ConstraintsBetweenIntegerValues
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package l1
Represents an (unknown) integer value.
Represents an (unknown) integer value.
Models the top value of this domain's lattice.
Abstracts over the concrete type of IllegalValue.
Abstracts over the concrete type of IllegalValue.
This type needs to be refined whenever the class IllegalValue
is refined or the type DomainValue is refined.
Abstracts over the concrete type of ReturnAddressValue.
Abstracts over the concrete type of ReturnAddressValue. Needs to be fixed
by some sub-trait/sub-class. In the simplest case (i.e., when neither the
Value trait nor the ReturnAddressValue trait was refined) it is sufficient
to write:
type DomainReturnAddressValue = ReturnAddressValue
Abstracts over the concrete type of Value.
Abstracts over the concrete type of Value. Needs to be refined by traits that
inherit from Domain and which extend Domain's Value trait.
A simple type alias of the type DomainValue.
A simple type alias of the type DomainValue.
Used to facilitate comprehension.
A type alias for Iterables of ExceptionValues.
A type alias for Iterables of ExceptionValues.
Primarily used to facilitate comprehension.
Represents a value that has no well defined state/type.
Represents a value that has no well defined state/type. Such values are the result of a join of two incompatible values and are generally only found in registers (in the locals) and then identify a value that is dead.
org.opalj.ai.Domain.Value for further details.
Abstracts over all values with computational type integer.
Abstracts over all values with computational type integer.
Represents a range of integer values.
Represents a range of integer values. The range's bounds are inclusive. Unless a range has only one value it is impossible to tell whether or not a value that is in the range will potentially occur at runtime.
Computation that returns a numeric value or an ObjectType.ArithmeticException.
Computation that returns a numeric value or an ObjectType.ArithmeticException.
An instruction's current register values/locals are represented using an array.
An instruction's current register values/locals are represented using an array.
An instruction's operands are represented using a list where the first element of the list represents the top level operand stack value.
An instruction's operands are represented using a list where the first element of the list represents the top level operand stack value.
Stores a single return address (i.e., a program counter/index into the code array).
Stores a single return address (i.e., a program counter/index into the code array).
Though the framework completely handles all aspects related to return address
values, it is nevertheless necessary that this class inherits from Value
as return addresses are stored on the stack/in the registers. However,
if the Value trait should be refined, all additional methods may – from
the point-of-view of OPAL-AI - just throw an OperationNotSupportedException
as these additional methods will never be called by OPAL-AI.
Abstracts over a concrete operand stack value or a value stored in one of the local variables/registers.
Abstracts over a concrete operand stack value or a value stored in one of the local variables/registers.
In general, subclasses and users of a Domain should not have/declare
a direct dependency on Value. Instead they should use DomainValue as otherwise
extensibility of a Domain may be hampered or even be impossible. The only
exceptions are, of course, classes that directly inherit from this class.
If you directly extend/refine this trait (i.e., in a subclass of the Domain trait
you write something like trait Value extends super.Value), make sure that
you also extend all classes/traits that inherit from this type
(this may require a deep mixin composition and that you refine the type
DomainType accordingly).
However, OPAL was designed such that extending this class should – in general
– not be necessary. It may also be easier to encode the desired semantics – as
far as possible – as part of the domain.
Standard inheritance from this trait is always supported and is the primary mechanism to model an abstract domain's lattice w.r.t. some special type of value. In general, the implementation should try to avoid creating new instances of values unless strictly required to model the domain's semantics. This will greatly improve the overall performance as this framework heavily uses reference-based equality checks to speed up the evaluation.
OPAL does not rely on any special equality semantics w.r.t. values and
never directly or indirectly calls a Value's equals or eq method. Hence,
a domain can encode equality such that it best fits its need.
However, some of the provided domains rely on the following semantics for equals:
Two domain values have to be equal (==) iff they represent the same
information. This includes additional information, such as, the value of
the origin.
E.g., a value (AnIntegerValue) that represents an arbitrary Integer value
has to return true if the domain value with which it is compared also
represents an arbitrary Integer value (AnIntegerValue). However,
it may still be necessary to use multiple objects to represent an arbitrary
integer value if, e.g., constraints should be attached to specific values.
For example, after a comparison of an integer value with a predefined
value (e.g., AnIntegerValue < 4) it is possible to constrain the respective
value on the subsequent paths (< 4 on one path and >= 4 on the other path).
To make that possible, it is however necessary to distinguish the
AnIntegervalue from some other AnIntegerValue to avoid constraining
unrelated values.
public void foo(int a,int b) {
if(a < 4) {
z = a - 2 // here a is constrained (< 4), b and z are unconstrained
}
else {
z = a + 2 // here a is constrained (>= 4), b and z are unconstrained
}
} In general, equals is only defined for values belonging to the same
domain. If values need to be compared across domains, they need to be adapted
to a target domain first.
Factory method to create a representation of a boolean value with the given initial value and origin.
Factory method to create a representation of a boolean value with the given initial value and origin.
The domain may ignore the information about the value and the origin (origin).
Factory method to create a representation of a boolean value if we know the origin of the value.
Factory method to create a representation of a boolean value if we know the origin of the value.
The domain may ignore the information about the origin (origin).
Factory method to create a DomainValue that represents the given byte value
and that was created (explicitly or implicitly) by the instruction with the
specified program counter.
Factory method to create a DomainValue that represents the given byte value
and that was created (explicitly or implicitly) by the instruction with the
specified program counter.
The domain may ignore the information about the value and the origin (origin).
Factory method to create a DomainValue that was created (explicitly or
implicitly) by the instruction with the specified program counter.
Factory method to create a DomainValue that was created (explicitly or
implicitly) by the instruction with the specified program counter.
The domain may ignore the information about the origin (origin).
Factory method to create a DomainValue that represents the given char value
and that was created (explicitly or implicitly) by the instruction with the
specified program counter.
Factory method to create a DomainValue that represents the given char value
and that was created (explicitly or implicitly) by the instruction with the
specified program counter.
Factory method to create a DomainValue that was created (explicitly or
implicitly) by the instruction with the specified program counter.
Factory method to create a DomainValue that was created (explicitly or
implicitly) by the instruction with the specified program counter.
The domain may ignore the information about the origin (origin).
The class tag for the type DomainValue.
The class tag for the type DomainValue.
Required to generate instances of arrays in which values of type
DomainValue can be stored in a type-safe manner.
In the sub-trait or class that fixes the type of DomainValue it is necessary
to implement this abstract val using:
val DomainValueTag : ClassTag[DomainValue] = implicitly(As of Scala 2.10 it is necessary that you do not use implicit in the subclass -
it will compile, but fail at runtime.)
Creates a new IntegerRange value with the given bounds.
Creates a new IntegerRange value with the given bounds.
Factory method to create a DomainValue that represents the given integer value
and that was created (explicitly or implicitly) by the instruction with the
specified program counter.
Factory method to create a DomainValue that represents the given integer value
and that was created (explicitly or implicitly) by the instruction with the
specified program counter.
The domain may ignore the information about the value and the origin (origin).
Factory method to create a DomainValue that was created (explicitly or
implicitly) by the instruction with the specified program counter.
Factory method to create a DomainValue that was created (explicitly or
implicitly) by the instruction with the specified program counter.
The domain may ignore the information about the origin (origin).
The result of the merge of two incompatible values has
to be reported as a MetaInformationUpdate[DomainIllegalValue].
The result of the merge of two incompatible values has
to be reported as a MetaInformationUpdate[DomainIllegalValue].
Factory method to create an instance of a ReturnAddressValue.
Factory method to create an instance of a ReturnAddressValue.
Factory method to create a DomainValue that represents the given short value
and that was created (explicitly or implicitly) by the instruction with the
specified program counter.
Factory method to create a DomainValue that represents the given short value
and that was created (explicitly or implicitly) by the instruction with the
specified program counter.
Factory method to create a DomainValue that was created (explicitly or
implicitly) by the instruction with the specified program counter.
Factory method to create a DomainValue that was created (explicitly or
implicitly) by the instruction with the specified program counter.
The domain may ignore the information about the origin (origin).
The singleton instance of the IllegalValue.
The singleton instance of the IllegalValue.
The singleton instance of ReturnAddressValues
The singleton instance of ReturnAddressValues
Factory method to create a representation of the integer constant value 0.
Factory method to create a representation of the integer constant value 0.
OPAL in particular uses this special value for performing subsequent computations against the fixed value 0 (e.g., for if_XX instructions).
(The origin (ValueOrigin) that is used is the ConstantValueOrigin to signify that this value was not created by the program.)
The domain may ignore the information about the value.
Creates a new IntegerRange value with the given bounds.
Creates a new IntegerRange value with the given bounds.
Creates a new IntegerRange value with the lower and upper bound set to the given value.
Creates a new IntegerRange value with the lower and upper bound set to the given value.
Extractor for IntegerRange values.
Extractor for IntegerRange values.
The result of merging two values should never be reported as a
StructuralUpdate if the computed value is an IllegalValue.
The result of merging two values should never be reported as a
StructuralUpdate if the computed value is an IllegalValue. The JVM semantics
guarantee that the value was not used in the first case and, hence, continuing
the interpretation is meaningless.
This method is solely defined for documentation purposes and to catch implementation errors early on.
Called by the abstract interpreter when the abstract interpretation of a method has ended.
Called by the abstract interpreter when the abstract interpretation of a method has ended. The abstract interpretation of a method ends if either the fixpoint is reached or the interpretation was aborted.
By default this method does nothing.
Domains that override this method are expected to also call
super.abstractInterpretationEnded(aiResult).
This methods is called by OPAL after the evaluation of the instruction with
the given pc with respect to targetPC, but before the values are propagated
(joined) and before it is checked whether the interpretation needs to be continued.
This methods is called by OPAL after the evaluation of the instruction with
the given pc with respect to targetPC, but before the values are propagated
(joined) and before it is checked whether the interpretation needs to be continued.
I.e., if the operands (newOperands) or locals (newLocals) are further refined
then the refined operands and locals are joined (if necessary).
During the evaluation of the instruction it is possible that this method
is called multiple times with different targetPCs. The latter is not only
true for control flow instructions, but also for those instructions
that may raise an exception.
This method can and is intended to be overridden to further refine the operand
stack/the locals. However, the overriding method should always forward the (possibly
refined) operands and locals to the super method (stackable traits).
This method is called immediately before a join operation with regard
to the specified pc is performed.
This method is called immediately before a join operation with regard
to the specified pc is performed.
This method is intended to be overwritten by clients to perform custom operations.
org.opalj.br.Code.cfPCs
Called by the framework after evaluating the instruction with the given pc.
Called by the framework after evaluating the instruction with the given pc. I.e., the state of all potential successor instructions was updated and the flow method was called – potentially multiple times – accordingly.
By default this method does nothing.
Called by the framework after performing a computation to inform the domain about the result.
Called by the framework after performing a computation to inform the domain
about the result.
That is, after evaluating the effect of the instruction with currentPC on the current
stack and register and (if necessary) joining the updated stack and registers with the stack
and registers associated with the instruction successorPC. (Hence, this method
is ONLY called for return instructions if the return instruction throws an
IllegalMonitorStateException.)
This function basically informs the domain about the instruction that
may be evaluated next. The flow function is called for every possible
successor of the instruction with currentPC. This includes all branch
targets as well as those instructions that handle exceptions.
In some cases it will even be the case that flow is called multiple times with
the same pair of program counters: (currentPC, successorPC). This may happen,
e.g., in case of a switch instruction where multiple values have the same
body/target instruction and we do not have precise information about the switch value.
E.g., as in the following snippet:
switch (i) { // pc: X => Y (for "1"), Y (for "2"), Y (for "3")
case 1:
case 2:
case 3: System.out.println("Great."); // pc: Y
default: System.out.println("Not So Great."); // pc: Z
}The flow function is also called after instructions that are domain independent
such as dup and load instructions which just manipulate the registers
and stack in a generic way.
This enables the domain to precisely follow the evaluation
progress and in particular to perform control-flow dependent analyses.
The program counter of the instruction that is currently evaluated by the abstract interpreter.
The current operands. I.e., the operand stack before the instruction is evaluated.
The current locals. I.e., the locals before the instruction is evaluated.
The program counter of an instruction that is a potential
successor of the instruction with currentPC. In general the AI framework
adds the pc of the successor instruction to the beginning of the worklist
unless it is a join instruction. In this case the pc is added to the end – in
the context of the current (sub)routine. Hence, the AI framework first evaluates
all paths leading to a join instruction before the join instruction will
be evaluated.
Yes if the successor instruction is or was scheduled.
I.e., Yes is returned if the worklist contains successorPC, No if the
worklist does not contain successorPC. Unknown is returned if the AI
framework did not process the worklist and doesn't know anything about
the scheduled successors. Note that this value is independent of the
subroutine in which the value may be scheduled. If an implementation schedules
successorPC the the super call has to set isSuccessorScheduled to Yes.
true if and only if the evaluation of
the instruction with the program counter currentPC threw an exception;
false otherwise. Hence, if this parameter is true the instruction
with successorPC is the first instruction of the handler.
> 0 if and only if we have an exceptional
control flow that terminates one or more subroutines.
In this case the successor instruction is scheduled (if at all) after all
subroutines that will be terminated by the exception.
true if a join was performed. I.e., the successor
instruction is an instruction (Code.cfJoins) that was already
previously evaluated and where multiple paths potentially join.
The current list of instructions that will be evaluated next.
If you want to force the evaluation of the instruction
with the program counter successorPC it is sufficient to test whether
the list already contains successorPC and – if not – to prepend it.
If the worklist already contains successorPC then the domain is allowed
to move the PC to the beginning of the worklist.
If the PC does not belong to the same (current) (sub)routine, it is not allowed to be moved to the beginning of the worklist. (Subroutines can only be found in code generated by old Java compilers; before Java 6. Subroutines are identified by jsr/ret instructions. A subroutine can be identified by going back in the worklist and by looking for specific "program counters" (e.g., SUBROUTINE_START, SUBROUTINE_END). These program counters mark the beginning of a subroutine. In other words, an instruction can be freely moved around unless a special program counter value is found. All special program counters use negative values. Additionally, neither the negative values nor the positive values between two negative values should be changed. Furthermore, no value (PC) should be put between negative values that capture subroutine information. If the domain updates the worklist, it is the responsibility of the domain to call the tracer and to inform it about the changes. Note that the worklist is not allowed to contain duplicates related to the evaluation of the current (sub-)routine.
The array that associates every instruction with its
operand stack that is in effect. Note, that only those elements of the
array contain values that are related to instructions that were
evaluated in the past; the other elements are null. Furthermore,
it identifies the operandsArray of the subroutine that will execute the
instruction with successorPC.
The operandsArray may be null for the current instruction (not the successor
instruction) if the execution of the current instruction leads to the termination
of the current subroutine. In this case the information about the operands
and locals associated with all instructions belonging to the subroutine is
reset.
The array that associates every instruction with its current
register values. Note, that only those elements of the
array contain values that are related to instructions that were evaluated in
the past. The other elements are null. Furthermore,
it identifies the localsArray of the subroutine that will execute the
instruction with successorPC.
The localsArray may be null for the current instruction (not the successor
instruction) if the execution of the current instruction leads to the termination
of the current subroutine. In this case the information about the operands
and locals associated with all instructions belonging to the subroutine is
reset.
The updated worklist. In most cases this is simply the given worklist.
The default case is also to return the given worklist.
A method that overrides this method must always call the super method to ensure that every domain that uses this hook gets informed about a flow.
,The domain is allowed to modify the worklist, operandsArray and
localsArray. However, the AI will not perform any checks. In case of
updates of the operandsArray or localsArray it is necessary to first
create a shallow copy before updating it.
If this is not done, it may happen that the locals associated
with other instructions are also updated.
Tests if the two given integer values are equal.
Tests if the two given integer values are equal.
A value with computational type integer.
A value with computational type integer.
Tests if the two given integer values are not equal.
Tests if the two given integer values are not equal.
A value with computational type integer.
A value with computational type integer.
This function is ONLY defined if a corresponding test (value1 == value2)
returned org.opalj.Unknown. I.e., this method is only allowed to be
called if there is something to establish!
I.e., the domain values are real ranges (not single values, e.g., [1,1])
that overlap.
This function is ONLY defined if a corresponding test (value1 != value2)
returned org.opalj.Unknown. I.e., this method is only allowed to be
called if there is something to establish!
I.e., the domain values are real ranges (not single values, e.g., [1,1])
that overlap.
This function is ONLY defined if a corresponding test (value1 < value2)
returned org.opalj.Unknown. I.e., this method is only allowed to be
called if there is something to establish!
I.e., the domain values are real ranges (not single values, e.g., [1,1])
that overlap.
This function is ONLY defined if a corresponding test (value1 <= value2)
returned org.opalj.Unknown. I.e., this method is only allowed to be
called if there is something to establish!
I.e., the domain values are real ranges (not single values, e.g., [1,1])
that overlap.
Sets the given domain value to theValue.
Sets the given domain value to theValue.
This function is called by OPAL before it starts to explore the branch where this condition has to hold. (This function is, e.g., called whenever we explore the branches of a switch-case statement.) I.e., the constraint is established before a potential join operation.
An integer domain value that does also, but not exclusively represents
theValue.
Tests if the given integer value is 0 or maybe 0.
Tests if the given integer value is 0 or maybe 0.
A value with computational type integer.
Tests if the first integer value is larger than the second value.
Tests if the first integer value is larger than the second value.
A value with computational type integer.
A value with computational type integer.
Tests if the given integer value is > 0 or maybe > 0.
Tests if the given integer value is > 0 or maybe > 0.
A value with computational type integer.
Tests if the first integer value is larger than or equal to the second value.
Tests if the first integer value is larger than or equal to the second value.
A value with computational type integer.
A value with computational type integer.
Tests if the given value is greater than or equal to 0 or maybe greater than or equal to 0.
Tests if the given value is greater than or equal to 0 or maybe greater than or equal to 0.
A value with computational type integer.
Tests if the first integer value is smaller than the second value.
Tests if the first integer value is smaller than the second value.
Tests if the given integer value is < 0 or maybe < 0.
Tests if the given integer value is < 0 or maybe < 0.
A value with computational type integer.
Tests if the first integer value is less than or equal to the second value.
Tests if the first integer value is less than or equal to the second value.
Tests if the given integer value is less than or equal to 0 or maybe less than or equal to 0.
Tests if the given integer value is less than or equal to 0 or maybe less than or equal to 0.
A value with computational type integer.
Tests if the given integer value is not 0 or maybe not 0.
Tests if the given integer value is not 0 or maybe not 0.
A value with computational type integer.
Returns Yes iff at least one possible extension of the given
value is in the specified range; that is, if the intersection of the range of
values captured by the given value and the specified range is non-empty.
Returns Yes iff at least one possible extension of the given
value is in the specified range; that is, if the intersection of the range of
values captured by the given value and the specified range is non-empty.
For example, if the given value captures all positive integer values and the
specified range is [-1,1] then the answer has to be Yes. If we know nothing
about the potential extension of the given value the answer will be Unknown.
The answer is No iff both ranges are non-overlapping.
A value that has to be of computational type integer.
The range's lower bound (inclusive).
The range's upper bound (inclusive).
Returns Yes iff at least one (possible) extension of a given value is
not in the specified range; that is, if the set difference of the range of
values captured by the given value and the specified range is non-empty.
Returns Yes iff at least one (possible) extension of a given value is
not in the specified range; that is, if the set difference of the range of
values captured by the given value and the specified range is non-empty.
For example, if the given value has the integer value 10 and the
specified range is [0,Integer.MAX_VALUE] then the answer has to be No. But,
if the given value represents the range [-5,Integer.MAX_VALUE] and the specified
range is again [0,Integer.MAX_VALUE] then the answer has to be Yes.
The answer is Yes iff the analysis determined that at runtime value will have
a value that is not in the specified range. If the analysis(domain) is not able
to determine whether the value is or is not in the given range then the answer
has to be Unknown.
A value that has to be of computational type integer.
The range's lower bound (inclusive).
The range's upper bound (inclusive).
If the given value encapsulates a precise integer value then the function
ifThen is called with the respective value otherwise orElse is called.
If the given value encapsulates a precise integer value then the function
ifThen is called with the respective value otherwise orElse is called.
Returns the current Int value represented by the domain value if it exists.
Returns the current Int value represented by the domain value if it exists.
This method returns None if the DomainValue does not represent an
Integer value or the precise value is not known. I.e., this method never fails.
Joins the given operand stacks and local variables.
Joins the given operand stacks and local variables.
In general there should be no need to refine this method. Overriding this method should only be done for analysis purposes.
This method heavily relies on reference comparisons to speed up the overall process of performing an abstract interpretation of a method. Hence, a computation should – whenever possible – return (one of) the original object(s) if that value has the same abstract state as the result. Furthermore, if all original values capture the same abstract state as the result of the computation, the "left" value/the value that was already used in the past should be returned.
The joined operand stack and registers.
Returns NoUpdate if this memory layout already subsumes the
other memory layout.
The operand stacks are guaranteed to contain compatible values w.r.t. the
computational type (unless the bytecode is not valid or OPAL contains
an error). I.e., if the result of joining two operand stack values is an
IllegalValue we assume that the domain implementation is incorrect.
However, the joining of two register values can result in an illegal value
which identifies the value is dead.
The size of the operands stacks that are to be joined and the number of registers/locals that are to be joined can be expected to be identical under the assumption that the bytecode is valid and the framework contains no bugs.
Enables the customization of the behavior of the base join method.
Enables the customization of the behavior of the base join method.
This method in particular enables, in case of a MetaInformationUpdate, to raise the update type to force the continuation of the abstract interpretation process.
Methods should always override this method and should call the super method.
The current update type. The level can be raised. It is an error to lower the update level.
The old operands, before the join. Should not be changed.
The old locals, before the join. Should not be changed.
The new operands; may be updated.
The new locals; may be updated.
The pc of the jsr(w) instruction.
Determines the maximum number of values captured by an integer value range.
Determines the maximum number of values captured by an integer value range.
This setting can be adapted at runtime.
Merges the given domain value v1 with the domain value v2 and returns
the merged value which is v1 if v1 is an abstraction of v2, v2 if v2
is an abstraction of v1 or some other value if a new value is computed that
abstracts over both values.
Merges the given domain value v1 with the domain value v2 and returns
the merged value which is v1 if v1 is an abstraction of v2, v2 if v2
is an abstraction of v1 or some other value if a new value is computed that
abstracts over both values.
This operation is commutative.
Returns a string representation of the properties associated with the instruction with the respective program counter.
Returns a string representation of the properties associated with the instruction with the respective program counter.
Associating properties with an instruction and maintaining those properties
is, however, at the sole responsibility of the Domain.
This method is predefined to facilitate the development of support tools and is not used by the abstract interpretation framework.
Domains that define (additional) properties should (abstract) override
this method and should return a textual representation of the property.
The pc of the ret instruction.
This function can be called when the instruction successorPC needs to be
scheduled.
This function can be called when the instruction successorPC needs to be
scheduled. The function will test if the instruction is already scheduled and
– if so – returns the given worklist. Otherwise the instruction
is scheduled in the correct (subroutine-)context.
Sets the code structure.
Sets the code structure.
This method is called by the AI framework immediately before the interpretation (continues).
Creates a summary of the given domain values by summarizing and
joining the given values.
Creates a summary of the given domain values by summarizing and
joining the given values. For the precise details
regarding the calculation of a summary see Value.summarize(...).
The program counter that will be used for the summary value if a new value is returned that abstracts over/summarizes the given values.
An Iterable over one or more values.
The current algorithm is generic and should satisfy most needs, but it is not very efficient. However, it should be easy to tailor it for a specific domain/domain values, if need be.
Returns the type(type bounds) of the given value.
Returns the type(type bounds) of the given value.
In general a single value can have multiple type bounds which depend on the
control flow.
However, all types that the value represents must belong to the same
computational type category. I.e., it is possible that the value either has the
type "NullPointerException or IllegalArgumentException", but it will never have
– at the same time – the (Java) types int and long. Furthermore,
it is possible that the returned type(s) is(are) only an upper bound of the
real type unless the type is a primitive type.
This default implementation always returns org.opalj.ai.TypeUnknown.
typeOfValueThis method is typically not implemented by a single Domain trait/object, but is
instead implemented collaboratively by all domains that implement the semantics
of certain values. To achieve that, other Domain traits that implement a
concrete domain's semantics have to abstract override this method and only
return the value's type if the domain knows anything about the type. If a method
that overrides this method has no knowledge about the given value, it should
delegate this call to its super method.
Example
trait FloatValues extends Domain[...] { ... abstract override def typeOfValue(value: DomainValue): TypesAnswer = value match { case r: FloatValue ⇒ IsFloatValue case _ ⇒ super.typeOfValue(value) } }
Replaces all occurrences of oldValue (using reference-quality) with newValue.
Replaces all occurrences of oldValue (using reference-quality) with newValue. If no
occurrences are found, the original operands and locals data structures
are returned.
Domain that traces the relationship between integer values.