Then you get to definitions like ": open ( string -- handle 1 | 0) ... ;" which describes returning algebraic type Maybe Handle unboxed on the stack. Algebraic types are fun, they can easily represent Peano arithmetic and get us into the realm Goedel incompleteness theorem very quickly.

Or you can deduce signature for EXEC EXEC sequence. EXEC's stack effect can be described as ( \alpha (\alpha -- \beta) -- \beta), where \greekletter is a placeholder for a stack part of arbitrary length. Notice that this type comment has nested brackets and does not adhere to Forth stack-effect comment convention.

When I thought about this more than fifteen years ago, I've got at least two equally valid types for the EXEC EXEC: one where xt at top of stack consumes all its input and leaves no output ( \alpha (\alpha -- \gamma) \beta (\beta -- ) -- \gamma) and when first EXEC produces something for second to execute upon ( \alpha \beta (\beta -- \gamma (\alpha \gamma -- \theta) -- \theta).

One can argue that second type of EXEC EXEC subsume first one, if greek-letter-named-stack-parts are allowed to be empty.

Still it shows that typing Forth, at the very least, needs unification on the Peano's arithmetic level, implementing deduction from length zero to unbounded length.

So, in my opinion, for LLM to dependably combine typed Forth/concatenative definitions, it needs to call external tool like Prolog to properly deduce type(s) of the sequence of Forth's (or concatenative language's) definitions.

And here we enter a realm interesting in itself.

Here it is: https://github.com/stassa/louise

This is a Prolog system to learn programs in polynomial time. For one example, it can one-shot-learn a grammar, without being "trained" on millions of samples.

So, should one use a LLM that either needs a paid access or just slow to run, or freely go where "old school" systems like Eurisco [1] and Cyc went?

[1] https://en.wikipedia.org/wiki/Eurisko

Eurisco demonstrated superhuman abilities in 1982-83. It also demonstrated knowledge transfer at the time, where rules from VLSI place-and-route algorithms were used to design winning Traveler TCS fleet.

R3forth: A concatenative language derived from ColorForth