haskell 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.cse.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 time-out: [@> timeOut' 1 (reverse [1..5\])@] @Value [5,4,3,2,1]@ [@> timeOut' 1 (reverse [1..\])@] @NonTermination@ The time-out functionality can be used to treat \"slow\" computations as bottoms: [@> let tweak = Tweak &#x7b; approxDepth = Just 5, timeOutLimit = Just 2 &#x7d;@] [@> semanticEq tweak (reverse [1..\], [1..\]) (bottom :: [Int\], [1..\] :: [Int\])@] @True@ [@> let tweak = noTweak &#x7b; timeOutLimit = Just 2 &#x7d;@] [@> semanticJoin tweak (reverse [1..\], True) ([\] :: [Int\], bottom)@] @Just ([],True)@ This can of course be dangerous: [@> let tweak = noTweak &#x7b; timeOutLimit = Just 0 &#x7d;@] [@> semanticEq tweak (reverse [1..100000000\]) (bottom :: [Integer\])@] @True@ Timeouts can also be applied to @IO@ computations: [@> let primes = unfoldr (\\(x:xs) -> Just (x, filter ((\/= 0) . (\`mod\` x)) xs)) [2..\]@] [@> timeOutMicro 100 (print $ filter ((== 1) . (\`mod\` 83)) primes)@] @[167,499,9NonTermination@ [@> timeOutMicro 100 (print $ take 6 $ filter ((== 1) . (\`mod\` 83)) primes)@] @[167,499,997,1163,1993NonTermination@ [@> timeOutMicro 100 (print $ take 6 $ filter ((== 1) . (\`mod\` 83)) primes)@] @[167,499,997,1163,1993,2657]@ [@ @] @Value ()@ 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.cse.chalmers.se/~nad/publications/danielsson-jansson-mpc2004.html>). The code has been tested using GHC. Most parts can probably be ported to other Haskell compilers, but this would require some work. The @TimeOut@ functions require preemptive scheduling, and most of the rest requires @Data.Generics@; @isBottom@ only requires exceptions, though.