John Shutt’s weird λ-calculus-based approaches to superunification:
A more straightforward solution, […] is to give up on chronological determinism and instead acquire mathematical determinism, by the arguably “obvious” strategy of supposing that the whole of spacetime evolves deterministically along an orthogonal dimension, converting unknown initial conditions (initial in the orthogonal dimension) into chronological nondeterminism. […]
The approach does, however, seem well-suited to a co-hygiene-directed theory. Church-Rosser-ness implies that term rewriting should be treated as reasoning rather than directly as chronological evolution, which seemingly puts term rewriting on a dimension orthogonal to spacetime. The earlier co-hygiene post noted that calculi, which converge to an answer via Church-Rosser-ness, contrast with grammars, which are also term-rewriting systems but exist for the purpose of diverging and are thus naturally allied with mathematical nondeterminism whereas calculi naturally ally with mathematical determinism. So our desire to exploit the calculus/physics analogy, together with our desire for abstract separability of parts, seems to favor this use of a rewriting dimension orthogonal to spacetime.
I bet Hackernews weighs in over-enthusiastically on this.
Especially string rewriting but you can do almost-anything rewriting.
- Semi-Thue systems
- Rewriting home page
- Emile Post’s Tag machines