What4.Utils.BVDomain.Bitwise

Provides a bitwise implementation of bitvector abstract domains.

Documentation

data Domain (w :: Nat)

A bitwise interval domain, defined via a bitwise upper and lower bound. The ordering used here to construct the interval is the pointwise ordering on bits. In particular x [= y iff x .|. y == y, and a value x is in the set defined by the pair (lo,hi) just when lo [= x && x [= hi.

Constructors

BVBitInterval !Integer !Integer !Integer

BVDBitInterval mask lo hi. mask caches the value of 2^w - 1

Instances

Show (Domain w)

Defined in What4.Utils.BVDomain.Bitwise

Methods

showsPrec :: Int -> Domain w -> ShowS

show :: Domain w -> String

showList :: [Domain w] -> ShowS

bitle :: Integer -> Integer -> Bool

proper :: NatRepr w -> Domain w -> Bool

Test if the domain satisfies its invariants

bvdMask :: Domain w -> Integer

Return the bitvector mask value from this domain

member :: Domain w -> Integer -> Bool

Test if the given integer value is a member of the abstract domain

pmember :: NatRepr n -> Domain n -> Integer -> Bool

Check that a domain is proper, and that the given value is a member

size :: Domain w -> Integer

Compute how many concrete elements are in the abstract domain

asSingleton :: Domain w -> Maybe Integer

Test if this domain contains a single value, and return it if so

nonempty :: Domain w -> Bool

Returns true iff there is at least on element in this bitwise domain.

eq :: Domain w -> Domain w -> Maybe Bool

domainsOverlap :: Domain w -> Domain w -> Bool

Returns true iff the domains have some value in common

bitbounds :: Domain w -> (Integer, Integer)

Bitwise lower and upper bounds

Operations

any :: NatRepr w -> Domain w

Bitwise domain containing every bitvector value

singleton :: NatRepr w -> Integer -> Domain w

Return a domain containing just the given value

range :: NatRepr w -> Integer -> Integer -> Domain w

Construct a domain from bitwise lower and upper bounds

interval :: Integer -> Integer -> Integer -> Domain w

Unsafe constructor for internal use.

union :: Domain w -> Domain w -> Domain w

intersection :: Domain w -> Domain w -> Domain w

concat :: NatRepr u -> Domain u -> NatRepr v -> Domain v -> Domain (u + v)

concat a y returns domain where each element in a has been concatenated with an element in y. The most-significant bits are a, and the least significant bits are y.

select :: (1 <= n, (i + n) <= w) => NatRepr i -> NatRepr n -> Domain w -> Domain n

select i n a selects n bits starting from index i from a.

zext :: (1 <= w, (w + 1) <= u) => Domain w -> NatRepr u -> Domain u

sext :: (1 <= w, (w + 1) <= u) => NatRepr w -> Domain w -> NatRepr u -> Domain u

testBit :: Domain w -> Natural -> Maybe Bool

shifts and rotates

shl :: NatRepr w -> Domain w -> Integer -> Domain w

lshr :: NatRepr w -> Domain w -> Integer -> Domain w

ashr :: 1 <= w => NatRepr w -> Domain w -> Integer -> Domain w

rol :: NatRepr w -> Domain w -> Integer -> Domain w

ror :: NatRepr w -> Domain w -> Integer -> Domain w

bitwise logical

and :: Domain w -> Domain w -> Domain w

or :: Domain w -> Domain w -> Domain w

xor :: Domain w -> Domain w -> Domain w

not :: Domain w -> Domain w

Correctness properties

genDomain :: NatRepr w -> Gen (Domain w)

Random generator for domain values. We always generate nonempty domain values.

genElement :: Domain w -> Gen Integer

genPair :: NatRepr w -> Gen (Domain w, Integer)

Generate a random nonempty domain and an element contained in that domain.

correct_any :: 1 <= n => NatRepr n -> Integer -> Property

correct_singleton :: 1 <= n => NatRepr n -> Integer -> Integer -> Property

correct_overlap :: Domain n -> Domain n -> Integer -> Property

correct_union :: 1 <= n => NatRepr n -> Domain n -> Domain n -> Integer -> Property

correct_intersection :: 1 <= n => Domain n -> Domain n -> Integer -> Property

correct_zero_ext :: (1 <= w, (w + 1) <= u) => NatRepr w -> Domain w -> NatRepr u -> Integer -> Property

correct_sign_ext :: (1 <= w, (w + 1) <= u) => NatRepr w -> Domain w -> NatRepr u -> Integer -> Property

correct_concat :: NatRepr m -> (Domain m, Integer) -> NatRepr n -> (Domain n, Integer) -> Property

correct_shrink :: NatRepr i -> NatRepr n -> (Domain (i + n), Integer) -> Property

correct_trunc :: n <= w => NatRepr n -> (Domain w, Integer) -> Property

correct_select :: (1 <= n, (i + n) <= w) => NatRepr i -> NatRepr n -> (Domain w, Integer) -> Property

correct_shl :: 1 <= n => NatRepr n -> (Domain n, Integer) -> Integer -> Property

correct_lshr :: 1 <= n => NatRepr n -> (Domain n, Integer) -> Integer -> Property

correct_ashr :: 1 <= n => NatRepr n -> (Domain n, Integer) -> Integer -> Property

correct_rol :: 1 <= n => NatRepr n -> (Domain n, Integer) -> Integer -> Property

correct_ror :: 1 <= n => NatRepr n -> (Domain n, Integer) -> Integer -> Property

correct_eq :: 1 <= n => NatRepr n -> (Domain n, Integer) -> (Domain n, Integer) -> Property

correct_and :: 1 <= n => NatRepr n -> (Domain n, Integer) -> (Domain n, Integer) -> Property

correct_or :: 1 <= n => NatRepr n -> (Domain n, Integer) -> (Domain n, Integer) -> Property

correct_not :: 1 <= n => NatRepr n -> (Domain n, Integer) -> Property

correct_xor :: 1 <= n => NatRepr n -> (Domain n, Integer) -> (Domain n, Integer) -> Property

correct_testBit :: 1 <= n => NatRepr n -> (Domain n, Integer) -> Natural -> Property