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
(). 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)) 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\]) >>= print@] @Value [5,4,3,2,1]@
[@> timeOut' 1 (reverse [1..\]) >>= print@] @NonTermination@
The time-out functionality can be used to treat \"slow\" computations as
bottoms:
[@> let tweak = Tweak { approxDepth = Just 5, timeOutLimit = Just 2 }@]
[@> semanticEq tweak (reverse [1..\], [1..\]) (bottom :: [Int\], [1..\] :: [Int\])@] @True@
[@> let tweak = noTweak { timeOutLimit = Just 2 }@]
[@> semanticJoin tweak (reverse [1..\], True) ([\] :: [Int\], bottom)@] @Just ([],True)@
This can of course be dangerous:
[@> let tweak = noTweak { timeOutLimit = Just 0 }@]
[@> 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) >>= print@] @[167,499NonTermination@
[@> timeOutMicro 100 (print $ take 4 $ filter ((== 1) . (\`mod\` 83)) primes) >>= print@] @[167,499,997NonTermination@
[@> timeOutMicro 100 (print $ take 4 $ filter ((== 1) . (\`mod\` 83)) primes) >>= print@] @[167,499,997,1163]@
[@ @] @Value ()@
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\"
().
The code has been tested under GHC 6.8. Most parts can probably be
ported to other Haskell compilers, but that would require some work.
The @TimeOut@ functions require preemptive scheduling, and most of the
rest requires @Data.Generics@; @isBottom@ only requires exceptions,
though.
Source code: .