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Haskell: Compiler as Theorem-Prover Greg Price ( price ) 2007 Nov 19 code samples: http://cluedumps.mit.edu/wiki/2007/11-19 Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 1 / 26 Software Transactional Memory 1

  1. Haskell: Compiler as Theorem-Prover Greg Price ( price ) 2007 Nov 19 code samples: http://cluedumps.mit.edu/wiki/2007/11-19 Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 1 / 26

  2. Software Transactional Memory 1 Protocol Types 2 More theorems 3 The Big Picture 4 References 5 Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 2 / 26

  3. Software Transactional Memory Concurrency: locking Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 4 / 26

  4. Software Transactional Memory Concurrency: locking costly, deadlocks, bugs. Optimistic transactions, restarting Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 4 / 26

  5. Software Transactional Memory Concurrency: locking costly, deadlocks, bugs. Optimistic transactions, restarting Worse bugs: void f() { void g() { begin_transaction(); begin_transaction(); if (x != y) x++; launch_missiles(); y++; end_transaction(); end_transaction(); } } Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 4 / 26

  6. Software Transactional Memory Concurrency: locking costly, deadlocks, bugs. Optimistic transactions, restarting Worse bugs: void f() { void g() { begin_transaction(); begin_transaction(); if (x != y) x++; launch_missiles(); y++; end_transaction(); end_transaction(); } } Restart side effects? Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 4 / 26

  7. Software Transactional Memory Concurrency: locking costly, deadlocks, bugs. Optimistic transactions, restarting Worse bugs: void f() { void g() { begin_transaction(); begin_transaction(); if (x != y) x++; launch_missiles(); y++; end_transaction(); end_transaction(); } } Restart side effects? & all the old bugs too Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 4 / 26

  8. Software Transactional Memory Solution: f = atomically $ do xv <- readTVar x yv <- readTVar y if xv /= yv then launch_missiles_soon else return () g = atomically $ do xv <- readTVar x; writeTVar x (xv+1) yv <- readTVar y; writeTVar y (yv+1) (see example STMExample ) Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 6 / 26

  9. Software Transactional Memory Solution: f = atomically $ do xv <- readTVar x yv <- readTVar y if xv /= yv then launch_missiles_soon else return () g = atomically $ do xv <- readTVar x; writeTVar x (xv+1) yv <- readTVar y; writeTVar y (yv+1) (see example STMExample ) can’t have (non-transactional) side effects Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 6 / 26

  10. Software Transactional Memory Solution: f = atomically $ do xv <- readTVar x yv <- readTVar y if xv /= yv then launch_missiles_soon else return () g = atomically $ do xv <- readTVar x; writeTVar x (xv+1) yv <- readTVar y; writeTVar y (yv+1) (see example STMExample ) can’t have (non-transactional) side effects no special compiler support (except runtime) Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 6 / 26

  11. Software Transactional Memory Solution: f = atomically $ do xv <- readTVar x yv <- readTVar y if xv /= yv then launch_missiles_soon else return () g = atomically $ do xv <- readTVar x; writeTVar x (xv+1) yv <- readTVar y; writeTVar y (yv+1) (see example STMExample ) can’t have (non-transactional) side effects no special compiler support (except runtime) other bugs ruled out too Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 6 / 26

  12. STM: Guaranteeing No Side Effects pure Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  13. STM: Guaranteeing No Side Effects pure putStr "hello" :: IO () Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  14. STM: Guaranteeing No Side Effects pure an IO action putStr "hello" :: IO () Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  15. STM: Guaranteeing No Side Effects pure an IO action putStr "hello" :: IO () sequenced: do { ...; f :: IO a; ... } Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  16. STM: Guaranteeing No Side Effects pure an IO action putStr "hello" :: IO () sequenced: do { ...; f :: IO a; ... } executed only through main : main :: IO () main = do putStr "Hello world!\n" launch_missiles Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  17. STM: Guaranteeing No Side Effects pure an IO action putStr "hello" :: IO () sequenced: do { ...; f :: IO a; ... } executed only through main : main :: IO () main = do putStr "Hello world!\n" launch_missiles ⇒ side effects only through type IO a Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 8 / 26

  18. STM: Guaranteeing No Side Effects side effects only through type IO a Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 10 / 26

  19. STM: Guaranteeing No Side Effects side effects only through type IO a atomically :: STM a -> IO a Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 10 / 26

  20. STM: Guaranteeing No Side Effects side effects only through type IO a atomically :: STM a -> IO a newTVar :: a -> STM (TVar a) readTVar :: TVar a -> STM a writeTVar :: TVar a -> a -> STM () Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 10 / 26

  21. STM: Guaranteeing No Side Effects side effects only through type IO a atomically :: STM a -> IO a newTVar :: a -> STM (TVar a) readTVar :: TVar a -> STM a writeTVar :: TVar a -> a -> STM () do { ...; f :: STM a; ... } (same) Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 10 / 26

  22. Software Transactional Memory 1 Protocol Types 2 More theorems 3 The Big Picture 4 References 5 Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 11 / 26

  23. Protocol Types spec :: Spec ((Snd Int :+: Snd String) :->: End) IOChan a protocol spec Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 13 / 26

  24. Protocol Types spec :: Spec ((Snd Int :+: Snd String) :->: End) IOChan � �� � s a protocol spec Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 13 / 26

  25. Protocol Types spec :: Spec ((Snd Int :+: Snd String) :->: End) IOChan � �� � s a protocol spec accept spec request spec Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 13 / 26

  26. Protocol Types spec :: Spec ((Snd Int :+: Snd String) :->: End) IOChan � �� � s a protocol spec accept spec :: (Extend M (ChanCap c s) e e’ n) => LinearT IO e e’ (LVar n) request spec :: (Dual s s’, Extend M (ChanCap c s’) e e’ n) => LinearT IO e e’ (LVar n) Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 13 / 26

  27. Protocol Types spec :: Spec ((Snd Int :+: Snd String) :->: End) IOChan � �� � s a protocol spec accept spec :: (Extend M (ChanCap c s) e e’ n) => LinearT IO e e’ (LVar n) request spec :: (Dual s s’, Extend M (ChanCap c s’) e e’ n) => LinearT IO e e’ (LVar n) runLinearT (accept spec >>>= ...) :: IO a executes protocol exactly Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 13 / 26

  28. Protocol Types: Means of Proof runLinearT :: LinearT IO Empty Empty a -> IO a Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 15 / 26

  29. Protocol Types: Means of Proof runLinearT :: LinearT IO Empty Empty a -> IO a environments of capabilities Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 15 / 26

  30. Protocol Types: Means of Proof runLinearT :: LinearT IO Empty Empty a -> IO a environments of capabilities send :: (Evolve n c (Snd a :->: x) e x e’) => LVar n -> a -> LinearT IO e e’ () recv :: (Evolve n c (Rcv a :->: x) e x e’) => LVar n -> LinearT IO e e’ a Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 15 / 26

  31. Protocol Types: Means of Proof runLinearT :: LinearT IO Empty Empty a -> IO a environments of capabilities send :: (Evolve n c (Snd a :->: x) e x e’) => LVar n -> a -> LinearT IO e e’ () recv :: (Evolve n c (Rcv a :->: x) e x e’) => LVar n -> LinearT IO e e’ a sel1 :: (Evolve n c ((x1:+:x2):->:y) e (x1:->:y) e’) => LVar n -> LinearT IO e e’ () Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 15 / 26

  32. Protocol Types: Generic Building Blocks data T class Prop a data F instance Prop T instance Prop F Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 17 / 26

  33. Protocol Types: Generic Building Blocks data T class Prop a data F instance Prop T instance Prop F class Prop b => Equal x y b | x y -> b Greg Price ( price ) () Haskell: Compiler as Theorem-Prover 2007 Nov 19 17 / 26

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