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The "bisimulation" property proved in #941 requires two extra assumptions on the Epoch type:
e<sucᵉ : ∀ {e : Epoch} → e < sucᵉ e
≤-predᵉ : ∀ {e e' : Epoch} → sucᵉ e ≤ sucᵉ e' → e ≤ e'These are rather ad-hoc since the relations < and ≤ on Epoch are derived from that on the type Slot while sucᵉ is primitive to Epoch.
In addition, it seems that:
Epochhas a least element and this is implicitly assumed to correspond to theEpochof the zeroth slotepoch 0#.- The semiring structure on
Slotought to interact with the partial order defined on it (monotonicity of binary operations e.g.,) , however these structures are totally independent atm. - The semiring structure assumed on
Slotcomes with its own notion of equality but in the rest this is unused and "replaced" by decidable propositional equality.
I think it would be a good idea to refactor this module in such a way that:
Epochhas its own partial order.Epochhas a least element.- The
Epochpartial order interacts well withsucᵉ. - The partial orders on
SlotandEpochare related viafirstSlotandepoch(both functions are monotone). Maybe evenepoch 0# = 0andfirstSlot 0 = 0#.
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