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Property-based testing

In addition to unit testing, Haskell has powerful libraries for property based testing. This is testing where you specify a property you think your program should have, and the testing library tries to find a counterexample.


Much like unit tests, the success of property tests is not a guarantee of your code's correctness, but it can be a extremely effective way to find bugs quickly.

repl example
import Test.QuickCheck -- (1)!

-- Assert that all lists have length 0
> quickCheck (\x -> length x == 0)
*** Failed! Falsified (after 2 tests):    -- (2)!              
[()] -- (3)!

-- Assert that all lists have length 0 or greater
> quickCheck (\x -> length x >= 0)
+++ OK, passed 100 tests.  

-- Assert that for any numbers a and b, a+b is the same as b+a
> quickCheck (\a b -> a + b == b + a)
+++ OK, passed 100 tests

> import Data.Maybe
-- Assert that if the left element of a tuple is not Nothing, neither is the right
> property = (\(x,y) -> isJust x ==> isJust y) -- (4)!
> quickCheck property
*** Failed! Falsified (after 1 test):                  
(Just (),Nothing)

-- sanity check custom sorting function
> import Data.List (sort) -- (5)!
> mkListProperty sortFn (ls :: [Int]) = sortFn ls == sort ls
> badSort = reverse -- (6)!
> quickCheck (mkListProperty badSort)
*** Failed! Falsified (after 5 tests and 3 shrinks):    
  1. This requires the QuickCheck package.
  2. QuickCheck generates lists randomly until it finds a counterexample to your claim, and then simplifies it to a minimal counterexample.
  3. In this case, the counterexample is the one element list containing the unit value (), namely [()]
  4. ==> is exported by QuickCheck; a ==> b (read: a implies b) evaluates to False if and only if a is True but b is False.
  5. sort is a trusted sorting function from Data.List.
  6. badSort is a bad sorting algorithm: it just reverses its input.


Try to avoid universal quantification when not necessary in properties. For example, property sortFn ls = sortFn ls == sort ls really ought to have a type signature, so that QuickCheck knows what the type of the elements of the list are, and can generate appropriate examples. Otherwise it will default to a type (usually ()).

Custom data types

Properties involving custom types require that you provide an instance of the Arbitrary typeclass for your type, like so:

import Test.QuickCheck (Arbitrary (arbitrary), elements, quickCheck)
import Data.List (sort)

data Piece = Bishop | Rook deriving (Eq, Show, Ord)

instance Arbitrary Piece where
    arbitrary = elements [Rook, Bishop] -- (1)!

exampleProperty :: [Piece] -> Bool -- (2)!
exampleProperty ls = sort ls == [Bishop, Rook]

main :: IO ()
main = quickCheck exampleProperty
  1. arbitrary is the function which generates a Piece. This implementation says: draw it as random from the list [Rook, Bishop].
  2. Because Piece has an Arbitrary instance, Haskell can automatically obtain an Arbitrary instance for [Piece], Maybe Piece, and so on.

Last update: February 10, 2023
Created: January 30, 2023