See below.

On 2017-08-09 15:14, Jack Andrews wrote:
  implementations. It is not supposed to include definitions which it would
require infinite resources to compute, since we want to create an
executable notation.

Do you always know if a definition takes finite resources?
We talk about the specification of a programming language, not a program. I don't know any relevant examples, I just answer to the in my view theoretical objections. In my view we should have the usefulness of the implementation in mind.

I don't understand the note about edge cases. There is a problem with most
programs we write in that they can not handle all cases. We don't know for
sure that they will always give correct results. That is a problem we want
to address.

Is this what you mean by "control" in your original email?
I see a problem in the control process of J development. We had some visionaries. Now it seems we do a lot of small changes. It is not clear to me what is the strategy and how we control further development.
This is about the vision of a future J and how to create the strategy.
How will your work differ from the work done on other "proven" languages?
I know very little about software proof and other languages commonly used when you need software proof to assure correct function. My idea is to have an executable notation which could be used to create such proof, and that the future of J would be to supply this notation. The idea might be useful or not.

Erling Hellenäs

On 2017-08-09 09:47, Raul Miller wrote:

Your 2 prohibits your algebra from being completely implemented as a
programming language (since you have to support whatever you are going
to describe before you can use that in specifications, and because
computers have finite resources). So you are talking about a notation,
and not an implementation. But hypothetically speaking, you could use
J as a notation which is independent of any specific implementation.
(You presumably would want to specify whichever edge cases mattered to
you, when you do this.)

Generally speaking, though, mathematical logic deals with infinities
and other future equivalencies.


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