Marpa::XS::Semantics::Infinite - How Marpa Deals with Infinite Cycles
Marpa will parse using an infinitely ambiguous grammar. (In the technical
literature, an infinite ambiguity is more usually called a
cycle or a
loop.)
An example of an infinitely ambiguous grammar is the following:
S ::= A
A ::= B
B ::= A
B :: 'x'
Given the input 'x', this grammar will produce these parses
S -> A -> B -> x
S -> A -> B -> A -> B -> x
S -> A -> B -> A -> B -> A -> B -> x
.
.
.
Because of the two rules "A ::= B" and "B ::= A", this list
of parses could go on forever. The two rules "A ::= B" and "B
::= A" form what is called a
cycle.
Typically, if a user has written an grammar with an infinite cycle, it was a
mistake and he wants to rewrite it before proceeding. By default, an
infinitely ambiguous grammar is a fatal error. This is the behavior most users
will want.
To produce parse results from an infinitely ambiguous grammar, the user must set
the grammar's "infinite_action" named argument to a value other than
""fatal"". The other choices are
""warn"" and ""quiet"".
Obviously, Marpa cannot list all of an infinite number of parse results. Marpa
deals with potentially infinite parses by limiting the cycle length.
Cycle
length is the number of times a parse derivation goes around a potentially
infinite cycle.
Marpa limits all cycles to a length of 1. There will always be a finite number
of these parse results.
Above I showed a set of parses from an example of an infinitely ambiguous
grammar. Here are those parses again, this time labeled with their cycle
length.
Cycle length 1: S -> A -> B -> x
Cycle length 2: S -> A -> B -> A -> B -> x
Cycle length 3: S -> A -> B -> A -> B -> A -> B -> x
Marpa would return a parse result only for the first parse tree in the list
above, the one whose cycle length is 1.
The precise behavior of Marpa's cycle detection is, at this point, not strictly
defined and applications should avoid relying on the details of its semantics.
The exact point at which a cycle is broken varies among implementations.
In future releases, Marpa's cycle detection may be more carefully defined. But
cycles at this point are universally considered useless, and there seems to be
literally nobody who cares about the details of their semantics. The quality
of the present implementation seems to be completely adequate in terms of the
present interest.
At this point it seems that a cycle should be broken when it is about to loop
back to the "same rule". But in current Marpa implementations, the
"same rule" means the same rule
after Marpa's rewriting of the
grammar, not the same rule as in the original grammar. If a more careful
semantics is created, it probably should be defined in terms of the rules as
the user sees them, rather than in terms of the rules as rewritten by Marpa's
internals.
Copyright 2012 Jeffrey Kegler
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