This section is a brief introduction to the most fundamental concepts of CindyScript.
All calculations in CindyScript are performed by executing functions. A function can be considered as a kind of calculation that takes the arguments of the function and produces some kind of output value. Many calculations can already be expressed using only elementary functions. Thus the code fragment
calculates the sum of the first 10 integers.
.. is a function that takes two integer numbers,
b, and generates as output the list of all integers from
1..10 generates a list of 10 integers:
The function sum(_) is unary (that is, it takes a single argument).
It takes as its argument a list of numbers as input and generates as output a number that corresponds to the sum of the list entries.
Thus if we type
sum(1..10) into the command shell, the system will respond with the result
Moreover, seemingly procedural statements, such as an
if-statement, are realized as functions.
For instance, the expression
x = 33; y = 7; if(x < y, print("Mine"), print("Yours"))
demonstrates the function
if, which takes three arguments.
It checks the condition of its first argument
x < y
and depending on the result, evaluates the second or the third argument,
that is, either
The result of this evaluation will be the result of the
Thus the above expression is equivalent to
print(if(x < y, "Mine", "Yours"))
Depending on the evaluation of the condition, the
if function returns the value of the second argument or the third argument.
If a function is evaluated in CindyScript, it may have “side effects”. Side effects are important for all kinds of interactions between a CindyScript program and a Cinderella construction. Typical side effects are:
Drawing: A CindyScript statement may cause drawing operations in the construction views.
Assignments: A CindyScript operation may change the position, color, size, etc. of geometric objects.
Variable assignments: A CindyScript statement can create variables and assign values to them.
Function creation: A CindyScript statement can create and define a function that can be used later.
For instance, the statement
produces the side effect of drawing a point at position
skip test: no geometry available here
sets the color of point A to white.
Most users are probably accustomed to sequential programming languages like C, Java, Pascal, and Basic.
In practice, writing sequential code in CindyScript is not so different from writing code in these languages.
CindyScript has a
‹statement1›;‹statement2› that simply first evaluates
statement1 and then
The return value of the
; operator is the result of the last non-empty statement.
Writing a sequential program is relatively simple, and it looks similar to a program written in a sequential language. For instance, the program
repeat(9,i, j=i*i; draw([i,j]); );
creates nine points on a parabola.
repeat(‹number›, ‹variable›, ‹program›) creates a loop that performs
In each run the variable
‹variable› is incremented (starting with
The body of the loop is the two lines
CindyScript is designed to provide a maximum of functionality with a minimum of syntactic overhead. Therefore, CindyScript does not have explicit typing of values. Like many other languages, CindyScript uses the concept of variables. However, in contrast to other languages, the variables do not belong to a specific type. Any value of any type can be assigned to any variable. On the one hand, this gives the programmer a great deal of freedom to generate powerful code. For instance, the following code fragment
defines a function
f(x,y) that could be used to add integers or complex numbers as well as vectors or matrices.
On the other hand, this freedom requires that the programmer take some responsibility while writing a program in order to produce code that is semantically meaningful.
When a function tries to evaluate a meaningless expression, the program will not automatically terminate.
Instead, the function will return the value
___, which stands for a meaningless expression.
So, in the above example,
f([1,2],[3,4]) will perform a vector addition and evaluate to
[4,5], whereas the expression
f(4,[3,4]) is meaningless and evaluates to
There are several loop-like constructions in CindyScript.
For instance, the operator
select(‹list›,‹condition‹) traverses all elements of
‹list› and returns a list of objects that satisfy the condition.
For this to occur, there must be a way to feed elements that are to be tested to the condition.
By default, CindyScript uses a variable #, which serves as a handle for the run variable.
For instance, the statement
[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]
returns a list of all odd numbers between
Moreover, loops use this run variable, and thus
1 2 3 4 5 6 7 8 9
prints all numbers from
It is also possible to use an explicit run variable by providing it as the second argument.
repeat(9,i,print(i)) are equivalent to the above statements.
As already mentioned, CindyScript does not have explicit typing. Nevertheless, any value of a variable belongs to an explicit type. The basic types of CindyScript are
- ‹number›: Any numeric value. Numbers can be integers, real numbers, or complex numbers.
- ‹list›: A list of arbitrary objects. Such a list may semantically also have the meaning of a vector or matrix.
- ‹string›: A text expression.
- ‹geo›: A geometric object that belongs to a construction.
- ‹boolean›: A value
The number type is particularly powerful, since it can contain integers, floating-point numbers, and complex numbers.
Since CindyScript does not have explicit typing for variables, it allows variables to be created “on the fly” as needed.
A variable is created when it is assigned for the first time.
x is not already being used, the statement
creates the variable
x and assigns the value
7 to it.
After a variable has been assigned, its value is accessible for the rest of the execution.
Values may also be temporarily overwritten by local variables of a function.
Thus in a function defined by
the values of
y are the local parameters of the function.
After the execution of the function is completed, the original value of
x is restored.
CindyScript employs dynamic scoping, not lexical scoping. So a function argument will overwrite a global variable of the same name even for code outside the body of the function.
a = 10; f(x) := a * x; g(a) := f(2) + a; g(3)
One can also produce additional local variables with the
This uses dynamic scoping, too.
g(x) := (regional(a); a = x + 1; f(2) + a); g(3)
Variables are also used as a kind of handle to geometric objects.
They form a major link of CindyScript to Cinderella and CindyLab.
If a variable has a name that is identical to the label of a geometric object, it provides a link to that geometric object.
The value of the variable can still be overloaded by an explicit assignment of a value to the variable.
The different properties of a geometric object (position, color, size, etc.) are accessible via the . operator.
A is a point in a geometric construction, the expression
A.size returns an integer that represents the size of the point.
A.xy=[3,4] assigns the point to the coordinate
Furthermore, properties relevant to physics simulation (mass, velocity, kinetic energy, etc.) are accessible via the . operator.
Many operators in CindyScript provide more functionality than one may notice at first glance. Usually these features can be accessed using so-called modifiers. The operators are defined in a way such that their default usage provides a suitable behavior for most situations. However, it may be necessary to modify the default behavior. To that end, one lists corresponding modifiers in the call of the operator. For instance, the statement
draws a point at position
By default, the point is green and of size 3.
draws a yellow point of size 15. Modifiers have to be separated by commas. They may occur in any order and at any position of the function call.
a = ; repeat(3, start->4; 5, a = a ++ [#]); a
[5, 6, 7]
CindyScript offers lists as elementary data types.
Lists are the fundamental paradigm that is used to define more complex data structures.
In addition to the obvious application as enumeration objects, lists can also be used to represent vectors and matrices.
A vector is a list of numbers.
A list of vectors whose vectors all have the same length will be interpreted as a matrix.
CindyScript provides the usual operations for combining vectors, matrices, and numbers.
Depending on the content of
b, the expression
a*b may represent a usual multiplication of numbers, a matrix product, or a matrix/vector multiplication.
In CindyScript there is no distinction between row vectors and column vectors on the level of vectors.
However, by the use of suitable functions one can convert a vector of length
n to an (n × 1) matrix or to a (1 × n) matrix.
CindyScript provides many statements with which one can draw directly on the canvas of the geometric views. Using this feature it is possible to enrich the behavior of Cinderella constructions significantly. It is possible to draw points, lines, segments, polygons, tables, functions, etc. However, it is important not to confuse a script-drawn geometric object with a geometric object that is active in geometry. It is not possible to use such script-drawn elements as definers in Cinderella modes.
If one wants to modify active elements using a script, then it is necessary to first construct them and then alter their positions using CindyScript statements. All free elements can be moved by setting their position parameters.
The script window of Cinderella in which one enters the CindyScript code contains several slots in which the text can be entered. The particular slots are called
- Timer Tick
- Simulation Start
- Simulation Stop
Each of these entries corresponds to the occasion that triggers the execution of the script. For instance, scripts in the Draw slot is executed directly before a screen refresh in the view. The Initialization slot is executed directly after the CindyScript code is parsed. Simulation Start is executed before starting an animation when the play button is pressed. Using this mechanism it is possible to write programs that react nicely to user events.
CindyScript runs in a runtime environment. In principle, every tiny move in a construction can cause the evaluation of a script. For this to happen, a reasonable design decision in the language had to be made concerning the occurrence of runtime errors. It would be very distractive if the usual user interaction was interrupted by error messages over and over (in particular, if a construction is used as an applet within an HTML page). For this reason, error handling in CindyScript at runtime reports only the first ten errors. However, runtime errors will never interrupt execution. Runtime errors (such as division by zero, or access to a nonexistent array index) are simply ignored in the program flow. Erroneous function evaluations simply produce an undefined result, and the calculation proceeds (perhaps causing more undefined results). This usually guarantees fluent performance of a construction even if errors occur.
This feature may make debugging of programs a little cumbersome, since runtime errors are not reported.
For this purpose a special function,
assert(‹boolean›,‹string›), was introduced to check whether a certain assumption about the current data is satisfied.
If the assumption in the first argument is not satisfied, the message in the second argument is printed.