  Matrix Code gives imperative programming a mathematical semantics and
heuristic power comparable in quality to functional and logic programming. A
program in Matrix Code is developed incrementally from a specification in
pre/post-condition form. The computations of a code matrix are characterized by
powers of the matrix when it is interpreted as a transformation in a space of
vectors of logical conditions. Correctness of a code matrix is expressed in
terms of a fixpoint of the transformation. The abstract machine for Matrix Code
is the dual-state machine, which we present as a variant of the classical
finite-state machine.
