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Semigroup

typeclass S: Semigroup {
    mul: (S, S) -> S
    mul_associative(a: S, b: S, c: S) {
        a * (b * c) = (a * b) * c
    }
}

The default semigroup uses the multiplication operator.. For an additive semigroup, see add_semigroup.ac.

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mul​

mul: (S, S) -> S

The binary operation that combines two elements of the semigroup.

mul_associative​

mul_associative(a: S, b: S, c: S) {
    a * (b * c) = (a * b) * c
}

The multiplication operation must be associative: (a * b) * c = a * (b * c).