udexon
commented
5 years ago Updates:
https://groups.google.com/d/msg/comp.lang.forth/UO2E9xHOq_g/NrzDaqf7DwAJ
-- start -- Hypothesis SM1: All mathematical and programming structures can be constructed using graph. As such, they can be constructed using stack machine reverse polish notation.
We may attempt to prove the above by induction.
Firstly, we may prove the generation of natural number. Write an RPN program to generate natural numbers and verify them manually. This is trivial.
Next, write other RPN programs, which can be used to inductively prove other theorems.
Repeat the above until the collection of RPN programs can generate programs automatically, and prove all (observable) physical observations.
-- end --
I think the above hypothesis SM1 is now self contained and well defined.
Comments welcome.
On Mon, Jan 7, 2019, 19:19 Sean B. Palmer notifications@github.com wrote:
On comp.lang.forth you hypothesized https://comp.lang.forth.narkive.com/U38oqt1m/graph-theory-representation-for-forth-stack-machine-features-constructs#post7: "All mathematical and programming structures can be constructed using graph. As such, they can be constructed using stack machine reverse polish notation."
You may be interested in Brent Kerby's Theory of Concatenative Combinators http://tunes.org/~iepos/joy.html, and in concatenative languages https://en.wikipedia.org/wiki/Concatenative_programming_language in general. Concatenative languages put FORTH on a more theoretical basis, and Kerby shows how you can perform any tree structure transformations using only a small set of combinators. Combinators are related conceptually to FORTH's words.
I wasn't sure whether to open an issue for this or to create a wiki page. In any case I hope this information is helpful to you.
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On comp.lang.forth you hypothesized: "All mathematical and programming structures can be constructed using graph. As such, they can be constructed using stack machine reverse polish notation."
You may be interested in Brent Kerby's Theory of Concatenative Combinators, and in concatenative languages in general. Concatenative languages put FORTH on a more theoretical basis, and Kerby shows how you can perform any tree structure transformations using only a small set of combinators. Combinators are related conceptually to FORTH's words.
I wasn't sure whether to open an issue for this or to create a wiki page. In any case I hope this information is helpful to you.