Numbering Peano An Example in Mind

miser> astraendo> A040601C> 2004-06-04 -15:19 -0700

Initial Example: The following text is from an e-mail plus two consecutive comments that were posted at Orcmid's Lair.  It is the first example for Numbering Peano and it will be further annotated by links and, perhaps, end notes.

2004-05-22-09:38 Blog Comment from Dennis in response to Bill Anderson:

I have in mind an example to work on. It starts as the following "precise" (but not-necessarily valid) statement in Java:

interface com.orcmid.cs.pa.Num
{
/* That is, defined in package com.orcmid.cs.pa
*/

com.orcmid.cs.pa.Num next();

com.orcmid.cs.pa.Num pred();

Boolean is0();
} // Num

Because I can't do much with typography and markup here, this use of Blogger comments is not going to work and we must find another venue. Notice there are several matters to ponder already:

1. What is the behavior that is part of the interface agreement, in terms of what an implementation must provide?
2. What is the abstraction in terms of which this is conveyed/explained? What do I/we mean by that?
3. How this behavior is exploited in accomplishing some other purpose by using it in/under the implementation of something we care about -- an application, if you will?
4. What is the (set of) tacit knowledge that applies here, who says, and how can you tell?
5. Where do we start and where do we end with this?

2004-05-22-10:30 E-mail Heads-Up from Dennis to Bill:

   0.    is how much of this is understood already, without any more information, and what is the basis for that?

2004-05-22-11:46 Addendum Blog Comment by Dennis:

The "Boolean" in the interface declaration, above, should be spelled "boolean".

One thing to allow for is the fact that there can be mistakes in an expression of something.

Then there can be revisions and updating.  Assume, for now, that this is in pre-ALPHA state.

There is tacit inheritance in the use of this interface and that will have to be dealt with as well.  It is one of the places where the tacit shall be made explicit.

Finally, there is no question that this interface definition is platform specific.  It belongs to a specific framework and while it is abstracted from specific computer hardware, there is no question there is a tacit platform assumption.  It is the Java platform and all that entails.

I am just putting down some notes that will be best taken up and made into an organized discussion and description. We can do that later.

2004-05-22-18:46 E-Mail Follow-Up from Bill . . .

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created 2004-06-03-18:50 -0700 (pdt) by orcmid $$Author: Orcmid $ $$Date: 04-06-04 15:20 $ $$Revision: 9 $