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Why does rationals_le use the concrete type nat? #30

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langston-barrett opened this issue Feb 10, 2017 · 1 comment
Open

Why does rationals_le use the concrete type nat? #30

langston-barrett opened this issue Feb 10, 2017 · 1 comment

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@langston-barrett
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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?
@spitters
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spitters commented Jun 4, 2017

I agree. It seems better to generalize this to general instances.

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@spitters @langston-barrett