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Profunctors seem like they'd be useful for representing the output of a program analysis. For example, given some information about a function $f$, the profunctor would tell you what information can be derived about compositions of $f$ with other functions.

Does anyone have any references to work along these lines?

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    I too think you should ask on [cstheory.SE](http://cstheory.stackexchange.com/). FWIW, sigfpe wrote a [blog post](http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html) on A Neighborhood of Infinity about Profunctors in Haskell. There are couple of references at the end.2012-02-16

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Mike, I am afraid, I do not fully understand what you mean. However, you definitely should take a look at the concept of "arrows" introduced as a kind of a generalisation of computational monads. Perhaps, the best introductory paper is thee following one:

B. Jacobs, C. Heunen, I. Hasuo, "Categorical semantics for arrows."