c

gapt.provers.escargot.impl

EscargotState

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

Source
state.scala
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Instance Constructors

  1. new EscargotState(ctx: MutableContext)

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from EscargotState to any2stringadd[EscargotState] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (EscargotState, B)
    Implicit
    This member is added by an implicit conversion from EscargotState to ArrowAssoc[EscargotState] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def DerivedCls(parent1: Cls, parent2: Cls, newProof: ResolutionProof): Cls
  7. def DerivedCls(parent: Cls, newProof: ResolutionProof): Cls
  8. def InputCls(proof: ResolutionProof): Cls
  9. def InputCls(clause: HOLSequent): Cls
  10. def SimpCls(parent: Cls, newProof: ResolutionProof): Cls
  11. def addIndex[T <: AnyRef](idx: Index[T]): Unit
  12. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  13. val atomToSatSolver: Map[Atom, Int]

    Map from assertion atoms to SAT solver atoms

  14. var avatarModel: Set[Int]

    Current propositional Avatar model.

  15. def choose(): Cls

    Chooses the next clause from usable.

  16. def clauseProcessing(): Unit

    Moves clauses from newlyDerived into usable and locked.

  17. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate() @throws( ... )
  18. val ctx: MutableContext
  19. def deintern(i: Int): Atom
  20. def deinternLiteral(i: Int): Formula
  21. val drup: Buffer[Line]
  22. 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.

  23. def ensuring(cond: (EscargotState) ⇒ Boolean, msg: ⇒ Any): EscargotState
    Implicit
    This member is added by an implicit conversion from EscargotState to Ensuring[EscargotState] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  24. def ensuring(cond: (EscargotState) ⇒ Boolean): EscargotState
    Implicit
    This member is added by an implicit conversion from EscargotState to Ensuring[EscargotState] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  25. def ensuring(cond: Boolean, msg: ⇒ Any): EscargotState
    Implicit
    This member is added by an implicit conversion from EscargotState to Ensuring[EscargotState] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  26. def ensuring(cond: Boolean): EscargotState
    Implicit
    This member is added by an implicit conversion from EscargotState to Ensuring[EscargotState] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  27. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  28. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  29. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from EscargotState to StringFormat[EscargotState] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  30. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  31. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  32. def inferenceComputation(given: Cls): Boolean

    Performs inferences between given and workedOff, and adds given to workedOff.

  33. var inferences: Seq[InferenceRule]
  34. def intern(assertions: HOLClause): Set[Int]
  35. def intern(atom: Atom): Int
  36. def isActive(assertion: Set[Int]): Boolean

    Is the assertion true in the current model?

  37. def isActive(assertion: HOLClause): Boolean

    Is the assertion true in the current model?

  38. def isActive(cls: Cls): Boolean

    Is the assertion of cls true in the current model?

  39. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  40. 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.

  41. def loop(): Option[ResolutionProof]

    Main inference loop.

  42. def mkSatProof(): ResolutionProof
  43. var nameGen: NameGenerator
  44. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  45. var newlyDerived: Set[Cls]

    Clauses that have been derived in the current iteration.

  46. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  47. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  48. def preprocessing(): Unit

    Pre-processes the clauses in newlyDerived.

    Pre-processes the clauses in newlyDerived. The result is again in newlyDerived.

  49. var preprocessingRules: Seq[PreprocessingRule]
  50. val satSolverToAtom: Map[Int, Atom]
  51. val solver: ISolver

    SAT solver instance

  52. def stateAsFormula: Formula

    This formula should always be unsatisfiable.

  53. var strategy: Int
  54. def switchToNewModel(): Unit
  55. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  56. var termOrdering: TermOrdering
  57. def toString(): String
    Definition Classes
    AnyRef → Any
  58. def trySetAssertion(assertion: Set[Int], value: Boolean): Unit
  59. def trySetAvatarAtom(atom: Int): Unit
  60. val usable: Set[Cls]

    We have not yet used these clauses in inferences.

  61. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  62. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  63. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  64. var workedOff: IndexedClsSet

    All inferences between these clauses have already been applied.

  65. def [B](y: B): (EscargotState, B)
    Implicit
    This member is added by an implicit conversion from EscargotState to ArrowAssoc[EscargotState] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @Deprecated @deprecated @throws( classOf[java.lang.Throwable] )
    Deprecated

    (Since version ) see corresponding Javadoc for more information.

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from EscargotState to any2stringadd[EscargotState]

Inherited by implicit conversion StringFormat from EscargotState to StringFormat[EscargotState]

Inherited by implicit conversion Ensuring from EscargotState to Ensuring[EscargotState]

Inherited by implicit conversion ArrowAssoc from EscargotState to ArrowAssoc[EscargotState]

Ungrouped