c

gapt.proofs.nd

InductionCase

case class InductionCase(proof: NDProof, constructor: Const, hypotheses: Seq[SequentIndex], eigenVars: Seq[Var]) 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 :- 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 NDProof 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)

Source
nd.scala
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Inherited
  1. InductionCase
  2. Serializable
  3. Serializable
  4. Product
  5. Equals
  6. AnyRef
  7. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
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Instance Constructors

  1. new InductionCase(proof: NDProof, constructor: Const, hypotheses: Seq[SequentIndex], eigenVars: Seq[Var])

    proof

    The NDProof 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)

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 to any2stringadd[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 to ArrowAssoc[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[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  8. val constructor: Const
  9. val eigenVars: Seq[Var]
  10. def ensuring(cond: (InductionCase) ⇒ Boolean, msg: ⇒ Any): InductionCase
    Implicit
    This member is added by an implicit conversion from InductionCase to Ensuring[InductionCase] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  11. def ensuring(cond: (InductionCase) ⇒ Boolean): InductionCase
    Implicit
    This member is added by an implicit conversion from InductionCase to Ensuring[InductionCase] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. def ensuring(cond: Boolean, msg: ⇒ Any): InductionCase
    Implicit
    This member is added by an implicit conversion from InductionCase to Ensuring[InductionCase] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. def ensuring(cond: Boolean): InductionCase
    Implicit
    This member is added by an implicit conversion from InductionCase to Ensuring[InductionCase] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  15. val fieldTypes: List[Ty]
  16. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  17. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from InductionCase to StringFormat[InductionCase] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  18. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  19. val hypVars: Seq[Var]
  20. val hypotheses: Seq[SequentIndex]
  21. val indTy: Ty
  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()
  25. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  26. val proof: NDProof
  27. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  28. val term: Expr
  29. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  30. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  31. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  32. def [B](y: B): (InductionCase, B)
    Implicit
    This member is added by an implicit conversion from InductionCase to ArrowAssoc[InductionCase] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Serializable

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from InductionCase to any2stringadd[InductionCase]

Inherited by implicit conversion StringFormat from InductionCase to StringFormat[InductionCase]

Inherited by implicit conversion Ensuring from InductionCase to Ensuring[InductionCase]

Inherited by implicit conversion ArrowAssoc from InductionCase to ArrowAssoc[InductionCase]

Ungrouped