Safe Haskell | Safe-Inferred |
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General operations on sets
- class Eq a => Lattice a where
- empty :: Lattice a => a
- universal :: Lattice a => a
- unions :: Lattice a => [a] -> a
- intersections :: Lattice a => [a] -> a
- lensedFixedPoint :: Lattice lat => Lens a lat -> Lens b lat -> (a -> b) -> a -> b
- lensedIndexedFixedPoint :: Lattice lat => Lens a lat -> Lens b lat -> (Int -> a -> b) -> a -> (b, Int)
- fixedPoint :: Lattice a => (a -> a) -> a -> a
- indexedFixedPoint :: Lattice a => (Int -> a -> a) -> a -> (a, Int)
- type Widening a = (Int -> a -> a) -> Int -> a -> a
- cutOffAt :: Lattice a => Int -> Widening a
- boundedLensedFixedPoint :: Lattice lat => Int -> Lens a lat -> Lens b lat -> (a -> b) -> a -> (b, Int)
Documentation
class Eq a => Lattice a whereSource
Lattice types
Lattice () | |
Lattice AnySize | |
BoundedInt a => Lattice (Range a) | |
(Lattice a, Lattice b) => Lattice (a, b) | Lattice product |
(Lattice a, Lattice b) => Lattice (:> a b) | |
(Lattice a, Lattice b, Lattice c) => Lattice (a, b, c) | Three-way product |
(Lattice a, Lattice b, Lattice c, Lattice d) => Lattice (a, b, c, d) | Four-way product |
(Lattice a, Lattice b, Lattice c, Lattice d, Lattice e) => Lattice (a, b, c, d, e) | Five-way product |
(Lattice a, Lattice b, Lattice c, Lattice d, Lattice e, Lattice f) => Lattice (a, b, c, d, e, f) | Six-way product |
(Lattice a, Lattice b, Lattice c, Lattice d, Lattice e, Lattice f, Lattice g) => Lattice (a, b, c, d, e, f, g) | Seven-way product |
intersections :: Lattice a => [a] -> aSource
Accumulated meet
Computing fixed points
lensedFixedPoint :: Lattice lat => Lens a lat -> Lens b lat -> (a -> b) -> a -> bSource
Generalization of fixedPoint
to functions whose argument and result
contain (i.e has a lens to) a common lattice
lensedIndexedFixedPoint :: Lattice lat => Lens a lat -> Lens b lat -> (Int -> a -> b) -> a -> (b, Int)Source
Generalization of indexedFixedPoint
to functions whose argument and
result contain (i.e has a lens to) a common lattice
fixedPoint :: Lattice a => (a -> a) -> a -> aSource
Take the fixed point of a function. The second argument is an initial
element. A sensible default for the initial element is bot
.
The function is not required to be monotonic. It is made monotonic internally by always taking the union of the result and the previous value.
indexedFixedPoint :: Lattice a => (Int -> a -> a) -> a -> (a, Int)Source
Much like fixedPoint
but keeps track of the number of iterations
in the fixed point iteration. Useful for defining widening operators.
type Widening a = (Int -> a -> a) -> Int -> a -> aSource
The type of widening operators. A widening operator modifies a function that is subject to fixed point analysis. A widening operator introduces approximations in order to guarantee (fast) termination of the fixed point analysis.
cutOffAt :: Lattice a => Int -> Widening aSource
A widening operator which defaults to top
when the number of
iterations goes over the specified value.
boundedLensedFixedPoint :: Lattice lat => Int -> Lens a lat -> Lens b lat -> (a -> b) -> a -> (b, Int)Source
A bounded version of lensedFixedPoint
. It will always do at least one
iteration regardless of the provided bound (in order to return something of
the right type).