Class

ap.theories.rationals

Fractions

Related Doc: package rationals

Permalink

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.

Linear Supertypes
Known Subclasses
Ordering
  1. Alphabetic
  2. By inheritance
Inherited
  1. Fractions
  2. RingWithDivision
  3. PseudoRing
  4. Theory
  5. AnyRef
  6. Any
  1. Hide All
  2. Show all
Visibility
  1. Public
  2. All

Instance Constructors

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

    Permalink

Value Members

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

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

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

    Permalink
    Definition Classes
    AnyRef → Any
  4. object Fraction

    Permalink

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

  5. object FractionSort extends ProxySort

    Permalink
  6. def additiveGroup: Group with Abelian with SymbolicTimes

    Permalink

    Addition gives rise to an Abelian group

    Addition gives rise to an Abelian group

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

    Permalink
    Definition Classes
    Any
  8. val axioms: Formula

    Permalink

    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

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

    Permalink

    Function used internally to represent the unique denominator for all fractions

  11. val dependencies: Iterable[Theory]

    Permalink

    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

    Permalink

    Division operation

    Division operation

    Definition Classes
    FractionsRingWithDivision
  13. val dom: Sort

    Permalink

    Domain of the ring

    Domain of the ring

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

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

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

    Permalink

    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]

    Permalink

    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

    Permalink

    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

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

    Permalink

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

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

    Permalink

    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]

    Permalink

    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]

    Permalink

    Interpreted functions of the theory

    Interpreted functions of the theory

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

    Permalink

    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[_]

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

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

    Permalink

    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
  28. def iPreprocess(f: IFormula, signature: Signature): (IFormula, Signature)

    Permalink

    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
  29. def individualsStream: Option[Stream[ITerm]]

    Permalink

    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
  30. val int: IFunction

    Permalink

    Function to embed integers in the ring of fractions

  31. def int2ring(s: ITerm): ITerm

    Permalink

    Conversion of an integer term to a ring term

    Conversion of an integer term to a ring term

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

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

    Permalink

    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
  34. def minus(s: ITerm): ITerm

    Permalink

    Additive inverses

    Additive inverses

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

    Permalink

    Difference between two terms

    Difference between two terms

    Definition Classes
    PseudoRing
  36. val modelGenPredicates: Set[Predicate]

    Permalink

    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
  37. def mul(s: ITerm, t: ITerm): ITerm

    Permalink

    Ring multiplication

    Ring multiplication

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

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

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

    Permalink
    Definition Classes
    AnyRef
  41. val one: ITerm

    Permalink

    The one element of this ring

    The one element of this ring

    Definition Classes
    FractionsPseudoRing
  42. val plugin: None.type

    Permalink

    Optionally, a plug-in implementing reasoning in this theory

    Optionally, a plug-in implementing reasoning in this theory

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

    Permalink

    Ring addition

    Ring addition

    Definition Classes
    FractionsPseudoRing
  44. def postSimplifiers: Seq[(IExpression) ⇒ IExpression]

    Permalink

    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
  45. def postprocess(f: Conjunction, order: TermOrder): Conjunction

    Permalink

    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
  46. val predicateMatchConfig: PredicateMatchConfig

    Permalink

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

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

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

    Permalink

    Interpreted predicates of the theory

    Interpreted predicates of the theory

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

    Permalink

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

    Permalink

    N-ary sums

    N-ary sums

    Definition Classes
    PseudoRing
  50. val reducerPlugin: ReducerPluginFactory

    Permalink

    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
  51. def simplifyFraction(n: ITerm, d: ITerm): (ITerm, ITerm)

    Permalink

    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
  52. val singleInstantiationPredicates: Set[Predicate]

    Permalink

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

    Permalink

    N-ary sums

    N-ary sums

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

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

    Permalink

    num * s

    num * s

    Definition Classes
    FractionsPseudoRing
  56. def toString(): String

    Permalink
    Definition Classes
    FractionsPseudoRing → AnyRef → Any
  57. val totalityAxioms: Conjunction

    Permalink

    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
  58. val triggerRelevantFunctions: Set[IFunction]

    Permalink

    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
  59. final def wait(): Unit

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

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

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

    Permalink

    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