I would not expect the compilers I have used (Algol, Fortran, Java, Lisp (interpreter), Pascal, C, C++) to produce the same result to the last bit for (x + 1)^2 and x^2 + 2x + 1. Would you?
On Mon, Jan 25, 2021 at 7:18 PM jon zingale <[email protected]> wrote: > Nick , > > Please pardon a second attempt to address your question. Let me grant your > definition of *rigor* as meaning *that which compiles*. *Clarity*, however, > I would like to treat differently. What strikes me as a structural > difference between *rigor* and *clarity* here is that the former (as > narrowly defined above) depends only on the property of being compilable. > Something, anything, was stated such that a program can run. The latter, to > my mind, would require a concept of two programs being equivalent (or at > least orderable). How else could we claim that one program was stated more > clearly than another? This equivalence can be shoddy as in an optimizing > function, ie. modulo some countable things I value, or actual equivalence. > Many computer languages do not allow for actual functional equivalence in > this sense, though there are some narrow examples. While you and I, and > some > algebraically focused languages, can immediately tell that *adding 1 to x > and then squaring the result* is the "same thing" as *adding together a > squared x to two times x and a 1*, many languages would require checking > every value to determine such an equivalence. In this way, *clarity* > appears > to me to require more structure than a notion of *rigor* does. To some > extent, I wish to reject the programmer/compiler dialectic, as it seems > that > it hides more useable observations. > > > > -- > 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 > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: http://friam.471366.n2.nabble.com/ > -- Frank Wimberly 140 Calle Ojo Feliz Santa Fe, NM 87505 505 670-9918 Research: https://www.researchgate.net/profile/Frank_Wimberly2
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