Package system horrors

Arcane Sentiment mentioned how the Lisp Machine used to handle package prefixes in this post, and it reminded me of an interesting problem.


When we were building the LMI K-machine we had to cross-compile from the existing Lisp Machine. Naturally, the cross-compiler would read the source code and intern the source code symbols as part of the process. But the K-machine had a different package setup. New packages weren't a particular problem, but the locations of some symbols were. In addition, some things that were implemented as macros in the Lisp Machine were implemented as compiler intrinsic special forms on the K-machine, and vice versa.


The compiler naturally uses symbol identity to determine how to handle a special form. If you want to compile a conditional, for example, the CAR of the form had better be the symbol CL:IF. A symbol named "IF" in a different package won't generally work.


Well, that's not exactly correct... When the Lisp Machine was built, there was no CL package. There was no Common Lisp. So when the CL package was added, it was necessary to make sure that the symbol named "IF" in the CL package was the same EQ symbol as the one the compiler used for conditionals. There are a couple of ways to arrange for this. The symbol could be explicitly interned in the CL package, or it could be visible to the CL package via inheritance.


We wanted to change some of these things on the K-machine, but the cross-compiler was running on the LMI Lambda and when it read the source code it would intern the symbols in the Lambda's packages. Munging the existing Lambda packages was out of the question. The ‘solution’ was to play some nasty tricks with the entire package system. We created two different packages, both named "COMMON-LISP". Some of the symbols were common between them, but others were not. The package inheritance was different, too. The trick was to dynamically switch how package names were resolved to package objects.


So if you have two different “package systems”, how do you refer explicitly to “the symbol IF in the other "COMMON-LISP" package? With a reader hack, of course. We made the triple colon ::: prefix indicate which package system to use to resolve the package name.


This kind of worked, but it was a horror. Most of the system didn't care, the rest didn't know, but if you accidentally had the wrong package system in place when you read a file, you would definitely trash the entire machine and need to reboot. We had a few helper functions that would try to ensure that the correct package system was selected before doing anything (for instance, when calling the cross-compiler, we'd switch out, and when it returned we'd switch back. Works great until you enter a debug repl...). The big problem was that it was impossible to ‘close’ over the correct context, so you could not in general guarantee seamless operation. (For example, if you referred to the K-machine's CL:READ symbol, you probably wanted to switch to the K-machine package set, but there was no way to do this automatically.)

Another little puzzle

Write a procedure that, given two integers L and R, produces the integer that results from interleaving the binary representation of L and R. For example, suppose L is 23 and R is 13. The binary representation of L is 10111. The binary representation of R is 1101. If we interleave the bits (starting with R and padding with zeros when necessary) we get 1001111011. The answer is therefore 635.

Of course this is easy if you print the numbers and then do string manipulation. Can you do it with arithmetic? Can you extend it to handle negative numbers?

20 minute puzzle

You have a list of names and a list of objects. Each object has 1 unique name. Neither list contains duplicates. Write a procedure that determines if every name in the list corresponds to an object. (Suppose the list never contains more than four names, would you change your program?)

Another quick(?) question

I was asked: In your opinion, from a Google perspective, what qualities make up a great CTO?

I'm not sure what a “Google perspective” is, but I can dig up an uniformed opinion or two (or three).

As an officer of a business, a CTO has the primary responsibility of keeping the business going and growing (“maximizing shareholder value”), with particular emphasis on the technological tools the company uses and perhaps creates. A good CTO would be well-informed about where the state-of-the-art is and where it will be in a few years and what tools will give the most advantage with the least cost and risk.

That's the business school answer. I didn't go to business school.

I have been employed by a few companies that were big enough to have a CTO, and I have a different opinion in that context. While I want the company to be successful, and I do my part to help, I don't have the responsibility to consider the “business issues” associated with the technology. I personally take into consideration the effect that the technology has on my job and my co-workers jobs. I went to a tech school because I like technology for its own sake. I like to hang out and work with others that feel the same way. As an employee, I want a CTO that does what is necessary for the business, but also provides sufficient tools and “toys” so that my job is interesting, exciting, and challenging. If the work is dull, tedious, and requires little thought, I start to daydream about something better.

You can see that my desires aren't perfectly aligned with the CTO's responsibilities, so a company with a “great” CTO might be anathema to me, but a CTO that indulges the engineers of a company much more than is strictly necessary for business would make me more interested in being employed there.

Recursion with no base case?

Here's my solution:

(define (all-descendants node-children root)
  (cons root
        (append-map (lambda (child)
                      (all-descendants node-children child))
                    (node-children root))))

I wasn't measuring, but it took me more than a minute. I spent most of that time thinking about transitive closures, queues, iterating over elements, etc., before I realized that since I'm working with a tree rather than a directed graph, I need not worry about shared structure or duplicate elements.

This is an example of a well-founded recursive program that does not have an explicit base case. append-map (mapappend in Common Lisp) implicitly does not call the mapped function if the list argument is empty, so the recursion ends at the nodes of the tree that have no children.

1 minute puzzle

Given a procedure that returns a list of the children of a given node of a tree, write a procedure that returns a list of all the descendants of that node.

jrm bloviates

I recently received an email asking me, “ Do you know of any good books about developing software or thinking in abstraction? I have books, but how did you train your mind?”

I'm not sure I even have a clue. I think that some of the things I've read and worked on were influential, but it isn't clear to me whether anyone else would agree. I've met people that have read the same books and their thought processes are completely alien to me. I know people that are very good at what they do, and reach solid, well-engineered solutions, but I cannot talk with them because they seem to have an insane basic approach to understanding. I've also been on the other end of this where I cannot seem to get the other person to understand a very simple idea on which everything hinges. But since this is a blog, I hardly need to be informed to express an opinion.

College was a huge influence on my thinking. I was fortunate enough to learn from some of the luminaries not only in Computer Science, but also in Math (Gian-Carlo Rota, Alar Toomre), Material Science (August Witt), Physics (I forget), Film (Richard Leacock), etc. What I noticed was that these really smart people spent an awful lot of their time and energy thinking about and talking about the basics and fundamentals. Over and over again they would stress going back to first principles. They invariably would lecture about “creating a model” to help in understanding. In the introductory courses, we'd focus on the commonly used models, but the professors would usually show us alternative models that had interesting properties. In the advanced courses, we would often use several different models. Sometimes the models were apparently contradictory, but were nonetheless useful.

6.001, Structure and Interpretation of Computer Programs, was heavily oriented towards controlling complexity with abstraction. To a large extent, it wasn't a programming course, but a survey course that explored a huge number of abstractions that have been found useful. The fact that it used Scheme as an expository language is irrelevant. The real point of the course was to look at the many different techniques of abstraction and to illustrate the commonalities and differences between them. However, the difficulty of the course tended to obscure this for many students. When you're trying to learn the syntax and semantics of a language, you can easily get bogged down in the minutiae and miss the big picture. For example, the “Triangle Language” problem set made heavy use of higher-order procedures.

The pedagogic goal was twofold: to become comfortable manipulating procedures as first-class objects, but also to be able to create an abstract model of picture composition through triangle-oriented primitives. At the abstract level, we had triangular `pictures' that could be decomposed by cutting larger triangles into sections, or composed by pasting smaller triangles together with scaling and rotation.

The Triangle Language is not a very complex language. It is not very general or useful. It is simply an example of a trivial domain-specific language. It is possible for a student to do the entire problem set, learn a huge amount about higher-order procedures, ace the quiz, and completely miss the point about solving a problem through creating a domain-specific toolkit. Many did. It was ok because every problem set contained some more examples of this. Eventually it will sink in.

6.004 also spent a lot of time talking about different abstractions, but it proceeded differently. We started with the linear model of a transistor, then developed the digital abstraction, from there we had switches. With a couple of more electronic elements, we could implement combinational logic. The combinational logic could be used to implement flip-flops and finite state machines. The state machines, combined with some memory, could implement simple push-down automata and stack machines. A stack machine is a good target for a higher level language, so we could write a compiler. The really interesting part of this course was the lab work where we'd wire these things up. Each week we'd augment the circuits built the previous week and we had built a small computer by the time we got to the end of the course. What was good about this was that you could see all the levels of abstraction at once. The little black transistors over on that side of the board were implementing a gate in a state machine that drove the clock for the microcode unit. You could look at the transistor as switching bits, computing part of a trivial function, or throttling electrons, whichever abstraction was the most relevant at the time.

I guess that the old maxim “practice makes perfect” is true. I trained my mind — They trained my mind by constantly teaching about various abstractions.

As for books, I obviously recommend Structure and Interpretation of Computer Programs, but there aren't many books that just talk about abstractions. It is well worth learning alternative abstractions to things you already know. Hamiltonian and Lagrangian physics has a different view than Newtonian physics, for example. (Unfortunately, it is hard to just get a simple introduction to Lagrangian and Hamiltonian physics.) It unfortunate that many useful alternative abstractions are very poorly taught. Try to find alternative abstractions that make sense to you. Try recasting familiar ideas in different abstractions (this can be fun and bizarre if the abstraction is from an unrelated subject). Rewrite a program based on a completely different abstract model. Try to simplify a complex program to the minimal abstraction possible. Just keep on practicing!