name: ChasingBottoms
version: 1.3.1.14
license: MIT
license-file: LICENCE
copyright: Copyright (c) Nils Anders Danielsson 2004-2022, 2024.
author: Nils Anders Danielsson
maintainer: http://www.cse.chalmers.se/~nad/
synopsis: For testing partial and infinite values.
description:
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)) 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 { 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 $ primes ())
> [2,NonTermination
> > timeOutMicro 10000 (print $ take 10 $ primes ())
> [2,3,5,7,11,13,17,19,23,29]
> 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\"
().
.
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.
category: Testing
tested-with: GHC == 8.0.2,
GHC == 8.2.2,
GHC == 8.4.4,
GHC == 8.6.5,
GHC == 8.8.4,
GHC == 8.10.5,
GHC == 9.0.2,
GHC == 9.2.8,
GHC == 9.4.8,
GHC == 9.6.5,
GHC == 9.8.2
cabal-version: >= 1.10
build-type: Simple
source-repository head
type: darcs
location: http://www.cse.chalmers.se/~nad/repos/ChasingBottoms/
library
exposed-modules:
Test.ChasingBottoms,
Test.ChasingBottoms.Approx,
Test.ChasingBottoms.ApproxShow,
Test.ChasingBottoms.ContinuousFunctions,
Test.ChasingBottoms.IsBottom,
Test.ChasingBottoms.Nat,
Test.ChasingBottoms.SemanticOrd,
Test.ChasingBottoms.TimeOut
other-modules: Test.ChasingBottoms.IsType
default-language: Haskell2010
if impl(ghc >= 7.4.1)
ghc-options: -fpedantic-bottoms
build-depends: QuickCheck >= 2.10 && < 2.16,
mtl >= 2 && < 2.4,
base >= 4.2 && < 4.20,
containers >= 0.5 && < 0.8,
random >= 1.0 && < 1.3,
syb >= 0.1.0.2 && < 0.8
test-suite ChasingBottomsTestSuite
type: exitcode-stdio-1.0
main-is: Test/ChasingBottoms/Tests.hs
other-modules: Test.ChasingBottoms.Approx,
Test.ChasingBottoms.Approx.Tests,
Test.ChasingBottoms.ApproxShow,
Test.ChasingBottoms.ApproxShow.Tests,
Test.ChasingBottoms.ContinuousFunctions,
Test.ChasingBottoms.ContinuousFunctions.Tests,
Test.ChasingBottoms.IsBottom,
Test.ChasingBottoms.IsBottom.Tests,
Test.ChasingBottoms.IsType,
Test.ChasingBottoms.IsType.Tests,
Test.ChasingBottoms.Nat,
Test.ChasingBottoms.Nat.Tests,
Test.ChasingBottoms.SemanticOrd,
Test.ChasingBottoms.SemanticOrd.Tests,
Test.ChasingBottoms.TestUtilities,
Test.ChasingBottoms.TestUtilities.Generators,
Test.ChasingBottoms.TimeOut
Test.ChasingBottoms.TimeOut.Tests
default-language: Haskell2010
if impl(ghc >= 7.4.1)
ghc-options: -fpedantic-bottoms
build-depends: QuickCheck >= 2.10 && < 2.16,
mtl >= 2 && < 2.4,
base >= 4.2 && < 4.20,
containers >= 0.5 && < 0.8,
random >= 1.0 && < 1.3,
syb >= 0.1.0.2 && < 0.8,
array >= 0.3 && < 0.6