Bind not strictly positive #2
Description
This snippet is taken from idris-free (https://github.com/idris-hackers/idris-free) which does not compile currently. This issue is about the error messages the compilation produces, not about the fact that Free does not compile:
data Free : (f : Type -> Type) -> (a : Type) -> Type where
Pure : a -> Free f a
Bind : f (Free f a) -> Free f a
instance Functor f => Functor (Free f) where
map f (Pure x) = Pure (f x)
map f (Bind x) = assert_total (Bind (map (map f) x))The first error message one gets is :
Prelude.Functor.Control.Monad.Free.Free f implementation of Prelude.Functor.Functor,
method map is possibly not total due to: Control.Monad.Free.Bind
Inspecting the docs of map gives the standard map function of the Functor interface which declares map to be total. This left me puzzled, because I was not able to get the totality state of this map implementation.
I then inspected the docs for Free
Data type Control.Monad.Free.Free : (f : Type -> Type) -> (a : Type) -> Type
Constructors:
Pure : a -> Free f a
Bind : f (Free f a) -> Free f a
(nothing unusual here) and finally Bind. The docs for Bind say:
Control.Monad.Free.Suspend : f (Free f a) -> Free f a
The function is not strictly positive
I tried to find out what "strictly positive" means. Some Adga and Coq resources later (which I am not fluent with), there seems to be a problem that Free occurs on the left hand side of the constructor arrow. Again I am puzzled - why does
(::) : a -> List a -> List a
work as a constructor for List then?
As a user of Idris, I would like that
- Idris reports that map is not total because Bind is not strictly positive
- Idris explains a bit better what exactly being strictly positive entitles
- as a bonus: that Idris provides error messages which link to an error message wiki page on Github, giving more detailed information about the nature of the error.