8. JSON In Line Math Expressions

JSON In-Line Math Expressions

Still under construction

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Quick Language Explanation

There are terms that might be confusing. So here are some synonyms and explanations:

• "returns" / "yields" / "results in": The result of an operation or function.
• "parameter" / "argument": The values you pass to an operation or function.

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Variables

• Names may not start with digits (0-9)
• Names may only contain letters (A-Z and a-z), digits (0-9) and underscores (_)

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Types

• int: Integers, eg. 0, 7, -87.
• double: Floating point numbers, eg. 0.0, 1.7, -43.467, 2.
• vec3: 3-dimensional vector made of 3 double elements representing any position or motion in a world.
• boolean: Boolean (logical) values, eg. either true or false.
• tag: NBT compound tags (see Minecraft wiki).
• string: A sequence of characters, eg. 'hello', 'ABCdef123_', 'Let us also do some Spaces!!'.

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Type Conversions

These are the possible type conversions (eg. whenever a double is required you can also put in a value of type int, but not the other way around):

• int -> double
• int -> string
• double -> string
• boolean -> string

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Type Literals

E.g. how to make type values with text:

• int: Just type the integer, eg. 0, 7, -87.
• double: Type the floating point number using a ., eg. 0.0, 1.7, -43.467, 2.
• vec3: Use the vec3 function mentioned below, eg. vec3(2, 4, 6).
• boolean: Type the logical values, eg. either true or false.
• tag: To make a new compound tag use the new_tag supplier function mentioned below and populate that using the put_nbt_* functions, eg. put_nbt_int(new_tag(), 'my_key', 7) makes a new tag and attaches the integer 7 with the key my_key resulting in {"my_key": 7}.
• string: Write the sequence of characters wrapped by ' characters, eg. 'hello', 'ABCdef123_', 'Let us also do some Spaces!!'.

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Operations

These tables represent all binary operations defined by types. If two operants have different types the resulting type is looked up and the non-matching operant is converted according to the type conversions definition. Eg. Adding a double and a int together will convert the later into a double first and then sum these two up.

Any operation between 2 types not being defined here means that it is also not defined in the system. Attempting such an operation will yield no result.

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Addition (+) / Subtraction (-)

+ / -	int	double
int	int	double
double	double	double

+ / -	vec3
vec3	vec3

The + operation also works with strings. Whenever a string is added together with another string, these are concatenated, eg. 'abc' + 'def' results in the string 'abcdef'.

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Multiplication (*) / Division (/)

* / /	int	double	vec3
int	int	double	vec3
double	double	double	vec3
vec3	vec3	vec3

Dividing by 0 yields no result.

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Remainder (%)

Works only with the int type. Remainder by 0 yields no result.

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Comparison (==, !=, >, >=, <, <=)

All of these comparison operators allow you to compare 2 values. They always yield a boolean as result depending on whether the comparison is true or false (eg. 0 <= 1 is obviously true, 'AB' == 'CD' is false because they are not equal). The comparison operators are available for the following types:

• == (equality): int, double, vec3, boolean, string
• != (inequality): int, double, vec3, boolean, string
• > (greater than): int, double
• >= (greater than or equal): int, double
• < (less than): int, double
• <= (less than or equal): int, double

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Boolean AND (&&)

&&	false	true
false	false	false
true	false	true

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Boolean OR (||)

&&	false	true
false	false	true
true	true	true

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Boolean NOT (!)

This is a unary operation where you write the ! symbol in front of the operant.

• !true -> false
• !false -> true

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Conditional (?:)

This is a ternary operation (3 operants) which yields the 2nd or 3rd operant depending on if the 1st operant is true or not:

• condition ? value_if_true : value_if_false

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Examples:

• a > b ? a : b will always return the bigger value of a or b (this is the same as the max function).
• flag ? var : 12 will return var if flag is true, otherwise returns 12.

You can also stack these:

• a ? b : (c ? d : e)

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Functions

All functions are explained here. This is to be read as function_name(argument_types) -> result_type:

• function_name: Name of the function
• argument_types: The amount of arguments and their types
• result_type: Every function yields a single result with a defined type

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Supplier Functions (no arguments)

• pi() -> double: The value of PI.
  • pi() -> 3.14159265359...
• tag() -> tag: Create a new empty nbt compound tag.
• sqrt2() -> double: The value of the square root of 2.
  • sqrt2() -> 1.41421356237...
• random_int() -> int: Any possible integer x with -2147483648 <= x <= 2147483647 (2 to the power of 32 different values).
  • random_int() -> -67
• random_double() -> int: Any possible double x with 0 <= x < 1.
  • random_double() -> 0.78125
• random_uuid() -> string: A random UUID.
  • random_uuid() -> '139AA4B1-D4EC-4A01-9BA0-18E5C32BFCF2'
• new_tag() -> tag: A new and empty NBT compound tag.

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Unary Functions (1 argument)

• round(double) -> int: Rounds the double number towards the closest int number with .5 being rounded up.
  • round(1.2) -> 1
  • round(2.5) -> 2
  • round(3.7) -> 4
  • round(-5.5) -> -5
  • round(-1.9) -> -2
  • round(6.0) -> 6
• floor(double) -> int: Rounds down the double number to an int number.
  • floor(1.2) -> 1
  • floor(2.5) -> 2
  • floor(3.7) -> 3
  • floor(-5.5) -> -6
  • floor(-1.9) -> -2
  • floor(6.0) -> 6
• ceil(double) -> int: Rounds up the double number to an int number.
  • ceil(1.2) -> 2
  • ceil(2.5) -> 3
  • ceil(3.7) -> 4
  • ceil(-5.5) -> -5
  • ceil(-1.9) -> -1
  • ceil(6.0) -> 6
• sqrt(double) -> double: Calculates the square root of a double number. This number must be positive.
  • sqrt(9.0) -> 3.0
  • sqrt(2) -> 1.41421356237...
• get_x(vec3) -> double: The x-coordinate of the vec3 vector.
• get_y(vec3) -> double: The y-coordinate of the vec3 vector.
• get_z(vec3) -> double: The z-coordinate of the vec3 vector.
• length(vec3) -> double: Calculates the length of the vec3 vector.
• normalize(vec3) -> vec3: Normalizes the vec3 vector (yields the argument vector divided by its length).
• sin(double) -> double: Calculates the sinus of the double angle, in radians.
• cos(double) -> double: Calculates the cosinus of the double angle, in radians.
• asin(double) -> double: Calculates the asinus (inverse sinus, or sin-1) of the double angle, in radians.
• acos(double) -> double: Calculates the acosinus (inverse cosinus, or cos-1) of the double angle, in radians.
• to_radians(double) -> double: Converts the double angle from radians to degrees.
• to_degrees(double) -> double: Converts the double angle from degrees to radians. . uuid_from_string(string) -> string: Takes any string as seed for the random generator to generate a new UUID from. Calling this method any amount of times with the same parameter always yields the same UUID as result.
• next_int(int) -> int: Generates a random positive integer up to but excluding the value of the parameter, eg. if x is the parameter and y is the result then 0 <= y < x.
  • next_int(10) -> 3

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Binary Functions (2 arguments)

• min(int, int) -> int / min(double, double) -> double: Gives you the lower value of the 2 arguments.
  • min(1, 2) -> 1
  • min(2, 1) -> 1
  • min(-5, -2) -> -5
  • min(-7, -7) -> -7
• max(int, int) -> int / max(double, double) -> double: Gives you the higher value of the 2 arguments.
  • max(1, 2) -> 2
  • max(2, 1) -> 2
  • max(-5, -2) -> -2
  • max(-7, -7) -> -7
• nbt_contains(tag, string) -> boolean: Returns true if the given tag contains a value of the given string name, otherwise returns false.
• get_nbt_int(tag, string) -> int: Returns the int that is on the given tag with the given string name.
• get_nbt_double(tag, string) -> int: Returns the double that is on the given tag with the given string name.
• get_nbt_boolean(tag, string) -> boolean: Returns the boolean that is on the given tag with the given string name.
• get_nbt_compound_tag(tag, string) -> tag: Returns the tag that is on the given tag with the given string name.
• get_nbt_string(tag, string) -> string: Returns the string that is on the given tag with the given string name.
• get_nbt_uuid(tag, string) -> string: Returns the string that is on the given tag with the given string name in form of a UUID.
• get_nbt_vec3(tag, string) -> vec3: Returns the vec3 that is on the given tag with the given string name in form of a list of type double.

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Ternary Functions (3 arguments)

• vec3(double, double, double) -> vec3: Constructs a vec3 made of the 3 double arguments, with the first double becoming the x-coordinate, the second double becoming the y-coordinate, and the third double becoming the z-coordinate.
• put_nbt_int(tag, string, int) -> tag: Makes a copy of the given tag and puts the given int on it under the given string name then returns this new tag.
• put_nbt_double(tag, string, double) -> tag: Makes a copy of the given tag and puts the given double on it under the given string name then returns this new tag.
• put_nbt_boolean(tag, string, boolean) -> tag: Makes a copy of the given tag and puts the given boolean on it under the given string name then returns this new tag.
• put_nbt_compound_tag(tag, string, boolean) -> tag: Makes a copy of the given tag (1st parameter) and puts the given tag (2nd parameter) on it under the given string name then returns this new tag.
• put_nbt_string(tag, string, string) -> tag: Makes a copy of the given tag and puts the given string (2nd parameter) on it under the given string name (3rd parameter) then returns this new tag.
• put_nbt_uuid(tag, string, string) -> tag: Makes a copy of the given tag and puts the given string (2nd parameter) on it under the given string name (3rd parameter) in form of a UUID then returns this new tag.
• put_nbt_vec3(tag, string, vec3) -> tag: Makes a copy of the given tag and puts the given vec3 on it under the given string name in form of a list of type double then returns this new tag.

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Compiler Grammar

More specifics about this compiler.

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Operator Precedence

• Binds strongest
• ()
• - / !
• * / / / %
• + / -
• > / >= / < / <=
• == / !=
• &&
• ||
• ?:
• Binds weakest

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Compiler Definition

This is the exact definition of the compiler, for those interested in it.

-> expression

variable      := ( letter | "_" ) { letter | digit | "_" } .
value         := digit { digit } [ "." { digit } ] .
function_call := letter { letter | digit | "_" } "(" [ expression { "," expression } ] ")" .

expression    := conditional .

conditional   := disjunction [ "?" disjunction ":" disjunction ] .

disjunction   := conjunction { "||" conjunction } .
conjunction   := comparison { "&&" comparison } .

comparison    := relation { ( "==" | "!=" ) relation } .
relation      := sum { ( ">" | ">=" | "<" | "<=" ) sum } .

sum           := product { ( "+" | "-" ) product } .
product       := factor { ( "*" | "/" | "%" ) factor } .

factor        := [ "-" | "!" ] ( variable | value | "(" expression ")" | function_call ) | "'" string "'" .