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, SMTValue 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! 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 .> 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)]

rangesWith :: forall a. (Ord a, Num a, SymVal a, SMTValue 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.