Wassily Kandinsky Willem de Kooning Joan Miro Russ Abbott, California State University, Los Angeles

5/10/2015What is abstraction?2  PHILOSOPHY conceptualization : the process by which people develop concepts either from experience or from other concepts. (Encarta.com)

5/10/2015What is abstraction?3  When an entity, biological or mechanical, makes a distinction (e.g. by behaving differently under different circumstances) it has not created an abstraction.  An abstraction is a reified distinction, a distinction for which the entity has a name and to which it can refer—abstractly.  Abstraction implies conceptualization, which implies a mind that holds the abstraction.

5/10/2015What is abstraction?4 eval(A + B, C) :- eval(A, AVal), eval(B, BVal), C is AVal + BVal. eval(A - B, C) :- eval(A, AVal), eval(B, BVal), C is AVal - BVal. eval(A * B, C) :- eval(A, AVal), eval(B, BVal), C is AVal * BVal. … eval(Expr, Result) :- Expr =.. [Op | Args], isArithmeticOp(Op), !, map(eval, Args, ArgsVals), Expr1 =.. [Op | ArgsVals], Result is Expr1. Liskov: Abstraction by parameterization extracts an essential core of some computational element and reifies it as a named element of its own, leaving parameters to be filled in when the abstraction is instantiated.

5/10/2015What is abstraction?5 switch (expression) { case 1: code_1; case 2: code_2; … } class SuperClass; class Class1 extends SuperClass; class Class2 extends SuperClass; … Convert a distinction ( switch ) into a concept ( class )

5/10/2015What is abstraction?6  Since abstraction results from the extraction and reification of the essence of something, one cannot extract an essence of something until that thing exists.  A significant thread in computer science is the process of becoming aware of and then reifying a thought process as an abstraction.  Backus conceived Fortran when he realized that it was possible to program a computer to do the same sort of translation that programmers did mentally.  Then came compiler generators, etc.

5/10/2015What is abstraction?7  Software composition involves (a) organizing software elements (b) to serve a given purpose.  Bottom-up. The pieces existed—even if only in one’s mind—before they could be organized.  Top-down. The intended meaning existed before the software could be written.  Software composition—i.e., implementing an abstraction—is where top-down meets bottom-up.  That’s the magic that we as human beings can do.

5/10/2015What is abstraction?8  Yes. We teach abstraction when we teach programming languages and techniques.  We are reasonably successful at doing this. Students can learn how to use abstractions. But learning abstraction tools requires a lot of work. primes = sieve [2.. ] where sieve (p:xs) = p:sieve [x | x  xs, (x `mod` p) /= 0] fib = 0 : 1 : zipWith (+) fib (tail fib)  Yes, self-awareness can be taught, but with difficulty.  To do that teach design patterns by giving problems for which a design pattern is a solution but require students to come with it themselves.  No, abstraction as brilliance cannot be taught.  But one can be taught to recognize good abstractions. This is similar to recognition (P) vs. generation (NP), which is typically much harder.

5/10/2015What is abstraction?9  To be successful software engineers students must be able to construct conceptual—i.e., abstract—models of different customer domains.  Give students as much experience as possible in seeing the world in different ways.  Teach how different disciplines model the world—especially how they use visualization and modeling programs to think.

5/10/2015What is abstraction?10  Abstraction by parameterization extracts an essential core of some computational element and reifies it as a named element of its own, leaving parameters to be filled in when the abstraction is instantiated.  Abstraction by specification abstracts from the implementation details (how the module is implemented) to the behavior users can depend on (what the module does).