# [Agda] list of types

Altenkirch Thorsten psztxa at exmail.nottingham.ac.uk
Mon Apr 15 16:33:32 CEST 2013

Actually, I think the type you have in mind is

data EachPositive (xs : List Nat) where
[] : EachPositive []
_::_ : forall {n} (EachPositive xs) -> EachPositive (n :: xs)

which isn't the same same as "map (\ n -> n > 0) xs" which is just a list
of types.

Another way would be to (fold \times \top) on this list to get a type
(replacing nil by \top and :: by \times. But I think the dependent type
given above is preferable.

Thorsten

On 15/04/2013 10:24, "Altenkirch Thorsten"
<psztxa at exmail.nottingham.ac.uk> wrote:

>Indeed, what would be an element of "EachPositive xs"?
>
>On 15/04/2013 06:17, "Andreas Abel" <andreas.abel at ifi.lmu.de> wrote:
>
>>On 15.04.2013 11:44, Serge D. Mechveliani wrote:
>>> Andreas Abel responded recently
>>>
>>>> A list of types is not a type.
>>>
>>> But why
>>>         EachPositive : List Nat -> List (Set _)
>>>         EachPositive xs =  map (\ n -> n > 0) xs
>>>
>>> is type-checked?
>>
>>This is fine, "List Set" is a type, but "EachPositive xs" is a list, and
>>cannot be used as a type, as in,
>>
>>   -> EachPositive xs -> ...
>>
>>
>>
>>
>>--
>>Andreas Abel  <><      Du bist der geliebte Mensch.
>>
>>Theoretical Computer Science, University of Munich
>>Oettingenstr. 67, D-80538 Munich, GERMANY
>>
>>andreas.abel at ifi.lmu.de
>>http://www2.tcs.ifi.lmu.de/~abel/
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