Recursion and towers of abstraction
Stefan
[…] Because this all isn’t quite complex enough yet, grammars themselves stack recursively. What are expressions (results) generated from one grammar can become primitives in another, higher-level one. For instance, Alexander’s pattern language builds on top of natural language, which builds on top of metaphorical structuring and kinesthetic image schemas, which builds on top of pattern matching external reality.
Prabros
Because this all isn’t quite complex enough yet, grammars themselves stack recursively. What are expressions (results) generated from one grammar can become primitives in another, higher-level one. For instance, Alexander’s pattern language builds on top of natural language, which builds on top of metaphorical structuring and kinesthetic image schemas, which builds on top of pattern matching external reality.
You might enjoy this paper by late Robin Milner (ML language inventor). Its about towers of models: https://www.cl.cam.ac.uk/archive/rm135/models-for-kahn.pdf
Richard Dedekind, Was sind und was sollen die Zahlen?
Prabros
- we (at least I am) might be starting to sound like two kids who just recently learnt Lojban and is training to speak in it with others not making much sense out of this conversation.
- regarding recursion and towers of abstraction, you might benefit from reading the paper “Was sind und was sollen die Zahlen?” by Richard Dedekind. It might be a bit heavy going on the math, but more than a few research threads of mine has lead up to that paper as being a canonical one in what directed proof theory, number theory, and logic (and thereby programming languages) towards recursion as the core concept of defining numbers. This looks like it might be an accessible intro to its background: https://www.math.uwaterloo.ca/~snburris/htdocs/scav/dedek/dedek.html
Stefan
- German original, slightly modernized version of the paper @prabos posted: http://www.opera-platonis.de/dedekind/Dedekind_Was_sind_2.pdf