# BitShiftMultiplication

### Related Doc: package theories

#### object BitShiftMultiplication extends MulTheory

Multiplication by means of axioms describing shift-and-add

Linear Supertypes
MulTheory, Theory, AnyRef, Any
Ordering
1. Alphabetic
2. By inheritance
Inherited
1. BitShiftMultiplication
2. MulTheory
3. Theory
4. AnyRef
5. Any
1. Hide All
2. Show all
Visibility
1. Public
2. All

### Type Members

1. #### class RichMulTerm extends AnyRef

Definition Classes
MulTheory

### Value Members

1. #### final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
2. #### final def ##(): Int

Definition Classes
AnyRef → Any
3. #### final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
4. #### final def asInstanceOf[T0]: T0

Definition Classes
Any
5. #### val axioms: Formula

Axioms defining the theory; such axioms are simply added as formulae to the problem to be proven, and thus handled using the standard reasoning techniques (including e-matching).

Axioms defining the theory; such axioms are simply added as formulae to the problem to be proven, and thus handled using the standard reasoning techniques (including e-matching).

Definition Classes
BitShiftMultiplicationTheory
6. #### def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
7. #### def convert(expr: IFormula): IFormula

Convert the given expression to this multiplication theory

Convert the given expression to this multiplication theory

Definition Classes
MulTheory
8. #### def convert(expr: ITerm): ITerm

Convert the given expression to this multiplication theory

Convert the given expression to this multiplication theory

Definition Classes
MulTheory
9. #### def convert(expr: IExpression): IExpression

Convert the given expression to this multiplication theory

Convert the given expression to this multiplication theory

Definition Classes
MulTheory
10. #### implicit def convert2RichMulTerm(term: ITerm): RichMulTerm

Definition Classes
MulTheory
11. #### val dependencies: Iterable[Theory]

Optionally, other theories that this theory depends on.

Optionally, other theories that this theory depends on. Specified dependencies will be loaded before this theory, but the preprocessors of the dependencies will be called after the preprocessor of this theory.

Definition Classes
Theory
12. #### def eDiv(numTerm: ITerm, denomTerm: ITerm): ITerm

Euclidian division

Euclidian division

Definition Classes
MulTheory
13. #### def eDivWithSpecialZero(num: ITerm, denom: ITerm): ITerm

Euclidian division, assuming the SMT-LIB semantics for division by zero.

Euclidian division, assuming the SMT-LIB semantics for division by zero.

Definition Classes
MulTheory
14. #### def eMod(numTerm: ITerm, denomTerm: ITerm): ITerm

Euclidian remainder

Euclidian remainder

Definition Classes
MulTheory
15. #### def eModWithSpecialZero(num: ITerm, denom: ITerm): ITerm

Euclidian remaining, assuming the SMT-LIB semantics for remainder by zero.

Euclidian remaining, assuming the SMT-LIB semantics for remainder by zero.

Definition Classes
MulTheory
16. #### final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
17. #### def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
18. #### def evalFun(f: IFunApp): Option[ITerm]

Optionally, a function evaluating theory functions applied to concrete arguments, represented as constructor terms.

Optionally, a function evaluating theory functions applied to concrete arguments, represented as constructor terms.

Definition Classes
Theory
19. #### def evalPred(p: IAtom): Option[Boolean]

Optionally, a function evaluating theory predicates applied to concrete arguments, represented as constructor terms.

Optionally, a function evaluating theory predicates applied to concrete arguments, represented as constructor terms.

Definition Classes
Theory
20. #### def extend(order: TermOrder): TermOrder

Add the symbols defined by this theory to the `order`

Add the symbols defined by this theory to the `order`

Definition Classes
Theory
21. #### def fDiv(numTerm: ITerm, denomTerm: ITerm): ITerm

Floor division

Floor division

Definition Classes
MulTheory
22. #### def fMod(numTerm: ITerm, denomTerm: ITerm): ITerm

Floor remainder

Floor remainder

Definition Classes
MulTheory
23. #### def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
24. #### val functionPredicateMapping: List[(IFunction, Predicate)]

Mapping of interpreted functions to interpreted predicates, used translating input ASTs to internal ASTs (the latter only containing predicates).

Mapping of interpreted functions to interpreted predicates, used translating input ASTs to internal ASTs (the latter only containing predicates).

Definition Classes
BitShiftMultiplicationTheory
25. #### val functionalPredicates: Set[Predicate]

Information which of the predicates satisfy the functionality axiom; at some internal points, such predicates can be handled more efficiently

Information which of the predicates satisfy the functionality axiom; at some internal points, such predicates can be handled more efficiently

Definition Classes
BitShiftMultiplicationTheory
26. #### val functions: List[IFunction]

Interpreted functions of the theory

Interpreted functions of the theory

Definition Classes
BitShiftMultiplicationTheory
27. #### def generateDecoderData(model: Conjunction): Option[TheoryDecoderData]

If this theory defines any `Theory.Decoder`, which can translate model data into some theory-specific representation, this function can be overridden to pre-compute required data from a model.

If this theory defines any `Theory.Decoder`, which can translate model data into some theory-specific representation, this function can be overridden to pre-compute required data from a model.

Definition Classes
Theory
28. #### final def getClass(): Class[_]

Definition Classes
AnyRef → Any
29. #### def hashCode(): Int

Definition Classes
AnyRef → Any
30. #### def iPostprocess(f: IFormula, signature: Signature): IFormula

Optionally, a post-processor that is applied to formulas output by the prover, for instance to interpolants or the result of quantifier elimination.

Optionally, a post-processor that is applied to formulas output by the prover, for instance to interpolants or the result of quantifier elimination. This method will be applied to the formula after calling `Internal2Inputabsy`.

Definition Classes
Theory
31. #### def iPreprocess(f: IFormula, signature: Signature): (IFormula, Signature)

Optionally, a pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover.

Optionally, a pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover. This method will be applied very early in the translation process.

Definition Classes
Theory
32. #### final def isInstanceOf[T0]: Boolean

Definition Classes
Any
33. #### def isSoundForSat(theories: Seq[Theory], config: Theory.SatSoundnessConfig.Value): Boolean

Check whether we can tell that the given combination of theories is sound for checking satisfiability of a problem, i.e., if proof construction ends up in a dead end, can it be concluded that a problem is satisfiable.

Check whether we can tell that the given combination of theories is sound for checking satisfiability of a problem, i.e., if proof construction ends up in a dead end, can it be concluded that a problem is satisfiable.

Definition Classes
BitShiftMultiplicationTheory
34. #### val modelGenPredicates: Set[Predicate]

Optionally, a set of predicates used by the theory to tell the `PresburgerModelFinder` about terms that will be handled exclusively by this theory.

Optionally, a set of predicates used by the theory to tell the `PresburgerModelFinder` about terms that will be handled exclusively by this theory. If a proof goal in model generation mode contains an atom `p(x)`, for `p` in this set, then the `PresburgerModelFinder` will ignore `x` when assigning concrete values to symbols.

Definition Classes
Theory
35. #### val mul: IFunction

Symbol representing proper (non-linear) multiplication

Symbol representing proper (non-linear) multiplication

Definition Classes
BitShiftMultiplicationMulTheory
36. #### def mult(t1: ITerm, t2: ITerm): ITerm

Multiply two terms, using the `mul` function if necessary; if any of the two terms is constant, normal Presburger multiplication will be used.

Multiply two terms, using the `mul` function if necessary; if any of the two terms is constant, normal Presburger multiplication will be used.

Definition Classes
MulTheory
37. #### def multSimplify(t1: ITerm, t2: ITerm): ITerm

Multiply two terms, using the `mul` function if necessary; if any of the two terms is constant, normal Presburger multiplication will be used, and simple terms will directly be simplified.

Multiply two terms, using the `mul` function if necessary; if any of the two terms is constant, normal Presburger multiplication will be used, and simple terms will directly be simplified.

Definition Classes
MulTheory
38. #### final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
39. #### final def notify(): Unit

Definition Classes
AnyRef
40. #### final def notifyAll(): Unit

Definition Classes
AnyRef
41. #### val plugin: Some[Plugin]

Optionally, a plug-in implementing reasoning in this theory

Optionally, a plug-in implementing reasoning in this theory

Definition Classes
BitShiftMultiplicationTheory
42. #### def postSimplifiers: Seq[(IExpression) ⇒ IExpression]

Optionally, simplifiers that are applied to formulas output by the prover, for instance to interpolants or the result of quantifier.

Optionally, simplifiers that are applied to formulas output by the prover, for instance to interpolants or the result of quantifier. Such simplifiers are invoked by with `ap.parser.Simplifier`.

Definition Classes
Theory
43. #### def postprocess(f: Conjunction, order: TermOrder): Conjunction

Optionally, a post-processor that is applied to formulas output by the prover, for instance to interpolants or the result of quantifier elimination.

Optionally, a post-processor that is applied to formulas output by the prover, for instance to interpolants or the result of quantifier elimination. This method will be applied to the raw formulas, before calling `Internal2Inputabsy`.

Definition Classes
Theory
44. #### def pow(basis: ITerm, expTerm: ITerm): ITerm

Exponentiation, with non-negative exponent

Exponentiation, with non-negative exponent

Definition Classes
MulTheory
45. #### val predicateMatchConfig: PredicateMatchConfig

Information how interpreted predicates should be handled for e-matching.

Information how interpreted predicates should be handled for e-matching.

Definition Classes
BitShiftMultiplicationTheory
46. #### val predicates: Seq[Predicate]

Interpreted predicates of the theory

Interpreted predicates of the theory

Definition Classes
BitShiftMultiplicationTheory
47. #### def preprocess(f: Conjunction, order: TermOrder): Conjunction

Optionally, a pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover.

Optionally, a pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover.

Definition Classes
Theory
48. #### val reducerPlugin: ReducerPluginFactory

Optionally, a plugin for the reducer applied to formulas both before and during proving.

Optionally, a plugin for the reducer applied to formulas both before and during proving.

Definition Classes
Theory
49. #### val singleInstantiationPredicates: Set[Predicate]

When instantiating existentially quantifier formulas, `EX phi`, at most one instantiation is necessary provided that all predicates in `phi` are contained in this set.

When instantiating existentially quantifier formulas, `EX phi`, at most one instantiation is necessary provided that all predicates in `phi` are contained in this set.

Definition Classes
BitShiftMultiplicationTheory
50. #### final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
51. #### def tDiv(numTerm: ITerm, denomTerm: ITerm): ITerm

Truncation division

Truncation division

Definition Classes
MulTheory
52. #### def tMod(numTerm: ITerm, denomTerm: ITerm): ITerm

Truncation remainder

Truncation remainder

Definition Classes
MulTheory
53. #### def toString(): String

Definition Classes
BitShiftMultiplication → AnyRef → Any
54. #### val totalityAxioms: Conjunction

Additional axioms that are included if the option `+genTotalityAxioms` is given to Princess.

Additional axioms that are included if the option `+genTotalityAxioms` is given to Princess.

Definition Classes
BitShiftMultiplicationTheory
55. #### val triggerRelevantFunctions: Set[IFunction]

A list of functions that should be considered in automatic trigger generation

A list of functions that should be considered in automatic trigger generation

Definition Classes
BitShiftMultiplicationTheory
56. #### final def wait(): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
57. #### final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
58. #### final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )