[REBOL] Re: Private/Public attributes
From: jan:skibinski:sympatico:ca at: 15-Nov-2002 23:51
Hi,
This is probably too far off topic, but since Joel
said <<where there's a "won't" there's a "will"! >>,
I'd like to share this bit about information hiding.
The only concept I know of that provides theoretical
support for true privacy is ADT (Abstract Data Type)
and a related to it existential quantification.
Existentially quantified types were first described
by Mitchell & Plotkin. There are some good papers
by Luca Cardelli explaining the basic idea.
In essence, objects described by abstract data types
display some abstract behaviour that is independent
of the representation type.
Users should not be allowed to break the abstraction via the
abstract data type interface. Once an abstract object is made,
its representation type can never be rediscovered.
There are many existential types that are too general to be
useful. The only useful kind of existential objects are those
packaged as pairs (cartesian products) made of an unknown value
and a function from that value to something specific, such as
integer. The corresponding signature of such an object 'x
would be something like this:
x :: Exists. a (a, a -> integer)
which loosely means "The object 'x is a pair made of a value
of unknown type 'a, and of a function from type 'a to integer".
The type 'a is not universal - as it would be the case
with FORALL 'a quantification, the above only means that there
EXISTS SOME type a' taken from a universe supported
by a language under consideration.
We do not know what this type is, and we do not
know how to discover the real structure of this packed
object 'x (is it a tree, or an array or a stack?).
But we can take advantage of its cartesian type to calculate
the value of the integer, by applying the second part of 'x
to the first one:
second x first x
== 43, say
A programmer packaging such an object knew exactly
what the first element was, say integer 5. But once packaged,
its value remains a secret for the receiving party.
Existential types have been introduced to Haskell
quite recently, as one of the extensions. I played with
them a bit and they seem quite convenient for certain
kind of applications. Functional languages Clean and Caml
and the functional-logical language Mercury also
support existential types.
Regards,
Jan
