Runtime type representation of terms with support for rank-1 polymorphic types with type variables of kind *.

The essence of this module is that we use the standard Typeable representation of Data.Typeable but we introduce a special (empty) data type TypVar which represents type variables. TypVar is indexed by an arbitrary other data type, giving you an unbounded number of type variables; for convenience, we define ANY, ANY1, .., ANY9.

Examples of isInstanceOf

-- We CANNOT use a term of type 'Int -> Bool' as 'Int -> Int'
> typeOf (undefined :: Int -> Int) `isInstanceOf` typeOf (undefined :: Int -> Bool)
Left "Cannot unify Int and Bool"

-- We CAN use a term of type 'forall a. a -> Int' as 'Int -> Int'
> typeOf (undefined :: Int -> Int) `isInstanceOf` typeOf (undefined :: ANY -> Int)
Right ()

-- We CAN use a term of type 'forall a b. a -> b' as 'forall a. a -> a'
> typeOf (undefined :: ANY -> ANY) `isInstanceOf` typeOf (undefined :: ANY -> ANY1)
Right ()

-- We CANNOT use a term of type 'forall a. a -> a' as 'forall a b. a -> b'
> typeOf (undefined :: ANY -> ANY1) `isInstanceOf` typeOf (undefined :: ANY -> ANY)
Left "Cannot unify Succ and Zero"

-- We CAN use a term of type 'forall a. a' as 'forall a. a -> a'
> typeOf (undefined :: ANY -> ANY) `isInstanceOf` typeOf (undefined :: ANY)
Right ()

-- We CANNOT use a term of type 'forall a. a -> a' as 'forall a. a'
> typeOf (undefined :: ANY) `isInstanceOf` typeOf (undefined :: ANY -> ANY)
Left "Cannot unify Skolem and ->"

-- We CAN use a term of type 'forall a. a -> m a' as 'Int -> Maybe Int'
> typeOf (undefined :: Int -> Maybe Int)
    `isInstanceOf` typeOf (undefined :: ANY1 -> ANY ANY1)
Left "Cannot unify Skolem and ->"

-- We CAN use a term of type 'forall a. Monad a => a -> m a' as 'Int -> Maybe Int'
-- 'Dict' comes from "Data.Constraint" in the package "constraints".
> typeOf ((\Dict -> return) :: Dict (Monad Maybe) -> Int -> Maybe Int)
    `isInstanceOf` typeOf ((\Dict -> return) :: Dict (Monad ANY) -> ANY1 -> ANY ANY1)
Right ()

(Admittedly, the quality of the type errors could be improved.)

When using -XPolyKinds, the type signatures with higher-kinded variables need to be given as

(\Dict -> return) `asTypeOf` (undefined :: Dict (Monad ANY) -> ANY1 -> ANY ANY1)

or

(\Dict -> return) :: Dict (Monad ANY) -> ANY1 -> ANY (ANY1 :: *)

Please, see tests/test.hs for examples of how to write the higher-kinded cases in ghc versions earlier than 7.8.3.

Examples of funResultTy

-- Apply fn of type (forall a. a -> a) to arg of type Bool gives Bool
> funResultTy (typeOf (undefined :: ANY -> ANY)) (typeOf (undefined :: Bool))
Right Bool

-- Apply fn of type (forall a b. a -> b -> a) to arg of type Bool gives forall a. a -> Bool
> funResultTy (typeOf (undefined :: ANY -> ANY1 -> ANY)) (typeOf (undefined :: Bool))
Right (ANY -> Bool) -- forall a. a -> Bool

-- Apply fn of type (forall a. (Bool -> a) -> a) to argument of type (forall a. a -> a) gives Bool
> funResultTy (typeOf (undefined :: (Bool -> ANY) -> ANY)) (typeOf (undefined :: ANY -> ANY))
Right Bool

-- Apply fn of type (forall a b. a -> b -> a) to arg of type (forall a. a -> a) gives (forall a b. a -> b -> b)
> funResultTy (typeOf (undefined :: ANY -> ANY1 -> ANY)) (typeOf (undefined :: ANY1 -> ANY1))
Right (ANY -> ANY1 -> ANY1)

-- Cannot apply function of type (forall a. (a -> a) -> a -> a) to arg of type (Int -> Bool)
> funResultTy (typeOf (undefined :: (ANY -> ANY) -> (ANY -> ANY))) (typeOf (undefined :: Int -> Bool))
Left "Cannot unify Int and Bool"