Data.SBV.Tools.Range

Single variable valid range detection.

Boundaries and ranges

data Boundary a

A boundary value

Constructors

Unbounded

Unbounded

Open a

Exclusive of the point

Closed a

Inclusive of the point

data Range a

A range is a pair of boundaries: Lower and upper bounds

Constructors

Range (Boundary a) (Boundary a)

Instances

Show a => Show (Range a)

Show instance for Range

Defined in Data.SBV.Tools.Range

Methods

showsPrec :: Int -> Range a -> ShowS

show :: Range a -> String

showList :: [Range a] -> ShowS

Computing valid ranges

ranges :: forall a. (Ord a, Num a, SymVal a, SatModel a, Metric a, SymVal (MetricSpace a), SatModel (MetricSpace a)) => (SBV a -> SBool) -> IO [Range a]

Given a single predicate over a single variable, find the contiguous ranges over which the predicate is satisfied. SBV will make one call to the optimizer, and then as many calls to the solver as there are disjoint ranges that the predicate is satisfied over. (Linear in the number of ranges.) Note that the number of ranges is large, this can take a long time!

Beware that, as of June 2021, z3 no longer supports optimization with SReal in the presence of strict inequalities. See https://github.com/Z3Prover/z3/issues/5314 for details. So, if you have SReal variables, it is important that you do not use a strict inequality, i.e., .>, .<, ./= etc. Inequalities of the form .<=, .>= should be OK. Please report if you see any fishy behavior due to this change in z3's behavior.

Some examples:

>>> ranges (\(_ :: SInteger) -> sFalse)
[]
>>> ranges (\(_ :: SInteger) -> sTrue)
[(-oo,oo)]
>>> ranges (\(x :: SInteger) -> sAnd [x .<= 120, x .>= -12, x ./= 3])
[[-12,3),(3,120]]
>>> ranges (\(x :: SInteger) -> sAnd [x .<= 75, x .>= 5, x ./= 6, x ./= 67])
[[5,6),(6,67),(67,75]]
>>> ranges (\(x :: SInteger) -> sAnd [x .<= 75, x ./= 3, x ./= 67])
[(-oo,3),(3,67),(67,75]]
>>> ranges (\(x :: SReal) -> sAnd [x .>= 3.2, x .<= 12.7])
[[3.2,12.7]]
>>> ranges (\(x :: SReal) -> sAnd [x .<= 12.7, x ./= 8])
[(-oo,8.0),(8.0,12.7]]
>>> ranges (\(x :: SReal) -> sAnd [x .>= 12.7, x ./= 15])
[[12.7,15.0),(15.0,oo)]
>>> ranges (\(x :: SInt8) -> sAnd [x .<= 7, x ./= 6])
[[-128,6),(6,7]]
>>> ranges $ \x -> x .>= (0::SReal)
[[0.0,oo)]
>>> ranges $ \x -> x .<= (0::SReal)
[(-oo,0.0]]
>>> ranges $ \(x :: SWord8) -> 2*x .== 4
[[2,3),(129,130]]

rangesWith :: forall a. (Ord a, Num a, SymVal a, SatModel a, Metric a, SymVal (MetricSpace a), SatModel (MetricSpace a)) => SMTConfig -> (SBV a -> SBool) -> IO [Range a]

Compute ranges, using the given solver configuration.