concatenation of lists and streams from an alphabet A: - formally given by the unique arrow to a terminal coalgebra - heuristically it is supposed to be thought of as erasing the comma between a pair of streams (a,b) But how is this to be understood computationally? eg. write down all the +ve odd integers and then all the even ones in reverse order to get a stream (1, 3, 5, ., 6, 4, 2) can this be made into a stream specification? ie. what is the behaviour of the dots in the middle? or even more interesting, a countable concatenation (limit ?) as in the so called Sarkovskii sequence uses in symbolic dynamics - Ref: http://hades.ph.tn.tudelft.nl/Internal/PHServices/Documentation/MathWorld/ma... It does not appear conceivable for a Turing machine to produce such a tape! (??) Then in what way can such streams be seen as arrows N --> N ?? Examining the details (Ref: J.J.M.M. Rutten) for the construction of the structure map A*xA* --> 1+AxA*xA* that gives rise to concatenation (for the functor 1+Ax_ ), it does not appear to arise out of universal properties (being an arrow from a product to a coproduct), as do the structure maps for various other operations. Is it distinguished in some particular way? I think of juxtaposition as THE fundamental syntactic operation I hope someone can help me please with formal concatenation. Thank you. .. Al Vilcius