An introduction to Differential Linear Logic: proof-nets, models and antiderivatives · HackerPapers discussions

An introduction to Differential Linear Logic: proof-nets, models and antiderivatives — mentioned by bmc7505

Sun, 02 May 2021 23:02:29 GMT

Surprisingly, there is an interesting proof-theoretic connection between differential and sequent calculus! For a more detailed account of differential linear logic (DiLL), see Erhard [1] and Kerjean [2]. More generally, the same rules from differential calculus have reappeared in strange and marvelous places throughout computer science, including formal language theory [3], parsing [4], type theory [5] and automata theory [6]. We do not attempt to cover all these topics, research is just beginning to understand how they are related. The general theme seems to be, how do you propagate local…

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An introduction to Differential Linear Logic: proof-nets, models and antiderivatives — mentioned by noelwelsh

Thu, 03 May 2018 11:59:33 GMT

For a loop, you can unroll it and define the derivative that way. But you're correct in general that there are programs that have no sensible derivative but automatic differentiation will still compute something. Going beyond AD there is a "differential lambda calculus" [1]. I don't really understand this work. It requires more background in programming languages, logic, and analysis than I have time to learn. My understanding is it allows you to compute more derivatives (e.g. for higher-order functions) and place conditions so only sensible derivatives are computed. There is also…

Paper and discussion history. A mention is not an endorsement.