# GroebnerMultiplication

### Related Doc: package nia

#### object GroebnerMultiplication extends MulTheory

Implementation of a theory of non-linear integer arithmetic. Currently the theory does Groebner basis calculation followed by interval propagation.

Linear Supertypes
MulTheory, Theory, AnyRef, Any
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1. GroebnerMultiplication
2. MulTheory
3. Theory
4. AnyRef
5. Any
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### 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

8. #### final def asInstanceOf[T0]: T0

Definition Classes
Any
9. #### val axioms: Conjunction

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
GroebnerMultiplicationTheory
10. #### def clone(): AnyRef

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

Convert the given expression to this multiplication theory

Convert the given expression to this multiplication theory

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

Convert the given expression to this multiplication theory

Convert the given expression to this multiplication theory

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

Convert the given expression to this multiplication theory

Convert the given expression to this multiplication theory

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

Definition Classes
MulTheory
15. #### val debug: Boolean

Attributes
protected[ap.theories.nia]
16. #### 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
17. #### def eDiv(numTerm: ITerm, denomTerm: ITerm): ITerm

Euclidian division

Euclidian division

Definition Classes
MulTheory
18. #### 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
19. #### def eMod(numTerm: ITerm, denomTerm: ITerm): ITerm

Euclidian remainder

Euclidian remainder

Definition Classes
MulTheory
20. #### 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
21. #### final def eq(arg0: AnyRef): Boolean

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

Definition Classes
AnyRef → Any
23. #### 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
24. #### 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
25. #### 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
26. #### def fDiv(numTerm: ITerm, denomTerm: ITerm): ITerm

Floor division

Floor division

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

Floor remainder

Floor remainder

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

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
29. #### 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
GroebnerMultiplicationTheory
30. #### 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
GroebnerMultiplicationTheory
31. #### val functions: List[IFunction]

Interpreted functions of the theory

Interpreted functions of the theory

Definition Classes
GroebnerMultiplicationTheory
32. #### def genMonomialOrder(predicates: Seq[Atom], baseOrder: TermOrder): MonomialOrdering

Conversion functions

Conversion functions

Attributes
protected[ap.theories.nia]
33. #### 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
34. #### final def getClass(): Class[_]

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

Definition Classes
AnyRef → Any
36. #### 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
37. #### 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
38. #### final def isInstanceOf[T0]: Boolean

Definition Classes
Any
39. #### 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
GroebnerMultiplicationTheory
40. #### 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
41. #### val mul: IFunction

Symbol representing proper (non-linear) multiplication

Symbol representing proper (non-linear) multiplication

Definition Classes
GroebnerMultiplicationMulTheory
42. #### 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
43. #### 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
44. #### final def ne(arg0: AnyRef): Boolean

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

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

Definition Classes
AnyRef
47. #### def plugin: Some[Plugin]

Optionally, a plug-in implementing reasoning in this theory

Optionally, a plug-in implementing reasoning in this theory

Definition Classes
GroebnerMultiplicationTheory
48. #### 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
49. #### 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
50. #### def pow(basis: ITerm, expTerm: ITerm): ITerm

Exponentiation, with non-negative exponent

Exponentiation, with non-negative exponent

Definition Classes
MulTheory
51. #### 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
GroebnerMultiplicationTheory
52. #### val predicates: List[Predicate]

Interpreted predicates of the theory

Interpreted predicates of the theory

Definition Classes
GroebnerMultiplicationTheory
53. #### 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
54. #### 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
GroebnerMultiplicationTheory
55. #### 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
GroebnerMultiplicationTheory
56. #### final def synchronized[T0](arg0: ⇒ T0): T0

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

Truncation division

Truncation division

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

Truncation remainder

Truncation remainder

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

Definition Classes
GroebnerMultiplication → AnyRef → Any
60. #### 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
GroebnerMultiplicationTheory
61. #### 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
GroebnerMultiplicationTheory
62. #### final def wait(): Unit

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

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

Definition Classes
AnyRef
Annotations
@throws( ... )