Software design is refinement, not abstraction

James Koppel tells us that software engineers keep using the word “abstraction” and that he does not think it means what they think it means. I believe that he is correct, and that the confusion over the term abstraction comes from thinking that programming is about abstraction.

Programming is refinement, not abstraction. You take your idea of what the software should be doing and you progressively refine that idea until what you get it so rote, so formulaic, so prescribed, that you can create a plan that a computer will follow reliably and accurately. Back in the day, that process used to be done literally in the order written as a sequence of distinct activities.

  • You take your idea of what the software should be doing: requirements gathering
  • refine that idea: software specification
  • create a plan that a computer will follow: construction
  • reliably and accurately: verification and validation

It doesn’t matter what paradigm you’re using, what tools, or whether you truly go from one step to the next as described here, what you’re doing is specifying the software you need, and getting so specific that you end up with instructions for a computer. Specific is the opposite of abstract: the process is the opposite of abstraction.

Thus Niklaus Wirth talks about Program Development by Stepwise Refinement. He describes a procedure for solving the 8 queens problem, then refines that procedure until it is entirely described in terms of Algol (more or less) instructions. He could have started by describing a function that turns the set of possible chess boards into the set of boards that solve 8 queens, or he could have started by describing the communication between the board and the queens that would cause them to solve 8 queens.

This is not to say that abstraction doesn’t appear in software development. Wirth’s starting point is an abstract procedure for solving a specific problem: you can follow that procedure to solve 8 queens, you just have to do a lot of colouring in yourself which a computer is incapable of. Maybe GPT-3 could follow that first procedure; maybe one of the intermediate ones.

And his end point is an abstract definition of the instructions the computer will do: you can say j<1 and the computer will do something along the lines of loading the word at the same address previously associated with j into an accumulator, subtracting one, checking the flags index, and conditionally modifying the program counter. And “loading the word at the same address” is itself an abstraction: what really happens might involve page faults, loading data from permanent storage, translation lookaside buffers, and other magic.

Abstractions in this view are a “meet in the middle” situation, not a goal: you can refine/specify your solution until you meet the thing that will do the rest of the work of refinement. Or sometimes a “meet off to the side” situation: if you can make your program’s data look like bags of tuples then you can use the relational model to do a lot of the storage and retrieval work, even if nothing in your problem description looks anything like bags of tuples.

Notice that Wirth’s last section is about generalisation, not abstraction: solving the “N queens” problem is not any less specific than solving the 8 queens problem.

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