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import Test.HUnit
import Library.Command
import Library.TypeVar
import Library.Term
import LibraryTheorem
import qualified Data.Set as Set
stdName :: String -> Name
stdName s = Name [] s
stdType :: Type
stdType = AType [] (TypeOp (stdName "atype"))
stdConst :: Const
stdConst = Const (stdName "const")
stdConstTerm :: Term
stdConstTerm = TConst stdConst stdType
stdTypeVarName :: Name
stdTypeVarName = stdName "typevar"
altTypeVarName :: Name
altTypeVarName = stdName "alttypevar"
stdTypeVar :: Type
stdTypeVar = TypeVar stdTypeVarName
altTypeVar :: Type
altTypeVar = TypeVar altTypeVarName
stdVar :: String -> Var
stdVar s = Var (stdName s) stdTypeVar
stdVarTerm :: String -> Term
stdVarTerm s = TVar (stdVar s)
altVar :: String -> Var
altVar s = Var (stdName s) altTypeVar
altVarTerm :: String -> Term
altVarTerm s = TVar (altVar s)
name1 = TestCase (assertEqual "for (name \"abc\")"
(Just (Name [] "abc"))
(name "\"abc\""))
name2 = TestCase (assertEqual "for (name \"first.second.third\")"
(Just (Name ["first","second"] "third"))
(name "\"first.second.third\""))
name3 = TestCase (assertEqual "for (name \"firs\\t.se\\cond.\\t\\h\\ird\")"
(Just (Name ["first","second"] "third"))
(name "\"firs\\t.se\\cond.\\t\\h\\ird\""))
name4 = TestCase (assertEqual "for (name abc)" Nothing (name "abc"))
number1 = TestCase (assertEqual "for (number \"90\")" (Just 90) (number "90"))
number2 = TestCase (assertEqual "for (number \"0\")" (Just 0) (number "0"))
number3 = TestCase (assertEqual "for (number \"-1\")" (Just (-1)) (number "-1"))
number4 = TestCase (assertEqual "for (number \"-0\")" Nothing (number "-0"))
number5 = TestCase (assertEqual "for (number \"1.2\")" Nothing (number "1.2"))
assume1 = TestCase (assertEqual "for (assume (TConst ...)"
(Just (Theorem (Set.singleton (TConst stdConst typeBool))
(TConst stdConst typeBool)))
(assume (TConst stdConst typeBool)))
assume2 = TestCase (assertEqual "for (assume (TConst ...) --with wrong type"
Nothing
(assume (TConst stdConst stdTypeVar)))
axiom1 = TestCase (assertEqual "for (axiom (TConst ...) [])"
(Just (Theorem Set.empty (TConst stdConst stdTypeVar)))
(axiom (TConst stdConst stdTypeVar) []))
axiom2 = TestCase (assertEqual "for (axiom (TConst ...) [term1, term2] --term1 has wrong type"
Nothing
(axiom (TConst stdConst stdTypeVar)
[(TConst stdConst stdTypeVar),(TConst stdConst typeBool)]))
alphaEquiv1 = TestCase (assertEqual "for ((\\xy -> x) `alphaEquiv` (\\yx -> x))"
False
(alphaEquiv (TAbs (stdVarTerm "x") (TAbs (stdVarTerm "y") (stdVarTerm "x")))
(TAbs (stdVarTerm "y") (TAbs (stdVarTerm "x") (stdVarTerm "x")))))
alphaEquiv2 = TestCase (assertEqual "for ((\\xy -> x) `alphaEquiv` (\\xy -> x))"
True
(alphaEquiv (TAbs (stdVarTerm "x") (TAbs (stdVarTerm "y") (stdVarTerm "x")))
(TAbs (stdVarTerm "x") (TAbs (stdVarTerm "y") (stdVarTerm "x")))))
alphaEquiv3 = TestCase (assertEqual "for ((\\xyx -> x) `alphaEquiv` (\\yxx -> x))"
True
(alphaEquiv (TAbs (stdVarTerm "x") (TAbs (stdVarTerm "y") (TAbs (stdVarTerm "x") (stdVarTerm "x"))))
(TAbs (stdVarTerm "y") (TAbs (stdVarTerm "x") (TAbs (stdVarTerm "x") (stdVarTerm "x"))))))
alphaEquiv4 = TestCase (assertEqual "for ((\\xyz -> y) `alphaEquiv` (\\zyx -> y))"
True
(alphaEquiv (TAbs (stdVarTerm "x") (TAbs (stdVarTerm "y") (TAbs (stdVarTerm "z") (stdVarTerm "y"))))
(TAbs (stdVarTerm "z") (TAbs (stdVarTerm "y") (TAbs (stdVarTerm "x") (stdVarTerm "y"))))))
alphaEquiv5 = TestCase (assertEqual "for ((\\x -> x) `alphaEquiv` (\\x -> x)) --x of lhs is different type to x of rhs"
False
(alphaEquiv (TAbs (stdVarTerm "x") (stdVarTerm "x"))
(TAbs (altVarTerm "x") (altVarTerm "x"))))
alphaEquiv6 = TestCase (assertEqual "for ((TAbs ...) `alphaEquiv` (TConst ...))"
False
(alphaEquiv (TAbs (stdVarTerm "x") (stdVarTerm "x"))
(TConst stdConst typeBool)))
substitute1 = TestCase (assertEqual "for (substitute ([],[(x',a)]) (TVar x'))"
(stdConstTerm)
(substitute ([],[((stdVar "x'"),stdConstTerm)]) (stdVarTerm "x'")))
substitute2 = TestCase (assertEqual "for (substitute ([],[(x',a)]) (TVar y'))"
(stdVarTerm "y'")
(substitute ([],[((stdVar "x'"),stdConstTerm)]) (stdVarTerm "y'")))
substitute3 = TestCase (assertEqual "for (substitute ([],[(x',a)]) (TApp (TVar x') (TVar x')))"
(TApp stdConstTerm stdConstTerm)
(substitute ([],[((stdVar "x'"),stdConstTerm)]) (TApp (stdVarTerm "x'") (stdVarTerm "x'"))))
substitute4 = TestCase (assertEqual "for (substitute ([],[(x',a)]) (\\y' -> x'))"
(TAbs (stdVarTerm "y'") stdConstTerm)
(substitute ([],[((stdVar "x'"),stdConstTerm)]) (TAbs (stdVarTerm "y'") (stdVarTerm "x'"))))
substitute5 = TestCase (assertEqual "for (substitute ([],[(x',y')]) (\\y' -> x'))"
(TAbs (stdVarTerm "y''") (stdVarTerm "y'"))
(substitute ([],[((stdVar "x'"),(stdVarTerm "y'"))]) (TAbs (stdVarTerm "y'") (stdVarTerm "x'"))))
substitute6 = TestCase (assertEqual "for (substitute ([(tx',ta)],[]) (z' with typevar tx'))"
(TVar (Var (stdName "z'") stdType))
(substitute ([(stdTypeVarName,stdType)],[]) (stdVarTerm "z'")))
substitute7 = TestCase (assertEqual "for (substitute ([(tx',ta)],[(y',b)]) (\\z' -> y')) --z' has type tx'"
(TAbs (TVar (Var (stdName "z'") stdType)) stdConstTerm)
(substitute ([(stdTypeVarName,stdType)],[((altVar "y'"),stdConstTerm)]) (TAbs (stdVarTerm "z'") (altVarTerm "y'"))))
substitute8 = TestCase (assertEqual "for (substitute ([],[(x',y'),(y',z')]) (x'))"
(stdVarTerm "z'")
(substitute ([],[((stdVar "x'"),(stdVarTerm "y'")),
((stdVar "y'"),(stdVarTerm "z'"))]) (stdVarTerm "x'")))
substitute9 = TestCase (assertEqual "for (substitute ([(tx',ty'),(ty',ta)],[]) (z' with typevar tx'))"
(TVar (Var (stdName "z'") stdType))
(substitute ([(stdTypeVarName,altTypeVar),(altTypeVarName,stdType)],[]) (stdVarTerm "z'")))
main =
do putStrLn "Command.name"
runTestTT $ TestList [name1,name2,name3,name4]
putStrLn "Command.number"
runTestTT $ TestList [number1,number2,number3,number4,number5]
putStrLn "Command.assume"
runTestTT $ TestList [assume1,assume2]
putStrLn "Command.axiom"
runTestTT $ TestList [axiom1,axiom2]
putStrLn "Term.alphaEquiv"
runTestTT $ TestList [alphaEquiv1,alphaEquiv2,alphaEquiv3,alphaEquiv4,alphaEquiv5,alphaEquiv6]
putStrLn "Term.substitute"
runTestTT $ TestList [substitute1,substitute2,substitute3,substitute4,substitute5,substitute6,substitute7,substitute8,substitute9]
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