  In Moyal's formulation of quantum mechanics, a quantum spin s is described in
terms of continuous symbols, i.e. by smooth functions on a two-dimensional
sphere. Such prescriptions to associate operators with Wigner functions, P- or
Q-symbols, are conveniently expressed in terms of operator kernels satisfying
the Stratonovich-Weyl postulates. In analogy to this approach, a discrete Moyal
formalism is defined on the basis of a modified set of postulates. It is shown
that appropriately modified postulates single out a well-defined set of kernels
which give rise to discrete symbols. Now operators are represented by functions
taking values on (2s+1)(2s+1) points of the sphere. The discrete symbols
contain no redundant information, contrary to the continuous ones. The
properties of the resulting discrete Moyal formalism for a quantum spin are
worked out in detail and compared to the continuous formalism, and it is
illustrated by the example of a spin 1/2.
