BROOM: A Matrix Language Chris Tobin Michael Weiss Gabe Glaser Brian Pellegrini

Broom Overview and Summary  A high-level language for manipulating matrices  Many useful built in matrix operations.  Ability to define and build more complicated functions for specialized analysis of information

Motivation  Matrices are universal mathematical constructs  Learning curve is not as steep  Specialized use, without extraneous things to understand other than what you need it for.  No need for expensive software

Goals  Intuitive syntax  High level  Very portable  Flexible  Useful and informative error checking

Broom Syntax  Intuitive  for ( ) … endfor  Freeform  whitespace inserted at will  Smooth built-in matrix operation syntax  A = inv(B); // finds the inverse of B  Features:  Control flow constructs: for, while, if  Nested logical operators and expressions  A wide range of built-in functions

Built-in Functions  Many useful built-in function calls:  det  colswap, rowswap  inv  gauss  appendUD, appendLR  setCol, setRow  Too numerous to list…22 total

Semantics  Broom features:  Function definitions  Allow for modularity, power, and reusable code.  Variable definitions  Two intuitive mathematical types  Number  Matrix  Scoping rules:  local – for functions  global – accessible by all  All functions call-by-value for simplicity

Compiler Components and Composition  There are 5 main components of BCC, the Broom translator  Lexer  Parser  Static Semantics Checker  W/Symbol Tables  BroomMatrix.java  Contains Matrix manipulation code and functions  Code Generator

ANTLR  The Lexer and Parser were implemented using ANTLR.  ANTLR’s AST class was used to create the Abstract Syntax Tree and Nodes.  The Static Semantics Checker was implemented as a TreeWalker of the ANTLR AST and maintained Symbol Tables for the various scopes.  Symbol Tables were written as a simple Java class  Code Generator was also implemented as a TreeWalker of ANTLR AST.  Accumulates a “program string” as it walks the AST and prints string to file upon finishing traversal

Block Diagram of Compiler

Example of Generated Code MyProgram.broom:MyProgram global Matrix myMatrix; myMatrix = [1,2; 3,4;]; 3,4;]; //function definitions here... start() Number value; value = det( myMatrix * [1,3; 7,8;]); 7,8;]); //print the value you got value.print(); //print the global Matrix myMatrix.print();endstart MyProgram.java public class MyProgram { BroomMatrix myMatrix; public MyProgram() { float[][] _temp0 = {{(float) 1, (float) 2}, {(float) 3, (float) 4}}; myMatrix = new BroomMatrix( _temp0); } public void start() { float value; float[][] _temp1 = {{(float) 1, (float) 3}, {(float) 7, (float) 8}}; value = BroomMatrix.det(BroomMatrix.multiply(m yMatrix, new BroomMatrix( _temp1))); BroomMatrix.printVariable(value);BroomMatrix.printVariable(myMatrix);} public static void main(String[] args) {MyProgram myProgram = new MyProgram(); myProgram.start();}}

Output of The Simple Program $ javac MyProgram.java $ java MyProgram

Error Checking  Two main types of errors  Semantic Errors  Invalid use of logical ops  Invalid type assignments  Use of reserved words as variable names, etc.  Run-Time Errors  Reference to non-existent index  Use of improperly formatted matrix. * Note: If “de ja vu” is experienced something in your matrix may have been changed.

Example Test Program wrongNumColls // Test for number of columns errors // Author Brian Pellegrini // This is supposed to make sure that error checking for //assignment of matrix values works...it is supposed to fail // MUA HAHAHHAHAHHAH global Matrix A,B; A= [1, 0, 1; 0, 1;]; B= [0, 1; 1, 0, 2;]; start() print ("If this printed checker didn't work"); endstart

Example Test Results BroomProgram did not compile; the following errors were detected: * Error in *global declaration* : invalid matrix specification. Expected a row with 3 elements, but got 2 Expected a row with 3 elements, but got 2 Error in *global declaration* : invalid matrix specification. Expected a row with 2 elements, but got 3 Expected a row with 2 elements, but got 3  BROOM compiler found all the errors!  During testing one has to be careful that errors being tested are the only ones present in the program  Inadvertent bugs can cause lots of lost time spend debugging “ghost bugs”

Lessons Learned  Leave no stone unturned  Need to test every possible error user might encounter  Need to test both errors in user’s code, and errors in generated JAVA code  Exhaustive testing pays off in the end  Have someone else try it!  Have a friend write a program, they might find errors that the testing team simply overlooked.