[FRIAM] now it's personal

[Frank Wimberly]

Thank you, Jon.  I'll have to ponder that but I probably won't have time to
grok it.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Thu, Oct 15, 2020, 11:20 AM jon zingale <jonzingale at gmail.com> wrote:

> "What's the function associated with it?  Words like derivative,
> differential, directional derivative, etc. mean something to me."
>
> Let me attempt a brief and likely rough answer. Terms from lambda calculus
> correspond to algorithms. There is a model of lambda calculus (as-well-as
> full linear logic) where types are interpreted as vector spaces over
> algebraically closed fields and the terms as power series on these spaces.
> In these models all functions are differentiable and a paper by Ehrhard and
> Regnier gives this derivative. Clift and Murfet then go on to flesh out
> (and
> coin) "Sweedler semantics" for this differential linear logic, named after
> the mathematician who studied these structures in the domain of Hopf
> algebras.
>
> In light of the recent discussions regarding maximally stateful and purely
> functional computation, this work is interesting exactly because of the
> differences which exist between theories of lambda calculi and Turing
> machines. While they both specify the same class of functions
> (Church-Turing), the former knows nothing of intensionality (time or space
> complexity, say). Clift and Murfet then follow the Church-Turing
> correspondence, using linear logic as the bridge, to show how
> differentiation of programs manifests in the real application of program
> synthesis, training neural nets for example.
>
>
>
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