Modeling the ST monad in Agda

Question

This recent SO question prompted me to write an unsafe and pure emulation of the ST monad in Haskell, a slightly modified version of which you can see below:

{-#         


        

Answer 1

Here's some form of a solution done by postulating a parametricity theorem. It also ensures that the postulate does not get in the way of computation.

http://code.haskell.org/~Saizan/ST/ST.agda

"darcs get http://code.haskell.org/~Saizan/ST/" for the full source

I'm not happy about the closed universe of types but it's the easy way to tailor the parametricity theorem to what we actually need.