Mike Schaeffer's Blog

Articles with tag: rpncalc
October 28, 2013

If you’ve played around with the basic version of the Java calculator from the last post in this series, you may have tried to enter multiple commands on the same prompt line:

Begin: class com.ksmpartners.rpncalc.basic.RpnCalc

> 1 2
Uncaught Exception: For input string: "1 2"
java.lang.NumberFormatException: For input string: "1 2"

This is a convenient way to enter calculator commands, but it doesn’t work for two reasons. This post discusses why it fails, and how to fix it:

The immediate failure is because the parser considers the entire input string as a single command, without regard to whitespace. The parser looks for a command named "1 2", fails to find it, and then attempts to parse the entire string as a number. The number parse then fails and throws an exception that kills the process. This part of the problem can be fixed by altering the parser to split the input string into tokens, and parsing each token separately as its own command. Unfortunately, this shows the second more structural problem. The way the REPL is currently written, it’s built to read and execute a single Command for each prompt:

Command cmd = parseCommandString(cmdLine.trim());
 
cmd.execute();

To correct the second problem, the data flow between parseCommandString and execute needs to be widened so that the parser can return multiple commands for a single input string. The easiest way to achieve this is to have the parser return a list of Commands.

List<Command> cmds = parseCommandString(cmdLine.trim());
 
for(Command cmd : cmds)
    cmd.execute();

This approach works well because it’s simple. It doesn’t add any additional class definitions, there’s still a single call site for execute(), and java.util.List is well-understood by developers that use Java. However, if you’re willing to trade some of that simplicity away, there’s an alternative approach to the problem. The alternative approach allows the original REPL to go unchanged, and still process groups of commands. It does this by introducing a new and more powerful kind of command object that can be used to compose lists of commands into single Command instances. The parser then uses these CompositeCommands to signal to the REPL that there are multiple commands to be executed:

private Command parseCommandString(String cmdStr)
    throws Exception
{
    List<Command> subCmds = new LinkedList<Command>();
 
    for (String subCmdStr : cmdStr.split("\\s+"))
        subCmds.add(parseSingleCommand(subCmdStr));
 
    return new CompositeCommand(subCmds);
}

There are a few things to notice about this code. The first is that the type signature of parseCommandString is unchanged: it’s still a function from String to Command. This is why the REPL doesn’t need to be updated. The second aspect of the code is that there’s still a list of command objects: The list of commands we introduced when we modified the REPL example is still present, even with the CompositeCommand. What the composite command object does is hide the list from the REPL; It wraps the list up, abstracts it away, and lets the REPL pretend that there aren’t any lists.

The internal machinery that lets composite command achieve this isn’t too involved. All CompositeCommand has to do is remember the Command objects it’s composing, and execute each of those commands as if they were entered individually:

private class CompositeCommand implements Command
{
    private List<Command> subCmds = new LinkedList<Command>();
 
    CompositeCommand(Collection<Command> subCmds)
    {
        this.subCmds.addAll(subCmds);
    }
 
    public void execute()
    {
        for(Command subCmd : subCmds)
            subCmd.execute();
    }
}

And that’s all there is to it. While this approach doesn’t have the surface simplicity of our first attempt, what it has done for us is give us a new abstraction for sequences of commands. This is fully a third of the ‘sequence’, ‘selection’, and ‘iteration’ that are necessary to express any computable program. That’s not a bad result for a single class definition.

October 21, 2013

The first implementation of the RPN calculator I’m going to look at is the basic Java implementation. The link takes you directly a a view of the source file for this version, but if you’d like to play with the code, you can also clone the whole project with git. Cloning the git project will bring down all the versions of the calculator, and also let you compile and run the software locally. I’ll discuss more about how the implementation works, after the jump:

When you run the calculator, it works a lot like an interactive programming language with a read-eval-print-loop (REPL). The calculator presents a prompt, reads a command, executes it, prints the result, and then loops back around until the user types quit. A user session that computes the sum of two and three looks like this (user entry in bold):

Begin: class com.ksmpartners.rpncalc.basic.RpnCalc

> 2

1> 2.0
> 3

1> 2.0
2> 3.0
> +

1> 5.0
> quit
end run.

The implementation has to address several problems:

  • The stack has to be stored.
  • The current state of the calculator needs to be displayed to the user.
  • Commands need to be accepted from the user.
  • User commands need to be dispatched to code that performs the requested action.

Storage of the stack is simple. The basic version of the calculator uses a Java collection stored as an instance variable of the calculator class:

public class RpnCalc extends Calculator
{
    //...
 
    private Deque<Double> stack = new LinkedList<Double>();

Printing the stack is also simple, although it’s made more verbose by the fact that the Java foreach loop requires an Iterable, rather than an Iterator:

private void showStack()
{
    int ii = 0;
 
    for (Iterator<Double> it = stack.descendingIterator(); it.hasNext(); ) {
        Double val = it.next();
 
        System.out.println((ii + 1) + ">" + val);
        ii++;
    }
}

Similarly, the read, eval, print loop looks almost exactly like you’d expect. The most interesting bits are these:

Command cmd = parseCommandString(cmdLine.trim());
 
cmd.execute();

The last two statements translate whatever the user entered into a Command, an object that encapsulates the user’s intent into something that can be stored and directly executed at a later point in time. It is a command in the sense of the GoF Command Pattern:

interface Command
{
    void execute();
}

The command themselves do their work via direct mutation of the state stored in the stack instance variable:

cmds.put("+", new Command() {
    public void execute() {
        Double x = stack.pop();
        Double y = stack.pop();
 
        stack.push(x + y);
    }});

One tricky detail of this design is hidden in the fact that every command string entered by the user ultimately goes through Command.execute(). There is no special case for entering numbers, which therefore must also be done via a command. What’s different about the numeric entry command is that it contains a bit of instance data representing the number to be entered. The command parser creates a separate instance of PushNumberCommand for each number that’s entered on the command line.

private class PushNumberCommand implements Command
    {
        Double number;
 
        PushNumberCommand(Double number) { this.number = number; }
        public void execute() { stack.push(number); }
    }

In this design, you can make a strong argument that parseCommandString serves as a rudimentary compiler. Rather than translating from Java into classfiles, it translates from text into command instances. While this specific implementation only translates from strings containing a single command into command objects that perform a single operation, there’s nothing inherent in the design that prevents it from parsing complex command strings into complex command objects:

private Command parseCommandString(String cmdStr)
    throws Exception
{
    Command cmd = cmds.get(cmdStr);
 
    if (cmd != null)
        return cmd;
    else
        return new PushNumberCommand(Double.parseDouble(cmdStr));
}

Next time, I’ll talk a bit more about generalizing parseCommandString into a more powerful kind of compiler. This will enrich both the user command entry syntax, and give us a more powerful example of the command pattern within the calculator.

October 3, 2013

One of the things I remember most about middle school math class is that I went through it in a perpetual state of disorganization. During one particularly bad spell, I lost two calculators within a week. The loss, and the reaction of my parents, drove me to try to fix the problem once and for all. My plan was simple: buy an expensive calculator with the hope that it’d serve as an incentive to keep track of my stuff. The next weekend, I took weeks of allowance money to the local Service Merchandise and bought a new HP-11C pocket calculator. Almost 30 years later, I still have both the calculator and a fascination for its unusual Reverse Polish Notation (RPN) user interface. Over those decades, I’ve also found out that RPN provides a good way to explore a number of fundamental ideas in the field of software design.

If you haven’t used an RPN calculator, your first attempt will probably be a confusing experience. Unlike most calculators, The HP didn’t have an ‘=’ key. Instead, it had a large button down the center labeled ‘Enter’, which pushed the most recently keyed number onto an internal four-level stack. The mathematical operations then worked against this stack. The ‘+’ key popped off two numbers, added them, and pushed the result back onto the stack. To add 2 and 3, you’d make the following keystrokes: [2][ENTER][3][+].

In detail:

  • [2] – Begin entering the number ‘2’ into the top level of the stack.
  • [ENTER] – Duplicate the number ‘2’ on the top of the stack so it’s in the top two levels.
  • [3] – Begin entering the number ‘3’ into the top level of the stack, replacing one of the copies of the number ‘2’.
  • [+] – Pop off the top two levels of the stack, pushing back the sum of the two numbers.

Because the display shows the top level of the stack, it shows the answer (5) as soon as the user presses [+]. Because the answer, 5, is on the top of the stack, it’s also immediately ready to be used as an input to another calculation. This last bit is why RPN calculators can be so compelling to use: they make it easy to start with a small calculation and extend it into something larger. As long as a number is on the stack, it can be used in a calculation; The origin of the number doesn’t matter to the way it can be used. In computer science terms, this is the beginning of Referential Transparency. The FORTH programming language builds on this foundation, extending the basic tenets of RPN into a complete programming language. RPN combined with functional decomposition gives the language a great deal of expressive power, but due to the simplicity of stacks a small FORTH can be implemented in a very small amount of memory.

As this series of blog posts continues, I intend to explore some of these ideas using a set of RPN calculator implementations written in Java and in Clojure. We’ll start off with a simple implementation in Java, spend a bit of time exploring the command pattern, and then move into more functional approaches to the problem.