class SimpleInductionProofU extends SimpleInductionProof
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Instance Constructors
- new SimpleInductionProofU(ExpSeq0: ExpansionSequent, ExpSeq1: ExpansionSequent, ExpSeq2: ExpansionSequent, t: List[FOLTerm], u: List[FOLTerm], inductionFormula: Formula = ...)
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
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def
+(other: String): String
- Implicit
- This member is added by an implicit conversion from SimpleInductionProofU to any2stringadd[SimpleInductionProofU] performed by method any2stringadd in scala.Predef.
- Definition Classes
- any2stringadd
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def
->[B](y: B): (SimpleInductionProofU, B)
- Implicit
- This member is added by an implicit conversion from SimpleInductionProofU to ArrowAssoc[SimpleInductionProofU] 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
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val
EndSequent: Sequent[Formula]
- Definition Classes
- SimpleInductionProof
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val
ExpSeq0: ExpansionSequent
- Definition Classes
- SimpleInductionProof
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val
ExpSeq1: ExpansionSequent
- Definition Classes
- SimpleInductionProof
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val
ExpSeq2: ExpansionSequent
- Definition Classes
- SimpleInductionProof
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def
F(x1: FOLTerm, x2: FOLTerm, x3: FOLTerm): Formula
- Attributes
- protected
- Definition Classes
- SimpleInductionProof
-
def
Fprime(x1: FOLTerm, x2: FOLTerm): FOLFormula
- Attributes
- protected
- Definition Classes
- SimpleInductionProofU → SimpleInductionProof
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val
Gamma0: HOLSequent
- Definition Classes
- SimpleInductionProof
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val
Gamma1: HOLSequent
- Definition Classes
- SimpleInductionProof
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val
Gamma2: HOLSequent
- Definition Classes
- SimpleInductionProof
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val
Sequent0: HOLSequent
- Definition Classes
- SimpleInductionProofU → SimpleInductionProof
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val
Sequent1: Sequent[Formula]
- Definition Classes
- SimpleInductionProofU → SimpleInductionProof
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val
Sequent2: Sequent[Formula]
- Definition Classes
- SimpleInductionProofU → SimpleInductionProof
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final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
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def
baseProof(pi0: LKProof): LKProof
- Definition Classes
- SimpleInductionProofU → SimpleInductionProof
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def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
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def
conclusionProof(pi2: LKProof): ForallLeftRule
- Definition Classes
- SimpleInductionProofU → SimpleInductionProof
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def
ensuring(cond: (SimpleInductionProofU) ⇒ Boolean, msg: ⇒ Any): SimpleInductionProofU
- Implicit
- This member is added by an implicit conversion from SimpleInductionProofU to Ensuring[SimpleInductionProofU] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
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def
ensuring(cond: (SimpleInductionProofU) ⇒ Boolean): SimpleInductionProofU
- Implicit
- This member is added by an implicit conversion from SimpleInductionProofU to Ensuring[SimpleInductionProofU] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
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def
ensuring(cond: Boolean, msg: ⇒ Any): SimpleInductionProofU
- Implicit
- This member is added by an implicit conversion from SimpleInductionProofU to Ensuring[SimpleInductionProofU] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
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def
ensuring(cond: Boolean): SimpleInductionProofU
- Implicit
- This member is added by an implicit conversion from SimpleInductionProofU to Ensuring[SimpleInductionProofU] 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
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def
finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
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- Annotations
- @throws( classOf[java.lang.Throwable] )
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def
formatted(fmtstr: String): String
- Implicit
- This member is added by an implicit conversion from SimpleInductionProofU to StringFormat[SimpleInductionProofU] performed by method StringFormat in scala.Predef.
- Definition Classes
- StringFormat
- Annotations
- @inline()
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final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
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def
hashCode(): Int
- Definition Classes
- AnyRef → Any
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def
indFormIsQuantified: Boolean
Returns true iff the induction formula needs to be quantified over.
Returns true iff the induction formula needs to be quantified over.
- Definition Classes
- SimpleInductionProof
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val
inductionFormula: Formula
- Definition Classes
- SimpleInductionProof
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
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def
isSchematic: Boolean
- returns
True if this is a schematic sip, i.e. the induction formula is unknown.
- Definition Classes
- SimpleInductionProof
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def
isSolved: Boolean
- Definition Classes
- SimpleInductionProof
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def
isSolved(prover: Prover): Boolean
- returns
True if the induction formula is in fact a solution.
- Definition Classes
- SimpleInductionProof
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final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
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final
def
notify(): Unit
- Definition Classes
- AnyRef
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final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
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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
- Definition Classes
- SimpleInductionProof
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def
stepProof(pi1: LKProof): LKProof
- Definition Classes
- SimpleInductionProofU → SimpleInductionProof
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final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
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val
t: List[FOLTerm]
- Definition Classes
- SimpleInductionProof
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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.
- Definition Classes
- SimpleInductionProofU → SimpleInductionProof
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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.
- Definition Classes
- SimpleInductionProof
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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.
- Definition Classes
- SimpleInductionProof
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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
- Definition Classes
- SimpleInductionProof
-
def
toLKProof(prover: Prover): LKProof
- prover
The prover used to generate π0 ,…,π2.
- Definition Classes
- SimpleInductionProof
-
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.
- Definition Classes
- SimpleInductionProof
-
def
toSipGrammar: SipGrammar
Extracts a SIP grammar from the SIP according to the paper.
Extracts a SIP grammar from the SIP according to the paper.
- returns
The grammar corresponding to the sip.
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def
toString(): String
- Definition Classes
- AnyRef → Any
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val
u: List[FOLTerm]
- Definition Classes
- SimpleInductionProof
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final
def
wait(): Unit
- Definition Classes
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- @throws( ... )
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final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
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- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
def
→[B](y: B): (SimpleInductionProofU, B)
- Implicit
- This member is added by an implicit conversion from SimpleInductionProofU to ArrowAssoc[SimpleInductionProofU] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc