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Merge pull request #1677 from AleoHQ/abnf-natural-to-numeral
Abnf natural to numeral
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Collin Chin
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@ -635,56 +635,56 @@ annotation-name = "@" identifier
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Go to: _[identifier](#user-content-identifier)_;
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A natural (number) is a sequence of one or more decimal digits.
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A numeral is a sequence of one or more decimal digits.
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We allow leading zeros, e.g. `007`.
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<a name="natural"></a>
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<a name="numeral"></a>
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```abnf
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natural = 1*decimal-digit
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numeral = 1*decimal-digit
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```
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Unsigned literals are naturals followed by unsigned types.
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Unsigned literals are numerals followed by unsigned types.
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<a name="unsigned-literal"></a>
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```abnf
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unsigned-literal = natural ( %s"u8" / %s"u16" / %s"u32" / %s"u64" / %s"u128" )
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unsigned-literal = numeral ( %s"u8" / %s"u16" / %s"u32" / %s"u64" / %s"u128" )
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```
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Go to: _[natural](#user-content-natural)_;
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Go to: _[numeral](#user-content-numeral)_;
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Signed literals are naturals followed by signed types.
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Signed literals are numerals followed by signed types.
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<a name="signed-literal"></a>
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```abnf
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signed-literal = natural ( %s"i8" / %s"i16" / %s"i32" / %s"i64" / %s"i128" )
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signed-literal = numeral ( %s"i8" / %s"i16" / %s"i32" / %s"i64" / %s"i128" )
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```
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Go to: _[natural](#user-content-natural)_;
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Go to: _[numeral](#user-content-numeral)_;
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Field literals are naturals followed by the type of field elements.
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Field literals are numerals followed by the type of field elements.
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<a name="field-literal"></a>
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```abnf
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field-literal = natural %s"field"
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field-literal = numeral %s"field"
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```
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Go to: _[natural](#user-content-natural)_;
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Go to: _[numeral](#user-content-numeral)_;
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There are two kinds of group literals.
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One is a single natural followed by the type of group elements,
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which denotes the scalar product of the generator point by the natural.
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One is a single numeral followed by the type of group elements,
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which denotes the scalar product of the generator point by the numeral.
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The other kind is not a token because it allows some whitespace inside;
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therefore, it is defined in the syntactic grammar.
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<a name="product-group-literal"></a>
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```abnf
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product-group-literal = natural %s"group"
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product-group-literal = numeral %s"group"
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```
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Go to: _[natural](#user-content-natural)_;
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Go to: _[numeral](#user-content-numeral)_;
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Boolean literals are the usual two.
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@ -991,7 +991,7 @@ An array type consists of an element type
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and an indication of dimensions.
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There is either a single dimension,
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or a tuple of one or more dimensions.
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Each dimension is a natural.
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Each dimension is a numeral.
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<a name="array-type"></a>
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```abnf
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@ -1003,10 +1003,10 @@ Go to: _[array-dimensions](#user-content-array-dimensions), [type](#user-content
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<a name="array-dimensions"></a>
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```abnf
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array-dimensions = natural / "(" natural *( "," natural ) ")"
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array-dimensions = numeral / "(" numeral *( "," numeral ) ")"
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```
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Go to: _[natural](#user-content-natural)_;
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Go to: _[numeral](#user-content-numeral)_;
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The keyword `Self` denotes the enclosing circuit type.
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@ -1069,10 +1069,10 @@ because it consists of affine point coordinates.
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<a name="group-coordinate"></a>
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```abnf
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group-coordinate = [ "-" ] natural / "+" / "-" / "_"
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group-coordinate = [ "-" ] numeral / "+" / "-" / "_"
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```
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Go to: _[natural](#user-content-natural)_;
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Go to: _[numeral](#user-content-numeral)_;
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<a name="affine-group-literal"></a>
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@ -1275,7 +1275,7 @@ Go to: _[expression](#user-content-expression)_;
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<a name="postfix-expression"></a>
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```abnf
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postfix-expression = primary-expression
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/ postfix-expression "." natural
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/ postfix-expression "." numeral
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/ postfix-expression "." identifier
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/ identifier function-arguments
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/ postfix-expression "." identifier function-arguments
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@ -1285,7 +1285,7 @@ postfix-expression = primary-expression
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/ postfix-expression "[" [expression] ".." [expression] "]"
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```
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Go to: _[expression](#user-content-expression), [function-arguments](#user-content-function-arguments), [identifier](#user-content-identifier), [named-type](#user-content-named-type), [natural](#user-content-natural), [postfix-expression](#user-content-postfix-expression), [primary-expression](#user-content-primary-expression)_;
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Go to: _[expression](#user-content-expression), [function-arguments](#user-content-function-arguments), [identifier](#user-content-identifier), [named-type](#user-content-named-type), [numeral](#user-content-numeral), [postfix-expression](#user-content-postfix-expression), [primary-expression](#user-content-primary-expression)_;
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Unary operators have the highest operator precedence.
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@ -59,7 +59,7 @@
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; usable as last resort in the definiens of a nonterminal.
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; While BNF allows arbitrary terminals,
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; ABNF uses only natural numbers as terminals,
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; ABNF uses only natural numbers (i.e. non-negative integers) as terminals,
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; and denotes them via:
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; (i) binary, decimal, or hexadecimal sequences,
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; e.g. `%b1.11.1010`, `%d1.3.10`, and `%x.1.3.A`
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@ -451,30 +451,30 @@ identifier = letter *( letter / decimal-digit / "_" )
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annotation-name = "@" identifier
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; A natural (number) is a sequence of one or more decimal digits.
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; A numeral is a sequence of one or more decimal digits.
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; We allow leading zeros, e.g. `007`.
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natural = 1*decimal-digit
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numeral = 1*decimal-digit
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; Unsigned literals are naturals followed by unsigned types.
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; Unsigned literals are numerals followed by unsigned types.
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unsigned-literal = natural ( %s"u8" / %s"u16" / %s"u32" / %s"u64" / %s"u128" )
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unsigned-literal = numeral ( %s"u8" / %s"u16" / %s"u32" / %s"u64" / %s"u128" )
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; Signed literals are naturals followed by signed types.
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; Signed literals are numerals followed by signed types.
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signed-literal = natural ( %s"i8" / %s"i16" / %s"i32" / %s"i64" / %s"i128" )
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signed-literal = numeral ( %s"i8" / %s"i16" / %s"i32" / %s"i64" / %s"i128" )
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; Field literals are naturals followed by the type of field elements.
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; Field literals are numerals followed by the type of field elements.
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field-literal = natural %s"field"
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field-literal = numeral %s"field"
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; There are two kinds of group literals.
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; One is a single natural followed by the type of group elements,
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; which denotes the scalar product of the generator point by the natural.
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; One is a single numeral followed by the type of group elements,
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; which denotes the scalar product of the generator point by the numeral.
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; The other kind is not a token because it allows some whitespace inside;
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; therefore, it is defined in the syntactic grammar.
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product-group-literal = natural %s"group"
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product-group-literal = numeral %s"group"
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; Boolean literals are the usual two.
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@ -640,11 +640,11 @@ tuple-type = "(" [ type 1*( "," type ) ] ")"
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; and an indication of dimensions.
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; There is either a single dimension,
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; or a tuple of one or more dimensions.
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; Each dimension is a natural.
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; Each dimension is a numeral.
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array-type = "[" type ";" array-dimensions "]"
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array-dimensions = natural / "(" natural *( "," natural ) ")"
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array-dimensions = numeral / "(" numeral *( "," numeral ) ")"
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; The keyword `Self` denotes the enclosing circuit type.
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; It is only allowed inside a circuit type declaration.
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@ -683,7 +683,7 @@ named-type = identifier / self-type / scalar-type
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; This is an affine group literal,
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; because it consists of affine point coordinates.
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group-coordinate = [ "-" ] natural / "+" / "-" / "_"
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group-coordinate = [ "-" ] numeral / "+" / "-" / "_"
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affine-group-literal = "(" group-coordinate "," group-coordinate %s")group"
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@ -793,7 +793,7 @@ circuit-expression = circuit-construction
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function-arguments = "(" [ expression *( "," expression ) ] ")"
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postfix-expression = primary-expression
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/ postfix-expression "." natural
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/ postfix-expression "." numeral
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/ postfix-expression "." identifier
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/ identifier function-arguments
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/ postfix-expression "." identifier function-arguments
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