add Decidable instances for ->, Neg and Either #4
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add instances `Decidable a => Decidable (Neg a)` `(Decidable a, Decidable b) => Decidable (a -> b)` `(Decidable a, Decidable b) => Decidable (Either a b)`
phadej
requested changes
Mar 23, 2023
| (Yes _, Yes b) -> Yes (const b) | ||
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| -- | Disjunctions are decidable | ||
| instance forall a b. (Decidable a, Decidable b) => Decidable (Either a b) where |
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This is not lawful instance as it prefers Left over right.
a should be a Proposition, i.e. the Yes answers should be unique.
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What is actually meant by the 'Yes' answers should be unique? Can you give an example how this breaks? (I don't know the use-case of this library so I can't think of why this instance is bad.) Preferring left over right corresponds to short-circuiting which is generally a welcome property in logic, no?
Decidability for `Neg a` is subsumed by decidability of implication. Avoid overlapping instances.
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add instances
Decidable a => Decidable (Neg a)(Decidable a, Decidable b) => Decidable (a -> b)(Decidable a, Decidable b) => Decidable (Either a b)