That sounds like the insight cdiggins based Cat's type system on, but I'm not entirely sure in part because I don't really understand Cat's type system. As an example, though, for the code

    popop    = { pop pop}

Cat infers the parametrically polymorphic typing judgment

    popop    : ('t0 't1 't2 -> 't2) 

where 't2 is the type of the rest of the stack, I guess, and juxtaposition of types is a sort of product operation (noncommutative, but I think associative, and thus perhaps a monoid).

Not sure what you mean about "projectional" — do you mean that "pop" is a "projection" in the relational sense, in that it maps, for example, the stack 3 8 1 (with the top on the left) and the stack 7 8 1 to the same resulting stack state 8 1?

I don't know anything about protein folding.

> I still haven't grokked your whole description of your Lisp reader, I'll have to sleep on it. Is it related in structure to the METAII meta compiler or parser combinators?

Well, I didn't really write much of a description of the reader. It's a recursive-descent predictive parser, same as Probst's reader, and probably most Lisp readers. READ sets up the input pointers and calls (READ), which is ((READ)), which discriminates between lists and atoms (which are numbers) by looking for a "(". If it doesn't find one, it calls READ-NUM to read a number. But if it does, it calls READ-TAIL, which recursively reads the list contents (by calling (READ)) until it finds a ")", then returns back up, consing up the list as it goes. Probst's code works the same way, with the correspondences READ ↔ LISP-LOAD-FROM-STRING, (READ) ↔ LISP-READ-LISP, ((READ)) ↔ _LISP-READ-LISP, READ-NUM ↔ LISP-READ-TOKEN/-NUMBER/-SYMBOL, and READ-TAIL ↔ LISP-READ-LIST.

META II has the similarity that it generates recursive-descent parsers with predictive parsing, but the dissimilarity that it's a domain-specific language for writing parsers. Parser combinators are a technique for embedding any domain-specific parsing language in a general-purpose host language, regardless of what parsing algorithm is used, though Packrat may be the most common choice, and Packrat has certain similarities to recursive-descent parsing.

Is that helpful?