The Quylthulg Programming Language

Overview

Here is what is known about the programming language Quylthulg. Quylthulg:

• is a programming language;
• is named Quylthulg;
• was designed by Chris Pressey;
• does not, quite apart from prevailing trends in programming practice, shun the use of goto;
• is, however, somewhat particular about where goto may be used (goto may only occur inside a data structure);
• is purely functional (in the sense that it does not allow "side-effectful" updates to values);
• forbids recursion;
• provides but a single looping construct: foreach, which applies an expression successively to each value in a data structure;
• is Turing-complete; and
• boasts an argument-less macro expansion facility (in which recursion is also forbidden.)

Syntax

The syntax for identifiers draws from the best parts of the esteemed languages BASIC and Perl. Like Perl, all identifiers must be preceded by a $ symbol, and like BASIC, all identifiers must be followed by a $ symbol. Well, OK, that's for strings anyway, but we don't care about their types really, so we use $ for everything. (Also, studies show that this syntax can help serious TeX addicts from "bugging out".)

A nice practical upshot of this is that identifier names may contain any characters whatsoever (excepting $), including whitespace.

Because of this, the syntax for string literals can be, and is, derived from the syntax for identifiers. A string literal is given by a ~ followed by an identifier; the textual content of the name of the identifier is used as the content of the string literal. A string literal consisting of a single $ symbol is given by ~~.

Many find the syntax for labels to be quite sumilar to that for identifiers. (Some even find it to be quite similar.) Labels are preceded and followed by : symbols, and may contain any symbol except for :.

Syntax for binary operations follows somewhat in the footsteps of the identifier syntax. It is a combination of prefix, infix, and postfix syntax, where the two terms must be preceeded, followed, and seperated by the same symbol. We call this notation panfix. It is perhaps worth noting that, like postfix, panfix does not require the deployment of arcane contrivances such as parentheses to override a default operator precedence. At the same time, panfix allows terms to be specified in the same order and manner as infix, an unquestionably natural and intuitive notation to those who have become accustomed to it.

So, we give some examples:

*+1+2+*3*
&~$The shoes are $&&~~&~$9.99 a pair.$&&

The first example might be stated as (1+2)*3 in conventional, icky parenthesis-ful notation, and evaluates to 9. The second evaluates to the string "The shoes are $9.99 a pair."

There are no unary operators in Quylthulg. (Note that ~ isn't really a unary operator, actually not an operator at all, because it must be followed by an identifier, not an expression. Well, maybe it's a special kind of operator then, an identifier-operator perhaps. But you see what I'm getting at, don't you? Hopefully not.)

There is a special 6-ary operator, foreach. It has its own syntax which will be covered below.

Data Types

Strings and Integers

Yes. Also a special type called abort, of which there is a single value abort, which you'll learn about later.

Lists

The sole data structure of note in Quylthulg is the list. Lists are essentially identical to those found in other functional languages such as Scheme: they are either the special value null, which suggests an empty list, or they consist of a cons cell, which is a pair of two other values. By convention, the first of this pair is the value of this list node, and the second is a sublist (a null or a cons) which represents the rest of this list.

The value of a list node may be any value: a scalar such as an integer or a string, another (embedded sub)list, or the special value abort. cons cells are constructed by the , panfix operator. Some examples follow:

,1,,2,,3,null,,,
,1,,2,3,,

The first example constructs a proper list. So-called "improper" lists, which purely by convention do not end with null, can also be constructed: that's the second example.

When all of the terms involved are literal constants embedded in the program text, there is a shorthand syntax for these list expressions, stolen from the Prolog/Erlang school:

[1, 2, 3]
[1, 2 | 3]

Note, however, that [] is not shorthand for null. Note also that when this syntax is used, all values must be literal constants: there will be no tolerance for variables. There will, however, be tolerance for gotos and labels; see below for more on that.

Cyclic Lists

Labels and the goto construct enable the definition of cyclic data structures like so:

:A:[1, 2, 3, goto $A$]
:B:[1, 2, :C:[3, 4, goto $B$], 5, 6, goto $C$]

Note that this can only be done in literal constant data structure expressions, not in , (consing) operations or expression involving a variable. This is to avoid the dynamic construction of labelled terms, which just a tad mind-bending and which I've decided to save for a sequel to Quylthulg, whatever and whenever that might be. Note also that labels have their own syntax during declaration, but (oh so helpfully) insist on being referred to in gotos by the $ syntax used for identifiers.

List Operators

The values contained in a cons cell can be extracted by the felicitous use of the binary operators < ('first') and > ('rest'). For both of these operators, the left-hand side is the cons cell to operate on, and the right-hand side is an expression which the operator will evaluate to in the case that it cannot successfully extract the value from the cons cell (e.g., the left-hand side is not in fact a cons cell but rather something else like a null or a number or a string or abort.

There is also an operator ; which appends one list (the right-hand side) onto the end of another list (the left-hand side.) This is probably not strictly necessary, since as we'll see later we can probably build something equivalent using foreaches and macros, but what the hell, we can afford it. Party down.

These list operators honour cyclic lists, so that >[:X: 4 | goto :X:]>abort>, to take just one instance, evaluates to 4.

Control Flow

Quylthulg's sole looping construct, foreach, is a recursing abortable "fold" operation. It is passed a data structure to traverse, an expression (called the body) that it will apply to each value it encounters in the traversed data structure, and an initial value called the accumulator. Inside the body, two identifiers are bound to two values: the value in the data structure that the body is currently being applied to, and the value of the current value. The names of the idenfiers so bound are specified in the syntax of the foreach operator. The value that the body evaluates to is used as the accumulator for the next time the body is evaluated, on the next value in the data structure. The value that foreach evaluates to is the value of the final accumulator (emphasis mine.) The full form of this operator is as follows:

foreach $var$ = data-expr with $acc$ = initial-expr be loop-expr else be otherwise-expr

foreach traverses the data structure in this manner: from beginning to end. It is:

• recursing, meaning if the current element of the list is itself a (sub)list, foreach will begin traversing that (sub)list (with the same body and current accumulator, natch) instead of passing the (sub)list to the body; and
• abortable, meaning that the loop-expr may evaluate to a special value abort, which causes traversal of the current (sub)list to cease immediately, returning to the traversal of the containing list, if any.

If the data-expr evaluates to some value besides a cons cell (for example, null or an integer or a string), then the loop-expr is ignored and the otherwise-expr is evaluated instead.

As an example,

-foreach $x$ = [2, 3, 4] with $a$ = 1 be *$a$*$x$* else be null-1-

will evaluate to 23. On the other hand,

foreach $x$ = null with $a$ = 1 be $a$ else be 23

will also evaluate to 23.

Macro System

Quylthulg boasts an argument-less macro expansion system. (Yes, there is no argument about it: it boasts it. It is quite arrogant, you know.) Where-ever text of the form {foo} appears in the source code, the contents of the macro named foo are inserted at that point, replacing {foo}. This process is called the expansion of foo. But it gets worse: whereever text of the form {bar} appears in the contents of that macro called foo, those too will be replaced by the contents of the macro called bar. And so on. Three things to note:

• If there is no macro called foo, {foo} will not be expanded.
• If {foo} appears in the contents of foo, it will not be expanded.
• Nor will it be expanded if it appears in the contents of foo as the result of expanding some other macro in the contents of foo.

(I stand corrected. That was more like 2.5 things to note.)

Macros can be defined and redefined with the special macro-like form {*[foo][bar]}. The first text between square brackets is the name of the macro being defined; the text between the second square brackets is the contents. Both texts can contain any symbols except unmatched ]'s. i.e. you can put square brackets in these texts as long as they nest properly.

Now you see why we don't need arguments to these macros: you can simply use macros as arguments. For example,

{*[SQR][*{X}*{X}*]}{*[X][5]}{SQR}

uses an "argument macro" called X which it defines as 5 before calling the SQR macro that uses it.

Note that macros are expanded before any scanning or parsing of the program text begins. Thus they can be used to define identifiers, labels, etc.

Comments

The macro system also provides a way to insert comments into a Quylthulg program. It should be noted that there are at least three schools of thought on this subject.

The first school (Chilton County High School in Clanton, Alabama) says that most comments that programmers write are next to useless anyway (which is absolutely true) so there's no point in writing them at all.

The second school (Gonzaga College S.J. in Dublin, Ireland — not to be confused with Gonzaga University in Spokane, Washington) considers comments to be valuable as comments, but not as source code. They advocate their use in Quylthulg by the definition of macros that are unlikely to be expanded for obscure syntactical reasons. For example, {*[}][This is my comment!]}. Note that that macro can be expanded in Quylthulg using {}}; it's just that the Gonzaga school hopes that you won't do that, and hopes you get a syntax error if you try.

The third school (a school of fish) believes that comments are valuable, not just as comments, but also as integral (or at least distracting) parts of the computation, and champions their use in Quylthulg as string literals involved in expressions that are ultimately discarded. For example, <~$Addition is fun!$<+1+2+<.

Integration with the Rest of the Language

To dispel the vicious rumours that the macro system used in Quylthulg and the Quylthulg language are really independent and separate entities which just happen to be sandwiched together there, we are quick to point out that they are bound by two very important means:

• At the beginning of the program, at a global scope, the identifier $Number of Macros Defined$ is bound to an integer constant containing the number of unique macros that were defined during macro expansion before the program was parsed.
• The panfix operator % applies macros to a Quylthulg string at runtime. The expression on the left-hand side should evaluate to a string which contains macro definitions. The expression on the right-hand side is the string to expand using these macro definitions.

Turing-Completeness

Now, I claim that Quylthulg is Turing-complete — that is, that it can compute anything that a Turing machine (or any other Turing-complete system) can. I would provide a proof, but since the point of a proof is to dispel doubt, and since you have not expressed any doubt so far (at least none that I have been able to observe from my vantage point), and since (statistically speaking anyway) you believe that fluoride in drinking water promotes dental health, that the sun is a giant nuclear furnace, that Wall Street is substantially different from Las Vegas, that a low-fat diet is an effective way to lose weight, that black holes exist, and that point of the War on Drugs is to stop people from harming themselves — well, in light of all that, a proof hardly seems called-for. Instead, I shall perform a series of short vignettes, each intended to invoke the spirit of a different forest animal or supermarket checkout animal. Then I shall spray you with a dose of a new household aerosol which I have invented and which I am marketing under the name "Doubt-B-Gone".

• We can use foreach as an if-then-else construct by using lists to represent booleans.

  Using null to represent false, and cons anything to represent true, we use the else part of foreach to accomplish a boolean if-then-else. We can employ ; to get boolean OR and nested foreaches to get boolean AND. (Detailed examples of these can be found in the unit tests of the Quylthulg reference interpreter, which is called "Qlzqqlzuup, Lord of Flesh".)

• We can construct an infinite loop by running foreach on a cyclic data structure.

  For example,

  foreach $x$ = :L:[1, 2, 3, goto $L$] with $a$ = 0 be $x$ else be null
  

  never finishes evaluating, and in the body, $x$ takes on the values 1, 2, 3, 1, 2, 3, ... ad infinitum.

• We can treat the accumulator of a foreach like an unbounded tape, just like on a Turing machine.

  We can pass in a cons cell where the first value is a list representing everything to the left of the head, and the second value is a list representing everything to the right of the head. Moving the head left or right can be accomplished by taking the first (<) off the appropriate list and cons (,) it onto the other list. There are also other ways to do it, of course. The point is that there is no bound specified on the length of a list in Quylthulg.

• We can, in fact, make foreach act like a while construct.

  We just combine the looping forever with an if-then-else which evaluates to abort when the condition comes true.

• We can give foreach a cyclic tree-like data structure which describes the finite control of a Turing machine.

  Although we don't have to — we could just use nested foreaches to make a lot of tests against constant values.

• We can even make foreach work like let if we need to.

  Just bind the accumulator to $Name$, refer to $Name$ in the body, and ignore the contents of the one-element list. Or use it to bind two variables in one foreach.

PHHSHHHHHHHHHHHHHHTt.

Discussion

Now I'm hardly the first person to suggest using cyclic lists as an equivalent alternative to a general looping construct such as while. It has long been a stylish LISP programming technique. However, to comply with the Nietzschean-Calvinist mandate of our society (that is, to sustain the progress that will thrust us toward the "Perfect Meat at the End of Time" of which Hegel spoke,) we must demonstrate that we have innovated:

• Quylthulg provides only this method of looping; without it, it would not be Turing-complete, and
• Unlike the extant stylish programming techniques, which require side-effecting operations such as rplacd to pull off, Quylthulg is a pure functional programming language without updatable storage.

Huzzah.

It is somewhat sad to consider just how long Quylthulg took to design and how much of that labour took place aboard airplanes. It is even sadder to consider some of the delusions I was occupied with while designing it. Some of the biggest were the idea that foreach somehow had to be recursable for this to work — it doesn't, but I left it in. For similar reasons I left in ;, the append operator. And I've already mentioned the headaches with allowing labels and gotos in expressions rather than only in literals.

Long live the new flesh, eh?
Chris Pressey
Seattle, Washington
Dec 6, 2008