abstract class SimpleInductionProof extends AnyRef

Models a simple induction proof.

Source
SIPs.scala
Linear Supertypes
Known Subclasses
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. SimpleInductionProof
  2. AnyRef
  3. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Instance Constructors

  1. new SimpleInductionProof(ExpSeq0: ExpansionSequent, ExpSeq1: ExpansionSequent, ExpSeq2: ExpansionSequent, t: List[FOLTerm], u: List[FOLTerm], inductionFormula: Formula = ...)

    ExpSeq0

    Instances for the induction base.

    ExpSeq1

    Instances for the induction step.

    ExpSeq2

    Instances for the conclusion.

    t

    Terms used in the induction step.

    u

    Terms used in the conclusion

    inductionFormula

    The formula induced over. This argument defaults to X(α, ν, γ) with X a second-order variable, i.e. an unknown induction formula.

Abstract Value Members

  1. abstract def Fprime(x1: FOLTerm, x2: FOLTerm): FOLFormula
    Attributes
    protected
  2. abstract def Sequent0: HOLSequent
  3. abstract def Sequent1: HOLSequent
  4. abstract def Sequent2: HOLSequent
  5. abstract def baseProof(pi0: LKProof): LKProof
    Attributes
    protected
  6. abstract def conclusionProof(pi2: LKProof): LKProof
    Attributes
    protected
  7. abstract def stepProof(pi1: LKProof): LKProof
    Attributes
    protected
  8. abstract def toInstanceLKProof(n: Int, pi0: LKProof, pi1: LKProof, pi2: LKProof, rename: Boolean): LKProof

    Computes the nth instance proof, with user-supplied proofs π0, π1, π2.

    Computes the nth instance proof, with user-supplied proofs π0, π1, π2.

    n

    A natural number

    pi0

    Proof of the induction base.

    pi1

    Proof of the induction step.

    pi2

    Proof of the conclusion.

    returns

    The nth instance of this sip.

Concrete 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 SimpleInductionProof to any2stringadd[SimpleInductionProof] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (SimpleInductionProof, B)
    Implicit
    This member is added by an implicit conversion from SimpleInductionProof to ArrowAssoc[SimpleInductionProof] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. val EndSequent: Sequent[Formula]
  7. val ExpSeq0: ExpansionSequent
  8. val ExpSeq1: ExpansionSequent
  9. val ExpSeq2: ExpansionSequent
  10. def F(x1: FOLTerm, x2: FOLTerm, x3: FOLTerm): Formula
    Attributes
    protected
  11. val Gamma0: HOLSequent
  12. val Gamma1: HOLSequent
  13. val Gamma2: HOLSequent
  14. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  15. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  16. def ensuring(cond: (SimpleInductionProof) ⇒ Boolean, msg: ⇒ Any): SimpleInductionProof
    Implicit
    This member is added by an implicit conversion from SimpleInductionProof to Ensuring[SimpleInductionProof] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  17. def ensuring(cond: (SimpleInductionProof) ⇒ Boolean): SimpleInductionProof
    Implicit
    This member is added by an implicit conversion from SimpleInductionProof to Ensuring[SimpleInductionProof] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  18. def ensuring(cond: Boolean, msg: ⇒ Any): SimpleInductionProof
    Implicit
    This member is added by an implicit conversion from SimpleInductionProof to Ensuring[SimpleInductionProof] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: Boolean): SimpleInductionProof
    Implicit
    This member is added by an implicit conversion from SimpleInductionProof to Ensuring[SimpleInductionProof] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  21. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  22. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  23. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from SimpleInductionProof to StringFormat[SimpleInductionProof] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  24. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  25. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  26. def indFormIsQuantified: Boolean

    Returns true iff the induction formula needs to be quantified over.

  27. val inductionFormula: Formula
  28. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  29. def isSchematic: Boolean

    returns

    True if this is a schematic sip, i.e. the induction formula is unknown.

  30. def isSolved: Boolean
  31. def isSolved(prover: Prover): Boolean

    returns

    True if the induction formula is in fact a solution.

  32. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  33. final def notify(): Unit
    Definition Classes
    AnyRef
  34. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  35. def solve(f: FOLFormula): SimpleInductionProofU

    TODO: Find a better name for this

    TODO: Find a better name for this

    f

    A FOLFormula

    returns

    This with the induction formula replaced by f

  36. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  37. val t: List[FOLTerm]
  38. def toInstanceLKProof(n: Int, prover: Prover, rename: Boolean): LKProof

    Computes the nth instance proof,

    Computes the nth instance proof,

    n

    A natural number

    prover

    The prover used to generate π0 ,…,π2.

    returns

    The nth instance of this sip.

  39. def toInstanceLKProof(n: Int, rename: Boolean): LKProof

    Computes the nth instance proof.

    Computes the nth instance proof. Uses prover9 to compute the subproofs.

    n

    A natural number

    returns

    The nth instance of this sip.

  40. def toLKProof: LKProof

    Converts this into an LKProof, calling prover9 to provide π0, π1, π2.

    Converts this into an LKProof, calling prover9 to provide π0, π1, π2.

    returns

    The LKProof represented by this object

  41. def toLKProof(prover: Prover): LKProof

    prover

    The prover used to generate π0 ,…,π2.

  42. def toLKProof(pi0: LKProof, pi1: LKProof, pi2: LKProof): LKProof

    Converts this into an LKProof, with user-supplied proofs π0, π1, π2.

    Converts this into an LKProof, with user-supplied proofs π0, π1, π2.

    pi0

    Proof of the induction base.

    pi1

    Proof of the induction step.

    pi2

    Proof of the conclusion.

    returns

    The LKProof represented by this object.

  43. def toString(): String
    Definition Classes
    AnyRef → Any
  44. val u: List[FOLTerm]
  45. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  46. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  47. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  48. def [B](y: B): (SimpleInductionProof, B)
    Implicit
    This member is added by an implicit conversion from SimpleInductionProof to ArrowAssoc[SimpleInductionProof] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from AnyRef

Inherited from Any

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

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

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

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

Ungrouped