Michael Eng Jervis Muindi Tim Sun COMS 4115 Project Proposal Description of Language The language we intend to design is an L system based fractal drawing language L systems use a variant of formal grammars to specify and generate fractals and other iterative sequences Our language will be translated from a set of rules to turtle graphics procedures in Java which will in turn be directly used to display the iterative sequence specified on screen Thus using our language it will be very easy for a user to write simple L system grammar like code and have us do the processing and computation necessary to paint and draw it for them In addition we also plan to support basic programming primitives to as to enable our language to be used to implement basic algorithms such as the the Euclidean algorithm Ideally we would like to minimize the amount of parsing required from a given program As such we d like to have Java classes that provide drawing and computational functionality that would execute alongside the outputted code from our compiler To clarify the compiler would output instructions for the drawing class to construct a fractal and these instructions would call methods from a pre made Java drawing class How Language should be used The language will be used to draw fractals and other iterative sequences We intend to include conditional statements and flow control functionality by allowing users to embed Java code directly into their programs That said our language will also support basic programming primitives and hence it can also be used as a basic general purpose programming language to implement algorithms such as the Euclidean algorithm to find the greatest common divisor An Interesting Representative Program The following program draws an n th order approximation to the Hilbert curve using an Lsystem and is based on the L system described in the Wikipedia article for the Hilbert curve The Hilbert curve is a fractal and a space filling curve hilbert n alphabet A B f r l s rules lambda s A A l B f r A f A r f B l B A B f r l s r A f turtle turtle turtle turtle l B f B l f B r forward 150 3 n rotate 60 rotate 60 place 0 0 display hilbert 5 Language Syntax examples alphabet is a keyword that lets users declare variable names to be used in their system rules is a keyword that lets users declare rules to be used in their system r turtle rotate 60 users will be able to specify turtle graphics style commands as rules similar to the syntax used in Logo Angle arguments will be interpreted as degree values instead of radians display will allow users to specify a system that they ve written to be drawn on screen Comment we will be using single line comments prefaced by the symbol Expression An expression is either a function call variable declaration or an assignment operation It represents a single complete instruction Boolean Expression This is an expression that evaluates to either true or false Statements A statement is made up of expressions and operators and it is terminated by a at the end Control Flow The syntax for program control flow will be similar to that exists in C and C derived languages and the specifics are given below if boolean expression Program statement goes here else Program statement goes here If the boolean expression is true then code in the subsequent block is executed and if it s false code in the else block is executed instead while boolean expr For as long as the boolean expression is true the code enclosed in the curly braces is executed Data types We also support the basic data types listed below int this is an integer double this is a floating point number with double precision string this is a sequence of characters Declarations Before a variable can be used it must be declared The assignment of a value to the variable can be done at the same time as the declaration variable type variable name variable type variable name variable value Concrete Examples int x declare x int x 1 declare x and instantiate with a value of x NB Unassigned variables i e variables that have been declared but not yet assigned a value do not have Operators Our language will support the following operators for dealing with floating point numbers and integers double a double b a b Addition a b Subtraction a b Multiplication a b Division a b Greater than a b Less than a b Equals a b Greater than or equal to a b Less than or equal to
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