Some times you need to change the tag you have lying around. Idiomatic usage is to make a new combinator for the relationship between the tags that you want to enforce, and define that combinator using retag.

 data Succ n
 reproxySucc :: Proxy n -> Proxy (Succ n)
 reproxySucc = reproxy

asProxyTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the tag of the second.

Convert from a Tagged representation to a representation based on a Proxy.

Convert from a representation based on a Proxy to a Tagged representation.