| Copyright | (c) Levent Erkok |
|---|---|
| License | BSD3 |
| Maintainer | erkokl@gmail.com |
| Stability | experimental |
| Safe Haskell | None |
| Language | Haskell2010 |
Data.SBV.Control
Contents
Description
Control sublanguage for interacting with SMT solvers.
- data Query a
- query :: Query a -> Symbolic a
- freshVar_ :: forall a. SymWord a => Query (SBV a)
- freshVar :: forall a. SymWord a => String -> Query (SBV a)
- data CheckSatResult
- checkSat :: Query CheckSatResult
- checkSatUsing :: String -> Query CheckSatResult
- checkSatAssuming :: [SBool] -> Query CheckSatResult
- checkSatAssumingWithUnsatisfiableSet :: [SBool] -> Query (CheckSatResult, Maybe [SBool])
- class SMTValue a where
- 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 String
- getUnsatCore :: Query [String]
- getProof :: Query String
- getAssertions :: Query [String]
- data SMTInfoFlag
- data SMTErrorBehavior
- data SMTReasonUnknown
- 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 ()
- (|->) :: SymWord a => SBV a -> a -> Assignment
- echo :: String -> Query ()
- mkSMTResult :: [Assignment] -> Query SMTResult
- exit :: Query ()
- ignoreExitCode :: SMTConfig -> Bool
- timeout :: Int -> Query a -> Query a
- io :: IO a -> Query a
- data SMTOption
- = DiagnosticOutputChannel FilePath
- | ProduceAssertions Bool
- | ProduceAssignments Bool
- | ProduceProofs Bool
- | ProduceUnsatAssumptions Bool
- | ProduceUnsatCores Bool
- | RandomSeed Integer
- | ReproducibleResourceLimit Integer
- | SMTVerbosity Integer
- | OptionKeyword String [String]
- | SetLogic Logic
- | SetInfo String [String]
- data Logic
Documentation
In certain cases, the user might want to take over the communication with the solver, programmatically querying the engine and issuing commands accordingly. Even with human guidance, perhaps, where the user can take a look at the engine state and issue commands to guide the proof. This is an advanced feature, as the user is given full access to the underlying SMT solver, so the usual protections provided by SBV are no longer there to prevent mistakes.
Having said that, 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:
- Data.SBV.Examples.Queries.AllSat: Simulating SBV's
allSatusing queries. - Data.SBV.Examples.Queries.CaseSplit: Performing a case-split during a query.
- Data.SBV.Examples.Queries.Enums: Using enumerations in queries.
- Data.SBV.Examples.Queries.FourFours: Solution to a fun arithmetic puzzle, coded using queries.
- Data.SBV.Examples.Queries.GuessNumber: The famous number guessing game.
- Data.SBV.Examples.Queries.UnsatCore: Extracting unsat-cores using queries.
User queries
A query is a user-guided mechanism to directly communicate and extract results from the solver.
Create a fresh variable
freshVar_ :: forall a. SymWord a => Query (SBV a) Source #
Similar to freshVar, except creates unnamed variable.
freshVar :: forall a. SymWord 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.
Checking satisfiability
checkSat :: Query CheckSatResult Source #
Check for satisfiability.
checkSatUsing :: String -> Query CheckSatResult Source #
Check for satisfiability with a custom check-sat-using command.
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.)
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
Usage note: getUnsatCore is usually easier to use than checkSatAssumingWithUnsatisfiableSet, as it
allows the use of named assertions, as obtained by namedAssert. If getUnsatCore
fills your needs, you should definitely prefer it over checkSatAssumingWithUnsatisfiableSet.
Querying the solver
Extracting values
class SMTValue a where Source #
A class which allows for sexpr-conversion to values
Instances
getUninterpretedValue :: HasKind a => SBV a -> Query String Source #
Get the value of an uninterpreted sort, as a String
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.
getSMTResult :: Query SMTResult Source #
Issue check-sat and get an SMT Result out.
getUnknownReason :: Query String Source #
Get the reason unknown. Only internally used.
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
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
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.
Extracting assertions
getAssertions :: Query [String] Source #
Retrieve assertions. Note you must have arranged for
assertions to be available first (via setOption $ ProduceAssertions True
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.
Getting solver information
data SMTInfoFlag Source #
Collectable information from the solver.
Constructors
| AllStatistics | |
| AssertionStackLevels | |
| Authors | |
| ErrorBehavior | |
| Name | |
| ReasonUnknown | |
| Version | |
| InfoKeyword String |
Instances
data SMTErrorBehavior Source #
Behavior of the solver for errors.
Constructors
| ErrorImmediateExit | |
| ErrorContinuedExecution |
Instances
data SMTReasonUnknown Source #
Reason for reporting unknown.
Constructors
| UnknownMemOut | |
| UnknownIncomplete | |
| UnknownOther String |
Instances
data SMTInfoResponse Source #
Collectable information from the solver.
Constructors
Instances
getInfo :: SMTInfoFlag -> Query SMTInfoResponse Source #
Ask solver for info.
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 getOption ProduceUnsatCoresNothing or Just (ProduceUnsatCores True) or Just (ProduceUnsatCores False).
Result will be Nothing if the solver does not support this option.
Entering and exiting assertion stack
push :: Int -> Query () Source #
Push the context, entering a new one. Pushes multiple levels if n > 1.
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.
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.
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
Resetting the solver state
resetAssertions :: Query () Source #
Reset the solver, by forgetting all the assertions. However, bindings are kept as is,
as opposed to reset. 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.
Communicating results back
Constructing assignments
(|->) :: SymWord a => SBV a -> a -> Assignment infix 1 Source #
Make an assignment. The type Assignment is abstract, see success for an example use case.
Miscellaneous
echo :: String -> Query () Source #
Echo a string. Note that the echoing is done by the solver, not by SBV.
Terminating the query
mkSMTResult :: [Assignment] -> Query SMTResult Source #
Produce the query result from an assignment.
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.
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.
Performing actions
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, useProduceAssertionsinstead.):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.
Constructors
Logics supported
SMT-Lib logics. If left unspecified SBV will pick the logic based on what it determines is needed. However, the
user can override this choice using the tactic SetOptions This is especially handy if one is experimenting with custom
logics that might be supported on new solvers. See http://smtlib.cs.uiowa.edu/logics.shtml for the official list.
Constructors
| AUFLIA | Formulas over the theory of linear integer arithmetic and arrays extended with free sort and function symbols but restricted to arrays with integer indices and values. |
| AUFLIRA | Linear formulas with free sort and function symbols over one- and two-dimentional arrays of integer index and real value. |
| AUFNIRA | Formulas with free function and predicate symbols over a theory of arrays of arrays of integer index and real value. |
| LRA | Linear formulas in linear real arithmetic. |
| QF_ABV | Quantifier-free formulas over the theory of bitvectors and bitvector arrays. |
| QF_AUFBV | Quantifier-free formulas over the theory of bitvectors and bitvector arrays extended with free sort and function symbols. |
| QF_AUFLIA | Quantifier-free linear formulas over the theory of integer arrays extended with free sort and function symbols. |
| QF_AX | Quantifier-free formulas over the theory of arrays with extensionality. |
| QF_BV | Quantifier-free formulas over the theory of fixed-size bitvectors. |
| QF_IDL | Difference Logic over the integers. Boolean combinations of inequations of the form x - y < b where x and y are integer variables and b is an integer constant. |
| QF_LIA | Unquantified linear integer arithmetic. In essence, Boolean combinations of inequations between linear polynomials over integer variables. |
| QF_LRA | Unquantified linear real arithmetic. In essence, Boolean combinations of inequations between linear polynomials over real variables. |
| QF_NIA | Quantifier-free integer arithmetic. |
| QF_NRA | Quantifier-free real arithmetic. |
| QF_RDL | Difference Logic over the reals. In essence, Boolean combinations of inequations of the form x - y < b where x and y are real variables and b is a rational constant. |
| QF_UF | Unquantified formulas built over a signature of uninterpreted (i.e., free) sort and function symbols. |
| QF_UFBV | Unquantified formulas over bitvectors with uninterpreted sort function and symbols. |
| QF_UFIDL | Difference Logic over the integers (in essence) but with uninterpreted sort and function symbols. |
| QF_UFLIA | Unquantified linear integer arithmetic with uninterpreted sort and function symbols. |
| QF_UFLRA | Unquantified linear real arithmetic with uninterpreted sort and function symbols. |
| QF_UFNRA | Unquantified non-linear real arithmetic with uninterpreted sort and function symbols. |
| QF_UFNIRA | Unquantified non-linear real integer arithmetic with uninterpreted sort and function symbols. |
| UFLRA | Linear real arithmetic with uninterpreted sort and function symbols. |
| UFNIA | Non-linear integer arithmetic with uninterpreted sort and function symbols. |
| QF_FPBV | Quantifier-free formulas over the theory of floating point numbers, arrays, and bit-vectors. |
| QF_FP | Quantifier-free formulas over the theory of floating point numbers. |
| QF_FD | Quantifier-free finite domains |
| Logic_ALL | The catch-all value |
| CustomLogic String | In case you need a really custom string! |