Lisp Interpreter

Motivation

Any serious attempt at studying the art of computer programming must include a component on programming languages. Code is a programmer's raw material, like paint to an artist or words to a writer. Starting out, we all tend to see a programming language as a set of directives that can be used to manipulate data. Code lives in one world and data another. This is a limit that holds you back from really jumping down the computation rabbit hole. The best way, that I've found, to really understand the idea "code is data" is to implement your own interpreter.

This project is focused on producing a Lisp interpreter, more specifically a Scheme interpreter. You may be wondering, why are we writing an interpreter for an outdated AI language? Lisp is a good project because the syntax is exceedingly simple. There is one main syntax construct and a few special cases that make up the entire language. This simplicity clears away a slew of problems and exposes the main insight of code/data equivalence.

Also, Lisp is worth learning because it makes you a better programmer. That's not only my opinion. Great hackers of the past have agreed with the sentiment.

Lisp is worth learning for the profound enlightenment experience you will have when you finally get it; that experience will make you a better programmer for the rest of your days, even if you never actually use Lisp itself a lot. -Eric Raymond

Prerequisites

Recursion: Before dealing with Lisp, you should have a firm grasp of recursion. The best resource I've found for exploring recursion is the book The Little Schemer.

Basic Lisp: It is helpful if you've downloaded a Lisp interpreter like Dr Racket and typed in a few commands. You don't need extensive knowledge, but an hour noodling around with the interpreter would be beneficial. Once again, I recommend The Little Schemer if you want a thorough introduction.

Problem Statement

In his landmark paper, Recursive Functions Of Symbolic Expressions And Their Computation By Machine, John McCarthy builds a programming language on a handful of primitive expressions. He called the language LISP for List Processing.

In this problem, Lisp will always refer to McCarthy's original Lisp.

For this project, your job is to write a Lisp Interpreter. The interpreter will take in a text file containing a Lisp program, execute it, and then display the result.

Here is a simple Lisp program:

( + 2 2 ) => 3 # => stands for "evalutes to"

Lisp is a functional language. Every Lisp expression evalutes to value. A Lisp expression is either an atom or a list. Atoms are strings of characters, basically anything except a parentheses. A list is a number of expressions enclosed within parentheses. Notice how I didn't say a list of atoms.

Examples of atoms:

1 + john burger

Let's take a look at these atom examples. 1 is just a number, similar to an int in C or Python. However, +, john and burger are a bit unusual. In Lisp, these are called symbols. You may find it tempting to draw an analogy of strings to symbols. Don't. They are completely different beasts.

The concept of a symbol is implicit in other languages, Lisp just exposes the concept explicitly. In other languages, symbols are used as variable names. To execute your programs, a compiler/interpreter will tokenize your source code and then identify these symbols. In Lisp, symbols are also used to as identifiers for variables, however you get to muck with them directly. Symbols are just entities that you can bind values to.

Now let's talk about lists. A list is just the symbol '(', followed by a series of elements separated by spaces, and then a closing ')'.

Example of lists:

( a b c ) ( john jack jim ) (( a b c ) ( 1 2 3 ) ( d e f )) # This list as 3 elements . Each element is also a list . ( + 1 1 ) # Yes , this is a list too .

Normal Forms

For the sake of simplicity, let's build a Lisp that only has 4 normal builtin functions:

+ - * /

They do exactly what you think they do: Add, subtract, multiply and divide.

The rules for evaluating a normal lisp expression or form is easy. Take first element in a list, look up it's value and apply it to the other elements in the list. For example:

(+ 1 2) => 3

Remember our discussion about symbols earlier? + is just a symbol which is by default bound to the function we know as addition. So when we enter the form (+ 1 2) into the interpreter, Lisp looks up the function associated with +, which is addition, and then applies it to the arguments 1 and 2.

If the arguments are also lists, rather than atoms, then evaluate the arguments first before evaluating the parent expression. Example:

( / ( + 2 10 ) 3 ) # => 4

The nesting of the expression completely defines the order of operations. This is nice because there is never any ambiguity.

Special Forms

Now here is where the magic happens. Remember how I said Lisp only has a handful of primitives? Here are ALL the primitives required for a fully functioning Lisp.

eq ? quote cons car cdr atom ? define lambda cond

Let's go through each in turn. Pay attention because some of these forms do not follow the normal evaluation order we learned above.

eq? just tests for equality. It returns True if the two arguments are the same, otherwise false.

( eq ? 1 1 ) # => True ( eq ? 1 2 ) # => False

quote is the first special form we will encounter. Quote says to Lisp, "don't evaluate what I'm about to pass in, just give me back the symbols exactly as I typed them".

( quote a ) # => ' a ( quote ' ( 1 2 3 ) # => ' ( 1 2 3 )

The little ', is Lisp's way of saying that everything that follows is a symbol.

cons, car and cdr go together. Cons is like a piece of velcro, it sticks two things together. Car let's you get back the first piece and cdr lets you get the second piece.

( define box ( cons 3 4 )) ( car box ) # => 3 ( cdr box ) # => 4

Lists are just boxes within boxes, like russian dolls. When you take the car of a list, you get back the first item. When you take the cdr, you get a list with the rest of the elements. When you keep opening them, eventually you get left with an empty box.

( define some - list ' ( 1 2 3 )) ( car some - list ) # => 1 ( cdr some - list ) # => ' ( 2 3 ) ( cdr ( cdr ( cdr some - list ))) # => ' () which is our empty list , sometimes called nil

atom? will tell you whether or not the argument is an atom.

( atom ? 3 ) # => True ( atom ? ' ( 1 2 3 ) # => False

define binds values to symbols.

( define a 5 ) a # => 5 ( define b ( + a 1 )) b # => 6 ( + a b ) # => 11

lambda creates a function. It takes in a list of parameters and a body and spits out a function that takes in the parameters and executes the body with the parameters substituted with the passed in values.

( define square ( lambda ( x ) ( * x x ))) ( square 5 ) # => 25 ( define divides_evenly ? ( lambda ( x y ) ( eq ? ( * x ( / x y )) y ))) ( divides_evenly ? 5 2 ) # => False

Finally we have cond, the generalized if statement. It is just a bunch of if/else blocks that executes the first matching condition and returns the associated value. Here is the example:

( define a 3 ) ( cond (( eq ? a 1 ) ' one ) (( eq ? a 2 ) ' two ) (( eq ? a 3 ) ' three ) ( else ' no - idea )) # => ' three

Your Task

Write a small Lisp interpreter that supports all the functionality described above.

Code References

Lispy - Peter Norvig

Lithp - Michael Fogus

Background Readings