Haskell testing

I aim to be able to define a collection of test methods and a collection of test cases (input/output data) and then execute all of their combinations. The goal is to avoid re-writing the same code over and over again when having say, 3 different implementations of the same function and 4 test cases that the function should satisfy. A naive approach would require me to write 12 lines of code:

testMethod1 testCase1

testMethod1 testCase2

...

testMethod3 testCase4

I've a gut feeling that Haskell should provide a way to abstract this pattern somehow. The best thing I've currently came up with is this piece of code:

import Control.Applicative

data TestMethod a = TM a
data TestData inp res = TD inp res

runMetod (TM m) (TD x res) = m x == res

runAllMethods ((m, inp):xs) = show (runMetod m inp) ++ "\n" ++ runAllMethods xs
runAllMethods _          = ""

head1 = head
head2 (x:xs) = x
testMethods = [TM head1, TM head2]
testData = [TD [1,2,3] 1, TD [4,5,6] 4]

combos = (,) <$> testMethods <*> testData

main = putStrLn $ runAllMethods combos

This works, computes 2 tests against two 2 functions and prints out 4 successes:

True
True
True
True

However, this works only for lists of the same type, even though the head function is list type agnostic. I would like to have a test data collection of any lists, like so:

import Control.Applicative

data TestMethod a = TM a
data TestData inp res = TD inp res

runMetod (TM m) (TD x res) = m x == res

runAllMethods ((m, inp):xs) = show (runMetod m inp) ++ "\n" ++ runAllMethods xs
runAllMethods _          = ""

head1 = head
head2 (x:xs) = x
testMethods = [TM head1, TM head2]
testData = [TD [1,2,3] 1, TD ['a','b','c'] 'a']

combos = (,) <$> testMethods <*> testData

main = putStrLn $ runAllMethods combos

but this fails with an error:

main.hs:12:21: error:
No instance for (Num Char) arising from the literal ‘1’
In the expression: 1
In the first argument of ‘TD’, namely ‘[1, 2, 3]’
In the expression: TD [1, 2, 3] 1

Is it possible to achieve this test-function X test-case cross testing somehow?