## To Mock a Mockingbird or: How I learned to stop worrying and learned combinatory logic

Yesterday I finished reading one of the most remarkable books I read in my life: “To Mock a Mockingbird and Other Logic Puzzles: Including an Amazing Adventure in Combinatory Logic” by Raymond Smullyan. When I finished reading The Little Schemer that book was listed as one of the suggested further readings. The title was quite intriguing so I got the book and started reading it. That was a year ago and I finished the book yesterday. Why? Because I got stuck and couldn’t understand some of the material. Luckily I now had some time to approach the book once again and grok it.

As the title suggests the book is a collection of logic puzzles. Out of six parts of the book – 25 chapters total – two are devoted to general logic puzzles, many of them about different aspects of truth telling. These can be regarded as a warm-up because in the third part the book makes a sudden turn towards combinatory logic. And this is the moment I found difficult in the book. Of course Smullyan doesn’t expect that readers work with combinators so he camouflages them as singing birds. Having some mathematical background I rejected this cover and tried to approach problems formally. Now, after reading the book, I think this was a major mistake that lead to my failure. I wasn’t able to deal with first 10 puzzles but I was more or less able to follow the solutions. Still I felt that reading solutions without being able to solve puzzles by myself was cheating so I gave up. A few months later I made another approach to the book but the results were exactly the same. Three weeks ago I made a third attempt, but I decided not to give up even if I won’t be able to come up with my own solutions. I figured that being able to only understand given solutions is completely fine. That decision turned out to be a good one. Although at first I wasn’t able to solve puzzles on my own at some point things just clicked. I solved one puzzle, then another and another and I realized that I know how to solve most of the puzzles. From now on the book went quite smoothly. Part four about logical paradoxes and inconsistencies in logical systems gave me some problems and I was afraid that each subsequent part will be equally challenging but it turned out that it was not the case. Part five gives a nice overview of computations using SKI combinators, while part six presents Church encoding of natural numbers and culminates with a proof of GĂ¶del’s theorem.

The book is challenging on the one hand but it is also very rewarding. One of the most satisfying moments was realizing that I am able to write expressions like

$g\tilde{a}\tilde{b}=Z\tilde{a}f(Z\tilde{b}t(g(P\tilde{a})(P\tilde{b})))$

# Summary

To “Mock a Mockingbrd” was a very insightful book and one of the most unusual ones I have read. It presents difficult material in a fun and entertaining way, but don’t be fooled – you will spend hours with pen and paper to complete this book. I highly recommend it to anyone interested in logic and functional programming. What functional programming has to do with it? Unrelated as it may seem I feel that this book has given me knowledge necessary to tackle type-level programming in Haskell. Just three weeks ago this seemed like a complete black magic and now it looks comprehensible.

### 5 Responses to “To Mock a Mockingbird or: How I learned to stop worrying and learned combinatory logic”

1. Kevin says:

Thanks for this reassurance! I’m trying the book for the second time, and these two attempts mirror your first two attempts so far. I’ll take your advice and keep going, though!

2. David says:

I love this book! I learned of it from Mark Steedman’s book “The Syntactic Process.” Since working through To Mock a Mockingbird, I’ve tried to get other people into it, alas to no avail. I was reading Moses Schoenfinkel’s original article at work and one of my co-workers accused me of reading “Vulcan porn.” By the way, have you thought very much about the title?

3. Jan Stolarek says:

You mean the title of the book or of the post?