class EscargotState extends AnyRef
Main class of the Escargot superposition prover.
A practical introduction to superposition provers can be found in [1], Section 3.
Essentially, we start with a set of clauses and apply inferences until we either: 1. have derived the empty clause, or 2. applied all possible inferences without producing new clauses
The clauses are stored in various sets, the main two ones are: * workedOff: all inferences between clauses in this set have already been applied * usable: these clauses have not yet been used in inferences
In every iteration of the prover (see the loop method), we 1. pick a "given" clause from usable (using the choose method) 2. perform all inferences between the given clause and all clauses in workedOff 2a. add the given clause to workedOff (unless discarded by an inference) 3. now newlyDerived contains the newly derived clauses, and we perform preprocessing on them 3a. the preprocessed clauses get moved to usable
(The names are non-standard and picked from different sources with no regard for consistency, sorry.)
Inferences: an InferenceRule is an operation that looks at the given clause, and the set of worked off clauses; it returns a set of new clauses, plus a set of clauses that should be discarded.
For example, StandardInferences.BackwardSubsumption is an inference rule: it returns no new clauses, but the subsumed clauses in usable are returned as discarded.
Avatar splitting: Escargot employs the Avatar splitting regime [2]. Clauses are annotated with propositional assertions, see gapt.proofs.resolution.ResolutionProof for the syntax. We always have a propositional model (avatarModel), and only consider clauses whose assertions are true in this model (called "active" here). Clauses whose assertions are false in the model are stored in locked. Whenever we derive an empty clause, we call the SAT solver to obtain a model in which every empty clause has a false assertion. If there is no such model, then we have found a proof!
[1] Weidenbach, Combining Superposition, Sorts and Splitting. Handbook of Automated Reasoning II, 2001 [2] Voronkov, AVATAR: The Architecture for first-order theorem provers. CAV 2014
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- state.scala
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- new EscargotState(ctx: MutableContext)
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- final def !=(arg0: Any): Boolean
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- final def ##(): Int
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- def +(other: String): String
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- This member is added by an implicit conversion from EscargotState toany2stringadd[EscargotState] performed by method any2stringadd in scala.Predef.
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- any2stringadd
- def ->[B](y: B): (EscargotState, B)
- Implicit
- This member is added by an implicit conversion from EscargotState toArrowAssoc[EscargotState] performed by method ArrowAssoc in scala.Predef.
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- @inline()
- final def ==(arg0: Any): Boolean
- Definition Classes
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- def DerivedCls(parent1: Cls, parent2: Cls, newProof: ResolutionProof): Cls
- def DerivedCls(parent: Cls, newProof: ResolutionProof): Cls
- def InputCls(proof: ResolutionProof): Cls
- def InputCls(clause: HOLSequent): Cls
- def SimpCls(parent: Cls, newProof: ResolutionProof): Cls
- def addIndex[T <: AnyRef](idx: Index[T]): Unit
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- val atomToSatSolver: Map[Atom, Int]
Map from assertion atoms to SAT solver atoms
- var avatarModel: Set[Int]
Current propositional Avatar model.
- def axiomClause(section: ContextSection, axiom: Axiom): (Set[Cls], Map[HOLSequent, ResolutionProof])
- def choose(): Cls
Chooses the next clause from usable.
- def clauseProcessing(): Unit
Moves clauses from newlyDerived into usable and locked.
- var clausesForInduction: List[HOLSequent]
- def clone(): AnyRef
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- @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
- val ctx: MutableContext
- def deintern(i: Int): Atom
- def deinternLiteral(i: Int): Formula
- val drup: Buffer[Line]
- var emptyClauses: Map[Set[Int], Cls]
* Empty clauses that have already been derived.
* Empty clauses that have already been derived. All assertions in the empty clauses are false.
- def ensuring(cond: (EscargotState) => Boolean, msg: => Any): EscargotState
- Implicit
- This member is added by an implicit conversion from EscargotState toEnsuring[EscargotState] performed by method Ensuring in scala.Predef.
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- Ensuring
- def ensuring(cond: (EscargotState) => Boolean): EscargotState
- Implicit
- This member is added by an implicit conversion from EscargotState toEnsuring[EscargotState] performed by method Ensuring in scala.Predef.
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- Ensuring
- def ensuring(cond: Boolean, msg: => Any): EscargotState
- Implicit
- This member is added by an implicit conversion from EscargotState toEnsuring[EscargotState] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- def ensuring(cond: Boolean): EscargotState
- Implicit
- This member is added by an implicit conversion from EscargotState toEnsuring[EscargotState] performed by method Ensuring in scala.Predef.
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- Ensuring
- final def eq(arg0: AnyRef): Boolean
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- def equals(arg0: AnyRef): Boolean
- Definition Classes
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- def formatted(fmtstr: String): String
- Implicit
- This member is added by an implicit conversion from EscargotState toStringFormat[EscargotState] performed by method StringFormat in scala.Predef.
- Definition Classes
- StringFormat
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- final def getClass(): Class[_ <: AnyRef]
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- @native() @IntrinsicCandidate()
- def hashCode(): Int
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- def inferenceComputation(given: Cls): Boolean
Performs inferences between given and workedOff, and adds given to workedOff.
- var inferences: Seq[InferenceRule]
- def intern(assertions: HOLClause): Set[Int]
- def intern(atom: Atom): Int
- def isActive(assertion: Set[Int]): Boolean
Is the assertion true in the current model?
- def isActive(assertion: HOLClause): Boolean
Is the assertion true in the current model?
- def isActive(cls: Cls): Boolean
Is the assertion of cls true in the current model?
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- val locked: Set[(Cls, Option[Set[Int]])]
Locked clauses have assertions that are false in the current model, or are subsumed by a clause whose assertion is true in the current model.
Locked clauses have assertions that are false in the current model, or are subsumed by a clause whose assertion is true in the current model.
The optional clause is the assertion of the subsuming clause.
- def loop(spin: Option[SuperpositionInductionProver] = None): Option[(ResolutionProof, Set[Axiom], Map[HOLSequent, ResolutionProof])]
Main inference loop.
- def mkSatProof(): ResolutionProof
- var nameGen: NameGenerator
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- var newlyDerived: Set[Cls]
Clauses that have been derived in the current iteration.
- final def notify(): Unit
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- @native() @IntrinsicCandidate()
- final def notifyAll(): Unit
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- def preprocessing(): Unit
Pre-processes the clauses in newlyDerived.
Pre-processes the clauses in newlyDerived. The result is again in newlyDerived.
- var preprocessingRules: Seq[PreprocessingRule]
- val satSolverToAtom: Map[Int, Atom]
- val solver: ISolver
SAT solver instance
- def stateAsFormula: Formula
This formula should always be unsatisfiable.
- var strategy: Int
- def switchToNewModel(): Unit
- final def synchronized[T0](arg0: => T0): T0
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- AnyRef
- var termOrdering: TermOrdering
- def toString(): String
- Definition Classes
- AnyRef → Any
- def trySetAssertion(assertion: Set[Int], value: Boolean): Unit
- def trySetAvatarAtom(atom: Int): Unit
- val usable: Set[Cls]
We have not yet used these clauses in inferences.
- final def wait(arg0: Long, arg1: Int): Unit
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- final def wait(arg0: Long): Unit
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- final def wait(): Unit
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- var workedOff: IndexedClsSet
All inferences between these clauses have already been applied.
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- Deprecated
(Since version ) see corresponding Javadoc for more information.
- def →[B](y: B): (EscargotState, B)
- Implicit
- This member is added by an implicit conversion from EscargotState toArrowAssoc[EscargotState] performed by method ArrowAssoc in scala.Predef.
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- ArrowAssoc
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- @deprecated
- Deprecated
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This is the API documentation for GAPT.
The main package is gapt.