 24 Mar, 2017 3 commits


Robbert Krebbers authored

Robbert Krebbers authored

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.
