? x. P(x)&R(x))";
   73.29  by (Blast_tac 1); 
   73.30  result();
   73.31 @@ -237,7 +237,7 @@
   73.32  writeln"Problem 28.  AMENDED";
   73.33  goal HOL.thy "(! x. P(x) --> (! x. Q(x))) &   \
   73.34  \       ((! x. Q(x)|R(x)) --> (? x. Q(x)&S(x))) &  \
   73.35 -\       ((? x.S(x)) --> (! x. L(x) --> M(x)))  \
   73.36 +\       ((? x. S(x)) --> (! x. L(x) --> M(x)))  \
   73.37  \   --> (! x. P(x) & L(x) --> M(x))";
   73.38  by (Blast_tac 1);  
   73.39  result();
   73.40 @@ -257,7 +257,7 @@
   73.41  result();
   73.42  
   73.43  writeln"Problem 31";
   73.44 -goal HOL.thy "~(? x.P(x) & (Q(x) | R(x))) & \
   73.45 +goal HOL.thy "~(? x. P(x) & (Q(x) | R(x))) & \
   73.46  \       (? x. L(x) & P(x)) & \
   73.47  \       (! x. ~ R(x) --> M(x))  \
   73.48  \   --> (? x. L(x) & M(x))";
   73.49 @@ -303,7 +303,7 @@
   73.50  
   73.51  writeln"Problem 37";
   73.52  goal HOL.thy "(! z. ? w. ! x. ? y. \
   73.53 -\          (P x z -->P y w) & P y z & (P y w --> (? u.Q u w))) & \
   73.54 +\          (P x z -->P y w) & P y z & (P y w --> (? u. Q u w))) & \
   73.55  \       (! x z. ~(P x z) --> (? y. Q y z)) & \
   73.56  \       ((? x y. Q x y) --> (! x. R x x))  \
   73.57  \   --> (! x. ? y. R x y)";
   73.58 @@ -380,7 +380,7 @@
   73.59  (*Hard because it involves substitution for Vars;
   73.60    the type constraint ensures that x,y,z have the same type as a,b,u. *)
   73.61  goal HOL.thy "(? x y::'a. ! z. z=x | z=y) & P(a) & P(b) & (~a=b) \
   73.62 -\               --> (! u::'a.P(u))";
   73.63 +\               --> (! u::'a. P(u))";
   73.64  by (Classical.safe_tac (!claset));
   73.65  by (res_inst_tac [("x","a")] allE 1);
   73.66  by (assume_tac 1);
   73.67 @@ -391,7 +391,7 @@
   73.68  
   73.69  writeln"Problem 50";  
   73.70  (*What has this to do with equality?*)
   73.71 -goal HOL.thy "(! x. P a x | (! y.P x y)) --> (? x. ! y.P x y)";
   73.72 +goal HOL.thy "(! x. P a x | (! y. P x y)) --> (? x. ! y. P x y)";
   73.73  by (Blast_tac 1);
   73.74  result();
   73.75  
    74.1 --- a/src/HOL/ex/meson.ML	Fri Oct 10 18:37:49 1997 +0200
    74.2 +++ b/src/HOL/ex/meson.ML	Fri Oct 10 19:02:28 1997 +0200
    74.3 @@ -25,8 +25,8 @@
    74.4  val not_conjD = prove_fun "~(P&Q) ==> ~P | ~Q";
    74.5  val not_disjD = prove_fun "~(P|Q) ==> ~P & ~Q";
    74.6  val not_notD = prove_fun "~~P ==> P";
    74.7 -val not_allD = prove_fun  "~(! x.P(x)) ==> ? x. ~P(x)";
    74.8 -val not_exD = prove_fun   "~(? x.P(x)) ==> ! x. ~P(x)";
    74.9 +val not_allD = prove_fun  "~(! x. P(x)) ==> ? x. ~P(x)";
   74.10 +val not_exD = prove_fun   "~(? x. P(x)) ==> ! x. ~P(x)";
   74.11  
   74.12  
   74.13  (*** Removal of --> and <-> (positive and negative occurrences) ***)
   74.14 @@ -44,17 +44,17 @@
   74.15  
   74.16  (*** Conjunction ***)
   74.17  
   74.18 -val conj_exD1 = prove_fun "(? x.P(x)) & Q ==> ? x. P(x) & Q";
   74.19 -val conj_exD2 = prove_fun "P & (? x.Q(x)) ==> ? x. P & Q(x)";
   74.20 +val conj_exD1 = prove_fun "(? x. P(x)) & Q ==> ? x. P(x) & Q";
   74.21 +val conj_exD2 = prove_fun "P & (? x. Q(x)) ==> ? x. P & Q(x)";
   74.22  
   74.23  (*** Disjunction ***)
   74.24  
   74.25  (*DO NOT USE with forall-Skolemization: makes fewer schematic variables!!
   74.26    With ex-Skolemization, makes fewer Skolem constants*)
   74.27 -val disj_exD = prove_fun "(? x.P(x)) | (? x.Q(x)) ==> ? x. P(x) | Q(x)";
   74.28 +val disj_exD = prove_fun "(? x. P(x)) | (? x. Q(x)) ==> ? x. P(x) | Q(x)";
   74.29  
   74.30 -val disj_exD1 = prove_fun "(? x.P(x)) | Q ==> ? x. P(x) | Q";
   74.31 -val disj_exD2 = prove_fun "P | (? x.Q(x)) ==> ? x. P | Q(x)";
   74.32 +val disj_exD1 = prove_fun "(? x. P(x)) | Q ==> ? x. P(x) | Q";
   74.33 +val disj_exD2 = prove_fun "P | (? x. Q(x)) ==> ? x. P | Q(x)";
   74.34  
   74.35  
   74.36  (**** Skolemization -- pulling "?" over "!" ****)
    75.1 --- a/src/HOL/ex/mesontest.ML	Fri Oct 10 18:37:49 1997 +0200
    75.2 +++ b/src/HOL/ex/mesontest.ML	Fri Oct 10 19:02:28 1997 +0200
    75.3 @@ -247,15 +247,15 @@
    75.4  by (safe_meson_tac 1);
    75.5  result(); 
    75.6  
    75.7 -goal HOL.thy "(? x. P --> Q x)  =  (P --> (? x.Q x))";
    75.8 +goal HOL.thy "(? x. P --> Q x)  =  (P --> (? x. Q x))";
    75.9  by (safe_meson_tac 1);
   75.10  result(); 
   75.11  
   75.12 -goal HOL.thy "(? x.P x --> Q) = ((! x.P x) --> Q)";
   75.13 +goal HOL.thy "(? x. P x --> Q) = ((! x. P x) --> Q)";
   75.14  by (safe_meson_tac 1);
   75.15  result(); 
   75.16  
   75.17 -goal HOL.thy "((! x.P x) | Q)  =  (! x. P x | Q)";
   75.18 +goal HOL.thy "((! x. P x) | Q)  =  (! x. P x | Q)";
   75.19  by (safe_meson_tac 1);
   75.20  result(); 
   75.21  
   75.22 @@ -307,7 +307,7 @@
   75.23  
   75.24  writeln"Problem 24";  (*The first goal clause is useless*)
   75.25  goal HOL.thy "~(? x. S x & Q x) & (! x. P x --> Q x | R x) &  \
   75.26 -\    (~(? x.P x) --> (? x.Q x)) & (! x. Q x | R x --> S x)  \
   75.27 +\    (~(? x. P x) --> (? x. Q x)) & (! x. Q x | R x --> S x)  \
   75.28  \   --> (? x. P x & R x)";
   75.29  by (safe_meson_tac 1); 
   75.30  result();
   75.31 @@ -340,7 +340,7 @@
   75.32  writeln"Problem 28.  AMENDED";  (*14 Horn clauses*)
   75.33  goal HOL.thy "(! x. P x --> (! x. Q x)) &   \
   75.34  \       ((! x. Q x | R x) --> (? x. Q x & S x)) &  \
   75.35 -\       ((? x.S x) --> (! x. L x --> M x))  \
   75.36 +\       ((? x. S x) --> (! x. L x --> M x))  \
   75.37  \   --> (! x. P x & L x --> M x)";
   75.38  by (safe_meson_tac 1);  
   75.39  result();
   75.40 @@ -361,7 +361,7 @@
   75.41  result();
   75.42  
   75.43  writeln"Problem 31";  (*10 Horn clauses; first negative clauses is useless*)
   75.44 -goal HOL.thy "~(? x.P x & (Q x | R x)) & \
   75.45 +goal HOL.thy "~(? x. P x & (Q x | R x)) & \
   75.46  \       (? x. L x & P x) & \
   75.47  \       (! x. ~ R x --> M x)  \
   75.48  \   --> (? x. L x & M x)";
   75.49 @@ -407,7 +407,7 @@
   75.50  
   75.51  writeln"Problem 37";  (*10 Horn clauses*)
   75.52  goal HOL.thy "(! z. ? w. ! x. ? y. \
   75.53 -\          (P x z --> P y w) & P y z & (P y w --> (? u.Q u w))) & \
   75.54 +\          (P x z --> P y w) & P y z & (P y w --> (? u. Q u w))) & \
   75.55  \       (! x z. ~P x z --> (? y. Q y z)) & \
   75.56  \       ((? x y. Q x y) --> (! x. R x x))  \
   75.57  \   --> (! x. ? y. R x y)";
   75.58 @@ -475,7 +475,7 @@
   75.59  writeln"Problem 46";  (*26 Horn clauses; 21-step proof*)
   75.60  goal HOL.thy
   75.61      "(! x. f x & (! y. f y & h y x --> g y) --> g x) &      \
   75.62 -\    ((? x.f x & ~g x) -->                                    \
   75.63 +\    ((? x. f x & ~g x) -->                                    \
   75.64  \     (? x. f x & ~g x & (! y. f y & ~g y --> j x y))) &    \
   75.65  \    (! x y. f x & f y & h x y --> ~j y x)                    \
   75.66  \     --> (! x. f x --> g x)";
   75.67 @@ -486,22 +486,22 @@
   75.68  writeln"Problem 47.  Schubert's Steamroller";
   75.69          (*26 clauses; 63 Horn clauses*)
   75.70  goal HOL.thy
   75.71 -    "(! x. P1 x --> P0 x) & (? x.P1 x) &     \
   75.72 -\    (! x. P2 x --> P0 x) & (? x.P2 x) &     \
   75.73 -\    (! x. P3 x --> P0 x) & (? x.P3 x) &     \
   75.74 -\    (! x. P4 x --> P0 x) & (? x.P4 x) &     \
   75.75 -\    (! x. P5 x --> P0 x) & (? x.P5 x) &     \
   75.76 -\    (! x. Q1 x --> Q0 x) & (? x.Q1 x) &     \
   75.77 -\    (! x. P0 x --> ((! y.Q0 y-->R x y) |    \
   75.78 -\                     (! y.P0 y & S y x &     \
   75.79 -\                          (? z.Q0 z&R y z) --> R x y))) &   \
   75.80 +    "(! x. P1 x --> P0 x) & (? x. P1 x) &     \
   75.81 +\    (! x. P2 x --> P0 x) & (? x. P2 x) &     \
   75.82 +\    (! x. P3 x --> P0 x) & (? x. P3 x) &     \
   75.83 +\    (! x. P4 x --> P0 x) & (? x. P4 x) &     \
   75.84 +\    (! x. P5 x --> P0 x) & (? x. P5 x) &     \
   75.85 +\    (! x. Q1 x --> Q0 x) & (? x. Q1 x) &     \
   75.86 +\    (! x. P0 x --> ((! y. Q0 y-->R x y) |    \
   75.87 +\                     (! y. P0 y & S y x &     \
   75.88 +\                          (? z. Q0 z&R y z) --> R x y))) &   \
   75.89  \    (! x y. P3 y & (P5 x|P4 x) --> S x y) &        \
   75.90  \    (! x y. P3 x & P2 y --> S x y) &        \
   75.91  \    (! x y. P2 x & P1 y --> S x y) &        \
   75.92  \    (! x y. P1 x & (P2 y|Q1 y) --> ~R x y) &       \
   75.93  \    (! x y. P3 x & P4 y --> R x y) &        \
   75.94  \    (! x y. P3 x & P5 y --> ~R x y) &       \
   75.95 -\    (! x. (P4 x|P5 x) --> (? y.Q0 y & R x y))      \
   75.96 +\    (! x. (P4 x|P5 x) --> (? y. Q0 y & R x y))      \
   75.97  \    --> (? x y. P0 x & P0 y & (? z. Q1 z & R y z & R x y))";
   75.98  by (safe_meson_tac 1);   (*119 secs*)
   75.99  result();
  75.100 @@ -518,14 +518,14 @@
  75.101  (*A similar example, suggested by Johannes Schumann and credited to Pelletier*)
  75.102  goal HOL.thy "(!x y z. P x y --> P y z --> P x z) --> \
  75.103  \       (!x y z. Q x y --> Q y z --> Q x z) --> \
  75.104 -\       (!x y.Q x y --> Q y x) -->  (!x y. P x y | Q x y) --> \
  75.105 -\       (!x y.P x y) | (!x y.Q x y)";
  75.106 +\       (!x y. Q x y --> Q y x) -->  (!x y. P x y | Q x y) --> \
  75.107 +\       (!x y. P x y) | (!x y. Q x y)";
  75.108  by (safe_best_meson_tac 1);          (*2.7 secs*)
  75.109  result();
  75.110  
  75.111  writeln"Problem 50";  
  75.112  (*What has this to do with equality?*)
  75.113 -goal HOL.thy "(! x. P a x | (! y.P x y)) --> (? x. ! y.P x y)";
  75.114 +goal HOL.thy "(! x. P a x | (! y. P x y)) --> (? x. ! y. P x y)";
  75.115  by (safe_meson_tac 1);
  75.116  result();
  75.117  
    76.1 --- a/src/HOL/ex/set.ML	Fri Oct 10 18:37:49 1997 +0200
    76.2 +++ b/src/HOL/ex/set.ML	Fri Oct 10 19:02:28 1997 +0200
    76.3 @@ -21,7 +21,7 @@
    76.4  
    76.5  (*** A unique fixpoint theorem --- fast/best/meson all fail ***)
    76.6  
    76.7 -val [prem] = goal HOL.thy "?!x.f(g(x))=x ==> ?!y.g(f(y))=y";
    76.8 +val [prem] = goal HOL.thy "?!x. f(g(x))=x ==> ?!y. g(f(y))=y";
    76.9  by (EVERY1[rtac (prem RS ex1E), rtac ex1I, etac arg_cong,
   76.10            rtac subst, atac, etac allE, rtac arg_cong, etac mp, etac arg_cong]);
   76.11  result();
    77.1 --- a/src/HOL/mono.ML	Fri Oct 10 18:37:49 1997 +0200
    77.2 +++ b/src/HOL/mono.ML	Fri Oct 10 19:02:28 1997 +0200
    77.3 @@ -91,12 +91,12 @@
    77.4  qed "imp_refl";
    77.5  
    77.6  val [PQimp] = goal HOL.thy
    77.7 -    "[| !!x. P(x) --> Q(x) |] ==> (EX x.P(x)) --> (EX x.Q(x))";
    77.8 +    "[| !!x. P(x) --> Q(x) |] ==> (EX x. P(x)) --> (EX x. Q(x))";
    77.9  by (blast_tac (!claset addIs [PQimp RS mp]) 1);
   77.10  qed "ex_mono";
   77.11  
   77.12  val [PQimp] = goal HOL.thy
   77.13 -    "[| !!x. P(x) --> Q(x) |] ==> (ALL x.P(x)) --> (ALL x.Q(x))";
   77.14 +    "[| !!x. P(x) --> Q(x) |] ==> (ALL x. P(x)) --> (ALL x. Q(x))";
   77.15  by (blast_tac (!claset addIs [PQimp RS mp]) 1);
   77.16  qed "all_mono";
   77.17  
    78.1 --- a/src/HOL/simpdata.ML	Fri Oct 10 18:37:49 1997 +0200
    78.2 +++ b/src/HOL/simpdata.ML	Fri Oct 10 19:02:28 1997 +0200
    78.3 @@ -102,7 +102,7 @@
    78.4     "(P | False) = P", "(False | P) = P",
    78.5     "(P | P) = P", "(P | (P | Q)) = (P | Q)",
    78.6     "((~P) = (~Q)) = (P=Q)",
    78.7 -   "(!x.P) = P", "(? x.P) = P", "? x. x=t", "? x. t=x", 
    78.8 +   "(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
    78.9     "(? x. x=t & P(x)) = P(t)",
   78.10     "(! x. t=x --> P(x)) = P(t)" ];
   78.11  
   78.12 @@ -122,21 +122,21 @@
   78.13  
   78.14  (*Miniscoping: pushing in existential quantifiers*)
   78.15  val ex_simps = map prover 
   78.16 -                ["(EX x. P x & Q)   = ((EX x.P x) & Q)",
   78.17 -                 "(EX x. P & Q x)   = (P & (EX x.Q x))",
   78.18 -                 "(EX x. P x | Q)   = ((EX x.P x) | Q)",
   78.19 -                 "(EX x. P | Q x)   = (P | (EX x.Q x))",
   78.20 -                 "(EX x. P x --> Q) = ((ALL x.P x) --> Q)",
   78.21 -                 "(EX x. P --> Q x) = (P --> (EX x.Q x))"];
   78.22 +                ["(EX x. P x & Q)   = ((EX x. P x) & Q)",
   78.23 +                 "(EX x. P & Q x)   = (P & (EX x. Q x))",
   78.24 +                 "(EX x. P x | Q)   = ((EX x. P x) | Q)",
   78.25 +                 "(EX x. P | Q x)   = (P | (EX x. Q x))",
   78.26 +                 "(EX x. P x --> Q) = ((ALL x. P x) --> Q)",
   78.27 +                 "(EX x. P --> Q x) = (P --> (EX x. Q x))"];
   78.28  
   78.29  (*Miniscoping: pushing in universal quantifiers*)
   78.30  val all_simps = map prover
   78.31 -                ["(ALL x. P x & Q)   = ((ALL x.P x) & Q)",
   78.32 -                 "(ALL x. P & Q x)   = (P & (ALL x.Q x))",
   78.33 -                 "(ALL x. P x | Q)   = ((ALL x.P x) | Q)",
   78.34 -                 "(ALL x. P | Q x)   = (P | (ALL x.Q x))",
   78.35 -                 "(ALL x. P x --> Q) = ((EX x.P x) --> Q)",
   78.36 -                 "(ALL x. P --> Q x) = (P --> (ALL x.Q x))"];
   78.37 +                ["(ALL x. P x & Q)   = ((ALL x. P x) & Q)",
   78.38 +                 "(ALL x. P & Q x)   = (P & (ALL x. Q x))",
   78.39 +                 "(ALL x. P x | Q)   = ((ALL x. P x) | Q)",
   78.40 +                 "(ALL x. P | Q x)   = (P | (ALL x. Q x))",
   78.41 +                 "(ALL x. P x --> Q) = ((EX x. P x) --> Q)",
   78.42 +                 "(ALL x. P --> Q x) = (P --> (ALL x. Q x))"];
   78.43  
   78.44  (*** Simplification procedure for turning  ? x. ... & x = t & ...
   78.45       into                                  ? x. x = t & ... & ...
   78.46 @@ -179,7 +179,7 @@
   78.47            in Some(prove_eq ceqt) end)
   78.48    | rearrange _ _ _ = None;
   78.49  
   78.50 -val pattern = read_cterm (sign_of HOL.thy) ("? x.P(x) & Q(x)",HOLogic.boolT)
   78.51 +val pattern = read_cterm (sign_of HOL.thy) ("? x. P(x) & Q(x)",HOLogic.boolT)
   78.52  
   78.53  in
   78.54  val defEX_regroup = mk_simproc "defined EX" [pattern] rearrange;
   78.55 @@ -242,9 +242,9 @@
   78.56    cases boil down to the same thing.*) 
   78.57  prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
   78.58  
   78.59 -prove "not_all" "(~ (! x.P(x))) = (? x.~P(x))";
   78.60 +prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
   78.61  prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
   78.62 -prove "not_ex"  "(~ (? x.P(x))) = (! x.~P(x))";
   78.63 +prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
   78.64  prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
   78.65  
   78.66  prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
    79.1 --- a/src/HOLCF/Cfun2.ML	Fri Oct 10 18:37:49 1997 +0200
    79.2 +++ b/src/HOLCF/Cfun2.ML	Fri Oct 10 19:02:28 1997 +0200
    79.3 @@ -9,7 +9,7 @@
    79.4  open Cfun2;
    79.5  
    79.6  (* for compatibility with old HOLCF-Version *)
    79.7 -qed_goal "inst_cfun_po" thy "(op <<)=(%f1 f2.fapp f1 << fapp f2)"
    79.8 +qed_goal "inst_cfun_po" thy "(op <<)=(%f1 f2. fapp f1 << fapp f2)"
    79.9   (fn prems => 
   79.10          [
   79.11  	(fold_goals_tac [less_cfun_def]),
   79.12 @@ -30,7 +30,7 @@
   79.13  (* Type 'a ->'b  is pointed                                                 *)
   79.14  (* ------------------------------------------------------------------------ *)
   79.15  
   79.16 -qed_goal "minimal_cfun" thy "fabs(% x.UU) << f"
   79.17 +qed_goal "minimal_cfun" thy "fabs(% x. UU) << f"
   79.18  (fn prems =>
   79.19          [
   79.20          (stac less_cfun 1),
   79.21 @@ -41,10 +41,10 @@
   79.22  
   79.23  bind_thm ("UU_cfun_def",minimal_cfun RS minimal2UU RS sym);
   79.24  
   79.25 -qed_goal "least_cfun" thy "? x::'a->'b::pcpo.!y.x<<y"
   79.26 +qed_goal "least_cfun" thy "? x::'a->'b::pcpo.!y. x<<y"
   79.27  (fn prems =>
   79.28          [
   79.29 -        (res_inst_tac [("x","fabs(% x.UU)")] exI 1),
   79.30 +        (res_inst_tac [("x","fabs(% x. UU)")] exI 1),
   79.31          (rtac (minimal_cfun RS allI) 1)
   79.32          ]);
   79.33  
   79.34 @@ -156,7 +156,7 @@
   79.35  (* ------------------------------------------------------------------------ *)
   79.36  
   79.37  qed_goal "lub_cfun_mono" thy 
   79.38 -        "is_chain(F) ==> monofun(% x.lub(range(% j.(F j)`x)))"
   79.39 +        "is_chain(F) ==> monofun(% x. lub(range(% j.(F j)`x)))"
   79.40  (fn prems =>
   79.41          [
   79.42          (cut_facts_tac prems 1),
   79.43 @@ -190,7 +190,7 @@
   79.44  (* ------------------------------------------------------------------------ *)
   79.45  
   79.46  qed_goal "cont_lubcfun" thy 
   79.47 -        "is_chain(F) ==> cont(% x.lub(range(% j.F(j)`x)))"
   79.48 +        "is_chain(F) ==> cont(% x. lub(range(% j. F(j)`x)))"
   79.49  (fn prems =>
   79.50          [
   79.51          (cut_facts_tac prems 1),
   79.52 @@ -209,7 +209,7 @@
   79.53  (* ------------------------------------------------------------------------ *)
   79.54  
   79.55  qed_goal "lub_cfun" thy 
   79.56 -  "is_chain(CCF) ==> range(CCF) <<| (LAM x.lub(range(% i.CCF(i)`x)))"
   79.57 +  "is_chain(CCF) ==> range(CCF) <<| (LAM x. lub(range(% i. CCF(i)`x)))"
   79.58  (fn prems =>
   79.59          [
   79.60          (cut_facts_tac prems 1),
    80.1 --- a/src/HOLCF/Cfun3.ML	Fri Oct 10 18:37:49 1997 +0200
    80.2 +++ b/src/HOLCF/Cfun3.ML	Fri Oct 10 19:02:28 1997 +0200
    80.3 @@ -7,7 +7,7 @@
    80.4  open Cfun3;
    80.5  
    80.6  (* for compatibility with old HOLCF-Version *)
    80.7 -qed_goal "inst_cfun_pcpo" thy "UU = fabs(%x.UU)"
    80.8 +qed_goal "inst_cfun_pcpo" thy "UU = fabs(%x. UU)"
    80.9   (fn prems => 
   80.10          [
   80.11          (simp_tac (HOL_ss addsimps [UU_def,UU_cfun_def]) 1)
   80.12 @@ -53,7 +53,7 @@
   80.13  
   80.14  qed_goal "contlub_cfun_fun" thy 
   80.15  "is_chain(FY) ==>\
   80.16 -\ lub(range FY)`x = lub(range (%i.FY(i)`x))"
   80.17 +\ lub(range FY)`x = lub(range (%i. FY(i)`x))"
   80.18  (fn prems =>
   80.19          [
   80.20          (cut_facts_tac prems 1),
   80.21 @@ -67,7 +67,7 @@
   80.22  
   80.23  qed_goal "cont_cfun_fun" thy 
   80.24  "is_chain(FY) ==>\
   80.25 -\ range(%i.FY(i)`x) <<| lub(range FY)`x"
   80.26 +\ range(%i. FY(i)`x) <<| lub(range FY)`x"
   80.27  (fn prems =>
   80.28          [
   80.29          (cut_facts_tac prems 1),
   80.30 @@ -83,7 +83,7 @@
   80.31  
   80.32  qed_goal "contlub_cfun" thy 
   80.33  "[|is_chain(FY);is_chain(TY)|] ==>\
   80.34 -\ (lub(range FY))`(lub(range TY)) = lub(range(%i.FY(i)`(TY i)))"
   80.35 +\ (lub(range FY))`(lub(range TY)) = lub(range(%i. FY(i)`(TY i)))"
   80.36  (fn prems =>
   80.37          [
   80.38          (cut_facts_tac prems 1),
   80.39 @@ -117,7 +117,7 @@
   80.40  (* ------------------------------------------------------------------------ *)
   80.41  
   80.42  qed_goal "cont2cont_fapp" thy 
   80.43 -        "[|cont(%x.ft x);cont(%x.tt x)|] ==> cont(%x. (ft x)`(tt x))"
   80.44 +        "[|cont(%x. ft x);cont(%x. tt x)|] ==> cont(%x. (ft x)`(tt x))"
   80.45   (fn prems =>
   80.46          [
   80.47          (cut_facts_tac prems 1),
   80.48 @@ -137,7 +137,7 @@
   80.49  (* ------------------------------------------------------------------------ *)
   80.50  
   80.51  qed_goal "cont2mono_LAM" thy 
   80.52 - "[| !!x.cont(c1 x); !!y.monofun(%x.c1 x y)|] ==> monofun(%x. LAM y. c1 x y)"
   80.53 + "[| !!x. cont(c1 x); !!y. monofun(%x. c1 x y)|] ==> monofun(%x. LAM y. c1 x y)"
   80.54  (fn [p1,p2] =>
   80.55          [
   80.56          (rtac monofunI 1),
   80.57 @@ -157,7 +157,7 @@
   80.58  (* ------------------------------------------------------------------------ *)
   80.59  
   80.60  qed_goal "cont2cont_LAM" thy 
   80.61 - "[| !!x.cont(c1 x); !!y.cont(%x.c1 x y) |] ==> cont(%x. LAM y. c1 x y)"
   80.62 + "[| !!x. cont(c1 x); !!y. cont(%x. c1 x y) |] ==> cont(%x. LAM y. c1 x y)"
   80.63  (fn [p1,p2] =>
   80.64          [
   80.65          (rtac monocontlub2cont 1),
   80.66 @@ -393,7 +393,7 @@
   80.67  (* ------------------------------------------------------------------------ *)
   80.68  
   80.69  qed_goal "iso_strict"  thy  
   80.70 -"!!f g.[|!y.f`(g`y)=(y::'b) ; !x.g`(f`x)=(x::'a) |] \
   80.71 +"!!f g.[|!y. f`(g`y)=(y::'b) ; !x. g`(f`x)=(x::'a) |] \
   80.72  \ ==> f`UU=UU & g`UU=UU"
   80.73   (fn prems =>
   80.74          [
   80.75 @@ -410,7 +410,7 @@
   80.76  
   80.77  
   80.78  qed_goal "isorep_defined" thy 
   80.79 -        "[|!x.rep`(abs`x)=x;!y.abs`(rep`y)=y; z~=UU|] ==> rep`z ~= UU"
   80.80 +        "[|!x. rep`(abs`x)=x;!y. abs`(rep`y)=y; z~=UU|] ==> rep`z ~= UU"
   80.81   (fn prems =>
   80.82          [
   80.83          (cut_facts_tac prems 1),
   80.84 @@ -424,7 +424,7 @@
   80.85          ]);
   80.86  
   80.87  qed_goal "isoabs_defined" thy 
   80.88 -        "[|!x.rep`(abs`x) = x;!y.abs`(rep`y)=y ; z~=UU|] ==> abs`z ~= UU"
   80.89 +        "[|!x. rep`(abs`x) = x;!y. abs`(rep`y)=y ; z~=UU|] ==> abs`z ~= UU"
   80.90   (fn prems =>
   80.91          [
   80.92          (cut_facts_tac prems 1),
   80.93 @@ -442,14 +442,14 @@
   80.94  (* ------------------------------------------------------------------------ *)
   80.95  
   80.96  qed_goal "chfin2chfin" thy "!!f g.[|! Y::nat=>'a. is_chain Y --> (? n. max_in_chain n Y); \
   80.97 -\ !y.f`(g`y)=(y::'b) ; !x.g`(f`x)=(x::'a::chfin) |] \
   80.98 +\ !y. f`(g`y)=(y::'b) ; !x. g`(f`x)=(x::'a::chfin) |] \
   80.99  \ ==> ! Y::nat=>'b. is_chain Y --> (? n. max_in_chain n Y)"
  80.100   (fn prems =>
  80.101          [
  80.102          (rewtac max_in_chain_def),
  80.103          (strip_tac 1),
  80.104          (rtac exE 1),
  80.105 -        (res_inst_tac [("P","is_chain(%i.g`(Y i))")] mp 1),
  80.106 +        (res_inst_tac [("P","is_chain(%i. g`(Y i))")] mp 1),
  80.107          (etac spec 1),
  80.108          (etac ch2ch_fappR 1),
  80.109          (rtac exI 1),
  80.110 @@ -465,8 +465,8 @@
  80.111          ]);
  80.112  
  80.113  
  80.114 -qed_goal "flat2flat" thy "!!f g.[|!x y::'a.x<<y --> x=UU | x=y; \
  80.115 -\ !y.f`(g`y)=(y::'b); !x.g`(f`x)=(x::'a)|] ==> !x y::'b.x<<y --> x=UU | x=y"
  80.116 +qed_goal "flat2flat" thy "!!f g.[|!x y::'a. x<<y --> x=UU | x=y; \
  80.117 +\ !y. f`(g`y)=(y::'b); !x. g`(f`x)=(x::'a)|] ==> !x y::'b. x<<y --> x=UU | x=y"
  80.118   (fn prems =>
  80.119          [
  80.120          (strip_tac 1),
  80.121 @@ -496,7 +496,7 @@
  80.122  (* ------------------------------------------------------------------------- *)
  80.123  
  80.124  qed_goal "flat_codom" thy 
  80.125 -"f`(x::'a)=(c::'b::flat) ==> f`(UU::'a)=(UU::'b) | (!z.f`(z::'a)=c)"
  80.126 +"f`(x::'a)=(c::'b::flat) ==> f`(UU::'a)=(UU::'b) | (!z. f`(z::'a)=c)"
  80.127   (fn prems =>
  80.128          [
  80.129          (cut_facts_tac prems 1),
  80.130 @@ -534,7 +534,7 @@
  80.131          (rtac refl 1)
  80.132          ]);
  80.133  
  80.134 -qed_goalw "cfcomp1" thy [oo_def] "(f oo g)=(LAM x.f`(g`x))" (fn _ => [
  80.135 +qed_goalw "cfcomp1" thy [oo_def] "(f oo g)=(LAM x. f`(g`x))" (fn _ => [
  80.136          (stac beta_cfun 1),
  80.137          (Simp_tac 1),
  80.138          (stac beta_cfun 1),
    81.1 --- a/src/HOLCF/Cfun3.thy	Fri Oct 10 18:37:49 1997 +0200
    81.2 +++ b/src/HOLCF/Cfun3.thy	Fri Oct 10 19:02:28 1997 +0200
    81.3 @@ -20,7 +20,7 @@
    81.4  defs
    81.5  
    81.6  Istrictify_def  "Istrictify f x == if x=UU then UU else f`x"    
    81.7 -strictify_def   "strictify == (LAM f x.Istrictify f x)"
    81.8 +strictify_def   "strictify == (LAM f x. Istrictify f x)"
    81.9  
   81.10  consts
   81.11          ID      :: "('a::cpo) -> 'a"
   81.12 @@ -32,7 +32,7 @@
   81.13  
   81.14  defs
   81.15  
   81.16 -  ID_def        "ID ==(LAM x.x)"
   81.17 -  oo_def        "cfcomp == (LAM f g x.f`(g`x))" 
   81.18 +  ID_def        "ID ==(LAM x. x)"
   81.19 +  oo_def        "cfcomp == (LAM f g x. f`(g`x))" 
   81.20  
   81.21  end
    82.1 --- a/src/HOLCF/Cont.ML	Fri Oct 10 18:37:49 1997 +0200
    82.2 +++ b/src/HOLCF/Cont.ML	Fri Oct 10 19:02:28 1997 +0200
    82.3 @@ -32,7 +32,7 @@
    82.4  
    82.5  
    82.6  qed_goalw "contI" thy [cont]
    82.7 - "! Y. is_chain(Y) --> range(% i.f(Y(i))) <<| f(lub(range(Y))) ==> cont(f)"
    82.8 + "! Y. is_chain(Y) --> range(% i. f(Y(i))) <<| f(lub(range(Y))) ==> cont(f)"
    82.9  (fn prems =>
   82.10          [
   82.11          (cut_facts_tac prems 1),
   82.12 @@ -40,7 +40,7 @@
   82.13          ]);
   82.14  
   82.15  qed_goalw "contE" thy [cont]
   82.16 - "cont(f) ==> ! Y. is_chain(Y) --> range(% i.f(Y(i))) <<| f(lub(range(Y)))"
   82.17 + "cont(f) ==> ! Y. is_chain(Y) --> range(% i. f(Y(i))) <<| f(lub(range(Y)))"
   82.18  (fn prems =>
   82.19          [
   82.20          (cut_facts_tac prems 1),
   82.21 @@ -89,7 +89,7 @@
   82.22  (* ------------------------------------------------------------------------ *)
   82.23  
   82.24  qed_goal "ub2ub_monofun" thy 
   82.25 - "[| monofun(f); range(Y) <| u|]  ==> range(%i.f(Y(i))) <| f(u)"
   82.26 + "[| monofun(f); range(Y) <| u|]  ==> range(%i. f(Y(i))) <| f(u)"
   82.27  (fn prems =>
   82.28          [
   82.29          (cut_facts_tac prems 1),
   82.30 @@ -213,7 +213,7 @@
   82.31          ]);
   82.32  
   82.33  qed_goal "ch2ch_MF2LR" thy 
   82.34 -"[|monofun(MF2); !f.monofun(MF2(f)); is_chain(F); is_chain(Y)|] ==> \
   82.35 +"[|monofun(MF2); !f. monofun(MF2(f)); is_chain(F); is_chain(Y)|] ==> \
   82.36  \  is_chain(%i. MF2(F(i))(Y(i)))"
   82.37   (fn prems =>
   82.38          [
   82.39 @@ -230,7 +230,7 @@
   82.40  
   82.41  qed_goal "ch2ch_lubMF2R" thy 
   82.42  "[|monofun(MF2::('a::po=>'b::po=>'c::cpo));\
   82.43 -\  !f.monofun(MF2(f)::('b::po=>'c::cpo));\
   82.44 +\  !f. monofun(MF2(f)::('b::po=>'c::cpo));\
   82.45  \       is_chain(F);is_chain(Y)|] ==> \
   82.46  \       is_chain(%j. lub(range(%i. MF2 (F j) (Y i))))"
   82.47  (fn prems =>
   82.48 @@ -250,7 +250,7 @@
   82.49  
   82.50  qed_goal "ch2ch_lubMF2L" thy 
   82.51  "[|monofun(MF2::('a::po=>'b::po=>'c::cpo));\
   82.52 -\  !f.monofun(MF2(f)::('b::po=>'c::cpo));\
   82.53 +\  !f. monofun(MF2(f)::('b::po=>'c::cpo));\
   82.54  \       is_chain(F);is_chain(Y)|] ==> \
   82.55  \       is_chain(%i. lub(range(%j. MF2 (F j) (Y i))))"
   82.56  (fn prems =>
   82.57 @@ -270,9 +270,9 @@
   82.58  
   82.59  qed_goal "lub_MF2_mono" thy 
   82.60  "[|monofun(MF2::('a::po=>'b::po=>'c::cpo));\
   82.61 -\  !f.monofun(MF2(f)::('b::po=>'c::cpo));\
   82.62 +\  !f. monofun(MF2(f)::('b::po=>'c::cpo));\
   82.63  \       is_chain(F)|] ==> \
   82.64 -\       monofun(% x.lub(range(% j.MF2 (F j) (x))))"
   82.65 +\       monofun(% x. lub(range(% j. MF2 (F j) (x))))"
   82.66  (fn prems =>
   82.67          [
   82.68          (cut_facts_tac prems 1),
   82.69 @@ -290,7 +290,7 @@
   82.70  
   82.71  qed_goal "ex_lubMF2" thy 
   82.72  "[|monofun(MF2::('a::po=>'b::po=>'c::cpo));\
   82.73 -\  !f.monofun(MF2(f)::('b::po=>'c::cpo));\
   82.74 +\  !f. monofun(MF2(f)::('b::po=>'c::cpo));\
   82.75  \       is_chain(F); is_chain(Y)|] ==> \
   82.76  \               lub(range(%j. lub(range(%i. MF2(F j) (Y i))))) =\
   82.77  \               lub(range(%i. lub(range(%j. MF2(F j) (Y i)))))"
   82.78 @@ -329,7 +329,7 @@
   82.79  
   82.80  qed_goal "diag_lubMF2_1" thy 
   82.81  "[|monofun(MF2::('a::po=>'b::po=>'c::cpo));\
   82.82 -\  !f.monofun(MF2(f)::('b::po=>'c::cpo));\
   82.83 +\  !f. monofun(MF2(f)::('b::po=>'c::cpo));\
   82.84  \  is_chain(FY);is_chain(TY)|] ==>\
   82.85  \ lub(range(%i. lub(range(%j. MF2(FY(j))(TY(i)))))) =\
   82.86  \ lub(range(%i. MF2(FY(i))(TY(i))))"
   82.87 @@ -373,7 +373,7 @@
   82.88  
   82.89  qed_goal "diag_lubMF2_2" thy 
   82.90  "[|monofun(MF2::('a::po=>'b::po=>'c::cpo));\
   82.91 -\  !f.monofun(MF2(f)::('b::po=>'c::cpo));\
   82.92 +\  !f. monofun(MF2(f)::('b::po=>'c::cpo));\
   82.93  \  is_chain(FY);is_chain(TY)|] ==>\
   82.94  \ lub(range(%j. lub(range(%i. MF2(FY(j))(TY(i)))))) =\
   82.95  \ lub(range(%i. MF2(FY(i))(TY(i))))"
   82.96 @@ -394,8 +394,8 @@
   82.97  (* ------------------------------------------------------------------------ *)
   82.98  
   82.99  qed_goal "contlub_CF2" thy 
  82.100 -"[|cont(CF2);!f.cont(CF2(f));is_chain(FY);is_chain(TY)|] ==>\
  82.101 -\ CF2(lub(range(FY)))(lub(range(TY))) = lub(range(%i.CF2(FY(i))(TY(i))))"
  82.102 +"[|cont(CF2);!f. cont(CF2(f));is_chain(FY);is_chain(TY)|] ==>\
  82.103 +\ CF2(lub(range(FY)))(lub(range(TY))) = lub(range(%i. CF2(FY(i))(TY(i))))"
  82.104   (fn prems =>
  82.105          [
  82.106          (cut_facts_tac prems 1),
  82.107 @@ -486,7 +486,7 @@
  82.108  (*********  Note "(%x.%y.c1 x y) = c1" ***********)
  82.109  
  82.110  qed_goal "mono2mono_MF1L_rev" thy
  82.111 -        "!y.monofun(%x.c1 x y) ==> monofun(c1)"
  82.112 +        "!y. monofun(%x. c1 x y) ==> monofun(c1)"
  82.113  (fn prems =>
  82.114          [
  82.115          (cut_facts_tac prems 1),
  82.116 @@ -499,7 +499,7 @@
  82.117          ]);
  82.118  
  82.119  qed_goal "cont2cont_CF1L_rev" thy
  82.120 -        "!y.cont(%x.c1 x y) ==> cont(c1)"
  82.121 +        "!y. cont(%x. c1 x y) ==> cont(c1)"
  82.122  (fn prems =>
  82.123          [
  82.124          (cut_facts_tac prems 1),
  82.125 @@ -524,8 +524,8 @@
  82.126  (* ------------------------------------------------------------------------ *)
  82.127  
  82.128  qed_goal "contlub_abstraction" thy
  82.129 -"[|is_chain(Y::nat=>'a);!y.cont(%x.(c::'a::cpo=>'b::cpo=>'c::cpo) x y)|] ==>\
  82.130 -\ (%y.lub(range(%i.c (Y i) y))) = (lub(range(%i.%y.c (Y i) y)))"
  82.131 +"[|is_chain(Y::nat=>'a);!y. cont(%x.(c::'a::cpo=>'b::cpo=>'c::cpo) x y)|] ==>\
  82.132 +\ (%y. lub(range(%i. c (Y i) y))) = (lub(range(%i.%y. c (Y i) y)))"
  82.133   (fn prems =>
  82.134          [
  82.135          (cut_facts_tac prems 1),
  82.136 @@ -540,7 +540,7 @@
  82.137          ]);
  82.138  
  82.139  qed_goal "mono2mono_app" thy 
  82.140 -"[|monofun(ft);!x.monofun(ft(x));monofun(tt)|] ==>\
  82.141 +"[|monofun(ft);!x. monofun(ft(x));monofun(tt)|] ==>\
  82.142  \        monofun(%x.(ft(x))(tt(x)))"
  82.143   (fn prems =>
  82.144          [
  82.145 @@ -558,7 +558,7 @@
  82.146  
  82.147  
  82.148  qed_goal "cont2contlub_app" thy 
  82.149 -"[|cont(ft);!x.cont(ft(x));cont(tt)|] ==> contlub(%x.(ft(x))(tt(x)))"
  82.150 +"[|cont(ft);!x. cont(ft(x));cont(tt)|] ==> contlub(%x.(ft(x))(tt(x)))"
  82.151   (fn prems =>
  82.152          [
  82.153          (cut_facts_tac prems 1),
  82.154 @@ -575,7 +575,7 @@
  82.155  
  82.156  
  82.157  qed_goal "cont2cont_app" thy 
  82.158 -"[|cont(ft);!x.cont(ft(x));cont(tt)|] ==>\
  82.159 +"[|cont(ft);!x. cont(ft(x));cont(tt)|] ==>\
  82.160  \        cont(%x.(ft(x))(tt(x)))"
  82.161   (fn prems =>
  82.162          [
  82.163 @@ -605,7 +605,7 @@
  82.164  (* The identity function is continuous                                      *)
  82.165  (* ------------------------------------------------------------------------ *)
  82.166  
  82.167 -qed_goal "cont_id" thy "cont(% x.x)"
  82.168 +qed_goal "cont_id" thy "cont(% x. x)"
  82.169   (fn prems =>
  82.170          [
  82.171          (rtac contI 1),
  82.172 @@ -618,7 +618,7 @@
  82.173  (* constant functions are continuous                                        *)
  82.174  (* ------------------------------------------------------------------------ *)
  82.175  
  82.176 -qed_goalw "cont_const" thy [cont] "cont(%x.c)"
  82.177 +qed_goalw "cont_const" thy [cont] "cont(%x. c)"
  82.178   (fn prems =>
  82.179          [
  82.180          (strip_tac 1),
    83.1 --- a/src/HOLCF/Cont.thy	Fri Oct 10 18:37:49 1997 +0200
    83.2 +++ b/src/HOLCF/Cont.thy	Fri Oct 10 19:02:28 1997 +0200
    83.3 @@ -28,10 +28,10 @@
    83.4  monofun         "monofun(f) == ! x y. x << y --> f(x) << f(y)"
    83.5  
    83.6  contlub         "contlub(f) == ! Y. is_chain(Y) --> 
    83.7 -                                f(lub(range(Y))) = lub(range(% i.f(Y(i))))"
    83.8 +                                f(lub(range(Y))) = lub(range(% i. f(Y(i))))"
    83.9  
   83.10  cont            "cont(f)   == ! Y. is_chain(Y) --> 
   83.11 -                                range(% i.f(Y(i))) <<| f(lub(range(Y)))"
   83.12 +                                range(% i. f(Y(i))) <<| f(lub(range(Y)))"
   83.13  
   83.14  (* ------------------------------------------------------------------------ *)
   83.15  (* the main purpose of cont.thy is to show:                                 *)
    84.1 --- a/src/HOLCF/Cprod2.ML	Fri Oct 10 18:37:49 1997 +0200
    84.2 +++ b/src/HOLCF/Cprod2.ML	Fri Oct 10 19:02:28 1997 +0200
    84.3 @@ -9,7 +9,7 @@
    84.4  open Cprod2;
    84.5  
    84.6  (* for compatibility with old HOLCF-Version *)
    84.7 -qed_goal "inst_cprod_po" thy "(op <<)=(%x y.fst x<<fst y & snd x<<snd y)"
    84.8 +qed_goal "inst_cprod_po" thy "(op <<)=(%x y. fst x<<fst y & snd x<<snd y)"
    84.9   (fn prems => 
   84.10          [
   84.11          (fold_goals_tac [less_cprod_def]),
   84.12 @@ -45,7 +45,7 @@
   84.13  
   84.14  bind_thm ("UU_cprod_def",minimal_cprod RS minimal2UU RS sym);
   84.15  
   84.16 -qed_goal "least_cprod" thy "? x::'a*'b.!y.x<<y"
   84.17 +qed_goal "least_cprod" thy "? x::'a*'b.!y. x<<y"
   84.18  (fn prems =>
   84.19          [
   84.20          (res_inst_tac [("x","(UU,UU)")] exI 1),
   84.21 @@ -116,7 +116,7 @@
   84.22  (* ------------------------------------------------------------------------ *)
   84.23  
   84.24  qed_goal "lub_cprod" thy 
   84.25 -"is_chain S ==> range S<<|(lub(range(%i.fst(S i))),lub(range(%i.snd(S i))))"
   84.26 +"is_chain S ==> range S<<|(lub(range(%i. fst(S i))),lub(range(%i. snd(S i))))"
   84.27   (fn prems =>
   84.28          [
   84.29          (cut_facts_tac prems 1),
   84.30 @@ -147,7 +147,7 @@
   84.31  
   84.32  *)
   84.33  
   84.34 -qed_goal "cpo_cprod" thy "is_chain(S::nat=>'a::cpo*'b::cpo)==>? x.range S<<| x"
   84.35 +qed_goal "cpo_cprod" thy "is_chain(S::nat=>'a::cpo*'b::cpo)==>? x. range S<<| x"
   84.36  (fn prems =>
   84.37          [
   84.38          (cut_facts_tac prems 1),
    85.1 --- a/src/HOLCF/Cprod3.ML	Fri Oct 10 18:37:49 1997 +0200
    85.2 +++ b/src/HOLCF/Cprod3.ML	Fri Oct 10 19:02:28 1997 +0200
    85.3 @@ -262,7 +262,7 @@
    85.4  
    85.5  qed_goalw "lub_cprod2" Cprod3.thy [cfst_def,csnd_def,cpair_def]
    85.6  "[|is_chain(S)|] ==> range(S) <<| \
    85.7 -\ <(lub(range(%i.cfst`(S i)))) , lub(range(%i.csnd`(S i)))>"
    85.8 +\ <(lub(range(%i. cfst`(S i)))) , lub(range(%i. csnd`(S i)))>"
    85.9   (fn prems =>
   85.10          [
   85.11          (cut_facts_tac prems 1),
    86.1 --- a/src/HOLCF/Cprod3.thy	Fri Oct 10 18:37:49 1997 +0200
    86.2 +++ b/src/HOLCF/Cprod3.thy	Fri Oct 10 19:02:28 1997 +0200
    86.3 @@ -26,9 +26,9 @@
    86.4  
    86.5  defs
    86.6  cpair_def       "cpair  == (LAM x y.(x,y))"
    86.7 -cfst_def        "cfst   == (LAM p.fst(p))"
    86.8 -csnd_def        "csnd   == (LAM p.snd(p))"      
    86.9 -csplit_def      "csplit == (LAM f p.f`(cfst`p)`(csnd`p))"
   86.10 +cfst_def        "cfst   == (LAM p. fst(p))"
   86.11 +csnd_def        "csnd   == (LAM p. snd(p))"      
   86.12 +csplit_def      "csplit == (LAM f p. f`(cfst`p)`(csnd`p))"
   86.13  
   86.14  
   86.15  
   86.16 @@ -43,7 +43,7 @@
   86.17  
   86.18  constdefs
   86.19    CLet           :: "'a -> ('a -> 'b) -> 'b"
   86.20 -  "CLet == LAM s f.f`s"
   86.21 +  "CLet == LAM s f. f`s"
   86.22  
   86.23  
   86.24  (* syntax for Let *)
   86.25 @@ -59,7 +59,7 @@
   86.26  
   86.27  translations
   86.28    "_CLet (_Cbinds b bs) e"  == "_CLet b (_CLet bs e)"
   86.29 -  "Let x = a in e"          == "CLet`a`(LAM x.e)"
   86.30 +  "Let x = a in e"          == "CLet`a`(LAM x. e)"
   86.31  
   86.32  
   86.33  (* syntax for LAM <x,y,z>.e *)
    87.1 --- a/src/HOLCF/Discrete.ML	Fri Oct 10 18:37:49 1997 +0200
    87.2 +++ b/src/HOLCF/Discrete.ML	Fri Oct 10 19:02:28 1997 +0200
    87.3 @@ -10,11 +10,11 @@
    87.4  Addsimps [undiscr_Discr];
    87.5  
    87.6  goal thy
    87.7 - "!!S::nat=>('a::term)discr. is_chain(S) ==> range(%i.f(S i)) = {f(S 0)}";
    87.8 + "!!S::nat=>('a::term)discr. is_chain(S) ==> range(%i. f(S i)) = {f(S 0)}";
    87.9  by(fast_tac (!claset addDs [discr_chain0] addEs [arg_cong]) 1);
   87.10  qed "discr_chain_f_range0";
   87.11  
   87.12 -goalw thy [cont,is_lub,is_ub] "cont(%x::('a::term)discr.f x)";
   87.13 +goalw thy [cont,is_lub,is_ub] "cont(%x::('a::term)discr. f x)";
   87.14  by(simp_tac (!simpset addsimps [discr_chain_f_range0]) 1);
   87.15  qed "cont_discr";
   87.16  AddIffs [cont_discr];
    88.1 --- a/src/HOLCF/Fix.ML	Fri Oct 10 18:37:49 1997 +0200
    88.2 +++ b/src/HOLCF/Fix.ML	Fri Oct 10 19:02:28 1997 +0200
    88.3 @@ -43,7 +43,7 @@
    88.4  (* ------------------------------------------------------------------------ *)
    88.5  
    88.6  qed_goalw "is_chain_iterate2" thy [is_chain] 
    88.7 -        " x << F`x ==> is_chain (%i.iterate i F x)"
    88.8 +        " x << F`x ==> is_chain (%i. iterate i F x)"
    88.9   (fn prems =>
   88.10          [
   88.11          (cut_facts_tac prems 1),
   88.12 @@ -57,7 +57,7 @@
   88.13  
   88.14  
   88.15  qed_goal "is_chain_iterate" thy  
   88.16 -        "is_chain (%i.iterate i F UU)"
   88.17 +        "is_chain (%i. iterate i F UU)"
   88.18   (fn prems =>
   88.19          [
   88.20          (rtac is_chain_iterate2 1),
   88.21 @@ -452,16 +452,16 @@
   88.22  (* ------------------------------------------------------------------------ *)
   88.23  
   88.24  qed_goalw "admI" thy [adm_def]
   88.25 -        "(!!Y. [| is_chain(Y); !i.P(Y(i)) |] ==> P(lub(range(Y)))) ==> adm(P)"
   88.26 +        "(!!Y. [| is_chain(Y); !i. P(Y(i)) |] ==> P(lub(range(Y)))) ==> adm(P)"
   88.27   (fn prems => [fast_tac (HOL_cs addIs prems) 1]);
   88.28  
   88.29  qed_goalw "admD" thy [adm_def]
   88.30 -        "!!P. [| adm(P); is_chain(Y); !i.P(Y(i)) |] ==> P(lub(range(Y)))"
   88.31 +        "!!P. [| adm(P); is_chain(Y); !i. P(Y(i)) |] ==> P(lub(range(Y)))"
   88.32   (fn prems => [fast_tac HOL_cs 1]);
   88.33  
   88.34  qed_goalw "admw_def2" thy [admw_def]
   88.35 -        "admw(P) = (!F.(!n.P(iterate n F UU)) -->\
   88.36 -\                        P (lub(range(%i.iterate i F UU))))"
   88.37 +        "admw(P) = (!F.(!n. P(iterate n F UU)) -->\
   88.38 +\                        P (lub(range(%i. iterate i F UU))))"
   88.39   (fn prems =>
   88.40          [
   88.41          (rtac refl 1)
   88.42 @@ -537,7 +537,7 @@
   88.43  (* ------------------------------------------------------------------------ *)
   88.44  
   88.45  qed_goalw "adm_max_in_chain"  thy  [adm_def]
   88.46 -"!Y. is_chain(Y::nat=>'a) --> (? n.max_in_chain n Y) ==> adm(P::'a=>bool)"
   88.47 +"!Y. is_chain(Y::nat=>'a) --> (? n. max_in_chain n Y) ==> adm(P::'a=>bool)"
   88.48   (fn prems =>
   88.49          [
   88.50          (cut_facts_tac prems 1),
   88.51 @@ -585,7 +585,7 @@
   88.52  (* ------------------------------------------------------------------------ *)
   88.53  
   88.54  qed_goalw "adm_less"  thy [adm_def]
   88.55 -        "[|cont u;cont v|]==> adm(%x.u x << v x)"
   88.56 +        "[|cont u;cont v|]==> adm(%x. u x << v x)"
   88.57   (fn prems =>
   88.58          [
   88.59          (cut_facts_tac prems 1),
   88.60 @@ -610,7 +610,7 @@
   88.61   (fn prems => [fast_tac (HOL_cs addEs [admD] addIs [admI]) 1]);
   88.62  Addsimps [adm_conj];
   88.63  
   88.64 -qed_goalw "adm_not_free"  thy [adm_def] "adm(%x.t)"
   88.65 +qed_goalw "adm_not_free"  thy [adm_def] "adm(%x. t)"
   88.66   (fn prems => [fast_tac HOL_cs 1]);
   88.67  Addsimps [adm_not_free];
   88.68  
   88.69 @@ -629,7 +629,7 @@
   88.70          ]);
   88.71  
   88.72  qed_goal "adm_all" thy  
   88.73 -        "!!P. !y.adm(P y) ==> adm(%x.!y.P y x)"
   88.74 +        "!!P. !y. adm(P y) ==> adm(%x.!y. P y x)"
   88.75   (fn prems => [fast_tac (HOL_cs addIs [admI] addEs [admD]) 1]);
   88.76  
   88.77  bind_thm ("adm_all2", allI RS adm_all);
   88.78 @@ -681,7 +681,7 @@
   88.79  local
   88.80  
   88.81    val adm_disj_lemma1 = prove_goal HOL.thy 
   88.82 -  "!n.P(Y n)|Q(Y n) ==> (? i.!j.R i j --> Q(Y(j))) | (!i.? j.R i j & P(Y(j)))"
   88.83 +  "!n. P(Y n)|Q(Y n) ==> (? i.!j. R i j --> Q(Y(j))) | (!i.? j. R i j & P(Y(j)))"
   88.84   (fn prems =>
   88.85          [
   88.86          (cut_facts_tac prems 1),
   88.87 @@ -689,7 +689,7 @@
   88.88          ]);
   88.89  
   88.90    val adm_disj_lemma2 = prove_goal thy  
   88.91 -  "!!Q. [| adm(Q); ? X.is_chain(X) & (!n.Q(X(n))) &\
   88.92 +  "!!Q. [| adm(Q); ? X. is_chain(X) & (!n. Q(X(n))) &\
   88.93    \   lub(range(Y))=lub(range(X))|] ==> Q(lub(range(Y)))"
   88.94   (fn _ => [fast_tac (!claset addEs [admD] addss !simpset) 1]);
   88.95  
   88.96 @@ -735,7 +735,7 @@
   88.97          [
   88.98          (cut_facts_tac prems 1),
   88.99          (etac exE 1),
  88.100 -        (res_inst_tac [("x","%m.if m<Suc(i) then Y(Suc(i)) else Y m")] exI 1),
  88.101 +        (res_inst_tac [("x","%m. if m<Suc(i) then Y(Suc(i)) else Y m")] exI 1),
  88.102          (rtac conjI 1),
  88.103          (rtac adm_disj_lemma3 1),
  88.104          (atac 1),
  88.105 @@ -854,7 +854,7 @@
  88.106          ]);
  88.107  
  88.108  val adm_disj = prove_goal thy  
  88.109 -        "!!P. [| adm P; adm Q |] ==> adm(%x.P x | Q x)"
  88.110 +        "!!P. [| adm P; adm Q |] ==> adm(%x. P x | Q x)"
  88.111   (fn prems =>
  88.112          [
  88.113          (rtac admI 1),
  88.114 @@ -876,10 +876,10 @@
  88.115  bind_thm("adm_disj",adm_disj);
  88.116  
  88.117  qed_goal "adm_imp"  thy  
  88.118 -        "!!P. [| adm(%x.~(P x)); adm Q |] ==> adm(%x.P x --> Q x)"
  88.119 +        "!!P. [| adm(%x.~(P x)); adm Q |] ==> adm(%x. P x --> Q x)"
  88.120   (fn prems =>
  88.121          [
  88.122 -        (subgoal_tac "(%x.P x --> Q x) = (%x. ~P x | Q x)" 1),
  88.123 +        (subgoal_tac "(%x. P x --> Q x) = (%x. ~P x | Q x)" 1),
  88.124           (Asm_simp_tac 1),
  88.125           (etac adm_disj 1),
  88.126           (atac 1),
  88.127 @@ -887,9 +887,9 @@
  88.128          (fast_tac HOL_cs 1)
  88.129          ]);
  88.130  
  88.131 -goal Fix.thy "!! P. [| adm (%x. P x --> Q x); adm (%x.Q x --> P x) |] \
  88.132 +goal Fix.thy "!! P. [| adm (%x. P x --> Q x); adm (%x. Q x --> P x) |] \
  88.133  \           ==> adm (%x. P x = Q x)";
  88.134 -by(subgoal_tac "(%x.P x = Q x) = (%x. (P x --> Q x) & (Q x --> P x))" 1);
  88.135 +by(subgoal_tac "(%x. P x = Q x) = (%x. (P x --> Q x) & (Q x --> P x))" 1);
  88.136  by (Asm_simp_tac 1);
  88.137  by (rtac ext 1);
  88.138  by (fast_tac HOL_cs 1);
    89.1 --- a/src/HOLCF/Fix.thy	Fri Oct 10 18:37:49 1997 +0200
    89.2 +++ b/src/HOLCF/Fix.thy	Fri Oct 10 19:02:28 1997 +0200
    89.3 @@ -20,14 +20,14 @@
    89.4  
    89.5  defs
    89.6  
    89.7 -iterate_def   "iterate n F c == nat_rec c (%n x.F`x) n"
    89.8 -Ifix_def      "Ifix F == lub(range(%i.iterate i F UU))"
    89.9 +iterate_def   "iterate n F c == nat_rec c (%n x. F`x) n"
   89.10 +Ifix_def      "Ifix F == lub(range(%i. iterate i F UU))"
   89.11  fix_def       "fix == (LAM f. Ifix f)"
   89.12  
   89.13  adm_def       "adm P == !Y. is_chain(Y) --> 
   89.14 -                        (!i.P(Y i)) --> P(lub(range Y))"
   89.15 +                        (!i. P(Y i)) --> P(lub(range Y))"
   89.16  
   89.17 -admw_def      "admw P == !F. (!n.P (iterate n F UU)) -->
   89.18 +admw_def      "admw P == !F. (!n. P (iterate n F UU)) -->
   89.19                              P (lub(range (%i. iterate i F UU)))" 
   89.20  
   89.21  end
    90.1 --- a/src/HOLCF/Fun2.ML	Fri Oct 10 18:37:49 1997 +0200
    90.2 +++ b/src/HOLCF/Fun2.ML	Fri Oct 10 19:02:28 1997 +0200
    90.3 @@ -9,7 +9,7 @@
    90.4  open Fun2;
    90.5  
    90.6  (* for compatibility with old HOLCF-Version *)
    90.7 -qed_goal "inst_fun_po" thy "(op <<)=(%f g.!x.f x << g x)"
    90.8 +qed_goal "inst_fun_po" thy "(op <<)=(%f g.!x. f x << g x)"
    90.9   (fn prems => 
   90.10          [
   90.11  	(fold_goals_tac [less_fun_def]),
   90.12 @@ -20,7 +20,7 @@
   90.13  (* Type 'a::term => 'b::pcpo is pointed                                     *)
   90.14  (* ------------------------------------------------------------------------ *)
   90.15  
   90.16 -qed_goal "minimal_fun" thy "(%z.UU) << x"
   90.17 +qed_goal "minimal_fun" thy "(%z. UU) << x"
   90.18  (fn prems =>
   90.19          [
   90.20          (simp_tac (!simpset addsimps [inst_fun_po,minimal]) 1)
   90.21 @@ -28,10 +28,10 @@
   90.22  
   90.23  bind_thm ("UU_fun_def",minimal_fun RS minimal2UU RS sym);
   90.24  
   90.25 -qed_goal "least_fun" thy "? x::'a=>'b::pcpo.!y.x<<y"
   90.26 +qed_goal "least_fun" thy "? x::'a=>'b::pcpo.!y. x<<y"
   90.27  (fn prems =>
   90.28          [
   90.29 -        (res_inst_tac [("x","(%z.UU)")] exI 1),
   90.30 +        (res_inst_tac [("x","(%z. UU)")] exI 1),
   90.31          (rtac (minimal_fun RS allI) 1)
   90.32          ]);
   90.33  
   90.34 @@ -52,7 +52,7 @@
   90.35  (* ------------------------------------------------------------------------ *)
   90.36  
   90.37  qed_goal "ch2ch_fun" thy 
   90.38 -        "is_chain(S::nat=>('a=>'b::po)) ==> is_chain(% i.S(i)(x))"
   90.39 +        "is_chain(S::nat=>('a=>'b::po)) ==> is_chain(% i. S(i)(x))"
   90.40  (fn prems =>
   90.41          [
   90.42          (cut_facts_tac prems 1),
   90.43 @@ -87,7 +87,7 @@
   90.44  
   90.45  qed_goal "lub_fun"  Fun2.thy
   90.46          "is_chain(S::nat=>('a::term => 'b::cpo)) ==> \
   90.47 -\        range(S) <<| (% x.lub(range(% i.S(i)(x))))"
   90.48 +\        range(S) <<| (% x. lub(range(% i. S(i)(x))))"
   90.49  (fn prems =>
   90.50          [
   90.51          (cut_facts_tac prems 1),
    91.1 --- a/src/HOLCF/Fun3.ML	Fri Oct 10 18:37:49 1997 +0200
    91.2 +++ b/src/HOLCF/Fun3.ML	Fri Oct 10 19:02:28 1997 +0200
    91.3 @@ -7,7 +7,7 @@
    91.4  open Fun3;
    91.5  
    91.6  (* for compatibility with old HOLCF-Version *)
    91.7 -qed_goal "inst_fun_pcpo" thy "UU = (%x.UU)"
    91.8 +qed_goal "inst_fun_pcpo" thy "UU = (%x. UU)"
    91.9   (fn prems => 
   91.10          [
   91.11          (simp_tac (HOL_ss addsimps [UU_def,UU_fun_def]) 1)
    92.1 --- a/src/HOLCF/IMP/Denotational.thy	Fri Oct 10 18:37:49 1997 +0200
    92.2 +++ b/src/HOLCF/IMP/Denotational.thy	Fri Oct 10 19:02:28 1997 +0200
    92.3 @@ -10,7 +10,7 @@
    92.4  
    92.5  constdefs
    92.6     dlift :: "(('a::term) discr -> 'b::pcpo) => ('a lift -> 'b)"
    92.7 -  "dlift f == (LAM x.case x of Undef => UU | Def(y) => f`(Discr y))"
    92.8 +  "dlift f == (LAM x. case x of Undef => UU | Def(y) => f`(Discr y))"
    92.9  
   92.10  consts D :: "com => state discr -> state lift"
   92.11  
    93.1 --- a/src/HOLCF/IOA/ABP/Correctness.ML	Fri Oct 10 18:37:49 1997 +0200
    93.2 +++ b/src/HOLCF/IOA/ABP/Correctness.ML	Fri Oct 10 19:02:28 1997 +0200
    93.3 @@ -6,7 +6,7 @@
    93.4  *)
    93.5  
    93.6  
    93.7 -goal Abschannel.thy "(? x.x=P & Q(x)) = Q(P)";
    93.8 +goal Abschannel.thy "(? x. x=P & Q(x)) = Q(P)";
    93.9  by (Fast_tac 1);
   93.10  qed"exis_elim";
   93.11  
   93.12 @@ -209,7 +209,7 @@
   93.13  (* 3 thms that do not hold generally! The lucky restriction here is 
   93.14     the absence of internal actions. *)
   93.15  goal Correctness.thy 
   93.16 -      "is_weak_ref_map (%id.id) sender_ioa sender_ioa";
   93.17 +      "is_weak_ref_map (%id. id) sender_ioa sender_ioa";
   93.18  by (simp_tac (!simpset addsimps [is_weak_ref_map_def]) 1);
   93.19  by (TRY(
   93.20     (rtac conjI 1) THEN
   93.21 @@ -225,7 +225,7 @@
   93.22  
   93.23  (* 2 copies of before *)
   93.24  goal Correctness.thy 
   93.25 -      "is_weak_ref_map (%id.id) receiver_ioa receiver_ioa";
   93.26 +      "is_weak_ref_map (%id. id) receiver_ioa receiver_ioa";
   93.27  by (simp_tac (!simpset addsimps [is_weak_ref_map_def]) 1);
   93.28  by (TRY(
   93.29     (rtac conjI 1) THEN
   93.30 @@ -240,7 +240,7 @@
   93.31  qed"receiver_unchanged";
   93.32  
   93.33  goal Correctness.thy 
   93.34 -      "is_weak_ref_map (%id.id) env_ioa env_ioa";
   93.35 +      "is_weak_ref_map (%id. id) env_ioa env_ioa";
   93.36  by (simp_tac (!simpset addsimps [is_weak_ref_map_def]) 1);
   93.37  by (TRY(
   93.38     (rtac conjI 1) THEN
    94.1 --- a/src/HOLCF/IOA/meta_theory/CompoExecs.ML	Fri Oct 10 18:37:49 1997 +0200
    94.2 +++ b/src/HOLCF/IOA/meta_theory/CompoExecs.ML	Fri Oct 10 19:02:28 1997 +0200
    94.3 @@ -193,7 +193,7 @@
    94.4  (* --------------------------------------------------------------------- *)
    94.5  
    94.6  goal thy "!s. (is_exec_frag (A||B) (s,xs) \
    94.7 -\  --> Forall (%x.fst x:act (A||B)) xs)";
    94.8 +\  --> Forall (%x. fst x:act (A||B)) xs)";
    94.9  
   94.10  by (pair_induct_tac "xs" [Forall_def,sforall_def,is_exec_frag_def] 1);
   94.11  (* main case *)
   94.12 @@ -212,7 +212,7 @@
   94.13  \    is_exec_frag B (snd s,Filter_ex2 (asig_of B)`(ProjB2`xs)) &\
   94.14  \    stutter (asig_of A) (fst s,(ProjA2`xs)) & \
   94.15  \    stutter (asig_of B) (snd s,(ProjB2`xs)) & \
   94.16 -\    Forall (%x.fst x:act (A||B)) xs \
   94.17 +\    Forall (%x. fst x:act (A||B)) xs \
   94.18  \    --> is_exec_frag (A||B) (s,xs)";
   94.19  
   94.20  by (pair_induct_tac "xs" [Forall_def,sforall_def,
   94.21 @@ -242,7 +242,7 @@
   94.22  \(Filter_ex (asig_of A) (ProjA ex) : executions A &\
   94.23  \ Filter_ex (asig_of B) (ProjB ex) : executions B &\
   94.24  \ stutter (asig_of A) (ProjA ex) & stutter (asig_of B) (ProjB ex) &\
   94.25 -\ Forall (%x.fst x:act (A||B)) (snd ex))";
   94.26 +\ Forall (%x. fst x:act (A||B)) (snd ex))";
   94.27  
   94.28  by (simp_tac (!simpset addsimps [executions_def,ProjB_def,
   94.29                                   Filter_ex_def,ProjA_def,starts_of_par]) 1);
    95.1 --- a/src/HOLCF/IOA/meta_theory/CompoExecs.thy	Fri Oct 10 18:37:49 1997 +0200
    95.2 +++ b/src/HOLCF/IOA/meta_theory/CompoExecs.thy	Fri Oct 10 19:02:28 1997 +0200
    95.3 @@ -45,7 +45,7 @@
    95.4  
    95.5  
    95.6  Filter_ex2_def
    95.7 -  "Filter_ex2 sig ==  Filter (%x.fst x:actions sig)"
    95.8 +  "Filter_ex2 sig ==  Filter (%x. fst x:actions sig)"
    95.9  
   95.10  stutter_def
   95.11    "stutter sig ex == ((stutter2 sig`(snd ex)) (fst ex) ~= FF)"
   95.12 @@ -70,7 +70,7 @@
   95.13          Int {ex. Filter_ex sigB (ProjB ex) : exB}
   95.14          Int {ex. stutter sigA (ProjA ex)}
   95.15          Int {ex. stutter sigB (ProjB ex)}
   95.16 -        Int {ex. Forall (%x.fst x:(actions sigA Un actions sigB)) (snd ex)},
   95.17 +        Int {ex. Forall (%x. fst x:(actions sigA Un actions sigB)) (snd ex)},
   95.18          asig_comp sigA sigB)"
   95.19  
   95.20  end
   95.21 \ No newline at end of file
    96.1 --- a/src/HOLCF/IOA/meta_theory/CompoScheds.ML	Fri Oct 10 18:37:49 1997 +0200
    96.2 +++ b/src/HOLCF/IOA/meta_theory/CompoScheds.ML	Fri Oct 10 19:02:28 1997 +0200
    96.3 @@ -160,7 +160,7 @@
    96.4  
    96.5  goalw thy [filter_act_def,Filter_ex2_def]
    96.6     "filter_act`(Filter_ex2 (asig_of A)`xs)=\
    96.7 -\   Filter (%a.a:act A)`(filter_act`xs)";
    96.8 +\   Filter (%a. a:act A)`(filter_act`xs)";
    96.9  
   96.10  by (simp_tac (!simpset addsimps [MapFilter,o_def]) 1);
   96.11  qed"lemma_2_1a";
   96.12 @@ -187,7 +187,7 @@
   96.13     is the same proposition, but we cannot change this one, when then rather lemma_1_1c  *)
   96.14  
   96.15  goal thy "!s. is_exec_frag (A||B) (s,xs) \
   96.16 -\  --> Forall (%x.x:act (A||B)) (filter_act`xs)";
   96.17 +\  --> Forall (%x. x:act (A||B)) (filter_act`xs)";
   96.18  
   96.19  by (pair_induct_tac "xs" [is_exec_frag_def,Forall_def,sforall_def] 1);
   96.20  (* main case *)
   96.21 @@ -207,9 +207,9 @@
   96.22    --------------------------------------------------------------------------- *)
   96.23  
   96.24  goal thy "! exA exB s t. \
   96.25 -\ Forall (%x.x:act (A||B)) sch  & \
   96.26 -\ Filter (%a.a:act A)`sch << filter_act`exA &\
   96.27 -\ Filter (%a.a:act B)`sch << filter_act`exB \
   96.28 +\ Forall (%x. x:act (A||B)) sch  & \
   96.29 +\ Filter (%a. a:act A)`sch << filter_act`exA &\
   96.30 +\ Filter (%a. a:act B)`sch << filter_act`exB \
   96.31  \ --> filter_act`(snd (mkex A B sch (s,exA) (t,exB))) = sch";
   96.32  
   96.33  by (Seq_induct_tac "sch" [Filter_def,Forall_def,sforall_def,mkex_def] 1);
   96.34 @@ -270,9 +270,9 @@
   96.35  
   96.36  
   96.37  goal thy "! exA exB s t. \
   96.38 -\ Forall (%x.x:act (A||B)) sch & \
   96.39 -\ Filter (%a.a:act A)`sch << filter_act`exA &\
   96.40 -\ Filter (%a.a:act B)`sch << filter_act`exB \
   96.41 +\ Forall (%x. x:act (A||B)) sch & \
   96.42 +\ Filter (%a. a:act A)`sch << filter_act`exA &\
   96.43 +\ Filter (%a. a:act B)`sch << filter_act`exB \
   96.44  \ --> stutter (asig_of A) (s,ProjA2`(snd (mkex A B sch (s,exA) (t,exB))))";
   96.45  
   96.46  by (mkex_induct_tac "sch" "exA" "exB");
   96.47 @@ -281,9 +281,9 @@
   96.48  
   96.49  
   96.50  goal thy "!! sch.[|  \
   96.51 -\ Forall (%x.x:act (A||B)) sch ; \
   96.52 -\ Filter (%a.a:act A)`sch << filter_act`(snd exA) ;\
   96.53 -\ Filter (%a.a:act B)`sch << filter_act`(snd exB) |] \
   96.54 +\ Forall (%x. x:act (A||B)) sch ; \
   96.55 +\ Filter (%a. a:act A)`sch << filter_act`(snd exA) ;\
   96.56 +\ Filter (%a. a:act B)`sch << filter_act`(snd exB) |] \
   96.57  \ ==> stutter (asig_of A) (ProjA (mkex A B sch exA exB))";
   96.58  
   96.59  by (cut_facts_tac [stutterA_mkex] 1);
   96.60 @@ -301,9 +301,9 @@
   96.61    --------------------------------------------------------------------------- *)
   96.62  
   96.63  goal thy "! exA exB s t. \
   96.64 -\ Forall (%x.x:act (A||B)) sch & \
   96.65 -\ Filter (%a.a:act A)`sch << filter_act`exA &\
   96.66 -\ Filter (%a.a:act B)`sch << filter_act`exB \
   96.67 +\ Forall (%x. x:act (A||B)) sch & \
   96.68 +\ Filter (%a. a:act A)`sch << filter_act`exA &\
   96.69 +\ Filter (%a. a:act B)`sch << filter_act`exB \
   96.70  \ --> stutter (asig_of B) (t,ProjB2`(snd (mkex A B sch (s,exA) (t,exB))))";
   96.71  
   96.72  by (mkex_induct_tac "sch" "exA" "exB");
   96.73 @@ -312,9 +312,9 @@
   96.74  
   96.75  
   96.76  goal thy "!! sch.[|  \
   96.77 -\ Forall (%x.x:act (A||B)) sch ; \
   96.78 -\ Filter (%a.a:act A)`sch << filter_act`(snd exA) ;\
   96.79 -\ Filter (%a.a:act B)`sch << filter_act`(snd exB) |] \
   96.80 +\ Forall (%x. x:act (A||B)) sch ; \
   96.81 +\ Filter (%a. a:act A)`sch << filter_act`(snd exA) ;\
   96.82 +\ Filter (%a. a:act B)`sch << filter_act`(snd exB) |] \
   96.83  \ ==> stutter (asig_of B) (ProjB (mkex A B sch exA exB))";
   96.84  
   96.85  by (cut_facts_tac [stutterB_mkex] 1);
   96.86 @@ -334,11 +334,11 @@
   96.87    --------------------------------------------------------------------------- *)
   96.88  
   96.89  goal thy "! exA exB s t. \
   96.90 -\ Forall (%x.x:act (A||B)) sch & \
   96.91 -\ Filter (%a.a:act A)`sch << filter_act`exA  &\
   96.92 -\ Filter (%a.a:act B)`sch << filter_act`exB \
   96.93 +\ Forall (%x. x:act (A||B)) sch & \
   96.94 +\ Filter (%a. a:act A)`sch << filter_act`exA  &\
   96.95 +\ Filter (%a. a:act B)`sch << filter_act`exB \
   96.96  \ --> Filter_ex2 (asig_of A)`(ProjA2`(snd (mkex A B sch (s,exA) (t,exB)))) =   \
   96.97 -\     Zip`(Filter (%a.a:act A)`sch)`(Map snd`exA)";
   96.98 +\     Zip`(Filter (%a. a:act A)`sch)`(Map snd`exA)";
   96.99  
  96.100  by (mkex_induct_tac "sch" "exA" "exB");
  96.101  
  96.102 @@ -360,8 +360,8 @@
  96.103    --------------------------------------------------------------------------- *)
  96.104  
  96.105  goal thy "!! sch ex. \
  96.106 -\ Filter (%a.a:act AB)`sch = filter_act`ex  \
  96.107 -\ ==> ex = Zip`(Filter (%a.a:act AB)`sch)`(Map snd`ex)";
  96.108 +\ Filter (%a. a:act AB)`sch = filter_act`ex  \
  96.109 +\ ==> ex = Zip`(Filter (%a. a:act AB)`sch)`(Map snd`ex)";
  96.110  by (asm_full_simp_tac (!simpset addsimps [filter_act_def]) 1);
  96.111  by (rtac (Zip_Map_fst_snd RS sym) 1);
  96.112  qed"trick_against_eq_in_ass";
  96.113 @@ -373,9 +373,9 @@
  96.114  
  96.115  
  96.116  goal thy "!!sch exA exB.\
  96.117 -\ [| Forall (%a.a:act (A||B)) sch ; \
  96.118 -\ Filter (%a.a:act A)`sch = filter_act`(snd exA)  ;\
  96.119 -\ Filter (%a.a:act B)`sch = filter_act`(snd exB) |]\
  96.120 +\ [| Forall (%a. a:act (A||B)) sch ; \
  96.121 +\ Filter (%a. a:act A)`sch = filter_act`(snd exA)  ;\
  96.122 +\ Filter (%a. a:act B)`sch = filter_act`(snd exB) |]\
  96.123  \ ==> Filter_ex (asig_of A) (ProjA (mkex A B sch exA exB)) = exA";
  96.124  by (asm_full_simp_tac (!simpset addsimps [ProjA_def,Filter_ex_def]) 1);
  96.125  by (pair_tac "exA" 1);
  96.126 @@ -398,11 +398,11 @@
  96.127  
  96.128  
  96.129  goal thy "! exA exB s t. \
  96.130 -\ Forall (%x.x:act (A||B)) sch & \
  96.131 -\ Filter (%a.a:act A)`sch << filter_act`exA  &\
  96.132 -\ Filter (%a.a:act B)`sch << filter_act`exB \
  96.133 +\ Forall (%x. x:act (A||B)) sch & \
  96.134 +\ Filter (%a. a:act A)`sch << filter_act`exA  &\
  96.135 +\ Filter (%a. a:act B)`sch << filter_act`exB \
  96.136  \ --> Filter_ex2 (asig_of B)`(ProjB2`(snd (mkex A B sch (s,exA) (t,exB)))) =   \
  96.137 -\     Zip`(Filter (%a.a:act B)`sch)`(Map snd`exB)";
  96.138 +\     Zip`(Filter (%a. a:act B)`sch)`(Map snd`exB)";
  96.139  
  96.140  (* notice necessary change of arguments exA and exB *)
  96.141  by (mkex_induct_tac "sch" "exB" "exA");
  96.142 @@ -417,9 +417,9 @@
  96.143  
  96.144  
  96.145  goal thy "!!sch exA exB.\
  96.146 -\ [| Forall (%a.a:act (A||B)) sch ; \
  96.147 -\ Filter (%a.a:act A)`sch = filter_act`(snd exA)  ;\
  96.148 -\ Filter (%a.a:act B)`sch = filter_act`(snd exB) |]\
  96.149 +\ [| Forall (%a. a:act (A||B)) sch ; \
  96.150 +\ Filter (%a. a:act A)`sch = filter_act`(snd exA)  ;\
  96.151 +\ Filter (%a. a:act B)`sch = filter_act`(snd exB) |]\
  96.152  \ ==> Filter_ex (asig_of B) (ProjB (mkex A B sch exA exB)) = exB";
  96.153  by (asm_full_simp_tac (!simpset addsimps [ProjB_def,Filter_ex_def]) 1);
  96.154  by (pair_tac "exA" 1);
  96.155 @@ -439,9 +439,9 @@
  96.156  
  96.157  goal thy "!s t exA exB. \
  96.158  \ Forall (%x. x : act (A || B)) sch &\
  96.159 -\ Filter (%a.a:act A)`sch << filter_act`exA  &\
  96.160 -\ Filter (%a.a:act B)`sch << filter_act`exB \
  96.161 -\  --> Forall (%x.fst x : act (A ||B))   \
  96.162 +\ Filter (%a. a:act A)`sch << filter_act`exA  &\
  96.163 +\ Filter (%a. a:act B)`sch << filter_act`exB \
  96.164 +\  --> Forall (%x. fst x : act (A ||B))   \
  96.165  \        (snd (mkex A B sch (s,exA) (t,exB)))";
  96.166  
  96.167  by (mkex_induct_tac "sch" "exA" "exB");
  96.168 @@ -456,8 +456,8 @@
  96.169  
  96.170  goal thy  
  96.171  "sch : schedules (A||B) = \
  96.172 -\ (Filter (%a.a:act A)`sch : schedules A &\
  96.173 -\  Filter (%a.a:act B)`sch : schedules B &\
  96.174 +\ (Filter (%a. a:act A)`sch : schedules A &\
  96.175 +\  Filter (%a. a:act B)`sch : schedules B &\
  96.176  \  Forall (%x. x:act (A||B)) sch)";
  96.177  
  96.178  by (simp_tac (!simpset addsimps [schedules_def, has_schedule_def]) 1);
    97.1 --- a/src/HOLCF/IOA/meta_theory/CompoScheds.thy	Fri Oct 10 18:37:49 1997 +0200
    97.2 +++ b/src/HOLCF/IOA/meta_theory/CompoScheds.thy	Fri Oct 10 19:02:28 1997 +0200
    97.3 @@ -67,8 +67,8 @@
    97.4         let schA = fst SchedsA; sigA = snd SchedsA; 
    97.5             schB = fst SchedsB; sigB = snd SchedsB       
    97.6         in
    97.7 -       (    {sch. Filter (%a.a:actions sigA)`sch : schA}
    97.8 -        Int {sch. Filter (%a.a:actions sigB)`sch : schB}
    97.9 +       (    {sch. Filter (%a. a:actions sigA)`sch : schA}
   97.10 +        Int {sch. Filter (%a. a:actions sigB)`sch : schB}
   97.11          Int {sch. Forall (%x. x:(actions sigA Un actions sigB)) sch},
   97.12          asig_comp sigA sigB)"
   97.13  
    98.1 --- a/src/HOLCF/IOA/meta_theory/CompoTraces.ML	Fri Oct 10 18:37:49 1997 +0200
    98.2 +++ b/src/HOLCF/IOA/meta_theory/CompoTraces.ML	Fri Oct 10 19:02:28 1997 +0200
    98.3 @@ -24,24 +24,24 @@
    98.4  \      | Def y => \
    98.5  \         (if y:act A then \
    98.6  \             (if y:act B then \ 
    98.7 -\                   ((Takewhile (%a.a:int A)`schA) \
    98.8 -\                         @@(Takewhile (%a.a:int B)`schB) \
    98.9 +\                   ((Takewhile (%a. a:int A)`schA) \
   98.10 +\                         @@(Takewhile (%a. a:int B)`schB) \
   98.11  \                              @@(y>>(mksch A B`xs   \
   98.12 -\                                       `(TL`(Dropwhile (%a.a:int A)`schA))  \
   98.13 -\                                       `(TL`(Dropwhile (%a.a:int B)`schB))  \
   98.14 +\                                       `(TL`(Dropwhile (%a. a:int A)`schA))  \
   98.15 +\                                       `(TL`(Dropwhile (%a. a:int B)`schB))  \
   98.16  \                    )))   \
   98.17  \              else  \
   98.18 -\                 ((Takewhile (%a.a:int A)`schA)  \
   98.19 +\                 ((Takewhile (%a. a:int A)`schA)  \
   98.20  \                      @@ (y>>(mksch A B`xs  \
   98.21 -\                              `(TL`(Dropwhile (%a.a:int A)`schA))  \
   98.22 +\                              `(TL`(Dropwhile (%a. a:int A)`schA))  \
   98.23  \                              `schB)))  \
   98.24  \              )   \
   98.25  \          else    \
   98.26  \             (if y:act B then  \ 
   98.27 -\                 ((Takewhile (%a.a:int B)`schB)  \
   98.28 +\                 ((Takewhile (%a. a:int B)`schB)  \
   98.29  \                       @@ (y>>(mksch A B`xs   \
   98.30  \                              `schA   \
   98.31 -\                              `(TL`(Dropwhile (%a.a:int B)`schB))  \
   98.32 +\                              `(TL`(Dropwhile (%a. a:int B)`schB))  \
   98.33  \                              )))  \
   98.34  \             else  \
   98.35  \               UU  \
   98.36 @@ -62,8 +62,8 @@
   98.37  
   98.38  goal thy "!!x.[|x:act A;x~:act B|]  \
   98.39  \   ==> mksch A B`(x>>tr)`schA`schB = \
   98.40 -\         (Takewhile (%a.a:int A)`schA) \
   98.41 -\         @@ (x>>(mksch A B`tr`(TL`(Dropwhile (%a.a:int A)`schA)) \
   98.42 +\         (Takewhile (%a. a:int A)`schA) \
   98.43 +\         @@ (x>>(mksch A B`tr`(TL`(Dropwhile (%a. a:int A)`schA)) \
   98.44  \                             `schB))";
   98.45  by (rtac trans 1);
   98.46  by (stac mksch_unfold 1);
   98.47 @@ -73,8 +73,8 @@
   98.48  
   98.49  goal thy "!!x.[|x~:act A;x:act B|] \
   98.50  \   ==> mksch A B`(x>>tr)`schA`schB = \
   98.51 -\        (Takewhile (%a.a:int B)`schB)  \
   98.52 -\         @@ (x>>(mksch A B`tr`schA`(TL`(Dropwhile (%a.a:int B)`schB))  \
   98.53 +\        (Takewhile (%a. a:int B)`schB)  \
   98.54 +\         @@ (x>>(mksch A B`tr`schA`(TL`(Dropwhile (%a. a:int B)`schB))  \
   98.55  \                            ))";
   98.56  by (rtac trans 1);
   98.57  by (stac mksch_unfold 1);
   98.58 @@ -84,10 +84,10 @@
   98.59  
   98.60  goal thy "!!x.[|x:act A;x:act B|] \
   98.61  \   ==> mksch A B`(x>>tr)`schA`schB = \
   98.62 -\            (Takewhile (%a.a:int A)`schA) \
   98.63 -\         @@ ((Takewhile (%a.a:int B)`schB)  \
   98.64 -\         @@ (x>>(mksch A B`tr`(TL`(Dropwhile (%a.a:int A)`schA)) \
   98.65 -\                            `(TL`(Dropwhile (%a.a:int B)`schB))))  \
   98.66 +\            (Takewhile (%a. a:int A)`schA) \
   98.67 +\         @@ ((Takewhile (%a. a:int B)`schB)  \
   98.68 +\         @@ (x>>(mksch A B`tr`(TL`(Dropwhile (%a. a:int A)`schA)) \
   98.69 +\                            `(TL`(Dropwhile (%a. a:int B)`schB))))  \
   98.70  \             )";
   98.71  by (rtac trans 1);
   98.72  by (stac mksch_unfold 1);
   98.73 @@ -208,7 +208,7 @@
   98.74  Delsimps [FiniteConc];
   98.75  
   98.76  goal thy "!! tr. [| Finite tr; is_asig(asig_of A); is_asig(asig_of B) |] ==> \
   98.77 -\   ! x y. Forall (%x.x:act A) x & Forall (%x.x:act B) y & \
   98.78 +\   ! x y. Forall (%x. x:act A) x & Forall (%x. x:act B) y & \
   98.79  \          Filter (%a. a:ext A)`x = Filter (%a. a:act A)`tr & \
   98.80  \          Filter (%a. a:ext B)`y = Filter (%a. a:act B)`tr &\
   98.81  \          Forall (%x. x:ext (A||B)) tr \
   98.82 @@ -283,7 +283,7 @@
   98.83  Delsimps [FilterConc]; 
   98.84  
   98.85  goal thy " !!bs. [| Finite bs; is_asig(asig_of A); is_asig(asig_of B);compatible A B|] ==>  \
   98.86 -\! y.Forall (%x.x:act B) y & Forall (%x. x:act B & x~:act A) bs &\
   98.87 +\! y. Forall (%x. x:act B) y & Forall (%x. x:act B & x~:act A) bs &\
   98.88  \    Filter (%a. a:ext B)`y = Filter (%a. a:act B)`(bs @@ z) \
   98.89  \    --> (? y1 y2.  (mksch A B`(bs @@ z)`x`y) = (y1 @@ (mksch A B`z`x`y2)) & \
   98.90  \                   Forall (%x. x:act B & x~:act A) y1 & \
   98.91 @@ -312,7 +312,7 @@
   98.92  Addsimps [FilterConc]; 
   98.93  by (asm_full_simp_tac (!simpset addsimps [FilterPTakewhileQnil,not_ext_is_int_or_not_act]) 1);
   98.94  (* apply IH *)
   98.95 -by (eres_inst_tac [("x","TL`(Dropwhile (%a.a:int B)`y)")] allE 1);
   98.96 +by (eres_inst_tac [("x","TL`(Dropwhile (%a. a:int B)`y)")] allE 1);
   98.97  by (asm_full_simp_tac (!simpset addsimps [ForallTL,ForallDropwhile])1);
   98.98  by (REPEAT (etac exE 1));
   98.99  by (REPEAT (etac conjE 1));
  98.100 @@ -321,7 +321,7 @@
  98.101  by (rotate_tac ~2 1); 
  98.102  by (Asm_full_simp_tac 1); 
  98.103  (* instantiate y1a and y2a *)
  98.104 -by (res_inst_tac [("x","Takewhile (%a.a:int B)`y @@ a>>y1")] exI 1);
  98.105 +by (res_inst_tac [("x","Takewhile (%a. a:int B)`y @@ a>>y1")] exI 1);
  98.106  by (res_inst_tac [("x","y2")] exI 1);
  98.107  (* elminate all obligations up to two depending on Conc_assoc *)
  98.108  by (asm_full_simp_tac (!simpset addsimps [ForallPTakewhileQ, intA_is_not_actB,
  98.109 @@ -338,7 +338,7 @@
  98.110  
  98.111  
  98.112  goal thy " !!as. [| Finite as; is_asig(asig_of A); is_asig(asig_of B);compatible A B|] ==>  \
  98.113 -\! x.Forall (%x.x:act A) x & Forall (%x. x:act A & x~:act B) as &\
  98.114 +\! x. Forall (%x. x:act A) x & Forall (%x. x:act A & x~:act B) as &\
  98.115  \    Filter (%a. a:ext A)`x = Filter (%a. a:act A)`(as @@ z) \
  98.116  \    --> (? x1 x2.  (mksch A B`(as @@ z)`x`y) = (x1 @@ (mksch A B`z`x2`y)) & \
  98.117  \                   Forall (%x. x:act A & x~:act B) x1 & \
  98.118 @@ -367,7 +367,7 @@
  98.119  Addsimps [FilterConc]; 
  98.120  by (asm_full_simp_tac (!simpset addsimps [FilterPTakewhileQnil,not_ext_is_int_or_not_act]) 1);
  98.121  (* apply IH *)
  98.122 -by (eres_inst_tac [("x","TL`(Dropwhile (%a.a:int A)`x)")] allE 1);
  98.123 +by (eres_inst_tac [("x","TL`(Dropwhile (%a. a:int A)`x)")] allE 1);
  98.124  by (asm_full_simp_tac (!simpset addsimps [ForallTL,ForallDropwhile])1);
  98.125  by (REPEAT (etac exE 1));
  98.126  by (REPEAT (etac conjE 1));
  98.127 @@ -376,7 +376,7 @@
  98.128  by (rotate_tac ~2 1); 
  98.129  by (Asm_full_simp_tac 1); 
  98.130  (* instantiate y1a and y2a *)
  98.131 -by (res_inst_tac [("x","Takewhile (%a.a:int A)`x @@ a>>x1")] exI 1);
  98.132 +by (res_inst_tac [("x","Takewhile (%a. a:int A)`x @@ a>>x1")] exI 1);
  98.133  by (res_inst_tac [("x","x2")] exI 1);
  98.134  (* elminate all obligations up to two depending on Conc_assoc *)
  98.135  by (asm_full_simp_tac (!simpset addsimps [ForallPTakewhileQ, intA_is_not_actB,
  98.136 @@ -434,7 +434,7 @@
  98.137  by (rotate_tac ~2 2);
  98.138  by (rotate_tac ~2 3);
  98.139  by (asm_full_simp_tac (HOL_basic_ss addsimps [mksch_cons3]) 2);
  98.140 -by (eres_inst_tac [("x","sb@@Takewhile (%a.a: int A)`a @@ Takewhile (%a.a:int B)`b@@(aaa>>nil)")] allE 2);
  98.141 +by (eres_inst_tac [("x","sb@@Takewhile (%a. a: int A)`a @@ Takewhile (%a. a:int B)`b@@(aaa>>nil)")] allE 2);
  98.142  by (eres_inst_tac [("x","sa")] allE 2);
  98.143  by (asm_full_simp_tac (!simpset addsimps [Conc_assoc])2);
  98.144  
  98.145 @@ -481,11 +481,11 @@
  98.146  goal thy 
  98.147  "!! A B. [| compatible A B; compatible B A;\
  98.148  \           is_asig(asig_of A); is_asig(asig_of B) |] ==> \
  98.149 -\ ! schA schB. Forall (%x.x:act A) schA & Forall (%x.x:act B) schB & \
  98.150 -\ Forall (%x.x:ext (A||B)) tr & \
  98.151 -\ Filter (%a.a:act A)`tr << Filter (%a.a:ext A)`schA &\
  98.152 -\ Filter (%a.a:act B)`tr << Filter (%a.a:ext B)`schB  \
  98.153 -\ --> Filter (%a.a:ext (A||B))`(mksch A B`tr`schA`schB) = tr";
  98.154 +\ ! schA schB. Forall (%x. x:act A) schA & Forall (%x. x:act B) schB & \
  98.155 +\ Forall (%x. x:ext (A||B)) tr & \
  98.156 +\ Filter (%a. a:act A)`tr << Filter (%a. a:ext A)`schA &\
  98.157 +\ Filter (%a. a:act B)`tr << Filter (%a. a:ext B)`schB  \
  98.158 +\ --> Filter (%a. a:ext (A||B))`(mksch A B`tr`schA`schB) = tr";
  98.159  
  98.160  by (Seq_induct_tac "tr" [Forall_def,sforall_def,mksch_def] 1);
  98.161  
  98.162 @@ -557,12 +557,12 @@
  98.163  
  98.164  goal thy "!! A B. [| compatible A B; compatible B A; \
  98.165  \ is_asig(asig_of A); is_asig(asig_of B) |] ==> \
  98.166 -\ Forall (%x.x:ext (A||B)) tr & \
  98.167 -\ Forall (%x.x:act A) schA & Forall (%x.x:act B) schB & \
  98.168 -\ Filter (%a.a:ext A)`schA = Filter (%a.a:act A)`tr &\
  98.169 -\ Filter (%a.a:ext B)`schB = Filter (%a.a:act B)`tr &\
  98.170 +\ Forall (%x. x:ext (A||B)) tr & \
  98.171 +\ Forall (%x. x:act A) schA & Forall (%x. x:act B) schB & \
  98.172 +\ Filter (%a. a:ext A)`schA = Filter (%a. a:act A)`tr &\
  98.173 +\ Filter (%a. a:ext B)`schB = Filter (%a. a:act B)`tr &\
  98.174  \ LastActExtsch A schA & LastActExtsch B schB  \
  98.175 -\ --> Filter (%a.a:act A)`(mksch A B`tr`schA`schB) = schA";
  98.176 +\ --> Filter (%a. a:act A)`(mksch A B`tr`schA`schB) = schA";
  98.177  
  98.178  by (res_inst_tac [("Q","%x. x:act B & x~:act A"),("x","tr")] take_lemma_less_induct 1);
  98.179  by (REPEAT (etac conjE 1));
  98.180 @@ -613,7 +613,7 @@
  98.181  
  98.182  (* eliminate the B-only prefix *)
  98.183  
  98.184 -by (subgoal_tac "(Filter (%a.a :act A)`y1) = nil" 1);
  98.185 +by (subgoal_tac "(Filter (%a. a :act A)`y1) = nil" 1);
  98.186  by (etac ForallQFilterPnil 2);
  98.187  by (assume_tac 2);
  98.188  by (Fast_tac 2);
  98.189 @@ -691,12 +691,12 @@
  98.190  
  98.191  goal thy "!! A B. [| compatible A B; compatible B A; \
  98.192  \ is_asig(asig_of A); is_asig(asig_of B) |] ==> \
  98.193 -\ Forall (%x.x:ext (A||B)) tr & \
  98.194 -\ Forall (%x.x:act A) schA & Forall (%x.x:act B) schB & \
  98.195 -\ Filter (%a.a:ext A)`schA = Filter (%a.a:act A)`tr &\
  98.196 -\ Filter (%a.a:ext B)`schB = Filter (%a.a:act B)`tr &\
  98.197 +\ Forall (%x. x:ext (A||B)) tr & \
  98.198 +\ Forall (%x. x:act A) schA & Forall (%x. x:act B) schB & \
  98.199 +\ Filter (%a. a:ext A)`schA = Filter (%a. a:act A)`tr &\
  98.200 +\ Filter (%a. a:ext B)`schB = Filter (%a. a:act B)`tr &\
  98.201  \ LastActExtsch A schA & LastActExtsch B schB  \
  98.202 -\ --> Filter (%a.a:act A)`(mksch A B`tr`schA`schB) = schA";
  98.203 +\ --> Filter (%a. a:act A)`(mksch A B`tr`schA`schB) = schA";
  98.204  
  98.205  by (strip_tac 1);
  98.206  by (rtac seq.take_lemma 1);
  98.207 @@ -730,7 +730,7 @@
  98.208  (* second side: schA = nil *)
  98.209  by (eres_inst_tac [("A","A")] LastActExtimplnil 1);
  98.210  by (Asm_simp_tac 1);
  98.211 -by (eres_inst_tac [("Q","%x.x:act B & x~:act A")] ForallQFilterPnil 1);
  98.212 +by (eres_inst_tac [("Q","%x. x:act B & x~:act A")] ForallQFilterPnil 1);
  98.213  by (assume_tac 1);
  98.214  by (Fast_tac 1);
  98.215  
  98.216 @@ -747,7 +747,7 @@
  98.217  (* schA = UU *)
  98.218  by (eres_inst_tac [("A","A")] LastActExtimplUU 1);
  98.219  by (Asm_simp_tac 1);
  98.220 -by (eres_inst_tac [("Q","%x.x:act B & x~:act A")] ForallQFilterPUU 1);
  98.221 +by (eres_inst_tac [("Q","%x. x:act B & x~:act A")] ForallQFilterPUU 1);
  98.222  by (assume_tac 1);
  98.223  by (Fast_tac 1);
  98.224  
  98.225 @@ -771,7 +771,7 @@
  98.226  
  98.227  (* eliminate the B-only prefix *)
  98.228  
  98.229 -by (subgoal_tac "(Filter (%a.a :act A)`y1) = nil" 1);
  98.230 +by (subgoal_tac "(Filter (%a. a :act A)`y1) = nil" 1);
  98.231  by (etac ForallQFilterPnil 2);
  98.232  by (assume_tac 2);
  98.233  by (Fast_tac 2);
  98.234 @@ -833,7 +833,7 @@
  98.235  
  98.236  (* assumption Forall schA *)
  98.237  by (dres_inst_tac [("s","schA"),
  98.238 -                   ("P","Forall (%x.x:act A)")] subst 1);
  98.239 +                   ("P","Forall (%x. x:act A)")] subst 1);
  98.240  by (assume_tac 1);
  98.241  by (asm_full_simp_tac (!simpset addsimps [ForallPTakewhileQ, int_is_act]) 1);
  98.242  
  98.243 @@ -933,12 +933,12 @@
  98.244  
  98.245  goal thy "!! A B. [| compatible A B; compatible B A; \
  98.246  \ is_asig(asig_of A); is_asig(asig_of B) |] ==> \
  98.247 -\ Forall (%x.x:ext (A||B)) tr & \
  98.248 -\ Forall (%x.x:act A) schA & Forall (%x.x:act B) schB & \
  98.249 -\ Filter (%a.a:ext A)`schA = Filter (%a.a:act A)`tr &\
  98.250 -\ Filter (%a.a:ext B)`schB = Filter (%a.a:act B)`tr &\
  98.251 +\ Forall (%x. x:ext (A||B)) tr & \
  98.252 +\ Forall (%x. x:act A) schA & Forall (%x. x:act B) schB & \
  98.253 +\ Filter (%a. a:ext A)`schA = Filter (%a. a:act A)`tr &\
  98.254 +\ Filter (%a. a:ext B)`schB = Filter (%a. a:act B)`tr &\
  98.255  \ LastActExtsch A schA & LastActExtsch B schB  \
  98.256 -\ --> Filter (%a.a:act B)`(mksch A B`tr`schA`schB) = schB";
  98.257 +\ --> Filter (%a. a:act B)`(mksch A B`tr`schA`schB) = schB";
  98.258  
  98.259  by (strip_tac 1);
  98.260  by (rtac seq.take_lemma 1);
  98.261 @@ -972,7 +972,7 @@
  98.262  (* second side: schA = nil *)
  98.263  by (eres_inst_tac [("A","B")] LastActExtimplnil 1);
  98.264  by (Asm_simp_tac 1);
  98.265 -by (eres_inst_tac [("Q","%x.x:act A & x~:act B")] ForallQFilterPnil 1);
  98.266 +by (eres_inst_tac [("Q","%x. x:act A & x~:act B")] ForallQFilterPnil 1);
  98.267  by (assume_tac 1);
  98.268  by (Fast_tac 1);
  98.269  
  98.270 @@ -989,7 +989,7 @@
  98.271  (* schA = UU *)
  98.272  by (eres_inst_tac [("A","B")] LastActExtimplUU 1);
  98.273  by (Asm_simp_tac 1);
  98.274 -by (eres_inst_tac [("Q","%x.x:act A & x~:act B")] ForallQFilterPUU 1);
  98.275 +by (eres_inst_tac [("Q","%x. x:act A & x~:act B")] ForallQFilterPUU 1);
  98.276  by (assume_tac 1);
  98.277  by (Fast_tac 1);
  98.278  
  98.279 @@ -1013,7 +1013,7 @@
  98.280  
  98.281  (* eliminate the A-only prefix *)
  98.282  
  98.283 -by (subgoal_tac "(Filter (%a.a :act B)`x1) = nil" 1);
  98.284 +by (subgoal_tac "(Filter (%a. a :act B)`x1) = nil" 1);
  98.285  by (etac ForallQFilterPnil 2);
  98.286  by (assume_tac 2);
  98.287  by (Fast_tac 2);
  98.288 @@ -1075,7 +1075,7 @@
  98.289  
  98.290  (* assumption Forall schB *)
  98.291  by (dres_inst_tac [("s","schB"),
  98.292 -                   ("P","Forall (%x.x:act B)")] subst 1);
  98.293 +                   ("P","Forall (%x. x:act B)")] subst 1);
  98.294  by (assume_tac 1);
  98.295  by (asm_full_simp_tac (!simpset addsimps [ForallPTakewhileQ, int_is_act]) 1);
  98.296  
  98.297 @@ -1173,8 +1173,8 @@
  98.298  "!! A B. [| is_trans_of A; is_trans_of B; compatible A B; compatible B A; \
  98.299  \           is_asig(asig_of A); is_asig(asig_of B)|] \
  98.300  \       ==>  tr: traces(A||B) = \
  98.301 -\            (Filter (%a.a:act A)`tr : traces A &\
  98.302 -\             Filter (%a.a:act B)`tr : traces B &\
  98.303 +\            (Filter (%a. a:act A)`tr : traces A &\
  98.304 +\             Filter (%a. a:act B)`tr : traces B &\
  98.305  \             Forall (%x. x:ext(A||B)) tr)";
  98.306  
  98.307  by (simp_tac (!simpset addsimps [traces_def,has_trace_def]) 1);
  98.308 @@ -1182,12 +1182,12 @@
  98.309   
  98.310  (* ==> *) 
  98.311  (* There is a schedule of A *)
  98.312 -by (res_inst_tac [("x","Filter (%a.a:act A)`sch")] bexI 1);
  98.313 +by (res_inst_tac [("x","Filter (%a. a:act A)`sch")] bexI 1);
  98.314  by (asm_full_simp_tac (!simpset addsimps [compositionality_sch]) 2);
  98.315  by (asm_full_simp_tac (!simpset addsimps [compatibility_consequence1,
  98.316                    externals_of_par,ext1_ext2_is_not_act1]) 1);
  98.317  (* There is a schedule of B *)
  98.318 -by (res_inst_tac [("x","Filter (%a.a:act B)`sch")] bexI 1);
  98.319 +by (res_inst_tac [("x","Filter (%a. a:act B)`sch")] bexI 1);
  98.320  by (asm_full_simp_tac (!simpset addsimps [compositionality_sch]) 2);
  98.321  by (asm_full_simp_tac (!simpset addsimps [compatibility_consequence2,
  98.322                    externals_of_par,ext1_ext2_is_not_act2]) 1);
    99.1 --- a/src/HOLCF/IOA/meta_theory/CompoTraces.thy	Fri Oct 10 18:37:49 1997 +0200
    99.2 +++ b/src/HOLCF/IOA/meta_theory/CompoTraces.thy	Fri Oct 10 19:02:28 1997 +0200
    99.3 @@ -25,24 +25,24 @@
    99.4        | Def y => 
    99.5           (if y:act A then 
    99.6               (if y:act B then 
    99.7 -                   ((Takewhile (%a.a:int A)`schA)
    99.8 -                      @@ (Takewhile (%a.a:int B)`schB)
    99.9 +                   ((Takewhile (%a. a:int A)`schA)
   99.10 +                      @@ (Takewhile (%a. a:int B)`schB)
   99.11                             @@ (y>>(h`xs
   99.12 -                                    `(TL`(Dropwhile (%a.a:int A)`schA))
   99.13 -                                    `(TL`(Dropwhile (%a.a:int B)`schB))
   99.14 +                                    `(TL`(Dropwhile (%a. a:int A)`schA))
   99.15 +                                    `(TL`(Dropwhile (%a. a:int B)`schB))
   99.16                      )))
   99.17                else
   99.18 -                 ((Takewhile (%a.a:int A)`schA)
   99.19 +                 ((Takewhile (%a. a:int A)`schA)
   99.20                    @@ (y>>(h`xs
   99.21 -                           `(TL`(Dropwhile (%a.a:int A)`schA))
   99.22 +                           `(TL`(Dropwhile (%a. a:int A)`schA))
   99.23                             `schB)))
   99.24                )
   99.25            else 
   99.26               (if y:act B then 
   99.27 -                 ((Takewhile (%a.a:int B)`schB)
   99.28 +                 ((Takewhile (%a. a:int B)`schB)
   99.29                       @@ (y>>(h`xs
   99.30                                `schA
   99.31 -                              `(TL`(Dropwhile (%a.a:int B)`schB))
   99.32 +                              `(TL`(Dropwhile (%a. a:int B)`schB))
   99.33                                )))
   99.34               else
   99.35                 UU
   99.36 @@ -56,8 +56,8 @@
   99.37         let trA = fst TracesA; sigA = snd TracesA; 
   99.38             trB = fst TracesB; sigB = snd TracesB       
   99.39         in
   99.40 -       (    {tr. Filter (%a.a:actions sigA)`tr : trA}
   99.41 -        Int {tr. Filter (%a.a:actions sigB)`tr : trB}
   99.42 +       (    {tr. Filter (%a. a:actions sigA)`tr : trA}
   99.43 +        Int {tr. Filter (%a. a:actions sigB)`tr : trB}
   99.44          Int {tr. Forall (%x. x:(externals sigA Un externals sigB)) tr},
   99.45          asig_comp sigA sigB)"
   99.46  
   100.1 --- a/src/HOLCF/IOA/meta_theory/Deadlock.ML	Fri Oct 10 18:37:49 1997 +0200
   100.2 +++ b/src/HOLCF/IOA/meta_theory/Deadlock.ML	Fri Oct 10 19:02:28 1997 +0200
   100.3 @@ -10,8 +10,8 @@
   100.4                 input actions may always be added to a schedule
   100.5  **********************************************************************************)
   100.6  
   100.7 -goal thy "!! sch. [| Filter (%x.x:act A)`sch : schedules A; a:inp A; input_enabled A; Finite sch|] \
   100.8 -\         ==> Filter (%x.x:act A)`sch @@ a>>nil : schedules A";
   100.9 +goal thy "!! sch. [| Filter (%x. x:act A)`sch : schedules A; a:inp A; input_enabled A; Finite sch|] \
  100.10 +\         ==> Filter (%x. x:act A)`sch @@ a>>nil : schedules A";
  100.11  by (asm_full_simp_tac (!simpset addsimps [schedules_def,has_schedule_def]) 1);
  100.12  by (safe_tac set_cs);
  100.13  by (forward_tac  [inp_is_act] 1);
  100.14 @@ -52,7 +52,7 @@
  100.15  **********************************************************************************)
  100.16  
  100.17  goal thy "!! sch. [| a : local A; Finite sch; sch : schedules (A||B); \
  100.18 -\            Filter (%x.x:act A)`(sch @@ a>>nil) : schedules A; compatible A B; input_enabled B |] \
  100.19 +\            Filter (%x. x:act A)`(sch @@ a>>nil) : schedules A; compatible A B; input_enabled B |] \
  100.20  \          ==> (sch @@ a>>nil) : schedules (A||B)";
  100.21  
  100.22  by (asm_full_simp_tac (!simpset addsimps [compositionality_sch,locals_def]) 1);
   101.1 --- a/src/HOLCF/IOA/meta_theory/Sequence.ML	Fri Oct 10 18:37:49 1997 +0200
   101.2 +++ b/src/HOLCF/IOA/meta_theory/Sequence.ML	Fri Oct 10 19:02:28 1997 +0200
   101.3 @@ -543,7 +543,7 @@
   101.4  
   101.5  section "Last";
   101.6  
   101.7 -goal thy "!! s.Finite s ==> s~=nil --> Last`s~=UU";
   101.8 +goal thy "!! s. Finite s ==> s~=nil --> Last`s~=UU";
   101.9  by (Seq_Finite_induct_tac  1);
  101.10  by (asm_simp_tac (!simpset setloop split_tac [expand_if]) 1);
  101.11  qed"Finite_Last1";
  101.12 @@ -790,11 +790,11 @@
  101.13  by (asm_full_simp_tac (!simpset setloop (split_tac [expand_if])) 1);
  101.14  qed"Takewhile_idempotent";
  101.15  
  101.16 -goal thy "Forall P s --> Takewhile (%x.Q x | (~P x))`s = Takewhile Q`s";
  101.17 +goal thy "Forall P s --> Takewhile (%x. Q x | (~P x))`s = Takewhile Q`s";
  101.18  by (Seq_induct_tac "s" [Forall_def,sforall_def] 1);
  101.19  qed"ForallPTakewhileQnP";
  101.20  
  101.21 -goal thy "Forall P s --> Dropwhile (%x.Q x | (~P x))`s = Dropwhile Q`s";
  101.22 +goal thy "Forall P s --> Dropwhile (%x. Q x | (~P x))`s = Dropwhile Q`s";
  101.23  by (Seq_induct_tac "s" [Forall_def,sforall_def] 1);
  101.24  qed"ForallPDropwhileQnP";
  101.25  
  101.26 @@ -807,7 +807,7 @@
  101.27  
  101.28  bind_thm("TakewhileConc",TakewhileConc1 RS mp);
  101.29  
  101.30 -goal thy "!! s.Finite s ==> Forall P s --> Dropwhile P`(s @@ t) = Dropwhile P`t";
  101.31 +goal thy "!! s. Finite s ==> Forall P s --> Dropwhile P`(s @@ t) = Dropwhile P`t";
  101.32  by (Seq_Finite_induct_tac 1);
  101.33  qed"DropwhileConc1";
  101.34  
  101.35 @@ -905,7 +905,7 @@
  101.36  qed"take_reduction1";
  101.37  
  101.38  
  101.39 -goal thy "!! n.[| x=y; s=t;!! k.k<n ==> seq_take k`y1 = seq_take k`y2|] \
  101.40 +goal thy "!! n.[| x=y; s=t;!! k. k<n ==> seq_take k`y1 = seq_take k`y2|] \
  101.41  \ ==> seq_take n`(x @@ (s>>y1)) =  seq_take n`(y @@ (t>>y2))";
  101.42  
  101.43  by (auto_tac (!claset addSIs [take_reduction1 RS spec RS mp],!simpset));
  101.44 @@ -927,7 +927,7 @@
  101.45  qed"take_reduction_less1";
  101.46  
  101.47  
  101.48 -goal thy "!! n.[| x=y; s=t;!! k.k<n ==> seq_take k`y1 << seq_take k`y2|] \
  101.49 +goal thy "!! n.[| x=y; s=t;!! k. k<n ==> seq_take k`y1 << seq_take k`y2|] \
  101.50  \ ==> seq_take n`(x @@ (s>>y1)) <<  seq_take n`(y @@ (t>>y2))";
  101.51  by (auto_tac (!claset addSIs [take_reduction_less1 RS spec RS mp],!simpset));
  101.52  qed"take_reduction_less";
  101.53 @@ -1168,17 +1168,17 @@
  101.54  
  101.55  goal thy "!! s. Finite s ==>  \
  101.56  \         Forall (%x. (~P x) | (~ Q x)) s  \
  101.57 -\         --> Filter (%x.P x & Q x)`s = nil";
  101.58 +\         --> Filter (%x. P x & Q x)`s = nil";
  101.59  by (Seq_Finite_induct_tac 1);
  101.60  by (asm_full_simp_tac (!simpset setloop split_tac [expand_if] ) 1);
  101.61  qed"Filter_lemma3";
  101.62  
  101.63  
  101.64  goal thy "Filter P`(Filter Q`s) = Filter (%x. P x & Q x)`s";
  101.65 -by (res_inst_tac [("A1","%x.True") 
  101.66 +by (res_inst_tac [("A1","%x. True") 
  101.67                   ,("Q1","%x.~(P x & Q x)"),("x1","s")]
  101.68                   (take_lemma_induct RS mp) 1);
  101.69 -(* FIX: better support for A = %.True *)
  101.70 +(* FIX: better support for A = %x. True *)
  101.71  by (Fast_tac 3);
  101.72  by (asm_full_simp_tac (!simpset addsimps [Filter_lemma1]) 1);
  101.73  by (asm_full_simp_tac (!simpset addsimps [Filter_lemma2,Filter_lemma3] 
  101.74 @@ -1195,7 +1195,7 @@
  101.75  
  101.76  
  101.77  goal thy "Map f`(x@@y) = (Map f`x) @@ (Map f`y)";
  101.78 -by (res_inst_tac [("A1","%x.True"),("x1","x")] (take_lemma_in_eq_out RS mp) 1);
  101.79 +by (res_inst_tac [("A1","%x. True"),("x1","x")] (take_lemma_in_eq_out RS mp) 1);
  101.80  by (Auto_tac());
  101.81  qed"MapConc_takelemma";
  101.82  
   102.1 --- a/src/HOLCF/IOA/meta_theory/Traces.ML	Fri Oct 10 18:37:49 1997 +0200
   102.2 +++ b/src/HOLCF/IOA/meta_theory/Traces.ML	Fri Oct 10 19:02:28 1997 +0200
   102.3 @@ -67,7 +67,7 @@
   102.4  goal thy "is_exec_fragC A = (LAM ex. (%s. case ex of \
   102.5  \      nil => TT \
   102.6  \    | x##xs => (flift1 \ 
   102.7 -\            (%p.Def ((s,p):trans_of A) andalso (is_exec_fragC A`xs) (snd p)) \
   102.8 +\            (%p. Def ((s,p):trans_of A) andalso (is_exec_fragC A`xs) (snd p)) \
   102.9  \             `x) \
  102.10  \   ))";
  102.11  by (rtac trans 1);
  102.12 @@ -163,7 +163,7 @@
  102.13  
  102.14  goal thy 
  102.15    "!! A. is_trans_of A ==> \
  102.16 -\ ! s. is_exec_frag A (s,xs) --> Forall (%a.a:act A) (filter_act`xs)";
  102.17 +\ ! s. is_exec_frag A (s,xs) --> Forall (%a. a:act A) (filter_act`xs)";
  102.18  
  102.19  by (pair_induct_tac "xs" [is_exec_frag_def,Forall_def,sforall_def] 1);
  102.20  (* main case *)
  102.21 @@ -174,7 +174,7 @@
  102.22  
  102.23  goal thy 
  102.24    "!! A.[|  is_trans_of A; x:executions A |] ==> \
  102.25 -\ Forall (%a.a:act A) (filter_act`(snd x))";
  102.26 +\ Forall (%a. a:act A) (filter_act`(snd x))";
  102.27  
  102.28  by (asm_full_simp_tac (!simpset addsimps [executions_def]) 1);
  102.29  by (pair_tac "x" 1);
  102.30 @@ -184,7 +184,7 @@
  102.31  
  102.32  goalw thy [schedules_def,has_schedule_def]
  102.33    "!! A.[|  is_trans_of A; x:schedules A |] ==> \
  102.34 -\   Forall (%a.a:act A) x";
  102.35 +\   Forall (%a. a:act A) x";
  102.36  
  102.37  by (fast_tac (!claset addSIs [exec_in_sig]) 1);
  102.38  qed"scheds_in_sig";
  102.39 @@ -208,7 +208,7 @@
  102.40  
  102.41  (* second prefix notion for Finite x *)
  102.42  
  102.43 -goal thy "! y s.is_exec_frag A (s,x@@y) --> is_exec_frag A (s,x)";
  102.44 +goal thy "! y s. is_exec_frag A (s,x@@y) --> is_exec_frag A (s,x)";
  102.45  by (pair_induct_tac "x" [is_exec_frag_def] 1);
  102.46  by (strip_tac 1);
  102.47  by (Seq_case_simp_tac "s" 1);
   103.1 --- a/src/HOLCF/IOA/meta_theory/Traces.thy	Fri Oct 10 18:37:49 1997 +0200
   103.2 +++ b/src/HOLCF/IOA/meta_theory/Traces.thy	Fri Oct 10 19:02:28 1997 +0200
   103.3 @@ -67,7 +67,7 @@
   103.4    "is_exec_fragC A ==(fix`(LAM h ex. (%s. case ex of 
   103.5        nil => TT
   103.6      | x##xs => (flift1 
   103.7 -            (%p.Def ((s,p):trans_of A) andalso (h`xs) (snd p)) 
   103.8 +            (%p. Def ((s,p):trans_of A) andalso (h`xs) (snd p)) 
   103.9               `x)
  103.10     )))" 
  103.11  
  103.12 @@ -96,7 +96,7 @@
  103.13  
  103.14  has_trace_def
  103.15    "has_trace ioa tr ==                                               
  103.16 -     (? sch:schedules ioa. tr = Filter (%a.a:ext(ioa))`sch)"
  103.17 +     (? sch:schedules ioa. tr = Filter (%a. a:ext(ioa))`sch)"
  103.18  
  103.19  traces_def
  103.20    "traces ioa == {tr. has_trace ioa tr}"
  103.21 @@ -104,7 +104,7 @@
  103.22  
  103.23  mk_trace_def
  103.24    "mk_trace ioa == LAM tr. 
  103.25 -     Filter (%a.a:ext(ioa))`(filter_act`tr)"
  103.26 +     Filter (%a. a:ext(ioa))`(filter_act`tr)"
  103.27  
  103.28  
  103.29  (*  ------------------- Implementation ------------------------------ *)
   104.1 --- a/src/HOLCF/Lift.ML	Fri Oct 10 18:37:49 1997 +0200
   104.2 +++ b/src/HOLCF/Lift.ML	Fri Oct 10 19:02:28 1997 +0200
   104.3 @@ -22,7 +22,7 @@
   104.4  (* flift1 is continuous in a variable that occurs only 
   104.5     in the Def branch *)
   104.6  
   104.7 -goal thy "!!f. [| !! a.cont (%y. (f y) a) |] ==> \
   104.8 +goal thy "!!f. [| !! a. cont (%y. (f y) a) |] ==> \
   104.9  \          cont (%y. lift_case UU (f y))";
  104.10  by (rtac cont2cont_CF1L_rev 1);
  104.11  by (strip_tac 1);
  104.12 @@ -34,7 +34,7 @@
  104.13  (* flift1 is continuous in a variable that occurs either 
  104.14     in the Def branch or in the argument *)
  104.15  
  104.16 -goal thy "!!f. [| !! a.cont (%y. (f y) a); cont g|] ==> \
  104.17 +goal thy "!!f. [| !! a. cont (%y. (f y) a); cont g|] ==> \
  104.18  \   cont (%y. lift_case UU (f y) (g y))";
  104.19  by (rtac cont2cont_app 1);
  104.20  back();
   105.1 --- a/src/HOLCF/Lift2.ML	Fri Oct 10 18:37:49 1997 +0200
   105.2 +++ b/src/HOLCF/Lift2.ML	Fri Oct 10 19:02:28 1997 +0200
   105.3 @@ -9,7 +9,7 @@
   105.4  open Lift2;
   105.5  
   105.6  (* for compatibility with old HOLCF-Version *)
   105.7 -qed_goal "inst_lift_po" thy "(op <<)=(%x y.x=y|x=Undef)"
   105.8 +qed_goal "inst_lift_po" thy "(op <<)=(%x y. x=y|x=Undef)"
   105.9   (fn prems => 
  105.10          [
  105.11          (fold_goals_tac [less_lift_def]),
  105.12 @@ -26,7 +26,7 @@
  105.13  
  105.14  bind_thm ("UU_lift_def",minimal_lift RS minimal2UU RS sym);
  105.15  
  105.16 -qed_goal "least_lift" thy "? x::'a lift.!y.x<<y"
  105.17 +qed_goal "least_lift" thy "? x::'a lift.!y. x<<y"
  105.18  (fn prems =>
  105.19          [
  105.20          (res_inst_tac [("x","Undef")] exI 1),
  105.21 @@ -57,7 +57,7 @@
  105.22  
  105.23  goal Lift2.thy
  105.24  "!!Y. [|? j.~Y(j)=Undef;is_chain(Y::nat=>('a)lift)|] \
  105.25 -\ ==> ? j.!i.j<i-->~Y(i)=Undef";
  105.26 +\ ==> ? j.!i. j<i-->~Y(i)=Undef";
  105.27  by Safe_tac;
  105.28  by (Step_tac 1);
  105.29  by (strip_tac 1);
  105.30 @@ -74,7 +74,7 @@
  105.31          "(! Y. is_chain(Y::nat=>('a)lift)-->(? n. max_in_chain n Y))";
  105.32  by (rewtac max_in_chain_def);  
  105.33  by (strip_tac 1);
  105.34 -by (res_inst_tac [("P","!i.Y(i)=Undef")] case_split_thm  1);
  105.35 +by (res_inst_tac [("P","!i. Y(i)=Undef")] case_split_thm  1);
  105.36  by (res_inst_tac [("x","0")] exI 1);
  105.37  by (strip_tac 1);
  105.38  by (rtac trans 1);
  105.39 @@ -82,7 +82,7 @@
  105.40  by (rtac sym 1);
  105.41  by (etac spec 1); 
  105.42  
  105.43 -by (subgoal_tac "!x y.x<<(y::('a)lift) --> x=Undef | x=y" 1);
  105.44 +by (subgoal_tac "!x y. x<<(y::('a)lift) --> x=Undef | x=y" 1);
  105.45  by (simp_tac (!simpset addsimps [inst_lift_po]) 2);
  105.46  by (rtac (chain_mono2_po RS exE) 1); 
  105.47  by (Fast_tac 1); 
  105.48 @@ -110,7 +110,7 @@
  105.49  (* Main Lemma: cpo_lift *)
  105.50  
  105.51  goal Lift2.thy  
  105.52 -  "!!Y. is_chain(Y::nat=>('a)lift) ==> ? x.range(Y) <<|x";
  105.53 +  "!!Y. is_chain(Y::nat=>('a)lift) ==> ? x. range(Y) <<|x";
  105.54  by (cut_inst_tac [] flat_imp_chain_finite_poo 1);
  105.55  by (Step_tac 1);
  105.56  by Safe_tac;
   106.1 --- a/src/HOLCF/Lift3.ML	Fri Oct 10 18:37:49 1997 +0200
   106.2 +++ b/src/HOLCF/Lift3.ML	Fri Oct 10 19:02:28 1997 +0200
   106.3 @@ -80,7 +80,7 @@
   106.4                   section"UU and Def";             
   106.5  (* ---------------------------------------------------------- *)
   106.6  
   106.7 -goal thy "x=UU | (? y.x=Def y)"; 
   106.8 +goal thy "x=UU | (? y. x=Def y)"; 
   106.9  by (lift.induct_tac "x" 1);
  106.10  by (Asm_simp_tac 1);
  106.11  by (rtac disjI2 1);
  106.12 @@ -100,7 +100,7 @@
  106.13  by (ALLGOALS Asm_simp_tac);
  106.14  qed "expand_lift_case";
  106.15  
  106.16 -goal thy "(x~=UU)=(? y.x=Def y)";
  106.17 +goal thy "(x~=UU)=(? y. x=Def y)";
  106.18  by (rtac iffI 1);
  106.19  by (rtac Lift_cases 1);
  106.20  by (REPEAT (fast_tac (HOL_cs addSIs lift.distinct) 1));
   107.1 --- a/src/HOLCF/Pcpo.ML	Fri Oct 10 18:37:49 1997 +0200
   107.2 +++ b/src/HOLCF/Pcpo.ML	Fri Oct 10 19:02:28 1997 +0200
   107.3 @@ -13,7 +13,7 @@
   107.4  (* derive the old rule minimal                                              *)
   107.5  (* ------------------------------------------------------------------------ *)
   107.6  
   107.7 -qed_goalw "UU_least" thy [ UU_def ] "!z.UU << z"
   107.8 +qed_goalw "UU_least" thy [ UU_def ] "!z. UU << z"
   107.9  (fn prems => [ 
  107.10          (rtac (select_eq_Ex RS iffD2) 1),
  107.11          (rtac least 1)]);
  107.12 @@ -83,7 +83,7 @@
  107.13  (* ------------------------------------------------------------------------ *)
  107.14  
  107.15  qed_goal "lub_equal" thy
  107.16 -"[| is_chain(C1::(nat=>'a::cpo));is_chain(C2);!k.C1(k)=C2(k)|]\
  107.17 +"[| is_chain(C1::(nat=>'a::cpo));is_chain(C2);!k. C1(k)=C2(k)|]\
  107.18  \       ==> lub(range(C1))=lub(range(C2))"
  107.19  (fn prems =>
  107.20          [
  107.21 @@ -206,7 +206,7 @@
  107.22          ]);
  107.23  
  107.24  qed_goal "chain_UU_I" thy
  107.25 -        "[|is_chain(Y);lub(range(Y))=UU|] ==> ! i.Y(i)=UU"
  107.26 +        "[|is_chain(Y);lub(range(Y))=UU|] ==> ! i. Y(i)=UU"
  107.27   (fn prems =>
  107.28          [
  107.29          (cut_facts_tac prems 1),
  107.30 @@ -219,7 +219,7 @@
  107.31  
  107.32  
  107.33  qed_goal "chain_UU_I_inverse" thy 
  107.34 -        "!i.Y(i::nat)=UU ==> lub(range(Y::(nat=>'a::pcpo)))=UU"
  107.35 +        "!i. Y(i::nat)=UU ==> lub(range(Y::(nat=>'a::pcpo)))=UU"
  107.36   (fn prems =>
  107.37          [
  107.38          (cut_facts_tac prems 1),
  107.39 @@ -257,7 +257,7 @@
  107.40  
  107.41  qed_goal "chain_mono2" thy 
  107.42  "[|? j.~Y(j)=UU;is_chain(Y::nat=>'a::pcpo)|]\
  107.43 -\ ==> ? j.!i.j<i-->~Y(i)=UU"
  107.44 +\ ==> ? j.!i. j<i-->~Y(i)=UU"
  107.45   (fn prems =>
  107.46          [
  107.47          (cut_facts_tac prems 1),
  107.48 @@ -279,11 +279,11 @@
  107.49  (* ------------------------------------------------------------------------ *)
  107.50  
  107.51  qed_goalw "flat_imp_chain_finite" thy [max_in_chain_def]
  107.52 -        "!Y::nat=>'a::flat.is_chain Y-->(? n.max_in_chain n Y)"
  107.53 +        "!Y::nat=>'a::flat. is_chain Y-->(? n. max_in_chain n Y)"
  107.54   (fn _ =>
  107.55          [
  107.56          (strip_tac 1),
  107.57 -        (case_tac "!i.Y(i)=UU" 1),
  107.58 +        (case_tac "!i. Y(i)=UU" 1),
  107.59          (res_inst_tac [("x","0")] exI 1),
  107.60  	(Asm_simp_tac 1),
  107.61   	(Asm_full_simp_tac 1),
   108.1 --- a/src/HOLCF/Pcpo.thy	Fri Oct 10 18:37:49 1997 +0200
   108.2 +++ b/src/HOLCF/Pcpo.thy	Fri Oct 10 19:02:28 1997 +0200
   108.3 @@ -17,7 +17,7 @@
   108.4  (* ****************************** *)
   108.5  axclass pcpo < cpo
   108.6  
   108.7 -  least         "? x.!y.x<<y"
   108.8 +  least         "? x.!y. x<<y"
   108.9  
  108.10  consts
  108.11    UU            :: "'a::pcpo"        
  108.12 @@ -26,16 +26,16 @@
  108.13    UU            :: "'a::pcpo"                           ("\\<bottom>")
  108.14  
  108.15  defs
  108.16 -  UU_def        "UU == @x.!y.x<<y"       
  108.17 +  UU_def        "UU == @x.!y. x<<y"       
  108.18  
  108.19  (* further useful classes for HOLCF domains *)
  108.20  
  108.21  axclass chfin<cpo
  108.22  
  108.23 -chfin 	"!Y.is_chain Y-->(? n.max_in_chain n Y)"
  108.24 +chfin 	"!Y. is_chain Y-->(? n. max_in_chain n Y)"
  108.25  
  108.26  axclass flat<pcpo
  108.27  
  108.28 -ax_flat	 	"! x y.x << y --> (x = UU) | (x=y)"
  108.29 +ax_flat	 	"! x y. x << y --> (x = UU) | (x=y)"
  108.30  
  108.31  end 
   109.1 --- a/src/HOLCF/Porder.ML	Fri Oct 10 18:37:49 1997 +0200
   109.2 +++ b/src/HOLCF/Porder.ML	Fri Oct 10 19:02:28 1997 +0200
   109.3 @@ -256,7 +256,7 @@
   109.4  (* ------------------------------------------------------------------------ *)
   109.5  
   109.6  qed_goal "lub_chain_maxelem" thy
   109.7 -"[|? i.Y i=c;!i.Y i<<c|] ==> lub(range Y) = c"
   109.8 +"[|? i. Y i=c;!i. Y i<<c|] ==> lub(range Y) = c"
   109.9   (fn prems =>
  109.10          [
  109.11          (cut_facts_tac prems 1),
  109.12 @@ -274,7 +274,7 @@
  109.13  (* the lub of a constant chain is the constant                              *)
  109.14  (* ------------------------------------------------------------------------ *)
  109.15  
  109.16 -qed_goal "lub_const" thy "range(%x.c) <<| c"
  109.17 +qed_goal "lub_const" thy "range(%x. c) <<| c"
  109.18   (fn prems =>
  109.19          [
  109.20          (rtac is_lubI 1),
   110.1 --- a/src/HOLCF/Porder.thy	Fri Oct 10 18:37:49 1997 +0200
   110.2 +++ b/src/HOLCF/Porder.thy	Fri Oct 10 19:02:28 1997 +0200
   110.3 @@ -24,7 +24,7 @@
   110.4  
   110.5  translations
   110.6  
   110.7 -  "LUB x. t"	== "lub(range(%x.t))"
   110.8 +  "LUB x. t"	== "lub(range(%x. t))"
   110.9  
  110.10  syntax (symbols)
  110.11  
  110.12 @@ -33,14 +33,14 @@
  110.13  defs
  110.14  
  110.15  (* class definitions *)
  110.16 -is_ub           "S  <| x == ! y.y:S --> y<<x"
  110.17 +is_ub           "S  <| x == ! y. y:S --> y<<x"
  110.18  is_lub          "S <<| x == S <| x & (! u. S <| u  --> x << u)"
  110.19  
  110.20  (* Arbitrary chains are total orders    *)                  
  110.21  is_tord         "is_tord S == ! x y. x:S & y:S --> (x<<y | y<<x)"
  110.22  
  110.23  (* Here we use countable chains and I prefer to code them as functions! *)
  110.24 -is_chain        "is_chain F == (! i.F(i) << F(Suc(i)))"
  110.25 +is_chain        "is_chain F == (! i. F(i) << F(Suc(i)))"
  110.26  
  110.27  (* finite chains, needed for monotony of continouous functions *)
  110.28  max_in_chain_def "max_in_chain i C == ! j. i <= j --> C(i) = C(j)" 
   111.1 --- a/src/HOLCF/Porder0.ML	Fri Oct 10 18:37:49 1997 +0200
   111.2 +++ b/src/HOLCF/Porder0.ML	Fri Oct 10 19:02:28 1997 +0200
   111.3 @@ -12,7 +12,7 @@
   111.4  (* ------------------------------------------------------------------------ *)
   111.5  (* minimal fixes least element                                              *)
   111.6  (* ------------------------------------------------------------------------ *)
   111.7 -bind_thm("minimal2UU",allI RS (prove_goal thy "!x::'a::po.uu<<x==>uu=(@u.!y.u<<y)"
   111.8 +bind_thm("minimal2UU",allI RS (prove_goal thy "!x::'a::po. uu<<x==>uu=(@u.!y. u<<y)"
   111.9  (fn prems =>
  111.10          [
  111.11          (cut_facts_tac prems 1),
   112.1 --- a/src/HOLCF/Sprod2.ML	Fri Oct 10 18:37:49 1997 +0200
   112.2 +++ b/src/HOLCF/Sprod2.ML	Fri Oct 10 19:02:28 1997 +0200
   112.3 @@ -9,7 +9,7 @@
   112.4  open Sprod2;
   112.5  
   112.6  (* for compatibility with old HOLCF-Version *)
   112.7 -qed_goal "inst_sprod_po" thy "(op <<)=(%x y.Isfst x<<Isfst y&Issnd x<<Issnd y)"
   112.8 +qed_goal "inst_sprod_po" thy "(op <<)=(%x y. Isfst x<<Isfst y&Issnd x<<Issnd y)"
   112.9   (fn prems => 
  112.10          [
  112.11  	(fold_goals_tac [less_sprod_def]),
  112.12 @@ -28,7 +28,7 @@
  112.13  
  112.14  bind_thm ("UU_sprod_def",minimal_sprod RS minimal2UU RS sym);
  112.15  
  112.16 -qed_goal "least_sprod" thy "? x::'a**'b.!y.x<<y"
  112.17 +qed_goal "least_sprod" thy "? x::'a**'b.!y. x<<y"
  112.18  (fn prems =>
  112.19          [
  112.20          (res_inst_tac [("x","Ispair UU UU")] exI 1),
  112.21 @@ -96,7 +96,7 @@
  112.22  
  112.23  qed_goal "lub_sprod" Sprod2.thy 
  112.24  "[|is_chain(S)|] ==> range(S) <<| \
  112.25 -\ Ispair (lub(range(%i.Isfst(S i)))) (lub(range(%i.Issnd(S i))))"
  112.26 +\ Ispair (lub(range(%i. Isfst(S i)))) (lub(range(%i. Issnd(S i))))"
  112.27  (fn prems =>
  112.28          [
  112.29          (cut_facts_tac prems 1),
  112.30 @@ -123,7 +123,7 @@
  112.31  
  112.32  
  112.33  qed_goal "cpo_sprod" Sprod2.thy 
  112.34 -        "is_chain(S::nat=>'a**'b)==>? x.range(S)<<| x"
  112.35 +        "is_chain(S::nat=>'a**'b)==>? x. range(S)<<| x"
  112.36  (fn prems =>
  112.37          [
  112.38          (cut_facts_tac prems 1),
   113.1 --- a/src/HOLCF/Sprod3.ML	Fri Oct 10 18:37:49 1997 +0200
   113.2 +++ b/src/HOLCF/Sprod3.ML	Fri Oct 10 19:02:28 1997 +0200
   113.3 @@ -134,7 +134,7 @@
   113.4          (res_inst_tac [("f1","Ispair")] (arg_cong RS cong) 1),
   113.5          (rtac sym 1),
   113.6          (rtac lub_chain_maxelem 1),
   113.7 -        (res_inst_tac [("P","%j.Y(j)~=UU")] exE 1),
   113.8 +        (res_inst_tac [("P","%j. Y(j)~=UU")] exE 1),
   113.9          (rtac (not_all RS iffD1) 1),
  113.10          (res_inst_tac [("Q","lub(range(Y)) = UU")] contrapos 1),
  113.11          (atac 1),
  113.12 @@ -315,7 +315,7 @@
  113.13  (* ------------------------------------------------------------------------ *)
  113.14  
  113.15  qed_goalw "beta_cfun_sprod" thy [spair_def]
  113.16 -        "(LAM x y.Ispair x y)`a`b = Ispair a b"
  113.17 +        "(LAM x y. Ispair x y)`a`b = Ispair a b"
  113.18   (fn prems =>
  113.19          [
  113.20          (stac beta_cfun 1),
  113.21 @@ -564,7 +564,7 @@
  113.22  
  113.23  qed_goalw "lub_sprod2" thy [sfst_def,ssnd_def,spair_def]
  113.24  "[|is_chain(S)|] ==> range(S) <<| \
  113.25 -\ (| lub(range(%i.sfst`(S i))), lub(range(%i.ssnd`(S i))) |)"
  113.26 +\ (| lub(range(%i. sfst`(S i))), lub(range(%i. ssnd`(S i))) |)"
  113.27   (fn prems =>
  113.28          [
  113.29          (cut_facts_tac prems 1),
   114.1 --- a/src/HOLCF/Sprod3.thy	Fri Oct 10 18:37:49 1997 +0200
   114.2 +++ b/src/HOLCF/Sprod3.thy	Fri Oct 10 19:02:28 1997 +0200
   114.3 @@ -24,10 +24,10 @@
   114.4          "(|x, y|)"      == "spair`x`y"
   114.5  
   114.6  defs
   114.7 -spair_def       "spair  == (LAM x y.Ispair x y)"
   114.8 -sfst_def        "sfst   == (LAM p.Isfst p)"
   114.9 -ssnd_def        "ssnd   == (LAM p.Issnd p)"     
  114.10 -ssplit_def      "ssplit == (LAM f. strictify`(LAM p.f`(sfst`p)`(ssnd`p)))"
  114.11 +spair_def       "spair  == (LAM x y. Ispair x y)"
  114.12 +sfst_def        "sfst   == (LAM p. Isfst p)"
  114.13 +ssnd_def        "ssnd   == (LAM p. Issnd p)"     
  114.14 +ssplit_def      "ssplit == (LAM f. strictify`(LAM p. f`(sfst`p)`(ssnd`p)))"
  114.15  
  114.16  end
  114.17  
   115.1 --- a/src/HOLCF/Ssum0.thy	Fri Oct 10 18:37:49 1997 +0200
   115.2 +++ b/src/HOLCF/Ssum0.thy	Fri Oct 10 19:02:28 1997 +0200
   115.3 @@ -15,7 +15,7 @@
   115.4   "Sinr_Rep == (%b.%x y p.(b~=UU --> y=b & ~p))"
   115.5  
   115.6  typedef (Ssum)  ('a, 'b) "++" (infixr 10) = 
   115.7 -	"{f.(? a.f=Sinl_Rep(a))|(? b.f=Sinr_Rep(b))}"
   115.8 +	"{f.(? a. f=Sinl_Rep(a))|(? b. f=Sinr_Rep(b))}"
   115.9  
  115.10  syntax (symbols)
  115.11    "++"		:: [type, type] => type	("(_ \\<oplus>/ _)" [21, 20] 20)
   116.1 --- a/src/HOLCF/Ssum1.thy	Fri Oct 10 18:37:49 1997 +0200
   116.2 +++ b/src/HOLCF/Ssum1.thy	Fri Oct 10 19:02:28 1997 +0200
   116.3 @@ -12,10 +12,10 @@
   116.4  
   116.5  defs
   116.6    less_ssum_def "(op <<) == (%s1 s2.@z.
   116.7 -         (! u x.s1=Isinl u & s2=Isinl x --> z = u << x)
   116.8 -        &(! v y.s1=Isinr v & s2=Isinr y --> z = v << y)
   116.9 -        &(! u y.s1=Isinl u & s2=Isinr y --> z = (u = UU))
  116.10 -        &(! v x.s1=Isinr v & s2=Isinl x --> z = (v = UU)))"
  116.11 +         (! u x. s1=Isinl u & s2=Isinl x --> z = u << x)
  116.12 +        &(! v y. s1=Isinr v & s2=Isinr y --> z = v << y)
  116.13 +        &(! u y. s1=Isinl u & s2=Isinr y --> z = (u = UU))
  116.14 +        &(! v x. s1=Isinr v & s2=Isinl x --> z = (v = UU)))"
  116.15  
  116.16  end
  116.17  
   117.1 --- a/src/HOLCF/Ssum2.ML	Fri Oct 10 18:37:49 1997 +0200
   117.2 +++ b/src/HOLCF/Ssum2.ML	Fri Oct 10 19:02:28 1997 +0200
   117.3 @@ -10,10 +10,10 @@
   117.4  
   117.5  (* for compatibility with old HOLCF-Version *)
   117.6  qed_goal "inst_ssum_po" thy "(op <<)=(%s1 s2.@z.\
   117.7 -\         (! u x.s1=Isinl u & s2=Isinl x --> z = u << x)\
   117.8 -\        &(! v y.s1=Isinr v & s2=Isinr y --> z = v << y)\
   117.9 -\        &(! u y.s1=Isinl u & s2=Isinr y --> z = (u = UU))\
  117.10 -\        &(! v x.s1=Isinr v & s2=Isinl x --> z = (v = UU)))"
  117.11 +\         (! u x. s1=Isinl u & s2=Isinl x --> z = u << x)\
  117.12 +\        &(! v y. s1=Isinr v & s2=Isinr y --> z = v << y)\
  117.13 +\        &(! u y. s1=Isinl u & s2=Isinr y --> z = (u = UU))\
  117.14 +\        &(! v x. s1=Isinr v & s2=Isinl x --> z = (v = UU)))"
  117.15   (fn prems => 
  117.16          [
  117.17          (fold_goals_tac [less_ssum_def]),
  117.18 @@ -67,7 +67,7 @@
  117.19  
  117.20  bind_thm ("UU_ssum_def",minimal_ssum RS minimal2UU RS sym);
  117.21  
  117.22 -qed_goal "least_ssum" thy "? x::'a++'b.!y.x<<y"
  117.23 +qed_goal "least_ssum" thy "? x::'a++'b.!y. x<<y"
  117.24  (fn prems =>
  117.25          [
  117.26          (res_inst_tac [("x","Isinl UU")] exI 1),
  117.27 @@ -174,7 +174,7 @@
  117.28  (* ------------------------------------------------------------------------ *)
  117.29  
  117.30  qed_goal "ssum_lemma1" thy 
  117.31 -"[|~(!i.? x.Y(i::nat)=Isinl(x))|] ==> (? i.! x.Y(i)~=Isinl(x))"
  117.32 +"[|~(!i.? x. Y(i::nat)=Isinl(x))|] ==> (? i.! x. Y(i)~=Isinl(x))"
  117.33   (fn prems =>
  117.34          [
  117.35          (cut_facts_tac prems 1),
  117.36 @@ -199,7 +199,7 @@
  117.37  
  117.38  qed_goal "ssum_lemma3" thy 
  117.39  "[|is_chain(Y);(? i x. Y(i)=Isinr(x::'b) & (x::'b)~=UU)|] ==>\
  117.40 -\ (!i.? y.Y(i)=Isinr(y))"
  117.41 +\ (!i.? y. Y(i)=Isinr(y))"
  117.42   (fn prems =>
  117.43          [
  117.44          (cut_facts_tac prems 1),
  117.45 @@ -231,7 +231,7 @@
  117.46          ]);
  117.47  
  117.48  qed_goal "ssum_lemma4" thy 
  117.49 -"is_chain(Y) ==> (!i.? x.Y(i)=Isinl(x))|(!i.? y.Y(i)=Isinr(y))"
  117.50 +"is_chain(Y) ==> (!i.? x. Y(i)=Isinl(x))|(!i.? y. Y(i)=Isinr(y))"
  117.51   (fn prems =>
  117.52          [
  117.53          (cut_facts_tac prems 1),
  117.54 @@ -249,7 +249,7 @@
  117.55  (* ------------------------------------------------------------------------ *)
  117.56  
  117.57  qed_goal "ssum_lemma5" thy 
  117.58 -"z=Isinl(x)==> Isinl((Iwhen (LAM x.x) (LAM y.UU))(z)) = z"
  117.59 +"z=Isinl(x)==> Isinl((Iwhen (LAM x. x) (LAM y. UU))(z)) = z"
  117.60   (fn prems =>
  117.61          [
  117.62          (cut_facts_tac prems 1),
  117.63 @@ -264,7 +264,7 @@
  117.64  (* ------------------------------------------------------------------------ *)
  117.65  
  117.66  qed_goal "ssum_lemma6" thy 
  117.67 -"z=Isinr(x)==> Isinr((Iwhen (LAM y.UU) (LAM x.x))(z)) = z"
  117.68 +"z=Isinr(x)==> Isinr((Iwhen (LAM y. UU) (LAM x. x))(z)) = z"
  117.69   (fn prems =>
  117.70          [
  117.71          (cut_facts_tac prems 1),
  117.72 @@ -279,7 +279,7 @@
  117.73  (* ------------------------------------------------------------------------ *)
  117.74  
  117.75  qed_goal "ssum_lemma7" thy 
  117.76 -"[|Isinl(x) << z; x~=UU|] ==> ? y.z=Isinl(y) & y~=UU"
  117.77 +"[|Isinl(x) << z; x~=UU|] ==> ? y. z=Isinl(y) & y~=UU"
  117.78   (fn prems =>
  117.79          [
  117.80          (cut_facts_tac prems 1),
  117.81 @@ -297,7 +297,7 @@
  117.82          ]);
  117.83  
  117.84  qed_goal "ssum_lemma8" thy 
  117.85 -"[|Isinr(x) << z; x~=UU|] ==> ? y.z=Isinr(y) & y~=UU"
  117.86 +"[|Isinr(x) << z; x~=UU|] ==> ? y. z=Isinr(y) & y~=UU"
  117.87   (fn prems =>
  117.88          [
  117.89          (cut_facts_tac prems 1),
  117.90 @@ -317,9 +317,9 @@
  117.91  (* ------------------------------------------------------------------------ *)
  117.92  
  117.93  qed_goal "lub_ssum1a" thy 
  117.94 -"[|is_chain(Y);(!i.? x.Y(i)=Isinl(x))|] ==>\
  117.95 +"[|is_chain(Y);(!i.? x. Y(i)=Isinl(x))|] ==>\
  117.96  \ range(Y) <<|\
  117.97 -\ Isinl(lub(range(%i.(Iwhen (LAM x.x) (LAM y.UU))(Y i))))"
  117.98 +\ Isinl(lub(range(%i.(Iwhen (LAM x. x) (LAM y. UU))(Y i))))"
  117.99   (fn prems =>
 117.100          [
 117.101          (cut_facts_tac prems 1),
 117.102 @@ -358,9 +358,9 @@
 117.103  
 117.104  
 117.105  qed_goal "lub_ssum1b" thy 
 117.106 -"[|is_chain(Y);(!i.? x.Y(i)=Isinr(x))|] ==>\
 117.107 +"[|is_chain(Y);(!i.? x. Y(i)=Isinr(x))|] ==>\
 117.108  \ range(Y) <<|\
 117.109 -\ Isinr(lub(range(%i.(Iwhen (LAM y.UU) (LAM x.x))(Y i))))"
 117.110 +\ Isinr(lub(range(%i.(Iwhen (LAM y. UU) (LAM x. x))(Y i))))"
 117.111   (fn prems =>
 117.112          [
 117.113          (cut_facts_tac prems 1),
 117.114 @@ -413,7 +413,7 @@
 117.115  *)
 117.116  
 117.117  qed_goal "cpo_ssum" thy 
 117.118 -        "is_chain(Y::nat=>'a ++'b) ==> ? x.range(Y) <<|x"
 117.119 +        "is_chain(Y::nat=>'a ++'b) ==> ? x. range(Y) <<|x"
 117.120   (fn prems =>
 117.121          [
 117.122          (cut_facts_tac prems 1),
   118.1 --- a/src/HOLCF/Ssum3.ML	Fri Oct 10 18:37:49 1997 +0200
   118.2 +++ b/src/HOLCF/Ssum3.ML	Fri Oct 10 19:02:28 1997 +0200
   118.3 @@ -156,7 +156,7 @@
   118.4  (* ------------------------------------------------------------------------ *)
   118.5  
   118.6  qed_goal "ssum_lemma9" Ssum3.thy 
   118.7 -"[| is_chain(Y); lub(range(Y)) = Isinl(x)|] ==> !i.? x.Y(i)=Isinl(x)"
   118.8 +"[| is_chain(Y); lub(range(Y)) = Isinl(x)|] ==> !i.? x. Y(i)=Isinl(x)"
   118.9   (fn prems =>
  118.10          [
  118.11          (cut_facts_tac prems 1),
  118.12 @@ -174,7 +174,7 @@
  118.13  
  118.14  
  118.15  qed_goal "ssum_lemma10" Ssum3.thy 
  118.16 -"[| is_chain(Y); lub(range(Y)) = Isinr(x)|] ==> !i.? x.Y(i)=Isinr(x)"
  118.17 +"[| is_chain(Y); lub(range(Y)) = Isinr(x)|] ==> !i.? x. Y(i)=Isinr(x)"
  118.18   (fn prems =>
  118.19          [
  118.20          (cut_facts_tac prems 1),
  118.21 @@ -615,7 +615,7 @@
  118.22  
  118.23  qed_goalw "thelub_ssum2b" Ssum3.thy [sinl_def,sinr_def,sswhen_def] 
  118.24  "[| is_chain(Y); !i.? x. Y(i) = sinr`x |] ==>\ 
  118.25 -\   lub(range(Y)) = sinr`(lub(range(%i. sswhen`(LAM y. UU)`(LAM x.x)`(Y i))))"
  118.26 +\   lub(range(Y)) = sinr`(lub(range(%i. sswhen`(LAM y. UU)`(LAM x. x)`(Y i))))"
  118.27   (fn prems =>
  118.28          [
  118.29          (cut_facts_tac prems 1),
  118.30 @@ -641,7 +641,7 @@
  118.31          ]);
  118.32  
  118.33  qed_goalw "thelub_ssum2a_rev" Ssum3.thy [sinl_def,sinr_def] 
  118.34 -        "[| is_chain(Y); lub(range(Y)) = sinl`x|] ==> !i.? x.Y(i)=sinl`x"
  118.35 +        "[| is_chain(Y); lub(range(Y)) = sinl`x|] ==> !i.? x. Y(i)=sinl`x"
  118.36   (fn prems =>
  118.37          [
  118.38          (cut_facts_tac prems 1),
  118.39 @@ -655,7 +655,7 @@
  118.40          ]);
  118.41  
  118.42  qed_goalw "thelub_ssum2b_rev" Ssum3.thy [sinl_def,sinr_def] 
  118.43 -        "[| is_chain(Y); lub(range(Y)) = sinr`x|] ==> !i.? x.Y(i)=sinr`x"
  118.44 +        "[| is_chain(Y); lub(range(Y)) = sinr`x|] ==> !i.? x. Y(i)=sinr`x"
  118.45   (fn prems =>
  118.46          [
  118.47          (cut_facts_tac prems 1),
  118.48 @@ -670,8 +670,8 @@
  118.49  
  118.50  qed_goal "thelub_ssum3" Ssum3.thy  
  118.51  "is_chain(Y) ==>\ 
  118.52 -\   lub(range(Y)) = sinl`(lub(range(%i. sswhen`(LAM x. x)`(LAM y.UU)`(Y i))))\
  118.53 -\ | lub(range(Y)) = sinr`(lub(range(%i. sswhen`(LAM y. UU)`(LAM x.x)`(Y i))))"
  118.54 +\   lub(range(Y)) = sinl`(lub(range(%i. sswhen`(LAM x. x)`(LAM y. UU)`(Y i))))\
  118.55 +\ | lub(range(Y)) = sinr`(lub(range(%i. sswhen`(LAM y. UU)`(LAM x. x)`(Y i))))"
  118.56   (fn prems =>
  118.57          [
  118.58          (cut_facts_tac prems 1),
   119.1 --- a/src/HOLCF/Ssum3.thy	Fri Oct 10 18:37:49 1997 +0200
   119.2 +++ b/src/HOLCF/Ssum3.thy	Fri Oct 10 19:02:28 1997 +0200
   119.3 @@ -17,11 +17,11 @@
   119.4  
   119.5  defs
   119.6  
   119.7 -sinl_def        "sinl   == (LAM x.Isinl(x))"
   119.8 -sinr_def        "sinr   == (LAM x.Isinr(x))"
   119.9 -sswhen_def      "sswhen   == (LAM f g s.Iwhen(f)(g)(s))"
  119.10 +sinl_def        "sinl   == (LAM x. Isinl(x))"
  119.11 +sinr_def        "sinr   == (LAM x. Isinr(x))"
  119.12 +sswhen_def      "sswhen   == (LAM f g s. Iwhen(f)(g)(s))"
  119.13  
  119.14  translations
  119.15 -"case s of sinl`x => t1 | sinr`y => t2" == "sswhen`(LAM x.t1)`(LAM y.t2)`s"
  119.16 +"case s of sinl`x => t1 | sinr`y => t2" == "sswhen`(LAM x. t1)`(LAM y. t2)`s"
  119.17  
  119.18  end
   120.1 --- a/src/HOLCF/Tr.thy	Fri Oct 10 18:37:49 1997 +0200
   120.2 +++ b/src/HOLCF/Tr.thy	Fri Oct 10 19:02:28 1997 +0200
   120.3 @@ -34,9 +34,9 @@
   120.4    TT_def      "TT==Def True"
   120.5    FF_def      "FF==Def False"
   120.6    neg_def     "neg == flift2 Not"
   120.7 -  ifte_def    "Icifte == (LAM b t e.flift1(%b.if b then t else e)`b)"
   120.8 -  andalso_def "trand == (LAM x y.If x then y else FF fi)"
   120.9 -  orelse_def  "tror == (LAM x y.If x then TT else y fi)"
  120.10 +  ifte_def    "Icifte == (LAM b t e. flift1(%b. if b then t else e)`b)"
  120.11 +  andalso_def "trand == (LAM x y. If x then y else FF fi)"
  120.12 +  orelse_def  "tror == (LAM x y. If x then TT else y fi)"
  120.13    If2_def     "If2 Q x y == If Q then x else y fi"
  120.14  
  120.15  end
   121.1 --- a/src/HOLCF/Up1.thy	Fri Oct 10 18:37:49 1997 +0200
   121.2 +++ b/src/HOLCF/Up1.thy	Fri Oct 10 19:02:28 1997 +0200
   121.3 @@ -23,7 +23,7 @@
   121.4  defs
   121.5    Iup_def     "Iup x == Abs_Up(Inr(x))"
   121.6    Ifup_def    "Ifup(f)(x)== case Rep_Up(x) of Inl(y) => UU | Inr(z) => f`z"
   121.7 -  less_up_def "(op <<) == (%x1 x2.case Rep_Up(x1) of                 
   121.8 +  less_up_def "(op <<) == (%x1 x2. case Rep_Up(x1) of                 
   121.9                 Inl(y1) => True          
  121.10               | Inr(y2) => (case Rep_Up(x2) of Inl(z1) => False       
  121.11                                              | Inr(z2) => y2<<z2))"
   122.1 --- a/src/HOLCF/Up2.ML	Fri Oct 10 18:37:49 1997 +0200
   122.2 +++ b/src/HOLCF/Up2.ML	Fri Oct 10 19:02:28 1997 +0200
   122.3 @@ -9,7 +9,7 @@
   122.4  open Up2;
   122.5  
   122.6  (* for compatibility with old HOLCF-Version *)
   122.7 -qed_goal "inst_up_po" thy "(op <<)=(%x1 x2.case Rep_Up(x1) of \               
   122.8 +qed_goal "inst_up_po" thy "(op <<)=(%x1 x2. case Rep_Up(x1) of \               
   122.9  \               Inl(y1) => True \
  122.10  \             | Inr(y2) => (case Rep_Up(x2) of Inl(z1) => False \
  122.11  \                                            | Inr(z2) => y2<<z2))"
  122.12 @@ -31,7 +31,7 @@
  122.13  
  122.14  bind_thm ("UU_up_def",minimal_up RS minimal2UU RS sym);
  122.15  
  122.16 -qed_goal "least_up" thy "? x::'a u.!y.x<<y"
  122.17 +qed_goal "least_up" thy "? x::'a u.!y. x<<y"
  122.18  (fn prems =>
  122.19          [
  122.20          (res_inst_tac [("x","Abs_Up(Inl ())")] exI 1),
  122.21 @@ -99,7 +99,7 @@
  122.22  (* Some kind of surjectivity lemma                                          *)
  122.23  (* ------------------------------------------------------------------------ *)
  122.24  
  122.25 -qed_goal "up_lemma1" thy  "z=Iup(x) ==> Iup(Ifup(LAM x.x)(z)) = z"
  122.26 +qed_goal "up_lemma1" thy  "z=Iup(x) ==> Iup(Ifup(LAM x. x)(z)) = z"
  122.27   (fn prems =>
  122.28          [
  122.29          (cut_facts_tac prems 1),
  122.30 @@ -111,8 +111,8 @@
  122.31  (* ------------------------------------------------------------------------ *)
  122.32  
  122.33  qed_goal "lub_up1a" thy 
  122.34 -"[|is_chain(Y);? i x.Y(i)=Iup(x)|] ==>\
  122.35 -\ range(Y) <<| Iup(lub(range(%i.(Ifup (LAM x.x) (Y(i))))))"
  122.36 +"[|is_chain(Y);? i x. Y(i)=Iup(x)|] ==>\
  122.37 +\ range(Y) <<| Iup(lub(range(%i.(Ifup (LAM x. x) (Y(i))))))"
  122.38   (fn prems =>
  122.39          [
  122.40          (cut_facts_tac prems 1),
  122.41 @@ -183,7 +183,7 @@
  122.42  *)
  122.43  
  122.44  qed_goal "cpo_up" thy 
  122.45 -        "is_chain(Y::nat=>('a)u) ==> ? x.range(Y) <<|x"
  122.46 +        "is_chain(Y::nat=>('a)u) ==> ? x. range(Y) <<|x"
  122.47   (fn prems =>
  122.48          [
  122.49          (cut_facts_tac prems 1),
   123.1 --- a/src/HOLCF/Up3.ML	Fri Oct 10 18:37:49 1997 +0200
   123.2 +++ b/src/HOLCF/Up3.ML	Fri Oct 10 19:02:28 1997 +0200
   123.3 @@ -274,7 +274,7 @@
   123.4          ]);
   123.5  
   123.6  
   123.7 -qed_goal "up_lemma2" thy  " (? x.z = up`x) = (z~=UU)"
   123.8 +qed_goal "up_lemma2" thy  " (? x. z = up`x) = (z~=UU)"
   123.9   (fn prems =>
  123.10          [
  123.11          (rtac iffI 1),
  123.12 @@ -317,7 +317,7 @@
  123.13  
  123.14  qed_goal "thelub_up3" thy  
  123.15  "is_chain(Y) ==> lub(range(Y)) = UU |\
  123.16 -\                lub(range(Y)) = up`(lub(range(%i. fup`(LAM x.x)`(Y i))))"
  123.17 +\                lub(range(Y)) = up`(lub(range(%i. fup`(LAM x. x)`(Y i))))"
  123.18   (fn prems =>
  123.19          [
  123.20          (cut_facts_tac prems 1),
   124.1 --- a/src/HOLCF/Up3.thy	Fri Oct 10 18:37:49 1997 +0200
   124.2 +++ b/src/HOLCF/Up3.thy	Fri Oct 10 19:02:28 1997 +0200
   124.3 @@ -14,12 +14,12 @@
   124.4  
   124.5  constdefs  
   124.6          up  :: "'a -> ('a)u"
   124.7 -       "up  == (LAM x.Iup(x))"
   124.8 +       "up  == (LAM x. Iup(x))"
   124.9          fup :: "('a->'c)-> ('a)u -> 'c"
  124.10 -       "fup == (LAM f p.Ifup(f)(p))"
  124.11 +       "fup == (LAM f p. Ifup(f)(p))"
  124.12  
  124.13  translations
  124.14 -"case l of up`x => t1" == "fup`(LAM x.t1)`l"
  124.15 +"case l of up`x => t1" == "fup`(LAM x. t1)`l"
  124.16  
  124.17  end
  124.18  
   125.1 --- a/src/HOLCF/ex/Dlist.ML	Fri Oct 10 18:37:49 1997 +0200
   125.2 +++ b/src/HOLCF/ex/Dlist.ML	Fri Oct 10 19:02:28 1997 +0200
   125.3 @@ -5,7 +5,7 @@
   125.4  (* ------------------------------------------------------------------------- *)
   125.5  
   125.6  bind_thm ("lmap_def2", fix_prover2 Dlist.thy lmap_def 
   125.7 -        "lmap = (LAM f s.case s of dnil => dnil | x ## l => f`x ## lmap`f`l )");
   125.8 +        "lmap = (LAM f s. case s of dnil => dnil | x ## l => f`x ## lmap`f`l )");
   125.9  
  125.10  (* ------------------------------------------------------------------------- *)
  125.11  (* recursive  properties   of lmap                                           *)
   126.1 --- a/src/HOLCF/ex/Dnat.ML	Fri Oct 10 18:37:49 1997 +0200
   126.2 +++ b/src/HOLCF/ex/Dnat.ML	Fri Oct 10 19:02:28 1997 +0200
   126.3 @@ -47,7 +47,7 @@
   126.4  val iterator_rews = 
   126.5  	[iterator1, iterator2, iterator3];
   126.6  
   126.7 -val dnat_flat = prove_goal Dnat.thy "!x y::dnat.x<<y --> x=UU | x=y" 
   126.8 +val dnat_flat = prove_goal Dnat.thy "!x y::dnat. x<<y --> x=UU | x=y" 
   126.9  (fn _ => [
  126.10  	(rtac allI 1),
  126.11  	(res_inst_tac [("x","x")] dnat.ind 1),
   127.1 --- a/src/HOLCF/ex/Focus_ex.ML	Fri Oct 10 18:37:49 1997 +0200
   127.2 +++ b/src/HOLCF/ex/Focus_ex.ML	Fri Oct 10 19:02:28 1997 +0200
   127.3 @@ -63,7 +63,7 @@
   127.4  by (REPEAT (etac conjE 1));
   127.5  by (etac conjI 1);
   127.6  by (strip_tac 1);
   127.7 -by (res_inst_tac [("x","fix`(LAM k.csnd`(f`<x,k>))")] exI 1);
   127.8 +by (res_inst_tac [("x","fix`(LAM k. csnd`(f`<x,k>))")] exI 1);
   127.9  by (rtac conjI 1);
  127.10   by (asm_simp_tac HOLCF_ss 1);
  127.11   by (rtac trans 1);
   128.1 --- a/src/HOLCF/ex/Focus_ex.thy	Fri Oct 10 18:37:49 1997 +0200
   128.2 +++ b/src/HOLCF/ex/Focus_ex.thy	Fri Oct 10 19:02:28 1997 +0200
   128.3 @@ -131,6 +131,6 @@
   128.4  
   128.5  def_g		"def_g g == (? f.
   128.6  			is_f f  & 
   128.7 -	      		g = (LAM x. cfst`(f`<x,fix`(LAM  k.csnd`(f`<x,k>))>)))" 
   128.8 +	      		g = (LAM x. cfst`(f`<x,fix`(LAM  k. csnd`(f`<x,k>))>)))" 
   128.9  
  128.10  end
   129.1 --- a/src/HOLCF/ex/Hoare.ML	Fri Oct 10 18:37:49 1997 +0200
   129.2 +++ b/src/HOLCF/ex/Hoare.ML	Fri Oct 10 19:02:28 1997 +0200
   129.3 @@ -20,7 +20,7 @@
   129.4          ]);
   129.5  
   129.6  val hoare_lemma3 = prove_goal HOLCF.thy 
   129.7 -" (!k.b1`(iterate k g x) = TT) | (? k. b1`(iterate k g x)~=TT)"
   129.8 +" (!k. b1`(iterate k g x) = TT) | (? k. b1`(iterate k g x)~=TT)"
   129.9   (fn prems =>
  129.10          [
  129.11          (fast_tac HOL_cs 1)
  129.12 @@ -177,8 +177,8 @@
  129.13  *)
  129.14  
  129.15  val hoare_lemma11 = prove_goal Hoare.thy 
  129.16 -"(? n.b1`(iterate n g x) ~= TT) ==>\
  129.17 -\ k=Least(%n.b1`(iterate n g x) ~= TT) & b1`(iterate k g x)=FF \
  129.18 +"(? n. b1`(iterate n g x) ~= TT) ==>\
  129.19 +\ k=Least(%n. b1`(iterate n g x) ~= TT) & b1`(iterate k g x)=FF \
  129.20  \ --> p`x = iterate k g x"
  129.21   (fn prems =>
  129.22          [
   130.1 --- a/src/HOLCF/ex/Loop.ML	Fri Oct 10 18:37:49 1997 +0200
   130.2 +++ b/src/HOLCF/ex/Loop.ML	Fri Oct 10 19:02:28 1997 +0200
   130.3 @@ -40,7 +40,7 @@
   130.4          ]);
   130.5  
   130.6  val while_unfold2 = prove_goal Loop.thy 
   130.7 -        "!x.while`b`g`x = while`b`g`(iterate k (step`b`g) x)"
   130.8 +        "!x. while`b`g`x = while`b`g`(iterate k (step`b`g) x)"
   130.9   (fn prems =>
  130.10          [
  130.11          (nat_ind_tac "k" 1),
  130.12 @@ -83,7 +83,7 @@
  130.13  (* --------------------------------------------------------------------------- *)
  130.14  
  130.15  val loop_lemma1 = prove_goal Loop.thy
  130.16 -"[|? y.b`y=FF; iterate k (step`b`g) x = UU|]==>iterate(Suc k) (step`b`g) x=UU"
  130.17 +"[|? y. b`y=FF; iterate k (step`b`g) x = UU|]==>iterate(Suc k) (step`b`g) x=UU"
  130.18   (fn prems =>
  130.19          [
  130.20          (cut_facts_tac prems 1),
  130.21 @@ -98,7 +98,7 @@
  130.22          ]);
  130.23  
  130.24  val loop_lemma2 = prove_goal Loop.thy
  130.25 -"[|? y.b`y=FF;iterate (Suc k) (step`b`g) x ~=UU |]==>\
  130.26 +"[|? y. b`y=FF;iterate (Suc k) (step`b`g) x ~=UU |]==>\
  130.27  \iterate k (step`b`g) x ~=UU"
  130.28   (fn prems =>
  130.29          [
  130.30 @@ -111,7 +111,7 @@
  130.31  
  130.32  val loop_lemma3 = prove_goal Loop.thy
  130.33  "[|!x. INV x & b`x=TT & g`x~=UU --> INV (g`x);\
  130.34 -\? y.b`y=FF; INV x|] ==>\
  130.35 +\? y. b`y=FF; INV x|] ==>\
  130.36  \iterate k (step`b`g) x ~=UU --> INV (iterate k (step`b`g) x)"
  130.37   (fn prems =>
  130.38          [
  130.39 @@ -266,7 +266,7 @@
  130.40  
  130.41  val loop_inv = prove_goal Loop.thy
  130.42  "[| P(x);\
  130.43 -\   !!y.P y ==> INV y;\
  130.44 +\   !!y. P y ==> INV y;\
  130.45  \   !!y.[| INV y; b`y=TT; g`y~=UU|] ==> INV (g`y);\
  130.46  \   !!y.[| INV y; b`y=FF|]==> Q y;\
  130.47  \   while`b`g`x ~= UU |] ==> Q (while`b`g`x)"
   131.1 --- a/src/HOLCF/ex/Stream.ML	Fri Oct 10 18:37:49 1997 +0200
   131.2 +++ b/src/HOLCF/ex/Stream.ML	Fri Oct 10 19:02:28 1997 +0200
   131.3 @@ -140,7 +140,7 @@
   131.4  	(rtac refl 1)
   131.5  	]);
   131.6  
   131.7 -qed_goal "chain_stream_take" thy "is_chain (%i.stream_take i`s)" (fn _ => [
   131.8 +qed_goal "chain_stream_take" thy "is_chain (%i. stream_take i`s)" (fn _ => [
   131.9  	rtac is_chainI 1,
  131.10  	subgoal_tac "!i s. stream_take i`s << stream_take (Suc i)`s" 1,
  131.11  	fast_tac HOL_cs 1,
  131.12 @@ -189,7 +189,7 @@
  131.13  *)
  131.14  
  131.15  val stream_take_lemma3 = prove_goal thy 
  131.16 - "!x xs.x~=UU --> stream_take n`(x && xs) = x && xs --> stream_take n`xs=xs"
  131.17 + "!x xs. x~=UU --> stream_take n`(x && xs) = x && xs --> stream_take n`xs=xs"
  131.18   (fn prems => [
  131.19  	(nat_ind_tac "n" 1),
  131.20  	(asm_simp_tac (HOL_ss addsimps stream.take_rews) 1),
   132.1 --- a/src/HOLCF/ex/loeckx.ML	Fri Oct 10 18:37:49 1997 +0200
   132.2 +++ b/src/HOLCF/ex/loeckx.ML	Fri Oct 10 19:02:28 1997 +0200
   132.3 @@ -3,7 +3,7 @@
   132.4  (* Loeckx & Sieber S.88                                 *)
   132.5  
   132.6  val prems = goalw Fix.thy [Ifix_def]
   132.7 -"Ifix F= lub (range (%i.%G.iterate i G UU)) F";
   132.8 +"Ifix F= lub (range (%i.%G. iterate i G UU)) F";
   132.9  by (stac thelub_fun 1);
  132.10  by (rtac ch2ch_fun 1);
  132.11  back();
  132.12 @@ -48,15 +48,15 @@
  132.13  
  132.14  val prems = goal Fix.thy  "cont(Ifix)";
  132.15  by (res_inst_tac 
  132.16 - [("t","Ifix"),("s","(%f.lub(range(%j.(LAM f. iterate j f UU)`f)))")]
  132.17 + [("t","Ifix"),("s","(%f. lub(range(%j.(LAM f. iterate j f UU)`f)))")]
  132.18    ssubst 1);
  132.19  by (rtac ext 1);
  132.20  by (rewtac Ifix_def );
  132.21  by (subgoal_tac 
  132.22 -  "range(% i.iterate i f UU) = range(%j.(LAM f. iterate j f UU)`f)" 1);
  132.23 +  "range(% i. iterate i f UU) = range(%j.(LAM f. iterate j f UU)`f)" 1);
  132.24  by (etac arg_cong 1);
  132.25  by (subgoal_tac 
  132.26 -        "(% i.iterate i f UU) = (%j.(LAM f. iterate j f UU)`f)" 1);
  132.27 +        "(% i. iterate i f UU) = (%j.(LAM f. iterate j f UU)`f)" 1);
  132.28  by (etac arg_cong 1);
  132.29  by (rtac ext 1);
  132.30  by (stac beta_cfun 1);
  132.31 @@ -79,7 +79,7 @@
  132.32  (* the proof in little steps *)
  132.33  
  132.34  val prems = goal Fix.thy  
  132.35 -"(% i.iterate i f UU) = (%j.(LAM f. iterate j f UU)`f)";
  132.36 +"(% i. iterate i f UU) = (%j.(LAM f. iterate j f UU)`f)";
  132.37  by (rtac ext 1);
  132.38  by (stac beta_cfun 1);
  132.39  by (rtac  cont2cont_CF1L 1);
  132.40 @@ -88,7 +88,7 @@
  132.41  val fix_lemma1 = result();
  132.42  
  132.43  val prems = goal Fix.thy  
  132.44 -" Ifix = (%f.lub(range(%j.(LAM f.iterate j f UU)`f)))";
  132.45 +" Ifix = (%f. lub(range(%j.(LAM f. iterate j f UU)`f)))";
  132.46  by (rtac ext 1);
  132.47  by (rewtac Ifix_def ); 
  132.48  by (stac fix_lemma1 1);