Hello everyone, I am stuck rewriting some code in the tagless style. My problem can be thought of as an interpreter for a very simple language:
data Exp = Lit Integer | Add Exp Exp | Mul Exp Exp deriving (Show)
But some complexity is added by the fact that my interpreter also needs to know the context in which literals appear in an expression. So given the example
t1 :: Exp t1 = (Lit 3 `Add` Lit 4) `Mul` Lit 2
I want to have access to the fact that the literal 3 appears on the left side of an addition. Therefore I created a type:
data Ctx = Empty | AddL Exp Ctx | AddR Exp Ctx | MulL Exp Ctx | MulR Exp Ctx deriving (Show)
This is almost a zipper over the Exp type. I left out a context for literals themselves because it wasn't necessary. Now I can create a simple evaluation function:
eval :: (a -> a -> a) -> (a -> a -> a) -> (Integer -> Ctx -> a) -> Exp -> a eval add mul lit = go Empty where go ctx (Lit n) = lit n ctx go ctx (Add x y) = let x' = go (AddL y ctx) x y' = go (AddR x ctx) y in x' `add` y' go ctx (Mul x y) = let x' = go (MulL y ctx) x y' = go (MulR x ctx) y in x' `mul` y'
This function can evaluate an expression to any type 'a', but it needs some additional functions to accomplish that: add, mul and lit. Notice how the 'lit' function has access to a literal's context. To interpret an Exp as an Integer I use:
evalInt :: Exp -> Integer evalInt = eval (+) (*) const
Or as a String:
evalStr1 :: Exp -> String evalStr1 = eval addStr mulStr (const . show)
addStr x y = "(" ++ x ++ " + " ++ y ++ ")" mulStr x y = "(" ++ x ++ " * " ++ y ++ ")"
Or a silly example which uses the context:
evalStr2 :: Exp -> String evalStr2 = eval addStr mulStr lit where lit _ (AddL (Lit 4) (MulL _ _)) = "Foo!" lit n _ = show n
The silly example replaces a literal with "Foo!" if it appears on the left side of an addition with 4, and the whole addition is the left side of a multiplication, like in (x + 4) * ?. All of this works. But I want to be able to add additional constructors to the Exp language without changing existing code. This looks like the expression problem. Ignoring the zipper-like context I came up with the following: First define the language:
class Lit a where lit :: Integer -> a class Add a where add :: a -> a -> a class Mul a where mul :: a -> a -> a
Integer interpreter:
instance Lit Integer where lit = fromInteger instance Add Integer where add = (+) instance Mul Integer where mul = (*)
String interpreter, using a newtype so I don't need TypeSynonymInstances:
newtype Str = Str {unS :: String} instance Show Str where show = show . unS
instance Lit Str where lit = Str . show instance Add Str where add x y = Str $ addStr (unS x) (unS y) instance Mul Str where mul x y = Str $ mulStr (unS x) (unS y)
Same example expression, now polymorphic:
t1 :: (Lit a, Add a, Mul a) => a t1 = (lit 3 `add` lit 4) `mul` lit 2
This expression can now be interpreted in multiple ways:
t1 :: Integer
14 t1 :: Str "((3 + 4) * 2)"
This solves the expression problem. I can add new structures to my language in other modules without having to change existing code. The necessary parts are mentioned in the type constraint (Lit a, Add a, Mul a). But I lost the power of the context! How do I get it back? Attached are the two approaches, WithTags.hs and Tagless.hs (but without context). Any help would be greatly appreciated!