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Grammars for aⁿbⁿ and aⁿbⁿcⁿ using constraint grammar (using only REMOVE).
"<w>"
"a"
"b"
"opt_a"
"opt_b"
"odd"
"even"
"^"
"$"
"<w>"
"a"
"b"
"opt_a"
"opt_b"
"odd"
"even"
"^"
"$"
"<w>"
"a"
"b"
"opt_a"
"opt_b"
"odd"
"even"
"^"
"$"
"<w>"
"a"
"b"
"opt_a"
"opt_b"
"odd"
"even"
"^"
"$"
"<w>"
"a"
"b"
"opt_a"
"opt_b"
"odd"
"even"
"^"
"$"
"<w>"
"a"
"b"
"opt_a"
"opt_b"
"odd"
"even"
"^"
"$"
"<.>"
DELIMITERS = "<.>" ;
LIST A = "a" ;
LIST B = "b" ;
LIST OPT_A = "opt_a" ;
LIST OPT_B = "opt_b" ;
LIST ODD = "odd" ;
LIST EVEN = "even" ;
LIST >>> = "^" ;
LIST <<< = "$" ;
SET ANY = A OR B ;
# create own magic tags
BEFORE-SECTIONS
REMOVE >>> (-1 ANY)
REMOVE <<< ( 1 ANY)
# mark even/odd cohorts
BEFORE-SECTIONS
REMOVE EVEN (0 >>>)
SECTION
REMOVE ODD (NOT 0 >>> LINK NOT -1 EVEN)
REMOVE EVEN (NOT -1 ODD)
AFTER-SECTIONS
REMCOHORT ANY (1* <<< LINK NOT 0 EVEN)
REMCOHORT <<< (NOT 0 EVEN)
# mark a/b
BEFORE-SECTIONS
SELECT A (0 >>>)
SELECT B (0 <<<)
SECTION
REMOVE OPT_B (-1C A)
REMOVE OPT_A ( 1C B)
SELECT A (NOT 0 OPT_B)
SELECT B (NOT 0 OPT_A)
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<w>"
"a"
"b"
"c"
"opt_a"
"opt_b"
"opt_c"
"x1"
"x2"
"x3"
"^"
"$"
"fst"
"snd"
"opt_fst"
"opt_snd"
"<.>"
DELIMITERS = "<.>" ;
LIST A = "a" ;
LIST B = "b" ;
LIST C = "c" ;
LIST OPT_A = "opt_a" ;
LIST OPT_B = "opt_b" ;
LIST OPT_C = "opt_c" ;
SET OPT_A_OR_B = OPT_A OR OPT_B ;
SET OPT_B_OR_C = OPT_B OR OPT_C ;
SET OPT_C_OR_A = OPT_C OR OPT_A ;
LIST X1 = "x1" ;
LIST X2 = "x2" ;
LIST X3 = "x3" ;
SET X1_OR_X2 = X1 OR X2 ;
SET X2_OR_X3 = X2 OR X3 ;
SET X3_OR_X1 = X3 OR X1 ;
LIST >>> = "^" ;
LIST <<< = "$" ;
LIST FST = "fst" ;
LIST SND = "snd" ;
LIST OPT_FST = "opt_fst" ;
LIST OPT_SND = "opt_snd" ;
SET NOT_FST = OPT_FST OR SND OR OPT_SND ;
SET NOT_SND = FST OR OPT_FST OR OPT_SND ;
SET ANY = A OR B OR C ;
# create own magic tags
BEFORE-SECTIONS
REMOVE >>> (-1 ANY)
REMOVE <<< ( 1 ANY)
# check if divisible by 3
BEFORE-SECTIONS
REMOVE X2_OR_X3 (0 >>>)
REMOVE X1_OR_X2 (0 <<<)
SECTION
REMOVE X3_OR_X1 (NOT 0 >>> LINK NOT -1 X2_OR_X3)
REMOVE X1_OR_X2 (NOT 0 >>> LINK NOT -1 X3_OR_X1)
REMOVE X2_OR_X3 (NOT 0 >>> LINK NOT -1 X1_OR_X2)
AFTER-SECTIONS
REMCOHORT ANY (1* <<< LINK NOT 0 X3)
REMCOHORT <<< (NOT 0 X3)
# mark first/second half
BEFORE-SECTIONS
REMOVE NOT_FST (0 >>>)
REMOVE NOT_SND (0 <<<)
SECTION
REMOVE OPT_SND (-1 FST LINK (NOT 0 NOT_FST))
REMOVE OPT_FST ( 1 SND LINK (NOT 0 NOT_SND))
REMOVE NOT_FST (0 FST LINK 0 SND LINK 0 OPT_FST LINK NOT 0 OPT_SND)
REMOVE NOT_SND (0 FST LINK 0 SND LINK 0 OPT_SND LINK NOT 0 OPT_FST)
BEFORE-SECTIONS
REMOVE OPT_B_OR_C (0 >>>)
REMOVE OPT_A_OR_B (0 <<<)
SECTION
REMOVE OPT_C_OR_A (0 FST LINK 1 SND LINK NOT 0 FST)
REMOVE OPT_C_OR_A (0 SND LINK -1 FST LINK NOT 0 SND)
SECTION
REMOVE OPT_B_OR_C (-1C A)
REMOVE OPT_A_OR_B ( 1C C)
SELECT A (0 OPT_A LINK NOT 0 OPT_B_OR_C)
SELECT C (0 OPT_C LINK NOT 0 OPT_A_OR_B)
REMOVE OPT_C_OR_A ( 1C B)
REMOVE OPT_C_OR_A (-1C B)
SELECT B (0 OPT_B LINK NOT 0 OPT_C_OR_A)
REMOVE OPT_B_OR_C (-1C A)
REMOVE OPT_A_OR_B ( 1C C)
SELECT A (0 OPT_A LINK NOT 0 OPT_B_OR_C)
SELECT C (0 OPT_C LINK NOT 0 OPT_A_OR_B)
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