Learning Lisp

Section 1.1 was deceptively simple, but things rapidly got heavy in section 1.2. The process of tree recursion was exceedingly difficult to visualize. Exercise 1.13 asked us to “use induction” to prove something. Plugging through exercise 1.20 was exceedingly painful back when I was working on my own. The march of technology added some complications to the later problems that caused me to dread going on… and the Miller-Rabin problem was completely mystifying. (I hacked out a Common Lisp version of the algorithm described on Wikipedia, but even that exercise failed to give me the insight necessary to understand the question. I haven’t been that befuddled since that problem from PAIP chapter 2….) Collectively, these experiences might lead one to believe that working through SICP was a lost cause….

A couple of things can really improve your chances of getting through it, though. One thing is to definitely watch the videos— they really make things interesting and more accessible. Another thing is just to have a friend or two that you can bounce things off of. “I tried x on problem y… is that what you think they wanted there? Also, are you getting something like z on problem w?” A few encouragements from a peer can really help you focus.

Continuing on into section 1.3 things got much easier. The lecture was outstanding. It is probably the definitive sales pitch for higher order thinking. If you ever wondered what people mean when they talk about “higher order procedures,” this is the place to go. The problems for the most part were straight-forward or about medium level. A lot of them push you to alter or imitate clear examples, so they are pretty “fair” as exercises go. Others require a modicum of persistence and experimentation, but are still pretty straight forward. I got through most of them with only a couple of minor questions. (Simpson’s rule in 1.29 didn’t work for me as it was advertised. The instruction to “show that the Golden Mean is a fixed-point transformation” is perhaps beyond my math skills. I wasn’t sure how to test my answer in 1.44, and I’m not quite sure where to go with 1.46.) But if the goal here was to get me to understand when and how to implement functions that take functions as arguments and that return a function for their value… then I’m there. They push the level of abstraction… and then push it some more… and then push it until I want the merry-go-round to stop. I used to think that mapcar was pretty darn cool. Now I have an entire new mental apparatus that I can apply regardless of the language or platform.

So I’ve got the bulk of the problems from the first chapter completed and it’s all culminated into a deeper understanding of how to apply and implement functional style abstractions. I’m really pleased with how far they’ve brought me in the text, but I begin to get anxious: I want to go code something… and I’m afraid of how far into the stratosphere they’re going to push my mind. I wanted at first to learn more powerful methods of creating general solutions… but really, I only wanted to get maybe half an order of magnitude better as a programmer. I had no idea that they would push my mind so far beyond its comfort zone. I had no idea that I even had a mental comfort zone! The experience gives me a new respect for MIT… and I’m glad I have a chance to experience a bit of what they put their computer science students through. (I want to also give my thanks to the SICP study group for providing me the inspiration and the encouragement to continue working through this book!)

Two minor things stand out for me, as far as mental processes go. One is the “faith oriented programming” that Sussman advocates in the lecture: if you’re not sure how to code a complex routine, just assume the hard parts are already done. If you can put a name on what’s missing, you’ll be able to easily address it later. Thankfully, DrScheme doesn’t auto-highlight “syntax errors” in this case! This worked surprisingly well for me when I went back and reworked the Pascal’s Triangle problem from section 1.2. Also, in section 1.3 they formalize the “guess-fudge” method that helped me do well in so many math classes in the past. The iterative approaches in the section mirror my own problem solving techniques: if you’re not sure of the answer, guess… then make small improvements or adjustments until it’s good enough. Combining these techniques gives you the key to solving recursion problems: start with a rough outline the covers the trivial cases… then “guess-fudge” the missing piece into existence with a function or two. This works for many of the problems in the text.

Anyways, if you got overwhelmed in section 1.2, just hang tight… it gets easier. Or maybe you get smarter. Something. They keep the pressure on, but they are very steady in section 1.3. It’s a lot of work– almost like learning to program all over again– but everything they make you do is part of their perfect plan to transform the way you think about algorithms. I can’t for the life of me imagine why so many people have complained about Scheme: it’s an exceeding beautiful language that gets out of the way so that you can express raw thought in its most elegant form. It’s hard to believe how much can be accomplished with only a handful primitives and parentheses….

For those that want to compare notes, here’s my code for exercises 1.29 to 1.33, 1.35 to 1.39, and 1.40 to 1.46. Also, here’s my algorithm for the Miller-Rabin test based on the instrictions from this Wikipedia entry.

I finally got around to watching the first of the SICP lectures. This first third of it is a real treat for those with a mathematical bent. I summarize Sussman’s Abelson’s argument here:

Computer Science is not a science.

Computer Science is not about computers.

Computer Science is not even “real.”

Geometry is not about Surveying or Surveying instruments.

Geometry is about an using axioms and logic to provide a framework for exploring declarative knowledge– identifying and articulating what is true.

Similarly, Computer Science is really about imperative knowledge– articulating how to do things.

Computer Science deals with idealized components. There’s not all that much difference between what you can build and what you can imagine. The constraints imposed in building large software systems are not physical constraints, but rather the constraints are the limitations imposed by your own mind.

Computer Science is therefore an abstract form of engineering.

The second portion of the lecture dealt with an overview of the course. SICP is going to focus on programming techniques for controlling complexity. Sussman made something as simple as Black Box Abstraction sound really interesting: the key to that was in how he highlighted that we’re not just going to build black boxes, but that we’re also also going to build black boxes that return other black boxes… and by passing black boxes as parameters, we’ll be able to obtain another order of magnitude of abstraction in our programming style that is far beyond what non-functional programmers tend to think in. He spent less time selling us on the Conventional Interfaces section, though he did mention that this part would hit on OOP somewhat. The final portion of the course on Making New Languages sounded the most exciting– but his brief description of Metalinguistic Abstraction sounded (at this point, mind you) pointlessly geeky and pedantic. I must as of yet lack some sort of illumination, because I suspect that my mind should be blown away by the mere hint of the magic of Eval and Apply….

In the last section of the lecture he went over a bare bones introduction to Lisp. He was using Scheme– and even though I have gotten DrScheme up and running with almost no hassle, I still recoil at the thought of spending any time away from Common Lisp, Slime, and Emacs. Nevertheless, the Scheme approach is very clean and slightly more intuitive than the traditional Common Lisp way of doing things. Just for fun I wrote a macro that implements some of the functionality of Scheme’s define operator:

CL-USER> (macroexpand-1 ‘(define (sq-a x) (* x x)))
(DEFUN SQ-A (X) (* X X))
T
CL-USER> (macroexpand-1 ‘(define sq-b (lambda (x) (* x x))))
(DEFUN SQ-B (X) ((LAMBDA (X) (* X X)) X))
T
CL-USER> (define (sq-a x) (* x x))
SQ-A
CL-USER> (sq-a 11)
121
CL-USER> (define sq-b (lambda (x) (* x x)))
SQ-B
CL-USER> (sq-b 12)
144

Note that the second case there was somewhat more tricky to implement. I tried several different ways of doing it with setf and defun before getting a version that would work identically to the first case. The key (or possibly the ‘hack’) was to define the function with the arguments from the lambda… and then splice those arguments in with ,@ after the lambda expression. I think I had this same difficulty when I was trying to understand Michael Harrison’s example from the Little Schemer a few weeks ago– Scheme and Common Lisp seem to work in subtly different manners in this case.  But working through this example has helped me understand the differences a little better.

Anyways, the most shocking thing in the lecture for me was when Sussman blithely tossed out the phrase “syntactic sugar.” (He defined it as “somewhat more convenient surface forms for typing something.”) I usually associate this phrase with smarty pants blogger types that really want to sound cool. Yeah, like all you need to do to sound cool is to criticize Java a little and throw this phrase around!! Now that I’ve seen it turn up here, I guess I’ll have to get down off my high horse the next time my hackles are raised over this….