# [Agda] recursive \times

Serge D. Mechveliani mechvel at botik.ru
Fri Apr 12 12:47:26 CEST 2013

Please, why the program below is not type-checked?

EachPositive : List Nat -> List (Set _)
EachPositive xs =  map (\ n -> n > 0) xs

f : (ns : List Nat) -> EachPositive ns -> Nat
f _ _ = 0

-- a contrived example:  f takes  ns  and needs to use a proof for n > 0
for each  n  in  ns.

If I comment out  f,  then  EachPositive  is compiled
(despite that I expected   "List (Set _)"  to be wrong).

What should be the intended signature for  f  ?

I attach to this letter     t.agda.zip

-- the variant with  ManyProduct  -- with applies \times  recursively.

1) Has Standard library something close to  ManyProduct ?
2) Can the attempt with  map (\ n -> n > 0)  be improved, or it is just a
basically wrong idea?

Thank you in advance for explanation,

------
Sergei
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