  We verify the functional form of the asymptotics of the spin - spin equal -
time correlation function for the XX-chain, predicted by the hypothesis of
conformal invariance at large distances and by the bosonization procedure. We
point out that bosonization also predicts the functional form of the
correlators for the chains of finite length. We found the exact expression for
the spin- spin equal- time correlator on finite lattice. We find the excellent
agreement of the exact correlator with the prediction given by the leading
asymptotics result up to the very small distances. We also establish the
correspondence between the value of the constant before the asymptotics for the
XX- chain with the expression for this constant proposed by Lukyanov and
Zamolodchikov. We also evaluate the constant corresponding to the subleading
term in the asymptotics in a way which is different from the previous studies.
