c

gapt.proofs.lk.rules

InductionCase

case class InductionCase(proof: LKProof, constructor: Const, hypotheses: Seq[SequentIndex], eigenVars: Seq[Var], conclusion: SequentIndex) extends Product with Serializable

Proof that a given data type constructor c preserves a formula F:

                                 (π)
F(x,,1,,), F(x,,2,,), ..., F(x,,n,,), Γ :- Δ, F(c(x,,1,,,...,x,,n,,,y,,1,,,...,y,,n,,))

The variables xi and yi are eigenvariables; xi are the eigenvariables of the same type as the inductive data type, yi are the other arguments of the constructor c. They can come in any order in the constructor.

proof

The LKProof ending in the sequent of this case.

constructor

The constructor c of the inductive data type that we're considering.

hypotheses

Indices of F(x1), ..., F(xn)

eigenVars

The eigenvariables of this case: x1, ..., xn, y1, ..., yn (these need to correspond to the order in c)

conclusion

Index of F(c(x1,...,xn,y1,...,yn))

Source
InductionCase.scala
Linear Supertypes
Serializable, Product, Equals, AnyRef, Any
Type Hierarchy
Ordering
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Inherited
  1. InductionCase
  2. Serializable
  3. Product
  4. Equals
  5. AnyRef
  6. 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 InductionCase(proof: LKProof, constructor: Const, hypotheses: Seq[SequentIndex], eigenVars: Seq[Var], conclusion: SequentIndex)

    proof

    The LKProof ending in the sequent of this case.

    constructor

    The constructor c of the inductive data type that we're considering.

    hypotheses

    Indices of F(x1), ..., F(xn)

    eigenVars

    The eigenvariables of this case: x1, ..., xn, y1, ..., yn (these need to correspond to the order in c)

    conclusion

    Index of F(c(x1,...,xn,y1,...,yn))

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 InductionCase toany2stringadd[InductionCase] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (InductionCase, B)
    Implicit
    This member is added by an implicit conversion from InductionCase toArrowAssoc[InductionCase] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  7. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  8. val conclusion: SequentIndex
  9. val constructor: Const
  10. val eigenVars: Seq[Var]
  11. def ensuring(cond: (InductionCase) => Boolean, msg: => Any): InductionCase
    Implicit
    This member is added by an implicit conversion from InductionCase toEnsuring[InductionCase] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. def ensuring(cond: (InductionCase) => Boolean): InductionCase
    Implicit
    This member is added by an implicit conversion from InductionCase toEnsuring[InductionCase] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. def ensuring(cond: Boolean, msg: => Any): InductionCase
    Implicit
    This member is added by an implicit conversion from InductionCase toEnsuring[InductionCase] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. def ensuring(cond: Boolean): InductionCase
    Implicit
    This member is added by an implicit conversion from InductionCase toEnsuring[InductionCase] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  15. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  16. val fieldTypes: List[Ty]
  17. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  18. val hypVars: Seq[Var]
  19. val hypotheses: Seq[SequentIndex]
  20. val indTy: Ty
  21. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  22. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  23. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  24. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  25. def productElementNames: Iterator[String]
    Definition Classes
    Product
  26. val proof: LKProof
  27. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  28. val term: Expr
  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 InductionCase toStringFormat[InductionCase] 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): (InductionCase, B)
    Implicit
    This member is added by an implicit conversion from InductionCase toArrowAssoc[InductionCase] 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 AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromInductionCase to any2stringadd[InductionCase]

Inherited by implicit conversion StringFormat fromInductionCase to StringFormat[InductionCase]

Inherited by implicit conversion Ensuring fromInductionCase to Ensuring[InductionCase]

Inherited by implicit conversion ArrowAssoc fromInductionCase to ArrowAssoc[InductionCase]

Ungrouped