  We analyze the polymer representation of quantum mechanics within the
deformation quantization formalism. In particular, we construct the Wigner
function and the star-product for the polymer representation as a
distributional limit of the Schr\"odinger representation for the Weyl algebra
in a Gaussian weighted measure, and we observe that the quasi-probability
distribution limit of this Schr\"odinger representation agrees with the Wigner
function for Loop Quantum Cosmology. Further, the introduced polymer
star-product fulfills Bohr's correspondence principle even though not all the
operators are well defined in the polymer representation. Finally, within our
framework, we also derive a generalized uncertainty principle which is
consistent to the ones usually obtained in theories assuming a fundamental
minimal length in their formulation.
