abstract class EqualityRule extends UnaryLKProof with CommonRule
Abstract class that performs most of the construction of left and right equality rules.
- Source
- EqualityRule.scala
- Alphabetic
- By Inheritance
- EqualityRule
- CommonRule
- ContextRule
- UnaryLKProof
- LKProof
- SequentProof
- DagProof
- Product
- Equals
- AnyRef
- Any
- by any2stringadd
- by StringFormat
- by Ensuring
- by ArrowAssoc
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- Public
- Protected
Instance Constructors
- new EqualityRule()
Abstract Value Members
- abstract def aux: SequentIndex
- abstract def canEqual(that: Any): Boolean
- Definition Classes
- Equals
- abstract def eq: SequentIndex
- abstract def mainFormulaSequent: Sequent[Formula]
- Attributes
- protected
- Definition Classes
- ContextRule
- abstract def productArity: Int
- Definition Classes
- Product
- abstract def productElement(n: Int): Any
- Definition Classes
- Product
- abstract def replacementContext: Abs
- abstract def subProof: LKProof
The immediate subproof of the rule.
The immediate subproof of the rule.
- Definition Classes
- EqualityRule → UnaryLKProof
Concrete Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##: Int
- Definition Classes
- AnyRef → Any
- def +(other: String): String
- Implicit
- This member is added by an implicit conversion from EqualityRule toany2stringadd[EqualityRule] performed by method any2stringadd in scala.Predef.
- Definition Classes
- any2stringadd
- def ->[B](y: B): (EqualityRule, B)
- Implicit
- This member is added by an implicit conversion from EqualityRule toArrowAssoc[EqualityRule] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc
- Annotations
- @inline()
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- def LKRuleCreationException(message: String): LKRuleCreationException
- Attributes
- protected
- Definition Classes
- LKProof
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- val auxFormula: Formula
- def auxFormulas: Seq[Seq[Formula]]
A list of lists containing the auxiliary formulas of the rule.
A list of lists containing the auxiliary formulas of the rule. The first list constains the auxiliary formulas in the first premise and so on.
- Definition Classes
- SequentProof
- def auxInConclusion: SequentIndex
- def auxIndices: Seq[Seq[SequentIndex]]
A list of lists of SequentIndices denoting the auxiliary formula(s) of the rule.
A list of lists of SequentIndices denoting the auxiliary formula(s) of the rule. The first list contains the auxiliary formulas in the first premise and so on.
- Definition Classes
- EqualityRule → SequentProof
- val by: Expr
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
- lazy val conclusion: Sequent[Formula]
The conclusion of the rule.
The conclusion of the rule.
- Definition Classes
- ContextRule → SequentProof
- def contexts: Seq[Sequent[Formula]]
- Attributes
- protected
- Definition Classes
- ContextRule
- def dagLike: DagLikeOps[LKProof]
Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see gapt.proofs.DagProof.DagLikeOps for a list.
Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see gapt.proofs.DagProof.DagLikeOps for a list.
- Definition Classes
- DagProof
- def depth: Int
Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.
Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.
- Definition Classes
- DagProof
- final def endSequent: HOLSequent
The end-sequent of the rule.
The end-sequent of the rule.
- Definition Classes
- LKProof
- def ensuring(cond: (EqualityRule) => Boolean, msg: => Any): EqualityRule
- Implicit
- This member is added by an implicit conversion from EqualityRule toEnsuring[EqualityRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- def ensuring(cond: (EqualityRule) => Boolean): EqualityRule
- Implicit
- This member is added by an implicit conversion from EqualityRule toEnsuring[EqualityRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- def ensuring(cond: Boolean, msg: => Any): EqualityRule
- Implicit
- This member is added by an implicit conversion from EqualityRule toEnsuring[EqualityRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- def ensuring(cond: Boolean): EqualityRule
- Implicit
- This member is added by an implicit conversion from EqualityRule toEnsuring[EqualityRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def eqInConclusion: SequentIndex
- def equals(that: Any): Boolean
- Definition Classes
- DagProof → Equals → AnyRef → Any
- def equation: Formula
- def formulasToBeDeleted: Seq[Seq[SequentIndex]]
- Definition Classes
- EqualityRule → ContextRule
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @IntrinsicCandidate()
- def getSequentConnector: SequentConnector
The object connecting the lower and upper sequents.auxFormulas
The object connecting the lower and upper sequents.auxFormulas
- Definition Classes
- UnaryLKProof
- val hashCode: Int
- Definition Classes
- DagProof
- def immediateSubProofs: Seq[LKProof]
The immediate subproofs of this rule.
The immediate subproofs of this rule.
- Definition Classes
- UnaryLKProof → DagProof
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- val leftToRight: Boolean
- def longName: String
The name of this rule (in words).
The name of this rule (in words).
- Definition Classes
- DagProof
- def mainFormula: Formula
- def mainFormulas: Seq[Formula]
The list of main formulas of the rule.
The list of main formulas of the rule.
- Definition Classes
- SequentProof
- def mainIndices: Vector[SequentIndex]
A list of SequentIndices denoting the main formula(s) of the rule.
A list of SequentIndices denoting the main formula(s) of the rule.
- Definition Classes
- ContextRule → SequentProof
- def name: String
The name of this rule (in symbols).
The name of this rule (in symbols).
- Definition Classes
- DagProof
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @IntrinsicCandidate()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @IntrinsicCandidate()
- def occConnectors: IndexedSeq[SequentConnector]
A list of occurrence connectors, one for each immediate subproof.
A list of occurrence connectors, one for each immediate subproof.
- Definition Classes
- ContextRule → SequentProof
- def premise: HOLSequent
The upper sequent of the rule.
The upper sequent of the rule.
- Definition Classes
- UnaryLKProof
- def premises: Seq[Sequent[Formula]]
The upper sequents of the rule.
The upper sequents of the rule.
- Definition Classes
- SequentProof
- def productElementName(n: Int): String
- Definition Classes
- Product
- def productElementNames: Iterator[String]
- Definition Classes
- Product
- def productIterator: Iterator[Any]
- Definition Classes
- Product
- def productPrefix: String
- Definition Classes
- Product
- def stepString(subProofLabels: Map[Any, String]): String
- Attributes
- protected
- Definition Classes
- SequentProof → DagProof
- def subProofAt(pos: List[Int]): LKProof
Returns the subproof at the given position: p.subProofAt(Nil) is p itself; p.subProofAt(i :: is) is the ith subproof of p.subProofAt(is).
Returns the subproof at the given position: p.subProofAt(Nil) is p itself; p.subProofAt(i :: is) is the ith subproof of p.subProofAt(is).
- Definition Classes
- DagProof
- def subProofs: Set[LKProof]
Set of all (transitive) sub-proofs including this.
Set of all (transitive) sub-proofs including this.
- Definition Classes
- DagProof
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def toString(): String
- Definition Classes
- DagProof → AnyRef → Any
- def treeLike: TreeLikeOps[LKProof]
Operations that view the sub-proofs as a tree, see gapt.proofs.DagProof.TreeLikeOps for a list.
Operations that view the sub-proofs as a tree, see gapt.proofs.DagProof.TreeLikeOps for a list.
- Definition Classes
- DagProof
- final def validateIndices(premise: HOLSequent, antecedentIndices: Seq[SequentIndex], succedentIndices: Seq[SequentIndex]): Unit
Checks whether indices are in the right place and premise is defined at all of them.
Checks whether indices are in the right place and premise is defined at all of them.
- premise
The sequent to be checked.
- antecedentIndices
Indices that should be in the antecedent.
- succedentIndices
Indices that should be in the succedent.
- Attributes
- protected
- Definition Classes
- LKProof
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- val what: Expr
Deprecated Value Members
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable]) @Deprecated
- Deprecated
- def formatted(fmtstr: String): String
- Implicit
- This member is added by an implicit conversion from EqualityRule toStringFormat[EqualityRule] performed by method StringFormat in scala.Predef.
- Definition Classes
- StringFormat
- Annotations
- @deprecated @inline()
- Deprecated
(Since version 2.12.16) Use
formatString.format(value)instead ofvalue.formatted(formatString), or use thef""string interpolator. In Java 15 and later,formattedresolves to the new method in String which has reversed parameters.
- def →[B](y: B): (EqualityRule, B)
- Implicit
- This member is added by an implicit conversion from EqualityRule toArrowAssoc[EqualityRule] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc
- Annotations
- @deprecated
- Deprecated
(Since version 2.13.0) Use
->instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.
This is the API documentation for GAPT.
The main package is gapt.