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26 //  A left semiring distributes on the left; a right semiring is
29 // A Weight class is required to be (at least) a left or right semiring.
41 // --> b = Divide(c, a, DIVIDE_LEFT) if a left semiring and b.Member()
48 // Typically the same type as Weight for a (both left and right) semiring.
49 // For the left string semiring, it is the right string semiring.
54 // Typically the identity mapping in a (both left and right) semiring.
55 // In the left string semiring, it maps to the reverse string
58 // LeftSemiring: indicates weights form a left semiring.
105 enum DivideType { DIVIDE_LEFT, // left division
114 // semiring is idempotent and (left and right) distributive. It is a
129 << "(left and right) distributive: " << W::Type();