[Agda] strange `case' requirement
kahl at cas.mcmaster.ca
Sat Oct 26 18:22:01 CEST 2013
On Sat, Oct 26, 2013 at 01:48:55PM +0400, Sergei Meshveliani wrote:
> I write
> _∙u_ : Op₂ uC
> (just x) ∙u (just y) = just (x ∙ y)
> m ∙u nothing = m
> nothing ∙u m = m
> for uC = Maybe C, and a semigroup operation _∙u_ : Op₂ C
> (this is extending a semigroup with unity represented as `nothing').
> Then I prove
> goal : (m : uC) → (nothing ∙u m) =u m
> goal m = IsEquivalence.refl uEquiv
> uSetoid = Data.Maybe.setoid setoid
> uEquiv = Setoid.isEquivalence uSetoid
> The report is
> nothing ∙u .m != .m of type Maybe (Setoid.Carrier ......)
> when checking that the expression uRefl has type
> nothing ∙u .m =u .m
> After several minutes I guess to try
> goal nothing = uRefl
> goal (just _) = uRefl,
> It does work. But looks ugly.
> 1) Why is not the first version type-checked by normalization?
Because the matching case here is the third case
of your definition of _∙u_, which is only reached
after matching the first two cases fails --- just like in Haskell.
You can prove the propositional equality corresponding to the third case
as a lemma (with two cases), and then use that in appropriate circumstances.
> 2) Why m is dotted in the report, has this sense?
(I don't really know --- but this is possibly not the dot of pattern matching,
but the prefix given to names that are not in scope --- this comes from the
type declaration of ``goal''?)
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