case class EqualityLeftRule(subProof: LKProof, eq: SequentIndex, aux: SequentIndex, replacementContext: Abs) extends EqualityRule with Product with Serializable
An LKProof ending with a left equality rule. There are two possible cases according to which direction the rule is applied in:
(π) (π)
A[s], s = t, Γ :- Δ A[t], s = t, Γ :- Δ
---------------------eq:l ---------------------eq:l
A[t], s = t, Γ :- Δ A[s], s = t, Γ :- Δ
- subProof
The subproof π.
- eq
The index of s = t.
- aux
The index of the formula in which the replacement is to be performed.
- replacementContext
A term λx.A[x] that designates the positions to be replaced.
- Source
- lk.scala
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- EqualityLeftRule
- Serializable
- Serializable
- EqualityRule
- CommonRule
- ContextRule
- UnaryLKProof
- LKProof
- SequentProof
- DagProof
- Product
- Equals
- AnyRef
- Any
- by any2stringadd
- by StringFormat
- by Ensuring
- by ArrowAssoc
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Instance Constructors
-
new
EqualityLeftRule(subProof: LKProof, eq: SequentIndex, aux: SequentIndex, replacementContext: Abs)
- subProof
The subproof π.
- eq
The index of s = t.
- aux
The index of the formula in which the replacement is to be performed.
- replacementContext
A term λx.A[x] that designates the positions to be replaced.
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 EqualityLeftRule to any2stringadd[EqualityLeftRule] performed by method any2stringadd in scala.Predef.
- Definition Classes
- any2stringadd
-
def
->[B](y: B): (EqualityLeftRule, B)
- Implicit
- This member is added by an implicit conversion from EqualityLeftRule to ArrowAssoc[EqualityLeftRule] 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
aux: SequentIndex
- Definition Classes
- EqualityLeftRule → EqualityRule
-
val
auxFormula: Formula
- Definition Classes
- EqualityRule
-
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
- Definition Classes
- EqualityRule
-
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
- Definition Classes
- EqualityRule
-
def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @native() @throws( ... )
-
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 DagProof.DagLikeOps for a list.
Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see 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: Sequent[Formula]
The end-sequent of the rule.
The end-sequent of the rule.
- Definition Classes
- LKProof
-
def
ensuring(cond: (EqualityLeftRule) ⇒ Boolean, msg: ⇒ Any): EqualityLeftRule
- Implicit
- This member is added by an implicit conversion from EqualityLeftRule to Ensuring[EqualityLeftRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: (EqualityLeftRule) ⇒ Boolean): EqualityLeftRule
- Implicit
- This member is added by an implicit conversion from EqualityLeftRule to Ensuring[EqualityLeftRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: Boolean, msg: ⇒ Any): EqualityLeftRule
- Implicit
- This member is added by an implicit conversion from EqualityLeftRule to Ensuring[EqualityLeftRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: Boolean): EqualityLeftRule
- Implicit
- This member is added by an implicit conversion from EqualityLeftRule to Ensuring[EqualityLeftRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
val
eq: SequentIndex
- Definition Classes
- EqualityLeftRule → EqualityRule
-
def
eqInConclusion: SequentIndex
- Definition Classes
- EqualityRule
-
def
equals(that: Any): Boolean
- Definition Classes
- DagProof → Equals → AnyRef → Any
-
def
equation: Formula
- Definition Classes
- EqualityRule
-
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 EqualityLeftRule to StringFormat[EqualityLeftRule] performed by method StringFormat in scala.Predef.
- Definition Classes
- StringFormat
- Annotations
- @inline()
-
def
formulasToBeDeleted: Seq[Seq[SequentIndex]]
- Definition Classes
- EqualityRule → ContextRule
-
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
-
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
- Definition Classes
- EqualityRule
-
def
longName: String
The name of this rule (in words).
The name of this rule (in words).
- Definition Classes
- DagProof
-
def
mainFormula: Formula
- Definition Classes
- EqualityRule
-
def
mainFormulaSequent: Sequent[Formula]
- Definition Classes
- EqualityLeftRule → ContextRule
-
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
- EqualityLeftRule → DagProof
-
final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
final
def
notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
-
final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
-
def
occConnectors: Seq[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: Sequent[Formula]
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
-
val
replacementContext: Abs
- Definition Classes
- EqualityLeftRule → EqualityRule
-
def
stepString(subProofLabels: Map[Any, String]): String
- Attributes
- protected
- Definition Classes
- SequentProof → DagProof
-
val
subProof: LKProof
- Definition Classes
- EqualityLeftRule → EqualityRule → UnaryLKProof
-
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 DagProof.TreeLikeOps for a list.
Operations that view the sub-proofs as a tree, see DagProof.TreeLikeOps for a list.
- Definition Classes
- DagProof
-
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(): 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
- @native() @throws( ... )
-
val
what: Expr
- Definition Classes
- EqualityRule
-
def
→[B](y: B): (EqualityLeftRule, B)
- Implicit
- This member is added by an implicit conversion from EqualityLeftRule to ArrowAssoc[EqualityLeftRule] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc
This is the API documentation for GAPT.
The main package is at.logic.gapt.