Lisp Fundamentals

NOTE: for all my non-computer friends and readers. If technical topics bother you or make you tense, perhaps todays post is not for you. If you are not given cold sweats when facing a new topic with the flavor of computers or programming, by all means please join me.

There are many things that Lisp, the programming language does right. It never ceases to amaze me and I am going to once again take a few minutes to discuss exactly what some of these things are and why they are so important.

Lisp was not originally conceived of as a programming language. It was invented by John Backus as a notation to enable discussion about Alonzo Church’s lambda calculus.

Lisp is characterized by the structure of its expressions, called forms. The simplest of these is the atom. An atom is a singular symbol or literal and represents a value. For instance, 42 is a numeric literal whose value is the number 42. Similarly, “Hello, world!” is a string literal that represents itself as its value. There are also symbols, which are strings of unquoted characters that are used as fundamental elements of Lisp. There are rules for how a valid symbol is form but for now it is sufficient to know that a symbol starts with a letter and then is composed of zero or more additional characters that can be either a letter, a number, or one of a collection of certain punctuation characters. Since the exact list of other characters varies among the dialects of Lisp, we will leave them unspecified at present.

The other type of form is a list. A list is comprised of a left parenthesis followed by zero or more forms and ending in a right parenthesis. Notice I said forms instead of symbols. The implication here is that you can have lists embedded in other lists as deeply nested as you like. This proves to be an interesting trait as we will soon see.

There is one more fundamentally interesting aspect of Lisp. That is that in a typical Lisp form the first element in a list after the left parenthesis is taken to be an operator. The subsequent elements in the list are considered arguments. The operator is either a function, a macro, or a special form. Macros and special forms, while extremely important and interesting are beyond the scope of this discussion.

That leaves us the operator as function. A typical Lisp function form is evaluated as follows. The first element is examined to determine what kind of form the list is. If it is a function, the rest of the arguments in the list are evaluated and collected in a list and the function is applied to them. If another list is encountered as one of the arguments, it is evaluated in exactly the same way.

For example, consider the expression (+ 4 (* 8 7) (/ (-26 8) 9)). The first operator is +. + is a symbol bound to the function that represents addition. The second item in the list is 4. It is a number that represents itself. The next element in the list is the list (* 8 7). When evaluated, the 8 and 7 are arguments to *, the multiplication function and the value returned by that function is 56. The final element in the top level list is (/ (- 26 8) 9). The / is taken as the division function and is applied to the evaluation of (- 26 8) which is the subtraction function that returns 18. When you divide 18 by 9. you get the value 2. Thus the top level argument list  consists of 4, 56, and 2. When you add all three of those numbers you get 62 which is the value that the expression ultimately returns.

This simple mathematical expression illustrates another fundamental aspect of Lisp. It is expressed as a list form which, given a set of bindings to arithmetic functions expresses a simple program. This identical representation of both data and programming in Lisp, called homoiconicity by the way, is at the heart of much of Lisp’s power. Since Lisp’s programs are indistinguishable from Lisp’s data, they can be manipulated by Lisp programs to great advantage.

Think of it like this. Lisp can, in some sense, think about how it is thinking and modify it as it desires. This is why artificial intelligence investigators like using Lisp so much, it is so similar to the simplified models of intelligence that they are building that the boundary begins to blur.

Sweet dreams, don’t forget to tell the ones you love that you love them, and most important of all, be kind.