class Fractions extends Theory with RingWithDivision
The theory of fractions s / t, with s, t
taken from some ring. The theory uses an encoding in which the same
(fixed, but arbitrary) denominator is used for all expressions. The
range of considered denominators is described by the
denomConstraint argument over the variable _0.
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- Fractions
- RingWithDivision
- PseudoRing
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Type Members
- case class SymbolEquation(symbol: ITerm) extends Product with Serializable
Rewrite an equation to the form
(num / denom) * symbol = remainder(where remainder does not contain the atomic termsymbol) and determine the coefficient and the remainder. - case class SymbolSum(symbol: ITerm) extends Product with Serializable
Rewrite a fractional term to the form
(num / denom) * symbol + remainder(where remainder does not contain the atomic termsymbol) and determine the coefficient and the remainder
Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##: Int
- Definition Classes
- AnyRef → Any
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- val addition: IFunction
Function to represent sums of terms.
- def additiveGroup: Group with Abelian with SymbolicTimes
Addition gives rise to an Abelian group
Addition gives rise to an Abelian group
- Definition Classes
- PseudoRing
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- val axioms: Formula
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).
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @HotSpotIntrinsicCandidate() @native()
- val denom: IFunction
Function used internally to represent the unique denominator for all fractions
- val denomT: ITerm
- Attributes
- protected
- 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
- def div(s: ITerm, t: ITerm): ITerm
Division operation
Division operation
- Definition Classes
- Fractions → RingWithDivision
- val division: IFunction
Function to represent division.
- val dom: Sort
Domain of the ring
Domain of the ring
- Definition Classes
- Fractions → PseudoRing
- def encodeExpr(t: IExpression, subres: Seq[IExpression], usedDenom: Array[Boolean]): IExpression
- Attributes
- protected
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef → Any
- 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
- 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
- def evaluatingSimplifier(t: IExpression): IExpression
A simplification function that applies the methods
evalFunandevalPredto some given expression (but not recursively).A simplification function that applies the methods
evalFunandevalPredto some given expression (but not recursively). This is used in theTheory.postSimplifiersmethods.- Definition Classes
- Theory
- def extend(order: TermOrder): TermOrder
Add the symbols defined by this theory to the
orderAdd the symbols defined by this theory to the
order- Definition Classes
- Theory
- def extraPredicates: Seq[Predicate]
- val frac: IFunction
Function to represent fractions, where numerator and denominator are expressions from the underlying ring
- def fracPreproc(f: IFormula, signature: Signature): (IFormula, Signature)
- val fromRing: IFunction
Function to embed ring elements in the ring of fractions.
- val funPredMap: Map[IFunction, Predicate]
- val functionPredicateMapping: List[(IFunction, Predicate)]
Mapping of interpreted functions to interpreted predicates, used translating input ASTs to internal ASTs (the latter only containing predicates).
- val functionalPredicates: Set[Predicate]
Information which of the predicates satisfy the functionality axiom; at some internal points, such predicates can be handled more efficiently
- val functions: List[IFunction]
Interpreted functions of the theory
- 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
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @HotSpotIntrinsicCandidate() @native()
- def hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @HotSpotIntrinsicCandidate() @native()
- 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
- 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.
- def individualsStream: Option[LazyList[ITerm]]
Optionally, a stream of the constructor terms for this domain can be defined (e.g., the fractions with co-prime numerator and denominator).
Optionally, a stream of the constructor terms for this domain can be defined (e.g., the fractions with co-prime numerator and denominator).
- Attributes
- protected
- def int2ring(s: ITerm): ITerm
Conversion of an integer term to a ring term
Conversion of an integer term to a ring term
- Definition Classes
- Fractions → PseudoRing
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def isNonZeroRingTerm(t: ITerm): Boolean
- Attributes
- protected
- 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.
- def minus(s: ITerm): ITerm
Additive inverses
Additive inverses
- Definition Classes
- Fractions → PseudoRing
- def minus(s: ITerm, t: ITerm): ITerm
Difference between two terms
Difference between two terms
- Definition Classes
- PseudoRing
- val modelGenPredicates: Set[Predicate]
Optionally, a set of predicates used by the theory to tell the
PresburgerModelFinderabout terms that will be handled exclusively by this theory.Optionally, a set of predicates used by the theory to tell the
PresburgerModelFinderabout terms that will be handled exclusively by this theory. If a proof goal in model generation mode contains an atomp(x), forpin this set, then thePresburgerModelFinderwill ignorexwhen assigning concrete values to symbols.- Definition Classes
- Theory
- def mul(s: ITerm, t: ITerm): ITerm
Ring multiplication
Ring multiplication
- Definition Classes
- Fractions → PseudoRing
- val multWithFraction: IFunction
Function to represent a product of a fraction, represented using numerator and denominator, with a fraction term.
- val multWithRing: IFunction
Function to represent a product of a ring term with a fraction term.
- val multiplication: IFunction
Function to represent products of terms.
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @HotSpotIntrinsicCandidate() @native()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @HotSpotIntrinsicCandidate() @native()
- val one: ITerm
The one element of this ring
The one element of this ring
- Definition Classes
- Fractions → PseudoRing
- val plugin: None.type
Optionally, a plug-in implementing reasoning in this theory
- def plus(s: ITerm, t: ITerm): ITerm
Ring addition
Ring addition
- Definition Classes
- Fractions → PseudoRing
- 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 theevaluatingSimplifier.- Definition Classes
- Theory
- def postprocess(f: Conjunction, signature: Signature): 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
- val predicateMatchConfig: PredicateMatchConfig
Information how interpreted predicates should be handled for e-matching.
- val predicates: Seq[Predicate]
Interpreted predicates of the theory
- def preprocess(f: Conjunction, signature: Signature): 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
- def product(terms: ITerm*): ITerm
N-ary sums
N-ary sums
- Definition Classes
- PseudoRing
- 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
- def simplifiers: List[(IExpression) => IExpression]
- Attributes
- protected
- def simplifyFraction(n: ITerm, d: ITerm): (ITerm, ITerm)
Method that can be overwritten in sub-classes to term concrete fractions into canonical form.
Method that can be overwritten in sub-classes to term concrete fractions into canonical form.
- Attributes
- protected
- val singleInstantiationPredicates: Set[Predicate]
When instantiating existentially quantifier formulas,
EX phi, at most one instantiation is necessary provided that all predicates inphiare contained in this set.When instantiating existentially quantifier formulas,
EX phi, at most one instantiation is necessary provided that all predicates inphiare contained in this set.- Definition Classes
- Theory
- def summation(terms: ITerm*): ITerm
N-ary sums
N-ary sums
- Definition Classes
- PseudoRing
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def times(num: ITerm, s: ITerm): ITerm
num * s, wherenummust be an integer term.num * s, wherenummust be an integer term.- Definition Classes
- Fractions → PseudoRing
- def times(num: IdealInt, s: ITerm): ITerm
num * snum * s- Definition Classes
- Fractions → PseudoRing
- def toString(): String
- Definition Classes
- Fractions → PseudoRing → AnyRef → Any
- val totalityAxioms: Conjunction
Additional axioms that are included if the option
+genTotalityAxiomsis given to Princess. - 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
- val triggerRelevantFunctions: Set[IFunction]
A list of functions that should be considered in automatic trigger generation
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- val zero: ITerm
The zero element of this ring
The zero element of this ring
- Definition Classes
- Fractions → PseudoRing
- object FracTerm
Extractor for fractions, where numerator and denominator are expressions from the underlying ring.
Extractor for fractions, where numerator and denominator are expressions from the underlying ring.
- Attributes
- protected
- object Fraction
Object to construct and identify fractions, consisting of a numerator and a denominator.
Object to construct and identify fractions, consisting of a numerator and a denominator. Fractions are internally represented using either the function
frac, for proper fractions, or functionfromRingfor ring elements cast to a fraction. - object FractionSort extends ProxySort with TheorySort
- object IncompletenessChecker extends ContextAwareVisitor[Unit, Unit]
The theory is not complete for the full first-order case; check whether the denom function occurs in the scope of a quantifier.
The theory is not complete for the full first-order case; check whether the denom function occurs in the scope of a quantifier.
- Attributes
- protected
- object RingCastTerm
Extractor for ring elements embedded into the ring of fractions.
Extractor for ring elements embedded into the ring of fractions.
- Attributes
- protected
Deprecated Value Members
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable]) @Deprecated
- Deprecated
(Since version 9)