Excerpt from the documentation at http://www.cs.chalmers.se/~nad/software/ChasingBottoms/docs/: Chasing Bottoms =============== Do you ever feel the need to test code involving bottoms (e.g. calls to the error function), or code involving infinite values? Then this library could be useful for you. It is usually easy to get a grip on bottoms by showing a value and waiting to see how much gets printed before the first exception is encountered. However, that quickly gets tiresome and is hard to automate using e.g. QuickCheck (http://www.cs.chalmers.se/~rjmh/QuickCheck/). With this library you can do the tests as simply as the following examples show. Testing explicitly for bottoms:

isBottom (head []) True isBottom bottom True isBottom (\_ -> bottom) False isBottom (bottom, bottom) False

Comparing finite, partial values:

((bottom, 3) :: (Bool, Int)) ==! (bottom, 2+5-4) True ((bottom, bottom) :: (Bool, Int)) <! (bottom, 8) True

Showing partial and infinite values (\/! is join and /\! is meet):

approxShow 4 $ (True, bottom) \/! (bottom, b) "Just (True, b)" approxShow 4 $ (True, bottom) /\! (bottom, b) "(_|_, _|_)" approxShow 4 $ ([1..] :: [Int]) "[1, 2, 3, _" approxShow 4 $ (cycle [bottom] :: [Bool]) "[_|_, _|_, _|_, _"

Approximately comparing infinite, partial values:

approx 100 [2,4..] ==! approx 100 (filter even [1..] :: [Int]) True approx 100 [2,4..] /=! approx 100 (filter even [bottom..] :: [Int]) True

The code above relies on the fact that bottom, just as error "...", undefined and pattern match failures, yield exceptions. Sometimes we are dealing with properly non-terminating computations, such as the following example, and then it can be nice to be able to apply a timeout.

let primes = unfoldr (\(x:xs) -> Just (x, filter ((/= 0) . (`mod` x)) xs)) [2..] timeOutMicro 100 (print $ filter ((== 1) . (`mod` 32)) primes) >>= print [97,193,257Nothing timeOutMicro 100 (print $ take 5 $ filter ((== 1) . (`mod` 32)) primes) >>= print [97,193,257,353Nothing timeOutMicro 100 (print $ take 5 $ filter ((== 1) . (`mod` 32)) primes) >>= print [97,193,257,353,449] Just ()

All the type annotations above are required. For the underlying theory and a larger example involving use of QuickCheck, see the article "Chasing Bottoms, A Case Study in Program Verification in the Presence of Partial and Infinite Values" (http://www.cs.chalmers.se/~nad/publications/danielsson-jansson-mpc2004.html). Source code: http://www.cs.chalmers.se/~nad/software/ChasingBottoms/chasing-bottoms.tar.g.... /NAD