bijection | Reversible conversions between types

I understand that many of the names in Haskell are inspired by category theory terminology, and I'm trying to understand exactly where the analogy begins and ends.

I already know that Hask is not (necessarily) a category due to some technical details about strictness/laziness and seq, but let's put that aside for now. For clarity,

• The objects of Hask are concrete types, that is, types of kind *. This includes function types like Int -> [Char], but not anything that requires a type parameter like Maybe :: * -> *. However, the concrete type Maybe Int :: * belongs to Hask. Type constructors / polymorphic functions are more like natural transformations (or other more general maps from Hask to itself), rather than morphisms.
• The morphisms of Hask are Haskell functions. For two concrete types A and B, the hom-set Hom(A,B) is the set of functions with signature A -> B.
• Function composition is given by f . g. If we are worried about strictness, we might redefine composition to be strict or be careful about defining equivalence classes of functions.

I don't think the technicalities above have anything to do with my confusion below. I think I understand it means to say that every instance of Functor is an endofunctor in the category Hask. Namely, if we have

We are using Chill-bijection for serializing/deserializing messages to and from Kafka with Kryo. Older version of our application is using Chill 0.6.0 which depends on com.esotericsoftware.kryo.kryo-2.21.jar and new version of our application uses Chill 0.9.5 which depends on com.esotericsoftware.kryo-shaded-4.0.2.jar.

In order to minimize downtime, new version of our application needs to be able to read messages which are written by old version of the application, but it fails with an error:

I am trying to reproduce with R an algorithm described in Sutton and Barto (2018), but I was not able to produce a matrix with arrows as the one described by the authors on page 65:

I tried to use the package "fields" for this purpose, but without much success.

In Python the solution proposed by Shangtong Zhang and Kenta Shimada relies on using the arrows symbols: ACTIONS_FIGS=[ '←', '↑', '→', '↓'] but this does not work nicely with R...

EDIT: I coded the initial actions and the action updates numerically as follows:

I am using lightbend cloudflow to develop my application that consumes from external kafka topic.

The external kafka topic contains avro records and if i try to use kafka-avro-console-consumer with schema-regestry, then able to fetch message.

but in the same case cloudflow is unable to deserialize the message and throws exception.

I have data as lists with length 3 to 25, using ascii (as integers). Example, x=[3,56,43,96,23]. Suppose I apply a sort so that y=sorted(x). What is the most efficient way to remember (like store a single byte) the sorting?

To try and be more clear. There are only 5! = 120 bijections from x to itself. Hence, I only need 2**7 bits (which is less than a byte) of information to remember any one sorting method. However it is unclear exactly how to efficiently map sortings to their binary representation.

Lets try to make this more precise, assuming x is length 5. What is the best way to write functions f(x) and g(y,b), where the output of f(x) is byte, b, such that if g is given the sorted version of x (which is y) and the byte, b, then g will output x again. Like,

I'm fairly new to Coq, and was doing some Katas on CodeWars for fun and learning.

I'm stuck with one of them and want to hear some ideas from you.

So, I have:

I have input in json format with two fields, (size : BigInteger and data : String). Here data contains ZStd compressed Avro records. The task is to decode these records. I am using Spark-avro for this. But getting, Task not serializable exception.

Sample Data

What is a good implementation of Power Set algorithm?

Recently I needed this algorithm for building a solver for my puzzle game. Generally, the solver should try strategies (sets of turns, the possible turns Power Set) and find the strategy that forms a solution.

I found out, that the naive implementation shown at Wikipedia page, as well as one from js-combinatorics library does not provide the stable order of items in generated subsets.

Also, the naive approach that utilise the bijection of the set to the natural numbers set and followed binary representation, is bounded by the size of the source set.

This limitation naturally occurs from the fact that internally the mentioned library uses 32-bit integer value for generating subsets.

I have an unordered bimap like this: