Safe Haskell | None |
---|---|

Language | Haskell2010 |

- User queries
- Create a fresh variable
- Create a fresh array
- Checking satisfiability
- Querying the solver
- Getting solver information
- Entering and exiting assertion stack
- Higher level tactics
- Resetting the solver state
- Constructing assignments
- Terminating the query
- Controlling the solver behavior
- Miscellaneous
- Solver options

Author : Levent Erkok License : BSD3 Maintainer: erkokl@gmail.com Stability : experimental

Control sublanguage for interacting with SMT solvers.

## Synopsis

- class MonadIO m => ExtractIO m where
- class Monad m => MonadQuery m where
- queryState :: m State

- class Queriable m a b | a -> b where
- type Query = QueryT IO
- query :: Query a -> Symbolic a
- freshVar_ :: SymVal a => Query (SBV a)
- freshVar :: SymVal a => String -> Query (SBV a)
- freshArray_ :: (SymArray array, HasKind a, HasKind b) => Maybe (SBV b) -> Query (array a b)
- freshArray :: (SymArray array, HasKind a, HasKind b) => String -> Maybe (SBV b) -> Query (array a b)
- data CheckSatResult
- checkSat :: Query CheckSatResult
- ensureSat :: Query ()
- checkSatUsing :: String -> Query CheckSatResult
- checkSatAssuming :: [SBool] -> Query CheckSatResult
- checkSatAssumingWithUnsatisfiableSet :: [SBool] -> Query (CheckSatResult, Maybe [SBool])
- class SMTValue a where
- sexprToVal :: SExpr -> Maybe a

- getValue :: SMTValue a => SBV a -> Query a
- getUninterpretedValue :: HasKind a => SBV a -> Query String
- getModel :: Query SMTModel
- getAssignment :: Query [(String, Bool)]
- getSMTResult :: Query SMTResult
- getUnknownReason :: Query SMTReasonUnknown
- getObservables :: Query [(String, CV)]
- getUnsatCore :: Query [String]
- getProof :: Query String
- getInterpolant :: [String] -> Query String
- getAssertions :: Query [String]
- data SMTInfoFlag
- data SMTErrorBehavior
- data SMTInfoResponse
- getInfo :: SMTInfoFlag -> Query SMTInfoResponse
- getOption :: (a -> SMTOption) -> Query (Maybe SMTOption)
- getAssertionStackDepth :: Query Int
- push :: Int -> Query ()
- pop :: Int -> Query ()
- inNewAssertionStack :: Query a -> Query a
- caseSplit :: Bool -> [(String, SBool)] -> Query (Maybe (String, SMTResult))
- resetAssertions :: Query ()
- (|->) :: SymVal a => SBV a -> a -> Assignment
- mkSMTResult :: [Assignment] -> Query SMTResult
- exit :: Query ()
- ignoreExitCode :: SMTConfig -> Bool
- timeout :: Int -> Query a -> Query a
- queryDebug :: [String] -> Query ()
- echo :: String -> Query ()
- io :: IO a -> Query a
- data SMTOption
- = DiagnosticOutputChannel FilePath
- | ProduceAssertions Bool
- | ProduceAssignments Bool
- | ProduceProofs Bool
- | ProduceInterpolants Bool
- | ProduceUnsatAssumptions Bool
- | ProduceUnsatCores Bool
- | RandomSeed Integer
- | ReproducibleResourceLimit Integer
- | SMTVerbosity Integer
- | OptionKeyword String [String]
- | SetLogic Logic
- | SetInfo String [String]

# Documentation

In certain cases, the user might want to take over the communication with the solver, programmatically querying the engine and issuing commands accordingly. Queries can be extremely powerful as they allow direct control of the solver. Here's a simple example:

module Test where import Data.SBV import Data.SBV.Control -- queries require this module to be imported! test :: Symbolic (Maybe (Integer, Integer)) test = do x <- sInteger "x" -- a free variable named "x" y <- sInteger "y" -- a free variable named "y" -- require the sum to be 10 constrain $ x + y .== 10 -- Go into the Query mode query $ do -- Query the solver: Are the constraints satisfiable? cs <- checkSat case cs of Unk -> error "Solver said unknown!" Unsat -> return Nothing -- no solution! Sat -> -- Query the values: do xv <- getValue x yv <- getValue y io $ putStrLn $ "Solver returned: " ++ show (xv, yv) -- We can now add new constraints, -- Or perform arbitrary computations and tell -- the solver anything we want! constrain $ x .> literal xv + literal yv -- call checkSat again csNew <- checkSat case csNew of Unk -> error "Solver said unknown!" Unsat -> return Nothing Sat -> do xv2 <- getValue x yv2 <- getValue y return $ Just (xv2, yv2)

Note the type of `test`

: it returns an optional pair of integers in the `Symbolic`

monad. We turn
it into an IO value with the `runSMT`

function: (There's also `runSMTWith`

that uses a user specified
solver instead of the default.)

pair :: IO (Maybe (Integer, Integer)) pair = runSMT test

When run, this can return:

*Test> pair Solver returned: (10,0) Just (11,-1)

demonstrating that the user has full contact with the solver and can guide it as the program executes. SBV provides access to many SMTLib features in the query mode, as exported from this very module.

For other examples see:

- Documentation.SBV.Examples.Queries.AllSat: Simulating SBV's
`allSat`

using queries. - Documentation.SBV.Examples.Queries.CaseSplit: Performing a case-split during a query.
- Documentation.SBV.Examples.Queries.Enums: Using enumerations in queries.
- Documentation.SBV.Examples.Queries.FourFours: Solution to a fun arithmetic puzzle, coded using queries.
- Documentation.SBV.Examples.Queries.GuessNumber: The famous number guessing game.
- Documentation.SBV.Examples.Queries.UnsatCore: Extracting unsat-cores using queries.
- Documentation.SBV.Examples.Queries.Interpolants: Extracting interpolants using queries.

# User queries

class MonadIO m => ExtractIO m where Source #

Monads which support `IO`

operations and can extract all `IO`

behavior for
interoperation with functions like `catches`

, which takes
an `IO`

action in negative position. This function can not be implemented
for transformers like `ReaderT r`

or `StateT s`

, whose resultant `IO`

actions are a function of some environment or state.

## Instances

ExtractIO IO Source # | Trivial IO extraction for |

ExtractIO m => ExtractIO (MaybeT m) Source # | IO extraction for |

ExtractIO m => ExtractIO (ExceptT e m) Source # | IO extraction for |

(Monoid w, ExtractIO m) => ExtractIO (WriterT w m) Source # | IO extraction for lazy |

(Monoid w, ExtractIO m) => ExtractIO (WriterT w m) Source # | IO extraction for strict |

class Monad m => MonadQuery m where Source #

Computations which support query operations.

Nothing

queryState :: m State Source #

queryState :: (MonadTrans t, MonadQuery m', m ~ t m') => m State Source #

## Instances

class Queriable m a b | a -> b where Source #

An queriable value.

^ Create a new symbolic value of type `a`

extract :: a -> QueryT m b Source #

^ Extract the current value in a SAT context

## Instances

(MonadIO m, SymVal a, SMTValue a) => Queriable m (SBV a) a Source # | Generic |

Queriable IO (S SInteger) (S Integer) Source # | Queriable instance for our state |

Queriable IO (S SInteger) (S Integer) Source # | Make our state queriable |

Queriable IO (S SInteger) (S Integer) Source # | Make our state queriable |

Queriable IO (S SInteger) (S Integer) Source # | Queriable instance for our state |

type Query = QueryT IO Source #

A query is a user-guided mechanism to directly communicate and extract results from the solver.

# Create a fresh variable

freshVar :: SymVal a => String -> Query (SBV a) Source #

Create a fresh variable in query mode. You should prefer
creating input variables using `sBool`

, `sInt32`

, etc., which act
as primary inputs to the model and can be existential or universal.
Use `freshVar`

only in query mode for anonymous temporary variables.
Such variables are always existential. Note that `freshVar`

should hardly be
needed: Your input variables and symbolic expressions should suffice for
most major use cases.

NB. For a version which generalizes over the underlying monad, see `freshVar`

# Create a fresh array

freshArray_ :: (SymArray array, HasKind a, HasKind b) => Maybe (SBV b) -> Query (array a b) Source #

Similar to `freshArray`

, except creates unnamed array.

NB. For a version which generalizes over the underlying monad, see `freshArray_`

freshArray :: (SymArray array, HasKind a, HasKind b) => String -> Maybe (SBV b) -> Query (array a b) Source #

Create a fresh array in query mode. Again, you should prefer
creating arrays before the queries start using `newArray`

, but this
method can come in handy in occasional cases where you need a new array
after you start the query based interaction.

NB. For a version which generalizes over the underlying monad, see `freshArray`

# Checking satisfiability

data CheckSatResult Source #

Result of a `checkSat`

or `checkSatAssuming`

call.

Sat | Satisfiable: A model is available, which can be queried with |

Unsat | Unsatisfiable: No model is available. Unsat cores might be obtained via |

Unk | Unknown: Use |

## Instances

Eq CheckSatResult Source # | |

Defined in Data.SBV.Control.Types (==) :: CheckSatResult -> CheckSatResult -> Bool # (/=) :: CheckSatResult -> CheckSatResult -> Bool # | |

Show CheckSatResult Source # | |

Defined in Data.SBV.Control.Types showsPrec :: Int -> CheckSatResult -> ShowS # show :: CheckSatResult -> String # showList :: [CheckSatResult] -> ShowS # |

checkSat :: Query CheckSatResult Source #

Check for satisfiability.

NB. For a version which generalizes over the underlying monad, see `checkSat`

ensureSat :: Query () Source #

Ensure that the current context is satisfiable. If not, this function will throw an error.

NB. For a version which generalizes over the underlying monad, see `ensureSat`

checkSatUsing :: String -> Query CheckSatResult Source #

Check for satisfiability with a custom check-sat-using command.

NB. For a version which generalizes over the underlying monad, see `checkSatUsing`

checkSatAssuming :: [SBool] -> Query CheckSatResult Source #

Check for satisfiability, under the given conditions. Similar to `checkSat`

except it allows making
further assumptions as captured by the first argument of booleans. (Also see `checkSatAssumingWithUnsatisfiableSet`

for a variant that returns the subset of the given assumptions that led to the `Unsat`

conclusion.)

NB. For a version which generalizes over the underlying monad, see `checkSatAssuming`

checkSatAssumingWithUnsatisfiableSet :: [SBool] -> Query (CheckSatResult, Maybe [SBool]) Source #

Check for satisfiability, under the given conditions. Returns the unsatisfiable
set of assumptions. Similar to `checkSat`

except it allows making further assumptions
as captured by the first argument of booleans. If the result is `Unsat`

, the user will
also receive a subset of the given assumptions that led to the `Unsat`

conclusion. Note
that while this set will be a subset of the inputs, it is not necessarily guaranteed to be minimal.

You must have arranged for the production of unsat assumptions first via

`setOption`

$`ProduceUnsatAssumptions`

`True`

for this call to not error out!

Usage note: `getUnsatCore`

is usually easier to use than `checkSatAssumingWithUnsatisfiableSet`

, as it
allows the use of named assertions, as obtained by `namedConstraint`

. If `getUnsatCore`

fills your needs, you should definitely prefer it over `checkSatAssumingWithUnsatisfiableSet`

.

NB. For a version which generalizes over the underlying monad, see `checkSatAssumingWithUnsatisfiableSet`

# Querying the solver

## Extracting values

class SMTValue a where Source #

A class which allows for sexpr-conversion to values

Nothing

sexprToVal :: SExpr -> Maybe a Source #

sexprToVal :: Read a => SExpr -> Maybe a Source #

## Instances

getValue :: SMTValue a => SBV a -> Query a Source #

Get the value of a term.

NB. For a version which generalizes over the underlying monad, see `getValue`

getUninterpretedValue :: HasKind a => SBV a -> Query String Source #

Get the value of an uninterpreted sort, as a String

NB. For a version which generalizes over the underlying monad, see `getUninterpretedValue`

getModel :: Query SMTModel Source #

Collect model values. It is implicitly assumed that we are in a check-sat
context. See `getSMTResult`

for a variant that issues a check-sat first and
returns an `SMTResult`

.

NB. For a version which generalizes over the underlying monad, see `getModel`

getAssignment :: Query [(String, Bool)] Source #

Retrieve the assignment. This is a lightweight version of `getValue`

, where the
solver returns the truth value for all named subterms of type `Bool`

.

You must have first arranged for assignments to be produced via

`setOption`

$`ProduceAssignments`

`True`

for this call to not error out!

NB. For a version which generalizes over the underlying monad, see `getAssignment`

getSMTResult :: Query SMTResult Source #

Issue check-sat and get an SMT Result out.

NB. For a version which generalizes over the underlying monad, see `getSMTResult`

getUnknownReason :: Query SMTReasonUnknown Source #

Get the reason unknown. Only internally used.

NB. For a version which generalizes over the underlying monad, see `getUnknownReason`

getObservables :: Query [(String, CV)] Source #

Get the observables recorded during a query run.

NB. For a version which generalizes over the underlying monad, see `getObservables`

## Extracting the unsat core

getUnsatCore :: Query [String] Source #

Retrieve the unsat-core. Note you must have arranged for unsat cores to be produced first via

`setOption`

$`ProduceUnsatCores`

`True`

for this call to not error out!

NB. There is no notion of a minimal unsat-core, in case unsatisfiability can be derived in multiple ways. Furthermore, Z3 does not guarantee that the generated unsat core does not have any redundant assertions either, as doing so can incur a performance penalty. (There might be assertions in the set that is not needed.) To ensure all the assertions in the core are relevant, use:

`setOption`

$`OptionKeyword`

":smt.core.minimize" ["true"]

Note that this only works with Z3.

NB. For a version which generalizes over the underlying monad, see `getUnsatCore`

## Extracting a proof

getProof :: Query String Source #

Retrieve the proof. Note you must have arranged for proofs to be produced first via

`setOption`

$`ProduceProofs`

`True`

for this call to not error out!

A proof is simply a `String`

, as returned by the solver. In the future, SBV might
provide a better datatype, depending on the use cases. Please get in touch if you
use this function and can suggest a better API.

NB. For a version which generalizes over the underlying monad, see `getProof`

## Extracting interpolants

getInterpolant :: [String] -> Query String Source #

Retrieve an interpolant after an `Unsat`

result is obtained. Note you must have arranged for
interpolants to be produced first via

`setOption`

$`ProduceInterpolants`

`True`

for this call to not error out!

To get an interpolant for a pair of formulas `A`

and `B`

, use a `constrainWithAttribute`

call to attach
interplation groups to `A`

and `B`

. Then call `getInterpolant`

`["A"]`

, assuming those are the names
you gave to the formulas in the `A`

group.

An interpolant for `A`

and `B`

is a formula `I`

such that:

A .=> I and B .=> sNot I

That is, it's evidence that `A`

and `B`

cannot be true together
since `A`

implies `I`

but `B`

implies `not I`

; establishing that `A`

and `B`

cannot
be satisfied at the same time. Furthermore, `I`

will have only the symbols that are common
to `A`

and `B`

.

N.B. As of Z3 version 4.8.0; Z3 no longer supports interpolants. Use the MathSAT backend for extracting interpolants. See Documentation.SBV.Examples.Queries.Interpolants for an example.

NB. For a version which generalizes over the underlying monad, see `getInterpolant`

## Extracting assertions

getAssertions :: Query [String] Source #

Retrieve assertions. Note you must have arranged for assertions to be available first via

`setOption`

$`ProduceAssertions`

`True`

for this call to not error out!

Note that the set of assertions returned is merely a list of strings, just like the
case for `getProof`

. In the future, SBV might provide a better datatype, depending
on the use cases. Please get in touch if you use this function and can suggest
a better API.

NB. For a version which generalizes over the underlying monad, see `getAssertions`

# Getting solver information

data SMTInfoFlag Source #

Collectable information from the solver.

AllStatistics | |

AssertionStackLevels | |

Authors | |

ErrorBehavior | |

Name | |

ReasonUnknown | |

Version | |

InfoKeyword String |

## Instances

Show SMTInfoFlag Source # | |

Defined in Data.SBV.Control.Types showsPrec :: Int -> SMTInfoFlag -> ShowS # show :: SMTInfoFlag -> String # showList :: [SMTInfoFlag] -> ShowS # |

data SMTErrorBehavior Source #

Behavior of the solver for errors.

## Instances

Show SMTErrorBehavior Source # | |

Defined in Data.SBV.Control.Types showsPrec :: Int -> SMTErrorBehavior -> ShowS # show :: SMTErrorBehavior -> String # showList :: [SMTErrorBehavior] -> ShowS # |

data SMTInfoResponse Source #

Collectable information from the solver.

## Instances

Show SMTInfoResponse Source # | |

Defined in Data.SBV.Control.Types showsPrec :: Int -> SMTInfoResponse -> ShowS # show :: SMTInfoResponse -> String # showList :: [SMTInfoResponse] -> ShowS # |

getInfo :: SMTInfoFlag -> Query SMTInfoResponse Source #

Ask solver for info.

NB. For a version which generalizes over the underlying monad, see `getInfo`

getOption :: (a -> SMTOption) -> Query (Maybe SMTOption) Source #

Retrieve the value of an 'SMTOption.' The curious function argument is on purpose here,
simply pass the constructor name. Example: the call

will return
either `getOption`

`ProduceUnsatCores`

`Nothing`

or `Just (ProduceUnsatCores True)`

or `Just (ProduceUnsatCores False)`

.

Result will be `Nothing`

if the solver does not support this option.

NB. For a version which generalizes over the underlying monad, see `getOption`

# Entering and exiting assertion stack

getAssertionStackDepth :: Query Int Source #

The current assertion stack depth, i.e., pops after start. Always non-negative.

NB. For a version which generalizes over the underlying monad, see `getAssertionStackDepth`

push :: Int -> Query () Source #

Push the context, entering a new one. Pushes multiple levels if *n* > 1.

NB. For a version which generalizes over the underlying monad, see `push`

pop :: Int -> Query () Source #

Pop the context, exiting a new one. Pops multiple levels if *n* > 1. It's an error to pop levels that don't exist.

NB. For a version which generalizes over the underlying monad, see `pop`

inNewAssertionStack :: Query a -> Query a Source #

Run the query in a new assertion stack. That is, we push the context, run the query commands, and pop it back.

NB. For a version which generalizes over the underlying monad, see `inNewAssertionStack`

# Higher level tactics

caseSplit :: Bool -> [(String, SBool)] -> Query (Maybe (String, SMTResult)) Source #

Search for a result via a sequence of case-splits, guided by the user. If one of
the conditions lead to a satisfiable result, returns `Just`

that result. If none of them
do, returns `Nothing`

. Note that we automatically generate a coverage case and search
for it automatically as well. In that latter case, the string returned will be Coverage.
The first argument controls printing progress messages See Documentation.SBV.Examples.Queries.CaseSplit
for an example use case.

NB. For a version which generalizes over the underlying monad, see `caseSplit`

# Resetting the solver state

resetAssertions :: Query () Source #

Reset the solver, by forgetting all the assertions. However, bindings are kept as is,
as opposed to a full reset of the solver. Use this variant to clean-up the solver
state while leaving the bindings intact. Pops all assertion levels. Declarations and
definitions resulting from the `setLogic`

command are unaffected. Note that SBV
implicitly uses global-declarations, so bindings will remain intact.

NB. For a version which generalizes over the underlying monad, see `resetAssertions`

# Constructing assignments

(|->) :: SymVal a => SBV a -> a -> Assignment infix 1 Source #

Make an assignment. The type `Assignment`

is abstract, the result is typically passed
to `mkSMTResult`

:

mkSMTResult [ a |-> 332 , b |-> 2.3 , c |-> True ]

End users should use `getModel`

for automatically constructing models from the current solver state.
However, an explicit `Assignment`

might be handy in complex scenarios where a model needs to be
created manually.

# Terminating the query

mkSMTResult :: [Assignment] -> Query SMTResult Source #

Produce the query result from an assignment.

NB. For a version which generalizes over the underlying monad, see `mkSMTResult`

Exit the solver. This action will cause the solver to terminate. Needless to say, trying to communicate with the solver after issuing "exit" will simply fail.

NB. For a version which generalizes over the underlying monad, see `exit`

# Controlling the solver behavior

ignoreExitCode :: SMTConfig -> Bool Source #

If true, we shall ignore the exit code upon exit. Otherwise we require ExitSuccess.

timeout :: Int -> Query a -> Query a Source #

Timeout a query action, typically a command call to the underlying SMT solver.
The duration is in microseconds (`1/10^6`

seconds). If the duration
is negative, then no timeout is imposed. When specifying long timeouts, be careful not to exceed
`maxBound :: Int`

. (On a 64 bit machine, this bound is practically infinite. But on a 32 bit
machine, it corresponds to about 36 minutes!)

Semantics: The call `timeout n q`

causes the timeout value to be applied to all interactive calls that take place
as we execute the query `q`

. That is, each call that happens during the execution of `q`

gets a separate
time-out value, as opposed to one timeout value that limits the whole query. This is typically the intended behavior.
It is advisible to apply this combinator to calls that involve a single call to the solver for
finer control, as opposed to an entire set of interactions. However, different use cases might call for different scenarios.

If the solver responds within the time-out specified, then we continue as usual. However, if the backend solver times-out using this mechanism, there is no telling what the state of the solver will be. Thus, we raise an error in this case.

NB. For a version which generalizes over the underlying monad, see `timeout`

# Miscellaneous

queryDebug :: [String] -> Query () Source #

If `verbose`

is `True`

, print the message, useful for debugging messages
in custom queries. Note that `redirectVerbose`

will be respected: If a
file redirection is given, the output will go to the file.

NB. For a version which generalizes over the underlying monad, see `queryDebug`

echo :: String -> Query () Source #

Echo a string. Note that the echoing is done by the solver, not by SBV.

NB. For a version which generalizes over the underlying monad, see `echo`

io :: IO a -> Query a Source #

Perform an arbitrary IO action.

NB. For a version which generalizes over the underlying monad, see `io`

# Solver options

Option values that can be set in the solver, following the SMTLib specification http://smtlib.cs.uiowa.edu/language.shtml.

Note that not all solvers may support all of these!

Furthermore, SBV doesn't support the following options allowed by SMTLib.

`:interactive-mode`

(Deprecated in SMTLib, use`ProduceAssertions`

instead.)`:print-success`

(SBV critically needs this to be True in query mode.)`:produce-models`

(SBV always sets this option so it can extract models.)`:regular-output-channel`

(SBV always requires regular output to come on stdout for query purposes.)`:global-declarations`

(SBV always uses global declarations since definitions are accumulative.)

Note that `SetLogic`

and `SetInfo`

are, strictly speaking, not SMTLib options. However, we treat it as such here
uniformly, as it fits better with how options work.