ChasingBottoms-1.3.1.2/ 0000755 0000000 0000000 00000000000 12772503660 012776 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Setup.hs 0000644 0000000 0000000 00000000057 12772503660 014434 0 ustar 00 0000000 0000000 import Distribution.Simple
main = defaultMain
ChasingBottoms-1.3.1.2/ChasingBottoms.cabal 0000644 0000000 0000000 00000013056 12772503660 016713 0 ustar 00 0000000 0000000 name: ChasingBottoms
version: 1.3.1.2
license: MIT
license-file: LICENCE
copyright: Copyright (c) Nils Anders Danielsson 2004-2016.
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 == 8.0.1
cabal-version: >= 1.9.2
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
build-depends: QuickCheck >= 2.1 && < 2.10,
mtl >= 1.1 && < 2.3,
base >= 4.0 && < 4.10,
containers >= 0.3 && < 0.6,
random >= 1.0 && < 1.2,
syb >= 0.1.0.2 && < 0.7
test-suite ChasingBottomsTestSuite
type: exitcode-stdio-1.0
main-is: Test/ChasingBottoms/Tests.hs
other-modules: Test.ChasingBottoms.Approx.Tests,
Test.ChasingBottoms.ApproxShow.Tests,
Test.ChasingBottoms.ContinuousFunctions.Tests,
Test.ChasingBottoms.IsBottom.Tests,
Test.ChasingBottoms.IsType.Tests,
Test.ChasingBottoms.Nat.Tests,
Test.ChasingBottoms.SemanticOrd.Tests,
Test.ChasingBottoms.TestUtilities,
Test.ChasingBottoms.TestUtilities.Generators,
Test.ChasingBottoms.TimeOut.Tests
build-depends: QuickCheck >= 2.1 && < 2.10,
mtl >= 1.1 && < 2.3,
base >= 4.0 && < 4.10,
containers >= 0.3 && < 0.6,
random >= 1.0 && < 1.2,
syb >= 0.1.0.2 && < 0.7,
array >= 0.3 && < 0.6
ChasingBottoms-1.3.1.2/LICENCE 0000644 0000000 0000000 00000002274 12772503660 013770 0 ustar 00 0000000 0000000 I have chosen to distribute this library under the MIT/Expat licence:
---------------------------------------------------------------------
Copyright (c) 2004-2016 Nils Anders Danielsson
Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
ChasingBottoms-1.3.1.2/Test/ 0000755 0000000 0000000 00000000000 12772503660 013715 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Test/ChasingBottoms.hs 0000644 0000000 0000000 00000001621 12772503660 017175 0 ustar 00 0000000 0000000 -- |
-- Module : Test.ChasingBottoms
-- Copyright : (c) Nils Anders Danielsson 2004-2016
-- License : See the file LICENCE.
--
-- Maintainer : http://www.cse.chalmers.se/~nad/
-- Stability : experimental
-- Portability : non-portable (GHC-specific)
--
-- This module just re-exports all the other modules.
module Test.ChasingBottoms
( module Test.ChasingBottoms.Approx
, module Test.ChasingBottoms.ApproxShow
, module Test.ChasingBottoms.ContinuousFunctions
, module Test.ChasingBottoms.IsBottom
, module Test.ChasingBottoms.Nat
, module Test.ChasingBottoms.SemanticOrd
, module Test.ChasingBottoms.TimeOut
) where
import Test.ChasingBottoms.Approx
import Test.ChasingBottoms.ApproxShow
import Test.ChasingBottoms.ContinuousFunctions
import Test.ChasingBottoms.IsBottom
import Test.ChasingBottoms.Nat
import Test.ChasingBottoms.SemanticOrd
import Test.ChasingBottoms.TimeOut
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/ 0000755 0000000 0000000 00000000000 12772503660 016641 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Test/ChasingBottoms/Nat.hs 0000644 0000000 0000000 00000006377 12772503660 017734 0 ustar 00 0000000 0000000 {-# LANGUAGE DeriveDataTypeable #-}
-- |
-- Module : Test.ChasingBottoms.Nat
-- Copyright : (c) Nils Anders Danielsson 2004-2016
-- License : See the file LICENCE.
--
-- Maintainer : http://www.cse.chalmers.se/~nad/
-- Stability : experimental
-- Portability : non-portable (GHC-specific)
--
-- A simple implementation of natural numbers on top of 'Integer's.
-- Note that since 'Integer's are used there is no infinite natural
-- number; in other words, 'succ' is strict.
module Test.ChasingBottoms.Nat(Nat, isSucc, fromSucc, natrec, foldN) where
import Test.QuickCheck
import qualified Data.Generics as G
import Data.Ratio ((%))
import Data.Typeable
default ()
-- | Natural numbers.
--
-- No 'G.Data' instance is provided, because the implementation should
-- be abstract.
-- Could add 'G.Data' instance based on unary representation of
-- natural numbers, but that would lead to inefficiencies.
newtype Nat = Nat { nat2int :: Integer } deriving (Eq, Ord, Typeable)
-- | @'isSucc' 0 == 'False'@, for other total natural numbers it is 'True'.
isSucc :: Nat -> Bool
isSucc (Nat 0) = False
isSucc _ = True
-- | @'fromSucc' 0 == 'Nothing'@, @'fromSucc' (n+1) == 'Just' n@ for a
-- total natural number @n@.
fromSucc :: Nat -> Maybe Nat
fromSucc (Nat 0) = Nothing
fromSucc n = Just $ pred n
-- | 'natrec' performs primitive recursion on natural numbers.
natrec :: a -> (Nat -> a -> a) -> Nat -> a
natrec g _ (Nat 0) = g
natrec g h n = let p = pred n in h p (natrec g h p)
-- | 'foldN' is a fold on natural numbers:
--
-- @
-- 'foldN' g h = 'natrec' g ('curry' '$' h . 'snd')
-- @
foldN :: a -> (a -> a) -> Nat -> a
foldN g h = natrec g (curry $ h . snd)
steal :: (Integer -> Integer -> Integer) -> Nat -> Nat -> Nat
steal op x y = fromInteger $ (nat2int x) `op` (nat2int y)
instance Num Nat where
(+) = steal (+)
(*) = steal (*)
x - y = let x' = nat2int x; y' = nat2int y
in if x' < y' then
error "Nat: x - y undefined if y > x."
else
fromInteger $ x' - y'
negate = error "Nat: negate undefined."
signum n = if isSucc n then 1 else 0
abs = id
fromInteger i | i < 0 = error "Nat: No negative natural numbers."
| otherwise = Nat i
instance Real Nat where
toRational = (%1) . nat2int
steal2 :: (Integer -> Integer -> (Integer, Integer))
-> Nat -> Nat -> (Nat, Nat)
steal2 op x y = let (x', y') = (nat2int x) `op` (nat2int y)
in (fromInteger x', fromInteger y')
instance Integral Nat where
toInteger = toInteger . fromEnum
a `quotRem` b = if b == 0 then
error "Nat: quotRem undefined for zero divisors."
else
steal2 quotRem a b
a `divMod` b = if b == 0 then
error "Nat: divMod undefined for zero divisors."
else
steal2 divMod a b
instance Enum Nat where
succ = (+ 1)
pred = subtract 1
toEnum = fromInteger . toInteger
fromEnum = fromInteger . nat2int
-- Add tests for enumFrom and friends if the default definitions are
-- overridden.
instance Show Nat where
showsPrec _ = showString . show . nat2int
instance Arbitrary Nat where
arbitrary = do
n <- arbitrary :: Gen Integer
return $ fromInteger $ abs n
shrink 0 = []
shrink n = [n - 1]
instance CoArbitrary Nat where
coarbitrary n = coarbitrary (toInteger n)
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/ApproxShow.hs 0000644 0000000 0000000 00000012363 12772503660 021314 0 ustar 00 0000000 0000000 {-# LANGUAGE ScopedTypeVariables,
FlexibleInstances, UndecidableInstances #-}
-- |
-- Module : Test.ChasingBottoms.ApproxShow
-- Copyright : (c) Nils Anders Danielsson 2004-2016
-- License : See the file LICENCE.
--
-- Maintainer : http://www.cse.chalmers.se/~nad/
-- Stability : experimental
-- Portability : non-portable (GHC-specific)
--
-- Functions for converting arbitrary (non-function, partial,
-- possibly infinite) values into strings.
module Test.ChasingBottoms.ApproxShow
( Prec
, ApproxShow(..)
) where
import Data.Generics
import Test.ChasingBottoms.IsBottom
import Test.ChasingBottoms.Nat
import Test.ChasingBottoms.IsType
import qualified Data.List as List
-- | Precedence level.
type Prec = Int
class ApproxShow a where
-- | The 'Data' instance of 'ApproxShow' makes sure that
-- @'approxShowsPrec' n@ behaves (more or less) like the derived
-- version of 'showsPrec', with the following differences:
--
-- * After @n@ levels of descent into a term the output is
-- replaced by @\"_\"@.
--
-- * All detectable occurences of bottoms are replaced by @\"_|_\"@.
--
-- * Non-bottom functions are displayed as @\"\\"@.
--
approxShowsPrec :: Nat -> Prec -> a -> ShowS
approxShows :: Nat -> a -> ShowS
approxShow :: Nat -> a -> String
approxShows n a = approxShowsPrec n 0 a
approxShow n a = approxShowsPrec n 0 a ""
instance Data a => ApproxShow a where
approxShowsPrec n p = gShowsPrec False n p
-- This is a gigantic hack (due to special treatment of lists and
-- strings). Now I realise how I should have written it:
-- A wrapper taking care of n == 0 and bottoms.
-- A generic case treating ordinary data types
-- Special cases (type specific extensions) for tuples, functions,
-- lists and strings.
-- I'm not sure if it's possible to have a type specific extension that
-- works for, for instance, all list types, though. I guess that it
-- would have to be monomorphic.
--
-- Anyway, I don't have time improving this right now. All tests go
-- through, so this should be fine.
gShowsPrec :: Data a => Bool -> Nat -> Prec -> a -> ShowS
gShowsPrec insideList n p (a :: a)
| n == 0 = showString "_"
| isBottom a = showString "_|_"
| isFunction a = showString ""
| isTuple a = showParen True $ drive $
List.intersperse (showString ", ") $
(continueR (:) [] minPrec a)
| isString a && isAtom a = when' (not insideList) (showString "\"") $
showString "\"" -- End of string.
| isString a = when' (not insideList) (showString "\"") $
gmapQr (.) id
( id -- Dummy.
`mkQ`
(\c -> if n == 1 then showString "_" else
if isBottom c then showString "_|_"
else showChar c)
`extQ`
(\(a :: String) -> if n == 1 then id else
if isBottom a then showString "_|_"
else gShowsPrec True (pred n) minPrec a
)
) a
| isList a && isAtom a = when' (not insideList) (showString "[") $
showString "]" -- End of list.
| isList a = when' (not insideList) (showString "[") $
gmapQr (.) id
( gShowsPrec False (pred n) minPrec
`extQ`
(\(a :: a) ->
if n == 1 then id
else if isBottom a then showString "_|_"
else (if not (isAtom a) then showString ", "
else id) .
gShowsPrec True (pred n) minPrec a
)
) a
| isInfix a = showParen (not (isAtom a) && p > appPrec) $
-- We know that we have at least two args,
-- because otherwise we would have a function.
let (arg1:arg2:rest) =
continueR (:) [] (succ appPrec) a
in (showParen (not (null rest)) $
arg1 .^. showCon a .^. arg2
) . drive rest
| otherwise = showParen (not (isAtom a) && p > appPrec) $
showCon a .
continueL (.^.) nil (succ appPrec) a
where
continueL f x p = gmapQl f x (gShowsPrec False (pred n) p)
continueR f x p = gmapQr f x (gShowsPrec False (pred n) p)
drive = foldr (.) id
nil = showString ""
f .^. g = f . showChar ' ' . g
appPrec = 10
minPrec = 0
-- Some infix constructors seem to have parentheses around them in
-- their conString representations. Maybe something should be done about
-- that. See the Q test case, and compare with ordinary lists.
showCon a = showString $ showConstr $ toConstr a
isAtom a = glength a == 0
isPrimitive a = not $ isAlgType (dataTypeOf a)
isInfix a = if isPrimitive a then
False
else
constrFixity (toConstr a) == Infix
wrap s = \s' -> s . s' . s
when' b s = if b then (s .) else (id .)
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/TestUtilities.hs 0000644 0000000 0000000 00000027321 12772503660 022015 0 ustar 00 0000000 0000000 {-# LANGUAGE CPP #-}
-- | Some utilities that are part of the testing framework.
module Test.ChasingBottoms.TestUtilities
( -- * Batch execution of QuickCheck tests
run
, runQuickCheckTests
-- * Various algebraic properties
, isAssociative
, isCommutative
, isIdempotent
-- ** Equivalence and congruence
, isEquivalenceRelation
, isCongruence
, eqIsCongruence
-- ** Partial and total orders
, isPartialOrder
, isTotalOrder
, isPartialOrderOperators
, isTotalOrderOperators
, ordIsTotalOrder
-- * Helper functions
, pair
, triple
, pair3
) where
import Test.QuickCheck
import Data.List
import Control.Arrow
import Control.Monad
import Text.Show.Functions
------------------------------------------------------------------------
-- Batch execution of QuickCheck tests
-- | Runs a single test, using suitable settings.
run :: Testable p => p -> IO Result
run = quickCheckWithResult (stdArgs { maxSuccess = 1000
#if MIN_VERSION_QuickCheck(2,5,0)
, maxDiscardRatio = 5
#else
, maxDiscard = 5000
#endif
})
-- | Runs a bunch of QuickCheck tests, printing suitable information
-- to standard output. Returns 'True' if no tests fail.
runQuickCheckTests :: [IO Result]
-- ^ Create the tests in this list from ordinary
-- QuickCheck tests by using 'run'.
-> IO Bool
runQuickCheckTests tests = do
results <- sequence tests
mapM_ (putStrLn . showTR) results
return $ all ok $ results
where
ok (Success {}) = True
ok (GaveUp {}) = False
ok (Failure {}) = False
ok (NoExpectedFailure {}) = False
showTR (Success {}) = "OK."
showTR (GaveUp { numTests = n }) =
"Gave up after " ++ show n ++ " tests."
showTR (Failure {}) = "Test failed."
showTR (NoExpectedFailure {}) =
"Test did not fail, but it should have."
------------------------------------------------------------------------
-- Testing various algebraic properties
-- | Test for associativity.
isAssociative
:: Show a
=> Gen (a, a, a)
-- ^ Generator for arbitrary elements, possibly related in some
-- way to make the test more meaningful.
-> (a -> a -> Bool)
-- ^ Equality test.
-> (a -> a -> a)
-- ^ The operation.
-> Property
isAssociative triple (==.) (+.) =
forAll triple $ \(x, y, z) ->
((x +. y) +. z) ==. (x +. (y +. z))
-- | Test for commutativity.
isCommutative
:: Show a
=> Gen (a, a)
-- ^ Generator for arbitrary elements, possibly related in some
-- way to make the test more meaningful.
-> (b -> b -> Bool)
-- ^ Equality test.
-> (a -> a -> b)
-- ^ The operation.
-> Property
isCommutative pair (==.) (+.) =
forAll pair $ \(x, y) ->
(x +. y) ==. (y +. x)
-- | Test for idempotence.
isIdempotent
:: Show a
=> Gen a
-- ^ Generator for arbitrary element.
-> (a -> a -> Bool)
-- ^ Equality test.
-> (a -> a -> a)
-- ^ The operation.
-> Property
isIdempotent element (==.) (+.) =
forAll element $ \x ->
(x +. x) ==. x
-- | Tests for an equivalence relation. Requires that the relation is
-- neither always false nor always true.
isEquivalenceRelation
:: Show a
=> Gen a
-- ^ Generator for arbitrary element.
-> (a -> Gen a)
-- ^ Generator for element equivalent to argument.
-> (a -> Gen a)
-- ^ Generator for element not equivalent to argument.
-> (a -> a -> Bool)
-- ^ The relation.
-> [Property]
isEquivalenceRelation element equalTo notEqualTo (===) =
[reflexive, symmetric1, symmetric2, transitive]
where
x /== y = not (x === y)
reflexive = forAll element $ \x ->
x === x
symmetric1 = forAll (pair element equalTo) $ \(x, y) ->
x === y && y === x
symmetric2 = forAll (pair element notEqualTo) $ \(x, y) ->
x /== y && y /== x
transitive = forAll (pair element equalTo) $ \(x, y) ->
forAll (equalTo y) $ \z ->
x === z
-- | Tests for a congruence. Also tests that the negated relation is
-- the negation of the relation.
isCongruence
:: (Show a, Eq b)
=> Gen a
-- ^ Generator for arbitrary element.
-> (a -> Gen a)
-- ^ Generator for element equivalent to argument.
-> (a -> Gen a)
-- ^ Generator for element not equivalent to argument.
-> (a -> a -> Bool)
-- ^ The relation.
-> (a -> a -> Bool)
-- ^ The negated relation.
-> Gen (a -> b)
-- ^ Generator for functions.
-> (b -> b -> Bool)
-- ^ Equality for function result type.
-> [Property]
isCongruence element equalTo notEqualTo (===) (/==) function (.===) =
isEquivalenceRelation element equalTo notEqualTo (===)
++ [cong, eq_neq1, eq_neq2]
where
cong = forAll function $ \f ->
forAll (pair element equalTo) $ \(x, y) ->
f x .=== f y
eq_neq1 = forAll (pair element equalTo) $ \(x, y) ->
x === y && not (x /== y)
eq_neq2 = forAll (pair element notEqualTo) $ \(x, y) ->
not (x === y) && x /== y
-- | Test that an 'Eq' instance is a congruence.
eqIsCongruence
:: (Show a, Eq a, Eq b)
=> Gen a
-- ^ Generator for arbitrary element.
-> (a -> Gen a)
-- ^ Generator for element equivalent to argument.
-> (a -> Gen a)
-- ^ Generator for element not equivalent to argument.
-> Gen (a -> b)
-- ^ Generator for functions.
-> [Property]
eqIsCongruence element equalTo notEqualTo function =
isCongruence element equalTo notEqualTo (==) (/=) function (==)
-- | Tests for a partial order.
isPartialOrder
:: Show a
=> Gen a
-- ^ Generator for arbitrary element.
-> (a -> Gen a)
-- ^ Generator for element equal to argument, according to
-- underlying equality relation.
-> (a -> Gen a)
-- ^ Generator for element different from argument, according to
-- underlying equality relation.
-> (a -> Gen a)
-- ^ Generator for element greater than or equal to argument.
-> (a -> a -> Bool)
-- ^ Underlying equality relation.
-> (a -> a -> Bool)
-- ^ The relation.
-> [Property]
isPartialOrder element equalTo differentFrom greaterThan (==.) (<=.) =
[reflexive, antisymmetric1, antisymmetric2, transitive]
where
reflexive =
forAll element $ \x ->
x <=. x
antisymmetric1 =
forAll (pair element equalTo) $ \(x, y) ->
((x <=. y) && (y <=. x)) && x ==. y
antisymmetric2 =
forAll (pair element differentFrom) $ \(x, y) ->
not ((x <=. y) && (y <=. x)) && not (x ==. y)
transitive = forAll (pair element greaterThan) $ \(x, y) ->
forAll (greaterThan y) $ \z ->
x <=. z
-- | Tests for a total order.
isTotalOrder
:: Show a
=> Gen a
-- ^ Generator for arbitrary element.
-> (a -> Gen a)
-- ^ Generator for element equal to argument, according to
-- underlying equality relation.
-> (a -> Gen a)
-- ^ Generator for element different from argument, according to
-- underlying equality relation.
-> (a -> Gen a)
-- ^ Generator for element greater than or equal to argument.
-> (a -> a -> Bool)
-- ^ Underlying equality relation.
-> (a -> a -> Bool)
-- ^ The relation.
-> [Property]
isTotalOrder element equalTo differentFrom greaterThan (==.) (<=.) =
isPartialOrder element equalTo differentFrom greaterThan (==.) (<=.)
++ [total]
where
total =
forAll element $ \x ->
forAll element $ \y ->
(x <=. y) || (y <=. x)
-- | Tests relating various partial order operators. Does not include
-- any tests from 'isPartialOrder'.
isPartialOrderOperators
:: Show a
=> Gen a
-- ^ Generator for arbitrary element.
-> (a -> Gen a)
-- ^ Generator for element greater than or equal to argument.
-> (a -> a -> Bool)
-- ^ Equal.
-> (a -> a -> Bool)
-- ^ Less than or equal.
-> (a -> a -> Bool)
-- ^ Less than.
-> (a -> a -> Bool)
-- ^ Greater than or equal.
-> (a -> a -> Bool)
-- ^ Greater than.
-> [Property]
isPartialOrderOperators element greaterThan (==.) (<=.) (<.) (>=.) (>.) =
[lt_le, gt_ge, ge_le, lt_gt]
where
twoElems = pair3 element greaterThan
lt_le =
forAll twoElems $ \(x, y) ->
(x <. y) == ((x <=. y) && not (x ==. y))
gt_ge =
forAll twoElems $ \(x, y) ->
(x >. y) == ((x >=. y) && not (x ==. y))
ge_le =
forAll twoElems $ \(x, y) ->
(x >=. y) == (y <=. x)
lt_gt =
forAll twoElems $ \(x, y) ->
(x <. y) == (y >. x)
-- | Tests relating various total order operators and functions. Does
-- not include any tests from 'isTotalOrder'.
isTotalOrderOperators
:: Show a
=> Gen a
-- ^ Generator for arbitrary element.
-> (a -> Gen a)
-- ^ Generator for element greater than or equal to argument.
-> (a -> a -> Bool)
-- ^ Equal.
-> (a -> a -> Bool)
-- ^ Less than or equal.
-> (a -> a -> Bool)
-- ^ Less than.
-> (a -> a -> Bool)
-- ^ Greater than or equal.
-> (a -> a -> Bool)
-- ^ Greater than.
-> (a -> a -> Ordering)
-- ^ Compare.
-> (a -> a -> a)
-- ^ Minimum.
-> (a -> a -> a)
-- ^ Maximum.
-> [Property]
isTotalOrderOperators element greaterThan
(==.) (<=.) (<.) (>=.) (>.) cmp mn mx =
isPartialOrderOperators element greaterThan (==.) (<=.) (<.) (>=.) (>.)
++ [compare_lt_eq_gt, compare_max, compare_min]
where
twoElems = pair3 element greaterThan
compare_lt_eq_gt =
forAll twoElems $ \(x, y) ->
case cmp x y of
LT -> x <. y
EQ -> x ==. y
GT -> x >. y
compare_max =
forAll twoElems $ \(x, y) ->
case cmp x y of
LT -> x `mx` y ==. y
GT -> x `mx` y ==. x
EQ -> elemBy (==.) (x `mx` y) [x, y]
compare_min =
forAll twoElems $ \(x, y) ->
case cmp x y of
LT -> x `mn` y ==. x
GT -> x `mn` y ==. y
EQ -> elemBy (==.) (x `mn` y) [x, y]
elemBy op x xs = any (`op` x) xs
-- | Tests that an 'Ord' instance should satisfy to be a total order.
ordIsTotalOrder
:: (Show a, Ord a)
=> Gen a
-- ^ Generator for arbitrary element.
-> (a -> Gen a)
-- ^ Generator for element equal to argument.
-> (a -> Gen a)
-- ^ Generator for element different from argument.
-> (a -> Gen a)
-- ^ Generator for element greater than or equal to argument.
-> [Property]
ordIsTotalOrder element equalTo differentFrom greaterThan =
isTotalOrderOperators element greaterThan
(==) (<=) (<) (>=) (>) compare min max
++ isTotalOrder element equalTo differentFrom greaterThan (==) (<=)
------------------------------------------------------------------------
-- Helper functions
-- | Given two generators, generates a pair where the second component
-- depends on the first.
pair :: Gen a -> (a -> Gen b) -> Gen (a, b)
pair gen1 gen2 = do
x <- gen1
y <- gen2 x
return (x, y)
-- | 'triple' works like 'pair', but for triples.
triple :: Gen a -> (a -> Gen b) -> (b -> Gen c) -> Gen (a, b, c)
triple gen1 gen2 gen3 = do
x <- gen1
y <- gen2 x
z <- gen3 y
return (x, y, z)
-- | Given two generators, where the second one depends on elements
-- generated by the first one, 'pair3' generates three kinds of pairs:
--
-- 1. Containing two elements from the first generator.
--
-- 2. Containing one element from the first and one from the second.
--
-- 3. Containing one element from the second and one from the first.
pair3 :: Gen a -> (a -> Gen a) -> Gen (a, a)
pair3 gen1 gen2 =
oneof [ liftM2 (,) gen1 gen1
, pair gen1 gen2
, fmap (snd &&& fst) $ pair gen1 gen2
]
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/Approx.hs 0000644 0000000 0000000 00000007224 12772503660 020453 0 ustar 00 0000000 0000000 {-# LANGUAGE ScopedTypeVariables,
FlexibleInstances, UndecidableInstances #-}
-- |
-- Module : Test.ChasingBottoms.Approx
-- Copyright : (c) Nils Anders Danielsson 2004-2016
-- License : See the file LICENCE.
--
-- Maintainer : http://www.cse.chalmers.se/~nad/
-- Stability : experimental
-- Portability : non-portable (GHC-specific)
--
module Test.ChasingBottoms.Approx
( Approx(..)
) where
import Test.ChasingBottoms.Nat
import Data.Function
import Data.Generics
import qualified Data.List as List
{-|
'Approx' is a class for approximation functions as described
in The generic approximation lemma, Graham Hutton and Jeremy
Gibbons, Information Processing Letters, 79(4):197-201, Elsevier
Science, August 2001, .
Instances are provided for all members of the 'Data' type class. Due
to the limitations of the "Data.Generics" approach to generic
programming, which is not really aimed at this kind of application,
the implementation is only guaranteed to perform correctly, with
respect to the paper (and modulo any bugs), on non-mutually-recursive
sum-of-products datatypes. In particular, nested and mutually
recursive types are not handled correctly with respect to the
paper. The specification below is correct, though (if we assume that
the 'Data' instances are well-behaved).
In practice the 'approxAll' function can probably be more useful than
'approx'. It traverses down /all/ subterms, and it should be possible
to prove a variant of the approximation lemma which 'approxAll'
satisfies.
-}
class Approx a where
-- | @'approxAll' n x@ traverses @n@ levels down in @x@ and replaces all
-- values at that level with bottoms.
approxAll :: Nat -> a -> a
-- | 'approx' works like 'approxAll', but the traversal and
-- replacement is only performed at subterms of the same monomorphic
-- type as the original term. For polynomial datatypes this is
-- exactly what the version of @approx@ described in the paper above
-- does.
approx :: Nat -> a -> a
instance Data a => Approx a where
approxAll = approxAllGen
approx = approxGen
-- From The generic approximation lemma (Hutton, Gibbons):
-- Generic definition for arbitrary datatype \mu F:
-- approx (n+1) = in . F (approx n) . out
-- Approximation lemma (valid if F is locally continuous),
-- for x, y :: \mu F:
-- x = y <=> forall n in Nat corresponding to natural numbers.
-- approx n x = approx n y
approxGen :: Data a => Nat -> a -> a
approxGen n | n == 0 = error "approx 0 = _|_"
| otherwise =
\(x :: a) -> gmapT (mkT (approxGen (pred n) :: a -> a)) x
-- We use mkT to only recurse on the original type. This solution is
-- actually rather nice! But sadly it doesn't work for nested or
-- mutually recursive types...
-- Note that the function is defined in the \n -> \x -> style, not
-- \n x -> which would mean something subtly different.
------------------------------------------------------------------------
-- Recurses on everything...
approxAllGen :: Data a => Nat -> a -> a
approxAllGen n | n == 0 = error "approx 0 = _|_"
| otherwise = \x -> gmapT (approxAllGen (pred n)) x
------------------------------------------------------------------------
-- Behaves exactly like approxGen. (?)
approxGen' :: Data a => Nat -> a -> a
approxGen' n
| n == 0 = error "approx 0 = _|_"
| otherwise = \x ->
let d = dataTypeOf x
n' = pred n
fun childTerm = if dataTypeOf childTerm === d then
approxGen' n' childTerm
else
childTerm
in gmapT fun x
where (===) = (==) `on` dataTypeRep
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/IsBottom.hs-boot 0000644 0000000 0000000 00000000067 12772503660 021701 0 ustar 00 0000000 0000000 module Test.ChasingBottoms.IsBottom where
bottom :: a
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/ContinuousFunctions.hs 0000644 0000000 0000000 00000036044 12772503660 023243 0 ustar 00 0000000 0000000 {-# LANGUAGE CPP, RankNTypes, ScopedTypeVariables,
GeneralizedNewtypeDeriving, DeriveDataTypeable #-}
-- TODO: Can we pattern match on functions?
-- What about functions of several arguments? Can we have interleaved
-- pattern matching? Do we need to use currying to achieve this? What
-- limitations does that lead to?
-- TODO: getMatches: What happens with infinite input? Hmm... We do want the
-- possibility of non-termination, right?
-- TODO: getMatches: Frequencies?
-- TODO: match: Document limitations. Can functions be handled?
-- |
-- Module : Test.ChasingBottoms.ContinuousFunctions
-- Copyright : (c) Nils Anders Danielsson 2005-2016
-- License : See the file LICENCE.
--
-- Maintainer : http://www.cse.chalmers.se/~nad/
-- Stability : experimental
-- Portability : non-portable (GHC-specific)
--
-- Note: /This module is unfinished and experimental. However, I do not think that I will ever finish it, so I have released it in its current state. The documentation below may not be completely correct. The source code lists some things which should be addressed./
--
-- A framework for generating possibly non-strict, partial,
-- continuous functions.
--
-- The functions generated using the standard QuickCheck 'Arbitrary'
-- instances are all strict. In the presence of partial and infinite
-- values testing using only strict functions leads to worse coverage
-- than if more general functions are used, though.
--
-- Using 'isBottom' it is relatively easy to generate possibly
-- non-strict functions that are, in general, not monotone. For
-- instance, using
--
-- > type Cogen a = forall b. a -> Gen b -> Gen b
-- >
-- > integer :: Gen Integer
-- > integer = frequency [ (1, return bottom), (10, arbitrary) ]
-- >
-- > coBool :: CoGen Bool
-- > coBool b | isBottom b = variant 0
-- > coBool False = variant 1
-- > coBool True = variant 2
-- >
-- > function :: Cogen a -> Gen b -> Gen (a -> b)
-- > function coGen gen = promote (\a -> coGen a gen)
--
-- we can generate possibly non-strict functions from 'Bool' to
-- 'Integer' using @function coBool integer@. There is a high
-- likelihood that the functions generated are not monotone, though.
-- The reason that we can get non-monotone functions in a language
-- like Haskell is that we are using the impure function 'isBottom'.
--
-- Sometimes using possibly non-monotone functions is good enough,
-- since that set of functions is a superset of the continuous
-- functions. However, say that we want to test that @x 'O.<=!' y@
-- implies that @f x 'O.<=!' f y@ for all functions @f@ (whenever the
-- latter expression returns a total result). This property is not
-- valid in the presence of non-monotone functions.
--
-- By avoiding 'isBottom' and, unlike the standard 'coarbitrary'
-- functions, deferring some pattern matches, we can generate
-- continuous, possibly non-strict functions. There are two steps
-- involved in generating a continuous function using the framework
-- defined here.
--
-- (1) First the argument to the function is turned into a
-- 'PatternMatch'. A 'PatternMatch' wraps up the pattern match on
-- the top-level constructor of the argument, plus all further
-- pattern matches on the children of the argument. Just like when
-- 'coarbitrary' is used a pattern match is represented as a
-- generator transformer. The difference here is that there is not
-- just one transformation per input, but one transformation per
-- constructor in the input. 'PatternMatch'es can be constructed
-- generically using 'match'.
--
-- (2) Then the result is generated, almost like for a normal
-- 'Arbitrary' instance. However, for each constructor generated a
-- subset of the transformations from step 1 are applied. This
-- transformation application is wrapped up in the function
-- 'transform'.
--
-- The net result of this is that some pattern matches are performed
-- later, or not at all, so functions can be lazy.
--
-- Here is an example illustrating typical use of this framework:
--
-- > data Tree a
-- > = Branch (Tree a) (Tree a)
-- > | Leaf a
-- > deriving (Show, Typeable, Data)
-- >
-- > finiteTreeOf :: MakeResult a -> MakeResult (Tree a)
-- > finiteTreeOf makeResult = sized' tree
-- > where
-- > tree size = transform $
-- > if size == 0 then
-- > baseCase
-- > else
-- > frequency' [ (1, baseCase)
-- > , (1, liftM2 Branch tree' tree')
-- > ]
-- > where
-- > tree' = tree (size `div` 2)
-- >
-- > baseCase =
-- > frequency' [ (1, return bottom)
-- > , (2, liftM Leaf makeResult)
-- > ]
--
-- Note the use of 'transform'. To use this function to generate
-- functions of type @Bool -> Tree Integer@ we can use
--
-- > forAll (functionTo (finiteTreeOf flat)) $
-- > \(f :: Bool -> Tree Integer) ->
-- > ...
module Test.ChasingBottoms.ContinuousFunctions
( -- * Basic framework
function
, functionTo
, PatternMatch(..)
, GenTransformer
, MakePM
, MakeResult
, transform
-- * Liftings of some QuickCheck functionality
, lift'
, arbitrary'
, choose'
, elements'
, oneof'
, frequency'
, sized'
, resize'
-- * Generic @MakePM@
, match
-- * Some @MakeResult@s
, flat
, finiteListOf
, infiniteListOf
, listOf
) where
import Test.QuickCheck
hiding ( (><)
, listOf
#if MIN_VERSION_QuickCheck(2,7,0)
, infiniteListOf
#endif
)
#if MIN_VERSION_QuickCheck(2,7,0)
import Test.QuickCheck.Gen.Unsafe (promote)
#endif
import Data.Sequence as Seq
import Data.Foldable as Seq (foldr)
import Prelude as P hiding (concat)
import Test.ChasingBottoms.IsBottom
import Control.Monad
import Control.Monad.Reader
import Control.Applicative
import Control.Arrow
import System.Random
import Data.Generics
import qualified Data.List as L
import qualified Test.ChasingBottoms.SemanticOrd as O
------------------------------------------------------------------------
-- Generation of functions
-- | Generator for continuous, not necessarily strict functions.
-- Functions are generated by first generating pattern matches, and
-- then generating a result.
function :: MakePM a -> MakeResult b -> Gen (a -> b)
function makePM makeResult =
promote $ \a -> run makeResult (singleton $ makePM a)
-- | 'functionTo' specialises 'function':
--
-- @
-- 'functionTo' = 'function' 'match'
-- @
functionTo :: Data a => MakeResult b -> Gen (a -> b)
functionTo = function match
------------------------------------------------------------------------
-- Pattern matching
-- | 'PatternMatch' packages up the possible outcomes of a pattern
-- match in a style suitable for generating functions. A pattern match
-- is a generator ('Gen') transformer based on the top-level
-- constructor, and a sequence (see
-- ) of
-- 'PatternMatch'es based on the children of that constructor.
data PatternMatch
= PatternMatch { apply :: GenTransformer
-- ^ A generator transformer, in the style of 'coarbitrary'.
, more :: Seq PatternMatch
-- ^ Further pattern matches made possible by this
-- match.
}
-- | The type of a generator transformer.
type GenTransformer = forall a. Gen a -> Gen a
-- | This newtype is (currently) necessary if we want to use
-- 'GenTransformer' as an argument to a type constructor.
newtype GenTransformer' = GenT GenTransformer
-- | The type of a 'PatternMatch' generator.
type MakePM a = a -> PatternMatch
------------------------------------------------------------------------
-- Generic MakePM
-- These functions provided inspiration for the generic one below.
matchFlat :: CoArbitrary a => MakePM a
matchFlat a = PatternMatch { apply = coarbitrary a, more = Seq.empty }
data Tree a
= Branch (Tree a) (Tree a)
| Leaf a
deriving (Show, Typeable, Data)
matchTree :: MakePM a -> MakePM (Tree a)
matchTree match t = PatternMatch { apply = toVariant t, more = moreT t }
where
toVariant (Branch {}) = variant 1
toVariant (Leaf {}) = variant 0
moreT (Branch l r) = fromList [matchTree match l, matchTree match r]
moreT (Leaf x) = singleton (match x)
-- | Generic implementation of 'PatternMatch' construction.
match :: forall a. Data a => MakePM a
match x = PatternMatch
{ apply = toVariant x
, more = more x
}
where
toVariant :: forall a b. Data a => a -> Gen b -> Gen b
toVariant x = case constrRep (toConstr x) of
AlgConstr n -> variant (n - 1) -- n >= 1.
IntConstr i -> coarbitrary i
FloatConstr d -> coarbitrary d
CharConstr s -> nonBottomError "match: Encountered CharConstr."
more :: forall a. Data a => a -> Seq PatternMatch
more = gmapQr (<|) Seq.empty match
------------------------------------------------------------------------
-- MakeResult monad
-- | Monad for generating results given previously generated pattern
-- matches.
--
-- A @'MakeResult' a@ should be implemented almost as other generators for
-- the type @a@, with the difference that 'transform' should be
-- used wherever the resulting function should be allowed to pattern
-- match (typically for each constructor emitted). See example above.
-- Note that we do not want to export a 'MonadReader' instance, so we
-- cannot define one...
newtype MakeResult a
= MR { unMR :: ReaderT PatternMatches Gen a }
deriving (Functor, Applicative, Monad)
type PatternMatches = Seq PatternMatch
-- | Lowering of a 'MakeResult'.
run :: MakeResult a -> PatternMatches -> Gen a
run mr pms = runReaderT (unMR mr) pms
-- | Lifting of a 'Gen'.
lift' :: Gen a -> MakeResult a
lift' gen = MR $ lift gen
-- | Returns the 'PatternMatches' in scope.
getPMs :: MakeResult PatternMatches
getPMs = MR ask
withPMs :: (PatternMatches -> Gen a) -> MakeResult a
withPMs f = do
pms <- getPMs
lift' $ f pms
-- | 'transform' makes sure that the pattern matches get to influence
-- the generated value. See 'MakeResult'.
transform :: MakeResult a -> MakeResult a
transform makeResult = withPMs $ \pms -> do
(GenT trans, keep) <- getMatches pms
trans (run makeResult keep)
-- | Extracts some pattern matches to trigger right away. These
-- triggered pattern matches may result in new pattern matches which
-- may in turn also be triggered, and so on.
getMatches :: Seq PatternMatch -> Gen (GenTransformer', Seq PatternMatch)
getMatches pms = do
-- Throw away pattern matches with probability 0.1.
(_, pms') <- partition' 9 pms
-- Use pattern matches with probability 0.33.
(use, keep) <- partition' 2 pms'
let transform = compose $ fmap apply use
further = concat $ fmap more use
if Seq.null further then
return (GenT transform, keep)
else do
(GenT transform', keep') <- getMatches further
return (GenT (transform . transform'), keep >< keep')
------------------------------------------------------------------------
-- Sequence helpers
-- | Concatenates arguments.
concat :: Seq (Seq a) -> Seq a
concat = Seq.foldr (><) Seq.empty
-- | Composes arguments.
compose :: Seq (a -> a) -> a -> a
compose = Seq.foldr (.) id
-- | Partitions a 'Seq'. The first argument (a positive integer) is
-- the relative probability with which elements end up in the second
-- part compared to the first one.
partition' :: Int -> Seq a -> Gen (Seq a, Seq a)
partition' freq ss = case viewl ss of
EmptyL -> return (Seq.empty, Seq.empty)
x :< xs -> do
(ys, zs) <- partition' freq xs
frequency [ (1, return (x <| ys, zs))
, (freq, return (ys, x <| zs))
]
------------------------------------------------------------------------
-- Lifting of QuickCheck's Gen monad
-- | Lifting of 'arbitrary'.
arbitrary' :: Arbitrary a => MakeResult a
arbitrary' = lift' arbitrary
-- | Lifting of 'choose'.
choose' :: Random a => (a, a) -> MakeResult a
choose' = lift' . choose
-- | Lifting of 'elements'.
elements' :: [a] -> MakeResult a
elements' = lift' . elements
-- | Lifting of 'oneof'.
oneof' :: [MakeResult a] -> MakeResult a
oneof' mrs = withPMs $ \pms -> oneof $ map (\mr -> run mr pms) mrs
-- | Lifting of 'frequency'.
frequency' :: [(Int, MakeResult a)] -> MakeResult a
frequency' freqs = withPMs $ \pms ->
frequency $ map (id *** flip run pms) freqs
-- | Lifting of 'sized'.
sized' :: (Int -> MakeResult a) -> MakeResult a
sized' mr = withPMs $ \pms -> sized (\size -> run (mr size) pms)
-- | Lifting of 'resize'.
resize' :: Int -> MakeResult a -> MakeResult a
resize' n mr = withPMs $ \pms -> resize n (run mr pms)
------------------------------------------------------------------------
-- Some predefined generators
-- | An implementation of @'MakeResult' a@ which is suitable when @a@
-- is flat and has an 'Arbitrary' instance. Yields bottoms around 10%
-- of the time.
flat :: Arbitrary a => MakeResult a
flat = transform $
frequency' [ (1, return bottom)
, (9, arbitrary')
]
-- | This 'MakeResult' yields finite partial lists.
finiteListOf :: MakeResult a -> MakeResult [a]
finiteListOf makeResult = sized' list
where
list size = transform $
if size == 0 then
baseCase
else
frequency' [ (1, baseCase)
, (9, liftM2 (:) makeResult (list (size - 1)))
]
baseCase =
frequency' [(1, return bottom), (1, return [])]
-- | This 'MakeResult' yields infinite partial lists.
infiniteListOf :: MakeResult a -> MakeResult [a]
infiniteListOf makeResult = transform $
liftM2 (:) makeResult (infiniteListOf makeResult)
-- | This 'MakeResult' yields finite or infinite partial lists.
listOf :: MakeResult a -> MakeResult [a]
-- Not really necessary to have a transform here...
listOf makeResult = transform $
oneof' [ finiteListOf makeResult
, infiniteListOf makeResult
]
------------------------------------------------------------------------
-- Failed attempt at a generic implementation of MakeResult
-- Main problem: Getting the frequencies right. Lists are very short
-- right now.
-- Other problem: Int and Float.
-- Further remark: We need finite and infinite versions of this
-- function.
makeResult :: forall a. Data a => MakeResult a
makeResult = transform (frequency' $ (1, return bottom) : others)
where
others = case dataTypeRep (dataTypeOf (undefined :: a)) of
AlgRep constrs ->
map (handle (L.genericLength constrs)) constrs
IntRep -> [(9, cast' (arbitrary' :: MakeResult Integer))]
FloatRep -> [(9, cast' (arbitrary' :: MakeResult Double))]
CharRep -> nonBottomError "makeResult: CharRep."
NoRep -> nonBottomError "makeResult: NoRep."
handle noConstrs con =
(freq, fromConstrM makeResult con :: MakeResult a)
where noArgs = glength (fromConstr con :: a)
-- Aim for at most 10% bottoms (on average).
freq = 1 `max` ceiling (9 / noConstrs)
cast' gen = flip fmap gen $ \x -> case cast x of
Just x' -> x'
Nothing -> nonBottomError $
"makeResult: Cannot handle Int and Float." ++
" Use Integer or Double instead."
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/SemanticOrd.hs 0000644 0000000 0000000 00000020773 12772503660 021416 0 ustar 00 0000000 0000000 {-# LANGUAGE ScopedTypeVariables, RankNTypes,
FlexibleInstances, UndecidableInstances #-}
-- |
-- Module : Test.ChasingBottoms.SemanticOrd
-- Copyright : (c) Nils Anders Danielsson 2004-2016
-- License : See the file LICENCE.
--
-- Maintainer : http://www.cse.chalmers.se/~nad/
-- Stability : experimental
-- Portability : non-portable (GHC-specific)
--
-- Generic semantic equality and order. The semantic order referred
-- to is that of a typical CPO for Haskell types, where e.g. @('True',
-- 'bottom') '<=!' ('True', 'False')@, but where @('True', 'True')@
-- and @('True', 'False')@ are incomparable.
--
-- The implementation is based on 'isBottom', and has the same
-- limitations. Note that non-bottom functions are not handled by any
-- of the functions described below.
--
-- One could imagine using QuickCheck for testing equality of
-- functions, but I have not managed to tweak the type system so that
-- it can be done transparently.
module Test.ChasingBottoms.SemanticOrd
( Tweak(..)
, noTweak
, SemanticEq(..)
, SemanticOrd(..)
) where
import Data.Generics
import Test.ChasingBottoms.IsBottom
import Test.ChasingBottoms.IsType
import qualified Data.Maybe as Maybe
import Test.ChasingBottoms.Nat
import Test.ChasingBottoms.Approx
infix 4 =!, >!, /=!
infix 5 \/!
infixl 5 /\!
-- | The behaviour of some of the functions below can be tweaked.
data Tweak = Tweak
{ approxDepth :: Maybe Nat
-- ^ If equal to @'Just' n@, an @'approxAll' n@ is performed on
-- all arguments before doing whatever the function is supposed to
-- be doing.
, timeOutLimit :: Maybe Int
-- ^ If equal to @'Just' n@, then all computations that take more
-- than @n@ seconds to complete are considered to be equal to
-- 'bottom'. This functionality is implemented using
-- 'isBottomTimeOut'.
}
deriving (Eq, Ord, Show)
-- | No tweak (both fields are 'Nothing').
noTweak :: Tweak
noTweak = Tweak
{ approxDepth = Nothing
, timeOutLimit = Nothing
}
-- | 'SemanticEq' contains methods for testing whether two terms are
-- semantically equal.
-- Note that we only allow a -> a -> Bool here, not a -> b ->
-- Bool. Otherwise we would allow behaviour like the following:
-- > (bottom : bottom :: [Int]) <=!! ("tr" :: String)
-- True
class SemanticEq a where
(==!), (/=!) :: a -> a -> Bool
semanticEq :: Tweak -> a -> a -> Bool
(/=!) = \x y -> not (x ==! y)
(==!) = semanticEq noTweak
-- | 'SemanticOrd' contains methods for testing whether two terms are
-- related according to the semantic domain ordering.
class SemanticEq a => SemanticOrd a where
(=!), (>!) :: a -> a -> Bool
semanticCompare :: Tweak -> a -> a -> Maybe Ordering
-- ^ @'semanticCompare' tweak x y@ returns 'Nothing' if @x@ and @y@ are
-- incomparable, and @'Just' o@ otherwise, where @o :: 'Ordering'@
-- represents the relation between @x@ and @y@.
(\/!) :: a -> a -> Maybe a
(/\!) :: a -> a -> a
semanticJoin :: Tweak -> a -> a -> Maybe a
semanticMeet :: Tweak -> a -> a -> a
-- ^ @x '\/!' y@ and @x '/\!' y@ compute the least upper and greatest
-- lower bounds, respectively, of @x@ and @y@ in the semantical
-- domain ordering. Note that the least upper bound may not always
-- exist.
-- This functionality was implemented just because it was
-- possible (and to provide analogues of 'max' and 'min' in the 'Ord'
-- class). If anyone finds any use for it, please let me know.
(>=!) = flip (<=!)
( x <=! y && x /=! y
(>!) = \x y -> x >=! y && x /=! y
x <=! y = case semanticCompare noTweak x y of
Just LT -> True
Just EQ -> True
_ -> False
(\/!) = semanticJoin noTweak
(/\!) = semanticMeet noTweak
instance Data a => SemanticEq a where
semanticEq tweak = liftAppr tweak semanticEq'
instance Data a => SemanticOrd a where
semanticCompare tweak = liftAppr tweak semanticCompare'
where
semanticCompare' tweak x y =
case ( semanticEq' tweak x y
, semanticLE' tweak x y
, semanticLE' tweak y x ) of
(True, _, _) -> Just EQ
(_, True, _) -> Just LT
(_, _, True) -> Just Prelude.GT
(_, _, _) -> Nothing
semanticJoin tweak = liftAppr tweak semanticJoin'
semanticMeet tweak = liftAppr tweak semanticMeet'
liftAppr :: (Data a, Data b) => Tweak -> (Tweak -> a -> a -> b) -> a -> a -> b
liftAppr tweak op x y = op tweak (appr x) (appr y)
where appr = maybe id approxAll (approxDepth tweak)
------------------------------------------------------------------------
type Rel' = forall a b. (Data a, Data b) => Tweak -> a -> b -> Bool
type Rel = forall a b. (Data a, Data b) => a -> b -> Bool
semanticEq', semanticLE' :: Rel'
semanticEq' tweak a b = case ( isBottomTimeOut (timeOutLimit tweak) a
, isBottomTimeOut (timeOutLimit tweak) b ) of
(True, True) -> True
(False, False) -> allOK (semanticEq' tweak) a b
_ -> False
semanticLE' tweak a b = case ( isBottomTimeOut (timeOutLimit tweak) a
, isBottomTimeOut (timeOutLimit tweak) b ) of
(True, _) -> True
(False, False) -> allOK (semanticLE' tweak) a b
_ -> False
allOK :: Rel -> Rel
allOK op a b =
-- It's really enough to test just a, since we restrict the types
-- above, but why complicate things?
if isFunction a || isFunction b then
-- cast' a `fop` cast' b
nonBottomError
"The generic versions of (==!) and friends do not accept non-bottom \
\functions."
else
a =^= b && childrenOK op a b
-- Check top-level. Note that this test always fails for "function
-- constructors".
(=^=) :: Rel
a =^= b = toConstr a == toConstr b
-- Check children.
childrenOK :: Rel -> Rel
childrenOK op = and .|.. gzipWithQ (\x y -> op x y)
where f .|.. g = \x y -> f (g x y)
------------------------------------------------------------------------
semanticMeet' :: (Data a, Data b) => Tweak -> a -> b -> b
semanticMeet' tweak a (b :: b) =
if isBottomTimeOut (timeOutLimit tweak) a ||
isBottomTimeOut (timeOutLimit tweak) b then
bottom
else if isFunction a || isFunction b then
nonBottomError "/\\! does not handle non-bottom functions."
else if not (a =^= b) then
bottom
else
gzipWithT (\x y -> semanticMeet' tweak x y) a b
semanticJoin' :: (Data a, Data b) => Tweak -> a -> b -> Maybe b
semanticJoin' tweak a (b :: b) =
case ( isBottomTimeOut (timeOutLimit tweak) a
, isBottomTimeOut (timeOutLimit tweak) b ) of
(True, True) -> Just bottom
(True, False) -> Just b
(False, True) -> cast a
(False, False)
| isFunction a || isFunction b ->
nonBottomError "\\/! does not handle non-bottom functions."
| not (a =^= b) -> Nothing
| otherwise -> gzipWithM (\x y -> semanticJoin' tweak x y) a b
------------------------------------------------------------------------
-- Variant of cast.
-- cast' :: (Typeable a, Typeable b) => a -> b
-- cast' = Maybe.fromJust . cast
------------------------------------------------------------------------
-- TODO: Implement a comparison operator which also works for functions.
-- newtype EqFun = EqFun { unEqFun ::
-- forall a b . (Data a, Data b) => a -> b -> Bool }
-- class SemanticFunEq a where
-- (!==!), (!/=!) :: a -> a -> Bool
-- (!/=!) = \x y -> not (x !==! y)
-- instance Data a => SemanticFunEq a where
-- x !==! y =
-- let test :: (Arbitrary b, Show b, Data c) =>
-- (b -> c1) -> (b -> c2) -> Bool
-- test f g = testIt (forAll arbitrary $ \(x :: b) -> f x !==!! g x)
-- in let ?funTest = EqFun test
-- in x !==!! y
-- (!==!!) :: (Data a, Data b, ?funTest :: EqFun) => a -> b -> Bool
-- x !==!! y = case (isBottom x, isBottom y) of
-- (True, True) -> True
-- (False, False) | isFunction x -> unEqFun ?funTest x y
-- | otherwise -> x =^= y && tmapQl (&&) True (!==!!) x y
-- _ -> False
-- This one works, but it only handles functions on the top level, not
-- functions inside e.g. lists.
-- instance (Show a, Arbitrary a, SemanticFunEq b) => SemanticFunEq (a -> b) where
-- f !==! g = case (isBottom f, isBottom g) of
-- (True, True) -> True
-- (False, False) -> testIt (forAll arbitrary $ \x -> f x !==! g x)
-- _ -> False
-- instance SemanticEq a => SemanticFunEq a where
-- a !==! b = case (isBottom a, isBottom b) of
-- (True, True) -> True
-- (False, False) -> -- We know that we are not dealing with functions.
-- a ==! b
-- _ -> False
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/IsBottom.hs 0000644 0000000 0000000 00000010602 12772503660 020734 0 ustar 00 0000000 0000000 {-# LANGUAGE ScopedTypeVariables #-}
-- The following (possibly unnecessary) options are included due to
-- the use of unsafePerformIO below.
{-# OPTIONS_GHC -fno-cse -fno-full-laziness #-}
-- |
-- Module : Test.ChasingBottoms.IsBottom
-- Copyright : (c) Nils Anders Danielsson 2004-2016
-- License : See the file LICENCE.
--
-- Maintainer : http://www.cse.chalmers.se/~nad/
-- Stability : experimental
-- Portability : non-portable (exceptions)
--
module Test.ChasingBottoms.IsBottom
( isBottom
, isBottomIO
, bottom
, nonBottomError
, isBottomTimeOut
, isBottomTimeOutIO
) where
import Prelude hiding (catch)
import qualified Control.Exception as E
import System.IO.Unsafe (unsafePerformIO)
import qualified Test.ChasingBottoms.TimeOut as T
-- | @'isBottom' a@ returns 'False' if @a@ is distinct from bottom. If
-- @a@ equals bottom and results in an exception of a certain kind
-- (see below), then @'isBottom' a = 'True'@. If @a@ never reaches a
-- weak head normal form and never throws one of these exceptions,
-- then @'isBottom' a@ never terminates.
--
-- The exceptions that yield 'True' correspond to \"pure bottoms\",
-- i.e. bottoms that can originate in pure code:
--
-- * 'E.ArrayException'
--
-- * 'E.ErrorCall'
--
-- * 'E.NoMethodError'
--
-- * 'E.NonTermination'
--
-- * 'E.PatternMatchFail'
--
-- * 'E.RecConError'
--
-- * 'E.RecSelError'
--
-- * 'E.RecUpdError'
--
-- Assertions are excluded, because their behaviour depends on
-- compiler flags (not pure, and a failed assertion should really
-- yield an exception and nothing else). The same applies to
-- arithmetic exceptions (machine dependent, except possibly for
-- 'E.DivideByZero', but the value infinity makes that case unclear as
-- well).
-- Should we use throw or throwIO below?
-- It doesn't seem to matter, and I don't think it matters, but
-- using throw won't give us any problems.
-- Check out a discussion about evaluate around
-- http://www.haskell.org/pipermail/glasgow-haskell-users/2002-May/003393.html.
-- From the docs:
-- evaluate undefined `seq` return () ==> return ()
-- catch (evaluate undefined) (\e -> return ()) ==> return ()
isBottom :: a -> Bool
isBottom = isBottomTimeOut Nothing
-- | 'bottom' generates a bottom that is suitable for testing using
-- 'isBottom'.
bottom :: a
bottom = error "_|_"
-- | @'nonBottomError' s@ raises an exception ('E.AssertionFailed')
-- that is not caught by 'isBottom'. Use @s@ to describe the
-- exception.
nonBottomError :: String -> a
nonBottomError = E.throw . E.AssertionFailed
-- | @'isBottomTimeOut' timeOutLimit@ works like 'isBottom', but if
-- @timeOutLimit@ is @'Just' lim@, then computations taking more than
-- @lim@ seconds are also considered to be equal to bottom. Note that
-- this is a very crude approximation of what a bottom is. Also note
-- that this \"function\" may return different answers upon different
-- invocations. Take it for what it is worth.
--
-- 'isBottomTimeOut' is subject to all the same vagaries as
-- 'T.timeOut'.
-- The following pragma is included due to the use of unsafePerformIO
-- below.
{-# NOINLINE isBottomTimeOut #-}
isBottomTimeOut :: Maybe Int -> a -> Bool
isBottomTimeOut timeOutLimit f =
unsafePerformIO $ isBottomTimeOutIO timeOutLimit f
-- | A variant of 'isBottom' that lives in the 'IO' monad.
isBottomIO :: a -> IO Bool
isBottomIO = isBottomTimeOutIO Nothing
-- | A variant of 'isBottomTimeOut' that lives in the 'IO' monad.
isBottomTimeOutIO :: Maybe Int -> a -> IO Bool
isBottomTimeOutIO timeOutLimit f =
maybeTimeOut (E.evaluate f) `E.catches`
[ E.Handler (\(_ :: E.ArrayException) -> return True)
, E.Handler (\(_ :: E.ErrorCall) -> return True)
, E.Handler (\(_ :: E.NoMethodError) -> return True)
, E.Handler (\(_ :: E.NonTermination) -> return True)
, E.Handler (\(_ :: E.PatternMatchFail) -> return True)
, E.Handler (\(_ :: E.RecConError) -> return True)
, E.Handler (\(_ :: E.RecSelError) -> return True)
, E.Handler (\(_ :: E.RecUpdError) -> return True)
]
where
maybeTimeOut io = case timeOutLimit of
Nothing -> do
io
return False
Just lim -> do
result <- T.timeOut lim io
case result of -- Note that evaluate bottom /= bottom.
T.Value _ -> return False
T.NonTermination -> return True
T.Exception e -> E.throw e -- Catch the exception above.
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/Tests.hs 0000644 0000000 0000000 00000005107 12772503660 020302 0 ustar 00 0000000 0000000 {-# LANGUAGE FlexibleInstances #-}
-- | Tests of almost everything related to "Test.ChasingBottoms".
module Main (main) where
import qualified Test.ChasingBottoms.Approx.Tests as Approx
import qualified Test.ChasingBottoms.ApproxShow.Tests as ApproxShow
import qualified Test.ChasingBottoms.ContinuousFunctions.Tests as ContinuousFunctions
import qualified Test.ChasingBottoms.IsBottom.Tests as IsBottom
import qualified Test.ChasingBottoms.IsType.Tests as IsType
import qualified Test.ChasingBottoms.Nat.Tests as Nat
import qualified Test.ChasingBottoms.SemanticOrd.Tests as SemanticOrd
import qualified Test.ChasingBottoms.TestUtilities.Generators as Generators
import qualified Test.ChasingBottoms.TimeOut.Tests as TimeOut
import System.Exit
-- | A class for things that can be tested.
class Test a where
test :: String -- ^ Description of test.
-> a -- ^ Test.
-> IO Bool -- ^ True if the test succeeded.
-- | @'indent' a@ shows @a@ and indents the output by two spaces. A
-- trailing newline is added if necessary.
-- This function could be more efficient.
indent :: (Show a) => a -> IO ()
indent a = putStr . maybeNL . unlines . map (" " ++) . lines $ show a
where maybeNL s | null s = "\n"
| last s == '\n' = s
| otherwise = s ++ "\n"
instance Test Bool where
test desc b = do
putStrLn desc
indent b
return b
instance Test [Bool] where
test desc bs = do
putStrLn desc
indent bs
return $ and bs
instance Test (IO Bool) where
test desc io = do
putStrLn desc
b <- io
indent b
return b
-- | This function runs all the tests, and prints out a message
-- indicating whether any failures were encountered.
main :: IO ()
main = do
ok <- fmap and $ sequence theTests
putStrLn ""
if ok then
putStrLn "All tests succeeded."
else do
putStrLn "At least one test failed."
exitFailure
where theTests = [ test "Approx:" Approx.tests
, test "ApproxShow:" ApproxShow.tests
, test "ContinuousFunctions:" ContinuousFunctions.tests
, test "Generators:" Generators.tests
, test "IsBottom:" IsBottom.tests
, test "IsType:" IsType.tests
, test "Nat:" Nat.tests
, test "SemanticOrd:" SemanticOrd.tests
, test "TimeOut:" TimeOut.tests
]
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/IsType.hs 0000644 0000000 0000000 00000002230 12772503660 020407 0 ustar 00 0000000 0000000 -- |
-- Module : Test.ChasingBottoms.IsType
-- Copyright : (c) Nils Anders Danielsson 2004-2016
-- License : See the file LICENCE.
--
-- Maintainer : http://www.cse.chalmers.se/~nad/
-- Stability : experimental
-- Portability : non-portable (GHC-specific)
--
-- Internal helper functions.
module Test.ChasingBottoms.IsType
( isFunction
, isTuple
, isList
, isString
) where
import Data.List
import Data.Typeable
-- | '@isFunction@ f' returns 'True' iff the top level \"constructor\"
-- of @f@ is a function arrow.
isFunction :: Typeable a => a -> Bool
isFunction f = con f == con not -- TyCon is abstract.
con :: Typeable a => a -> TyCon
con = typeRepTyCon . typeOf
-- | This function is rather fragile, but should be OK. It is only
-- used by "Test.ChasingBottoms.ApproxShow", which should only be used
-- for debugging purposes anyway. The unit type is not considered to
-- be a tuple.
isTuple :: Typeable a => a -> Bool
isTuple x = "(," `isPrefixOf` show (con x)
isString :: Typeable a => a -> Bool
isString x = isList x && typeRepArgs (typeOf x) == typeRepArgs (typeOf "")
isList :: Typeable a => a -> Bool
isList x = con x == con ""
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/TimeOut.hs 0000644 0000000 0000000 00000010533 12772503660 020565 0 ustar 00 0000000 0000000 {-# LANGUAGE ScopedTypeVariables, DeriveDataTypeable #-}
-- |
-- Module : Test.ChasingBottoms.TimeOut
-- Copyright : (c) Nils Anders Danielsson 2004-2016
-- License : See the file LICENCE.
--
-- Maintainer : http://www.cse.chalmers.se/~nad/
-- Stability : experimental
-- Portability : non-portable (preemptive scheduling)
--
-- When dealing with \"hard bottoms\", i.e. non-terminating
-- computations that do not result in exceptions, the following functions
-- may be handy.
--
-- Note that a computation is considered to have terminated when it
-- has reached weak head normal form (i.e. something distinct from
-- bottom).
module Test.ChasingBottoms.TimeOut
( Result(..)
, timeOut
, timeOut'
, timeOutMicro
, timeOutMicro'
) where
import Control.Concurrent
import Data.Dynamic
import qualified Control.Exception as E
import {-# SOURCE #-} qualified Test.ChasingBottoms.IsBottom as B
data Result a
= Value a
| NonTermination
| Exception E.SomeException
deriving (Show, Typeable)
-- | @'timeOut' n c@ runs @c@ for at most @n@ seconds (modulo
-- scheduling issues).
--
-- * If the computation terminates before that, then @'Value' v@ is
-- returned, where @v@ is the resulting value. Note that this
-- value may be equal to bottom, e.g. if @c = 'return'
-- 'B.bottom'@.
--
-- * If the computation does not terminate, then 'NonTermination' is
-- returned.
--
-- * If the computation raises an exception, then @'Exception' e@ is
-- returned, where @e@ is the exception.
--
-- Note that a user-defined exception is used to terminate the
-- computation, so if @c@ catches all exceptions, or blocks
-- asynchronous exceptions, then 'timeOut' may fail to function
-- properly.
timeOut :: Int -> IO a -> IO (Result a)
timeOut = timeOutMicro . (* 10^6)
-- | 'timeOutMicro' takes a delay in microseconds. Note that the
-- resolution is not necessarily very high (the last time I checked it
-- was 0.02 seconds when using the standard runtime system settings
-- for GHC).
timeOutMicro :: Int -> IO a -> IO (Result a)
timeOutMicro delay io = do
mv <- newEmptyMVar
let putException = putMVar mv . Exception
ioThread <- forkIO $
(io >>= putMVar mv . Value)
`E.catch` (\(e :: E.SomeException) ->
case E.fromException e of
Just Die -> return () -- Thread properly killed.
Nothing -> putException e)
reaper <- forkIO $ do
threadDelay delay
putMVar mv NonTermination
result <- takeMVar mv
killThread' ioThread
killThread reaper
return result
-- Since 'ioThread' above should return exceptions raised in the code
-- it seems like a bad idea to kill the thread using killThread, which
-- raises @'AsyncException' 'ThreadKilled'@. We use the locally
-- defined type 'Die' instead.
data Die = Die deriving (Show, Typeable)
instance E.Exception Die
killThread' threadId = E.throwTo threadId Die
-- | 'timeOut'' is a variant which can be used for pure
-- computations. The definition,
--
-- @
-- 'timeOut'' n = 'timeOut' n . 'E.evaluate'
-- @
--
-- ensures that @'timeOut'' 1 'B.bottom'@ usually returns @'Exception'
-- \@. (@'timeOut' 1 ('return' 'B.bottom')@ usually
-- returns @'Value' 'B.bottom'@; in other words, the computation
-- reaches whnf almost immediately, defeating the purpose of the
-- time-out.)
timeOut' :: Int -> a -> IO (Result a)
timeOut' n = timeOut n . E.evaluate
-- | 'timeOutMicro'' is the equivalent variant of 'timeOutMicro':
--
-- @
-- 'timeOutMicro'' n = 'timeOutMicro' n . 'E.evaluate'
-- @
timeOutMicro' :: Int -> a -> IO (Result a)
timeOutMicro' n = timeOutMicro n . E.evaluate
------------------------------------------------------------------------
-- There shouldn't be any memory leaks in the code above. Profiling
-- the code below also seems to suggest that there aren't any
-- problems. However, GHCi (with :set +r) eats up more and more memory
-- if the computation below is rerun a couple of times. Hmm, that
-- seems to be the case also when running simply (reverse [1..]). It
-- probably means that GHCi never releases any memory.
main = do
let n = 1; d = 000000
{-# SCC "a" #-} timeOut' n (reverse [1..]) >>= print
threadDelay d
{-# SCC "b" #-} timeOut' n (reverse [1..]) >>= print
threadDelay d
{-# SCC "c" #-} timeOut' n (reverse [1..]) >>= print
threadDelay d
{-# SCC "d" #-} timeOut' n (reverse [1..]) >>= print
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/Nat/ 0000755 0000000 0000000 00000000000 12772503660 017363 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Test/ChasingBottoms/Nat/Tests.hs 0000644 0000000 0000000 00000014732 12772503660 021030 0 ustar 00 0000000 0000000 {-# LANGUAGE ScopedTypeVariables #-}
-- | Tests for "Test.ChasingBottoms.Nat".
-- The automatically derived 'Typeable' instance is not tested.
module Test.ChasingBottoms.Nat.Tests (tests) where
import Test.ChasingBottoms.Nat
import Test.ChasingBottoms.SemanticOrd
import Test.ChasingBottoms.TestUtilities
import Test.QuickCheck
import Data.Maybe
import Data.List
import Data.Ratio
default ()
-- The default versions of succ and pred go via Ints, and hence
-- perform incorrectly in the presence of large natural numbers. Hence
-- this generator is needed. Other tests can possibly also fail in the
-- presence of large natural numbers, but QuickCheck does not handle
-- large numbers very well, especially not when coarbitrary is used,
-- so we do not use this generator for all tests. Furthermore
-- defaulting is turned off here and in Test.ChasingBottoms.Nat, and
-- that should minimise surprises.
largeNat :: Gen Nat
largeNat = do
n <- choose (0, 2 * toInteger (maxBound :: Int))
return (fromInteger n)
-- Testing isSucc.
prop_isSucc n = isSucc n == (n > 0)
-- Testing fromSucc.
prop_fromSucc n | n == 0 = fromSucc n == Nothing
| otherwise = fromSucc n == Just (n-1)
-- Testing natrec.
-- How do you test something as versatile as natrec? Well, at least we
-- can verify that we can use it to implement addition.
prop_natrec_add m n = natrec m (\_ o -> succ o) n == m + n
-- There is no need to test foldN, since it is specified by its
-- definition.
-- Testing Enum.
prop_Nat_Enum_succ =
forAll largeNat $ \n ->
succ n == n + 1
prop_Nat_Enum_pred =
forAll largeNat $ \n ->
n > 0 ==> pred n == n - 1
prop_Nat_Enum_toEnum (n :: Int) =
n >= 0 ==> (toEnum n :: Nat) == fromInteger (toInteger n)
prop_Nat_Enum_fromEnum (n :: Nat) =
n <= fromInteger (toInteger (maxBound :: Int)) ==>
toInteger (fromEnum n) == toInteger n
-- enumFrom and friends have default definitions.
-- Testing Eq.
prop_Nat_Eq_congruence =
eqIsCongruence arbitrary equalTo notEqualTo
(arbitrary :: Gen (Nat -> Integer))
equalTo (n :: Nat) = return n
notEqualTo (n :: Nat) = do
m <- fmap succ arbitrary -- m >= 1.
if m <= n then
elements [n - m, n + m]
else
return (n + m)
-- Testing Show.
prop_Nat_Show (m :: Nat) = show m == show (toInteger m)
-- Testing Ord.
prop_Nat_Ord_total_order = ordIsTotalOrder arbitrary
equalTo notEqualTo greaterThanOrEqual
greaterThanOrEqual (n :: Nat) = do
m <- arbitrary
return (n + m)
-- Testing Num.
prop_Nat_mul_iterated_sum (m :: Nat) n =
m * n == foldr (+) 0 (genericReplicate m n)
prop_Nat_plus_assoc (m :: Nat) n o = m + (n + o) == (m + n) + o
prop_Nat_plus_comm (m :: Nat) n = m + n == n + m
prop_Nat_mul_assoc (m :: Nat) n o = m * (n * o) == (m * n) * o
prop_Nat_mul_comm (m :: Nat) n = m * n == n * m
prop_Nat_mul_plus_left_dist (m :: Nat) n o = m * (n + o) == m * n + m * o
prop_Nat_mul_plus_zero (m :: Nat) = m + 0 == m
prop_Nat_mul_mul_unit (m :: Nat) = m * 1 == m
prop_Nat_minus n =
forAll (greaterThanOrEqual n) $ \m ->
(m - n) + n == m
prop_Nat_signum_abs (m :: Nat) = signum m * abs m == m
prop_Nat_signum_zero = (signum 0 :: Nat) == 0
prop_Nat_fromInteger_plus m n =
m >= 0 && n >= 0 ==>
fromInteger m + fromInteger n == (fromInteger (m + n) :: Nat)
prop_Nat_fromInteger_mul m n =
m >= 0 && n >= 0 ==>
fromInteger m * fromInteger n == (fromInteger (m * n) :: Nat)
-- negate is undefined.
-- Testing Integral.
prop_Nat_to_from (m :: Nat) = fromInteger (toInteger m) == m
prop_Nat_from_to i = i >= 0 ==> toInteger (fromInteger i :: Nat) == i
prop_Nat_quotRem (m :: Nat) n =
n /= 0 ==> m `quotRem` n == (m `quot` n, m `rem` n)
prop_Nat_divMod (m :: Nat) n =
n /= 0 ==> m `divMod` n == (m `div` n, m `mod` n)
prop_Nat_quot_rem (m :: Nat) n =
n /= 0 ==> (m `quot` n) * n + m `rem` n == m
prop_Nat_div_mod (m :: Nat) n =
n /= 0 ==> (m `div` n) * n + m `mod` n == m
-- Testing Real.
prop_Nat_toRational (m :: Nat) = toRational m == toInteger m % 1
-- Since the implementation is based on Integers I'd like to test that
-- we can't construct values of the form "Nat i" where i is a negative
-- Integer. (This can be seen as a test of the observation function
-- toInteger.)
prop_Nat_closed = [ unary (fromJust . fromSucc)
-- Ord
, binary max
, binary min
-- Enum
-- enumFrom and friends have default definitions.
, unary succ
, unary pred
, unary' toEnum
-- Num
, binary (+)
, binary (-)
, binary (*)
, unary negate
, unary abs
, unary signum
, unary' fromInteger
-- Integral
, binary quot
, binary rem
, binary div
, binary mod
, binary (fst .^^ quotRem)
, binary (snd .^^ quotRem)
, binary (fst .^^ divMod)
, binary (snd .^^ divMod)
]
where
ok (n :: Nat) = (toInteger n >= 0) <=! True
unary (f :: Nat -> Nat) = unary' f
unary' f =
forAll arbitrary $ \x ->
ok (f x)
binary f =
forAll arbitrary $ \(m :: Nat) ->
forAll arbitrary $ \(n :: Nat) ->
ok (f m n)
f .^^ g = \x y -> f (g x y)
-- | All tests collected together.
tests :: IO Bool
tests = runQuickCheckTests theTests
where
theTests = map run (concat testLists) ++ singleTests
singleTests =
[ run prop_isSucc
, run prop_fromSucc
, run prop_natrec_add
, run prop_Nat_Enum_succ
, run prop_Nat_Enum_pred
, run prop_Nat_Enum_toEnum
, run prop_Nat_Enum_fromEnum
, run prop_Nat_Show
, run prop_Nat_mul_iterated_sum
, run prop_Nat_plus_assoc
, run prop_Nat_plus_comm
, run prop_Nat_mul_assoc
, run prop_Nat_mul_comm
, run prop_Nat_mul_plus_left_dist
, run prop_Nat_mul_plus_zero
, run prop_Nat_mul_mul_unit
, run prop_Nat_minus
, run prop_Nat_signum_abs
, run prop_Nat_signum_zero
, run prop_Nat_fromInteger_plus
, run prop_Nat_fromInteger_mul
, run prop_Nat_to_from
, run prop_Nat_from_to
, run prop_Nat_quotRem
, run prop_Nat_divMod
, run prop_Nat_quot_rem
, run prop_Nat_div_mod
, run prop_Nat_toRational
]
testLists =
[ prop_Nat_Eq_congruence
, prop_Nat_Ord_total_order
, prop_Nat_closed
]
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/SemanticOrd/ 0000755 0000000 0000000 00000000000 12772503660 021051 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Test/ChasingBottoms/SemanticOrd/Tests.hs 0000644 0000000 0000000 00000011145 12772503660 022511 0 ustar 00 0000000 0000000 {-# LANGUAGE RankNTypes #-}
-- | Tests for "Test.ChasingBottoms.SemanticOrd". The functions using
-- tweaks are currently not tested.
module Test.ChasingBottoms.SemanticOrd.Tests (tests) where
import Test.ChasingBottoms.SemanticOrd
import Test.ChasingBottoms.TestUtilities
import Test.ChasingBottoms.TestUtilities.Generators hiding (tests)
import Test.QuickCheck
import Data.Generics
import Control.Monad
import Data.Maybe
------------------------------------------------------------------------
-- The actual tests
prop_SemanticEq_congruence :: (Data a, Show a)
=> Gen a
-> NotEqualGen a
-> Cogen a
-> [Property]
prop_SemanticEq_congruence element notEqualTo coGen =
isCongruence element return notEqualTo (==!) (/=!)
(function coGen integer) (==!)
prop_SemanticOrd_partial_order :: (Data a, Show a)
=> Gen a
-> NotEqualGen a
-> GreaterEqualGen a
-> JoinableGen a
-> [Property]
prop_SemanticOrd_partial_order element notEqualTo greaterThan joinable =
isPartialOrder element return notEqualTo greaterThan (==!) (<=!) ++
isPartialOrderOperators element greaterThan (==!) (<=!) (=!) (>!) ++
[ compare
, meet_associative, meet_commutative, meet_idempotent, meet_lt
, join_associative, join_commutative, join_idempotent, join_lt
, join_meet_absorption, meet_join_absorption
]
where
twoElems = pair3 element greaterThan
compare =
forAll twoElems $ \(x, y) ->
case semanticCompare noTweak x y of
Nothing -> not (x <=! y) && not (x >=! y)
Just LT -> x x ==! y
Just Prelude.GT -> x >! y
meet_associative = isAssociative (oneof [ liftM3 (,,) element element element
, triple element joinable joinable
]
)
(==!) (/\!)
meet_commutative = isCommutative (oneof [ liftM2 (,) element element
, pair element joinable
]
)
(==!) (/\!)
meet_idempotent = isIdempotent element (==!) (/\!)
join_associative =
forAll (triple element joinable joinable) $ \(x, y, z) ->
(x \/! y >>= (\/! z)) ==! ((x \/!) =<< y \/! z)
join_commutative = isCommutative (pair element joinable) (==!) (\/!)
join_idempotent =
forAll element $ \x ->
x \/! x ==! Just x
join_meet_absorption =
forAll jmPair $ \(x, y) ->
x \/! (x /\! y) ==! Just x
where jmPair = oneof [ liftM2 (,) element element
, pair element joinable
]
meet_join_absorption =
forAll (pair element joinable) $ \(x, y) ->
x /\! fromJust (x \/! y) ==! x
twoElems' = frequency [ (2, twoElems), (1, pair element joinable) ]
meet_lt =
forAll twoElems' $ \(x, y) ->
(x <=! y) == (x /\! y ==! x)
join_lt =
forAll twoElems' $ \(x, y) ->
(x <=! y) == (x \/! y ==! Just y)
-- | All tests collected together.
tests :: IO Bool
tests = runQuickCheckTests $ map run $ concat theTests
where
theTests =
[ prop_SemanticEq_congruence bool neBool coBool
, prop_SemanticEq_congruence integer neInteger coInteger
, prop_SemanticEq_congruence (finiteListOf bool)
(neListOf bool neBool finiteListOf)
(coListOf coBool)
, prop_SemanticEq_congruence (finiteTreeOf integer)
(neTreeOf integer neInteger finiteTreeOf)
(coTreeOf coInteger)
, prop_SemanticOrd_partial_order bool neBool geBool joinBool
, prop_SemanticOrd_partial_order integer neInteger geInteger joinInteger
, prop_SemanticOrd_partial_order (finiteListOf bool)
(neListOf bool neBool finiteListOf)
(geListOf bool geBool finiteListOf)
(joinListOf bool joinBool finiteListOf)
, prop_SemanticOrd_partial_order (finiteTreeOf integer)
(neTreeOf integer neInteger finiteTreeOf)
(geTreeOf integer geInteger finiteTreeOf)
(joinTreeOf integer joinInteger
finiteTreeOf)
]
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/IsBottom/ 0000755 0000000 0000000 00000000000 12772503660 020401 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Test/ChasingBottoms/IsBottom/Tests.hs 0000644 0000000 0000000 00000004546 12772503660 022050 0 ustar 00 0000000 0000000 {-# LANGUAGE ScopedTypeVariables #-}
-- The code below intentionally triggers some GHC warnings, so these
-- warnings are turned off.
{-# OPTIONS_GHC -fno-warn-missing-methods -fno-warn-missing-fields #-}
-- | Tests of the functions in "Test.ChasingBottoms.IsBottom".
--
-- Note that the warnings given when compiling this module are
-- intentional. See the internal comments for more information.
module Test.ChasingBottoms.IsBottom.Tests (tests) where
import Test.ChasingBottoms.IsBottom
import System.IO.Unsafe
import Data.Array
import System.Exit
import qualified Control.Exception as E
isException f = unsafePerformIO $
(E.evaluate f >> return False)
`E.catch` (\(_ :: E.SomeException) -> return True)
bot = bot
notbot x = notbot x
data T' a = L' | B' (T' a) (T' a) deriving Eq
instance Functor T'
leftInfinite' = B' leftInfinite' L'
infiniteRecursion = leftInfinite' == leftInfinite'
data A2 = A2 { aaa :: A2 } | C { ccc :: A2 }
tests :: [Bool]
tests =
-- Basic cases.
[ isBottom bottom
, isBottom undefined
, isBottom (error "...")
-- This sometimes leads to a stack overflow.
-- , isBottom bot
-- const bottom /= bottom.
, not (isBottom notbot)
, not (isBottom (const bottom))
-- Other types also lifted.
, not (isBottom (bottom, bottom))
, not (isBottom (Just bottom))
-- Pattern match failure.
, isBottom (let (x, y) = bottom in x :: Bool)
, isBottom (let Just x = Nothing in x :: Char)
-- Nonterminating, but not bottom.
, not (isBottom [1..])
-- Missing methods.
-- Skip this test to avoid compiler warnings.
, isBottom (fmap id L')
-- Array stuff.
, isBottom (array (1,0) [] ! 0)
, isBottom (array (0,0) [] ! 0)
-- Record stuff.
-- Skip the first one to avoid compiler warnings.
, isBottom (let x = A2 {} in aaa x)
, isBottom (let x = A2 { aaa = x } in ccc x)
, isBottom (let x = A2 { aaa = x } in x { ccc = x })
-- Infinite recursion, no data produced, should yield stack
-- overflow...
-- Not a quick test (on some machines, anyway). And the result
-- might be optimisation dependent.
-- , isException (isBottom infiniteRecursion)
-- Some other exceptions that are not caught, including
-- nonBottomError.
, isException (isBottom (unsafePerformIO $ exitWith ExitSuccess))
, isException (isBottom (1 `div` 0))
, isException (nonBottomError "...")
]
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/Approx/ 0000755 0000000 0000000 00000000000 12772503660 020112 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Test/ChasingBottoms/Approx/Tests.hs 0000644 0000000 0000000 00000013752 12772503660 021560 0 ustar 00 0000000 0000000 {-# LANGUAGE ScopedTypeVariables, RankNTypes,
DeriveDataTypeable #-}
-- | Tests of the functions in "Test.ChasingBottoms.Approx".
module Test.ChasingBottoms.Approx.Tests (tests) where
-- Improve the testing here. (Use QuickCheck when there is some proper
-- infrastructure for testing bottoms and infinite stuff. Hmm... This
-- module is part of that infrastructure, so be careful.)
import Test.ChasingBottoms.Approx
import Test.ChasingBottoms.IsBottom
import Test.ChasingBottoms.SemanticOrd
import Test.ChasingBottoms.Nat
import Data.Generics
data Tree = Lf | Br Tree Tree deriving (Typeable, Data)
leftInfinite = Br leftInfinite Lf
twoLevels = Br (Br bottom bottom) Lf
threeLevels = Br (Br (Br bottom bottom) Lf) Lf
-- A nested type:
data PerfectTree t = PL t | PB (PerfectTree (t, t))
deriving (Show, Typeable, Data)
pTree :: PerfectTree Int
pTree = PB (PB (PL ((1, 2), (3, 4))))
-- Full form of PerfectTree: PT A = Lift (A + PT (Lift (A x A))).
-- Define F G A = Lift (A + G (Lift (A x A))).
type F g a = Either a (g (a, a))
-- Assume that F is locally continuous. We have PT = mu F = F (mu F),
-- i.e. PT a = F PT a, with operations
-- in :: F PT a -> PT a
-- out :: PT a -> F PT a
-- map :: (forall a . G a -> G' a) -> F G a -> F G' a
in_PT :: F PerfectTree t -> PerfectTree t
in_PT x = case x of
Left t -> PL t
Right tt -> PB tt
out_PT :: PerfectTree t -> F PerfectTree t
out_PT x = case x of
PL t -> Left t
PB tt -> Right tt
-- Pattern type signature added just for clarity.
map_PT :: (forall t . g t -> g' t) -> F g t' -> F g' t'
map_PT f x = case x of
Left t -> Left t
Right (tt :: g (t, t)) -> Right (f tt)
-- Note that we get a boring map using this kind of functor for nested
-- types:
fullMap_PT :: (forall a . a -> a) -> PerfectTree a -> PerfectTree a
fullMap_PT f = in_PT . map_PT (fullMap_PT f) . out_PT
-- And now we can define approx for this type:
approx_PT :: Nat -> PerfectTree a -> PerfectTree a
approx_PT n | n == 0 = error "approx 0 == _|_"
| otherwise = in_PT . map_PT (approx_PT (pred n)) . out_PT
-- Some types with several parameters.
data A a b = A0 a | A1 b deriving (Typeable, Data)
data C a b = C0 (C a b) | C1 a b deriving (Typeable, Data)
-- Mutually recursive types:
data G a = G1 a | G2 (H a) deriving (Typeable, Data)
data H a = H1 (G a) | H2 a deriving (Typeable, Data)
{-
GH a (r1, r2) = (Lift (a + r2), Lift (r1 + a))
G a = fst (mu (GH a))
H a = snd (mu (GH a))
--> is used for arrows in the product category:
(a1, a2) --> (b1, b2) = (a1 -> b1, a2 -> b2)
in :: GH a (mu (GH a)) --> mu (GH a)
out :: GH a (mu (GH a)) <-- mu (GH a)
map_GH :: (p1 --> p2) -> (GH a p1 --> GH a p2)
-}
-- The following is an approximation, since we don't have proper
-- products. However, if no one breaks the abstraction this won't be a
-- problem.
-- Sadly I cannot write "type GH a (r1, r2) = (Either a r2, Either r1 a)".
type GH a r1 r2 = (Either a r2, Either r1 a)
type M a = (G a, H a)
-- And "type (a1, a2) :--> (b1, b2) = (a1 -> b1, a2 -> b2)" doesn't
-- work either...
type ProdArr a1 a2 b1 b2 = (a1 -> b1, a2 -> b2)
-- in_GH :: GH a (M a) :--> M a
in_GH :: ProdArr (Either a (H a)) (Either (G a) a) (G a) (H a)
in_GH = (in_G, in_H)
where
in_G e = case e of
Left a -> G1 a
Right m -> G2 m
in_H e = case e of
Left m -> H1 m
Right a -> H2 a
-- out_GH :: M a :--> GH a (M a)
out_GH :: ProdArr (G a) (H a) (Either a (H a)) (Either (G a) a)
out_GH = (out_G, out_H)
where
out_G m = case m of
G1 a -> Left a
G2 m -> Right m
out_H m = case m of
H1 m -> Left m
H2 a -> Right a
-- map_GH :: ((a1, a2) :--> (b1, b2)) -> (GH a a1 a2 :--> GH a b1 b2)
map_GH :: ProdArr a1 a2 b1 b2 -> ProdArr (Either a a2) (Either a1 a)
(Either a b2) (Either b1 a)
map_GH gh = (map_G, map_H)
where
(g, h) = gh
map_G e = case e of
Left a -> Left a
Right a2 -> Right (h a2)
map_H e = case e of
Left a1 -> Left (g a1)
Right a -> Right a
(.*.) :: ProdArr b1 b2 c1 c2 -> ProdArr a1 a2 b1 b2 -> ProdArr a1 a2 c1 c2
(g1, h1) .*. (g2, h2) = (g1 . g2, h1 . h2)
-- approx_GH :: Nat -> (M a :--> M a)
approx_GH :: Nat -> ProdArr (G a) (H a) (G a) (H a)
approx_GH n | n == 0 = error "approx 0 == _|_"
| otherwise = in_GH .*. map_GH (approx_GH (pred n)) .*. out_GH
approx_G :: Nat -> G a -> G a
approx_G = fst . approx_GH
approx_H :: Nat -> H a -> H a
approx_H = snd . approx_GH
g1 = G2 (H1 (G2 (H2 'a')))
h1 = H1 (G2 (H1 (G1 'b')))
tests :: [Bool]
tests =
-- approx 0 = bottom.
[ approx 0 ==! (bottom :: Int -> Int)
, approx 0 ==! (bottom :: Char -> Char)
, approx 0 True ==! (bottom :: Bool)
-- approx (Succ n) /= bottom.
, approx 1 /=! (bottom :: Int -> Int)
, approx 1 /=! (bottom :: Char -> Char)
-- approx n descends n levels.
, approx 3 "test" ==! "tes" ++ bottom
, approx 3 "tes" ==! "tes" ++ bottom
, approx 3 "te" ==! "te"
, approx 3 "t" ==! "t"
-- This also works for infinite and multiply branching
-- structures.
, approx 2 leftInfinite ==! twoLevels
, approx 3 leftInfinite ==! threeLevels
-- Multiple parameter data types shouldn't pose a problem.
, approx 1 (A0 (A1 True) :: A (A Char Bool) Char) ==! A0 (A1 True)
, approx 2 (C0 (C1 'a' True)) ==! C0 (C1 'a' True)
, approx 1 (C0 (C1 'a' True)) ==! C0 bottom
-- Multiple parameter data types shouldn't pose a problem for
-- approxAll either.
, approxAll 1 (A0 (A1 True) :: A (A Char Bool) Char) ==! A0 bottom
, approxAll 1 (C0 (C1 'a' True)) ==! C0 bottom
-- approxAll doesn't descend only on the original type...
, approxAll 1 (Just (Just (Just True))) ==! (Just bottom)
, approxAll 2 pTree ==! approx_PT 2 pTree
, approxAll 2 g1 ==! approx_G 2 g1
-- ...but approx does...
, approx 1 (Just (Just (Just True))) ==! (Just (Just (Just True)))
-- ...more or less:
, approx 2 pTree /=! approx_PT 2 pTree
, approx 2 g1 /=! approx_G 2 g1
-- Note that a perfect implementation would have equalities here.
]
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/TestUtilities/ 0000755 0000000 0000000 00000000000 12772503660 021454 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Test/ChasingBottoms/TestUtilities/Generators.hs 0000644 0000000 0000000 00000030371 12772503660 024125 0 ustar 00 0000000 0000000 {-# LANGUAGE CPP, RankNTypes, DeriveDataTypeable #-}
-- | Generators that are part of the testing framework.
-- This module contains _many_ generators. Maybe they should be
-- exported, not just from this module, but from the library as well.
module Test.ChasingBottoms.TestUtilities.Generators
( -- * Basic types and functions
Cogen
, function
, NotEqualGen
, GreaterEqualGen
, JoinableGen
-- ** @Bool@ generators
, bool
, coBool
, neBool
, geBool
, joinBool
-- ** @Integer@ generators
, integer
, coInteger
, neInteger
, geInteger
, joinInteger
-- ** @[]@ generators
, finiteListOf
, infiniteListOf
, coListOf
, neListOf
, geListOf
, joinListOf
-- ** @Tree@ generators
, Tree(..)
, finiteTreeOf
, infiniteTreeOf
, coTreeOf
, neTreeOf
, geTreeOf
, joinTreeOf
-- * Tests of the generators
, tests
) where
import Test.ChasingBottoms.IsBottom
import Test.ChasingBottoms.SemanticOrd
import Test.ChasingBottoms.TestUtilities
import Test.QuickCheck
#if MIN_VERSION_QuickCheck(2,7,0)
hiding (infiniteListOf)
#endif
#if MIN_VERSION_QuickCheck(2,7,0)
import Test.QuickCheck.Gen.Unsafe (promote)
#endif
import Data.Generics
import Control.Monad
import Data.Maybe
import Test.ChasingBottoms.ApproxShow
import Test.ChasingBottoms.Nat
------------------------------------------------------------------------
-- Data types
-- | Binary trees with information in the leaves.
data Tree a
= Branch (Tree a) (Tree a)
| Leaf a
deriving (Show, Typeable, Data)
------------------------------------------------------------------------
-- Basic generators
integer :: Gen Integer
integer = frequency [ (1, return bottom), (10, arbitrary) ]
bool :: Gen Bool
bool = elements [bottom, False, True]
finiteListOf :: Gen a -> Gen [a]
finiteListOf gen = sized finList
where
finList size | size == 0 = baseCase
| otherwise =
frequency [ (1, baseCase)
, (10, do elem <- gen
l <- finList (size - 1)
return (elem : l)
)
]
baseCase = elements [bottom, []]
finiteTreeOf :: Gen a -> Gen (Tree a)
finiteTreeOf gen = sized finTree
where
finTree size | size == 0 = baseCase
| otherwise =
frequency [ (1, baseCase)
, (2, do left <- finTree (size `div` 2)
right <- finTree (size `div` 2)
return (Branch left right)
)
]
baseCase = frequency [(1, bottom), (3, liftM Leaf gen)]
-- | Definitely infinite lists.
infiniteListOf :: Gen a -> Gen [a]
infiniteListOf gen = liftM2 (:) gen (infiniteListOf gen)
-- | Possibly infinite trees.
infiniteTreeOf :: Gen a -> Gen (Tree a)
infiniteTreeOf gen = infTree
where
infTree = frequency [ (1, return bottom)
, (1, liftM Leaf gen)
, (3, liftM2 Branch infTree infTree)
]
testGen :: (Show a, Data a) => Nat -> Gen a -> IO ()
testGen depth gen = quickCheck $ forAll gen $ \n ->
collect (approxShow depth n) $ True
------------------------------------------------------------------------
-- Cogenerators
-- | A mapping from an argument to a generator transformer, like the
-- 'coarbitrary' function.
--
-- Note that the functions generated by the cogenerators in this
-- module are not necessarily monotone.
type Cogen a = forall b. a -> Gen b -> Gen b
coBool :: Cogen Bool
coBool b | isBottom b = variant 0
coBool False = variant 1
coBool True = variant 2
coInteger :: Cogen Integer
coInteger i | isBottom i = variant 0
| otherwise = variant 1 . coarbitrary i
coListOf :: Cogen a -> Cogen [a]
coListOf cog xs | isBottom xs = variant 0
coListOf cog [] = variant 1
coListOf cog (x:xs) = variant 2 . cog x . coListOf cog xs
coTreeOf :: Cogen a -> Cogen (Tree a)
coTreeOf cog xs | isBottom xs = variant 0
coTreeOf cog (Leaf x) = variant 1 . cog x
coTreeOf cog (Branch l r) = variant 2 . coTreeOf cog l . coTreeOf cog r
-- | Given a 'Cogen' and a 'Gen', generate a function.
-- Note that the functions generated by 'promote' below are all
-- non-bottom.
function :: Cogen a -> Gen b -> Gen (a -> b)
function coGen gen = frequency [ (1, return bottom)
, (50, promote (\a -> coGen a gen))
]
testFunction :: (Data a, Data b) => Nat -> Cogen a -> Gen b -> [a] -> IO ()
testFunction depth coGen gen inputs =
quickCheck $ forAll (function coGen gen) $ \f ->
collect (map (\x -> approxShow depth (x, f x)) inputs) $ True
------------------------------------------------------------------------
-- Generators for element not equal to argument
-- | Mapping from argument to generator of elements not equal to
-- argument.
type NotEqualGen a = a -> Gen a
neBool :: NotEqualGen Bool
neBool b | isBottom b = elements [False, True]
neBool False = elements [bottom, True]
neBool True = elements [bottom, False]
neInteger :: NotEqualGen Integer
neInteger i | isBottom i = arbitrary
| otherwise =
frequency [ (1, return bottom)
, (10, do j <- arbitrary
let j' = if j >= 0 then j + 1 else j - 1
return (i + j')
)
]
neListOf :: Gen a -> NotEqualGen a -> (Gen a -> Gen [a]) -> NotEqualGen [a]
neListOf gen neg listOf xs = neList xs
where
neList xs
| isBottom xs = frequency [ (1, return []), (10, nonEmpty gen) ]
| otherwise = case xs of
[] -> frequency [ (1, return bottom), (10, nonEmpty gen) ]
(y:ys) -> frequency [ (1, return bottom)
, (1, return [])
, (5, nonEmpty (neg y))
, (5, do y' <- neg y
return (y':ys)
)
, (5, do ys' <- neList ys
return (y:ys')
)
]
nonEmpty headGen = do x <- headGen
xs <- listOf gen
return (x:xs)
neTreeOf :: Gen a
-> NotEqualGen a
-> (Gen a -> Gen (Tree a))
-> NotEqualGen (Tree a)
neTreeOf gen neg treeOf t = neTree t
where
neTree t
| isBottom t = frequency [ (1, leaf gen), (10, node) ]
| otherwise = case t of
Leaf x -> frequency [ (1, smallTreeNE x), (2, node) ]
Branch l r -> frequency [ (1, return bottom)
, (2, leaf gen)
, (2, do l' <- neTree l
return (Branch l' r)
)
, (2, do r' <- neTree r
return (Branch l r')
)
, (2, do l' <- neTree l
r' <- node
return (Branch l' r')
)
, (2, do l' <- node
r' <- neTree r
return (Branch l' r')
)
]
leaf g = liftM Leaf g
smallTreeNE x = frequency [(1, return bottom), (3, leaf (neg x))]
node = do l <- treeOf gen
r <- treeOf gen
return (Branch l r)
prop_notEqualGen element gen =
forAll (pair element gen) $ \(x, y) ->
x /=! y
testGenPair :: (Show a, Data a) => Nat -> Gen a -> (a -> Gen a) -> IO ()
testGenPair depth gen gen' = quickCheck $
forAll (pair gen gen') $ \(x, y) ->
collect (approxShow depth (x, y)) $ True
------------------------------------------------------------------------
-- Generators for element greater than or equal to argument
-- | Mapping from argument to generator of elements greater than or
-- equal to argument.
type GreaterEqualGen a = a -> Gen a
-- | 'GreaterEqualGen' for flat CPOs.
flatGEGen :: Gen a -> GreaterEqualGen a
flatGEGen gen x | isBottom x = gen
| otherwise = return x
geBool :: GreaterEqualGen Bool
geBool = flatGEGen bool
geInteger :: GreaterEqualGen Integer
geInteger = flatGEGen integer
geListOf :: Gen a
-> GreaterEqualGen a
-> (Gen a -> Gen [a])
-> GreaterEqualGen [a]
geListOf gen geGen listOf xs
| isBottom xs = listOf gen
| otherwise = case xs of
[] -> return []
y:ys -> do y' <- geGen y
ys' <- geListOf gen geGen listOf ys
return (y':ys')
geTreeOf :: Gen a
-> GreaterEqualGen a
-> (Gen a -> Gen (Tree a))
-> GreaterEqualGen (Tree a)
geTreeOf gen geGen treeOf t
| isBottom t = treeOf gen
| otherwise = case t of
Leaf x -> liftM Leaf (geGen x)
Branch l r -> do l' <- geTreeOf gen geGen treeOf l
r' <- geTreeOf gen geGen treeOf r
return (Branch l' r')
prop_greaterEqualGen element gen =
forAll (pair element gen) $ \(x, y) ->
x <=! y
------------------------------------------------------------------------
-- Generators for pairs whose components' join exists
-- | Mapping from argument to generator of elements whose join with
-- the argument is likely to exist.
--
-- Note that the meet of these elements is also likely to be
-- \"interesting\".
type JoinableGen a = a -> Gen a
-- | 'JoinableGen' for flat CPOs.
flatJoinGen :: Gen a -> JoinableGen a
flatJoinGen gen x | isBottom x = gen
| otherwise = frequency [(1, return bottom), (4, return x)]
joinBool :: JoinableGen Bool
joinBool = flatJoinGen bool
joinInteger :: JoinableGen Integer
joinInteger = flatJoinGen integer
joinListOf :: Gen a -> JoinableGen a -> (Gen a -> Gen [a]) -> JoinableGen [a]
joinListOf gen joinGen listOf xs
| isBottom xs = listOf gen
| otherwise = case xs of
[] -> frequency [(1, return bottom), (4, return [])]
y:ys -> frequency [ (1, return bottom)
, (10, do y' <- joinGen y
ys' <- joinListOf gen joinGen listOf ys
return (y':ys')
)
]
joinTreeOf :: Gen a
-> JoinableGen a
-> (Gen a -> Gen (Tree a))
-> JoinableGen (Tree a)
joinTreeOf gen joinGen treeOf t
| isBottom t = treeOf gen
| otherwise = case t of
Leaf x -> frequency [(1, return bottom), (4, liftM Leaf (joinGen x))]
Branch l r -> frequency [ (1, return bottom)
, (5, do l' <- joinTreeOf gen joinGen treeOf l
r' <- joinTreeOf gen joinGen treeOf r
return (Branch l' r')
)
]
prop_joinableGen element gen =
forAll (pair element gen) $ \(x, y) ->
isJust (x \/! y)
------------------------------------------------------------------------
-- | All tests collected together.
tests :: IO Bool
tests = runQuickCheckTests $ map run theTests
where
theTests =
[ prop_notEqualGen bool neBool
, prop_notEqualGen integer neInteger
, prop_notEqualGen (finiteListOf bool)
(neListOf bool neBool finiteListOf)
, prop_notEqualGen (finiteTreeOf integer)
(neTreeOf integer neInteger finiteTreeOf)
, prop_greaterEqualGen bool geBool
, prop_greaterEqualGen integer geInteger
, prop_greaterEqualGen (finiteListOf bool)
(geListOf bool geBool finiteListOf)
, prop_greaterEqualGen (finiteTreeOf integer)
(geTreeOf integer geInteger finiteTreeOf)
, prop_joinableGen bool joinBool
, prop_joinableGen integer joinInteger
, prop_joinableGen (finiteListOf bool)
(joinListOf bool joinBool finiteListOf)
, prop_joinableGen (finiteTreeOf integer)
(joinTreeOf integer joinInteger finiteTreeOf)
]
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/ContinuousFunctions/ 0000755 0000000 0000000 00000000000 12772503660 022700 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Test/ChasingBottoms/ContinuousFunctions/Tests.hs 0000644 0000000 0000000 00000016255 12772503660 024347 0 ustar 00 0000000 0000000 {-# LANGUAGE ScopedTypeVariables, DeriveDataTypeable #-}
-- TODO: Tests passed even though for finiteTreeOf and finiteListOf
-- transform was only applied once at the top-level!
-- | Tests for "Test.ChasingBottoms.ContinuousFunctions". So far the
-- tests are rather weak.
module Test.ChasingBottoms.ContinuousFunctions.Tests (tests) where
import Test.ChasingBottoms.ContinuousFunctions
import Test.ChasingBottoms.IsBottom
import Test.ChasingBottoms.SemanticOrd
import Test.ChasingBottoms.TestUtilities
import qualified Test.ChasingBottoms.TestUtilities.Generators as Gen
import Test.ChasingBottoms.TestUtilities.Generators (Tree(..))
import Test.ChasingBottoms.ApproxShow
import Data.Generics
import Test.QuickCheck
import Test.ChasingBottoms.TestUtilities
import Control.Arrow
import Control.Monad
import Data.List
import Data.Ratio
------------------------------------------------------------------------
-- Example data type
finiteTreeOf :: MakeResult a -> MakeResult (Tree a)
finiteTreeOf makeResult = sized' tree
where
tree size = transform $
if size == 0 then
baseCase
else
frequency' [ (1, baseCase)
, (1, liftM2 Branch tree' tree')
]
where
tree' = tree (size `div` 2)
baseCase =
frequency' [ (1, return bottom)
, (2, liftM Leaf makeResult)
]
------------------------------------------------------------------------
-- Helpers
integer :: Gen Integer
integer = frequency [ (1, return bottom)
, (9, arbitrary)
]
length' :: Num b => [a] -> b
length' xs | isBottom xs = 0
length' [] = 1
length' (x:xs) = 1 + length' xs
depth :: (Ord b, Num b) => Tree a -> b
depth t | isBottom t = 0
depth (Leaf {}) = 1
depth (Branch l r) = 1 + (depth l `max` depth r)
------------------------------------------------------------------------
-- Tests
-- Interesting properties for the function generators:
--
-- * Surjectivity.
--
-- * Decent distribution.
--
-- How do we test these properties?
testDistribution test t = do
result <- run t
let (ok, msg) = apply test result
unless ok $ putStrLn msg
return ok
where
apply test Success{labels = labels} = test labels
apply _ _ = (False, "Test failed.")
spread labels = (uniqueShare >= 3%4, "uniqueShare: " ++ show uniqueShare)
where
noUniqueArgs = length labels
noArgs = sum $ map snd labels
uniqueShare = noUniqueArgs % noArgs
len max avg short labels =
( maxLen >= max && averageLen >= avg && shortShare >= 1%10
, "maxLen: " ++ show maxLen ++
", averageLen: " ++ show averageLen ++
", shortShare: " ++ show shortShare
)
where
lengths = map (read *** toInteger) labels :: [(Integer, Integer)]
noArgs = sum (map snd lengths)
maxLen = maximum $ map fst lengths
averageLen = sum (map (uncurry (*)) lengths) % noArgs
noShortLists = sum . map snd . filter ((<= short) . fst) $ lengths
shortShare = noShortLists % noArgs
-- | We want to make sure that we can generate many different kinds of
-- lazy functions.
prop_many_functions_rather_lazy = testDistribution spread $
forAll (functionTo (finiteTreeOf (finiteTreeOf flat))) $
\(f :: Tree Integer -> Tree (Tree Bool)) ->
f bottom /=! bottom && f (Leaf bottom)
collect (map (approxShow 100 . f) [bottom, Leaf bottom, Leaf 1]) $
True
-- | The generated lists should not be too short.
prop_lists_have_decent_length = testDistribution (len 20 5 5) $
forAll (functionTo (finiteListOf flat)) $ \(f :: Integer -> [Bool]) ->
forAll integer $ \(i :: Integer) ->
collect (length' (f i) :: Integer) $
True
-- | The generated trees should not be too shallow.
prop_trees_have_decent_depth = testDistribution (len 6 2 2) $
forAll (functionTo (finiteTreeOf flat)) $ \(f :: Integer -> Tree Bool) ->
forAll integer $ \(i :: Integer) ->
collect (depth (f i) :: Integer) $
True
-- | In one version of Data.Generics the following equations were
-- valid:
--
-- * @'toConstr' ('bottom' :: ()) = 'toConstr' ()@
--
-- * @'toConstr' ('bottom' :: One) = _|_@
--
-- 'toConstr' should be strict. There is a workaround for this (using
-- seq) in "Test.ChasingBottoms.ContinuousFunctions", and the
-- following two tests check that this workaround works.
data One
= One
deriving (Typeable, Data)
prop_some_lazy_unit =
forAll (functionTo (finiteTreeOf flat)) $ \(f :: () -> Tree Bool) ->
f bottom
True
prop_some_lazy_One =
forAll (functionTo (finiteTreeOf flat)) $ \(f :: One -> Tree Bool) ->
f bottom
True
-- | Example from documentation. Here mostly to check that it type
-- checks.
prop_example_works =
forAll (functionTo (finiteTreeOf flat)) $
\(f :: Bool -> Tree Integer) ->
f bottom <=! f True && f bottom <=! f False
-- | Generated functions should be monotone.
prop_functions_monotone =
forAll (functionTo (finiteListOf flat))
$ \(f :: Tree Integer -> [Bool]) ->
forAll (pair (Gen.finiteTreeOf Gen.integer)
(Gen.geTreeOf Gen.integer Gen.geInteger Gen.finiteTreeOf))
$ \(x, y) ->
x <=! y && f x <=! f y
------------------------------------------------------------------------
-- | All tests collected together.
tests :: IO Bool
tests = do
b1 <- fmap and $ sequence theIOTests
b2 <- runQuickCheckTests $ map run $ concat theTests
return (b1 && b2)
where
theIOTests :: [IO Bool]
theIOTests = []
-- Disabled, because occasionally one or more of the tests failed,
-- and (at the time of writing in 2015) I have no interest in
-- fixing test suite bugs in old, unfinished and experimental
-- code. Known problems:
-- * Division by zero, presumably because noArgs is 0.
-- * After reducing maxSuccess from 1000 to 100 I once observed
-- that "averageLen" was 199 % 100, but if I am not mistaken the
-- test requires it to be >= 2.
-- theIOTests = [ prop_many_functions_rather_lazy
-- , prop_lists_have_decent_length
-- , prop_trees_have_decent_depth
-- ]
theTests :: [[Property]]
theTests = [ [ prop_example_works
, prop_some_lazy_unit
, prop_some_lazy_One
, prop_functions_monotone
]
]
------------------------------------------------------------------------
-- Manual inspection of function tables
viewFun :: (ApproxShow b, Data a) => MakeResult b -> [a] -> IO ()
viewFun (makeResult :: MakeResult b) (inputs :: [a]) = quickCheck $
forAll (functionTo makeResult) $ \(f :: a -> b) ->
collect (map (approxShow 5 . f) inputs) $ True
bool = undefined :: Bool
int = undefined :: Int
float = undefined :: Float
treeOfBool = undefined :: Tree Bool
test0 = viewFun (flat :: MakeResult Bool) [bottom, False, True]
test1 = viewFun (finiteTreeOf flat :: MakeResult (Tree Bool))
[bottom, False, True]
test2 = viewFun (finiteTreeOf flat :: MakeResult (Tree Bool))
[bottom, Leaf bottom, Leaf False]
test4 = viewFun (flat :: MakeResult Int) [bottom, False, True]
test5 = viewFun (flat :: MakeResult Float) [bottom, False, True]
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/IsType/ 0000755 0000000 0000000 00000000000 12772503660 020056 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Test/ChasingBottoms/IsType/Tests.hs 0000644 0000000 0000000 00000001212 12772503660 021510 0 ustar 00 0000000 0000000 -- | Tests of the functions in "Test.ChasingBottoms.IsType".
module Test.ChasingBottoms.IsType.Tests (tests) where
import Test.ChasingBottoms.IsType
tests :: [Bool]
tests =
-- isFunction identifies functions.
[ isFunction (id :: Char -> Char) == True
, isFunction ((==) :: Char -> Char -> Bool) == True
, isFunction 'c' == False
, isFunction [not] == False
, isTuple [not] == False
, isTuple () == False
, isTuple ('a', 'c') == True
, isList "" == True
, isList [not] == True
, isList ('a', 'c') == False
, isString "" == True
, isString [not] == False
, isString ('a', 'c') == False
]
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/TimeOut/ 0000755 0000000 0000000 00000000000 12772503660 020227 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Test/ChasingBottoms/TimeOut/Tests.hs 0000644 0000000 0000000 00000001714 12772503660 021670 0 ustar 00 0000000 0000000 -- | Tests of the functions in "Test.ChasingBottoms.TimeOut".
module Test.ChasingBottoms.TimeOut.Tests (tests) where
-- The "Micro" variants are not tested directly, but they are used
-- internally by the functions below.
import Test.ChasingBottoms.TimeOut
import Test.ChasingBottoms.Approx
import Test.ChasingBottoms.IsBottom
import Test.ChasingBottoms.SemanticOrd
tests :: IO Bool
tests = do
r1 <- timeOut n bottom
r1b <- timeOut n $ return bottom
r2 <- timeOut' n bottom
r3 <- timeOut n $ return list
r4 <- timeOut' n list
r5 <- timeOut n $ return $ reverse list
r6 <- timeOut' n $ reverse list
let result = case (r1, r1b, r2, r3, r4, r5, r6) of
( Exception _, Value b, Exception _, Value xs, Value ys
, Value _nt, NonTermination)
-> isBottom b && xs =~= list && ys =~= list
_ -> False
return result
where n = 1
list = [1..] :: [Integer]
xs =~= ys = appr xs ==! appr ys
appr = approxAll 20
ChasingBottoms-1.3.1.2/Test/ChasingBottoms/ApproxShow/ 0000755 0000000 0000000 00000000000 12772503660 020753 5 ustar 00 0000000 0000000 ChasingBottoms-1.3.1.2/Test/ChasingBottoms/ApproxShow/Tests.hs 0000644 0000000 0000000 00000003034 12772503660 022411 0 ustar 00 0000000 0000000 {-# LANGUAGE DeriveDataTypeable #-}
-- | Tests of the functions in "Test.ChasingBottoms.ApproxShow".
module Test.ChasingBottoms.ApproxShow.Tests (tests) where
import Test.ChasingBottoms.ApproxShow
import Test.ChasingBottoms.IsBottom
import Data.Generics
data T = L | B T T deriving (Typeable, Data)
left = B left L
data Q a = Q a ::: a | Q deriving (Typeable, Data)
pr n x template = do
let s = approxShow n x
putStr $ show (s == template)
putStr " |"
putStr s
putStrLn "|"
tst n x template = approxShow n x == template
tests :: [Bool]
tests =
[ tst 4 left "B (B (B (B _ _) L) L) L"
, tst 4 (bottom :: Bool) "_|_"
, tst 4 not ""
, tst 4 ('a','b') "('a', 'b')"
, tst 1 ('a','b') "(_, _)"
, tst 4 (Q ::: 'a' ::: 'b' ::: 'c') "((Q ::: 'a') ::: 'b') ::: 'c'"
, tst 2 (Q ::: 'a' ::: 'b' ::: 'c') "(_ ::: _) ::: 'c'"
, tst 4 "abc" "\"abc\""
, tst 4 [True, False, False] "[True, False, False]"
, tst 2 "abc" "\"a_"
, tst 2 [True, False, False] "[True, _"
, tst 1 "" "\"\""
, tst 1 ([] :: [Bool]) "[]"
, tst 0 "" "_"
, tst 0 ([] :: [Bool]) "_"
, tst 4 ('a' : bottom : bottom) "\"a_|__|_"
, tst 4 ('a' : bottom : bottom : []) "\"a_|__|_\""
, tst 4 [True, bottom] "[True, _|_]"
, tst 4 (True : bottom : bottom) "[True, _|__|_"
, tst 4 (bottom ::: bottom ::: 'b' ::: 'c') "((_|_ ::: _|_) ::: 'b') ::: 'c'"
, tst 2 ('a' : bottom : bottom) "\"a_"
, tst 2 [True, bottom] "[True, _"
, tst 2 (True : bottom : bottom) "[True, _"
, tst 2 (bottom ::: bottom ::: 'b' ::: 'c') "(_ ::: _) ::: 'c'"
]