In Haskell it is easy, you can not create cyclic data structures ;-)
$ ghci
GHCi, version 8.0.2: http://www.haskell.org/ghc/ :? for help
Prelude> let ones = 1 : ones
Prelude> take 50 ones
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
Obviously, this is a trivial example, you can do much more interesting things with mutually recursive bindings.
let cycle = "cycle " ++ cycleUsing strict data types, I think you agree that cycles can not be created. Non strict data structures I agree can be seen as cyclic, but I prefer seeing them as infinite.