x = x a + b Now use high school algebra x = x*a + b x - x*a = b x*(1-a) = b x = b / (1-a) x = b * 1/(1-a) Now you have to remember that the Taylor series expansion of 1/(1-a) is 1/(1-a) = 1 + a + a^2 + a^3 + a^4 + ...
OK, now put your grammar hat back on. What's 1 | a | aa | aaa | aaaa | ... it's just an arbitrary number of a:s, i.e., a* (or 'many a' in parsec). So finally expr = b a*
nice!-) different viewpoints yield new perspectives. this made me wonder what those missing algebra operations would mean in terms of parsing/language generation; it hurts a bit to think about your algebraic manipulations in that way, but if i got the interpretations right, they might be quite useful additions: l1 - l2: things in l1 that are not in l2; generalising elimination of keywords from valid ids l1 / l2: things that can be completed to be in l1, via suffixes in l2; standard tool in ides thanks for the interesting detour, claus