2021-04-11 Update

I know I said I was going to focus on Clojure, but I looked at some other things in the past week.

I am looking into some Amazon certification for AWS. There is a big push to get certified at my current employer, and I would like to do something different.

I started the org-mode tutorial from Udemy.

I also looked at The Seasoned Schemer. I think that having already gone through Simply Scheme I may have gotten some of the concepts. A lot of it deals with recursion.

Chapter 12 dealt with “letrec”. letrec is like let, but instead of binding a name to a variable or data, you can bind a name to a function, and you can call that function recursively.

One thing this can allow you to do is it can relieve you of the need to call a helper function. In Simply Scheme, I made all the functions tail-recursive. To do this, you usually need a parameter that is the “accumulator” or the output (see this answer on Stack Overflow or my post here).

In The Seasoned Schemer, they use letrec for functions in which one argument does not change and one does, such as checking if an atom is a member of a list, or performing a union of two lists:

I know I think the whole argument about Lisp/Scheme being hard to read because of all the parentheses is usually exaggerated, here I think for these letrec examples there might be something to it. These were hard to type correctly from the book. For example, the internal function has to be after the “(set-1)” which is the argument to the “lambda”, but before the closing parens for “lambda”. And the call to the internal function has to be before the closing call to “letrec”. You can have multiple functions defined in a “letrec”, and your call to the internal functions can be in a cond.

A helper function to do the actual work with tail-recursion might be more lines of code, but I think it is easier to understand.

Chapter 13 is about let/cc, combining let with “call-with-current-continuation”. I think some people consider this Scheme’s defining feature.

They have a function rember-upto-last which takes an atom and a list of atoms and removes everything in the list before the last instance of the atom as well as the atom.

Here it is:

Here is a tail-recursive version:

Both of these have a commented out call to “(R (cdr lat)” (with a second arg in the tail-recursive version) below the call to “skip”.[Note 1]. In the tail-recursive version, either  call gives the proper result. In the regular version, we are building our answer through a chain of calls to “cons”. The “skip” eliminates all the pending “cons” calls, and the function is called anew with whatever the then-current values are. In the tail-recursive version, we can get rid of those “pending” values ourselves.

I think Java might get continuations soon.

You’re welcome.

[Note 1]: For some reason, the code formatter I am using does not always color comments correctly. In all variants of Lisp that I have seen, comments start with a semi-colon.

Image from Psalterium Gallicanum with Cantica, a 9th century manuscript from the monastery of St. Gall, housed at Central Library of Zurich. Image from e-Codices. This image is assumed to be allowed under Fair Use.

2021-03-28 Update

There is not a whole lot to report this month. I have not had a lot of time to look at Clojure.

You’re welcome.

Image from Collected Fragments Volume II from the Abbey Library of St. Gall, written around the 8th century from the monastery of St. Gall. Image from e-Codices. This image is assumed to be allowed under Fair Use.

Every and Any in Clojure

Today we look at a few functions in Clojure that take predicates and look at collections: any?, every?, not-every? and not-any?

any? seems to return true for any argument. According to the docs, it is used for clojure.spec. Maybe when I learn more about spec, that will make sense. You would think a function called “any?” would be useful if you had a collection of numbers, and wanted to know if any of them are odd, or greater than 10, or something like that. Perhaps they could have given it a better name than “any?”

every?, not-any? and not-every? behave as you would expect them to. You can always simulate “intuituve-any?” by calling “not-any?” and then calling “not”.

You’re welcome.

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Reduce In Clojure

The last of the Big Three Higher Order Functions in Clojure is reduce. In other languages it is called fold, accumulate, aggregate, compress or inject.

Sometimes reduce is compared to aggregate functions in databases, like average, count, sum, min or max. These functions take multiple values, and produce one value. Some functions in Clojure, like the four main math functions (+, -, * and /) are processed through reduce if they are called with more than two values.

I would like to point out that unlike the other aggregation functions that databases have, “average” cannot be done with reduce. To do an average, you sum the amounts, and then divide by the number of elements. No implementation of reduce (or fold or whatever you call it) keeps track of the number of elements and allows for an additional operation at the end. Maybe some languages or implementations have a reduce and an enhanced-reduce to cover this case.

The first parameter to Clojure’s reduce is a function that takes two parameters. There is an optional parameter that is an initial value, and the last argument is the collection you want to process. Reduce takes either the option initial value and the first element of the collection, or the first two elements of the collection, and passes them to the function. The output of the function is then used along with the next element in the collection. Reduce keeps using the output from the previous element and the next element as arguments to the function until the collection is exhausted.

I cannot find it now, but I remember reading somewhere that reduce can be hard to understand because “reduce” is frankly not a good name for it, and there are many functions that do what reduce does. As stated, some of the functions in Clojure (like max, min, and some math functions) call reduce. So you are actually using reduce a lot under the covers.

There is a cartoon about this. A teacher gives a student a few chances to say what is “2 + 3” equal to. The student says it equal to “2 + 3” and it is also equal to “3 + 2”. The student gets an F. The cartoon ends with: “Sad fact: many math teachers do not know the difference between equality and reduction.” I admit I do not either. A lot of the cartoons are about Haskell, which I have no desire to learn.

You’re welcome.

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Focusing On Clojure

I have decided to focus on Clojure going forward.

I think of all the Lisps, Clojure right now has the most momentum. And I got a couple of inquiries about Clojure positions.

I have been going through the Clojure API, inspired by an article called “One Weird Trick To Become a Clojure Expert“. The article advocates going through the API alphabetically. Maybe I should have done that, but I think I might be better off going through a few books.

I know at some point I have to stop learning and start making something. But I think that going through the API might not be the best way. And the two are not mutually exclusive.

One of the books I will go through is the third edition of Programming Clojure. One of the co-authors is Alex Miller, who helps make Clojure at Cognitect. Clojure does things differently than other languages, and if anyone can explain it, it is the people at Cognitect. The same publishing company has a book called Getting Clojure, which is written by Russ Olsen, who also works at Cognitect.

Reading books by Cognitect employees is one way you can get Clojure.

You’re welcome.

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The Map Function In Clojure

The next member of the Big Three Higher Order Functions is “map“.

I don’t think “map” is a good name for it because 1. There is a data structure named “map” (which has different names in different languages) and 2. I don’t think it is the most descriptive name for it. “apply-to-every” or “apply-to-all” might be better.

The “map” function takes a function and one or more collections, and applies the function to each member in the collection. In Clojure, if you send multiple collections, they will be concatenated into one output collection.

I think the reason it is called “map” is that you are using a function to map a collection onto another collection.

Clojure also has “mapv” which does the same thing as “map” except that it returns a vector, and “mapcat” which takes functions that take collections as arguments. The functions sent to map and mapv take single arguments (if you send one collection) or multiple args, but not collections.

You’re welcome.

Maps In Clojure

I was planning on looking into Clojure’s map function, the second of the Big Three Higher-Order Functions. But looking over my Clojure API page, I noticed there were a few functions with the word “map” in it that I had not gone over yet that deal with the map data structure.

Just as “map” is a noun and a verb in Clojure, the map data structure goes by different names in different programming languages: associative array, map, dictionary, symbol table, hash, hash table.

Anyway, I have looked at some of these functions earlier, but here are some more functions dealing with maps:

You’re welcome.

Clojure Filter

The first higher-order function in Clojure I will look at is filter. It takes a predicate and a collection. It returns all the members of the collection for which the predicate is true. The docs say that it takes a “predicate”, but that predicate duty is frequently fulfilled by a function.

I tried calling filter with “true” as the predicate, and it did not work. I guess in Clojure (and probably all Lisps), a predicate is just a function that returns a boolean.

Filter is one of the Big Three Higher-Order Functions, the other two being Map and Reduce. This one actually has a name that describes what it does.

Clojure has two versions of filter: filter and filterv. The difference is that filter returns a lazy sequence, and filterv returns a vector.

If filter is called with just the predicate, it will return a transducer. I will cover transducers later.

There are also another “filter” function in the clojure.core.reducers namespace. It takes the same arguments as the core filter, but when I tried it in a REPL I got an error. After looking at the Clojure page on reducers, I think the functions in that namespace only work if you chain them together.

You’re welcome.

Chapter 9 of ‘The Little Schemer’

I finally finished chaper 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:

 

You’re welcome.

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Update on ‘The Little Schemer’

I am almost through with The Little Schemer. I got through the first seven chapters fairly quickly. There are no exercises per se. They will ask questions, invite you to figure out the answer, and show you. I admit, a few times I peeked, but only after trying to get it myself.

There were a few things in chapter 8 that were mind-bending. One was using higher-order functions for code-reuse.

In chapter 3, the authors introduce a few functions. One is “rember”, which removes an element (or member) from a list:

Another is “insertR”, which inserts a new element to the right of an old element in a list:

The third is “insertL”, which inserts a new element to the left of an old element:

The functions are pretty much identical. In chapter 8, they make a base function, and then make three more to cover the three different requirements.

It works just like the original:

This reminds me of something that Eric Normand showed in Purely Functional, where he puts anonymous functions in the values of a map. I wrote about that in August of 2018.

The truly mind-bending part was the “collectors”. Dark arts, these are.

They define a function that does the usual removing of members. It takes an additional parameter which is a function that does some calculations/manipulations on the resulting list. But in the recursive calls, the function uses inline lambdas to make additional collections.

Here is their explanation from page 140; the function is (multirember&co a lat f), where “a” is an atom, “lat” is a list of atoms, and “f’ is a function: It looks at every atom of the lat to see whether it is eq? to a. Those atoms that are not are collected in one list ls1 ; the others for which the answer is true are collected in a second list ls2 . Finally, it determines the value of (f ls1 ls2 ).

Here is the multirember&co function:

Here is the function we will use in our test:

The second argument is unused in last-friend. So when you use last-friend, it will count how many elements are not equal to the first argument. If it returned the length of y, it would tell us how many times the first argument is in the list.

Here are the tests in Racket:

Later, they use collectors on functions that work on multi-level lists. There is a recursive call within the collector.

I think I understand this, but I am not entirely sure about it. I was able to figure out some of the collector examples as they went along. Truly this is unholy power.

You’re welcome.

Image from Corpus Agrimensorum Romanorum, a 6th century manuscript on land surveying housed at the Herzog August Library in  Wolfenbüttel. According to Wikipedia, “It is one of the few surviving non-literary and non-religious illuminated manuscripts from late antiquity.” This image is assumed to be allowed under Fair Use.