The Z_n problem doesn't seem to be different from the problem of arrays or bitvectors of a statically-checkable size. If you prefer a decimal specification of the modulus, you may find the following articles relevant. Implementation of fixed-precision decimal types: Main> BV D1 0 Bitvector of width 1 and value 0 Main> BV (D1,D2) 123 Bitvector of width 12 and value 123 Main> BV (D5,D7,D9) 31415 Bitvector of width 579 and value 31415 It appears that modulus in the Z_n problem plays the same role as the bitvector width in the bitvector problem. An attempt to perform an operation on bitvectors of different sizes results in a compiler error: Main> (BV (D1,D0) 10) `b_and` (BV (D1,D1) 7) ERROR - Type error in application *** Expression : b_and (BV (D1,D0) 10) (BV (D1,D1) 7) *** Term : BV (D1,D0) 10 *** Type : BitVector (D1,D0) *** Does not match : BitVector (D1,D1) http://groups.google.com/groups?selm=7eb8ac3e.0202201753.473a5cb2%40posting.... Arbitrary precision decimal types, e.g.: Main> BV (D1 $ D2 $ D3 $ D4 $ D5 $ D6 $ D7 $ D8 $ D9 $ D0 $ D9 $ D8 $ D7 $ D6 $ D5 $ D4 $ D3 $ D2 $ D1 $ Dim) 1234567879 Bitvector of width 1234567890987654321 and value 1234567879 which are slightly more general and less convenient, are described in: http://groups.google.com/groups?selm=7eb8ac3e.0202230221.62d98db8%40posting.... Both implementations work in any Haskell-98 system. Multi-parameter classes, existential types or other extensions are not needed.