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 <[email protected]> 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. > > > > -- > Sent from: http://friam.471366.n2.nabble.com/ > > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > archives: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC http://friam-comic.blogspot.com/ >
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