X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Fnotation.ma;h=f53dcf86710a2615e9d3a8acebda1f0e334b60a4;hb=53f874fba5b9c39a788085515a4fefe5d29281da;hp=dc4bda3964f7604728ef139cd78a4349153cdcce;hpb=1efc4c2c7be1e4aff0ccccabf905d45795b3865f;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/basic_2/notation.ma b/matita/matita/contribs/lambda_delta/basic_2/notation.ma
index dc4bda396..f53dcf867 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/notation.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/notation.ma
@@ -16,7 +16,7 @@
 
 (* Grammar ******************************************************************)
 
-notation "hvbox( ⓪ )"
+notation "⓪"
  non associative with precedence 90
  for @{ 'Item0 }.
 
@@ -24,7 +24,7 @@ notation "hvbox( ⓪ { I } )"
  non associative with precedence 90
  for @{ 'Item0 $I }.
 
-notation "hvbox( ⋆ )"
+notation "⋆"
  non associative with precedence 90
  for @{ 'Star }.
 
@@ -40,48 +40,72 @@ notation "hvbox( § term 90 p )"
  non associative with precedence 90
  for @{ 'GRef $p }.
 
-notation "hvbox( ② term 90 T1 . break term 90 T )"
- non associative with precedence 90
+notation "hvbox( ② term 55 T1 . break term 55 T )"
+ non associative with precedence 55
  for @{ 'SnItem2 $T1 $T }.
 
-notation "hvbox( ② { I } break term 90 T1 . break term 90 T )"
- non associative with precedence 90
+notation "hvbox( ② { I } break term 55 T1 . break term 55 T )"
+ non associative with precedence 55
  for @{ 'SnItem2 $I $T1 $T }.
 
-notation "hvbox( ⓑ { I } break term 90 T1 . break term 90 T )"
- non associative with precedence 90
- for @{ 'SnBind2 $I $T1 $T }.
+notation "hvbox( ⓑ { a , I } break term 55 T1 . break term 55 T )"
+ non associative with precedence 55
+ for @{ 'SnBind2 $a $I $T1 $T }.
 
-notation "hvbox( ⓕ { I } break term 90 T1 . break term 90 T )"
- non associative with precedence 90
+notation "hvbox( + ⓑ { I } break term 55 T1 . break term 55 T )"
+ non associative with precedence 55
+ for @{ 'SnBind2Pos $I $T1 $T }.
+
+notation "hvbox( - ⓑ { I } break term 55 T1 . break term 55 T )"
+ non associative with precedence 55
+ for @{ 'SnBind2Neg $I $T1 $T }.
+
+notation "hvbox( ⓕ { I } break term 55 T1 . break term 55 T )"
+ non associative with precedence 55
  for @{ 'SnFlat2 $I $T1 $T }.
 
-notation "hvbox( ⓓ  term 90 T1 . break term 90 T2 )"
- non associative with precedence 90
- for @{ 'SnAbbr $T1 $T2 }.
+notation "hvbox( ⓓ { a } term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbbr $a $T1 $T2 }.
 
-notation "hvbox( ⓛ  term 90 T1 . break term 90 T2 )"
- non associative with precedence 90
- for @{ 'SnAbst $T1 $T2 }.
+notation "hvbox( + ⓓ term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbbrPos $T1 $T2 }.
 
-notation "hvbox( ⓐ  term 90 T1 . break term 90 T2 )"
- non associative with precedence 90
+notation "hvbox( - ⓓ term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbbrNeg $T1 $T2 }.
+
+notation "hvbox( ⓛ { a } term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbst $a $T1 $T2 }.
+
+notation "hvbox( + ⓛ term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbstPos $T1 $T2 }.
+
+notation "hvbox( - ⓛ term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbstNeg $T1 $T2 }.
+
+notation "hvbox( ⓐ  term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
  for @{ 'SnAppl $T1 $T2 }.
 
-notation "hvbox( ⓣ  term 90 T1 . break term 90 T2 )"
- non associative with precedence 90
+notation "hvbox( ⓝ  term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
  for @{ 'SnCast $T1 $T2 }.
 
-notation "hvbox( Ⓐ term 90 T1 . break term 90 T )"
- non associative with precedence 90
+notation "hvbox( Ⓐ term 55 T1 . break term 55 T )"
+ non associative with precedence 55
  for @{ 'SnApplV $T1 $T }.
 
 notation > "hvbox( T . break ②{ I } break term 47 T1 )"
  non associative with precedence 46
  for @{ 'DxBind2 $T $I $T1 }.
 
-notation "hvbox( T . break ⓑ { I } break term 90 T1 )"
- non associative with precedence 89
+notation "hvbox( T . break ⓑ { I } break term 48 T1 )"
+ non associative with precedence 47
  for @{ 'DxBind2 $T $I $T1 }.
 
 notation "hvbox( T1 . break ⓓ T2 )"
@@ -93,251 +117,363 @@ notation "hvbox( T1 . break ⓛ T2 )"
  for @{ 'DxAbst $T1 $T2 }.
 
 notation "hvbox( T . break ④ { I } break { T1 , break T2 , break T3 } )"
- non associative with precedence 47
+ non associative with precedence 50
  for @{ 'DxItem4 $T $I $T1 $T2 $T3 }.
 
-notation "hvbox( # [ x ] )"
+notation "hvbox( # { x } )"
  non associative with precedence 90
  for @{ 'Weight $x }.
 
-notation "hvbox( # [ x , break y ] )"
+notation "hvbox( # { x , break y } )"
  non associative with precedence 90
  for @{ 'Weight $x $y }.
 
-notation "hvbox( 𝐒 [ T ] )"
+notation "hvbox( 𝐒  ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'Simple $T }.
 
-notation "hvbox( L ⊢ break term 90 T1 ≈ break T2 )"
+notation "hvbox( L ⊢ break term 46 T1 ≈ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'Hom $L $T1 $T2 }.
 
-notation "hvbox( T1 ≃ break T2 )"
+notation "hvbox( T1 ≃ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'Iso $T1 $T2 }.
 
-notation "hvbox( T1 break [ d , break e ] ≼ break T2 )"
-   non associative with precedence 45
-   for @{ 'SubEq $T1 $d $e $T2 }.
-
 (* Substitution *************************************************************)
 
-notation "hvbox( L ⊢ break [ d , break e ] break 𝐑 [ T ] )"
+notation "hvbox( ⇧ [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
    non associative with precedence 45
-   for @{ 'Reducible $L $d $e $T }.
-
-notation "hvbox( L ⊢ break [ d , break e ] break 𝐈 [ T ] )"
-   non associative with precedence 45
-   for @{ 'NotReducible $L $d $e $T }.
+   for @{ 'RLift $d $e $T1 $T2 }.
 
-notation "hvbox( L ⊢ break [ d , break e ] break 𝐍 [ T ] )"
+notation "hvbox( T1 break ≼ [ d , break e ] break term 46 T2 )"
    non associative with precedence 45
-   for @{ 'Normal $L $d $e $T }.
+   for @{ 'SubEq $T1 $d $e $T2 }.
 
-notation "hvbox( ⇧ [ d , break e ] break T1 ≡ break T2 )"
+notation "hvbox( ≽ [ d , break e ] break term 46 T2 )"
    non associative with precedence 45
-   for @{ 'RLift $d $e $T1 $T2 }.
+   for @{ 'SubEqBottom $d $e $T2 }.
 
-notation "hvbox( ⇩ [ e ] break L1 ≡ break L2 )"
+notation "hvbox( ⇩ [ e ] break term 46 L1 ≡ break term 46 L2 )"
    non associative with precedence 45
    for @{ 'RDrop $e $L1 $L2 }.
 
-notation "hvbox( ⇩ [ d , break e ] break L1 ≡ break L2 )"
+notation "hvbox( ⇩ [ d , break e ] break term 46 L1 ≡ break term 46 L2 )"
    non associative with precedence 45
    for @{ 'RDrop $d $e $L1 $L2 }.
 
-notation "hvbox( L ⊢ break ⌘ [ T ] ≡ break k )"
+notation "hvbox( ⦃ L1, break T1 ⦄ > break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'SupTerm $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( L ⊢ break ⌘ ⦃ T ⦄ ≡ break term 46 k )"
    non associative with precedence 45
    for @{ 'ICM $L $T $k }.
 
-notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ▶ break T2 )"
+notation "hvbox( L ⊢ break term 46 T1 break ▶ [ d , break e ] break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PSubst $L $T1 $d $e $T2 }.
 
 (* Unfold *******************************************************************)
 
-notation "hvbox( @ [ T1 ] break f ≡ break T2 )"
+notation "hvbox( @ ⦃ T1 , break f ⦄ ≡ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'RAt $T1 $f $T2 }.
 
-notation "hvbox( T1 ▭ break T2 ≡ break T )"
+notation "hvbox( T1 ▭ break term 46 T2 ≡ break term 46 T )"
    non associative with precedence 45
    for @{ 'RMinus $T1 $T2 $T }.
 
-notation "hvbox( ⇧ * [ e ] break T1 ≡ break T2 )"
+notation "hvbox( ⇧ * [ e ] break term 46 T1 ≡ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'RLiftStar $e $T1 $T2 }.
 
-notation "hvbox( ⇩ * [ e ] break L1 ≡ break L2 )"
+notation "hvbox( ⇩ * [ e ] break term 46 L1 ≡ break term 46 L2 )"
    non associative with precedence 45
    for @{ 'RDropStar $e $L1 $L2 }.
 
-notation "hvbox( T1 break [ d , break e ] ▶* break T2 )"
+notation "hvbox( ⦃ L1, break T1 ⦄ > * break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'SupTermStar $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( T1 break ▶ * [ d , break e ] break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PSubstStar $T1 $d $e $T2 }.
 
-notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ▶* break T2 )"
+notation "hvbox( L ⊢ break term 46 T1 break ▶ * [ d , break e ] break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PSubstStar $L $T1 $d $e $T2 }.
 
-notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ▶▶* break T2 )"
+notation "hvbox( L ⊢ break term 46 T1 break ▶ ▶ * [ d , break e ] break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PSubstStarAlt $L $T1 $d $e $T2 }.
 
-notation "hvbox( T1 break [ d , break e ] ≡ break T2 )"
+notation "hvbox( T1 break ⊢ ▶ * [ d , break e ] break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'PSubstStarSn $T1 $d $e $T2 }.
+
+notation "hvbox( T1 break ⊢ ▶ ▶ * [ d , break e ] break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'PSubstStarSnAlt $T1 $d $e $T2 }.
+
+notation "hvbox( ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'TSubst $T1 $d $e $T2 }.
 
-notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ≡ break T2 )"
+notation "hvbox( L ⊢ break ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'TSubst $L $T1 $d $e $T2 }.
 
+notation "hvbox( ▼ ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'TSubstAlt $T1 $d $e $T2 }.
+
+notation "hvbox( L ⊢ break ▼ ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'TSubstAlt $L $T1 $d $e $T2 }.
+
 (* Static typing ************************************************************)
 
-notation "hvbox( L ⊢ break term 90 T ÷ break A )"
+notation "hvbox( L ⊢ break term 46 T ⁝ break term 46 A )"
    non associative with precedence 45
    for @{ 'AtomicArity $L $T $A }.
 
-notation "hvbox( T1 ÷ ⊑ break T2 )"
+notation "hvbox( T1 ⁝ ⊑ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'CrSubEqA $T1 $T2 }.
 
-notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 90 T1 • break T2 )"
+notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T ÷ break term 46 A )"
    non associative with precedence 45
-   for @{ 'StaticType $h $L $T1 $T2 }.
-
-(* Unwind *******************************************************************)
+   for @{ 'BinaryArity $h $L $T $A }.
 
-notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 90 T1 •* break T2 )"
+notation "hvbox( h ⊢ break term 46 L1 ÷ ⊑ break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'StaticTypeStar $h $L $T1 $T2 }.
+   for @{ 'CrSubEqB $h $L1 $L2 }.
 
-(* Reducibility *************************************************************)
+notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 • break [ g , break l ] break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'StaticType $h $g $l $L $T1 $T2 }.
 
-notation "hvbox( 𝐑 [ T ] )"
+notation "hvbox( h ⊢ break term 46 L1 • ≃ [ g ] break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'Reducible $T }.
+   for @{ 'CCongS $h $g $L1 $L2 }.
 
-notation "hvbox( L ⊢ break 𝐑 [ T ] )"
+notation "hvbox( h ⊢ break term 46 L1 • ⊑ [ g ] break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'Reducible $L $T }.
+   for @{ 'CrSubEqS $h $g $L1 $L2 }.
+
+(* Unwind *******************************************************************)
 
-notation "hvbox( 𝐈 [ T ] )"
+notation "hvbox( L1 ⊢ ⧫ * break term 46 T ≡ break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'NotReducible $T }.
+   for @{ 'Unwind $L1 $T $L2 }.
+
+(* Reducibility *************************************************************)
 
-notation "hvbox( L ⊢ break 𝐈 [ T ] )"
+notation "hvbox( L ⊢ break 𝐑 ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'NotReducible $L $T }.
+   for @{ 'Reducible $L $T }.
 
-notation "hvbox( 𝐍 [ T ] )"
+notation "hvbox( L ⊢ break 𝐈 ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'Normal $T }.
+   for @{ 'NotReducible $L $T }.
 
-notation "hvbox( L ⊢ break 𝐍 [ T ] )"
+notation "hvbox( L ⊢ break 𝐍 ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'Normal $L $T }.
 
-notation "hvbox( 𝐖𝐇𝐑 [ T ] )"
+(* this might be removed *)
+notation "hvbox( 𝐇𝐑 ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'WHdReducible $T }.
+   for @{ 'HdReducible $T }.
 
-notation "hvbox( L ⊢ break 𝐖𝐇𝐑 [ T ] )"
+(* this might be removed *)
+notation "hvbox( L ⊢ break 𝐇𝐑  ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'WHdReducible $L $T }.
+   for @{ 'HdReducible $L $T }.
 
-notation "hvbox( 𝐖𝐇𝐈 [ T ] )"
+(* this might be removed *)
+notation "hvbox( 𝐇𝐈  ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'NotWHdReducible $T }.
+   for @{ 'NotHdReducible $T }.
 
-notation "hvbox( L ⊢ break 𝐖𝐇𝐈 [ T ] )"
+(* this might be removed *)
+notation "hvbox( L ⊢ break 𝐇𝐈 ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'NotWHdReducible $L $T }.
+   for @{ 'NotHdReducible $L $T }.
 
-notation "hvbox( 𝐖𝐇𝐍 [ T ] )"
+(* this might be removed *)
+notation "hvbox( 𝐇𝐍 ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'WHdNormal $T }.
+   for @{ 'HdNormal $T }.
 
-notation "hvbox( L ⊢ break 𝐖𝐇𝐍 [ T ] )"
+(* this might be removed *)
+notation "hvbox( L ⊢ break 𝐇𝐍 ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'WHdNormal $L $T }.
+   for @{ 'HdNormal $L $T }.
 
-notation "hvbox( T1 ➡ break T2 )"
+notation "hvbox( T1 ➡ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PRed $T1 $T2 }.
 
-notation "hvbox( L ⊢ break term 90 T1 ➡ break T2 )"
+notation "hvbox( L ⊢ break term 46 T1 ➡ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PRed $L $T1 $T2 }.
 
-notation "hvbox( L1 ⊢ ➡ break L2 )"
+notation "hvbox( ⦃ L1 ⦄ ➡ break ⦃ L2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPRed $L1 $L2 }.
+
+notation "hvbox( ⦃ L1, break T1 ⦄ ➡ break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPRed $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( L ⊢ break ⦃ L1, break T1 ⦄ ➡ break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPRed $L $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( ⦃ L1 ⦄ ➡ ➡ break ⦃ L2 ⦄ )"
    non associative with precedence 45
-   for @{ 'CPRed $L1 $L2 }.
+   for @{ 'FocalizedPRedAlt $L1 $L2 }.
+
+notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 • ➡ break [ g ] break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'XPRed $h $g $L $T1 $T2 }.
+
+notation "hvbox( h ⊢ break ⦃ L1, break T1 ⦄ • ⥸ break [ g ] break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'YPRed $h $g $L1 $T1 $L2 $T2 }.
 
 (* Computation **************************************************************)
 
-notation "hvbox( T1 ➡* break T2 )"
+notation "hvbox( T1 ➡ * break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PRedStar $T1 $T2 }.
 
-notation "hvbox( L ⊢ break term 90 T1 ➡* break T2 )"
+notation "hvbox( L ⊢ break term 46 T1 ➡ * break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PRedStar $L $T1 $T2 }.
 
-notation "hvbox( L1 ⊢ ➡* break L2 )"
+notation "hvbox( T1 ➡ ➡ * break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'PRedStarAlt $T1 $T2 }.
+
+notation "hvbox( ⦃ L1 ⦄ ➡ * break ⦃ L2 ⦄ )"
    non associative with precedence 45
-   for @{ 'CPRedStar $L1 $L2 }.
+   for @{ 'FocalizedPRedStar $L1 $L2 }.
 
-notation "hvbox( L ⊢ break term 90 T1 ➡* break 𝐍 [ T2 ] )"
+notation "hvbox( ⦃ L1 , T1 ⦄ ➡ * break ⦃ L2 , T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPRedStar $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( ⦃ L1 ⦄ ➡ ➡ * break ⦃ L2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPRedStarAlt $L1 $L2 }.
+
+notation "hvbox( ⦃ L1 , T1 ⦄ ➡ ➡ * break ⦃ L2 , T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPRedStarAlt $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( L ⊢ break term 46 T1 ➡ * break 𝐍 ⦃ T2 ⦄ )"
    non associative with precedence 45
    for @{ 'PEval $L $T1 $T2 }.
 
-notation "hvbox( ⬇ * T  )"
+notation "hvbox( ⬊ * term 46 T )"
    non associative with precedence 45
    for @{ 'SN $T }.
 
-notation "hvbox( L ⊢ ⬇ * T )"
+notation "hvbox( L ⊢ ⬊ * break term 46 T )"
    non associative with precedence 45
    for @{ 'SN $L $T }.
 
-notation "hvbox( L ⊢ ⬇ * * T )"
+notation "hvbox( L ⊢ ⬊ ⬊ * break term 46 T )"
    non associative with precedence 45
-   for @{ 'SNStar $L $T }.
+   for @{ 'SNAlt $L $T }.
 
-notation "hvbox( ⦃ L, break T ⦄ break [ R ] ϵ break 〚 A 〛 )"
+notation "hvbox( ⦃ L, break T ⦄ ϵ break [ R ] break 〚 A 〛 )"
    non associative with precedence 45
    for @{ 'InEInt $R $L $T $A }.
 
-notation "hvbox( T1 break [ R ] ⊑ break T2 )"
+notation "hvbox( T1 ⊑ break [ R ] break term 46 T2 )"
    non associative with precedence 45
    for @{ 'CrSubEq $T1 $R $T2 }.
 
+notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 • ➡ * break [ g ] break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'XPRedStar $h $g $L $T1 $T2 }.
+
+notation "hvbox( ⦃ h , break L ⦄ ⊢ • ⬊ * break [ g ] break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'XSN $h $g $L $T }.
+
+notation "hvbox( h ⊢ break ⦃ L1, break T1 ⦄ • ⥸  * break [ g ] break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'YPRedStar $h $g $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( h ⊢ break ⦃ L1, break T1 ⦄ • ⭃ * break [ g ] break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'YPRedStepStar $h $g $L1 $T1 $L2 $T2 }.
+
 (* Conversion ***************************************************************)
 
-notation "hvbox( L ⊢ break term 90 T1 ⬌ break T2 )"
+notation "hvbox( L ⊢ break term 46 T1 ⬌ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PConv $L $T1 $T2 }.
 
-notation "hvbox( T1 ⊢ ⬌ break T2 )"
+notation "hvbox( ⦃ L1 ⦄ ⬌ break ⦃ L2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPConv $L1 $L2 }.
+
+notation "hvbox( ⦃ L1 , break T1 ⦄ ⬌ break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPConv $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( ⦃ L1 ⦄ ⬌ ⬌ break ⦃ L2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPConvAlt $L1 $L2 }.
+
+notation "hvbox( ⦃ L1 , break T1 ⦄ ⬌ ⬌ break ⦃ L2 , break T2 ⦄ )"
    non associative with precedence 45
-   for @{ 'CPConv $T1 $T2 }.
+   for @{ 'FocalizedPConvAlt $L1 $T1 $L2 $T2 }.
 
 (* Equivalence **************************************************************)
 
-notation "hvbox( L ⊢ break term 90 T1 ⬌* break T2 )"
+notation "hvbox( L ⊢ break term 46 T1 ⬌* break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PConvStar $L $T1 $T2 }.
 
-notation "hvbox( T1 ⊢ ⬌* break T2 )"
+notation "hvbox( ⦃ L1 ⦄ ⬌ * break ⦃ L2 ⦄ )"
    non associative with precedence 45
-   for @{ 'CPConvStar $T1 $T2 }.
+   for @{ 'FocalizedPConvStar $L1 $L2 }.
+
+notation "hvbox( ⦃ L1 , break T1 ⦄ ⬌ * break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPConvStar $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( ⦃ L1 ⦄ ⬌ ⬌ * break ⦃ L2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPConvStarAlt $L1 $L2 }.
+
+notation "hvbox( ⦃ L1 , break T1 ⦄ ⬌ ⬌ * break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPConvStarAlt $L1 $T1 $L2 $T2 }.
 
 (* Dynamic typing ***********************************************************)
 
-notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 90 T1 : break T2 )"
+notation "hvbox( ⦃ h , break L ⦄ ⊩ break term 46 T : break [ g ] )"
+   non associative with precedence 45
+   for @{ 'NativeValid $h $g $L $T }.
+
+notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : break term 46 T2 )"
    non associative with precedence 45
    for @{ 'NativeType $h $L $T1 $T2 }.
 
-notation "hvbox( h ⊢ break term 90 L1 : ⊑ break L2 )"
+notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : : break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'NativeTypeAlt $h $L $T1 $T2 }.
+
+(* Higher order dynamic typing **********************************************)
+
+notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : * break term 46 T2 )"
    non associative with precedence 45
-   for @{ 'CrSubEqN $h $L1 $L2 }.
+   for @{ 'NativeTypeStar $h $L $T1 $T2 }.