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Comment by zerr | Hacker News Reader

The valuable prose aside, I never liked that code examples were in a pseudo assembly language.

There are M/MIX assemblers and interpreters you can download and run - in some ways they're better than "real" programming languages because they're explicitly for instruction so usability concerns like package managers and build automation support don't get in "the way" of operating them.

It's the only thing he could've done if he wanted the books to stand the test of time

No, a useful language can be just as understandable in the far away future, but also way more approachable in the now/near future

I agree with that opinion. He started writing TAOCP in 1968, and could have switched to Pascal in 1972.

Pascal is simple and clear, and can be translated easily to anything from LISP, Fortran, Python to C or C++ (in fact, subsets of Pascal are often used as sample language in books about compilers, including in Pascal inventor N. Wirth's own compiler book (which, unlike Knuth's, was completed timely):

Wirth, Niklaus, Compilers (1996), 101pp., 2rd revision, 2017, online: https://people.inf.ethz.ch/wirth/CompilerConstruction/Compil..., last accessed 2026-07-07).

It does not matter that Pascal is not much in use anymore, because due to its readability, it's timeless. It nearly reads like English prose, yet is automatically executable. It has also been standardized, and there is a book-sized language description available, as are several -- commercial and open source -- implementations.

In contrast, his pseudo-assembler is arcane. Whenever I wanted to implement an algorithm following Knuth TACOP, I had to work off his English pseudo-code description rather than the associated pseudo-assembler code.

You might have skipped the introduction, but the pseudo-assembler is MIX assembly language, and the hypothetical mythical machine is a central part of TAoCP. The main idea is to show how a computer works at the machine level and implement everything from the ground up, using first principles and mathematical rigor. You are right that the mythical machine itself got old, which is why it was superseded by MMIX.

So no, it’s not a blunder by DEK to avoid abstracting the complexity into higher-level languages, nor to have not written it as a handbook. TAoCP is not a handbook-like book, it is well beyond that. There are plenty of books for that. For that purposes, you might consider consulting CLRS or Skiena instead.

consider the alternatives. it could have been written in PL-1 and rapidly become dated. or it could have been written in a slightly higher level custom language and that would also have to be taught and would be less clear about what was going on under the hood. or a kind of pseudo-code that would also admit ambiguity. or it could have been rewritten in pascal, and then java, and then javascript and then rust.

given the timespan and the focus on complete analysis of running times and not just asymptotics, in the end maybe it wasn't so terrible a choice.

Well, even as-is, it turns out that the kind of assembly language that Knuth originally wrote it in itself had a very short lifespan. MIX assumes a single accumulator register for arithmetic, which hasn't been a common processor architecture since around the 1980s. MMIX is redesigned to be more RISC, but it also uses a dynamic register window concept (which itself I think was only used on Itanium, and we all know how that architecture went down).

And unfortunately, for a lot of modern algorithms, you're going to have dive into SIMD-like algorithms, something MMIX doesn't have. Also, a lot of modern processors have a decent suite of bitwise operations (e.g., count leading/trailing zeros/ones, popcount) that is also missing from MMIX.

The programming languages that are in favor may change from decade to decade, but so to does most of the assembly language techniques.

MMIX uses register windows to make stack frame pointer offsets unnecessary when referring to PUSHed arguments. Don is trying to make the algorithms understandable and correct, and by hiding some details that are handled efficiently by compilers (keeping track of FP and offsets), it benefits the human reader.

Don's first computer was the IBM 650 https://en.wikipedia.org/wiki/IBM_650?useskin=vector see also http://ed-thelen.org/comp-hist/KnuthIBM650Appreciation.pdf so MIX was a simplified version of the 650 because, well, it's well-defined and simple -- and Don knew a popular IBM machine very well. And there's this, in Vol 1:

This series of books is affectionately dedicated to the Type 650 computer once installed at Case Institute of Technology, in remembrance of many pleasant evenings.

MMIX is for all you youngsters who think RISC is all the rage ;-) and I think he does an admirable job creating a fully-defined machine that does use more modern hardware techniques. The fact that he fully defines his underlying machine is exactly correct, because it lays the foundation for precisely expressing the algorithms, and for giving Time and Space (runtime) estimates.

I believe it's fundamentally incorrect to think of these abstract machines as 'assembly language' but rather, I think, they define a stable foundation onto which accurately described algorithms can be expressed. You're supposed to 'play computer' and follow along -- step by step -- to understand the deep details of the algorithms.

I mean, a virtual ISA (think PTX, LLVM IR, WASM) is going to do a better job of giving you an abstract machine than something like MMIX. Virtual registers and call arguments/return values as nary arguments rather than fixed registers give you most of what you want, and it's easy to augment it with a large slice of primitive operations that is a superset rather than subset of assembly languages.

(There's another criticism to level at pseudo-assembly language, which is that modern high-performance processors are superscalar with cache hierarchies, which makes the analysis of execution time itself difficult from the kind of first principles that Knuth is working at. I can appreciate why Knuth is working differently from the more traditional big-O notation of typical algorithms classes, but it does need to be acknowledged that it does sap the treatise of its supposedly timeless quality.)

I take the previous point about missing MMX / Vector instructions. Presumably, that's a straightforward optimization, when code is vectorizable? That is, yes, it would be nice to have sections on vector instruction use to demonstrate some appropriate algorithms; point taken.

I think, tho, the fundamental reason is: he specs the machine. It does exactly what he says it does. No edge cases, no surprising behavior that LLVM IR or WASM might have; also, I'm sure he spec'd it to make the algorithms he implements elegant or at least more understandable.

I suspect part our views comes from the purity of Mathematics (Knuth) and the actuality of Computer Science. I'm even sympathetic to your view, because then we could verbatim copy Knuth's algos to WASM etc and run them, and we get a twofer: a deeper understanding of the algo AND a deeper understanding of the underlying V-ISA (PTX, BEAM, WASM, LLVM IR, etc).

I think the learning / understanding of the algos Knuth presents partially comes from us Playing Computer, and manually going through the code. It's that pedagogy comes first, I think.

Next time I run into Don, I'll ask him about this. 'cause you're also correct about L1...Ln caches affecting performance drastically.

(And, yes, I had wondered why Don did MMIX he didn't create a "RISC-V" before there was a RISC-V; that is, why didn't he create the Next Great RISC Machine? He said he talked with John Hennessy and Richard Sites. This was in 1990.)

Here's HN on RISC-V vs MMIX: https://news.ycombinator.com/item?id=14635361

Sparc and Xtensa also have register windows, although each has a slightly different implementation.

They were all the rage for a while, because they make procedure calls fast but turn out to have subtle issues in highly-multithreaded scenarios.

The Sparc and Xtensa register windows are fixed-size, not dynamic like Itanium's.

Whould would you have preferred?

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