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.)

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Generally speaking, though, mathematical logic deals with infinities and other future equivalencies. Thanks, -- Raul On Wed, Aug 9, 2017 at 2:57 AM, Erling Hellenäs <erl...@erlinghellenas.se> wrote: > See comments below. > > > On 2017-08-08 12:09, Jack Andrews wrote: >>> >>> too complicated for any single person or company to handle >> >> jsoftware might disagree. but very few programs built over years of effort >> are pure >> >>> to build a language similar to J as a system of axioms and identities, >> >> why not just use J? it allows identities and axioms. > > 1. The problem was to control J development. > 2. Because I want the identities to have mathematical/logical validity and > hold for all values of the inputs. > > >> >> >> >> >> On 8 August 2017 at 17:27, Erling Hellenäs <erl...@erlinghellenas.se> >> wrote: >> >>> Hi all ! >>> >>> I see a problem in the control of future J development. It is too >>> complicated for any single person or company to handle, as I see it. Yet >>> a lot of coordination is needed. >>> >>> I think the solutions is to create a J algebra, something similar to >>> mathematics and logics, but executable. An executable proof system. I >>> think a program could be it's own executable combination of proof and >>> axioms. >>> >>> The way to start, I think, is to build a language similar to J as a >>> system of axioms and identities, definitions built on these axioms and >>> other known identities. The language is as much as possible defined in >>> it's own terms. It's own proof. The number of axioms are minimized. We >>> then try to simplify. We complement the language definition with >>> identities between different language concepts. >>> >>> The resulting algebra is then used as definition of the new, hopefully >>> J-like, language. The algebra can then be freely extended as long as the >>> axioms it is built on is not modified and the identities still hold. >>> Like mathematics and logics is freely extended today. >>> >>> What i mean here is real mathematical and logical proof. If a and b are >>> integers and c is the mathematically correct result, we should get the >>> correct c for all values of a and b. Or we have to prove that, given the >>> a and b we have, we will always get the correct c. >>> >>> I think the essence of what J is about is to create an executable >>> algebraic system, a parallel universe to mathematics, logics and >>> notations building on mathematics and logics. An executable algebraic >>> system in which we can prove that our programs will always give the >>> correct results. >>> >>> Cheers, >>> >>> Erling Hellenäs >>> >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm