Our answer is algebra.

First of all, algebra is sufficiently abstract: languages like C++ distract the students with all sorts of details like memory management, pointers, and so forth. But the programmer who uses a search engine, a spreadsheet, or a word processor does not encounter any of these details.

Second, is algebra a programming language? Surely we can all agree upon the following definition of a programming language: A precise notation for expressing computations. Now let's look at a few algebraic expressions:

• 1 + 2 is a computation that says, ``compute 1, then 2, then add the results together and return the answer''.
• 1 + 2 x 3.5 is a computation that says, ``compute 2 and 3.5, multiply them, take the result, add 1, and return the answer''.
• In algebra, we can also define functions, such as f(x) = x^2 - 3. When we apply the function, like so---f(4)---we first substitute all instance of x with 4, then proceed as before (multiplying, subtracting, and returning the answer).

But algebra is not a very precise language---there are lots of informal ways of writing algebraic expressions---so it can't usually be executed directly on a computer. To remedy this, we can use a programming language that behaves exactly like algebra, but has the benefit of running on contemporary computers.

Last modified at 22:37:03 CST on Sunday, February 08, 1998