Anthony Clayden wrote:

newtype Foo = Foo Int deriving (Read, Show, Typeable, Data, ...) someFoo = Foo 7 ... What I want is to get the based-on type baked inside `someFoo` -- that is: `Int` (It would also be handy to get the name of the data constr, just in case it's different to the type.)

If we have a data type declaration data C a b = D1 a Int b | D2 a | D3 [a] we use methods of module Typeable to get information about the left-hand-side of the equation (about the type expression C a b and its structure, an application of a type constructor C to two arguments). We use methods of module Data.Data to get information about the right-hand-side of the equation (about _data_ constructors D1, D2 and D3 and their arguments). Here is an example:

{-# LANGUAGE DeriveDataTypeable, ScopedTypeVariables #-}

import Data.Data

data C a b = D1 a Int b | D2 a | D3 [a] deriving (Data, Typeable)

A sample datum of type C

someC = undefined :: C Int Char

*Main> typeOf someC C Int Char meaning someC has the type C Int Char. *Main> dataTypeOf someC DataType {tycon = "Main.C", datarep = AlgRep [D1,D2,D3]} Now we see something about the right-hand-side of the equation defining C: C a b is a data type and it has three data constructors, D1, D2 and D3. How to get information about their arguments? First, we extract constructors

getCtor :: Data a => Int -> a -> Constr getCtor i x = case dataTypeRep $ dataTypeOf x of AlgRep cs -> cs !! i

*Main> getCtor 0 someC D1 Now, we reify a data constructor by unfolding it in a particular way

newtype DTInfo a = DTInfo [TypeRep]

-- Get information about the given ctor of a given algebraic data type -- (the data type value may be undefined -- we only need its type) ctorInfo :: forall a. Data a => a -> Constr -> [TypeRep] ctorInfo _ ctor = case go ctor of DTInfo reps -> reverse reps where go :: Constr -> DTInfo a go = gunfold (\ (DTInfo infos :: DTInfo (b->r)) -> DTInfo (typeOf (undefined:: b) : infos)) (\r -> DTInfo [])

*Main> ctorInfo someC $ getCtor 0 someC [Int,Int,Char] meaning that D1 of the type C Int Char has three arguments, Int, Int, Char -- in that order. *Main> ctorInfo someC $ getCtor 1 someC [Int] *Main> ctorInfo someC $ getCtor 2 someC [[Int]] It is easy to answer the original question about someFoo *Main> getCtor 0 someFoo Foo *Main> ctorInfo someFoo $ getCtor 0 someFoo [Int] -- A faster way for a defined datum *Main> ctorInfo someFoo $ toConstr someFoo [Int] So, someFoo is constructed by data constructor Foo and that data constructor has one Int argument.