Equational Programming

Introduction

Equational programming is a programming paradigm that specifies functions via conditional equations. EP is both a programming language for equational programming and a translator that generates Java classes from conditional equations. The fact that EP generates Java makes it easy to combine equational programs with ordinary Java programs and furthermore guarantees an efficient execution of equational programs. The spirit of EP is best demonstrated with an example. The following set of conditional equations specifies symbolic differentiation.

      Expr = Number(Double value)
           + Variable(String name)
           + Sum(Expr lhs, Expr rhs) 
           + Difference(Expr lhs, Expr rhs)
           + Product(Expr lhs, Expr rhs)     
           + Quotient(Expr lhs, Expr rhs);
      
      diff: Expr * String -> Expr;
      
      Number(value).diff(x) = Number(0.0);
      
      v.equals(x) -> Variable(v).diff(x) = Number(1.0);
      Variable(v).diff(x) = Number(0.0);
      
      Sum(lhs, rhs).diff(x) = Sum(lhs.diff(x), rhs.diff(x));
      
      Difference(lhs, rhs).diff(x) = Difference(lhs.diff(x), rhs.diff(x));
      
      Product(lhs, rhs).diff(x)    = Sum(Product(lhs.diff(x), rhs), Product(lhs, rhs.diff(x)));
      
      Quotient(lhs, rhs).diff(x)   = Quotient( Difference(Product(lhs.diff(x), rhs), 
                                               Product(lhs, rhs.diff(x))), Product(rhs, rhs) );

This file is translated into the following Java classes: Expr.java, Number.java, Variable.java, Sum.java, Difference.java, Product.java, and Quotient.java. To test these classes, use the class Main.java. The tutorial gives a short overview of EP.

Download and Installation

The software EP can be downloaded as ep.tar.gz. EP is implemented in Java 5.0 and should therefore run with any operating system but the following description assumes that you are working with either Linux or Unix. Let us assume that there is a directory called Software which is a subdirectory of your home directory and that EP should be installed into this directory. If it is to be installed somewhere else, simply change every occurrence of the string ~/Software in the following description accordingly.

Start a shell in the directory containing the file ep.tar.gz and move the file ep.tar.gz to the directory ~/Software by issuing the commands
```
 % mv ep.tar.gz ~/Software 
```
Change to the directory ~/Software
```
cd ~/Software
```
Unzip the file ep.tar.gz
```
gunzip ep.tar.gz
```
This command should create the file ep.tar.
Untar the file ep.tar:
```
untar xf ep.tar
```
This command should produce the directory EP as a subdirectory of the directory ~/Software. The directory EP contains three subdirectories:
- src contains the Java sources together with the class files.
- doc contains the documentation.
- examples contains the example file expr.ep that specifies symbolic differentiation using equational programming.
The directory EP also contains the file antlr-2.7.5.jar. This file contains Antlr which is a parser generator written by Terence Parr. There are two more files in the directory EP: The file copyright.txt informs you that EP is subject to the Gnu General Public License. For your convenience, this license is reproduced in the file gpl.txt.
To test EP, change to the directory examples and start EP using the commands:
```
cd ~/Software/EP/examples
```
```
export CLASSPATH=~/Software/EP/antlr-2.7.5.jar:/Software/EP/src
```
```
java EP expr
```
This invocation of EP will generate a number of Java files implementing symbolic differentiation. To test these generated files, first compile them using the command
```
javac *.java
```
Next, execute the command
```
java Main
```
This should produce the result
```
Product(Variable(x), Variable(x))/dx = Sum(Product(Number(1.0), Variable(x)), Product(Variable(x), Number(1.0)))
```

Karl Stroetmann

Last modified: Fri Mar 3 17:46:56 CET 2006