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c

gapt.provers.viper.aip.axioms

SequentialInductionAxioms

case class SequentialInductionAxioms(vsel: VariableSelector = allVariablesSelector( _ )( _ ), fsel: FormulaSelector = firstFormulaSelector( _ )) extends AxiomFactory with Product with Serializable

Generates sequential induction axioms.

vsel

The variables for which an induction axiom is generated.

fsel

The formula of a sequent for which induction axioms are generated.

Source
SequentialInductionAxioms.scala
Type Hierarchy
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Inherited
  1. SequentialInductionAxioms
  2. Serializable
  3. Product
  4. Equals
  5. AxiomFactory
  6. AnyRef
  7. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new SequentialInductionAxioms(vsel: VariableSelector = allVariablesSelector( _ )( _ ), fsel: FormulaSelector = firstFormulaSelector( _ ))

    vsel

    The variables for which an induction axiom is generated.

    fsel

    The formula of a sequent for which induction axioms are generated.

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from SequentialInductionAxioms toany2stringadd[SequentialInductionAxioms] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (SequentialInductionAxioms, B)
    Implicit
    This member is added by an implicit conversion from SequentialInductionAxioms toArrowAssoc[SequentialInductionAxioms] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def :/\:(otherFactory: AxiomFactory): AxiomFactory
    Definition Classes
    AxiomFactory
  6. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  7. def apply(sequent: Sequent[(String, Formula)])(implicit ctx: Context): ThrowsError[List[Axiom]]

    Computes sequential induction axioms for a sequent.

    Computes sequential induction axioms for a sequent.

    sequent

    The sequent for which the axioms are generated.

    ctx

    The context defining types, constants, etc.

    returns

    Failure if the one of the given variables is not of inductive type. Otherwise a list of induction axioms of the form: ∀A∀{X < x}( IC(x,c1) ∧ ... ∧ IC(x,cl) -> ∀x∀{X > x}∀{X'}F ), where the input variables are X the input formula is of the form F' = ∀{X U X'}F FV(F') = A x in X {X < x} and {X > x} are subsets of X containing all variables with index smaller/greater than the index of x.

    Definition Classes
    SequentialInductionAxiomsAxiomFactory
  8. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  9. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  10. def ensuring(cond: (SequentialInductionAxioms) => Boolean, msg: => Any): SequentialInductionAxioms
    Implicit
    This member is added by an implicit conversion from SequentialInductionAxioms toEnsuring[SequentialInductionAxioms] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  11. def ensuring(cond: (SequentialInductionAxioms) => Boolean): SequentialInductionAxioms
    Implicit
    This member is added by an implicit conversion from SequentialInductionAxioms toEnsuring[SequentialInductionAxioms] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. def ensuring(cond: Boolean, msg: => Any): SequentialInductionAxioms
    Implicit
    This member is added by an implicit conversion from SequentialInductionAxioms toEnsuring[SequentialInductionAxioms] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. def ensuring(cond: Boolean): SequentialInductionAxioms
    Implicit
    This member is added by an implicit conversion from SequentialInductionAxioms toEnsuring[SequentialInductionAxioms] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  15. def forAllVariables: SequentialInductionAxioms
  16. def forFormula(formula: Formula): SequentialInductionAxioms
  17. def forLabel(label: String): SequentialInductionAxioms
  18. def forVariables(variables: Var*): SequentialInductionAxioms
  19. def forVariables(variables: List[Var]): SequentialInductionAxioms
  20. val fsel: FormulaSelector
  21. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  22. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  23. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  24. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  25. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  26. def productElementNames: Iterator[String]
    Definition Classes
    Product
  27. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  28. val vsel: VariableSelector
  29. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  30. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  31. 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
  2. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from SequentialInductionAxioms toStringFormat[SequentialInductionAxioms] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @deprecated @inline()
    Deprecated

    (Since version 2.12.16) Use formatString.format(value) instead of value.formatted(formatString), or use the f"" string interpolator. In Java 15 and later, formatted resolves to the new method in String which has reversed parameters.

  3. def [B](y: B): (SequentialInductionAxioms, B)
    Implicit
    This member is added by an implicit conversion from SequentialInductionAxioms toArrowAssoc[SequentialInductionAxioms] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @deprecated
    Deprecated

    (Since version 2.13.0) Use -> instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from AxiomFactory

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromSequentialInductionAxioms to any2stringadd[SequentialInductionAxioms]

Inherited by implicit conversion StringFormat fromSequentialInductionAxioms to StringFormat[SequentialInductionAxioms]

Inherited by implicit conversion Ensuring fromSequentialInductionAxioms to Ensuring[SequentialInductionAxioms]

Inherited by implicit conversion ArrowAssoc fromSequentialInductionAxioms to ArrowAssoc[SequentialInductionAxioms]

Ungrouped