What is the difference between a variable and a symbol in LISP?

Question

In terms of scope? Actual implementation in memory? The syntax? For eg, if (let a 1) Is \'a\' a variable or a symbol?

Answer 1

Quoting from the Common Lisp HyperSpec:

symbol n. an object of type symbol.

variable n. a binding in the “variable” namespace.

binding n. an association between a name and that which the name denotes. (…)

Explanation time.

What Lisp calls symbols is fairly close to what many languages call variables. In a first approximation, symbols have values; when you evaluate the expression x, the value of the expression is the value of the symbol x; when you write (setq x 3), you assign a new value to x. In Lisp terminology, (setq x 3) binds the value 3 to the symbol x.

A feature of Lisp that most languages don't have is that symbols are ordinary objects (symbols are first-class objects, in programming language terminology). When you write (setq x y), the value of x becomes whatever the value of y was at the time of the assignment. But you can write (setq x 'y), in which case the value of x is the symbol y.

Conceptually speaking, there is an environment which is an association table from symbols to values. Evaluating a symbol means looking it up in the current environment. (Environments are first-class objects too, but this is beyond the scope of this answer.) A binding refers to a particular entry in an environment. However, there's an additional complication.

Most Lisp dialects have multiple namespaces, at least a namespace of variables and a namespace of functions. An environment can in fact contain multiple entries for one symbol, one entry for each namespace. A variable, strictly speaking, is an entry in an environment in the namespace of variables. In everyday Lisp terminology, a symbol is often referred to as a variable when its binding as a variable is what you're interested in.

For example, in (setq a 1) or (let ((a 1)) ...), a is a symbol. But since the constructs act on the variable binding for the symbol a, it's common to refer to a as a variable in this context.

On the other hand, in (defun a (...) ...) or (flet ((a (x) ...)) ...), a is a also symbol, but these constructs act on its function binding, so a would not be considered a variable.

In most cases, when a symbol appears unquoted in an expression, it is evaluated by looking up its variable binding. The main exception is that in a function call (foo arg1 arg2 ...), the function binding for foo is used. The value of a quoted symbol 'x or (quote x) is itself, as with any quoted expression. Of course, there are plenty of special forms where you don't need to quote a symbol, including setq, let, flet, defun, etc.