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I wonder if this correspondence could be used for program transformations/optimizations?

code -tx-> polynomial -tx-> simplification -tx-> [possibly more efficient] code




My burgeoning conjecture (as hinted at in a previous comment) is that all can be unified, transformed, and optimized for modern hardware under the matrix model of computation -- type theory, the lambda calculus, the actor model, neural nets, graph computing -- I'm starting to see a path to where all models are aligned across vectors of unity.

Here are some the correspondences I've been looking at...

* Graph algos in the lang of linear algebra now realized and encoded into GraphBLAS [1]

* The three normed division algebras are unified under a complex Hilbert space [2]

* Ascent sequences and the bijections discovered between four classes of combinatorial objects [3]

* Dependent Types and Homotopy Type Theory [4]

* Bruhat–Tits buildings, symmetry, and spatial decomposition [5]

* Distributed lattices, topological encodings, and succinct representations [6]

* Zonotopes and Matroids and Minkowski Sums [7]

* Holographic associative memory and entanglement renormalization [8]

[1] Graph Algorithms in the Language of Linear Algebra (Jeremy Kepner) http://www.mit.edu/~kepner/ Discussion: https://news.ycombinator.com/item?id=18099520

[2] Division Algebras and Quantum Theory (John Baez) http://math.ucr.edu/home/baez/rch.pdf

[3] (2 + 2)-free posets, ascent sequences and pattern avoiding permutations [pdf] https://www.sciencedirect.com/science/article/pii/S009731650...

[4] Cartesian Cubical Computational Type Theory: Constructive Reasoning with Paths and Equalities [pdf] https://www.cs.cmu.edu/~rwh/papers/cartesian/paper.pdf

[5] Bruhat–Tits buildings and p-adic Lie groups https://en.wikipedia.org/wiki/Building_(mathematics)

[6] Distributive lattices and Stone-space dualities https://en.wikipedia.org/wiki/Distributive_lattice#Represent...

[7] Solving Low-Dimensional Optimization Problems via Zonotope Vertex Enumeration [video] https://www.youtube.com/watch?v=NH_CpMYe3tw https://en.wikipedia.org/wiki/Zonohedron

[8] Entanglement Renormalization (G Vidal) https://authors.library.caltech.edu/9242/1/VIDprl07.pdf?hovn... Holography https://en.wikipedia.org/wiki/Holographic_associative_memory

Google Scholar: https://scholar.google.com/scholar?q=related:Yi-GtarGxh0J:sc...


Can you expand on what you mean? What is "the matrix model of computation" and "vectors of unity"?

Which actor model are you talking about? The variants are very different and Hewitt's original paper is mainly referenced for coming up with the name rather and kicking off the field than inventing a usable model.

Type theory is even vaster. Are we talking homotopy type theory? Calculus of constructions? System F?


You might like this:

http://www.haskellforall.com/2014/09/morte-intermediate-lang...

Basically, it's a calculus of constructions that guarantees equivalent funtions get compiled to the same thing. It's really intended as an intermediate form for some higher-level language, and we have Annah as just such an example:

https://github.com/Gabriel439/Haskell-Annah-Library




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