[Haskell-cafe] Specialize a function on types of arguments?

[Olaf Klinke]

> 
> The top-level story is that I am trying to create a monad that somehow
> records the "intermediate steps" of computation.
> 

If it is only for knowing where things went wrong, isn't that what the Either monad is for? The semantics of (Either YourErrorType) is that it returns `Right result' when all steps went through, and `Left errmsg' from the first place where something went wrong. You'd have to define YourErrorType to incorporate the relevant error information. 

If you also want something like a call stack, i.e. a message like 
"computation failed in step 3 with message: foo" 
Then you need to stack a state transformer on top, e.g. StateT CallStack (Either YourErrorType) which decodes to
  CallStack -> Either YourErrorType (resultType,CallStack)

An example using mtl transformers:

import Control.Monad.State.Strict
import Control.Monad.Except
type CallStack = (Int,[String])
type YourErrorType = String
type M a = StateT CallStack (Except YourError) a

fancyFunc :: Show a => (a -> b) -> (a -> M b)
fancyFunc f a = do
  (n,stack) <- get
  put (n+1,show a : stack)
  return b

fancyMaybe :: Show a => (a -> Maybe b) -> (a -> M b)
fancyMaybe f a = do
  (n,stack) <- get
  case (f a) of
    Nothing -> throwError $ "Failed at step "++(show n)++" on input "++(show a)
    Just b  -> do
      put (n+1,show a : stack)
      return b

runChainOfComputations = runStateT (1,[])

I once wrote a type 'ProvenienceT' which is a bit fancier than the above. It is a monadic EDSL and constructs a graph where nodes are (Markup of) intermediate steps of a computation and where edges are (user-supplied descriptions of) functions. It is inspired by the Javelin software of the 80s which pre-dates Excel spreadsheets. The result can be rendered as html. Can provide code if anyone is interested. 

Cheers,
Olaf