Example of how to automatically lift a haskell function into a function on some AST

lift.hs

import Control.Monad
import Control.Monad.Error

instance Error (RuntimeError a) where

data Expr = Number Int
          | SomethingElse 
  deriving (Show, Eq, Ord)

data Type = Func Type Type
          | IntType
  deriving (Show, Eq, Ord)

data RuntimeError x = ExpectedNumberGot x
                    | InvalidNumberOfArgs
    deriving (Show, Eq, Ord)
    
    

class BType a where
  fType :: a -> Type 
  
instance BType Int where
  fType _ = IntType
  
instance (BType a, BType b) => BType (a -> b) where
  fType f = (\a -> Func (fType a) (fType $ f a)) undefined -- some sillyness to get the types to play nice
      
      
class FromExpr a where
  fromExpr :: Expr -> Either (RuntimeError Expr) a
  
instance FromExpr Int where
  fromExpr (Number x) = Right x
  fromExpr x = Left (ExpectedNumberGot x)
  
  
  
class ToExpr a where
  toExpr :: a -> Expr
  
instance ToExpr Int where
  toExpr x = Number x
  
  
  
class FConvert b where
  fConvert :: (FromExpr a) => (a -> b) -> [Expr] -> Either (RuntimeError Expr) (Expr, [Expr])
  
instance FConvert Int where
  fConvert f (x:xs) = do
    x' <- fromExpr x
    return (toExpr $ f x', xs)
  fConvert f _ = Left InvalidNumberOfArgs
  
instance (FromExpr a, FConvert b) => FConvert (a -> b) where
  fConvert f (x:xs) = do
    x' <- fromExpr x
    fConvert (f x') xs 
  fConvert f _ = Left InvalidNumberOfArgs
  
  
add :: Int -> Int -> Int
add = (+)

test1 = fConvert add [Number 123, Number 532]
-- == Right (Number 655,[])

test2 = fType add
-- == Func IntType (Func IntType IntType)