Comment by zmgsabst

Modern mathematics deals with ISA design from the perspective of application:

A CPU, an FPGA, and an GPU are all Turing complete substrates, yet they’re useful for wildly different things.

Category theory, type theory, and set theory all can embed arbitrary mathematics — but the encodings you get lend themselves to different applications.

Eg, category theory is very useful at abstracting structures to check if they’re “the same”.