A very brief search recovered this likely connection between surreal numbers and linear logic via combinatorial games and compact closed categories, respectively: http://pages.cpsc.ucalgary.ca/~gscruttw/publications/CGC.pdf
To contribute to your bullet points, I also wonder about an interpretation of other intensional/complexity domains like algorithmic stability. In particular, is there a nice extension of the theory to account for robustness[♠] à la David Ackley? For example, where traditionally lambda calculus is ill-equipped to distinguish the value of Qsort over Bubblesort in time, lambda calculus is also ill-equipped to distinguish the value of Bubblesort over Qsort in robustness. [♠] https://www.cs.unm.edu/~ackley/be-201301131528.pdf -- 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/
