coya (hackage): Take some log semiring R. Then, for any two x,y :: R, the following holds:  x ^ log y == y ^ log x == e ^ (log x * log y)  A Coya monoid is some commutative monoid (R, #), where x # y = x ^ log y. The following laws hold:  e # x = x (Left Identity)  x # e = x (Right Identity)  (x # y) # z == x # (y # z) (Associativity)  x # y == y # x (Commutativity)  If the R is a poset where all elements in R are greater than one, then R also forms a group:  x # (e ^ (1 / log (x))) == x
Keywords: bsd3|data|library|math