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Robbert Krebbers authored
Instead, I have introduced a type class `Monoid` that is used by the big operators: Class Monoid {M : ofeT} (o : M → M → M) := { monoid_unit : M; monoid_ne : NonExpansive2 o; monoid_assoc : Assoc (≡) o; monoid_comm : Comm (≡) o; monoid_left_id : LeftId (≡) monoid_unit o; monoid_right_id : RightId (≡) monoid_unit o; }. Note that the operation is an argument because we want to have multiple monoids over the same type (for example, on `uPred`s we have monoids for `∗`, `∧`, and `∨`). However, we do bundle the unit because: - If we would not, the unit would appear explicitly in an implicit argument of the big operators, which confuses rewrite. By bundling the unit in the `Monoid` class it is hidden, and hence rewrite won't even see it. - The unit is unique. We could in principle have big ops over setoids instead of OFEs. However, since we do not have a canonical structure for bundled setoids, I did not go that way.
Robbert Krebbers authoredInstead, I have introduced a type class `Monoid` that is used by the big operators: Class Monoid {M : ofeT} (o : M → M → M) := { monoid_unit : M; monoid_ne : NonExpansive2 o; monoid_assoc : Assoc (≡) o; monoid_comm : Comm (≡) o; monoid_left_id : LeftId (≡) monoid_unit o; monoid_right_id : RightId (≡) monoid_unit o; }. Note that the operation is an argument because we want to have multiple monoids over the same type (for example, on `uPred`s we have monoids for `∗`, `∧`, and `∨`). However, we do bundle the unit because: - If we would not, the unit would appear explicitly in an implicit argument of the big operators, which confuses rewrite. By bundling the unit in the `Monoid` class it is hidden, and hence rewrite won't even see it. - The unit is unique. We could in principle have big ops over setoids instead of OFEs. However, since we do not have a canonical structure for bundled setoids, I did not go that way.