That depends on the type system of the language and the types that have been given. $ math Mathematica 12.1.1 Kernel for Linux x86 (64-bit) Copyright 1988-2020 Wolfram Research, Inc.
In[1]:= Expand[(x+1)^2] == x^2+2x+1 Out[1]= True From: Friam <[email protected]> On Behalf Of Frank Wimberly Sent: Monday, January 25, 2021 6:28 PM To: The Friday Morning Applied Complexity Coffee Group <[email protected]> Subject: Re: [FRIAM] Acronyms 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]<mailto:[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<http://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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