LR(k)

[Logical Language Group <lojbab@ACCESS.DIGEX.NET>]

>From: Paulo Barreto <BARRETO%VELAHF@ECCSA.TR.UNISYS.COM>
>Subject:      LR(k) Lojban Grammar
>
>lojbab:
>>But  even LR(4) would not eliminate a couple of the lexer/preparser
>>constructs, since some (like numbers) are not LR(k) for any k, though
>>it would have allowed the grammar to be significantly simpler.
>
>Do you have a proof of this?  In which way do numbers destroy the LR(k)
>property?

As Cowan has posted on the preparser algorithm, I can answer this.

The Lojban grammar not only uses the Preparser, but also uses YACC error
recovery as an integral part of its design, since that error recovery
determines the insertion of elidable terminators.  This can cause
violations of strict LR(1) that YACC resolves without ambiguity.

The grammar allows an indefinite (and theoretically infinite) string of
digits in numbers.

I think the argument goes like this.  There are constructs starting with
numbers that cannot be resolved until you know the token following the
last digit of the number (e.g. number+ROI vs. number+MOI), and hence
resolving such a grammatical construct, starting from the beginning of
the number, takes an infinite look ahead.

Tenses are also potentially infinite in length, and also have a very
complex subgrammar.  Both tenses and numbers are resolved in the
preparser to prevent them impacting on the YACC grammar.  But it is also
safe to say that ALL lexer constructs defined in the grammar, relate to
a specifically non-LR(1) grammar feature in the language.

lojbab