Uncommon Lisp

19 March 1997

Lisp is a nice little language with a long and illustrious history. Originally conceived by John McCarthy in 19561 and perpetuated through various implementations until 1981 when everyone decided to get together and agree on what is now known as Common Lisp, it is a simple but powerful language. Illustrious histories aside, Lisp has the amicable characteristics of a very simple syntax2 and a small but flexible set of constructs with which to work.

The fundamental programming construct in Lisp is the list. Sure, you've got your integers and strings (also known as atoms), but the real action is in the lists. Everything is expressed in terms of a list. A program is a list of expressions. An expression is either a literal or a list of expressions. A function call is a list where the first element is the name of the function to call and the remaining elements of the list are the arguments.3

To get a feel for the syntax, here is a little Lisp program:

   (setq a 5)
   (setq b (+ a 15))
   (print "value of b = " b ", value of a = " a);

Given the extremely simple nature of the syntax, writing a parser for Lisp is great fun. Being the kind of person that likes to do great things especially when they're fun, I did just that. I'll be telling you how it all works in the rest of this installment of Deep Magic.

Scanning the horizon
A program begins its life as a sequence of characters4. As a first step in attempting to make some sense of it, the scanner breaks the text up into a sequence of chunks that are slightly more sensible than a plain old character. These chunks are called tokens and they are generally very simple themselves. Tokens are things like integer literals (like 25), string literals (like frobbotzim) and simple punctuation characters (like ().

Tokenizing is generally a very drudgerous process and fortunately, Java provides a built in class (java.io.StreamTokenizer) to do the job for me. I simply configured it to understand my brand of tokens and off I went. By default, the StreamTokenizer treats pretty much everything as its own token except strings enclosed by a user specified quote character and letters (a to z, upper and lower case) that have no spaces between them. I just had to let it know that underscores are a kosher token character (so that it will return my_function as one token instead of my, _, and function) and I was pretty much all set5.

Parsing the parser
Before I dive into how the parser is implemented, let's take a moment to consider how one would represent a Lisp program6 internally. It turns out to be very useful to regard everything as one polymorphic object. This object can either take the value of one of the primitive types (int, string, etc.) or be a list of said objects. Function definitions are simply lists with a particular form (name, argument list, statement list.) Function calls are similarly a simple list.

This uniformity allows for a very simple parser. It has to recognize simple literals and open and close parentheses. When it encounters an open parenthesis, it recursively calls itself to parse the contents of the list until it encounters a close parenthesis. For ease of later discussion, a parsed expression is called an S-expression7. An S-expression can be as simple as a single integer literal or as complex as a function call whose arguments are function calls, whose arguments are function calls, ad infinitum. For the most part, it's whatever is between two parenthesis.

This particular implementation goes the extra mile and also handles the short-form of the quote function. This means that it has to allow a tick before any terminal which indicates that the terminal should be interpreted literally (i.e. 'foo means the string "foo" not the variable foo and '(a b c) means a list containing three elements, not the invocation of function a with arguments b and c.)

The specifics of data representation are also of interest. java.lang.Object is used as an untyped object reference and atoms are objects of type Integer, String, Vector and Function (although Function objects are never part of the parse tree). This also allows the interpreter to utilize ClassCastExceptions to easily handle run-time type mismatches.

Interpret her? You brought her
Now that I've parsed this once lowly sequence of characters into an elegantly structured list of lists of lists (of lists8), I can set down to the task of interpreting it. Here the extant simplicity of Lisp abets me once more9.

The whole program is one big S-expression the value of which is a quoted list of S-expressions. Every S-expression can be evaluated. In the case of an integer or string literal, it is the value of that literal. In the case of a quoted list, it is the list. In the case of a variable, it is the value bound to that variable. In the case of an unquoted list (a function call), it is the value obtained by evaluating the last statement of the function (after evaluating all the previous statements in the function of course.)

What you should be envisioning at this point is something along the lines of a little switch statement and a lot of recursion. This is exactly what the interpreter looks like. Its crux is a function by the name of evaluateSExp10 which does precisely what it claims. It gets a little help from it's friend functions when it comes to manipulating the values of variables and creating a local environment for a function call, but sooner or later, everyone ends up back at good old evaluateSExp.

Variable value manipulation is achieved very simply by storing the variable bindings in a Hashtable object. Lookups retrieve the atom from the hash table, sets store an atom into the hash table.

The interpreter uses dynamic scoping when binding values to variables. This means that when a value is bound to a variable, that value is visible in any code that is executed subsequently until the function in which the value was bound returns (if variables are bound at the top level, then they are visible everywhere for the duration of the execution of the program). Bear in mind that later on, another function could define a variable of the same name which would shadow the first value until the return of the second defining function.

To achieve this, when variables are bound, their previous value is placed into a shadowed table until the completion of the binding construct at which time their old values are restored to the environment. This implementation is known as shallow binding. Another implementation called deep binding achieves this same result but with lesser efficiency.

Function invocation is very simple as well. User defined functions are invoked by first storing any previously bound variables that are to be bound in this function invocation, then inserting the arguments to the function call into the environment under the appropriate names. Finally the interpreter is called recursively to evaluate the S-expression list that makes up the body of the function. The result of the evaluation of the last statement is returned as the result of the function invocation, and away we go.

Built-in functions are handled a little differently. If the interpreter looks up a function in the environment and does not find one, it then attempts to instantiate a Java class who's name is a derivative of the function name. If such a class is found (and that class derives from the class Function) it is then treated as a built-in function, inserted into the environment for future access and passed the current S-expression for evaluation11.

There's one last thing to mention before we can proudly stand up and say "Look Mom, I know how this Lisp interpreter works!" That is: how do user defined functions end up in the environment so that they can later be called? As I described before, the parser just creates a big list of lists8, it doesn't stick anything into the environment. Perhaps you were even thinking that this was conspicuously absent from my explanation until now, or perhaps you're just staring at the screen trying to figure out what all the squiggly lines mean.

In any case, that job is performed by the handy built-in function "defun". defun inteprets its first argument as a list of variables that make up the argument list and its subsequent arguments as a list of S-expressions that are the "statements" of this function. It packages those up into a UserFunction object and sticks it into the environment where it will later be found and called from Lisp code.

Since a function is simply another type of atom, we have another built-in function called "lambda" that returns a function defined by its arguments. This function can then be placed into the environment as the value of a variable. To elucidate, the following two pieces of code do the same thing:

  (defun beavisp ()
    (not (strcmp (says) "Uh, yeah. Huh-huh."))

  (setq beavisp
    (lambda ()
      (not (strcmp (says) "Uh, yeah. Huh-huh."))

Now that you've got the straight dope on it all, try it out in the applet below. If you've never encountered Lisp before, take a look at some of the examples to get a feel for the language and then whip something up yourself.

There would be a lovely Lisp interpreter applet here if your browser supported Java.
Implemented built-in functions
Operators + - * / < <= > >= =
Built-ins add sub mul div lt lte gt gte eq if while setq defun print println

If you're feeling especially clever, you can write an editor in Lisp and then write some macros that make it easier to edit your lisp code. It would be sort of an "extensible editor" made up of a plethora of Editor MACroS that helped with the job of text editing. Oh wait, that's already been done before. Never mind.

In case you get any wild ideas about writing other interpreters in Java, you might want to take a look at what's already out there. Robert Tolksdorf has compiled a nice list of interpreters written in Java and similar feats of programming prowess.

While it may not be the most efficient Lisp interpreter on the block, it sure was a lot of fun to write12 and it demonstrates some of the fundamentals of language parsing and interpreting. A more challenging endeavor would be to write a Lisp compiler that generates Java byte codes, but I think I'll leave that as an exercise for the reader. *

-- Michael <mdb@go2net.com> is now furiously working on a Java interpreter written in Lisp so that he may properly complete the circle.

Source code to the lisp interpreter and applet as a gzipped tar file or a zip file.