abstract class SimpleInductionProof extends AnyRef
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Instance Constructors
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new
SimpleInductionProof(ExpSeq0: ExpansionSequent, ExpSeq1: ExpansionSequent, ExpSeq2: ExpansionSequent, t: List[FOLTerm], u: List[FOLTerm], inductionFormula: HOLFormula = ...)
- 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
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abstract
def
Fprime(x1: FOLTerm, x2: FOLTerm): FOLFormula
- Attributes
- protected
- abstract def Sequent0: HOLSequent
- abstract def Sequent1: HOLSequent
- abstract def Sequent2: HOLSequent
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abstract
def
baseProof(pi0: LKProof): LKProof
- Attributes
- protected
-
abstract
def
conclusionProof(pi2: LKProof): LKProof
- Attributes
- protected
-
abstract
def
stepProof(pi1: LKProof): LKProof
- Attributes
- protected
-
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
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final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
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final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
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
-
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()
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final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- val EndSequent: Sequent[HOLFormula]
- val ExpSeq0: ExpansionSequent
- val ExpSeq1: ExpansionSequent
- val ExpSeq2: ExpansionSequent
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def
F(x1: FOLTerm, x2: FOLTerm, x3: FOLTerm): HOLFormula
- Attributes
- protected
- val Gamma0: HOLSequent
- val Gamma1: HOLSequent
- val Gamma2: HOLSequent
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final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
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
-
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
-
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
-
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
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final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
equals(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
def
finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] )
-
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()
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final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
-
def
hashCode(): Int
- Definition Classes
- AnyRef → Any
-
def
indFormIsQuantified: Boolean
Returns true iff the induction formula needs to be quantified over.
- val inductionFormula: HOLFormula
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
def
isSchematic: Boolean
- returns
True if this is a schematic sip, i.e. the induction formula is unknown.
- def isSolved: Boolean
-
def
isSolved(prover: Prover): Boolean
- returns
True if the induction formula is in fact a solution.
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final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
final
def
notify(): Unit
- Definition Classes
- AnyRef
-
final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
-
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
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final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
- val t: List[FOLTerm]
-
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.
-
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.
-
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
-
def
toLKProof(prover: Prover): LKProof
- prover
The prover used to generate π0 ,…,π2.
-
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.
-
def
toString(): String
- Definition Classes
- AnyRef → Any
- val u: List[FOLTerm]
-
final
def
wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
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