[Haskell-cafe] Type checking with Haskell

Stefan O'Rear stefanor at cox.net
Thu Apr 12 10:00:03 EDT 2007

On Thu, Apr 12, 2007 at 01:04:13PM +0100, Joel Reymont wrote:
> Folks,
> The ghc/compiler/typecheck directory holds a rather large body of  
> code and quick browsing through did not produce any insight.
> How do you implement type checking in haskell?
> Assume I have an Expr type with a constructor per type and functions  
> can take lists of expressions. Do I create a function taking an Expr,  
> pattern-matching on appropriate constructor and returning True on a  
> match and False otherwise?

The Glasgow Haskell typechecker is big not because type checking is
hard, but because GHC Haskell is a very big language.  Also, GHC runs
typechecking *before* desugaring, apparently thinking error messages
are more important than programmer sanity :)

A typechecker for a simpler language can be implemented quite easily:

--- Simply typed lambda calculus

data Typ = Int | Real | Bool | Fn Typ Typ
data Exp = Lam Typ Exp | Var Int | App Exp Exp

typeCheck' :: [Typ] -> Exp -> Maybe Typ
typeCheck' cx (Lam ty bd) = fmap (Fn ty) (typeCheck' (ty:cx) bd)
typeCheck' cx (Var i)     = Just (cx !! i)
typeCheck' cx (App fn vl) = do Fn at rt <- typeCheck' cx fn
                               pt       <- typeCheck' cx vl
                               guard (at == pt)
                               return rt

Your problem, as I understand it, is even simpler than most since
there are no higher order functions and no arguments.


data Typ = Real | Int | Bool | String

tc2 a b ta tb tr | typeCheck a == ta && typeCheck b == tb = Just tr
                 | otherwise                              = Nothing

typeCheck :: Exp -> Maybe Typ
typeCheck (IAdd a b) = tc2 a b Int Int Int

(That said, it would probably be better to fuse parsing and type
checking in this case so that you do not need to track source


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