Comments on: Well-Founded Recursion and Accessibility http://www.iis.sinica.edu.tw/~scm/2008/well-founded-recursion-and-accessibility/ Research Blog of 穆信成 Shin-Cheng Mu Mon, 01 Dec 2008 20:50:20 +0000 http://wordpress.org/?v=2.6.2 By: Shin http://www.iis.sinica.edu.tw/~scm/2008/well-founded-recursion-and-accessibility/#comment-4063 Shin Sun, 28 Sep 2008 16:45:25 +0000 http://www.iis.sinica.edu.tw/~scm/?p=51#comment-4063 Oleg, thanks for the Twelf code! It is new to me that termination of f91 can be proved using lexicographic induction, rather than downward induction. Perhaps that allows you to use a more natural definition of <: and <=:, while I had to create the funny ordering _≤′′_. Meanwhile, as you can see, I have been studying expressing general recursion using coinductive types, which also allows me to prove termination separately from the program. I should try to redo your proof in Agda some day. Oleg, thanks for the Twelf code! It is new to me that termination of f91 can be proved using lexicographic induction, rather than downward induction. Perhaps that allows you to use a more natural definition of <: and <=:, while I had to create the funny ordering _≤′′_.

Meanwhile, as you can see, I have been studying expressing general recursion using coinductive types, which also allows me to prove termination separately from the program. I should try to redo your proof in Agda some day.

]]> By: Oleg http://www.iis.sinica.edu.tw/~scm/2008/well-founded-recursion-and-accessibility/#comment-3618 Oleg Tue, 09 Sep 2008 10:17:12 +0000 http://www.iis.sinica.edu.tw/~scm/?p=51#comment-3618 Perhaps you might find it curious to see how the function f91 is handled in Twelf. Twelf can't see that f91 is terminating either (let alone that this is the maximum function of two naturals). We have to make the explicit proof. We do not modify the function definition however. Rather, we state the desired property of f91 separately, and constructively prove it. The proof relies on structural induction (because Twelf can hardly do anything else). Here is the proof http://okmij.org/ftp/Computation/proving-f91.elf Perhaps you might find it curious to see how the function f91 is handled in Twelf. Twelf can’t see that f91 is terminating either (let alone that this is the maximum function of two naturals). We have to make the explicit proof. We do not modify the function definition however. Rather, we state the desired property of f91 separately, and constructively prove it. The proof relies on structural induction (because Twelf can hardly do anything else).
Here is the proof
http://okmij.org/ftp/Computation/proving-f91.elf

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