title: Compose functions at runtime based on user input in Haskell
body: <p>Let's say I have 100 functions of various simple signatures (start with monomorphic, but would like to make the polymorphic case work too) a -> b (Int -> Int, Int -> String, String -> Double, MyType -> MyOtherType, etc.)</p>
  
  <p>Let's say I show a list of those to the user. The user selects one. I show a list of functions whose parameter is compatible with the selected function's output. The user selects one.</p>
  
  <p>How could I now compose those two functions? The general case is a series of compositions, but this simple case I think covers the problem I'm working with.</p>
  
  <p>I know I could try unsafeCoerce or Data.Dynamic, but I'm trying to see if I can avoid that, and those apparently are restricted to monomorphic types which is causing a problem.</p>
  
  <p>I thought perhaps somehow I could create a data structure of all the functions and what they could be composed with, but I'm not sure about that. And when including polymorphic cases, it seems like it would be impossible.</p>