rocq-community / rocq-community/math-classes
Why does rationals_le use the concrete type nat?
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Description
I was surprised when unfolding rationals_le to see that it specifies that le x y if there is a fraction p/q made of nats such that y=x+p/q:
Instance rationals_le `{Rationals Q} : Le Q | 10 := λ x y,
∃ num, ∃ den, y = x + naturals_to_semiring nat Q num / naturals_to_semiring nat Q den.
Why not use any type that is an instance of Naturals?
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Research direction
Start at orders/rationals.v lines 89-90 and inspect naturals_to_semiring and the typeclass constraints used by rationals_le. Trace whether the concrete nat is intentional and whether a Naturals instance can be abstracted safely. Done when the issue has a documented decision and any accepted change is covered by the repository's existing checks.
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Assessment
- Domain
- tooling
- Issue type
- Refactor
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Stale
- Clarity
- Mostly clear
- Newbie friendliness
- 35/100