kitten VS lawvere

While not quite a Forth, Kitten is a stack language:

https://kittenlang.org/

Since you're making a statically-typed concatenative language, I'll point you to a joy reference, kitten, notes to motivate type checking stack languages, and a paper that formalizes type checking for stack languages. Since this looks like a relatively high-level stack language (given the presence of ADTs), you may find that you want to add quotes to your language, specifically opaque quotes since your language is typed. In that case, you'll realize that you'll need a better way to formulate polymorphism over stacks, and the paper on type checking will provide that to you.

Well, there is Kitten, although it hasn't seen an update in two years and was moving quite slowly before that too.

https://kittenlang.org/

Author ended up doing a lot of work on Kitten https://github.com/evincarofautumn/kitten

Kitten lang

You may like https://kittenlang.org/

A conditional probability is a probabilistic function.

It goes from a value x to a probability distribution of Y.

It is more general than a non-deterministic computation. You get a list of results with weights attached to it. (ignoring continuous distributions)

Grouping can be regarded as a non-deterministic computation.

It goes from a value x to a list of Y.

Computing averages or other aggregations from lists or distributions is another step.

https://dennybritz.com/posts/probability-monads-from-scratch...

https://github.com/mattearnshaw/lawvere/blob/master/pdfs/196...

The study of conceptual mathematics can be motivated by noting the conceptual nature of comprehension and by recognizing the learnable-and-teachable nature of mathematics.

Category of Categories https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1966-category-of-categories-as-a-foundation-for-mathematics.pdf

P.S. Reality consists of reflective parts (Lawvere & Schanuel, Conceptual Mathematics, 2nd ed., pp. 84-85).

(plz see F. William Lawvere, Perugia Notes, pp. iii-iv)

We all know one zero: quantity 0. There's another zero we need: quality 0. Can r/OpenAI help us in this longstanding mathematical quest (pure 😉 To put it all in perspective, mathematics is about qualities (resulting from quantitative changes) represented as structures (geometric objectification of concepts) in a structureless background. Ideally, one would like to print on a blank page, with the blankness being zero cohesion and zero change i.e., quality 0 (see F. William Lawvere, Axiomatization and Education).

In spite of the fact that variable quantities provide a more accurate description of reality, constant quantities---both historically and conceptually---are primary in the theory of variable quantities (Lawvere, 1972, Perugia Notes, p. iii).

And here are some papers by Lawvere which claim to be inspired by Hegel's Science of Logic: https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1992-categories-of-space-and-quantity.pdf

Speaking of TIME, "in Indo-European languages 'time' is not typically just an abstract one-dimensional continuum; the abstract time is a dialectical negation of the idea of time as the rich environment of external conditions that may influence our system, but which we can influence only negligibly: In Italian tempo (time) also means weather, in Danish the word for time is tid, which is old English for tide. In a Zeit-ung like the Times the tidings describe the whole tempestuous march of events over which the reader has little control. In English we have 'the worst of times' and 'the best of times', and 'the times are a-changing', something a mere smooth line cannot be or do" (https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2001-categorical-algebra-for-continuum-micro-physics.pdf, p. 278).