[The documentation is a lot better now.
nad**20040617203012] {
hunk ./ChasingBottoms/Approx.hs 5
-  , module ChasingBottoms.Nat
hunk ./ChasingBottoms/Approx.hs 178
- F is a functor : C^C x C^C -> (C x C)^C.
+ F is a functor : (C x C)^C -> (C x C)^C.
hunk ./ChasingBottoms/Approx.hs 182
- Hence given an arrow (natural transformation) : (G, H) -> (G', H')
- (G, G', H and H' objects (functors) in C^C) F yields an arrow
+ Hence given an arrow (natural transformation)
+  : forall a . G a -> (H a, K a)
+ (G, H and K objects (functors) in C^C) F yields an arrow
hunk ./ChasingBottoms/ApproxShow.hs 9
-  , module ChasingBottoms.Nat
addfile ./ChasingBottoms/Header
hunk ./ChasingBottoms/Header 1
+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 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>).
+
+The code is developed and tested under GHC. Most parts can probably be
+ported to other Haskell compilers, but that would require some work.
hunk ./ChasingBottoms/SemanticOrd.hs 15
-  , module ChasingBottoms.IsBottom
hunk ./ChasingBottoms/TimeOut.hs 22
--- resolution is not too great.
+-- resolution is not necessarily very high (the last time I checked it
+-- was 0.02 seconds).
hunk ./ChasingBottoms/package 5
-ls ChasingBottoms/*hs | grep -v '/IsType.hs$' | \
-  xargs haddock -h -oChasingBottoms/docs
-tar zcvf ChasingBottoms/chasing-bottoms.tar.gz ChasingBottoms/*hs ChasingBottoms/docs/*
+ls ChasingBottoms.hs ChasingBottoms/*hs | grep -v '/IsType.hs$' | \
+  xargs haddock -h --title="Chasing Bottoms" --prologue=ChasingBottoms/Header \
+  -oChasingBottoms/docs \
+  && \
+  tar zcvf ChasingBottoms/chasing-bottoms.tar.gz ChasingBottoms.hs \
+           ChasingBottoms/*hs ChasingBottoms/docs/*
addfile ./ChasingBottoms.hs
hunk ./ChasingBottoms.hs 1
+-- | This module just re-exports all the other modules.
+
+module ChasingBottoms
+  ( module ChasingBottoms.Approx
+  , module ChasingBottoms.ApproxShow
+  , module ChasingBottoms.IsBottom
+  , module ChasingBottoms.Nat
+  , module ChasingBottoms.SemanticOrd
+  , module ChasingBottoms.TimeOut
+  ) where
+
+import ChasingBottoms.Approx
+import ChasingBottoms.ApproxShow
+import ChasingBottoms.IsBottom
+import ChasingBottoms.Nat
+import ChasingBottoms.SemanticOrd
+import ChasingBottoms.TimeOut
}