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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Instance Constructors
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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
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
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final
def
##(): Int
- Definition Classes
- AnyRef → Any
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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
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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
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- @inline()
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final
def
==(arg0: Any): Boolean
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final
def
asInstanceOf[T0]: T0
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def
clone(): AnyRef
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- protected[java.lang]
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- AnyRef
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- @native() @throws( ... )
- val constructor: Const
- val eigenVars: Seq[Var]
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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
-
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
-
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
-
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
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final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- val fieldTypes: List[Ty]
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def
finalize(): Unit
- Attributes
- protected[java.lang]
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- @throws( classOf[java.lang.Throwable] )
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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()
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final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
- val hypVars: Seq[Var]
- val hypotheses: Seq[SequentIndex]
- val indTy: Ty
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
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final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
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final
def
notify(): Unit
- Definition Classes
- AnyRef
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- @native()
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final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
- val proof: NDProof
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final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
- val term: Expr
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final
def
wait(): Unit
- Definition Classes
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final
def
wait(arg0: Long, arg1: Int): Unit
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final
def
wait(arg0: Long): Unit
- Definition Classes
- AnyRef
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- @native() @throws( ... )
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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
This is the API documentation for GAPT.
The main package is gapt.