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-- | Test copilot-libraries:Copilot.Library.PTLTL
module Test.Copilot.Library.PTLTL
(tests)
where
-- External imports
import Test.Framework (Test, testGroup)
import Test.Framework.Providers.QuickCheck2 (testProperty)
import Test.QuickCheck (Gen, Property)
-- External imports: Copilot
import Copilot.Language (extern)
import qualified Copilot.Language.Operators.Boolean as Copilot
import Copilot.Language.Stream (Stream)
import Copilot.Theorem.What4 (SatResult (..))
-- Internal imports: auxiliary functions
import Test.Extra (arbitraryBoolExpr, testWithInterpreter, testWithTheorem)
-- Internal imports: Modules being tested
import Copilot.Library.PTLTL (eventuallyPrev, previous)
-- * Constants
-- | Unit tests for copilot-libraries:Copilot.Library.PTLTL.
tests :: Test.Framework.Test
tests =
testGroup "Copilot.Library.PTLTL"
[ testProperty "previous x ==> eventuallyPrev x (theorem)"
testProvePreviousEventually
, testProperty "previous x ==> eventuallyPrev x (interpreter)"
testCheckPreviousEventually
]
-- * Individual tests
-- | Test that Z3 is able to prove the following expression valid:
-- @
-- previous x ==> eventuallyPrev x
-- @
testProvePreviousEventually :: Property
testProvePreviousEventually = testWithTheorem pair
where
pair :: Gen (Stream Bool, SatResult)
pair = pure (stream, expectation)
stream :: Stream Bool
stream =
previous boolStream Copilot.==> eventuallyPrev boolStream
where
boolStream = extern "x" Nothing
expectation :: SatResult
expectation = Valid
-- | Test that the following stream is always true:
-- @
-- previous x ==> eventuallyPrev x
-- @
testCheckPreviousEventually :: Property
testCheckPreviousEventually = testWithInterpreter pair
where
pair :: Gen (Stream Bool, [Bool])
pair = do
-- We discard the expectation from the expression; the temporal formula
-- holds at all times regardless.
boolStream <- fst <$> arbitraryBoolExpr
let prop = previous boolStream Copilot.==> eventuallyPrev boolStream
return (prop, expectation)
expectation :: [Bool]
expectation = repeat True
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