## Archive for the ‘C++’ Category

### Back from NWERC 2011

Monday, November 28th, 2011

Hi folks!

This weekend I participated at the North Western European Regional Contest, a regional preliminary round for the ACM ICPC. It is an international students contest about solving as many as possible out of 10 algorithmic problems in 5 hours in teams of three students and one PC. It was my first time there and it was quite fun.

At saturday we visited the historic harbour of Bremen Vegesack, which was partly boring and partly quite nice. At sunday there was the actual contest at the quite decadent and walled Campus of Jacobs University in Bremen (you even have to pay tuition of ~€25000, ~$33000 per year, at public universities you pay about €400-1400, I could live from it for long time, but even at elitist economical universities like EBS and WHU you have to pay much less). We used KDevelop 4.2 for solving the tasks and enjoyed the nice completion, source code reformatting (nice when you are not sure any longer which braces belong together and do not have much time :)), and inline documentation of STL functions. Thank you, KDevelop guys. Our team from RWTH solved only three out of 10 tasks (30st place out of 70). B and E were quite trivial (I did not even had to read B since my team members solved it). I want to tell a bit about the other problems, I hope it is interesting for some of you. Of course you may try to solve the problems your self, it is quite a lot of fun. ### A Given a natural number x<10^15 we should compute all n,k such that binomial(n,k)=x. It was quite simple, but we had a bug in our implementation and I do not have any clue what the problem was. We chose to check the cases binomial(n,1)=n and binomial(n,2)=n·(n-1)/2 manually and brute force the solution for all other cases by computing lines of Pascal’s triangle for k values such that binomial(n,k)≤x and terminating when binomial(n,2)>x. Alternatively you could check more terms explicitly (the team from LMU did it) and compute the whole triangle for the remaining values or use binary search to find the parameters. ### C Given a sequence of films watched by a person we should answer for each time position how many different films have been watched since the last time he watched the current one. By maintaining a binary tree containing the films ordered by the last time they were watched and a map containing this time for each movie this queries can be easily answered to if you have a way to get the number of nodes after a specific one in the tree in O(log n). That for you would have to store the size of each subtree and STL set/map unfortunately do not support this. Thus we decided to write our own tree, we went for a Treap with random priorities since it is the easiest way to avoid degeneration (easier to implement than AVL and Red-Black trees). Unfortunately we did not have enough time for debugging the tree and we even forgot to update the counters when balancing the tree after insertion. There were simplier solutions using segment trees. For this task there were particularly many wrong submissions (the man presenting the solutions assumed that many teams tried to solve this one because the first team solved it yet after 20 minutes and thought it would be the easiest one, he even presented a very funny solution using java.lang.String. a linear time Java indexOf() call, which was of course way too slow). ### D This task was about deciding whether it is possible to partition a given pattern of black and white square into disjoint, L-shaped “puzzle pieces” of one black (in the corner) and two white squares. We had no idea how to solve that, we thought a lot about backtracking, but there semt to be no clever way to do that in polynomial time. The trick was to encode this problem in Boolean formulas and to use a standard algorithm (e.g. resolution) for the 2-SAT problem using variables encoding “white square x,y belongs to the same puzzle piece as the white square x+1,y+1“ etc. ### F Nobody solved this problem at the contest (though there were some people at the semi-live contest at Spoj solving it, a coach of another team said he knew a very similiar task from a different contest). Look at it, it looks like really complicated spam. Only one team tried. Cool geometric structures, quad-trees etc. will not help you to solve this problem: 500×500 fields, each one is either water or grass. You want to build a pool area. The border has to be grass and every pool of water has to be surrounded by a wall, which will cost$a per wall. You can transform water fields into grass, which will cost $b per field, and grass into water for$c. You want to build the cheapest pool area possible.

Actually it is a simple max-flow problem, since a minimum cut in a certain flow encoding the landscape is the optimal solution. You have a source, a sink and a node for every field. A cut should divide the nodes into water-nodes and grass-nodes. Source-to-x edges should have a capacity of the price needed to transform x into a grass-field and x-to-sink edges should have a capacity refering of the price needed to transform x into a water-field, unless the node represents a field at the border, then the capacity should be infinity. Additionally you add x-to-y nodes with a capacity of the price needed to build a wall for adjacent nodes x and y. That is it (if I am not wrong, I hope so :D). Really awesome.

### G

I will post a full description later. For each observation you can yield an inueqility and you can complete the information in a Floyd-Warshall-like manner.

### H

Spam. You have 13 out of 52 regular playing cards and want to partition it into as few as possible bunches of single cards, pairs, triples, quadruples, full-houses and streets of at least five consecutive cards. You can simply use brute force: Test all combinations of up to two full-houses and up to two streets (cannot be more for 13 cards) and greedily take the remaining cards as quadruples, triples, pairs and single cards. We tried that with a lot of copy-and-paste code and our program printed wrong answers, but we have no idea in which cases it failed. Alternatively you can choose a probably more compact solution by building a directed acyclic graph of all 2^13 combinations of your cards where edges represents adding one of the allowed bunches. Then you use breadth-first-search to get the solution. This was one of those typical tasks with useless information in the input (cards were encoded as 4h for ♥4 and Jd for a ♦Jack, in fact the suits did not even matter).

### I

Given integer coordinates of up to 10000 RFID chips, 250000 RFID sensors and 25 walls compute which sensors can detect which chips. Each sensor can detect any chip within a radius of r, while walls reduce the radius by 1. No two sensors are closer to each other than r (“due to interference”^^). We used a sweep-line algorithm. Whenever the sweep line reaches the value x where x+r is the abscissa of a product we add the product to an ordered binary tree (std::set in C++) ordered by the ordinate. When reaching the value x where x-r is the abscissa of a chip we erase it from the tree. If x-r is the abscissa of a sensor we query all products in the tree with ordinates between y-r and y+r using lower_bound and upper_bound where y is the ordinate of the sensor. We count the number of walls intersecting the line between sensor and chip (we check that by adding up angle(p1, q1, p2)+angle(q1, p2, q2)+angle(p1, q2, p2)+angle(q1, p1, q2), which should be 2π (aka 360 degrees) for intersecting line segments) and check whether the chip is within the resulting reduced radius. This solution has a complexity of O((n+m)log(n+m)+n·w) where n is the number of chips, m the number of sensors and w the number of walls. This is guaranteed since the distance between any two sensors is at least r, thus at most 7 sensors can detect one chip (imagine a regular hexagon of sensors with one sensor in the center). Thus for many walls you would probably require a more sophisticated algorithm taking walls into account when sweeping.

Surprisingly only 7 teams solved it, I thought it would be kinda a standard-geometric-sweep-line-problem, it was even easier than E for us (there we used int instead of long long :D). Alternatively you can use binning (since the coordinate space is limited) or quad-trees to solve this problem.

### J

You have a couple of train-stations and ≤1000 connections between these stations. Each connection will be once an hour at a certain minute (e.g. 13:47, 14:47 and so on). However, there is a certain probability that the train will be too late. If it is too late the delay is uniformly distributed in a range from 1 to some number ≤120. You have to compute the minimum expected duration of a trip from the start to the target. We solved that problem by a fixed-point iteration: For each station and each minute (0≤m<60) we store the best known expected duration to the target. We propagate that information till it does not change any longer. Unfortunately it timed out, probably because of floating point issues: we recognised changes which where insignificant or caused by rounding. Only one team solved this problem, three teams tried.

### Subsumption

Yesterday I returned from Bremen, entered the first train at about 17:00, arrived at 0:45 and slept till 12:00. It was a really nice experience. If you are a student, like algorithms and want to participate: go ahead, look for two comrades, ask your professor to register you and join your regional contest! (at some universities there is a local preliminary contest)

PS:
Some visual impressions:

:)

The camera of my N97 mini mobile phone had a bug or something like that, however, when trying to photograph an ugly super market or something like that in the early evening and accidentally moving the camera too early I got this nice photo. Could not reproduce.

Could not reproduce :(

PPS:
The contest was sponsored by Facebook and we had to attend a boring presentation of a Facebook employee. It was quite funny how he tried to make advertisement to work there. He assumed everybody in the room would use Facebook, what? We could get free t-shirts when answering his silly questions, did he think we would like to work there because of a t-shirt? It happened multiple times that he said that he is not allowed to tell about xy, really a great opportunity to work for a company where you cannot even superficially talk openly about the things you are doing there. And he told us that they would finally delete all messages six days after you have pressed the delete-button, haha.

PPPS:
I have pushed some solutions here.

### KDevelop-PG-Qt 1.0 Beta

Tuesday, October 4th, 2011

Today KDevelop-PG-Qt 1.0 Beta (aka 0.9.82) got released, the parser generator used by several KDevelop (and Quanta) language plugins. There are some new features, and various bugs have been reported in the last few months since 0.9.5 and are now fixed.

### New features

Most effort has been spent for implementing the lexer generation. You can now write a simple specification of the lexical structure by using regular expressions, the generated token stream class, which generates tokens from the input-data, can be used directly by the generated parser, but you can also just create a lexer without a parser. Thus, despite the name, KDevelop-PG-Qt is no longer just a parser generator. My motivation for writing the lexer generator was the lack of decent Unicode support in most lexers. Quex is quite good, but it is not free software (despite the LGPL based license) because of excluding military usage. The lexer can not only read different encodings, but also use different encodings for internal processing, e.g. it can either convert a UTF-8 stream to UTF-32 first or directly operate on UTF-8 bytes. Simple example:

%lexer ->
for FOR ;
"some keyword" SOME_KEYWORD ;
{alphabetic}* WORD ;
;

It does also include limited support for look-ahead (full support like in Flex make generated code more complicated and inefficient), and a simlar – but in my experience more useful for modern languages – feature called “barriers” which will be explained in the documentation soon.

The API used by the generated files has been cleaned up, some method names were very counterintuitive, some methods were not used at all. This break requires updating KDevelop-PG-Qt to build the latest versions of PHP, QMake, SGML and CSS plugins (you may have to do a clean build).

There are also some minor new features: AST structs now get forward declared reducing dependencies, code which relied on definitions at some places has been fixed some time ago. The token types do not get declared by the parser any longer. Additionally you no longer need “;;” in the grammer files, though it is still supported for compatibility.

### Bug fixes

The bug fixes include proper line numbering. In GCC you can now see correct line numbers refering to the location of wrong code in the grammer file, for other compilers you may have to activate the –use-line-directive, then it will use the #line directive instead of the GCC specific syntax, but you will not see the location in the generated code. The CMake-macro will do that automatically. Some compatibility errors have been reported reported by Fedora and Debian packagers and fixed, special thanks to them. KDevelop-PG-Qt builds with QT_STRICT_ITERATOS now and also builds under Windows with MSVC (MSVC is not perfect for C++11 and Flex is not perfect for Windows). Annoying wrongly formated error messages in the lexer and parser of KDevelop-PG-Qt have been fixed, too.

Some bug fixes might be necessary, thus there is this beta-version first. There is some work to do now first: The documentation and the kate grammar file for proper syntax highlighting have to be updated.

### C++11

This is the second release using C++11 features, especially the auto keyword and STL hashes (unordered_map and unordered_set). I had used variadic templates before to construct UTF-8 automata, but for compatibility with MSVC it has been replaced with a Ruby script generating some code, the variadic template had been quite ugly anyway.

### Future development of KDevelop-PG-Qt

• Parser and lexer should be rewritten using KDevelop-PG-Qt
• Long requested: there should be a way to mark conflicts as resolved, that for the conflict reporting has to be refactored a bit
• The next release will hopefully support LL(k) parsing, making some stupid look-aheads obsolete
• Cleaning up further code

Special thanks to Milian Wolff for all his patience, bug reports and support with the release.

I will post the link to the tar-ball as soon as it is uploaded, there is only the tag for now.Tar-ball can be found here.

### Unexpected Bottle Neck: vector<bool>

Tuesday, August 23rd, 2011

Hi folks!

The last paragraph is actually the interesting one for every C++-programmer, the leading-in might not be understandable.

The new lexer component of KDevelop-PG-Qt is not very fast, it can take several minutes with complex grammars, especially when using UTF-8 as internal encoding for the automata. Of course, first I want to finish the most important features and that for I am writing an example lexer for PHP to check its capabilities to spot bugs and missing features, but now I was curious and asked Valgrind/Callgrind for analysis. I expected a lot of useless copying/assignments because I have not done any optimisation yet and tried to be “defensive” by using too much copying. Indeed: For my first example about 78% of the runtime were spent on copying. But then I tried a full (as far as it is finished) PHP example with UTF-8 and it was a real surprise:

KCacheGrind Overview

It spends most of the time with comparing instances of std::vector<bool>! For the powerset construction I have to maintain following states for subsets of states in the NFA and after that I map those subsets to new unique IDs for the states of the DFA. For both cases I wanted to use a map with vector<bool> (a subset of states) as key_type, I could not decide if I should use map or unordered_map – I used map, but there is also some code to make it possible to use QBitArray with unordered_map, just for the case. However: I expected the minimisation to be a bottle neck (disclaimer: I stopped valgrind after some time, maybe it becomes a bottle neck later), but now the comparisons used in the map-implementation are crucial. I was not very economical with those map-operations – I could have done the mapping while computing the necessary subsets, it has to be optimised and I may use unordered_map and unordered_set (hashes) instead of map and set, but that is not the reason why I am writing this blog post.

The interesting thing about it is the usage of std::_Bit_reference. std::vector<bool> has a specialised implementation, the booleans get packed, thus it will only need size()/8+const Bytes when it is full. There is a special hashing-implementation directly using the integers used to store the bits, but there is only a generic comparison implementation. Thus it will iterate over all the bits, instead of using comparisons of chunks (like 32 or 64 bit, depending on the CPU). Of course it will be much slower, keep in mind that each iteration requires some bit-manipulation. Especially in my case of a red-black-tree the vector will get compared to very similar ones next to it in the tree, and in that case it takes especially long time. Be aware of vector<bool>, it is often awesome (safe a lot of memory), but something like this slow comparison may happen, and always keep in mind that the index-operator might be slower than for vector<char&gt. Unfortunately there seems to be no API for accessing the integer-chunks. Btw. QBitArray does not support comparison at all. I have filed a bug-report to GCC/libstdc++.

### Regarding Dynamic Typing

Sunday, July 10th, 2011

Currenty there seems to be a big hype about EcmaScript (JavaScript). Google probably wants to enslave the world with Chrome OS, where the system is not much more than an EcmaScript virtual machine provider (maybe it will support native applications through NaCl, like Android does not only allow Java…), Microsoft wants to reimplement their Windows interface, Qt invented QML, the EcmaScript extension we all know about, providing cool declarative features. Today I want to talk about a fundamental property of EcmaScript and why it just sucks: dynamic typing.

### Clarification

First let us clarify the meaning of “dynamic typing”. “Dynamic typing” means that the type of expressions gets checked at runtime, expressions which may have any type are possible. It should not be confused with duck typing, e.g. many types using dynamic typing have a lot of built-in functions relying on specific types (“the frog will not get accepted”), e.g. most functions in PHP’s standard library (expecting string, integer, array or what ever). But for example C++ function templates in etc. provide duck typing (they will accept anything looking like an iterator), or the signatures in old g++ versions provided duck typing. Determining types may happen at compile time (type inference) even with dynamic typing, and of course optimising compilers/interpreters are doing that.

### Impact on Development

Let us talk about an argument for dynamic typing: it makes life easier. Actually, that can be right, there are domains where you just do not want to care about such stuff, for example when writing a shell script with few lines of code or when quickly doing some calculations with a computer algebra system. But Typo3, MediaWiki, Windows, Plasma etc. are much more than that. Why do I doubt that dynamic typing makes life easier in those contexts? Because it is error-prone. It is always better when errors get detected at compile time. It is good to fulfill contracts when programming, and they should get verified at compile time, such that they can be easily found and will not annoy the user. A type of contract (not the only one, cf. design by contract) which has been used for long time is the type system. The programmer assures that a variable has a certain type. What happens in dynamically typed languages? You do not have to state the contract, the compiler (or code checker) will usually not be able to check it, it is just in your brain, but of course you will still rely on that contract, the type is something you rely on most of the time when programming, I know that x is an integer when using x for some arithmetics. But you will do mistakes and you get buggy software. That is the fundamental disadvantage when programming, but of course I have to compare it to the advantages of dynamic typing: you can write code quickly and efficiently not mentioning the type everywhere. But there are more proper ways to achieve that: use type inference. The type of a variable will be determined by the compiler when initialising it and you will get an error when you are trying to change the type. That is good because in most cases the type of a variable will not change. And you will get informed about undefined variables (a typo should not cause a runtime error, but in dynamically typed languages it does). For the case that you need a structure allowing different types at the same position there are algebraic data types. With algebraic data types you can state a contract with only few tokens (instead of a nested array/dictionary data structure with a layout which is just implicitly given by the manipulation of it, that does often happen in dynamically typed languages), for variable declaration you only need one token, maybe a single character. That minimalistic overhead in code length is definitely worth it once the software has reached a certain complexity. That threshold is probably not very high, annoying mistakes which could have been avoided with static type checking can already occur in small programs just computing some stuff or something like that.

### Performance

Dynamic typing causes big overhead because instructions have to be choosen at runtime based on type information all the time. Of course it is much more complicated to optimise dynamically typed languages, there might be corner cases where the type is not the expected one, but the runtime has to care about it etc. I often read statements like “the performance critical parts are implemented natively” etc., but regarding the amount of applications running using such languages (JavaScript, PHP, Ruby, Python, Lua) we have to state: it is performance critical, PHP is used for more than a preprocessor, QML is used for more than just representing the UI, JavaScript is used for drawing a lot of complex stuff in the browser, Python gets used for scientific computations, and Ruby is establishing new standards regarding overhead (that is not true, Scheme has been that slow before ;), but Ruby allows modifying a lot of stuff at runtime, too). There is reasonable overhead—for abstraction, generalisation, internationalisation etc., but dynamic typing affects nearly any operation when running the program, that is unreasonable and of course it will sum up to significant overhead, although it is simply not needed (and bad for environment ;)).

### Special Issues

#### Regarding extreme flexibility

First of all: in 95% of applications you do not need it, you do not have to modify types at runtime, adding member functions to classes or objects and all that stuff. Sometimes it may be a good way to establish abstraction etc., but in those cases there are usually alternatives: meta-programming can be done at compile time, when manipulating all the types in Ruby they usually could have been manipulated at compile time, too, but Ruby does not support sophisticated compile time meta programming (ML and Template Haskell do, in C++ and D it is kinda limited). Regarding collection of information, debugging etc. using such features: debugging facilities should not influence the performance and cleanness, I am sure by involvement of meta programming you could implement language features allowing that when debugging without neglecting the type system. And of course a lot of flexibility at runtime can be achieved without allowing any type everywhere: dynamic dispatch (including stuff like inheritance, interfaces, signatures and even multi-dispatch), variant types at few places (e.g. QVariant, although I think it is used too often, signals can be implemented in a type safe way, and there are those type safe plugin factories as alternative to QtScript and Kross), signals and slots, aspects etc.

#### Regarding EcmaScript

You might say that EcmaScript is becoming fast enough because of good compilers and extensions like type safe arrays (e.g. containing only floating points). But EcmaScript will stay EcmaScript, it will keep the downsides of dynamic typing, those type safe arrays are an ugly hack to make it feasible for some specific applications. It is simply lacking a proper type system and it will not get it.

#### Regarding QML

Using EcmaScript for QtScript was a pragmatic choice, no awesome innovation: there were many web developers knowing about JavaScript. Unfortunately that caused yet another way to integrate scripts and certainly not the most flexible one (cf. my previous blog post), for some reason they did not want to reuse KDE’s innovation (like QtCreator and KDevelop, but that is really a different topic…). QML is based on EcmaScript because QtScript had been based on it before. Dynamic typing is definitely not an inherent property of such declarative UI, most of it could have looked the same with a native implementation based on C++, but also implementations in Ruby or whatever would be easily possible. I have to admit that C++ is not perfect, it does not provide sophisticated meta programming, algebraic types or one-letter type inference (“auto” has four letters ;)), the last one may be a small problem, but overall it is simply not simple enough ;), languages like Scala, D and OCaml have certain problems, too. Hence some of the non-declarative code in QML would have been disproportionately complicated compared to the declarative code. The general approach of declarative UI is certainly good, and now we probably have to accept that it has been implemented using EcmaScript, we can accept it, as long as it is still possible to write Plasmoids using C++ or whatever etc.—obviously that is the case. Thus QML is generally a good development in my opinion, although implementing program logic in it is often not a good idea and although dynamic typing leaves a bitter aftertaste.

I hope you have got my points about dynamic typing. Any opinions?

Wednesday, March 23rd, 2011

Hi!

#include <iostream>
using namespace std;

// a struct, because there are no partial specializations
// for functions
template<typename... args>
struct Print
{
// checking, because you cannot explicitly construct
// a parameter pack of strings
static_assert((sizeof...(args)) == 0, "illegal arguments");
static void exec()
{
}
};

template<typename... args>
struct Print<string, args...>
{
static void exec(string x, args... rest)
{
cout << x << endl;
// recursion, because there is no static-for (ammendment: unlike the foreach for tuples in D)
print(rest...);
}
};

// that function works
// but it would be probably three lines in D
template<typename... T>
void print(T... args)
{
Print<T...>
::exec(args...);
}

I think you see what I meant, variadic templates are nice for printf and tuples, but for any slidely different tasks they are still ugly.

Yes, I used it, really (skip deleted files and minor edits), it was ugly, but it provides some abstraction making the code – probably not readable – at least less redundant (I do not like copy&paste programming, the reason for copy&paste programming the lack of nice meta-programming features). Some last words why I am not using D: in C++ I can achieve anything using templates and implicit casts, and I have real value-semantics, D did not want to be like Java, but it forbids some stuff which is responsible for a lot of flexibility in C++. And if I would switch the language, I would try to choose a language involving some new, innovative and consistent concepts, that is not the case for D, maybe for Scala, but it does not allow value-semantics, too.

### Equal rights for the void!

Wednesday, March 9th, 2011

Hi!

This post may sound strange, but it is about programming languages, so do not care, if you are not interested in programming.

Well, today I want to talk about the type “void” in many programming languages. It is a really special type, because actually it does nothing. In Java you cannot do a lot with this type, I think the only valid usage of “void” is for methods’ result-type, void is not really a type in Java, it is more like the procedure-keyword in Pascal. In Java there are some relicts from C which do not actually fit into the concepts of the language (e.g. switch). However, in C and C++ you can do more with void, it is somehow a “real” type. Such features may appear weird at the first look, but I think they are really nice:

• You have void-pointers, you can cast any pointer into a void-pointer – explicitly or implicitly
• You can cast any value into a void-value, which you canot use then – explicitly or implicitly (cf. the definition of Q_UNUSED)
• You can return any value from a void-function

Well, for long time I could not imagine what this could be good for. But now I think: that is really beautiful. When should implicit casts be allowed? When thinking about it, you may notice two cases: coercion from one type into a more powerful one (e.g. int → long), and coercion from one type into a more general, weaker one (e.g. QWidget* → QObject* or iostream& → istream&). But it is basically the same, consider types as sets or families of possible values/objects, implicit coercion from type A into type B is possible, iff A ⊂ B (A subset of B). And any operation supported for elements of B should be supported by elements of A. Which operations are supported for values of the type void? No operations, so all operations supported for void are supported for all the other types, why should we not cast from any type to void?
That is supported by C++. But unfortunately there are limitations: You cannot have void-variables or constants, but that would nicely fit into the concept and sometimes it would make generic programming easier. You cannot dereference a void-pointer, but why should it not simply be a void-value as usual? And of course it should be possible to allocate void on the heap, it should be just NULL, and the address of a void-value should be NULL, too. It is okay for me, if the compiler wants to warn you about your usage of void, but just for consistency in the language void should not be that different from the other types, and not having variables of that type is simply not very nice. Equal ights for the void!

However, there are two things which may be not so nice: 1. When considering two sets represented by two types and one set should be a superset of the other set, you have to consider some elements of those different sets being equal, and of course in practice you do it all the time when comparing ints with shorts etc., but for voids that is impossible, you cannot decide, if two void-values are equal, and 2. you cannot explicitly cast back from a void-value to a non-void-value. However, void-values are not the only ones, where comparison is impossible, though for the most frequently used types it is of course possible. Consider functions (handled at runtime) internally stored using some kind of an arithmetic formulas, Turing-machines, Lambda-calculus or whatever. Generally it is not possible to decide, if two of such functions are equal (unless the arithmetics are too simplistic), notice that there are many different representations for the same function. So requiring values to be comparable is not very clever in a general-purpose programming language. In practice for some types you may not even want to support the equality-test, because it may be difficult to implement or very slow or something like that. That are my reasons, why I think that the first issue is void. I currently cannot imagine any two types different from void where explicit casting is only possible in one direction. Maybe you can? However, if the type does not support equality-checking, after casting back and forth you cannot even say that the value is identical to the original one. But this issue remains unsolved. However, altogether I think that void should be a real type in our programming languages, because it is very consistent, and it should be different from nil/NULL/None, because nil/NULL/None should indicate the absence of a value of one specific type, and not the void.

Or I can put it that way: The void is like qualia: it is everywhere, it is contained in each individual, it does not express anything specific, you cannot differentiate between “my” and “your”, and of course you cannot cast it back to the individual with its personality.

PS: My statements about allocation a position 0 were wrong in my opinion. Cf. the comments.