[Agda] parameters vs indices

[Thorsten Altenkirch]

Thank you. Now I remember, this actually allows us to write inductive
definitions when we were only able to write recursive ones due to size
constraints. The example in your 2nd link shows this nicely:

data All {a p} {A : Set a} (P : A → Set p) : List A → Set p where
	[]  : All P []
	_∷_ : ∀ {x xs} (px : P x) (pxs : All P xs) → All P (x ∷ xs)

before we were only able to define this by recursion:

All' : ∀ {a p}{A : Set a} (P : A → Set p) → List A → Set p
All' P [] = Lift ⊤
All' P (x ∷ xs) = P x × All' P xs


which is a bit sad since inductive predicates work often better.

I was wondering about the semantics. One way would be to translate forced
indices into recursive definitions but aybe there is a more direct way.

Thorsten



On 11/07/2017, 12:02, "Roman" <effectfully at gmail.com> wrote:

>Hi.
>
>> Why don't we force people to be Honest instead of just being Good?
>
>No need to force people when you can force indices:
>https://hackage.haskell.org/package/Agda-2.5.2/docs/Agda-TypeChecking-Forc
>ing.html
>
>With forcing some things are smaller than without it, see e.g. this
>issue: https://github.com/agda/agda/issues/1676





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