Re: non-consecutive ranges

[Ehud Lamm <mslamm@mscc.huji.ac.il>]

The idea of non consecutive ranges come up many times. I find it very
remarkable. Consider how costly vvalidity checks for such types can be.
Consider a type which is based on integer, but consists of only the prime
numbers...

This is a nic example of "over abstracting." This idea ofranges is so
appealing in many situations that we tend to quite simply SEE how the
abstraction is logically extended to such "sets of ranges." Many don't
even see this as new, and are surprised to see that some syntax they come
up with, doesn't compile.

This is one of example of the amazing power of good abstractions - we lose
site of the implementation details altogether, and so don't know where the
applicability of the abstraction ends.

We can connect this to the idea of abstraction in general. Great
scientists are usually regarded to be those that aside from using various
scientific abstractions (like differntial equations, newtonian mechanics,
thermodynamics etc.), grasp the inner details - thus knowing when things
are applicable and when they are not and the theory etc. needs to be
modified.

Analogy can many times be the key here, but knowing where the analogies
end is the crucial part. (This sentence may be seen as a pointer to Doug
Hofstadter's theories of analogy making).

Ehud Lamm     mslamm@pluto.mscc.huji.ac.il