Functional programming and William Lawvere's notion of "variable sets"(vs topos of "static sets") in a Topos ...

Hello Haskellers, I have been re-reading William Lawvere's description of "variable sets" (a functor category) in "a elementary topoi" on a discrete poset/preset vs a "abstract sets" in the topos of abstract sets . In Haskell( and other FPLs .. ) aren't "pure" computations just over the topos of abstract sets and "mutable" /"time-varying/stateful" computations aren't just "variable sets" (i.e. a functor over a discrete preset-poset)?? Please forgive my bad English :-( If uncertain aboyt my Englsih, please say so. Kind regards, Vasya P.S. Yes I am familiar with Eugenio Moggi's papers on using monads for stateful computations ..

On Sat, Aug 02, 2014 at 01:28:41AM -0500, Vasili I. Galchin wrote:
In Haskell( and other FPLs .. ) aren't "pure" computations just over the topos of abstract sets and "mutable" /"time-varying/stateful" computations aren't just "variable sets" (i.e. a functor over a discrete preset-poset)??
If you think this is the case could you please make an exposition of the correspondance. It's unlikely anyone here will be able to understand your conclusion without such. Tom
participants (2)
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Tom Ellis
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Vasili I. Galchin