An implementation of the Xenakis Sieve, providing a Sieve from a string expression that filters integer sequences into iterators of integers, Boolean states, or interval widths. Sieves are built from Residuals, defined as a modulus (M) and a shift (S), notated `M@S`. Sieve string expressions, and Sieve structs, support complementation, intersection, symmetric difference, and union operations on Residuals with operators `!`, `&`, `^` and `|`, respectively.