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CosmicOS version "cosmic.0.6"(latest version always available at CosmicOS homepage)verbose source form of message, table of contents
The high-level structure of the message is as follows. There are some basic preliminaries (enumerating numbers etc) to introduce the low-level syntax and semantics of the message. This is followed by many examples of relational operators and basic functional notation. Once a sufficient set of operators is avalailable, most new concepts are introduced both by examples and a definition in terms of what is already known. The message consists of a sequence of statements that can be evaluated, and each statement evaluates to true. The message can refer to its own syntax, and a statement can change that syntax. Thus the form of the message changes over its course, with the introduction of shorthand forms, object-oriented notation, etc. The goal of current work on the message is to bring it to a point where it is easy to write statements about a MUD (a simulated world consisting of (things that act like) locations, movable objects, and people). This MUD will be used to communicate Freudenthal-style tales. The advantage of using a programming-code-like language is that the reader can play with hypothethicals at any time, and experiment to evaluate alternative statements that are not in the message. Current status: just reached the MUD -- keep needing to go back and put in new infrastructure. Lots of rough spots in the message to smooth over. An automatic checker is now in place, to make sure the message is consistent, when interpreted as code. This flushes out a lot of bugs. (more version notes at bottom of this page)
Estimate of message entropy in final form: 9.6 kB. |
| Index of lessons |
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(all lessons)
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| Message visualization |
 (magnify) The image reads diagonally, starting at the top left. It is handy for spotting phase changes in the message (e.g. the transition from using unary to binary, or - more importantly - bugs). Breaks between statements are white dots, zeros are greenish, ones are reddish, parentheses are different shades of blue. |
| Further notes |
number symbol meaning
0 . binary digit zero
1 : binary digit one
2 ( marks beginning of an expression
3 ) marks end of an expression
4 ; marks end of sentence
There are constraints in the possible transitions between these symbols that would allow a simple and shorter encoding if desired.
Numbers are encoded as binary digits between parentheses, e.g. (:::.) is 1110 base 2 which is 14 in decimal. A set of numbers between parentheses constitutes an expression. Expressions can be nested. Expressions followed by a semicolon should evaluate to be true, once the rules for evaluation have been introduced.
In the human-readable form of the message, decimal numbers can be used. There are converted to the above form. Identifiers can also be used. Identifiers are mapped onto arbitrarily assigned numbers. In the message, there is nothing to distinguish identifiers from numbers. The actual language is carefully constructed so that this distinction is never necessary.
The first number in an expression is treated as an index into an environment that returns a function. When the lambda notation is introduced, it works by modifying that (nested) environment. Expressions are evaluated from the outermost inwards, from left to right, and the "if" form is introduced as lazy.
This "functional style" of expression is not always particularly easy to follow, even for a human, but it is certainly very expressive. Currently functional definitions are given alongside numerous examples that are in many cases sufficient by themselves to communicate the definition, at least for working purposes. It is probably important to maintain this duality and perhaps extend it with other forms of expression. There are so many models of computation, why not use all of them? Perhaps one will be easier for the reader to follow than the others.
While it is tempting to try to make the message airtight from a formal point of view, defining everything in terms of axioms, this is just one didactic approach - and may be counter-productive or impossible for a a large-scale message that includes AI-complete concepts.
Currently there is a conflict between using definitions of functions that are easy to communicate, and definitions that are efficient (or external). This will require some more thought. For example, it would be nice to introduce "if" in its pure lambda calculus form, but to do so would slow checking down right now. The "if" function is instead built in, and (to add insult to injury) introduced with lazy evaluation. It would be more consistent to keep everything eager to begin with, and then show the evaluator being rewritten to facilitate laziness -- easy using the standard trick of wrapping conditional expressions in single-argument functions.
There are going to be bugs in the message -- it is being cobbled together quite hastily. Please be forgiving. It'll all get fixed in an instant of galactic time...