SICP

These are my solutions to the CS classic Structure and Interpretation of Computer Programs. I have looked up the answer for some exercises on the Scheme Community Wiki. Such exercise have a mark in their respective script.

You can use the Scheme implementation by the MIT to run these scripts. In Arch, execute pacman -S mit-scheme to install it. Then run the scripts via mit-scheme --quiet < script.scm.

This is currently (2020/12/16) work in progress.

Chapter 1

The first chapter of SICP starts by explaining the Scheme syntax. The first couple of exercises are simple enough. However, already at 1.5, the book foreshadows some of the difficulty that is about to come.

(define (p) (p))
(define (test x y)
  (if (= x 0) 0 y))

The goal is to decide whether Scheme uses applicative-order-evaluation or normal-order-evaluation based on the above code. I have initially found the exercise confusing, but the code triggering an infinite loop is a clear indication of Scheme (or at least my version of Scheme, MIT Scheme) using applicative-order-evaluation.

After this exercise, things get more comfortable again. The book proceeds to introduce if-else clauses, conditionals, as well as recursion. The book uses these primitives to compare iterative and recursive procedures based on a couple of typical CS example functions such as computing Fibonacci numbers, greatest common divisor, and fast exponentiation.

Two new insights I had how using modulo instead of subtracting the divisor speeds up the GCD algorithm I learned in middle school and how exponentiation can run in O(log n) by halving even exponents.

I wasn't able to prove the Golden Ration exercise at the time of working through this chapter. My knowledge of induction and proofs was too limited. I found that depressing at the time, and I wish they hadn't included that exercise.

Nevertheless, the book moves on to further essential CS concepts such as Prime numbers and the Fermat primality test. Funnily enough, I used that probabilistic Prime test for a Project Euler exercise, wondering why I wasn't able to get the correct results. It turns out that this test detects probable primes (the book mentions that a little later and introduces the Miller-Rabin test that pseudoprimes cannot fool). On the one hand, it was cool to use an algorithm from a book directly. On the other hand, I was undoubtedly a bit annoyed by that story.

The book moves on to discuss the runtime of some of the algorithms discussed to this point. It introduces some other mathematical concepts, such as calculating roots via the fixed-point method, Euler expansions, and the Newton method for finding minima/maxima. It was cool to see how the fixed-point method can be used to implement the Newton method if you plug the derivate of a function into it. I did my project presentation for math in high school about the Newton method. So this brought up cool memories. I wish I still had that presentation.

Finally, SICP introduces the evaluation model for stateless functions and concludes with some exercises that require second-order procedures: procedures that take other procedures as arguments.

Chapter 2