case class ETSkolemQuantifier(shallow: Formula, skolemTerm: Expr, skolemDef: Expr, child: ExpansionTree) extends ETQuantifier with UnaryExpansionTree with Product with Serializable
A tree representing a formula beginning with a strong quantifier, i.e., a positive universal or a negative existential.
As an example let us consider an expansion proof of ∀z P(c,z) :- ∃x ∀y P(x,y).
For Skolemization we introduce the Skolem function s_1
(for the single strong quantifier), this function
has the Skolem definition λx ∀y P(x,y)
(see gapt.expr.hol.SkolemFunctions for details).
The natural expansion proof has the deep formula P(c,s_1(c)) :- P(c,s_1(c))
, so we need a Skolem node with the
shallow formula ∀y P(c,y)
, and deep formula P(c,s_1(c))
. This Skolem node is constructed as
ETSkolemQuantifier(∀y P(c,y), s_1(c), λx ∀y P(x,y), ETAtom(P(c,s_1(c)), InSuc))
.
- shallow
Shallow formula of the expansion tree.
- skolemTerm
Skolem term that instantiates the strong quantifier, e.g. s_3(c)
- skolemDef
Skolem definition for the Skolem symbol, see gapt.expr.hol.SkolemFunctions
- child
Expansion tree of the instantiated formula.
- Source
- expansionTrees.scala
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- ETSkolemQuantifier
- Serializable
- Serializable
- UnaryExpansionTree
- ETQuantifier
- ExpansionTree
- DagProof
- Product
- Equals
- AnyRef
- Any
- by any2stringadd
- by StringFormat
- by Ensuring
- by ArrowAssoc
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- Public
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Instance Constructors
-
new
ETSkolemQuantifier(shallow: Formula, skolemTerm: Expr, skolemDef: Expr, child: ExpansionTree)
- shallow
Shallow formula of the expansion tree.
- skolemTerm
Skolem term that instantiates the strong quantifier, e.g. s_3(c)
- skolemDef
Skolem definition for the Skolem symbol, see gapt.expr.hol.SkolemFunctions
- child
Expansion tree of the instantiated formula.
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 ETSkolemQuantifier to any2stringadd[ETSkolemQuantifier] performed by method any2stringadd in scala.Predef.
- Definition Classes
- any2stringadd
-
def
->[B](y: B): (ETSkolemQuantifier, B)
- Implicit
- This member is added by an implicit conversion from ETSkolemQuantifier to ArrowAssoc[ETSkolemQuantifier] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc
- Annotations
- @inline()
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
def
apply(pos: HOLPosition): Set[ExpansionTree]
- Definition Classes
- ExpansionTree
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
- val boundVar: Var
-
val
child: ExpansionTree
- Definition Classes
- ETSkolemQuantifier → UnaryExpansionTree
-
def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @native() @throws( ... )
-
def
dagLike: DagLikeOps[ExpansionTree]
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
deep: Formula
The formula represented by this tree, fully instantiated.
The formula represented by this tree, fully instantiated.
- Definition Classes
- ETSkolemQuantifier → ExpansionTree
-
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
-
def
ensuring(cond: (ETSkolemQuantifier) ⇒ Boolean, msg: ⇒ Any): ETSkolemQuantifier
- Implicit
- This member is added by an implicit conversion from ETSkolemQuantifier to Ensuring[ETSkolemQuantifier] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: (ETSkolemQuantifier) ⇒ Boolean): ETSkolemQuantifier
- Implicit
- This member is added by an implicit conversion from ETSkolemQuantifier to Ensuring[ETSkolemQuantifier] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: Boolean, msg: ⇒ Any): ETSkolemQuantifier
- Implicit
- This member is added by an implicit conversion from ETSkolemQuantifier to Ensuring[ETSkolemQuantifier] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: Boolean): ETSkolemQuantifier
- Implicit
- This member is added by an implicit conversion from ETSkolemQuantifier to Ensuring[ETSkolemQuantifier] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
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
- Implicit
- This member is added by an implicit conversion from ETSkolemQuantifier to StringFormat[ETSkolemQuantifier] performed by method StringFormat in scala.Predef.
- Definition Classes
- StringFormat
- Annotations
- @inline()
-
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
-
val
hashCode: Int
- Definition Classes
- DagProof
-
def
immediateSubProofs: Seq[ExpansionTree]
The immediate subproofs of this rule.
The immediate subproofs of this rule.
- Definition Classes
- UnaryExpansionTree → DagProof
-
def
instances: Iterable[(Expr, ExpansionTree)]
- Definition Classes
- ETSkolemQuantifier → ETQuantifier
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
def
longName: String
The name of this rule (in words).
The name of this rule (in words).
- Definition Classes
- DagProof
-
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()
-
final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
-
val
polarity: Polarity
- Definition Classes
- ETSkolemQuantifier → ExpansionTree
- val qfFormula: Formula
-
val
shallow: Formula
- Definition Classes
- ETSkolemQuantifier → ExpansionTree
- val skolemArgs: List[Expr]
- val skolemConst: Const
- val skolemDef: Expr
- val skolemTerm: Expr
-
def
stepString(subProofLabels: Map[Any, String]): String
- Attributes
- protected
- Definition Classes
- DagProof
-
def
subProofAt(pos: List[Int]): ExpansionTree
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[ExpansionTree]
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
toSigRelativeString(implicit sig: BabelSignature): String
- Definition Classes
- ExpansionTree
-
def
toString(): String
- Definition Classes
- ExpansionTree → DagProof → AnyRef → Any
-
def
treeLike: TreeLikeOps[ExpansionTree]
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
-
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): (ETSkolemQuantifier, B)
- Implicit
- This member is added by an implicit conversion from ETSkolemQuantifier to ArrowAssoc[ETSkolemQuantifier] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc
This is the API documentation for GAPT.
The main package is gapt.