Copyright	(c) Levent Erkok
License	BSD3
Maintainer	erkokl@gmail.com
Stability	experimental
Safe Haskell	None
Language	Haskell2010

Documentation.SBV.Examples.Lists.BoundedMutex

Description

Demonstrates use of bounded list utilities, proving a simple mutex algorithm correct up to given bounds.

Synopsis

data State
- = Idle
- | Ready
- | Critical
type SState = SBV State
idle :: SState
ready :: SState
critical :: SState
mutex :: Int -> SList State -> SList State -> SBool
validSequence :: Int -> Integer -> SList Integer -> SList State -> SBool
validTurns :: Int -> SList Integer -> SList State -> SList State -> SBool
checkMutex :: Int -> IO ()
notFair :: Int -> IO ()

Documentation

data State Source #

Each agent can be in one of the three states

Constructors

Idle	Regular work
Ready	Intention to enter critical state
Critical	In the critical state

Instances

Eq State Source #
Instance details Defined in Documentation.SBV.Examples.Lists.BoundedMutex Methods (==) :: State -> State -> Bool # (/=) :: State -> State -> Bool #
Data State Source #
Instance details Defined in Documentation.SBV.Examples.Lists.BoundedMutex Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> State -> c State # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c State # toConstr :: State -> Constr # dataTypeOf :: State -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c State) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c State) # gmapT :: (forall b. Data b => b -> b) -> State -> State # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> State -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> State -> r # gmapQ :: (forall d. Data d => d -> u) -> State -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> State -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> State -> m State # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> State -> m State # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> State -> m State #
Ord State Source #
Instance details Defined in Documentation.SBV.Examples.Lists.BoundedMutex Methods compare :: State -> State -> Ordering # (<) :: State -> State -> Bool # (<=) :: State -> State -> Bool # (>) :: State -> State -> Bool # (>=) :: State -> State -> Bool # max :: State -> State -> State # min :: State -> State -> State #
Read State Source #
Instance details Defined in Documentation.SBV.Examples.Lists.BoundedMutex Methods readsPrec :: Int -> ReadS State # readList :: ReadS [State] # readPrec :: ReadPrec State # readListPrec :: ReadPrec [State] #
Show State Source #
Instance details Defined in Documentation.SBV.Examples.Lists.BoundedMutex Methods showsPrec :: Int -> State -> ShowS # show :: State -> String # showList :: [State] -> ShowS #
HasKind State Source #
Instance details Defined in Documentation.SBV.Examples.Lists.BoundedMutex Methods kindOf :: State -> Kind Source # hasSign :: State -> Bool Source # intSizeOf :: State -> Int Source # isBoolean :: State -> Bool Source # isBounded :: State -> Bool Source # isReal :: State -> Bool Source # isFloat :: State -> Bool Source # isDouble :: State -> Bool Source # isUnbounded :: State -> Bool Source # isUninterpreted :: State -> Bool Source # isChar :: State -> Bool Source # isString :: State -> Bool Source # isList :: State -> Bool Source # isSet :: State -> Bool Source # isTuple :: State -> Bool Source # isMaybe :: State -> Bool Source # isEither :: State -> Bool Source # showType :: State -> String Source #
SymVal State Source #
Instance details Defined in Documentation.SBV.Examples.Lists.BoundedMutex Methods mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV State) Source # literal :: State -> SBV State Source # fromCV :: CV -> State Source # isConcretely :: SBV State -> (State -> Bool) -> Bool Source # forall :: MonadSymbolic m => String -> m (SBV State) Source # forall_ :: MonadSymbolic m => m (SBV State) Source # mkForallVars :: MonadSymbolic m => Int -> m [SBV State] Source # exists :: MonadSymbolic m => String -> m (SBV State) Source # exists_ :: MonadSymbolic m => m (SBV State) Source # mkExistVars :: MonadSymbolic m => Int -> m [SBV State] Source # free :: MonadSymbolic m => String -> m (SBV State) Source # free_ :: MonadSymbolic m => m (SBV State) Source # mkFreeVars :: MonadSymbolic m => Int -> m [SBV State] Source # symbolic :: MonadSymbolic m => String -> m (SBV State) Source # symbolics :: MonadSymbolic m => [String] -> m [SBV State] Source # unliteral :: SBV State -> Maybe State Source # isConcrete :: SBV State -> Bool Source # isSymbolic :: SBV State -> Bool Source #
SatModel State Source #	Make `State` a symbolic enumeration
Instance details Defined in Documentation.SBV.Examples.Lists.BoundedMutex Methods parseCVs :: [CV] -> Maybe (State, [CV]) Source # cvtModel :: (State -> Maybe b) -> Maybe (State, [CV]) -> Maybe (b, [CV]) Source #
SMTValue State Source #
Instance details Defined in Documentation.SBV.Examples.Lists.BoundedMutex Methods sexprToVal :: SExpr -> Maybe State Source #

type SState = SBV State Source #

The type synonym SState is mnemonic for symbolic state.

idle :: SState Source #

Symbolic version of Idle

ready :: SState Source #

Symbolic version of Ready

critical :: SState Source #

Symbolic version of Critical

mutex :: Int -> SList State -> SList State -> SBool Source #

A bounded mutex property holds for two sequences of state transitions, if they are not in their critical section at the same time up to that given bound.

validSequence :: Int -> Integer -> SList Integer -> SList State -> SBool Source #

A sequence is valid upto a bound if it starts at Idle, and follows the mutex rules. That is:

From Idle it can switch to Ready or stay Idle
From Ready it can switch to Critical if it's its turn
From Critical it can either stay in Critical or go back to Idle

The variable me identifies the agent id.

validTurns :: Int -> SList Integer -> SList State -> SList State -> SBool Source #

The mutex algorithm, coded implicity as an assignment to turns. Turns start at 1, and at each stage is either 1 or 2; giving preference to that process. The only condition is that if either process is in its critical section, then the turn value stays the same. Note that this is sufficient to satisfy safety (i.e., mutual exclusion), though it does not guarantee liveness.

checkMutex :: Int -> IO () Source #

Check that we have the mutex property so long as validSequence and validTurns holds; i.e., so long as both the agents and the arbiter act according to the rules. The check is bounded up-to-the given concrete bound; so this is an example of a bounded-model-checking style proof. We have:

>>> checkMutex 20
All is good!

notFair :: Int -> IO () Source #

Our algorithm is correct, but it is not fair. It does not guarantee that a process that wants to enter its critical-section will always do so eventually. Demonstrate this by trying to show a bounded trace of length 10, such that the second process is ready but never transitions to critical. We have:

ghci> notFair 10
Fairness is violated at bound: 10
P1: [Idle,Idle,Ready,Critical,Idle,Idle,Ready,Critical,Idle,Idle]
P2: [Idle,Ready,Ready,Ready,Ready,Ready,Ready,Ready,Ready,Ready]
Ts: [1,2,1,1,1,1,1,1,1,1]

As expected, P2 gets ready but never goes critical since the arbiter keeps picking P1 unfairly. (You might get a different trace depending on what z3 happens to produce!)

Exercise for the reader: Change the validTurns function so that it alternates the turns from the previous value if neither process is in critical. Show that this makes the notFair function below no longer exhibits the issue. Is this sufficient? Concurrent programming is tricky!