Expressions are anything that you type into the Racket interpreter.
For example,
2
is an expression. So is
(+ 2 3)
A combination, as shown above, is an expression where paretheses are used to
show when a procedure is called. The procedure, in this case +, is called the
operator, and the arguments, in this case 2 and 3 are called the
operands. The value of a combination is obtained by applying the operator to the operands.
You've already been introduced to prefix notation in Unit 0.1, so here's a quick recap.
In Racket, we use prefix notation. So, instead of typing in 2 + 3 into the
interpreter, we type in (+ 2 3) --that is, the operator comes before the operands, or arguments.
This has a few benefits. The most obvious one right now is that it can take
procedures, such as + or *, that take a variable number of arguments. For
example, in prefix notation, adding 5 numbers would look like (+ 1 2 3 4 5),
whereas in infix notation, it would look like 1 + 2 + 3 + 4 + 5.
Another benefit is that it makes nesting procedures within each other very easy.
For example, (+ (- 4 3) (/ 4 2)) evaluates to 3. The depth of these
expressions can be arbitrarily extended, so that
(+ (- (/ 4 2) (+ 3 4 2 (/ 4 3))) (* 4 (- 3 4)))
is also valid Racket expression, though one that is very difficult for us humans to understand.
Another advantage is that it makes parsing Racket very easy, which comes in useful when writing an interpreter. If you have no idea what this means yet, don't worry about it.
Even with the most complicated expressions, the interpreter does the same thing: it reads the expression, evaluates it, and prints it to the screen. This is known as the read-eval-print loop .