- we polarized binders to control zeta reduction

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / notation.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/notation.ma b/matita/matita/contribs/lambda_delta/basic_2/notation.ma
index 3051f1e113d4d93294e524bec55bd1344974d8bb..d6d38ef61ab87616203e0d6e7deb3a5ca59d5596 100644 (file)
--- 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 }.
 
@@ -48,27 +48,51 @@ 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 55 T1 . break term 55 T )"
+notation "hvbox( ⓑ { a , I } break term 55 T1 . break term 55 T )"
  non associative with precedence 55
- for @{ 'SnBind2 $I $T1 $T }.
+ for @{ 'SnBind2 $a $I $T1 $T }.
+
+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 55 T1 . break term 55 T2 )"
+notation "hvbox( ⓓ { a } term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbbr $a $T1 $T2 }.
+
+notation "hvbox( + ⓓ term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbbrPos $T1 $T2 }.
+
+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 @{ 'SnAbbr $T1 $T2 }.
+ for @{ 'SnAbstPos $T1 $T2 }.
 
-notation "hvbox( ⓛ  term 55 T1 . break term 55 T2 )"
+notation "hvbox( - ⓛ term 55 T1 . break term 55 T2 )"
  non associative with precedence 55
- for @{ 'SnAbst $T1 $T2 }.
+ for @{ 'SnAbstNeg $T1 $T2 }.
 
 notation "hvbox( ⓐ  term 55 T1 . break term 55 T2 )"
  non associative with precedence 55
  for @{ 'SnAppl $T1 $T2 }.
 
-notation "hvbox( â\93£  term 55 T1 . break term 55 T2 )"
+notation "hvbox( â\93\9d  term 55 T1 . break term 55 T2 )"
  non associative with precedence 55
  for @{ 'SnCast $T1 $T2 }.
 
@@ -104,7 +128,7 @@ 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 }.
 
@@ -116,21 +140,17 @@ notation "hvbox( T1 ≃ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'Iso $T1 $T2 }.
 
-notation "hvbox( T1 break [ d , break e ] ≼ break term 46 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( L ⊢ break 𝐑 [ d , break e ] break ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'Reducible $L $d $e $T }.
 
-notation "hvbox( L ⊢ break [ d , break e ] break 𝐈 [ T ] )"
+notation "hvbox( L ⊢ break  𝐈 [ d , break e ] break ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'NotReducible $L $d $e $T }.
 
-notation "hvbox( L ⊢ break [ d , break e ] break 𝐍 [ T ] )"
+notation "hvbox( L ⊢ break 𝐍 [ d , break e ] break ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'Normal $L $d $e $T }.
 
@@ -138,6 +158,14 @@ notation "hvbox( ⇧ [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'RLift $d $e $T1 $T2 }.
 
+notation "hvbox( T1 break ≼ [ d , break e ] break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'SubEq $T1 $d $e $T2 }.
+
+notation "hvbox( ≽ [ d , break e ] break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'SubEqBottom $d $e $T2 }.
+
 notation "hvbox( ⇩ [ e ] break term 46 L1 ≡ break term 46 L2 )"
    non associative with precedence 45
    for @{ 'RDrop $e $L1 $L2 }.
@@ -146,11 +174,11 @@ 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 term 46 k )"
+notation "hvbox( L ⊢ break ⌘ ⦃ T ⦄ ≡ break term 46 k )"
    non associative with precedence 45
    for @{ 'ICM $L $T $k }.
 
-notation "hvbox( L ⊢ break term 46 T1 break [ d , break e ] ▶ break term 46 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 }.
 
@@ -172,31 +200,31 @@ 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 term 46 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 46 T1 break [ d , break e ] ▶* break term 46 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 46 T1 break [ d , break e ] ▶▶* break term 46 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 term 46 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 46 T1 break [ d , break e ] ≡ break term 46 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( T1 break [ d , break e ] ≡≡ break term 46 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 term 46 T1 break [ d , break e ] ≡≡ break term 46 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 }.
 
@@ -210,71 +238,75 @@ notation "hvbox( T1 ⁝ ⊑ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'CrSubEqA $T1 $T2 }.
 
-notation "hvbox( L ⊢ break term 46 T ÷ break term 46 A )"
+notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T ÷ break term 46 A )"
    non associative with precedence 45
-   for @{ 'BinaryArity $L $T $A }.
+   for @{ 'BinaryArity $h $L $T $A }.
 
-notation "hvbox( T1 ÷ ⊑ break term 46 T2 )"
+notation "hvbox( h ⊢ break term 46 L1 ÷ ⊑ break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'CrSubEqB $T1 $T2 }.
+   for @{ 'CrSubEqB $h $L1 $L2 }.
 
-notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 • break term 46 T2 )"
+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 $L $T1 $T2 }.
+   for @{ 'StaticType $h $g $l $L $T1 $T2 }.
+
+notation "hvbox( h ⊢ break term 46 L1 • ⊑ [ g ] break term 46 L2 )"
+   non associative with precedence 45
+   for @{ 'CrSubEqS $h $g $L1 $L2 }.
 
 (* Unwind *******************************************************************)
 
-notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 •* break term 46 T2 )"
+notation "hvbox( L1 ⊢ ⧫* break term 46 T ≡ break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'StaticTypeStar $h $L $T1 $T2 }.
+   for @{ 'Unwind $L1 $T $L2 }.
 
 (* Reducibility *************************************************************)
 
-notation "hvbox( 𝐑 [ T ] )"
+notation "hvbox( 𝐑  ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'Reducible $T }.
 
-notation "hvbox( L ⊢ break 𝐑 [ T ] )"
+notation "hvbox( L ⊢ break 𝐑 ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'Reducible $L $T }.
 
-notation "hvbox( 𝐈 [ T ] )"
+notation "hvbox( 𝐈  ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'NotReducible $T }.
 
-notation "hvbox( L ⊢ break 𝐈 [ T ] )"
+notation "hvbox( L ⊢ break 𝐈 ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'NotReducible $L $T }.
 
-notation "hvbox( 𝐍 [ T ] )"
+notation "hvbox( 𝐍  ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'Normal $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 ] )"
+notation "hvbox( 𝐖𝐇𝐑 ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'WHdReducible $T }.
 
-notation "hvbox( L ⊢ break 𝐖𝐇𝐑 [ T ] )"
+notation "hvbox( L ⊢ break 𝐖𝐇𝐑  ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'WHdReducible $L $T }.
 
-notation "hvbox( 𝐖𝐇𝐈 [ T ] )"
+notation "hvbox( 𝐖𝐇𝐈  ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'NotWHdReducible $T }.
 
-notation "hvbox( L ⊢ break 𝐖𝐇𝐈 [ T ] )"
+notation "hvbox( L ⊢ break 𝐖𝐇𝐈 ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'NotWHdReducible $L $T }.
 
-notation "hvbox( 𝐖𝐇𝐍 [ T ] )"
+notation "hvbox( 𝐖𝐇𝐍 ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'WHdNormal $T }.
 
-notation "hvbox( L ⊢ break 𝐖𝐇𝐍 [ T ] )"
+notation "hvbox( L ⊢ break 𝐖𝐇𝐍 ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'WHdNormal $L $T }.
 
@@ -290,6 +322,18 @@ notation "hvbox( L1 ⊢ ➡ break term 46 L2 )"
    non associative with precedence 45
    for @{ 'CPRed $L1 $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( ⦃ 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 }.
+
 (* Computation **************************************************************)
 
 notation "hvbox( T1 ➡* break term 46 T2 )"
@@ -304,30 +348,38 @@ notation "hvbox( L1 ⊢ ➡* break term 46 L2 )"
    non associative with precedence 45
    for @{ 'CPRedStar $L1 $L2 }.
 
-notation "hvbox( L ⊢ break term 46 T1 ➡* break 𝐍 [ T2 ] )"
+notation "hvbox( L ⊢ break term 46 T1 ➡* break 𝐍 ⦃ T2 ⦄ )"
    non associative with precedence 45
    for @{ 'PEval $L $T1 $T2 }.
 
-notation "hvbox( â¬\87 * term 46 T  )"
+notation "hvbox( â¬\8a * term 46 T  )"
    non associative with precedence 45
    for @{ 'SN $T }.
 
-notation "hvbox( L â\8a¢ â¬\87 * term 46 T )"
+notation "hvbox( L â\8a¢ â¬\8a * break term 46 T )"
    non associative with precedence 45
    for @{ 'SN $L $T }.
 
-notation "hvbox( L â\8a¢ â¬\87 â¬\87 * term 46 T )"
+notation "hvbox( L â\8a¢ â¬\8a â¬\8a * break term 46 T )"
    non associative with precedence 45
    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 term 46 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 }.
+
 (* Conversion ***************************************************************)
 
 notation "hvbox( L ⊢ break term 46 T1 ⬌ break term 46 T2 )"
@@ -350,14 +402,20 @@ notation "hvbox( T1 ⊢ ⬌* break term 46 T2 )"
 
 (* Dynamic typing ***********************************************************)
 
+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 L ⦄ ⊢ break term 46 T1 :: break term 46 T2 )"
+notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : : break term 46 T2 )"
    non associative with precedence 45
    for @{ 'NativeTypeAlt $h $L $T1 $T2 }.
 
-notation "hvbox( h ⊢ break term 46 L1 : ⊑ break term 46 L2 )"
+(* 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 }.