case class CutRule(leftSubProof: LKProof, aux1: SequentIndex, rightSubProof: LKProof, aux2: SequentIndex) extends BinaryLKProof with CommonRule with Product with Serializable
An LKProof ending with a cut:
(π1) (π2)
Γ :- Δ, A A, Π :- Λ
------------------------
Γ, Π :- Δ, Λ
- leftSubProof
The proof π1.
- aux1
The index of A in π1.
- rightSubProof
The proof π2.
- aux2
The index of A in π2.
- Source
- lk.scala
- Alphabetic
- By Inheritance
- CutRule
- Serializable
- Serializable
- CommonRule
- ContextRule
- BinaryLKProof
- LKProof
- SequentProof
- DagProof
- Product
- Equals
- AnyRef
- Any
- by any2stringadd
- by StringFormat
- by Ensuring
- by ArrowAssoc
- Hide All
- Show All
- Public
- All
Instance Constructors
-
new
CutRule(leftSubProof: LKProof, aux1: SequentIndex, rightSubProof: LKProof, aux2: SequentIndex)
- leftSubProof
The proof π1.
- aux1
The index of A in π1.
- rightSubProof
The proof π2.
- aux2
The index of A in π2.
Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
##(): Int
- Definition Classes
- AnyRef → Any
- def +(other: String): String
- def ->[B](y: B): (CutRule, B)
-
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 aux1: SequentIndex
- val aux2: SequentIndex
-
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
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
- CutRule → SequentProof
-
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 cutFormula: Formula
-
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: (CutRule) ⇒ Boolean, msg: ⇒ Any): CutRule
- def ensuring(cond: (CutRule) ⇒ Boolean): CutRule
- def ensuring(cond: Boolean, msg: ⇒ Any): CutRule
- def ensuring(cond: Boolean): CutRule
-
final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
equals(that: Any): Boolean
- Definition Classes
- DagProof → Equals → AnyRef → Any
-
def
finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] )
- def formatted(fmtstr: String): String
-
def
formulasToBeDeleted: Seq[Seq[SequentIndex]]
- Attributes
- protected
- Definition Classes
- ContextRule
-
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
-
def
getLeftSequentConnector: SequentConnector
The object connecting the lower and left upper sequents.
The object connecting the lower and left upper sequents.
- Definition Classes
- BinaryLKProof
-
def
getRightSequentConnector: SequentConnector
The object connecting the lower and right upper sequents.
The object connecting the lower and right upper sequents.
- Definition Classes
- BinaryLKProof
-
val
hashCode: Int
- Definition Classes
- DagProof
-
def
immediateSubProofs: Seq[LKProof]
The immediate subproofs of this rule.
The immediate subproofs of this rule.
- Definition Classes
- BinaryLKProof → DagProof
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
def
leftPremise: Sequent[Formula]
The left upper sequent of the rule.
The left upper sequent of the rule.
- Definition Classes
- BinaryLKProof
-
val
leftSubProof: LKProof
- Definition Classes
- CutRule → BinaryLKProof
-
def
longName: String
The name of this rule (in words).
The name of this rule (in words).
- Definition Classes
- DagProof
-
def
mainFormulaSequent: Sequent[Nothing]
- Definition Classes
- CutRule → 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).
-
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
premises: Seq[Sequent[Formula]]
The upper sequents of the rule.
The upper sequents of the rule.
- Definition Classes
- SequentProof
-
def
rightPremise: Sequent[Formula]
The right upper sequent of the rule.
The right upper sequent of the rule.
- Definition Classes
- BinaryLKProof
-
val
rightSubProof: LKProof
- Definition Classes
- CutRule → BinaryLKProof
-
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 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( ... )
- def →[B](y: B): (CutRule, B)
This is the API documentation for GAPT.
The main package is at.logic.gapt.