Can you create a programming language with just one symbol? - brainfuck

Can you create a programming language with just one symbol like brainfuck.

Yes, it has been done before - see Unary.
Basically it's a strange encoding of brainfuck. Treat each BF command as a number. The whole program is then also a number, created by concatenating the commands together (with an extra 1 at front, for unambiguous decoding). Convert the number to unary numeric system (aka the number of digits is your number) and you're done.
Note however the programs in this tend to be very large - a cat implemented in Unary is (according to the information on page) 56623 characters long.
MGIFOS, Lenguage and Ellipsis follow the same principle. Note that e.g. a hello world in MGIFOS
has more characters than particles in the observable universe
Then Len(language,encoding) extends this principle to any language.

They are called OISC One Instruction Set Compiler.
The first one know of is Melzak's Arithmetic Machine (1961), with the instruction:
z = x-y or jump if y>x
You also have Zero Instruction Set Computer, which are more like neural nets.
Not forgetting the amazing FRACTRAN of Conway & Guy (1996), with no instruction but interprets a series of fractions (the program) in a Tuning complete way.

Related

In Python (or any language) what does an "upper" function do to Hindi, Amharric and other non-Latin character sets?

Subject says it all. Been looking for an answer, but cannot seem to find it.
I am writing a web app that will store data in a database and also have language files translated into a wide variety of character sets. At various moments, the text will be presented. I want to control presentation such as spurious blank spaces at the beginning and end of strings. Also I want to ensure some letters are upper or lower case.
My question is: what happens in upper/lower case functions when the character set only has one case?
EDIT Sub question: Are there any unexpected side effects to be aware of?
My guess is that you simply get back the one and only character.
EDIT - Added Description
The main reason for asking this question is that I am writing a webapp that will be distributed and run on machines in remote areas with little or no chance to fix "on-the-spot" bugs. It's not a complicated webapp, but will run with many different language char sets. I want to be certain of my footing before releasing the server.
First of all the upper() and lower() method in python can be applied to Hindi, Amharric and non-letter character sets.
For instance will the upper() method converts the lowercase characters if an equivalent uppercase of this char exists. If not, then not.
Or better said, if there is nothing to convert, it stays the same.

Japanese COBOL Code: rules for G literals and identifiers?

We are processing IBMEnterprise Japanese COBOL source code.
The rules that describe exactly what is allowed in G type literals,
and what are allowed for identifiers are unclear.
The IBM manual indicates that a G'....' literal
must have a SHIFT-OUT as the first character inside the quotes,
and a SHIFT-IN as the last character before the closing quote.
Our COBOL lexer "knows" this, but objects to G literals
found in real code. Conclusion: the IBM manual is wrong,
or we are misreading it. The customer won't let us see the code,
so it is pretty difficult to diagnose the problem.
EDIT: Revised/extended below text for clarity:
Does anyone know the exact rules of G literal formation,
and how they (don't) match what the IBM reference manuals say?
The ideal answer would a be regular expression for the G literal.
This is what we are using now (coded by another author, sigh):
#token non_numeric_literal_quote_g [STRING]
"<G><squote><ShiftOut> (
(<NotLineOrParagraphSeparatorNorShiftInNorShiftOut>|<squote><squote>|<ShiftOut>)
(<NotLineOrParagraphSeparator>|<squote><squote>)
| <ShiftIn> ( <NotLineOrParagraphSeparatorNorApostropheNorShiftInNorShiftOut>|
<ShiftIn>|<ShiftOut>)
| <squote><squote>
)* <ShiftIn><squote>"
where <name> is a macro that is another regular expression. Presumably they
are named well enough so you can guess what they contain.
Here is the IBM Enterprise COBOL Reference.
Chapter 3 "Character Strings", subheading "DBCS literals" page 32 is relevant reading.
I'm hoping that by providing the exact reference, an experienced IBMer can tell us how we misread it :-{ I'm particularly unclear on what the phrase "DBCS-characters" means
when it says "one or more characters in the range X'00...X'FF for either byte"
How can DBCS-characters be anything but pairs of 8-bit character codes?
The existing RE matches 3 types of pairs of characters if you examine it.
One answer below suggests that the <squote><squote> pairing is wrong.
OK, I might believe that, but that means the RE would only reject
literal strings containing single <squote>s. I don't believe that's
the problem we are having as we seem to trip over every instance of a G literal.
Similarly, COBOL identifiers can apparantly be composed
with DBCS characters. What is allowed for an identifier, exactly?
Again a regular expression would be ideal.
EDIT2: I'm beginning to think the problem might not be the RE.
We are reading Shift-JIS encoded text. Our reader converts that
text to Unicode as it goes. But DBCS characters are really
not Shift-JIS; rather, they are binary-coded data. Likely
what is happening is the that DBCS data is getting translated
as if it were Shift-JIS, and that would muck up the ability
to recognize "two bytes" as a DBCS element. For instance,
if a DBCS character pair were :81 :1F, a ShiftJIS reader
would convert this pair into a single Unicode character,
and its two-byte nature is then lost. If you can't count pairs,
you can't find the end quote. If you can't find the end quote,
you can't recognize the literal. So the problem would appear
to be that we need to switch input-encoding modes in the middle
of the lexing process. Yuk.
Try to add a single quote in your rule to see if it passes by making this change,
<squote><squote> => <squote>{1,2}
If I remember it correctly, one difference between N and G literals is that G allows single quote. Your regular expression doesn't allow that.
EDIT: I thought you got all other DBCS literals working and just having issues with G-string so I just pointed out the difference between N and G. Now I took a closer look at your RE. It has problems. In the Cobol I used, you can mix ASCII with Japanese, for example,
G"ABC<ヲァィ>" <> are Shift-out/shift-in
You RE assumes the DBCS only. I would loose this restriction and try again.
I don't think it's possible to handle G literals entirely in regular expression. There is no way to keep track of matching quotes and SO/SI with a finite state machine alone. Your RE is so complicated because it's trying to do the impossible. I would just simplify it and take care of mismatching tokens manually.
You could also face encoding issues. The code could be in EBCDIC (Katakana) or UTF-16, treating it as ASCII will not work. SO/SI sometimes are converted to 0x1E/0x1F on Windows.
I am just trying to help you shoot in the dark without seeing the actual code :)
Does <NotLineOrParagraphSeparatorNorApostropheNorShiftInNorShiftOut> also include single and double quotation marks, or just apostrophes? That would be a problem, as it would consume the literal closing character sequence >' ...
I would check the definition of all other macros to make sure. The only obvious problem that I can see is the <squote><squote> that you already seem to be aware of.

If Ascii operators are definable, why not Unicode Symbols?

I'm sure I join many in being glad there's finally a powerful language tied tightly to a mainstream GUI/Database/Communication framework.
I haven't been sure where to post this, but here seems the best spot.
I need to use Unicode symbol characters either as operators or as function names. I'd like syntactic sugar, but I don't need it.
Guy Steele pointed out in Communications of the ACM that "*" was a forced choice when it was adopted from Ascii as multiply, but my software works in Unicode, so I'm not tethered to Ascii anymore.
!$%&*+-./<=>?,#^|~:
Part of localization includes local programmers. Why limit the set of operators that can be defined in F#? It isn’t orthogonal to C#'s and F#'s acceptance of many Unicode IsLetter in identifiers.
Also, F# is likely to be used for symbolic manipulation of problems from logic, math, physicists, etc. It makes work much easier if there’s a direct mapping into the language of the basic operators. (F# and C# accept many Unicode IsLetter? as well as IsDigit’? This is a request to allow Unicode IsSymbol? As operators with the precedence of, for example, *, or, since “+” is both a unary and binary operator, I could put up with the precedence of + and make up the difference with parenthesized groupings.
Consider the domain-specific needs of logicians, mathematicians, physicists, etc. I’d rather write a symbolic differentiator or integrator using math symbols than Ascii permutations of already-taken operators.
Logic: ∀ ∃ ⇒
Math: ∑ ∫ ∂
Group theory: ≤ ≥ ∈ ∉
Set Theory: ⊆ ⊇ ⊃ ∪ ∩
Tensors: ⊗
I’ve written many languages in other languages, but because F# is tightly .Net-integrated, this issue poses special challenges without language support:
It’s trivial to cobble up a translator that takes Unicode-operator F# source and maps it, line-by-line, to Ascii-operator F# source.
But when debugging, how do I make sure the programmer still sees their untranslated source? And that they can see variable values.
Operators and converts them is trivial. But how do I ensure the translation is what gets compiled, while the programmer sees their own source? If I map line-for-line correctly, how do I ensure they can still point at a variable and see its value?
There is a math (Unicode) symbol extension for F# available in the Visual Studio Gallery.
This allows you to define Unicode symbols, e.g.:
let inline (~∑) xs = xs |> Seq.sum
let total = ∑myList
You may be interested in Project Fortress which is a new functional programming language that embraces the Unicode character set (among many other features). In particular, see the Mathematical Syntax in Fortress page which contains some sample code.
For an interesting discussion on this check: http://cs.hubfs.net/forums/thread/9690.aspx
Other languages, such as Scala, do permit operators from outside the ASCII range -- mathematical symbols(Sm) and other symbols(So)

How should I handle digits from different sets of UNICODE digits in the same string?

I am writing a function that transliterates UNICODE digits into ASCII digits, and I am a bit stumped on what to do if the string contains digits from different sets of UNICODE digits. So for example, if I have the string "\x{2463}\x{24F6}" ("④⓶"). Should my function
return 42?
croak that the string contains mixed sets?
carp that the string contains mixed sets and return 42?
give the user an additional argument to specify one of the three above behaviours?
do something else?
Your current function appears to do #1.
I suggest that you should also write another function to do #4, but only when the requirement appears, and not before .
I'm sure Joel wrote about "premature implementation" in a blog article sometime recently, but I can't find it.
I'm not sure I see a problem.
You support numeric conversion from a range of scripts, which is to say, you are aware of the Unicode codepoints for their numeric characters.
If you find an unknown codepoint in your input data, it is an error.
It is up to you what you do in the event of an error; you may insert a space or underscore, or you may abort conversion. What you would do will depend on the environment in which your function executes; it is not something we can tell you.
My initial thought was #4; strictly based on the fact that I like options. However, I changed my mind, when I viewed your function.
The purpose of the function seems to be, simply, to get the resulting digits 0..9. Users may find it useful to send in mixed sets (a feature :) . I'll use it.
If you ever have to handle input in bases greater than 10, you may end up having to treat many variants on the first 6 letters of the Latin alphabet ('ABCDEF') as digits in all their forms.

Theory: "Lexical Encoding"

I am using the term "Lexical Encoding" for my lack of a better one.
A Word is arguably the fundamental unit of communication as opposed to a Letter. Unicode tries to assign a numeric value to each Letter of all known Alphabets. What is a Letter to one language, is a Glyph to another. Unicode 5.1 assigns more than 100,000 values to these Glyphs currently. Out of the approximately 180,000 Words being used in Modern English, it is said that with a vocabulary of about 2,000 Words, you should be able to converse in general terms. A "Lexical Encoding" would encode each Word not each Letter, and encapsulate them within a Sentence.
// An simplified example of a "Lexical Encoding"
String sentence = "How are you today?";
int[] sentence = { 93, 22, 14, 330, QUERY };
In this example each Token in the String was encoded as an Integer. The Encoding Scheme here simply assigned an int value based on generalised statistical ranking of word usage, and assigned a constant to the question mark.
Ultimately, a Word has both a Spelling & Meaning though. Any "Lexical Encoding" would preserve the meaning and intent of the Sentence as a whole, and not be language specific. An English sentence would be encoded into "...language-neutral atomic elements of meaning ..." which could then be reconstituted into any language with a structured Syntactic Form and Grammatical Structure.
What are other examples of "Lexical Encoding" techniques?
If you were interested in where the word-usage statistics come from :
http://www.wordcount.org
This question impinges on linguistics more than programming, but for languages which are highly synthetic (having words which are comprised of multiple combined morphemes), it can be a highly complex problem to try to "number" all possible words, as opposed to languages like English which are at least somewhat isolating, or languages like Chinese which are highly analytic.
That is, words may not be easily broken down and counted based on their constituent glyphs in some languages.
This Wikipedia article on Isolating languages may be helpful in explaining the problem.
Their are several major problems with this idea. In most languages, the meaning of a word, and the word associated with a meaning change very swiftly.
No sooner would you have a number assigned to a word, before the meaning of the word would change. For instance, the word "gay" used to only mean "happy" or "merry", but it is now used mostly to mean homosexual. Another example is the morpheme "thank you" which originally came from German "danke" which is just one word. Yet another example is "Good bye" which is a shortening of "God bless you".
Another problem is that even if one takes a snapshot of a word at any point of time, the meaning and usage of the word would be under contention, even within the same province. When dictionaries are being written, it is not uncommon for the academics responsible to argue over a single word.
In short, you wouldn't be able to do it with an existing language. You would have to consider inventing a language of your own, for the purpose, or using a fairly static language that has already been invented, such as Interlingua or Esperanto. However, even these would not be perfect for the purpose of defining static morphemes in an ever-standard lexicon.
Even in Chinese, where there is rough mapping of character to meaning, it still would not work. Many characters change their meanings depending on both context, and which characters either precede or postfix them.
The problem is at its worst when you try and translate between languages. There may be one word in English, that can be used in various cases, but cannot be directly used in another language. An example of this is "free". In Spanish, either "libre" meaning "free" as in speech, or "gratis" meaning "free" as in beer can be used (and using the wrong word in place of "free" would look very funny).
There are other words which are even more difficult to place a meaning on, such as the word beautiful in Korean; when calling a girl beautiful, there would be several candidates for substitution; but when calling food beautiful, unless you mean the food is good looking, there are several other candidates which are completely different.
What it comes down to, is although we only use about 200k words in English, our vocabularies are actually larger in some aspects because we assign many different meanings to the same word. The same problems apply to Esperanto and Interlingua, and every other language meaningful for conversation. Human speech is not a well-defined, well oiled-machine. So, although you could create such a lexicon where each "word" had it's own unique meaning, it would be very difficult, and nigh on impossible for machines using current techniques to translate from any human language into your special standardised lexicon.
This is why machine translation still sucks, and will for a long time to come. If you can do better (and I hope you can) then you should probably consider doing it with some sort of scholarship and/or university/government funding, working towards a PHD; or simply make a heap of money, whatever keeps your ship steaming.
It's easy enough to invent one for yourself. Turn each word into a canonical bytestream (say, lower-case decomposed UCS32), then hash it down to an integer. 32 bits would probably be enough, but if not then 64 bits certainly would.
Before you ding for giving you a snarky answer, consider that the purpose of Unicode is simply to assign each glyph a unique identifier. Not to rank or sort or group them, but just to map each one onto a unique identifier that everyone agrees on.
How would the system handle pluralization of nouns or conjugation of verbs? Would these each have their own "Unicode" value?
As a translations scheme, this is probably not going to work without a lot more work. You'd like to think that you can assign a number to each word, then mechanically translate that to another language. In reality, languages have the problem of multiple words that are spelled the same "the wind blew her hair back" versus "wind your watch".
For transmitting text, where you'd presumably have an alphabet per language, it would work fine, although I wonder what you'd gain there as opposed to using a variable-length dictionary, like ZIP uses.
This is an interesting question, but I suspect you are asking it for the wrong reasons. Are you thinking of this 'lexical' Unicode' as something that would allow you to break down sentences into language-neutral atomic elements of meaning and then be able to reconstitute them in some other concrete language? As a means to achieve a universal translator, perhaps?
Even if you can encode and store, say, an English sentence using a 'lexical unicode', you can not expect to read it and magically render it in, say, Chinese keeping the meaning intact.
Your analogy to Unicode, however, is very useful.
Bear in mind that Unicode, whilst a 'universal' code, does not embody the pronunciation, meaning or usage of the character in question. Each code point refers to a specific glyph in a specific language (or rather the script used by a group of languages). It is elemental at the visual representation level of a glyph (within the bounds of style, formatting and fonts). The Unicode code point for the Latin letter 'A' is just that. It is the Latin letter 'A'. It cannot automagically be rendered as, say, the Arabic letter Alif (ﺍ) or the Indic (Devnagari) letter 'A' (अ).
Keeping to the Unicode analogy, your Lexical Unicode would have code points for each word (word form) in each language. Unicode has ranges of code points for a specific script. Your lexical Unicode would have to a range of codes for each language. Different words in different languages, even if they have the same meaning (synonyms), would have to have different code points. The same word having different meanings, or different pronunciations (homonyms), would have to have different code points.
In Unicode, for some languages (but not all) where the same character has a different shape depending on it's position in the word - e.g. in Hebrew and Arabic, the shape of a glyph changes at the end of the word - then it has a different code point. Likewise in your Lexical Unicode, if a word has a different form depending on its position in the sentence, it may warrant its own code point.
Perhaps the easiest way to come up with code points for the English Language would be to base your system on, say, a particular edition of the Oxford English Dictionary and assign a unique code to each word sequentially. You will have to use a different code for each different meaning of the same word, and you will have to use a different code for different forms - e.g. if the same word can be used as a noun and as a verb, then you will need two codes
Then you will have to do the same for each other language you want to include - using the most authoritative dictionary for that language.
Chances are that this excercise is all more effort than it is worth. If you decide to include all the world's living languages, plus some historic dead ones and some fictional ones - as Unicode does - you will end up with a code space that is so large that your code would have to be extremely wide to accommodate it. You will not gain anything in terms of compression - it is likely that a sentence represented as a String in the original language would take up less space than the same sentence represented as code.
P.S. for those who are saying this is an impossible task because word meanings change, I do not see that as a problem. To use the Unicode analogy, the usage of letters has changed (admittedly not as rapidly as the meaning of words), but it is not of any concern to Unicode that 'th' used to be pronounced like 'y' in the Middle ages. Unicode has a code point for 't', 'h' and 'y' and they each serve their purpose.
P.P.S. Actually, it is of some concern to Unicode that 'oe' is also 'œ' or that 'ss' can be written 'ß' in German
This is an interesting little exercise, but I would urge you to consider it nothing more than an introduction to the concept of the difference in natural language between types and tokens.
A type is a single instance of a word which represents all instances. A token is a single count for each instance of the word. Let me explain this with the following example:
"John went to the bread store. He bought the bread."
Here are some frequency counts for this example, with the counts meaning the number of tokens:
John: 1
went: 1
to: 1
the: 2
store: 1
he: 1
bought: 1
bread: 2
Note that "the" is counted twice--there are two tokens of "the". However, note that while there are ten words, there are only eight of these word-to-frequency pairs. Words being broken down to types and paired with their token count.
Types and tokens are useful in statistical NLP. "Lexical encoding" on the other hand, I would watch out for. This is a segue into much more old-fashioned approaches to NLP, with preprogramming and rationalism abound. I don't even know about any statistical MT that actually assigns a specific "address" to a word. There are too many relationships between words, for one thing, to build any kind of well thought out numerical ontology, and if we're just throwing numbers at words to categorize them, we should be thinking about things like memory management and allocation for speed.
I would suggest checking out NLTK, the Natural Language Toolkit, written in Python, for a more extensive introduction to NLP and its practical uses.
Actually you only need about 600 words for a half decent vocabulary.