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ap.theories.nia

GroebnerMultiplication

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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Inherited
  1. GroebnerMultiplication
  2. MulTheory
  3. Theory
  4. AnyRef
  5. Any
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Visibility
  1. Public
  2. Protected

Type Members

  1. class RichMulTerm extends AnyRef
    Definition Classes
    MulTheory
  2. type GBCache = LRUCache[(Seq[Atom], TermOrder), (Basis, Seq[Atom], MonomialOrdering)]
    Attributes
    protected[nia]

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. val AC: AC_NIA.type
    Attributes
    protected[nia]
  5. val DISCRETE_SPLITTING_LIMIT: Int
  6. val PROPAGATION_UPDATE_LIMIT: Int
  7. def RANDOMISE_CASES(goal: Goal): Boolean
  8. val RANDOMISE_VARIABLE_ORDER: Boolean
  9. val SMALL_INTERVAL_BOUND: Int
  10. val SPLITTER_BASE_PRIORITY: Int
  11. def VALUE_ENUMERATOR(goal: Goal): Boolean
  12. val _mul: Predicate
  13. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  14. 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
    GroebnerMultiplication → Theory
  15. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @HotSpotIntrinsicCandidate() @native()
  16. def convert(expr: IFormula): IFormula

    Convert the given expression to this multiplication theory

    Convert the given expression to this multiplication theory

    Definition Classes
    MulTheory
  17. def convert(expr: ITerm): ITerm

    Convert the given expression to this multiplication theory

    Convert the given expression to this multiplication theory

    Definition Classes
    MulTheory
  18. def convert(expr: IExpression): IExpression

    Convert the given expression to this multiplication theory

    Convert the given expression to this multiplication theory

    Definition Classes
    MulTheory
  19. implicit def convert2RichMulTerm(term: ITerm): RichMulTerm
    Definition Classes
    MulTheory
  20. val debug: Boolean
    Attributes
    protected[nia]
  21. val dependencies: List[IntValueEnumTheory]

    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
    GroebnerMultiplication → Theory
  22. def eDiv(numTerm: ITerm, denomTerm: ITerm): ITerm

    Euclidian division

    Euclidian division

    Definition Classes
    MulTheory
  23. 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
  24. def eMod(numTerm: ITerm, denomTerm: ITerm): ITerm

    Euclidian remainder

    Euclidian remainder

    Definition Classes
    MulTheory
  25. 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
  26. def eagerActions(goal: Goal, gbCache: GBCache): Seq[Action]
    Attributes
    protected[nia]
  27. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  28. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  29. 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
  30. 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
  31. def evaluatingSimplifier(t: IExpression): IExpression

    A simplification function that applies the methods evalFun and evalPred to some given expression (but not recursively).

    A simplification function that applies the methods evalFun and evalPred to some given expression (but not recursively). This is used in the Theory.postSimplifiers methods.

    Definition Classes
    Theory
  32. 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
  33. def fDiv(numTerm: ITerm, denomTerm: ITerm): ITerm

    Floor division

    Floor division

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

    Floor remainder

    Floor remainder

    Definition Classes
    MulTheory
  35. def filterActions(actions: Seq[Action], order: TermOrder): Seq[Action]
    Attributes
    protected[nia]
  36. 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
    GroebnerMultiplication → Theory
  37. 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
    GroebnerMultiplication → Theory
  38. val functions: List[IFunction]

    Interpreted functions of the theory

    Interpreted functions of the theory

    Definition Classes
    GroebnerMultiplication → Theory
  39. 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
  40. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @HotSpotIntrinsicCandidate() @native()
  41. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @HotSpotIntrinsicCandidate() @native()
  42. 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
  43. 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
  44. def intervals2Actions(intervalSet: IntervalSet, predicates: IndexedSeq[Atom], goal: Goal, label2Assumptions: (BitSet) => Seq[Formula]): Seq[Action]
    Attributes
    protected[nia]
  45. def intervals2Formula(intervalSet: IntervalSet, predicates: IndexedSeq[Atom], goal: Goal): Conjunction
    Attributes
    protected[nia]
  46. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  47. 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
    GroebnerMultiplication → Theory
  48. 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
  49. val mul: IFunction

    Symbol representing proper (non-linear) multiplication

    Symbol representing proper (non-linear) multiplication

    Definition Classes
    GroebnerMultiplication → MulTheory
  50. 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
  51. 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
  52. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  53. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @HotSpotIntrinsicCandidate() @native()
  54. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @HotSpotIntrinsicCandidate() @native()
  55. def plugin: Some[Plugin]

    Optionally, a plug-in implementing reasoning in this theory

    Optionally, a plug-in implementing reasoning in this theory

    Definition Classes
    GroebnerMultiplication → Theory
  56. 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 ap.parser.Simplifier. By default, this list will only include the evaluatingSimplifier.

    Definition Classes
    Theory
  57. def postprocess(f: Conjunction, signature: Signature): 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
  58. def pow(basis: ITerm, expTerm: ITerm): ITerm

    Exponentiation, with non-negative exponent

    Exponentiation, with non-negative exponent

    Definition Classes
    MulTheory
  59. 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
    GroebnerMultiplication → Theory
  60. val predicates: List[Predicate]

    Interpreted predicates of the theory

    Interpreted predicates of the theory

    Definition Classes
    GroebnerMultiplication → Theory
  61. def preprocess(f: Conjunction, signature: Signature): 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
  62. def printActions(t: String, actions: Seq[Action]): Unit
    Attributes
    protected[nia]
  63. def printNIAgoal(t: String, goal: Goal): Unit
    Attributes
    protected[nia]
  64. 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
    GroebnerMultiplication → Theory
  65. def simpleLinearizers(goal: Goal): Set[ConstantTerm]

    Find a set of constants that are sufficient to make all product constraints linear: assigning concrete values to the constants will make products become linear.

  66. 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
    GroebnerMultiplication → Theory
  67. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  68. def tDiv(numTerm: ITerm, denomTerm: ITerm): ITerm

    Truncation division

    Truncation division

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

    Truncation remainder

    Truncation remainder

    Definition Classes
    MulTheory
  70. def toString(): String
    Definition Classes
    GroebnerMultiplication → AnyRef → Any
  71. 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
    GroebnerMultiplication → Theory
  72. lazy val transitiveDependencies: Iterable[Theory]

    Dependencies closed under transitivity, i.e., also including the dependencies of dependencies.

    Dependencies closed under transitivity, i.e., also including the dependencies of dependencies.

    Definition Classes
    Theory
  73. 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
    GroebnerMultiplication → Theory
  74. val valueEnumerator: IntValueEnumTheory
  75. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  76. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  77. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated

    (Since version 9)

Inherited from MulTheory

Inherited from Theory

Inherited from AnyRef

Inherited from Any

Ungrouped