717 lines
24 KiB
Plaintext
717 lines
24 KiB
Plaintext
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This module defines test cases for the unification algorithm, divided
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into those which must succeed, those which should block (possibly
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succeeding partially), and those which must fail.
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> module Test where
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> import Unbound.Generics.LocallyNameless
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> import Kit
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> import Tm
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> import Unify
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> import Context
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> import Check
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The |test| function executes the constraint solving algorithm on the
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given metacontext.
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> test :: [Entry] -> IO ()
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> test = runTest (const True)
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Allocate a fresh name so the counter starts from 1, to avoid clashing
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with s2n (which generates names with index 0):
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> initialise :: Contextual ()
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> initialise = (fresh (s2n "init") :: Contextual (Name VAL)) >> return ()
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> runTest :: (ProblemState -> Bool) -> [Entry] -> IO ()
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> runTest q es = do putStrLn $ "Initial context:\n" ++
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> render (runPretty (prettyEntries es))
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> let r = runContextual (B0, map Right es)
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> (initialise >> ambulando [] [] >> validate q)
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> case r of
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> Left err -> putStrLn $ "Error: " ++ err
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> Right ((), cx) -> putStrLn $ "Final context:\n" ++ pp cx ++ "\n"
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> runTestSolved, runTestStuck, runTestFailed :: IO ()
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> runTestSolved = mapM_ (runTest (== Solved)) tests
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> runTestStuck = mapM_ (runTest (not . isFailed)) stucks
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> runTestFailed = mapM_ (runTest isFailed) fails
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> isFailed :: ProblemState -> Bool
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> isFailed (Failed _) = True
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> isFailed _ = False
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> lifted :: Nom -> Type -> [Entry] -> [Entry]
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> lifted x _T es = lift [] es
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> where
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> lift :: Subs -> [Entry] -> [Entry]
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> lift g (E a _A d : as) = E a (_Pi x _T (substs g _A)) d :
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> lift ((a, meta a $$ var x) : g) as
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> lift g (Prob a p s : as) = Prob a (allProb x _T (substs g p)) s : lift g as
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> lift _ [] = []
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> boy :: String -> Type -> [Entry] -> [Entry]
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> boy = lifted . s2n
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> gal :: String -> Type -> Entry
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> gal x _T = E (s2n x) _T HOLE
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> eq :: String -> Type -> VAL -> Type -> VAL -> Entry
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> eq x _S s _T t = Prob (ProbId (s2n x)) (Unify (EQN _S s _T t)) Active
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> tests, stucks, fails :: [[Entry]]
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> tests = [
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> -- test 0: solve B with A
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> ( gal "A" SET
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> : gal "B" SET
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> : eq "p" SET (mv "A") SET (mv "B")
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> : [])
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> -- test 1: solve B with \ _ . A
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> , ( gal "A" SET
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> : gal "B" (mv "A" --> SET)
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> : boy "x" (mv "A")
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> ( eq "p" SET (mv "A") SET (mv "B" $$ vv "x")
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> : [])
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> )
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> -- test 2: restrict B to second argument
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> , ( gal "A" SET
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> : boy "x" (mv "A")
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> ( boy "y" (mv "A")
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> ( gal "B" (mv "A" --> mv "A" --> SET)
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> : eq "p" SET (mv "B" $$$ [vv "y", vv "x"])
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> SET (mv "B" $$$ [vv "x", vv "x"])
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> : [])
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> )
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> )
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> -- test 3: X unchanged
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> , [ gal "X" (_PI "A" SET (vv "A" --> SET))
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> , eq "p" SET (mv "X" $$$ [SET, SET])
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> SET (mv "X" $$$ [SET, SET])
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> ]
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> -- test 4: solve A with SET
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> , [ gal "A" SET
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> , eq "p" SET (mv "A") SET SET
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> ]
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> -- test 5: solve A with B -> B
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> , [ gal "A" SET
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> , gal "B" SET
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> , gal "C" SET
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> , eq "p" SET (mv "A") SET (mv "B" --> mv "B")
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> ]
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> -- test 6: solve A with \ X . B -> X
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> , ( gal "A" (SET --> SET)
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> : gal "B" SET
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> : boy "X" SET
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> ( eq "p" SET (mv "A" $$ vv "X") SET (mv "B" --> vv "X")
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> : [])
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> )
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> -- test 7: solve A with \ _ X _ . B X -> X
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> , ( gal "A" (SET --> SET --> SET --> SET)
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> : gal "B" (SET --> SET)
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> : boy "X" SET
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> ( boy "Y" SET
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> (eq "p" SET (mv "A" $$$ [vv "Y", vv "X", vv "Y"])
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> SET (mv "B" $$ vv "X" --> vv "X")
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> : [])
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> )
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> )
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> -- test 8: solve S with A and T with B
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> , [ gal "A" SET
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> , gal "S" SET
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> , gal "B" (mv "A" --> SET)
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> , gal "T" (mv "S" --> SET)
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> , eq "p" SET (PI (mv "A") (mv "B"))
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> SET (PI (mv "S") (mv "T"))
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> ]
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> -- test 9: solve M with \ y . y
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> , [ gal "M" (SET --> SET)
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> , eq "p" (SET --> SET) (ll "y" (vv "y"))
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> (SET --> SET) (ll "y" (mv "M" $$ vv "y"))
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> ]
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> -- test 10: solve A with \ _ X _ . X -> X and B with \ X _ _ . X
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> , ( gal "A" (SET --> SET --> SET --> SET)
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> : boy "X" SET
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> ( boy "Y" SET
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> ( gal "B" (SET --> SET)
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> : eq "q" SET (mv "A" $$$ [vv "Y", vv "X", vv "Y"])
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> SET (mv "B" $$ vv "Y" --> vv "X")
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> : eq "p" SET (mv "A" $$$ [vv "Y", vv "X", vv "Y"])
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> SET (vv "X" --> vv "X")
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> : [])
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> )
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> )
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> -- test 11: solve A with \ _ y . y
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> , [ gal "A" (_PI "X" SET (vv "X" --> vv "X"))
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> , eq "p" (_PI "X" SET (vv "X" --> vv "X")) (ll "X" (ll "y" (vv "y")))
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> (_PI "X" SET (vv "X" --> vv "X")) (ll "X" (mv "A" $$ vv "X"))
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> ]
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> -- test 12: solve f with \ _ y . y after lifting type
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> , ( gal "f" (_PI "Y" SET (vv "Y" --> vv "Y"))
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> : boy "X" SET
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> ( eq "p" (vv "X" --> vv "X") (ll "y" (vv "y"))
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> (vv "X" --> vv "X") (mv "f" $$ vv "X")
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> : [])
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> )
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> -- test 13: intersection with nonlinearity, restrict F to first two args
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> , ( gal "F" (SET --> SET --> SET --> SET)
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> : boy "X" SET
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> ( boy "Y" SET
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> ( eq "p" SET (mv "F" $$$ [vv "X", vv "X", vv "Y"])
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> SET (mv "F" $$$ [vv "X", vv "X", vv "X"])
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> : [])
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> )
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> )
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> -- test 14: heterogeneous equality; solve A and B with SET
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> , [ gal "A" SET
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> , gal "B" SET
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> , eq "p" (mv "A" --> SET) (ll "a" SET)
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> (mv "B" --> SET) (ll "b" (mv "B"))
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> , eq "q" SET (mv "A") SET (mv "B")
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> ]
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> -- test 15: sigma metavariable; solve A with ((?, Set), ?)
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> , [ gal "A" (_SIG "X" (SET *: SET) (vv "X" %% Tl))
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> , eq "p" SET SET SET (mv "A" %% Hd %% Tl)
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> ]
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> -- test 16: sigma variable; solve A with \ X Y . X * Y
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> , ( gal "A" (SET --> SET --> SET)
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> : boy "B" (_SIG "X" SET (vv "X" *: SET))
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> ( eq "p" SET (mv "A" $$ (vv "B" %% Hd) $$ (vv "B" %% Tl %% Tl))
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> SET ((vv "B" %% Hd) *: (vv "B" %% Tl %% Tl))
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> : [])
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> )
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> -- test 17: sigma variable; restrict A to \ _ X . ?A' X
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> , ( gal "A" (SET --> SET --> SET)
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> : boy "B" (_SIG "X" SET (vv "X" *: SET))
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> ( eq "p" SET (mv "A" $$$ [vv "B" %% Hd, vv "B" %% Tl %% Tl])
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> SET (mv "A" $$$ [vv "B" %% Tl %% Tl, vv "B" %% Tl %% Tl])
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> : [])
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> )
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> -- test 18: sigma variable; solve B with \ X z . ?A X (z -)
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> , ( gal "A" (SET --> SET --> SET)
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> : gal "B" (_PI "X" SET (vv "X" *: SET --> SET))
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> : boy "C" (_SIG "X" SET (vv "X" *: SET))
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> ( eq "p" SET (mv "A" $$$ [vv "C" %% Hd, vv "C" %% Tl %% Tl])
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> SET (mv "B" $$$ [vv "C" %% Hd, vv "C" %% Tl])
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> : [])
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> )
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> -- test 19: sigma metavariable and equation; solve A
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> , [ gal "A" (_SIG "X" SET (vv "X"))
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> , eq "p" (_SIG "X" SET (vv "X" *: SET))
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> (PAIR (mv "A" %% Hd) (PAIR (mv "A" %% Tl) (SET --> SET)))
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> (_SIG "X" SET (vv "X" *: SET))
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> (PAIR (SET --> SET) (PAIR (ll "z" (vv "z")) (mv "A" %% Hd)))
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> ]
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> -- test 20: solve A with X ! and a with X -
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> , ( boy "X" (_SIG "Y" SET (vv "Y"))
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> ( gal "A" SET
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> : gal "a" (mv "A")
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> : eq "p" (_SIG "Y" SET (vv "Y")) (vv "X")
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> (_SIG "Y" SET (vv "Y")) (PAIR (mv "A") (mv "a"))
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> : [])
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> )
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> -- test 21: solve A with f
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> , ( boy "f" (SET --> SET)
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> ( gal "A" (SET --> SET)
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> : eq "p" (SET --> SET) (vv "f")
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> (SET --> SET) (ll "x" (mv "A" $$ vv "x"))
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> : [])
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> )
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> -- test 22: solve A with SET
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> , ( boy "X" ((SET --> SET) *: SET)
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> ( gal "A" SET
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> : eq "p" SET (vv "X" %% Hd $$ SET) SET (vv "X" %% Hd $$ mv "A")
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> : [])
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> )
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> -- test 23: solve SS with [S', S']
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> , ( gal "SS" (SET *: SET)
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> : boy "f" (SET --> SET --> SET)
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> ( eq "p" SET (vv "f" $$$ [mv "SS" %% Tl, mv "SS" %% Hd])
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> SET (vv "f" $$$ [mv "SS" %% Hd, mv "SS" %% Tl])
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> : [])
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> )
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> -- test 24: solve A with SET
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> , [ gal "A" SET
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> , eq "p" (mv "A" --> SET) (ll "a" (mv "A"))
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> (SET --> SET) (ll "a" SET)
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> ]
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> -- test 25: solve with extensionality and refl
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> , [ gal "A" SET
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> , eq "p" (mv "A" --> SET) (ll "x" SET)
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> (SET --> SET) (ll "x" SET)
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> ]
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> -- test 26: solve A with \ _ Y . Y
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> , ( gal "A" (SET --> SET --> SET)
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> : boy "X" SET
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> ( eq "p" (mv "A" $$ vv "X" $$ vv "X" --> SET)
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> (ll "Y" (mv "A" $$ vv "X" $$ vv "Y"))
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> (vv "X" --> SET)
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> (ll "Y" (vv "X"))
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> : [])
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> )
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> -- test 27: solve A with SET
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> , [ gal "A" SET
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> , eq "p" SET (_PI "X" (SET --> SET) (vv "X" $$ mv "A"))
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> SET (_PI "X" (SET --> SET) (vv "X" $$ SET))
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> ]
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> -- test 28: prune and solve A with \ _ . B -> B
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> , ( gal "A" (SET --> SET)
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> : boy "x" (_SIG "Y" SET (vv "Y"))
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> ( gal "B" SET
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> : eq "p" SET (mv "A" $$ (vv "x" %% Hd))
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> SET (mv "B" --> mv "B")
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> : [])
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> )
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> -- test 29: prune A and solve B with A
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> , ( gal "A" (SET --> SET)
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> : gal "B" SET
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> : eq "p" (SET --> SET) (ll "X" (mv "A" $$ (vv "X" --> vv "X")))
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> (SET --> SET) (ll "X" (mv "B"))
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> : [])
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> -- test 30: prune A and solve B with A
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> , ( gal "B" SET
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> : gal "A" (SET --> SET)
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> : eq "p" (SET --> SET) (ll "X" (mv "A" $$ (vv "X" --> vv "X")))
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> (SET --> SET) (ll "X" (mv "B"))
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> : [])
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> -- test 31: solve A with SET and f with \ x . x
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> , ( gal "A" SET
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> : gal "f" (mv "A" --> SET)
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> : eq "p" (mv "A" --> SET) (mv "f")
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> (mv "A" --> mv "A") (ll "x" (vv "x"))
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> : eq "q" SET (mv "A" --> SET) SET (mv "A" --> mv "A")
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> : [])
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> -- test 32: prune B and solve A with B -> B
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> , ( gal "A" SET
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> : gal "B" (SET --> SET)
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> : eq "p" (SET --> SET) (ll "Y" (mv "A"))
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> (SET --> SET) (ll "X" ((mv "B" $$ mv "A") -->
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> (mv "B" $$ vv "X")))
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> : [])
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> -- test 33: eta-contract pi
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> , ( gal "A" ((SET --> SET) --> SET)
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> : boy "f" (SET --> SET)
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|
|
> ( eq "p" SET (mv "A" $$ (ll "y" (vv "f" $$ vv "y")))
|
||
|
|
> SET (vv "f" $$ SET)
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 34: eta-contract sigma
|
||
|
|
> , ( gal "A" (SET *: SET --> SET)
|
||
|
|
> : boy "b" (SET *: SET)
|
||
|
|
> ( eq "p" SET (mv "A" $$ (PAIR (vv "b" %% Hd) (vv "b" %% Tl)))
|
||
|
|
> SET (vv "b" %% Hd)
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 35: eta-contract pi and sigma
|
||
|
|
> , ( gal "A" ((SET *: SET --> SET) --> SET)
|
||
|
|
> : boy "f" (SET *: SET --> SET)
|
||
|
|
> ( eq "p" SET (mv "A" $$ (ll "b" (vv "f" $$ PAIR (vv "b" %% Hd) (vv "b" %% Tl))))
|
||
|
|
> SET (vv "f" $$ PAIR SET SET)
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 36: A/P Flattening Sigma-types
|
||
|
|
> , ( gal "u" ((SET --> SET *: SET) --> SET)
|
||
|
|
> : boy "z1" (SET --> SET)
|
||
|
|
> ( boy "z2" (SET --> SET)
|
||
|
|
> ( eq "p" SET (mv "u" $$ (ll "x" (PAIR (vv "z1" $$ vv "x") (vv "z2" $$ vv "x"))))
|
||
|
|
> SET SET
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 37: A/P Eliminating projections
|
||
|
|
> , ( gal "u" ((SET --> SET) --> SET)
|
||
|
|
> : boy "y" (SET --> SET *: SET)
|
||
|
|
> ( eq "p" SET (mv "u" $$ (ll "x" (vv "y" $$ vv "x" %% Hd)))
|
||
|
|
> SET (vv "y" $$ SET %% Hd)
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 38: prune A and solve B with A
|
||
|
|
> , ( gal "B" SET
|
||
|
|
> : gal "A" (SET --> SET)
|
||
|
|
> : eq "p" (SET --> SET) (ll "X" (mv "B"))
|
||
|
|
> (SET --> SET) (ll "X" (mv "A" $$ (vv "X" --> vv "X")))
|
||
|
|
>
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> -- test 39: solve u with \ _ x . x
|
||
|
|
> , ( gal "u" (_PI "v" (_SIG "S" SET (vv "S" *: (vv "S" --> SET))) ((vv "v" %% Tl %% Tl $$ (vv "v" %% Tl %% Hd)) --> (vv "v" %% Tl %% Tl $$ (vv "v" %% Tl %% Hd))))
|
||
|
|
> : boy "A" SET
|
||
|
|
> ( boy "a" (vv "A")
|
||
|
|
> ( boy "f" (vv "A" --> SET)
|
||
|
|
> ( eq "p" ((vv "f" $$ vv "a") --> (vv "f" $$ vv "a")) (mv "u" $$ PAIR (vv "A") (PAIR (vv "a") (vv "f")))
|
||
|
|
> ((vv "f" $$ vv "a") --> (vv "f" $$ vv "a")) (ll "x" (vv "x"))
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 40: restrict A to second argument
|
||
|
|
> , ( gal "A" (SET --> SET --> SET)
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( boy "Y" SET
|
||
|
|
> ( eq "p" (SET --> SET) (mv "A" $$ vv "X")
|
||
|
|
> (SET --> SET) (ll "Z" (mv "A" $$ vv "Y" $$ vv "Z"))
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 41: solve A with [ SET , SET ]
|
||
|
|
> , ( gal "A" (SET *: SET)
|
||
|
|
> : eq "p" (SET *: SET) (mv "A")
|
||
|
|
> (SET *: SET) (PAIR (mv "A" %% Tl) SET)
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> -- test 42
|
||
|
|
> , ( gal "T" (SET --> SET)
|
||
|
|
> : gal "A" (_PI "Y" SET (mv "T" $$ vv "Y" --> SET))
|
||
|
|
> : gal "B" SET
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( boy "t" (mv "T" $$ vv "X")
|
||
|
|
> ( eq "p" SET (mv "B") SET (mv "A" $$ vv "X" $$ vv "t" --> SET)
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 43
|
||
|
|
> , ( gal "A" (SET --> SET)
|
||
|
|
> : gal "F" (SET --> SET)
|
||
|
|
> : gal "B" SET
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( eq "p" SET (mv "B")
|
||
|
|
> SET (mv "A" $$ (mv "F" $$ vv "X") --> mv "A" $$ vv "X")
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 44: false occurrence
|
||
|
|
> , ( gal "A" SET
|
||
|
|
> : gal "B" SET
|
||
|
|
> : gal "C" SET
|
||
|
|
> : eq "p" (mv "C" --> SET) (lamK (mv "B"))
|
||
|
|
> (mv "C" --> SET) (lamK (mv "A"))
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> -- test 45
|
||
|
|
> , ( gal "A" SET
|
||
|
|
> : gal "B" (mv "A" --> SET)
|
||
|
|
> : gal "C" (mv "A" --> SET)
|
||
|
|
> : boy "x" (mv "A")
|
||
|
|
> ( boy "y" (mv "A")
|
||
|
|
> ( eq "p" SET (mv "B" $$ vv "x")
|
||
|
|
> SET (mv "C" $$ vv "x")
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 46: prune p to learn B doesn't depend on its argument
|
||
|
|
> , ( gal "A" (SET --> SET)
|
||
|
|
> : boy "Z" SET
|
||
|
|
> ( gal "B" (SET --> SET)
|
||
|
|
> : gal "C" SET
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( boy "Y" SET
|
||
|
|
> ( eq "p" SET (mv "A" $$ (mv "B" $$ mv "C"))
|
||
|
|
> SET (mv "B" $$ vv "Y")
|
||
|
|
> : eq "q" SET (mv "B" $$ mv "C") SET (vv "Z")
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 47
|
||
|
|
> , ( gal "A" (_PI "X" SET (vv "X" --> SET))
|
||
|
|
> : gal "B" SET
|
||
|
|
> : boy "Y" SET
|
||
|
|
> ( boy "y" (vv "Y")
|
||
|
|
> ( eq "p" SET (mv "B")
|
||
|
|
> SET (mv "A" $$ vv "Y" $$ vv "y")
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 48
|
||
|
|
> , ( gal "A" (SET --> SET)
|
||
|
|
> : gal "B" SET
|
||
|
|
> : eq "p" SET (mv "B")
|
||
|
|
> SET (_PI "X" SET (mv "A" $$ vv "X"))
|
||
|
|
>
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> -- test 49: don't prune A too much
|
||
|
|
> , ( gal "F" (SET --> SET --> SET)
|
||
|
|
> : gal "A" (_PI "X" SET (mv "F" $$ SET $$ vv "X" --> SET))
|
||
|
|
> : gal "B" (SET --> SET)
|
||
|
|
> : boy "Y" SET
|
||
|
|
> ( eq "p" (SET --> SET) (mv "B")
|
||
|
|
> (mv "F" $$ SET $$ vv "Y" --> SET) (mv "A" $$ vv "Y")
|
||
|
|
> : boy "y" (mv "F" $$ SET $$ vv "Y")
|
||
|
|
> ( eq "q" SET (mv "F" $$ vv "Y" $$ vv "Y") SET SET
|
||
|
|
> : eq "r" SET (mv "A" $$ vv "Y" $$ vv "y")
|
||
|
|
> (mv "F" $$ SET $$ vv "Y") (vv "y")
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 50: Miller's nasty non-pruning example
|
||
|
|
> , ( boy "a" SET
|
||
|
|
> ( gal "X" ((SET --> SET) --> SET --> SET)
|
||
|
|
> : boy "y" SET
|
||
|
|
> ( eq "p" SET (mv "X" $$ (ll "z" (vv "a")) $$ vv "y")
|
||
|
|
> SET (vv "a")
|
||
|
|
> : eq "q" ((SET --> SET) --> SET --> SET) (mv "X")
|
||
|
|
> ((SET --> SET) --> SET --> SET) (ll "z1" (ll "z2" (vv "z1" $$ vv "z2")))
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- test 51
|
||
|
|
> , ( gal "A" (_PI "X" SET (_PI "x" (vv "X") SET))
|
||
|
|
> : gal "B" SET
|
||
|
|
> : eq "p" SET (mv "B")
|
||
|
|
> SET (_PI "X" SET (_PI "x" (vv "X") (mv "A" $$ vv "X" $$ vv "x")))
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> ]
|
||
|
|
|
||
|
|
|
||
|
|
> stucks = [
|
||
|
|
|
||
|
|
> -- stuck 0: nonlinear
|
||
|
|
> ( gal "A" (SET --> SET --> SET --> SET)
|
||
|
|
> : gal "B" (SET --> SET)
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( boy "Y" SET
|
||
|
|
> ( eq "p" SET (mv "A" $$$ [vv "Y", vv "X", vv "Y"])
|
||
|
|
> SET (mv "B" $$ vv "Y" --> vv "X")
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- stuck 1: nonlinear
|
||
|
|
> , ( gal "F" (SET --> SET --> SET)
|
||
|
|
> : gal "G" (SET --> SET --> SET)
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( eq "p" SET (mv "F" $$$ [vv "X", vv "X"])
|
||
|
|
> SET (mv "G" $$$ [vv "X", vv "X"])
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- stuck 2: nonlinear
|
||
|
|
> , ( boy "X" SET
|
||
|
|
> ( gal "f" (vv "X" --> vv "X" --> vv "X")
|
||
|
|
> : boy "Y" SET
|
||
|
|
> ( boy "x" (vv "X")
|
||
|
|
> ( eq "p" (vv "Y" --> vv "X") (ll "y" (mv "f" $$ vv "x" $$ vv "x"))
|
||
|
|
> (vv "Y" --> vv "X") (ll "y" (vv "x"))
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- stuck 3: nonlinear
|
||
|
|
> , ( gal "B" (SET --> SET --> SET)
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( gal "A" SET
|
||
|
|
> : eq "p" (mv "A" --> SET) (ll "a" (mv "B" $$ vv "X" $$ vv "X"))
|
||
|
|
> (mv "A" --> SET) (ll "a" (vv "X"))
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- stuck 4: double meta
|
||
|
|
> , [ gal "A" (SET --> SET)
|
||
|
|
> , gal "B" (SET --> SET)
|
||
|
|
> , gal "D" SET
|
||
|
|
> , gal "C" SET
|
||
|
|
> , eq "p" SET (mv "A" $$ (mv "B" $$ mv "C")) SET (mv "D")
|
||
|
|
> ]
|
||
|
|
|
||
|
|
> -- stuck 5: solution does not typecheck
|
||
|
|
> , ( gal "A" SET
|
||
|
|
> : gal "f" (mv "A" --> SET)
|
||
|
|
> : eq "p" (mv "A" --> SET) (mv "f")
|
||
|
|
> (mv "A" --> mv "A") (ll "x" (vv "x"))
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> -- stuck 6: weak rigid occurrence should not cause failure
|
||
|
|
> , ( gal "A" ((SET --> SET) --> SET)
|
||
|
|
> : boy "f" (SET --> SET)
|
||
|
|
> ( eq "p" SET (mv "A" $$ vv "f")
|
||
|
|
> SET (vv "f" $$ (mv "A" $$ (ll "X" (vv "X"))) --> SET)
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- stuck 7: prune second argument of B and get stuck
|
||
|
|
> , ( gal "A" SET
|
||
|
|
> : gal "B" (SET --> SET --> SET)
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( eq "p" SET (mv "A")
|
||
|
|
> SET (mv "B" $$ mv "A" $$ vv "X")
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- stuck 8: prune argument of A
|
||
|
|
> , ( boy "f" (SET --> SET)
|
||
|
|
> ( gal "A" (SET --> SET)
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( boy "Y" SET
|
||
|
|
> ( eq "p" SET (mv "A" $$ vv "X")
|
||
|
|
> SET (vv "f" $$ (mv "A" $$ vv "Y"))
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- stuck 9 (requires sigma-splitting of twins)
|
||
|
|
> , ( gal "A" SET
|
||
|
|
> : gal "B" (SET --> mv "A" --> SET)
|
||
|
|
> : gal "S" SET
|
||
|
|
> : gal "T" (SET --> mv "S" --> SET)
|
||
|
|
> : eq "p" (SIG (mv "A") (mv "B" $$ SET) --> SET)
|
||
|
|
> (ll "x" (mv "B" $$ SET $$ (vv "x" %% Hd)))
|
||
|
|
> (SIG (mv "S") (mv "T" $$ SET) --> SET)
|
||
|
|
> (ll "x" (mv "T" $$ SET $$ (vv "x" %% Hd)))
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> -- stuck 10: awkward occurrence (TODO: should this get stuck or fail?)
|
||
|
|
> , ( gal "A" SET
|
||
|
|
> : gal "a" (mv "A")
|
||
|
|
> : gal "f" (mv "A" --> SET)
|
||
|
|
> : eq "p" SET (mv "A") SET ((mv "f" $$ mv "a") --> SET)
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> -- stuck 12: twins with matching spines (stuck on B Set == T Set)
|
||
|
|
> , ( gal "A" SET
|
||
|
|
> : gal "B" (SET --> mv "A" --> SET)
|
||
|
|
> : gal "S" SET
|
||
|
|
> : gal "T" (SET --> mv "S" --> SET)
|
||
|
|
> : eq "p" (SIG (mv "A") (mv "B" $$ SET) --> mv "A")
|
||
|
|
> (ll "x" (vv "x" %% Hd))
|
||
|
|
> (SIG (mv "S") (mv "T" $$ SET) --> mv "S")
|
||
|
|
> (ll "x" (vv "x" %% Hd))
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> -- stuck 13
|
||
|
|
> , ( gal "A" (SET --> SET)
|
||
|
|
> : gal "B" (SET --> SET)
|
||
|
|
> : gal "a" (mv "A" $$ SET)
|
||
|
|
> : gal "b" (mv "B" $$ SET)
|
||
|
|
> : eq "p" (SIG SET (mv "B")) (PAIR SET (mv "b"))
|
||
|
|
> (mv "A" $$ SET) (mv "a")
|
||
|
|
> : eq "q" SET (SIG SET (mv "B")) SET (mv "A" $$ SET)
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> -- stuck 14 (TODO: should this be solvable by pruning?)
|
||
|
|
> , ( gal "A" (SET --> SET)
|
||
|
|
> : gal "B" SET
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( eq "p" SET (mv "A" $$ (mv "A" $$ vv "X"))
|
||
|
|
> SET (mv "B")
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- stuck 15
|
||
|
|
> , ( gal "F" (SET --> SET)
|
||
|
|
> : gal "A" (_PI "X" SET (mv "F" $$ vv "X"))
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( boy "Y" SET
|
||
|
|
> ( eq "p" (mv "F" $$ vv "X") (mv "A" $$ vv "X")
|
||
|
|
> (mv "F" $$ vv "Y") (mv "A" $$ vv "Y")
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- stuck 16
|
||
|
|
> , ( gal "B" (SET --> SET)
|
||
|
|
> : gal "F" (mv "B" $$ SET --> SET)
|
||
|
|
> : eq "p" (mv "B" $$ SET --> SET) (ll "Y" (mv "F" $$ vv "Y"))
|
||
|
|
> (SET --> SET) (ll "Y" (vv "Y"))
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> -- test 53: solve C with A despite B being in the way
|
||
|
|
> , ( gal "A" SET
|
||
|
|
> : gal "C" SET
|
||
|
|
> : gal "B" (SET --> SET)
|
||
|
|
> : gal "F" (mv "B" $$ SET --> SET)
|
||
|
|
> : eq "p" (_PI "X" (mv "B" $$ SET) ((mv "F" $$ vv "X") --> SET))
|
||
|
|
> (ll "X" (ll "x" (mv "A")))
|
||
|
|
> (_PI "X" SET (vv "X" --> SET))
|
||
|
|
> (ll "X" (ll "x" (mv "C")))
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> ]
|
||
|
|
|
||
|
|
> fails = [
|
||
|
|
|
||
|
|
> -- fail 0: occur check failure (A occurs in A -> A)
|
||
|
|
> [ gal "A" SET
|
||
|
|
> , eq "p" SET (mv "A") SET (mv "A" --> mv "A")
|
||
|
|
> ]
|
||
|
|
|
||
|
|
> -- fail 1: flex-rigid fails because A cannot depend on X
|
||
|
|
> , ( gal "A" SET
|
||
|
|
> : gal "B" SET
|
||
|
|
> : boy "X" SET
|
||
|
|
> ( eq "p" SET (mv "A") SET (mv "B" --> vv "X")
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- fail 2: rigid-rigid clash
|
||
|
|
> , ( boy "X" SET
|
||
|
|
> ( boy "Y" SET
|
||
|
|
> ( eq "p" SET (vv "X") SET (vv "Y")
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- fail 3: spine mismatch
|
||
|
|
> , ( boy "X" (SET *: SET)
|
||
|
|
> ( eq "p" SET (vv "X" %% Hd) SET (vv "X" %% Tl)
|
||
|
|
> : [])
|
||
|
|
> )
|
||
|
|
|
||
|
|
> -- fail 4: rigid-rigid constant clash
|
||
|
|
> , ( eq "p" SET SET SET (SET --> SET)
|
||
|
|
> : [])
|
||
|
|
|
||
|
|
> ]
|