Packages

abstract class SaturationProcedure extends Theory

Class to simplify the implementation of saturation procedures as part of theory plugins. A saturation procedure is a procedure waiting for patterns to occur in a proof goal (e.g., formulas of a certain shape), and can apply proof rules for every such occurrence. Saturation will be implemented by adding tasks to the task queue of every goal, so that the prover can globally schedule the different rules to be applied.

This procedure does not take into account that applications points might get rewritten during the proof process; e.g., a variable x could turn into y when the equation x = y appears. In such cases, the saturation rule could get applied repeatedly for the same point.

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Theory, AnyRef, Any
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Instance Constructors

  1. new SaturationProcedure(name: String)

Type Members

  1. abstract type ApplicationPoint

    Type representing the cases in which the saturation procedure applies.

    Type representing the cases in which the saturation procedure applies. Those could be formulas or terms occurring in a goal, etc.

  2. class PointHandler extends TheoryProcedure

    Scheduled tasks of the saturation procedure.

    Scheduled tasks of the saturation procedure. Each of those tasks takes care of one application point.

Abstract Value Members

  1. abstract def applicationPriority(goal: Goal, p: ApplicationPoint): Int

    The priority of performing the given saturation.

    The priority of performing the given saturation. Lower numbers represent higher priority.

  2. abstract def extractApplicationPoints(goal: Goal): Iterator[ApplicationPoint]

    Determine all points at which this saturation procedure could be applied in a goal.

  3. abstract def handleApplicationPoint(goal: Goal, p: ApplicationPoint): Seq[Action]

    Actions to be performed for one particular application point.

    Actions to be performed for one particular application point. The method will be called exactly once for each persistent application point, i.e., for each application point that does eventually disappear as the result of some rule applications. The method should check whether the application point still exists in the goal; in case the application point has already disappeared from the goal at the point of calling this method, the method should return an empty sequence.

Concrete Value Members

  1. val axioms: Conjunction

    Axioms defining the theory; such axioms are simply added as formulae to the problem to be proven, and thus handled using the standard reasoning techniques (including e-matching).

    Axioms defining the theory; such axioms are simply added as formulae to the problem to be proven, and thus handled using the standard reasoning techniques (including e-matching).

    Definition Classes
    SaturationProcedureTheory
  2. val dependencies: Iterable[Theory]

    Optionally, other theories that this theory depends on.

    Optionally, other theories that this theory depends on. Specified dependencies will be loaded before this theory, but the preprocessors of the dependencies will be called after the preprocessor of this theory.

    Definition Classes
    Theory
  3. def evalFun(f: IFunApp): Option[ITerm]

    Optionally, a function evaluating theory functions applied to concrete arguments, represented as constructor terms.

    Optionally, a function evaluating theory functions applied to concrete arguments, represented as constructor terms.

    Definition Classes
    Theory
  4. def evalPred(p: IAtom): Option[Boolean]

    Optionally, a function evaluating theory predicates applied to concrete arguments, represented as constructor terms.

    Optionally, a function evaluating theory predicates applied to concrete arguments, represented as constructor terms.

    Definition Classes
    Theory
  5. def evaluatingSimplifier(t: IExpression): IExpression

    A simplification function that applies the methods evalFun and evalPred to some given expression (but not recursively).

    A simplification function that applies the methods evalFun and evalPred to some given expression (but not recursively). This is used in the Theory.postSimplifiers methods.

    Definition Classes
    Theory
  6. def extend(order: TermOrder): TermOrder

    Add the symbols defined by this theory to the order

    Add the symbols defined by this theory to the order

    Definition Classes
    Theory
  7. val functionPredicateMapping: List[Nothing]

    Mapping of interpreted functions to interpreted predicates, used translating input ASTs to internal ASTs (the latter only containing predicates).

    Mapping of interpreted functions to interpreted predicates, used translating input ASTs to internal ASTs (the latter only containing predicates).

    Definition Classes
    SaturationProcedureTheory
  8. val functionalPredicates: Set[Predicate]

    Information which of the predicates satisfy the functionality axiom; at some internal points, such predicates can be handled more efficiently

    Information which of the predicates satisfy the functionality axiom; at some internal points, such predicates can be handled more efficiently

    Definition Classes
    SaturationProcedureTheory
  9. val functions: List[Nothing]

    Interpreted functions of the theory

    Interpreted functions of the theory

    Definition Classes
    SaturationProcedureTheory
  10. def generateDecoderData(model: Conjunction): Option[TheoryDecoderData]

    If this theory defines any Theory.Decoder, which can translate model data into some theory-specific representation, this function can be overridden to pre-compute required data from a model.

    If this theory defines any Theory.Decoder, which can translate model data into some theory-specific representation, this function can be overridden to pre-compute required data from a model.

    Definition Classes
    Theory
  11. def iPostprocess(f: IFormula, signature: Signature): IFormula

    Optionally, a post-processor that is applied to formulas output by the prover, for instance to interpolants or the result of quantifier elimination.

    Optionally, a post-processor that is applied to formulas output by the prover, for instance to interpolants or the result of quantifier elimination. This method will be applied to the formula after calling Internal2Inputabsy.

    Definition Classes
    Theory
  12. def iPreprocess(f: IFormula, signature: Signature): (IFormula, Signature)

    Optionally, a pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover.

    Optionally, a pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover. This method will be applied very early in the translation process.

    Definition Classes
    Theory
  13. def id2point(id: Int): ApplicationPoint
  14. def isSoundForSat(theories: Seq[Theory], config: Theory.SatSoundnessConfig.Value): Boolean

    Check whether we can tell that the given combination of theories is sound for checking satisfiability of a problem, i.e., if proof construction ends up in a dead end, can it be concluded that a problem is satisfiable.

    Check whether we can tell that the given combination of theories is sound for checking satisfiability of a problem, i.e., if proof construction ends up in a dead end, can it be concluded that a problem is satisfiable.

    Definition Classes
    SaturationProcedureTheory
  15. val modelGenPredicates: Set[Predicate]

    Optionally, a set of predicates used by the theory to tell the PresburgerModelFinder about terms that will be handled exclusively by this theory.

    Optionally, a set of predicates used by the theory to tell the PresburgerModelFinder about terms that will be handled exclusively by this theory. If a proof goal in model generation mode contains an atom p(x), for p in this set, then the PresburgerModelFinder will ignore x when assigning concrete values to symbols.

    Definition Classes
    Theory
  16. def plugin: Some[Plugin]

    Optionally, a plug-in implementing reasoning in this theory

    Optionally, a plug-in implementing reasoning in this theory

    Definition Classes
    SaturationProcedureTheory
  17. def point2id(p: ApplicationPoint): Int
  18. val pointPred: Predicate

    Predicate to record, in a proof goal, that a handler has been spawned for a certain application point.

    Predicate to record, in a proof goal, that a handler has been spawned for a certain application point. This is done by assigning a unique id to every application point; the argument of this predicate is the id.

  19. def postSimplifiers: Seq[(IExpression) => IExpression]

    Optionally, simplifiers that are applied to formulas output by the prover, for instance to interpolants or the result of quantifier.

    Optionally, simplifiers that are applied to formulas output by the prover, for instance to interpolants or the result of quantifier. Such simplifiers are invoked by ap.parser.Simplifier. By default, this list will only include the evaluatingSimplifier.

    Definition Classes
    Theory
  20. def postprocess(f: Conjunction, order: TermOrder): Conjunction

    Optionally, a post-processor that is applied to formulas output by the prover, for instance to interpolants or the result of quantifier elimination.

    Optionally, a post-processor that is applied to formulas output by the prover, for instance to interpolants or the result of quantifier elimination. This method will be applied to the raw formulas, before calling Internal2Inputabsy.

    Definition Classes
    Theory
  21. val predicateMatchConfig: PredicateMatchConfig

    Information how interpreted predicates should be handled for e-matching.

    Information how interpreted predicates should be handled for e-matching.

    Definition Classes
    SaturationProcedureTheory
  22. val predicates: List[Predicate]

    Interpreted predicates of the theory

    Interpreted predicates of the theory

    Definition Classes
    SaturationProcedureTheory
  23. def preprocess(f: Conjunction, order: TermOrder): Conjunction

    Optionally, a pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover.

    Optionally, a pre-processor that is applied to formulas over this theory, prior to sending the formula to a prover.

    Definition Classes
    Theory
  24. val reducerPlugin: ReducerPluginFactory

    Optionally, a plugin for the reducer applied to formulas both before and during proving.

    Optionally, a plugin for the reducer applied to formulas both before and during proving.

    Definition Classes
    Theory
  25. val singleInstantiationPredicates: Set[Predicate]

    When instantiating existentially quantifier formulas, EX phi, at most one instantiation is necessary provided that all predicates in phi are contained in this set.

    When instantiating existentially quantifier formulas, EX phi, at most one instantiation is necessary provided that all predicates in phi are contained in this set.

    Definition Classes
    Theory
  26. val totalityAxioms: Conjunction

    Additional axioms that are included if the option +genTotalityAxioms is given to Princess.

    Additional axioms that are included if the option +genTotalityAxioms is given to Princess.

    Definition Classes
    SaturationProcedureTheory
  27. lazy val transitiveDependencies: Iterable[Theory]

    Dependencies closed under transitivity, i.e., also including the dependencies of dependencies.

    Dependencies closed under transitivity, i.e., also including the dependencies of dependencies.

    Definition Classes
    Theory
  28. val triggerRelevantFunctions: Set[IFunction]

    A list of functions that should be considered in automatic trigger generation

    A list of functions that should be considered in automatic trigger generation

    Definition Classes
    SaturationProcedureTheory