PL/MIX

PL/MIX would have been a programming language that runs on the MIX computer. Donald Knuth would have described and implemented PL/MIX in The Art of Computer Programming volume 5 (chapter 10: Parsing), in the future of the alternate universe where he would have written volume 4 and 5 so quickly that they appeared before the MIX computer became obsolete.

PL/MIX would have been higher level than MIXAL, allowing you to use arithmetic expressions of the kind you see in Fortran or algol.

The only evidence in our universe that PL/MIX would have existed is a few mentions in The Art of Computer Programming chapter 1. Since MIX is now obsolete, replaced by MMIX, Knuth will never create that interpreted language, and will instead describe a totally different interpreter in chapter 10. We will probably never find out what PL/MIX is like.

Quotations

Actually MIX has two symbolic languages for low-level programming: MIXAL, a machine-oriented language that is designed to facilitate one-pass translation by a very simple assembly program; and PL/MIX, which more adequately reflects data and control structures and which looks rather like the Remarks field of MIXAL programs.
—D. E. Knuth, Volume 1, 3rd edition, Section 1.3.2. The MIX Assembly Language, The Art of Computer Programming, 155-156.

We now write in computer language, say MIXAL or PL/MIX or a higher-level language; we start this time with the lowest level subroutines, and do the main program last.
—D. E. Knuth, Volume 1, 3rd edition, Section 1.4.1. Subroutines, The Art of Computer Programming, 190.

Links

Usenet thread from 2007 with fan guesses about what the language would be like