The Universe of Discourse

Parcels and motes

I said recently:

Is there any good terminology for a value of type f a when f is an arbitrary functor? I will try calling an f t value a “t parcel” and see how that works.

The more I think about “parcel” the happier I am with it. It strongly suggests container types, of course, so that a t parcel might be a boxful of ts. But it also hints at some other possible situations:

• You might open the parcel and find it empty. (Maybe t)
• You might open the parcel and find, instead of the t you expected, a surprising prank snake. (Either ErrorMessage t)
• You might open the parcel and find that your t has been shipped with assembly required. (env -> t)
• The parcel might explode when you open it. (IO t)
• And, of course, a burrito is a sort of parcel of meat and beans.

I coined “parcel” thinking that one would want different terminology for values of type f t depending on whether f was a functor (“parcel”) or also a monad (“mote”). Of course every mote is a parcel, but not always vice versa. Now I'm not sure that both terms are needed. Non-monadic functors are unusual, and non-applicative functors rare, so perhaps one term will do for all three.

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