Class

ap.theories.rationals

Fractions

Related Doc: package rationals

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class Fractions extends Theory with RingWithDivision

The theory of fractions s / t, with s, t taken from some ring. The theory uses an encoding in which the same (fixed, but arbitrary) denominator is used for all expressions. The range of considered denominators is described by the denomConstraint argument over the variable _0.

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Inherited
  1. Fractions
  2. RingWithDivision
  3. PseudoRing
  4. Theory
  5. AnyRef
  6. Any
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Instance Constructors

  1. new Fractions(name: String, underlyingRing: Ring, denomConstraint: IFormula)

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Value Members

  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

  5. object FractionSort extends ProxySort

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  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

  11. val dependencies: Iterable[Theory]

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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
    Theory
  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

  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. final def getClass(): Class[_]

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

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    Definition Classes
    AnyRef → Any
  27. 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
  28. 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
  29. val int: IFunction

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    Function to embed integers in the ring of fractions

  30. 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
  31. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  32. 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
  33. def minus(s: ITerm): ITerm

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    Additive inverses

    Additive inverses

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

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    Difference between two terms

    Difference between two terms

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

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    Ring multiplication

    Ring multiplication

    Definition Classes
    FractionsPseudoRing
  36. final def ne(arg0: AnyRef): Boolean

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

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

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    Definition Classes
    AnyRef
  39. val one: ITerm

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    The one element of this ring

    The one element of this ring

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

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    Ring addition

    Ring addition

    Definition Classes
    FractionsPseudoRing
  42. 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
  43. val predicates: Seq[Predicate]

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    Interpreted predicates of the theory

    Interpreted predicates of the theory

    Definition Classes
    FractionsTheory
  44. 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
  45. def product(terms: ITerm*): ITerm

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    N-ary sums

    N-ary sums

    Definition Classes
    PseudoRing
  46. 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
  47. 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
  48. 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
  49. def summation(terms: ITerm*): ITerm

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    N-ary sums

    N-ary sums

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

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

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    num * s

    num * s

    Definition Classes
    FractionsPseudoRing
  52. def toString(): String

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    Definition Classes
    FractionsPseudoRing → AnyRef → Any
  53. 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
  54. 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
  55. final def wait(): Unit

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

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

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

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    The zero element of this ring

    The zero element of this ring

    Definition Classes
    FractionsPseudoRing

Inherited from RingWithDivision

Inherited from PseudoRing

Inherited from Theory

Inherited from AnyRef

Inherited from Any

Ungrouped