I finally finished chapter 9 of *The Little Schemer*. This was about partial functions, total functions, and ended with the applicative-order Y combinator.

Frankly, what I understood in this chapter I did not see the point of, and I am not sure there is much point in the parts I do not understand. I think a total function returns a unique value for every input, and partial functions do not. Some of the functions they described as partial sometimes did not return values. Which to me sounds like a badly-designed function.

Maybe Godel’s incompleteness theorem has seeped into our collective consciousness to such a degree that the idea that some functions cannot be computed seems obvious.

Maybe I am not smart enough to be one of those super high-level math/language theory people. I realize I do not have the inclination to do so. I do not have much interest in conjectures about functions that do not return values. I will have to ask a few people I know who have been through SICP if this is the sort of thing in that book. I will finish *The Little Schemer* and go on to *The Seasoned Schemer* in a while.

I went through the part about the Y combinator a second time, and I am not too sure I understand it or see the point. Is there a point? According to some guy named Mike, the point of the Y combinator is: *The Y combinator allows us to define recursive functions in computer languages that do not have built-in support for recursive functions, but that do support first-class functions.*

Are there languages that fit that description? I did some googling, and I found a Hacker News discussion about “The Why of Y” on Dreamsongs (an interesting website I hope to explore in depth someday). As one commenter points out, the article goes into the How of Y, but never the Why.

*The Seasoned Schemer* says you only need to understand the first eight chapters of *The Little Schemer* to go through TSS. So hopefully I should be fine. I was hoping to get through TLS more quickly. I am more busy at work, and chapters 8 and 9 were a lot harder (and had more concepts that were new to me) than the first seven.

I have not gone through these yet, but here are a few more links I found about total and partial functions:

- Total and Partial Functions in FP –
- Pure Functions and Total Functions –
- Functional Programming Is Not What You Think –

You’re welcome.

*Image from World Digital Library, assumed allowed under Fair Use. Image from the Ashburnham Pentateuch, or Tours Pentateuch, a Latin manuscript of the first five books of the Old Testament from the 6th century or 7th century. Its place of origin is unknown.*

Informative article, just what I was looking for.