@hackage / monoid-semiring

The monoid semiring M ->0 S and its generalized Cauchy product

Latest0.1.0.0

Changelog

Revision history for monoid-semiring

0.1.0.0 — 2026-06-11

  • First release. The monoid semiring M →₀ S: finitely supported functions from a monoid M to a semiring S (the Semiring class of the semirings package), multiplied by the generalized Cauchy product (f * g)(s) = Σ_{uv = s} f(u) · g(v).
  • Representation invariant: no explicit zero coefficients, so derived equality coincides with equality of functions.
  • Oracle test suite: the seven semiring laws at three (M, S) instances (polynomials, formal languages, tropical multivariate), differential test against the naive definition, Fibonacci (A000045) and Catalan (A000108) generating-function coefficients against vendored OEIS b-files.