Re: Self pointer in limited record

["Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>]

On Mon, 03 Sep 2007 22:14:09 +0200, Georg Bauhaus wrote:

> On Mon, 2007-09-03 at 21:17 +0200, Dmitry A. Kazakov wrote:
>> On Mon, 03 Sep 2007 17:55:33 +0200, Jean-Pierre Rosen wrote:
>> 
>>> Dmitry A. Kazakov a �crit :
>>>> It is difficult to see how an abstract state machine is not a type. The
>>>> very word abstract assumes generalization, reuse and instances. It is types
>>>> and generics, the tools to express the idea of instances.
>>>> 
>>> Sorry, but I beg to disagree here.
>>> 
>>> Abstraction is about the reduction of a real world objet to those 
>>> elements that are relevant for a given point of view.
>> 
>> Of just one object? I think that an abstraction always apply to a set of
>> things. What could be an abstraction of Spike, the dog?
> 
> (Hope you don't mind be stepping in here.)
> 
> The abstraction could be: Those elements of Spike that are relevant
> for the given point of view on Spike?

"Elements of Spike" is plural. Do you abstract Spike or its elements?

> I wonder, though, why then we can still talk about abstract data
> type and abstract state machine.

Abstract data type is an abstraction of concrete data types.

Abstract state machine is an abstraction of concrete state machines.

>>> A singleton is an abstraction of a single object, and does not need a 
>>> type. I don't see anything in the word abstract that assumes generalization.
>> 
>> There is little abstraction in being alone. This is actually the reason why
>> no type is need for a singleton: no abstraction, no instances, no type.
> 
> Is there little abstraction in being alone (hm, who said that being
> along is the source of the thing being an abstract?)
> or is there no abstraction?
> 
>> In my view an abstract state machine has nothing to do with singletons. A
>> state machine might be a singleton, per chance.
> 
> Could you say what you mean by "having nothing to do with"?

Let A, B be two concepts defined as subsets of some common domain set X.

_def_ A has nothing to do with B = not (A in B or B in A)

in = equal or subset of

if � were a truth-valued set measure chosen on X, then having �A you could
not deduce anything certain about �B and reverse:

   not (�A |= �B or �B |= �A)

Neither implies another.

Was that enough pedantic? (:-))

>>  But an *abstract* state
>> machine is definitely a type that generalizes many concrete state machines.
> 
> By what definition of type is an ASM a type that generalizes many
> concrete state machines (=what, in Ada terms?)?

   type State is (...);
   type Transition_Relation is array (State, State) of Boolean;
   type ASM is private;
   function Create (Initial : State; Wiring : Transition_Relation)
      return ASM;
   procedure Step (Machine : in out ASM; Input : State);

This machine is abstract because its wiring is a parameter (abstracted).
The set of states can also be abstracted, but I wished not to complicate
otherwise obvious, I hope, things.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de