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.
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Instance Constructors
- 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
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##(): Int
- Definition Classes
- AnyRef → Any
- 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
- 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()
- final def :/\:(otherFactory: AxiomFactory): AxiomFactory
- Definition Classes
- AxiomFactory
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- def apply(sequent: Sequent[(String, Formula)])(implicit ctx: MutableContext): 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
- SequentialInductionAxioms → AxiomFactory
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
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- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native()
- 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
- 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
- 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
- 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
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable])
- def forAllVariables: SequentialInductionAxioms
- def forFormula(formula: Formula): SequentialInductionAxioms
- def forLabel(label: String): SequentialInductionAxioms
- def forVariables(variables: Var*): SequentialInductionAxioms
- def forVariables(variables: List[Var]): SequentialInductionAxioms
- 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
- @inline()
- val fsel: FormulaSelector
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- final def notify(): Unit
- Definition Classes
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- Annotations
- @native()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
- def productElementNames: Iterator[String]
- Definition Classes
- Product
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- val vsel: VariableSelector
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
Deprecated Value Members
- 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
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This is the API documentation for GAPT.
The main package is gapt.