Object

ap.theories.rationals

Rationals

Related Doc: package rationals

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object Rationals extends Fractions with Field with OrderedRing with RingWithIntConversions

The theory and field of rational numbers.

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  1. Rationals
  2. RingWithIntConversions
  3. OrderedRing
  4. RingWithOrder
  5. Field
  6. CommutativeRing
  7. CommutativePseudoRing
  8. Ring
  9. Fractions
  10. RingWithDivision
  11. PseudoRing
  12. Theory
  13. AnyRef
  14. Any
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  1. final def !=(arg0: Any): Boolean

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

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

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    Definition Classes
    AnyRef → Any
  4. object Fraction

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    Extractor for fractions, where numerator and denominator are expressions from the underlying ring

    Extractor for fractions, where numerator and denominator are expressions from the underlying ring

    Definition Classes
    Fractions
  5. object FractionSort extends ProxySort

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    Definition Classes
    Fractions
  6. def additiveGroup: Group with Abelian

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    Addition gives rise to an Abelian group

    Addition gives rise to an Abelian group

    Definition Classes
    PseudoRing
  7. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any
  8. val axioms: Formula

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    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
    FractionsTheory
  9. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  10. val denom: IFunction

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    Function used internally to represent the unique denominator for all fractions

    Function used internally to represent the unique denominator for all fractions

    Definition Classes
    Fractions
  11. val dependencies: List[nia.GroebnerMultiplication.type]

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    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
    RationalsTheory
  12. def div(s: ITerm, t: ITerm): ITerm

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    Division operation

    Division operation

    Definition Classes
    FractionsRingWithDivision
  13. val dom: Sort

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    Domain of the ring

    Domain of the ring

    Definition Classes
    FractionsPseudoRing
  14. final def eq(arg0: AnyRef): Boolean

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

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

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    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
  17. def evalPred(p: IAtom): Option[Boolean]

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    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
  18. def extend(order: TermOrder): TermOrder

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    Add the symbols defined by this theory to the order

    Add the symbols defined by this theory to the order

    Definition Classes
    Theory
  19. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  20. val frac: IFunction

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    Function to represent fractions, where numerator and denominator are expressions from the underlying ring

    Function to represent fractions, where numerator and denominator are expressions from the underlying ring

    Definition Classes
    Fractions
  21. val functionPredicateMapping: List[(IFunction, Predicate)]

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    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
    FractionsTheory
  22. val functionalPredicates: Set[Predicate]

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    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
    FractionsTheory
  23. val functions: List[IFunction]

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    Interpreted functions of the theory

    Interpreted functions of the theory

    Definition Classes
    FractionsTheory
  24. def generateDecoderData(model: Conjunction): Option[TheoryDecoderData]

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    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
  25. def geq(s: ITerm, t: ITerm): IFormula

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    Greater-than-or-equal operator

    Greater-than-or-equal operator

    Definition Classes
    RingWithOrder
  26. final def getClass(): Class[_]

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    Definition Classes
    AnyRef → Any
  27. def gt(s: ITerm, t: ITerm): IFormula

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    Greater-than operator

    Greater-than operator

    Definition Classes
    RingWithOrder
  28. def hashCode(): Int

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    Definition Classes
    AnyRef → Any
  29. def iPreprocess(f: IFormula, signature: Signature): (IFormula, Signature)

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    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
    FractionsTheory
  30. def individualsStream: Option[Stream[ITerm]]

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    Optionally, a stream of the constructor terms for this domain can be defined (e.g., the fractions with co-prime numerator and denominator).

    Optionally, a stream of the constructor terms for this domain can be defined (e.g., the fractions with co-prime numerator and denominator).

    Attributes
    protected
    Definition Classes
    RationalsFractions
  31. val int: IFunction

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    Function to embed integers in the ring of fractions

    Function to embed integers in the ring of fractions

    Definition Classes
    Fractions
  32. def int2ring(s: ITerm): ITerm

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    Conversion of an integer term to a ring term

    Conversion of an integer term to a ring term

    Definition Classes
    FractionsPseudoRing
  33. def inverse(s: ITerm): ITerm

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    Definition Classes
    Field
  34. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  35. def isInt(s: ITerm): IFormula

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    Test whether a rational is integer.

    Test whether a rational is integer.

    Definition Classes
    RationalsRingWithIntConversions
  36. def isSoundForSat(theories: Seq[Theory], config: Theory.SatSoundnessConfig.Value): Boolean

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    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
    FractionsTheory
  37. def leq(s: ITerm, t: ITerm): IFormula

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    Less-than-or-equal operator

    Less-than-or-equal operator

    Definition Classes
    RationalsRingWithOrder
  38. def lt(s: ITerm, t: ITerm): IFormula

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    Less-than operator

    Less-than operator

    Definition Classes
    RationalsRingWithOrder
  39. def minus(s: ITerm): ITerm

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    Additive inverses

    Additive inverses

    Definition Classes
    FractionsPseudoRing
  40. def minus(s: ITerm, t: ITerm): ITerm

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    Difference between two terms

    Difference between two terms

    Definition Classes
    PseudoRing
  41. def mul(s: ITerm, t: ITerm): ITerm

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    Ring multiplication

    Ring multiplication

    Definition Classes
    FractionsPseudoRing
  42. def multiplicativeGroup: Group with Abelian

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    Non-zero elements now give rise to an Abelian group

    Non-zero elements now give rise to an Abelian group

    Definition Classes
    Field
  43. def multiplicativeMonoid: Monoid with Abelian

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    Multiplication gives rise to an Abelian monoid

    Multiplication gives rise to an Abelian monoid

    Definition Classes
    CommutativeRingRing
  44. final def ne(arg0: AnyRef): Boolean

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

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

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    Definition Classes
    AnyRef
  47. val one: ITerm

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    The one element of this ring

    The one element of this ring

    Definition Classes
    FractionsPseudoRing
  48. val plugin: None.type

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    Optionally, a plug-in implementing reasoning in this theory

    Optionally, a plug-in implementing reasoning in this theory

    Definition Classes
    FractionsTheory
  49. def plus(s: ITerm, t: ITerm): ITerm

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    Ring addition

    Ring addition

    Definition Classes
    FractionsPseudoRing
  50. val predicateMatchConfig: PredicateMatchConfig

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

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

    Definition Classes
    FractionsTheory
  51. val predicates: Seq[Predicate]

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    Interpreted predicates of the theory

    Interpreted predicates of the theory

    Definition Classes
    FractionsTheory
  52. def preprocess(f: Conjunction, order: TermOrder): Conjunction

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    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
  53. def product(terms: ITerm*): ITerm

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    N-ary sums

    N-ary sums

    Definition Classes
    PseudoRing
  54. val reducerPlugin: ReducerPluginFactory

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    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
  55. def ring2int(s: ITerm): ITerm

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    Conversion of a rational term to an integer term, the floor operator.

    Conversion of a rational term to an integer term, the floor operator.

    Definition Classes
    RationalsRingWithIntConversions
  56. def simplifyFraction(n: ITerm, d: ITerm): (ITerm, ITerm)

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    Method that can be overwritten in sub-classes to term concrete fractions into canonical form.

    Method that can be overwritten in sub-classes to term concrete fractions into canonical form.

    Attributes
    protected
    Definition Classes
    RationalsFractions
  57. val singleInstantiationPredicates: Set[Predicate]

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    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
    Theory
  58. def summation(terms: ITerm*): ITerm

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    N-ary sums

    N-ary sums

    Definition Classes
    PseudoRing
  59. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef
  60. def times(num: IdealInt, s: ITerm): ITerm

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    num * s

    num * s

    Definition Classes
    FractionsPseudoRing
  61. def toString(): String

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    Definition Classes
    FractionsPseudoRing → AnyRef → Any
  62. val totalityAxioms: Conjunction

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    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
    FractionsTheory
  63. val triggerRelevantFunctions: Set[IFunction]

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    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
    FractionsTheory
  64. final def wait(): Unit

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

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

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  67. val zero: ITerm

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    The zero element of this ring

    The zero element of this ring

    Definition Classes
    FractionsPseudoRing

Inherited from RingWithIntConversions

Inherited from OrderedRing

Inherited from RingWithOrder

Inherited from Field

Inherited from CommutativeRing

Inherited from CommutativePseudoRing

Inherited from Ring

Inherited from Fractions

Inherited from RingWithDivision

Inherited from PseudoRing

Inherited from Theory

Inherited from AnyRef

Inherited from Any

Ungrouped