Arrows n=m+1 example
Mon, 26 Apr 1999 05:48:45 +0400
>'n', 'm', and '1' would be arrows (selectors) from sets of atoms:
>'n' and 'm' would be part of a particular user context vocabulary
>(called an ontology), and '1' would be an arrow from the set of
>natural or integer or whatever kinds of numbers (again, in a graph).
>this looks like a good place to start discussion... any comments?
It is easy for me to imagine a '+' graph or a '=' graph because I know
intuitively that the concepts behind these need to be linked (by arrows)
to their arguments.
But I have a problem to see 'n', 'm' and '1' as sets of arrows.
Sure these are sets of 'things' but it is strange for me to make
these things arrows. It seems to me that the arrow system must come
to a point where it does not reference arrows of a graph, but simply
'things' of a set of 'things'.
So it seems more intuitive to define an arrow as having two slots that
can reference either an arrow or an 'atom (or object)'. I guess this must be
wrong for you, since it would means to lose the homo-iconic property.
But I don't see by myself yet why it would be so bad.
This example have shown to me that graphs (set of arrows) are
the way semantics get bound to arrows. I now tend to see the evaluation
like an actor that add an arrow to the 'evaluate to' graph. By example
an actor to add natural numbers, that do its job
by looking inside the '+' graph for arrows whose both slots arrows are
member of the 'natural numbers', and if so, add the two numbers and
build an arrow with slot 0 referencing the arrow in the '+' graph,
and slot 1 with a reference to
the sum of the two numbers. This newly created arrow is then added to
the 'evaluate to' graph.
For me these numbers are just element of a set of objects. For you they
are element of the set of 'natural numbers'. But then how does an
arrow of this set became bound with the, let's say, five semantics.
In my way of defining a slot of an arrow as either referencing an
arrow or an object, I simply reference to a record that say where to
find the object, what size it has and there I would find the sequence
of bits 00000101.
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