Orchid XP v8 wrote:
>> An abstract data type has to define the operators also.
> 
> Yeah, I was talking about *algebraic* data type when I said "all Haskell 
> types are ADTs". ;-)

Sorry. I get them mixed up, since the definitions changed since I studied 
them. I don't hold that "objects" or "classes" are "abstract data types" at 
all, so the two terms mean the same for me.

>>> As for "like say a stack", I'm not really sure what you mean.
>>
>> Well, an ADT has to define the type in terms of the operations on that 
>> type, not in terms of a list of values/literals.
> 
> I think we're still talking about two different meanings of ADT. ;-)

Possibly.

> I always wandered what a abstract data type actually is...

That's what it is. There's even a programming language called "ACT.ONE" (or 
maybe "ACT.1", I forget which) that really has abstract/algebraic data 
types, in that you (for example) don't give actual sequential steps for 
pushing and popping, but you actually wrote the kind of thing that I wrote.

> The Eiffel guy had a chapter implementing a stack and "proving" that it 
> matches the spec. 

That's actually impossible to do, since Eiffel isn't a formal language. 
There's no definition for what "X = Y" means in the language (as in 
assignment operator) so he can't mathematically prove it matches the spec.

> (He attempted to claim that the code *is* the spec.)

Well, it's the spec for what his code does, but that's trivially true of any 
safe language.

 > I think he was trying to counter the old "there is no mathematical theory
> to OOP".

And for the most part there isn't. There's hand-waving mathematics, but not 
something precise enough you can automate it.

> At the time, I believed him. Having seen Haskell, and its evil twin the 
> Lambda Calculus, I now understand what they mean by "no theory of OOP"...!

Yep, exactly. ADTs are the sorts of high-level data types you build out of 
lambda-calculus type rewrite rules. LOTOS is the only actual programming 
language I know of that goes all the way down to that level of mathematical 
detail.

-- 
   Darren New, San Diego CA, USA (PST)
   Why is there a chainsaw in DOOM?
   There aren't any trees on Mars.

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