Contents

• JSON -- JavaScript Object Notation
• : Purpose
• : See Also
• : Syntax of JSON
• : : Standard Syntactic Shorthand
• : : Lexical rules
• : : Objects
• : : Arrays
• : : Values
• : Static Semantics of JSON -- UML -- Abstract Syntax
• : Semantics of JSON

JSON -- JavaScript Object Notation

Purpose

A light weight and language independent notation for exchanging data between different programs. It is based on the Javascript notations.

Compare YAML [ languages.html#YAML ] and XML [ languages.html#XML ] which have similar purposes but different philosophies.

See Also

1. JSON::= See http://www.json.org/. [ JSON ] (wikipedia entry).

   Syntax of JSON

   Based on JSON above.

   Standard Syntactic Shorthand

   1. #X::= "" | X #X.
   2. O(X)::= ""|X, optional.
   3. L(x)::= X | X "," L(X), lists.
   4. N(X)::= X #X.

      Lexical rules

      Extra whitespace between lexemes are ignored.

      Objects

   5. object::= "{" "}" | "{" L(member) "}".
   6. member::= string ":" value.

       	{"species":"Snake", "id":1234, "length":5.5, "male":true}

      Arrays

   7. array::="[" L(value) "]".

       	[1,4,9,16]

       	[true,false,true,false]

      JSON arrays can be heterogenous

       	[1,true,"foo"]

      with thanks to Laurent(5:30pm California time Apr 17 2012).

      Values

   8. value::= string | number | object | array | true | false| null.

   9. true::lexeme.
   10. false::lexeme.
   11. null::lexeme.

   12. string::=quotes quotes | quotes N(char) quotes.
   13. quotes::lexeme= "\"".

   14. char::=any Unicode character except quotes or backslash or control character | escaped_character | unicoded_character.
   15. backslash::lexeme= "\\".

   16. escaped_character::= backslash ( quotes | backslash | slash | "b" | "f" | "n"| "r" | "t").
       Table

       Escaped Character	Meaning
       \"	"
       \\	\
       \/	/
       \b	Backspace
       \f	Formfeed
       \n	Newline
       \r	Return
       \t	Horizontal tab

       
       (Close Table)
       

   17. unicode_character::= hex_digit ^ 4, four hex digits.

   18. hex_digit::= "0..9" | ignore_case("A".."F"), (Stephen Parker checked this out on April 17th 2012.

   19. number::= int | int frac | int exp | int frac exp.

   20. int::=O("-") ( digit | digit1_9 digits ).

   21. digits::= N(digit), 1 or more digits.
   22. digit::="0".."9".
   23. digit1_9::="1".."9".

   24. frac::= dot digits.
   25. exp::=e digits.

   26. dot::lexeme= ".".
   27. e::= ("e"|"E")O("+"|"-").

   . . . . . . . . . ( end of section Syntax of JSON) <<Contents | End>>

   Static Semantics of JSON -- UML -- Abstract Syntax

   

   Note: above needs some work!

   Semantics of JSON

   JSON describes data/objects by a human readable interpretation of the different Values:
   1. JSON_Value::= String | Numbers | @ | {{}} | String <>-> JSON_Value | Nat0<>->JSON_Value.

      The semantic sets map nicely into MATHS sets.

   2. String::=#Unicode. [ maths/types.html#Unicode ]

   3. Numbers::=Integer | Real.
   4. Integer::= See http://csci.csusb.edu/dick/maths/logic_6_Numbers..Strings.html#Integer.
   5. Real::= See http://csci.csusb.edu/dick/maths/math_42_Numbers.html#Real Numbers.

      We use a partial maps ( dom <>-> cod) to represent the meaning of JSON objects and arrays. Nat0 is the standard symbol for the set of natural numbers including 0.

   6. Nat0::= See http://csci.csusb.edu/dick/maths/math_42_Numbers.html#Nat0.

      Next we describe the meaning map from the syntax to the semantics. The traditional symbol for this mapping is μ.

   7. μ::=meaning.
   8. meaning:: Value -> JSON_Value.

      I define it "piecewise" on each type of value in turn --

   9. μ(true)::= STANDARD.true.
   10. μ(false)::= STANDARD.false.
   11. μ(null)::={}, possibly.
   12. μ("")::="".
   13. For m: Member, μ(m)::= (m.string +> m.value).
   14. For x:Object, μ(x)::= |[m:x.member]μ(x).
   15. For z:Array, TBD.

   . . . . . . . . . ( end of section Semantics of JSON) <<Contents | End>>

. . . . . . . . . ( end of section JSON -- JavaScript Object Notation) <<Contents | End>>

End