[Haskell-cafe] The mother of all functors/monads/categories

[Roman Leshchinskiy]

On 27/06/2010, at 19:54, Max Bolingbroke wrote:

> Q: What is the "mother of all X", where X is some type class?
> A: It is a data type D such that:
> 
> 1. There exist total functions:
> 
>> lift :: X d => d a -> D a
>> lower :: X d => D a -> d a

Are those universally quantified over d? If so, then none of your examples fit this definition. I assume you mean this:

lift :: X d => d a -> D d a
lower :: X d => D d a -> d a

In that case, isn't D just the dictionary for (X d) and a value of type (d a)? I.e., couldn't we always define it as:

data D d a where { D :: X d => d a -> D d a }

Roman