CastleScript language
Simple scripting language for Castle Game Engine

1. Introduction

CastleScript (previously "KambiScript") is a simple scripting language used in our Castle Game Engine. You can use it in VRML/X3D Script nodes. Also it's syntax of mathematical expressions is used throughout our engine, for example glplotter and gen_function (which are completely not related to X3D) use this syntax to define function expressions.

The language is deliberately very simple. It's a scripting language, with features inspired by many other languages, and by author's laziness. For example I was too lazy to add if, while and such constructs to the grammar, instead you have built-in functions like if(condition, then_code, else_code). This language doesn't try to compete with other scripting languages (like ECMAScript, commonly used in VRML/X3D scripting). It's not suitable for larger programs (for starters, you cannot define your own types). Also it's specific to our engine, and probably always will be.

That said, the language is powerful enough for many uses. You can process all X3D field types with it, including strings, vectors, matrices and even images. Also arrays (MFXxx fields) are covered. There are many built-in functions and operators, heavily overloaded for all types where they apply (for example, you can add numbers, vectors, matrices or strings). It's an integral part of our engine, without the need for any external libraries. And do note that our engine doesn't support (yet) ECMAScript for X3D scripting at all, so this is the only way to do scripting for now (without writing and compiling any ObjectPascal code).

Programmers may also be interested that language implementation is flexible, you can extend it easily from ObjectPascal (adding new data-types and built-in functions), for many uses (not necessarily related with X3D). The language is completely safe (that is, there's no possibility for malicious script author to do something harmful) simply because the language is a closed data-processing language (the only I/O routines are image_load(url) and writeln(string), and they expose functionality that is possible anyway with pure non-scripted X3D).

2. Writing scripts inside X3D Script URLs

URLs in Script node starting with castlescript: are understood to contain program in CastleScript language. URLs to external files with extension .castlescript point to whole files in CastleScript language. (Deprecated: also kambiscript: as a protocol and .kambiscript as an extension are recognized.) Like

Script {
  inputOnly SFFloat foo
  outputOnly SFFloat foo_plus_one

  url "castlescript:
function foo(value, timestamp)
foo_plus_one := value + 1
"
}

Script {
  url "my_script.castlescript"
}

3. Examples

Some examples of simple mathematical expressions for glplotter:

  sin(x) ^ 10
  2 * (cos(ln(x)) - 1)
  sin(x) > cos(x)
  or( sin(x) > cos(x), sin(x) > 0 )

Some example of simple program for X3D script node:

Script {
  # Let's assume some TouchSensor.touchTime is routed here.
  # When user clicks on this touch sensor, you want to close the door
  # if they are open, or open them if they are closed.
  inputOnly SFTime touch_time

  initializeOnly SFBool open FALSE

  # Let's assume this is routed to some TimeSensor.set_startTime
  # that starts closing animation.
  outputOnly SFTime close_time

  # Let's assume this is routed to some TimeSensor.set_startTime
  # that starts opening animation.
  outputOnly SFTime open_time

  url "castlescript:
function touch_time(value, timestamp)
if (open,
    close_time := timestamp,
    open_time := timestamp);
open := not(open)
"
}

Example script behavior above could also be done by combining BooleanToggle, BooleanFilter, TimeTrigger X3D nodes. But script is already simpler and shorter, and allows you to trivially add other interesting things.

# Simple converter from SFString to MFString using built-in array function.
Script {
  inputOnly SFString input
  outputOnly MFString output
    url "castlescript:
function input(value, timestamp)
  output := array(value)
"
}

Some larger examples:

  • ball_game.x3dv — a small X3D game, with whole game logic implemented in CastleScript (key handling by KeySensor node). Can be played in any X3D browser supporting CastleScript, like view3dscene or any of the example X3D browser components in engine sources.

  • edit_texture.x3dv — a toy image editor. Again, it's a pure X3D file (you can open it and use with any X3D browser supporting CastleScript). Uses CastleScript to implement various simple image editing functions. It's a toy, not to be treated as a serious image editor of course (there is no possibility to save created image for starter, since CastleScript doesn't allow to save files from X3D for safety reasons.) But it shows that even image processing is quite easy with CastleScript.

  • particles.x3dv — a simple particle engine. Whole particles animation, logic (randomization, speed, gravity) is implemented in CastleScript. "Particles" are rendered as points and lines (PointSet, IndexedLineSet).

4. Syntax

Syntax is free-form, the only use of whitespace (including newlines, or any indentation) is to separate tokens when needed (for example, between two identifiers).

Comments are within curly braces: { this is a comment } (Pascal-like).

4.1. Types and constants

Types are never explicitly declared, and are checked at runtime. Four core types are available:

  1. Integers. Syntax of integer constants is obvious, like 123. Built-in function int(...) allows you to convert other core types into integer.

    We use 64-bit signed integers (although for X3D long/int32 fields, they will have to fit within 32-bit.)

    Specifically for comfortable processing of X3D KeySensor node events actionKeyPress/Release you have 20 key constants available: ACTION_KEY_F1, ... ACTION_KEY_F12, ACTION_KEY_HOME, etc. (see KeySensor specification for full list).

  2. Floats. Syntax of float constants is also obvious, like 3.1415. You have constants pi and enat (Euler's number). Built-in function float(...) allows you to convert other core types into float.

    Precision: uses the best floating-point type precision on given platform, which means at least Double, and on many platforms Extended.

  3. Booleans. Two obvious constants are available, false and true (case is ignored, as usual in CastleScript, so you can also write uppercase FALSE or TRUE like in classic encoding). Built-in function bool(...) allows you to convert other core types into boolean.

  4. Strings. Syntax of constants is Pascalish (in apostrophes, and two consecutive apostrophes inside mean that you want a single literal apostrophe character). For example 'He said "It''s mine."'. Apostrophe was chosen not only because, y'know, it's Pascalish :), but also because it makes embedding CastleScript code within VRML/X3D string easier (no need to escape quotes by backslashes). You can make actual newlines within the string, like in VRML/X3D. For example:

    Script {
      # Let's assume some TouchSensor.touchTime is routed here.
      inputOnly SFTime touch_time
      outputOnly MFString text
    
      url "castlescript:
    function touch_time(value, timestamp)
      text := array(
        'First string of text clicked on ' + string(value),
        'Second string of text.
    Still second string of text.
    Simply make a newline in the string literal to get a newline inside the string.'
      )
    "
    }
    

    Built-in function string(...) allows you to convert other core types into string.

The one and only implicit type conversion (promotion) of types is from integer to float (for example, my_float := 44 works, you don't have to write my_float := 44.0). In particular, note that boolean type is not interchangeable with integer like in C. If you want to convert between boolean and integer, you have to convert explicitly by bool(my_int) or int(my_bool), like in Pascal. The only exception is when using CastleScript solely for mathematical expressions (like in glplotter and gen_function, internally using ParseFloatExpression function): in this case, result is always implicitly converted to float, like it would be embedded within float(...) call.

When using CastleScript inside X3D scripts, internally you have all the X3D field types available (which means that vec2f, vec3f, vec4f, matrix, image and others are included). There is no special syntax for reading/writing other types, instead you have many functions to construct and set them. For example for vec3f type you have "constructor" vector(x, y, z) , reader for particular component vector_get(vector, index), and setter for particular component vector_set(vector, index, component_value). Even images have functions to create and modify them, which means that you can use CastleScript to perform basic image creation and processing.

Also array types are internally available, for X3D multiple-value (MFXxx) types. Again no special syntax is available (sorry, no bracket parenthesis), but there are functions to construct array array(item1, item2, ...), read component array_get(array, index) and set component array_set(array, index, component_value).

4.2. Programs and expressions

Program is just a set of functions. The engine will take care to call function xxx when input event of the same name will arrive.

Expressions and instructions are the same thing within the language. For example, "assignment" is an instruction, since it causes calculation of the right operand and assigning it to the left operand, but it's also an "expression", since it returns the value (the assigned value). So "chained" assignment, like in C, is possible (although usually discouraged, to not obfuscate the code): a := b := x + y works. In the rest of this description, terms "instruction" and "expression" mean exactly the same thing.

Function starts from the function keyword, then function name (identifier), then list of 0 or more parameters (identifiers separated by commas), always within parenthesis. For functions within X3D Script nodes: initialize and shutdown must take exactly one parameter (timestamp of the event: SFTime), functions called by incoming events must take exactly two parameters (value send to the event, and timestamp: SFTime).

Function body is just a sequence of expressions separated by semicolon. Formally, function body is actually a single expression, but we have a semicolon operator: A;B means "calculate A, ignore result, then calculate and return result of B". For now, result of functions body is ignored (so all our functions are in fact procedures). Semicolon works like a delimiter (not a terminator, so it's used only between instructions).

Note that the way semicolon and expressions are defined means that we don't need any special syntax for compound instruction (like begin end in Pascal or { } in C). Instead, normal parenthesis may be used if necessary to group instructions.

An assignment instruction is an operand, followed by the assignment operator := (Pascal-like), followed by an expression to calculate value to assign.

For X3D scripts, you are allowed to assign to output events and to fields (exposed or not). Events sending behavior follows ECMAScript standard:

  • Assigning value to initializeOnly (not exposed) field is simple, it just assigns value to this field. You can use initializeOnly fields as "variables" available for your scripts (since CastleScript doesn't allow you to declare or use new variables within the program, for now).

  • Assigning value to output event results in sending this event, assigning to exposed field results in sending this to input event of this field.

    Following ECMAScript standard, events are not send immediately (right at the assignment), instead they are stacked and send when script function finished execution. When you assigned multiple values for the same field/event, only the last one is send. In case of multiple-value fields, the combined end value is send. For example, assuming output is an outputOnly event of MFFloat type:

    function foo(value, timestamp)
      output := array(0.0, 1.0, 2.0, 3.0);
      array_set(output, 1, 666.0);
      array_set(output, 2, 44.0)
    

    The example above will send one output event with value (0.0, 666.0, 44.0, 3.0).

Right side of the assignment instruction is the value to calculate and assign. In short, a normal mathematical expression is allowed there, just like you seen in all programming languages. We have multiplicative operators (/, *, ^, %), we have additive operators (+, -) with lower priority, we have comparison operators (<, >, <=, >=, = or <>) with even lower priority. We have all standard math functions. Built-in functions and operators are overloaded for all suitable types. Section below gives a full list of operators and functions.

5. Built-in functions

5.1. Type conversion

  • int(...) converts a "core" type to an integer.

    Float is converted to int by discarding it's fractional part (like in C; for positive numbers, this is like floor, for negative this is like ceil). There are also functions floor, ceil and round that convert float to an integer with other rounding modes.

    Bool is converted to 0 (false) or 1 (true). Yes, unlike most languages that usually don't guarantee "true" value (saying "true" is anything <> 0), CastleScript actually guarantees that "true" will result in 1. This is sometimes useful in smart mathematical expressions (like my_int := 1 - int(my_bool)).

    String is converted to int by, well, converting string to integer using standard decimal notation (int('123') = 123).

  • float(...) converts a "core" type to a float.

    Integer is converted obviously. Actually it's never needed to explicitly cast integer to float, this conversion happens automatically, like in most programming languages.

    Bool is converted to 0.0 (false) or 1.0 (true).

    String is converted to float by parsing number from string, like float('3.14') = 3.14.

  • bool(...) converts a "core" type to a boolean.

    Integers and floats are converted to "false" if equal zero, "true" otherwise.

    Strings are converted to booleans recognizing 'false' and 'true' strings (and making errors in other cases).

  • string(...) converts a "core" type to a string.

    Not much to write here, numbers (integers and floats) are converted to normal notation and boolean is converted to 'false' or 'true'.

All four basic conversion functions accept also variables that already have the necessary type. For example, converting float to float is a valid (and harmless) operation.

5.2. Control flow

if(condition, then_code, else_code) is our conditional instruction. condition is first calculated, must be a boolean value. If it's true, then then_code is executed and returned as "if" value. Otherwise, else_code is executed and returned as "if" value. You may note that (because of CastleScript unification of "instruction" and "expression" terms) this can be used in both functional and imperative form. That is, all below are valid:

  { imperative form }
  if(x > 3, y := 'yes', y := 'no');

  { functional form, equivalent to above, looks more elegant in this case }
  y := if(x > 3, 'yes', 'no');

  { actually, even this is possible if you need it: }
  y_copy := if(x > 3, y := 'yes', y:= 'no');

when(condition, then_code) is a conditional instruction without the "else" clause. It's equivalent to if(condition, then_code, false), so it simply returns false when condition is not satisfied. (This is considered a good thing that the normal if requires the else clause; this way we avoid trivial errors when programmer forgets to write else clause; similar when expression may be found e.g. in Lisp and Nemerle.)

while(condition, loop_code) performs a while loop. Calculate condition (must yield a boolean value), if true then execute loop_code and again calculate condition, if it's still true then execute loop_code again, ... you get the idea.

for(counter, begin_value, end_value, loop_code) performs a for loop. counter must be an assignable integer variable (note that for now you cannot declare new variables for CastleScript; you usually need to overuse initializeOnly field of X3D script node for this). begin_value, end_value must also be integer values, will be calculated once at the beginning of the loop. We will assign to counter variable integer values from begin_value to end_value, and for each counter value we will execute loop_code. It's undefined what happens when loop_code changes directly the counter value.

for and while loops return the value of last executed loop_code, or false if loop_code did not get executed even once.

5.3. Number (integer and float) functions

Self-explanatory math functions are listed below. They all take a float type, and return a float type unless otherwise noted:

  • sin, cos, tan, cotan
  • arcsin, arccos, arctan, arccotan
  • sinh, cosh, tanh, cotanh
  • log2 (same as log(2, x)), ln, log, power2 (same as power(2, x) = 2^x), exp (same as power(enat, x) = enat^x), power, sqr, sqrt
  • sgn (returns integer), abs
  • max, min (any number of arguments >= 1 allowed; works on either floats or ints)
  • lerp(fraction, a, b)

5.3.1. Random numbers functions

random() returns a random float number within 0...1 range (0 included, 1 excluded).

random(int) returns a random integer number strictly less than int and >= 0. (int argument must be > 0).

5.4. Boolean functions

Basic boolean operations: or(bool1, bool2...), and(bool1, bool2...) (any number of arguments >= 1), not(bool1).

5.5. String functions

You can add (concatenate) and compare (case-sensitive) strings by normal operators. Converting other core types (numbers, booleans) to string may be done by the string(...) function.

writeln(my_string) outputs a string. How exactly it is displayed depends on the application: normal 3D browsers (like view3dscene) display it on the console (standard error output, if --debug-log is used), games (like The Castle) display it as in-game notification. As a developer, you can configure how this is handled, see OnScriptMessage in CastleScript unit. By default, it results in CastleLog.WritelnLog, see the manual about logging.

Most array functions can also treat the string as an array of characters. We do not have a special type for a "character" — we just use a string with length 1. You can get / set the length of the string with array_get_count(string) / array_set_count(string, count). And you can get / set a specific character of the string with array_get(string, index) / array_set(string, index, character). Indexes for characters inside string are zero-based, like for all arrays in CastleScript.

character_from_code(int) converts integer character code to a 1-letter string with this character. Only the ASCII character codes are guaranteed to work in the long run. In the future, all Unicode character codes will be accepted here, and rendered if present in the font. Currently, our font rendering is limited to 256-character encodings.

shortcut(name) returns a nice string describing the named key/mouse shortcut in the game. It's useful if you want to show a message describing some shortcut, for example writeln('Hint: you can open this door using the ' + shortcut('interact')). Depending on user current key definitions, we will show something like Hint: you can open this door using the key "e" or Hint: you can open this door using the mouse "left". See CastleInputs for available shortcut names, additionally games may define their own key shortcuts by creating new TInputConfiguration instances.

A lot of string functions are trivial to add — report if you need some particular function.

5.6. Array functions

array(item1, item2, ...) constructs an array. At least one argument is required. All arguments must have the same type (X3D multiple-value fields can't have mixed types).

Note that parameter-less array() call is not allowed, because we wouldn't know then the resulting type (is it an empty array of floats? empty array of integers? etc.) Don't worry, you can use array_set_count(my_array, 0) for making array empty.

Note that floating-point values in arrays are stored only with single- or double- precision. This contrasts with singleton values, which are always stored in the best precision possible. Having explicit single- or double- precision arrays is better for storage and allows faster copying between X3D fields. Normal array with float parameters will create an array of single-precision values (that is, X3D MFFloat). You have to call array_d to request double-precision storage (suitable for X3D MFDouble or MFTime).

array_get_count(my_array) and array_set_count(my_array, new_count) get and set array count. When you grow array, newly added items have undefined values. When you shrink array, excessive values are discarded.

array_get(my_array, index) gets an item from array on given index. In "normal" programming languages, implemented by less lazy programmers, this is written as my_array[index] :) Analogous array_set(my_array, index, component_value) sets a value of item in an array. In "normal" programming languages you would write my_array[index] := component_value.

array_set and array_set_count also return the new array (that is, they return the new value of their 1st argument), this may be comfortable sometimes.

You can glue (concatenate) two or more arrays by the "+" operator.

5.6.1. Curves

hermine_tense_spline example
hermine_tense_spline example, scaled by x

An array can be used to define a curve which can then be evaluated. This is cool for designing curves, for example for movement or some game balance! Since the curve is a function, you can easily combine it with other functions.

For example this is a simple "three increasing bumps" function:

hermite_tense_spline(x, true,
  array(0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0),
  array(0.0, 1.0, 0.0, 2.0, 0.0, 4.0, 0.0))

You can easily scale it up, as the x increases:

(1 + x * 0.1) *
hermite_tense_spline(x, true,
  array(0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0),
  array(0.0, 1.0, 0.0, 2.0, 0.0, 4.0, 0.0))

The available curves functions are:

  • catmull_rom_spline(x: float, loop: boolean, arguments: array of float, values: array of float): returns float
  • hermite_spline(x: float, loop: boolean, arguments: array of float, values: array of float, tangents: array of float): returns float
  • hermite_tense_spline(x: float, loop: boolean, arguments: array of float, values: array of float): returns float

Try these functions with latest glplotter to see the curves shapes when rendered. For the detailed documentation, see the corresponding ObjectPascal API documentation CatmullRomSpline, HermiteSpline, HermiteTenseSpline and the wikipedia about Hermite and Catmull-Rom splines.

5.7. Vector functions

vector(x, y), vector(x, y, z), vector(x, y, z, w) create a single-precision vectors (called SFVec2f, SFVec3f, SFVec4f in X3D). Suffix _d means that you want double-precision vectors: vector_d(x, y), vector_d(x, y, z), vector_d(x, y, z, w).

vector_get(my_vec, index) gets vector component. Allowed index values obviously depend on vector size, for example on SFVec3f you can use index 0, 1, 2. vector_set(my_vec, index, component_value) sets given vector component (and returns new vector, for comfort).

vector_get_count(my_vec) is available, for analogy with array_get_count. Vector has a fixed number of components, so there is no vector_set_count.

Standard vector math utilities are available: vector_length(v), vector_sqr_length(v), vector_dot(v1, v2) (see vector dot product in wikipedia), vector_cross(v1, v2) (see vector cross product in wikipedia, only on 3-component vectors). max(vector1, vector2), min(vector1, vector2) also work (make max/min on corresponding vector components).

You can also add, subtract, multiply by scalar, divide by scalar, compare vectors by normal operators. Linear interpolation by lerp(fraction, vector1, vector2) on vectors also works.

Color functions: grayscale(v) takes a vec3f, treats it as RGB color, and converts it to a single float — color intensity (calculated much like an average of vector components, but taking into account human eye sensitivity).

5.7.1. Rotation functions

Rotations (X3D SFRotation, or an element of MFRotation array) are, in CastleScript, just 4-value single-precision vectors. First three scalars are rotation axis (should be always normalized, VRML/X3D require this), 4th item is the rotation angle (in radians). So you can operate on rotations from CastleScript using all normal functions on vectors.

Some functions specially suitable for rotations are also available:

  • orientation_from_direction_up(dir, up) converts a direction and up 3D vectors into an orientation. This is a rotation that transforms default direction (0, 0, -1) and default up (0, 1, 0) into your desired direction and up vectors. This is suitable for example for calculating VRML/X3D Viewpoint.orientation.

    Given here direction and up vectors do not have to be normalized (they only must not be zero). They also do not have to be orthogonal (we will internally fix the up vector, if needed, to be orthogonal to direction).

  • rotate(rotation, point) rotates given 3D point. rotation parameter contains an axis (first three components) and an angle in radians (last component), so it's compatible with VRML/X3D SFRotation.

  • orientation_to_direction(rotation) determines direction vector back from an orientation, inverting what orientation_from_direction_up did. Similarly orientation_to_up(rotation). Resulting direction and up vectors are always normalized.

    These functions are equivalent to using rotate(rotation, (0, 0, -1)) (for orientation_to_direction) and rotate(rotation, (0, 1, 0)) (for orientation_to_up).

  • slerp(value, rotation1, rotation2) calculates a spherical linear interpolation between two rotations. For value = 0 the result is rotation1, for value = 1 the result is rotation2, and between (and outside) the result is a nicely interpolated rotation on a unit sphere.

Example: see rotations.x3dv for a simple X3D Script using above rotation functions.

5.8. Matrix functions

3x3 and 4x4 matrices are supported. Single- and double- precision. X3D calls these matrix types SFMatrix3f, SFMatrix4f, SFMatrix3d, SFMatrix4d. Matrix is treated similar to an array of vectors (array of columns).

matrix(column1, column2, column3), matrix(column1, column2, column3, column4) create a matrix. Each column argument is a vector. Number or arguments determines if it's 3x3 or 4x4 matrix. Type of arguments (single- or double- precision vectors) determines if matrix is single or double precision.

matrix_get(my_matrix, column_index) gets matrix column. Allowed index values obviously depend on matrix size, for example on SFMatrix4f you can use index 0, 1, 2, 3. matrix_set(my_matrix, column_index, column_value) sets given matrix column (and returns new matrix, for comfort).

matrix_get_count(my_vec) is available, for analogy with array_get_count and vector_get_count. Returns number of columns, 3 or 4. For now, non-uniform matrices are not supported, so this is also the number of rows.

You can add, subtract, negate, multiply (by another matrix, or by scalar, or by vector on the right side), divide (by scalar), compare matrix using normal operators. Linear interpolation by lerp(fraction, matrix1, matrix2) on matrices also works.

5.9. Image functions

image(width, height, components) creates a new image. components is the number of image components, like in X3D SFImage field:

  • 1 component is grayscale image,
  • 2 components is grayscale image with alpha channel,
  • 3 components is RGB image,
  • 4 components is RGB image with alpha channel.

Note that image contents are not initialized (meaning: they are filled with random garbage in memory) by image function. This is for the sake of speed.

image_load(url) loads an image from file. This is quite powerful utility, allowing you to load textures at any time from a script. (It's not a security problem, since you can do the same from normal X3D nodes like ImageTexture.) URL may be relative to X3D file containing the Script node.

image_width(my_image), image_height(my_image), image_components(my_image) return width, height and number of image components.

For functions that get/set image contents, there are 3 variants of each of them:

  • Functions with _color suffix operate only on non-alpha channels of the image. For 1 and 2 component images, they take/return a single floating point value describing color intensity (in 0..1 range). For 3 and 4 component images, they take/return a 3-element vector with single precision, describing RGB color value.

  • Functions with _alpha operate only on alpha channel of the image. They take/return a single floating point value describing alpha (opacity), in 0..1 range.

  • Finally functions without alpha/color suffix operate on all image channels at once. For 1 component images, they take/return a single floating point value. For 2,3,4 component images, they take/return a vector (with single precision) describing color with alpha value. For images without alpha value (1 or 3 components), these functions are exactly equivalent to _color functions.

Functions to get/set image contents:

  • image_get      (my_image, x, y),
    image_get_color(my_image, x, y),
    image_get_alpha(my_image, x, y)
    Get single pixel's color/alpha.

  • image_set      (my_image, x, y, color_with_alpha),
    image_set_color(my_image, x, y, color),
    image_set_alpha(my_image, x, y, alpha)
    Set single pixel to given color/alpha.

  • More "set" functions were planned, like image_set_rectangle, image_apply_decal, but finally I didn't have the nerve to implement everything possible :) Report if you would like any function to be added to CastleScript for images.

For comfort, set functions return back the image (that is, the new value of 1st argument).

For example CastleScript programs that generate and process images, see e.g. mkimage_gradient.castlescript (generate simple gradient image) and mkimage_sobel_edge.castlescript (process any image with Sobel operator (edge detection)).

5.10. X3D node functions

None for now. Currently, you cannot process X3D nodes directly by CastleScript. Whether it will ever be allowed in CastleScript, depends on the "success" of CastleScript — if you write your own scripts in CastleScript and feel that you need this, please report. Michalis will be more than happy to add them :)

6. Precise grammar

  Operand (aka "something that can be assigned") = Identifier

  Factor = Operand |
           Constant |
           "-" Factor |
           "(" Expression ")" |
           FunctionName [ "(" Expression [{"," Expression}] ")" ]
  FactorOperator = "^" | "*" | "/" | "%"

  # In other words, all multiplicative operators have the same priority
  # and are left-associative.
  # "^" operator is for power.
  #     X ^ Y = Power(X, Y)
  #     This works for non-integer Y, but in this case Y has to be >= 0.
  # "%" operator is for modulo (remainder of division).
  #     X % Y = X - Floor(X/Y) * Y
  # "/" does division. Like in C, when both operands are integers,
  #     this performs an integer division (that is, it's the floor of
  #     actual division result, corresponding to Pascal's "div" operator).
  #     When either operand is float then this is normal float division
  #     (more precisely, if only one operand is float, the other will be
  #     promoted to float then; and then float division will be done.)

  Term = Factor [{FactorOperator Factor}]
  TermOperator = "+" | "-"

  ComparisonArgument = Term [{TermOperator Term}]
  ComparisonOperator = "<" | ">" | "<=" | ">=" | "=" | "<>"

  # Note that comparisons on float types (this also includes vectors, matrices
  # and arrays based on float types) perform exact comparison
  # (like in all programming languages).
  # This means that adding 1.0 one hundred times will not necessarily yield result
  # equal to literal 100.0. You can compare with some epsilon, like
  # "abs(a-b) < 0.001", if needed.

  NonAssignmentExpression = ComparisonArgument [{ComparisonOperator ComparisonArgument}] |

  # Programmers using our engine: note that CastleScriptParser.ParseFloatExpression
  # parses exactly "NonAssignmentExpression" token, as defined above,
  # with the Factor definition hacked to also allow only NonAssignmentExpression
  # inside parenthesis. In other words, ParseFloatExpression takes care to only
  # parse a calculated expression, without any assignments or sequence.

  PossiblyAssignmentExpression = NonAssignmentExpression |
                                 Operand ":=" PossiblyAssignmentExpression

  Expression = PossiblyAssignmentExpression [{";" PossiblyAssignmentExpression}]

  Function = "function" "(" [Identifier [{"," Identifier}] ")" Expression
  Program = [{Function}]

  # Programmers using our engine: note that CastleScriptParser.ParseProgram
  # parses exactly "Program" token defined above.

  # ------------------------------------------------
  # Programmers using our engine: note that above part of the grammar
  # was handled inside CastleScriptParser. Grammar below is handled
  # inside CastleScriptLexer.
  # A "token" returned by CastleScriptLexer corresponds to a non-terminal
  # symbol in the part of the grammar below, resolved by lexer.

  # Identifier is just a sequence of letters, underscores, digits,
  # not starting with a digit.
  Identifier = Letter [{Letter | Digit}]
  Letter = 'a' .. 'z' | 'A' .. 'Z' | "_"
  Digit = '0' .. '9'

  Constant = "pi" | "enat" |
             Digit [{Digit}] ["." Digit [{Digit}] ] |
             "true" | "false" |
             string constant in apostrophes

  FunctionName = (see list of built-in functions above)

Generally, at least one whitespace is required between two tokens. But there are many exceptions, when situation is unambiguous, for example no whitespace is needed between identifiers and parenthesis. In case of uncertainty lexer is greedy, that is lexer tries to eat as much characters as it can for a single token.

Case sensitivity: language is not case-sensitive. That said, in the future in may be partially case-sensitive, in places where you specify field/event names of X3D since whole X3D is case-sensitive. So always specify X3D field/event names with matching case.