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Re:Gödel Without (Too Many) Tears by jerf on Monday September 30, 2013 @10:28PM (#6473669)
It is unclear to me whether you are advocating for a programming style that you think is desirable but nonexistent, or if you're advocating for a programming style without naming it.

If the former, you should know you are not alone and serious attempts to create such programming languages are afoot. It's hard for me to find any solid, single web page to point you at, but you want to look at the more theoretical end of Haskell, and Agda and Coq, for some examples. Interesting Google terms include "structural recursion" and various other recursion schemes, and also things like http://blog.sigfpe.com/2007/07/data-and-codata.html .

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