In a Haskell script, how does one programatically obtain the type signature of a function? - function

Question

In Haskell (GHC), how can one obtain the type signature of the list of functions shown below?
[tail,init,reverse]
I unsuccessfully tried using the typeOf function of the Data.Typeable module. Specifically, I try to run the following Haskell script:
import Data.Typeable
import Test.HUnit
myTest = TestCase
( assertEqual "\n\nShould have been \"[[a] -> [a]]\""
"[[a] -> [a]]"
(show ( typeOf [tail,init,reverse] )) )
tests = TestList [ (TestLabel "myTest" myTest) ]
However, GHC responds with the following error:
C:\>ghci my_script.hs
GHCi, version 8.0.2: http://www.haskell.org/ghc/ :? for help
[1 of 1] Compiling Main ( my_script.hs, interpreted )
my_script.hs:7:21: error:
* No instance for (Typeable a0) arising from a use of `typeOf'
* In the first argument of `show', namely
`(typeOf [tail, init, reverse])'
In the third argument of `assertEqual', namely
`(show (typeOf [tail, init, reverse]))'
In the first argument of `TestCase', namely
`(assertEqual
"\n\
\\n\
\Should have been \"[[a] -> [a]]\""
"[[a] -> [a]]"
(show (typeOf [tail, init, reverse])))'
Failed, modules loaded: none.
Prelude>
Update: The following HUnit test case isn't quite what I wanted, but I did get it to pass (based on David Young's suggestion). This test case at least forces the compiler to confirm that [tail,init,reverse] is of type [ [a] -> [a] ].
import Data.Typeable
import Test.HUnit
myTest = TestCase
( assertEqual "\n\nShould have been 3"
3
( length ( [tail,init,reverse] :: [[a]->[a]] ) ) )
tests = TestList [ (TestLabel "myTest" myTest) ]
C:\>my_script.hs
GHCi, version 8.0.2: http://www.haskell.org/ghc/ :? for help
[1 of 1] Compiling Main ( my_script.hs, interpreted )
Ok, modules loaded: Main.
*Main> runTestTT tests
Cases: 1 Tried: 1 Errors: 0 Failures: 0

Answer 1

You don't need a unit test to check a function's type. A unit tests runs after the code has been compiled, it's a dynamic test. However, type checking is a static test: all types are tested during the compilation of your program. Therefore, we can use GHC as a minimal static type checker and reduce your program to:
main :: IO ()
main = return ()
where
tailInitReverseAreListFunctions :: [[a] -> [a]]
tailInitReverseAreListFunctions = [tail, init, reverse]
You don't even need that test anymore the moment you actually test your functions with real data, because that application will (statically) test the function's type too.
Remember, Haskell is a statically typed language. The types are checked during compilation, before your code is run. Any type checking unit-test is therefore more or less a code-smell, because it can only pass.