git @ Cat's Eye Technologies beta-Juliet / master

Tree @master (Download .tar.gz)


Version 2.0 | Entry @ | Wiki entry @ | See also: Squishy2KNested Modal Transducers

β-Juliet is a minimal event-oriented language which, as of version 2.0 (see historical note below), is probably Turing-complete.


β-Juliet is a fairly minimal event-oriented language. In β-Juliet, the world is modelled as a set of events which have no inherent organization or order. Each event can be denoted with a symbol, such as DominoFalls, CatMeows, or SunSets, or (in version 2.0) a string of symbols, such as Address Line Six Goes High or Greengrocer Falls Asleep on Subway.

Each event can cause other events to occur — these are termed consequences of the event. In addition, this causation may be conditional, but the only condition that is possible to check is: given two events, which one happened more recently?


// Description of a weather-sensitive robot tarpaulin in beta-Juliet

event RainBegins;
event RainEnds;

event SystemActivated;
event SystemDeactivated;

event CloseTarpaulin,
 caused after RainBegins when SystemActivated > SystemDeactivated;

event OpenTarpaulinTimer,
 duration 10 m,
 caused after RainEnds when SystemActivated > SystemDeactivated;

event OpenTarpaulin,
 caused after OpenTarpaulinTimer.

Basic Grammar

The basic grammar of β-Juliet is given here in EBNF. Version 1.0 uses this grammar as it stands; version 2.0 extends many of the productions.

betaJuliet ::= Decl {";" Decl} ".".
Decl       ::= Event.
Event      ::= "event" EventDecl {"," Property}.
EventDecl  ::= Symbol.
Property   ::= Caused | Causes | Duration.
Caused     ::= "caused" TimePrep EventAppl {WhenTerm}.
Causes     ::= "causes" EventAppl ["immediately"] {WhenTerm}
Duration   ::= "duration" TimeSpec.
TimePrep   ::= "before" | "after" | "by".
TimeSpec   ::= RationalNumber TimeUnit.
TimeUnit   ::= "ms" | "s" | "m" | "h" | "d".
EventAppl  ::= Symbol.
WhenTerm   ::= "when" EventAppl ">" EventAppl.
Symbol     ::= <<one or more alphanumeric characters>>.
Number     ::= <<rational number in decimal format>>.

Some Explanations

The syntax A > B can be read as "A has occurred more recently than B". If A has occurred but B has never occurred, A > B is still true; however, if neither event has ever occurred, both A > B and B > A are false.

caused and causes are two equivalent ways of expressing the causality rules between events. If we say one event is caused by or caused after some other event, that is equivalent to saying the other event causes the one event. Similarly, if we say one event is caused before some other event, that is equivalent to saying the other event causes the one event immediately.

When we define an event like

event Foo,
    causes Bar,
    causes Baz.

or like this

event Bar, caused by Foo;
event Baz, caused by Foo.

...and during execution, after Foo happens, it is not guaranteed that either Baz > Bar or Bar > Baz is true; the order in which these two consequences occur does not necessarily follow source code order. (But it is guaranteed that one or the other will be true, as both events will have happened.)

If you require an ordering guarantee in a case like this, you should use an intermediate event, like

event Foo,
    causes Temp,
    causes Bar;
event Temp,
    causes Baz.

After Temp happens, Baz > Bar should be true.

caused before

Alternately, in theory, you can use caused before, as in:

event Bar, caused before Foo;
event Baz, caused after Foo.

After Foo happens, Baz > Bar should be true.

Some words on the purpose of caused before are in order. In the original vision, after and by were synonyms, but before was meant to actually cause the event on which the caused before clause was attached, strictly before the event named in the clause.

However, unless the event being caused can somehow cancel the event that it's being caused before, there is no semantic difference between before and after when it comes to "when" the event is triggered -- except, as we note here, the ordering guarantee.

So before does not now necessarily mean strictly before the event; it could mean after the event, but before any other consequences that are given in after clauses.

Still, multiple before consequences are nondeterministic, so in

event Bar, caused before Foo;
event Baz, caused before Foo.

...after Foo happens, it is still not guaranteed that either Baz > Bar or Bar > Baz is true.


Portia is a pre-processor language designed specifically for β-Juliet version 1.0. It is solely concerned with expanding parameterized events into series of concrete events, for example creating events DominoOneFalls, DominoTwoFalls, etc., from the generalized event schema Domino(N=Domino)Falls where Domino is an alphabet over the range of dominoes.

This mechanism (in fact, an extended form of it) is included in version 2.0 of the β-Juliet language itself, so no pre-processor is needed for it.

Computational Power

The state space of a system described in β-Juliet version 1.0 is always finite, so β-Juliet version 1.0 cannot be Turing-complete. The state space of a system described using Portia and β-Juliet version 1.0 may be much, much bigger than one described using just β-Juliet version 1.0, but it is still finite.

Since β-Juliet version 2.0 allows unbounded sets of events to be described, it is more likely that it is Turing-complete.


β-Juliet version 2.0 introduces event patterns. When the name of an event is given by a string of symbols, some of those symbols may actually be parameters which act something like wildcards. Each parameter ranges over a specified alphabet. When an event occurs which matches the name of an event, the parameters in that name are bound to the literal symbols in the occurring event. These bound parameters may then be used in substitutions in the consequences.

For example, if we have an alphabet called Animal that consists of the symbols Dog Cat Ferret, we can have an event (X=Animal) Licks Itself which has, as a consequence, (X) Becomes Clean. Here X is a parameter. This event will happen should some other event cause Cat Licks Itself, and in this case, X will be bound to Cat, and this event will thus subsequently cause the event Cat Becomes Clean.


Unlike events, alphabets are ordered. Each symbol (except the first) in an alphabet has one and only one predecessor, and each symbol (except the last) has one and only one successor.

So the range of symbols in an alphabet is bounded. However, when considering a string of symbols (which I'll call a symbol-string), such as the name of an event, we can use lexicographic ordering to concoct something resembling Peano arithmetic to generate an unbounded sequence of symbol-strings, so long as each symbol in a string is in the same alphabet.

Thus, for some alphabet, every symbol-string has one and only one successor. Again, though, there is one symbol-string which has no predecessor — the symbol-string which is one symbol long, where that symbol is the first symbol of the alphabet.

These concepts are implemented in β-Juliet version 2.0 with modifiers. When a parameter is named in a consequence, it is replaced by the value it is bound to, and this can be altered by one of the following modifiers:

  • next — assuming the value is a single symbol, use the next symbol in its alphabet instead;
  • prev — assuming the value is a single symbol, use the previous symbol in its alphabet instead;
  • succ — assuming the value is a symbol-string, use the successor symbol-string over its alphabet;
  • pred — assuming the value is a symbol-string, use the predecessor symbol-string over its alphabet instead.

Note that all of these modifiers (except succ) can fail. In this case, an alternate or failure-mode modifier or symbol can be given, and this will be used instead.

Extended Grammar

The grammar for β-Juliet version 2.0 builds on the productions from version 1.0, while replacing or adding the following productions.

First, it allows alphabets as well as events to be declared. It also explicitly reserves syntax for implementation-specific pragmas and system events (but does not define the meaning of any of these itself.)

Decl          ::= Pragma | Alphabet | Event.
Pragma        ::= "pragma" <<<implementation-specific>>>.
Alphabet      ::= "alphabet" AlphabetName {"," Symbol}.
AlphabetName  ::= Symbol.

It extends the causes syntax to include specifying a duration as part of it, using the after keyword. The duration syntax is still supported; if it is given as a property of an event, the duration specified in it will be applied to all causes clauses on the event which do not include their own after delay.

Note also that caused clauses do not support an after delay.

Causes        ::= "causes" EventAppl ["after" TimeSpec] {WhenTerm}.

Lastly, it significantly extends the syntax for declaring, and using, an event, to include multi-symbol events and event patterns.

EventDecl     ::= EventDeclComp {EventDeclComp}.
EventDeclComp ::= Symbol | "(" ParamName "=" MatchExpr ")".
ParamName     ::= Symbol.
MatchExpr     ::= AlphabetName ["+"].

EventAppl     ::= EventApplComp {EventApplComp}.
EventApplComp ::= SymbolName | "(" AlphabetExpr ")".

AlphabetExpr    ::= AlphabetTerm {"|" AlphabetTerm}.
AlphabetTerm    ::= "succ" ParamName
                  | "pred" ParamName
                  | "next" ParamName
                  | "prev" ParamName
                  | "first" AlphabetName
                  | "last" AlphabetName
                  | SymbolName

Extra conditions, however, are placed on caused by clauses. Both the name of the event which is the cause, and the name of the event which is being caused, must be literal symbol strings, not patterns.


There is a crude implementation of β-Juliet version 1.0 in the form of a Perl 5 script. It does not implement delays, but it does implement the ordering guarantees between caused before and caused after.

The reference implementation of β-Juliet version 2.0, called 2iota, is written in C. It implements delays (when compiled as ANSI C they have second granularity; when compiled as C99 with POSIX, they have millisecond granularity.) It does not yet, however, properly implement the ordering guarantees between caused before and caused after clauses; nor does it parse immediately.

Historical Note

In 2012 I decided that the languages β-Juliet and 2Iota are really too similar to be seperate languages. So, as of this repo, they've been merged like this:

  • This language is called β-Juliet (a.k.a. beta-Juliet).
  • The language previously referred to as β-Juliet is now β-Juliet 1.0.
  • The language previously referred to as 2Iota (plus minor modifications) is now β-Juliet 2.0.
  • The reference interpreter for β-Juliet 2.0 is called 2iota.
  • The file extension of a β-Juliet source file is typically .bj, although you may see .2i used as well. The latter suggests that the source relies on features only in version 2.0.
  • The optional pre-processor for β-Juliet 1.0 is still called Portia. Portia is not needed with β-Juliet 2.0, and may or may not work with it; I don't know yet.