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ap.theories.bitvectors

ModuloArithmetic

object ModuloArithmetic extends Theory

Theory for performing bounded modulo-arithmetic (arithmetic modulo some number N). This in particular includes bit-vector/machine arithmetic.

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Theory, AnyRef, Any
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Type Members

  1. class BVNAryOp extends IndexedBVOp
  2. abstract class IndexedBVOp extends SortedIFunction

    Generic class to represent families of functions, indexed by a vector of bit-widths.

  3. case class ModSort(lower: IdealInt, upper: IdealInt) extends ProxySort with TheorySort with Product with Serializable

    Modulo sorts, representing the interval [lower, upper] with wrap-around arithmetic.

  4. class NAryBVPred extends SortedPredicate
  5. class ShiftFunction extends SortedIFunction
  6. class ShiftPredicate extends SortedPredicate

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. val AC: AC_MODULO_ARITHMETIC.type
    Attributes
    protected[bitvectors]
  5. val MultTheory: nia.GroebnerMultiplication.type
  6. val _bv_and: Predicate
  7. val _bv_extract: Predicate
  8. val _bv_xor: Predicate
  9. val _l_shift_cast: ShiftPredicate
  10. val _mod_cast: SortedPredicate
  11. val _r_shift_cast: ShiftPredicate
  12. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  13. 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
    ModuloArithmetic → Theory
  14. def bv(width: Int, num: IdealInt): ITerm
  15. val bv_add: BVNAryOp
  16. val bv_and: BVNAryOp
  17. val bv_ashr: BVNAryOp
  18. val bv_comp: BVComp.type
  19. val bv_concat: BVConcat.type
  20. val bv_extract: BVExtract.type
  21. val bv_lshr: BVNAryOp
  22. val bv_mul: BVNAryOp
  23. val bv_neg: BVNAryOp
  24. val bv_nego: NAryBVPred
  25. val bv_not: BVNAryOp
  26. val bv_or: BVNAryOp
  27. val bv_saddo: NAryBVPred
  28. val bv_sdiv: BVNAryOp
  29. val bv_sdivo: NAryBVPred
  30. val bv_shl: BVNAryOp
  31. val bv_sle: NAryBVPred
  32. val bv_slt: NAryBVPred
  33. val bv_smod: BVNAryOp
  34. val bv_smulo: NAryBVPred
  35. val bv_srem: BVNAryOp
  36. val bv_ssubo: NAryBVPred
  37. val bv_sub: BVNAryOp
  38. val bv_uaddo: NAryBVPred
  39. val bv_udiv: BVNAryOp
  40. val bv_ule: NAryBVPred
  41. val bv_ult: NAryBVPred
  42. val bv_umulo: NAryBVPred
  43. val bv_urem: BVNAryOp
  44. val bv_usubo: NAryBVPred
  45. val bv_xor: BVNAryOp
  46. def bvadd(t1: ITerm, t2: ITerm): ITerm
  47. def bvand(t1: ITerm, t2: ITerm): ITerm
  48. def bvashr(t1: ITerm, t2: ITerm): ITerm
  49. def bvcomp(t1: ITerm, t2: ITerm): ITerm
  50. def bvlshr(t1: ITerm, t2: ITerm): ITerm
  51. def bvmul(t1: ITerm, t2: ITerm): ITerm
  52. def bvneg(t: ITerm): ITerm
  53. def bvnego(t: ITerm): IFormula
  54. def bvnot(t: ITerm): ITerm
  55. def bvor(t1: ITerm, t2: ITerm): ITerm
  56. def bvsaddo(t1: ITerm, t2: ITerm): IFormula
  57. def bvsdiv(t1: ITerm, t2: ITerm): ITerm
  58. def bvsdivo(t1: ITerm, t2: ITerm): IFormula
  59. def bvsge(t1: ITerm, t2: ITerm): IFormula
  60. def bvsgt(t1: ITerm, t2: ITerm): IFormula
  61. def bvshl(t1: ITerm, t2: ITerm): ITerm
  62. def bvsle(t1: ITerm, t2: ITerm): IFormula
  63. def bvslt(t1: ITerm, t2: ITerm): IFormula
  64. def bvsmod(t1: ITerm, t2: ITerm): ITerm
  65. def bvsmulo(t1: ITerm, t2: ITerm): IFormula
  66. def bvsrem(t1: ITerm, t2: ITerm): ITerm
  67. def bvssubo(t1: ITerm, t2: ITerm): IFormula
  68. def bvsub(t1: ITerm, t2: ITerm): ITerm
  69. def bvuaddo(t1: ITerm, t2: ITerm): IFormula
  70. def bvudiv(t1: ITerm, t2: ITerm): ITerm
  71. def bvuge(t1: ITerm, t2: ITerm): IFormula
  72. def bvugt(t1: ITerm, t2: ITerm): IFormula
  73. def bvule(t1: ITerm, t2: ITerm): IFormula
  74. def bvult(t1: ITerm, t2: ITerm): IFormula
  75. def bvumulo(t1: ITerm, t2: ITerm): IFormula
  76. def bvurem(t1: ITerm, t2: ITerm): ITerm
  77. def bvusubo(t1: ITerm, t2: ITerm): IFormula
  78. def bvxor(t1: ITerm, t2: ITerm): ITerm
  79. def cast2Int(t: ITerm): ITerm

    Cast a term to an integer term.

  80. def cast2Interval(lower: IdealInt, upper: IdealInt, t: ITerm): ITerm

    Cast a term to an integer interval, with modulo semantics.

  81. def cast2SignedBV(bits: Int, t: ITerm): ITerm

    Cast a term to a signed bit-vector term.

  82. def cast2Sort(sort: ModSort, t: ITerm): ITerm

    Cast a term to a modulo sort.

  83. def cast2UnsignedBV(bits: Int, t: ITerm): ITerm

    Cast a term to an unsigned bit-vector term.

  84. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @HotSpotIntrinsicCandidate() @native()
  85. def commonBitsLB(a: IdealInt, b: IdealInt): Option[Int]

    Compute the smallest number n such that all numbers in the interval [min(a, b), max(a, b)] have bits at and above n in common. For instance, commonBitsLB(11, 14) == Some(3) and commonBitsLB(1, -1) == None. 11 = 1011_2 14 = 1110_2

    Compute the smallest number n such that all numbers in the interval [min(a, b), max(a, b)] have bits at and above n in common. For instance, commonBitsLB(11, 14) == Some(3) and commonBitsLB(1, -1) == None. 11 = 1011_2 14 = 1110_2

    Attributes
    protected[bitvectors]
  86. def concat(t1: ITerm, t2: ITerm): ITerm
  87. val debug: Boolean
    Attributes
    protected[bitvectors]
  88. 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
    ModuloArithmetic → Theory
  89. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  90. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  91. def evalExtract(start: IdealInt, end: IdealInt, number: IdealInt): IdealInt

    Evaluate bv_extract with concrete arguments

  92. 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
    ModuloArithmetic → Theory
  93. def evalModCast(lower: IdealInt, upper: IdealInt, number: IdealInt): IdealInt

    Evaluate mod_cast with concrete arguments

  94. def evalPred(a: 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
    ModuloArithmetic → Theory
  95. 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
  96. 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
  97. def extract(begin: Int, end: Int, t: ITerm): ITerm
  98. val functionPredicateMapping: List[(SortedIFunction, Predicate)]

    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
    ModuloArithmetic → Theory
  99. val functionTranslation: Map[IFunction, Predicate]
  100. 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
    ModuloArithmetic → Theory
  101. val functions: List[SortedIFunction]

    Interpreted functions of the theory

    Interpreted functions of the theory

    Definition Classes
    ModuloArithmetic → Theory
  102. 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
  103. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @HotSpotIntrinsicCandidate() @native()
  104. def getLowerUpper(arguments: Seq[Term]): (IdealInt, IdealInt)
    Attributes
    protected[bitvectors]
  105. def getModulus(a: Atom): IdealInt
    Attributes
    protected[bitvectors]
  106. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @HotSpotIntrinsicCandidate() @native()
  107. 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
    ModuloArithmetic → Theory
  108. 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
    ModuloArithmetic → Theory
  109. val int_cast: MonoSortedIFunction

    Function to map the modulo-sorts back to integers.

    Function to map the modulo-sorts back to integers. Semantically this is just the identify function

  110. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  111. 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
    ModuloArithmetic → Theory
  112. val l_shift_cast: ShiftFunction

    Function for multiplying any number t with 2^n and mapping to an interval [lower, upper].

    Function for multiplying any number t with 2^n and mapping to an interval [lower, upper]. The function is applied as l_shift_cast(lower, upper, t, n).

  113. val mod_cast: SortedIFunction

    Function for mapping any number to an interval [lower, upper].

    Function for mapping any number to an interval [lower, upper]. The function is applied as mod_cast(lower, upper, number)

  114. 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
  115. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  116. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @HotSpotIntrinsicCandidate() @native()
  117. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @HotSpotIntrinsicCandidate() @native()
  118. val order: TermOrder
  119. val otherPreds: List[NAryBVPred]
  120. val plugin: Some[ModPlugin.type]

    Optionally, a plug-in implementing reasoning in this theory

    Optionally, a plug-in implementing reasoning in this theory

    Definition Classes
    ModuloArithmetic → Theory
  121. 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
  122. 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
  123. def pow2(bits: IdealInt): IdealInt
    Attributes
    protected[bitvectors]
  124. def pow2(bits: Int): IdealInt
    Attributes
    protected[bitvectors]
  125. def pow2MinusOne(bits: IdealInt): IdealInt
    Attributes
    protected[bitvectors]
  126. def pow2MinusOne(bits: Int): IdealInt
    Attributes
    protected[bitvectors]
  127. def pow2Mod(bits: IdealInt, modulus: IdealInt): IdealInt
    Attributes
    protected[bitvectors]
  128. val preAxioms: Formula
  129. 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
    ModuloArithmetic → Theory
  130. val predicates: Seq[Predicate]

    Interpreted predicates of the theory

    Interpreted predicates of the theory

    Definition Classes
    ModuloArithmetic → Theory
  131. 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
    ModuloArithmetic → Theory
  132. val r_shift_cast: ShiftFunction

    Function for dividing any number t by 2^n, rounding towards negative, and mapping to an interval [lower, upper].

    Function for dividing any number t by 2^n, rounding towards negative, and mapping to an interval [lower, upper]. The function is applied as r_shift_cast(lower, upper, t, n).

  133. 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
    ModuloArithmetic → Theory
  134. def repeat(n: Int, t: ITerm): ITerm
  135. val rotate_left: BVNAryOp
  136. val rotate_right: BVNAryOp
  137. def rotateleft(t: ITerm, bits: ITerm): ITerm
  138. def rotateright(t: ITerm, bits: ITerm): ITerm
  139. def runLengthEnc(v: IdealInt, size: Int): Seq[Int]

    Run-length encoding of the least-significant size bits of a number, starting with the number of least-significant zeroes.

    Run-length encoding of the least-significant size bits of a number, starting with the number of least-significant zeroes. Bits beyond size are ignored.

  140. def shiftLeft(sort: ModSort, shifted: ITerm, bits: ITerm): ITerm

    Shift the term shifted a number of bits to the left, staying within the given sort.

  141. def shiftRight(sort: ModSort, shifted: ITerm, bits: ITerm): ITerm

    Shift the term shifted a number of bits to the right, staying within the given sort.

  142. def sign_extend(addWidth: Int, t: ITerm): ITerm
  143. 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
    ModuloArithmetic → Theory
  144. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  145. def toString(): String
    Definition Classes
    ModuloArithmetic → AnyRef → Any
  146. 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
    ModuloArithmetic → Theory
  147. 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
  148. 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
    ModuloArithmetic → Theory
  149. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  150. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  151. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  152. def zero_extend(addWidth: Int, t: ITerm): ITerm
  153. val zero_extend: ZeroExtend.type
  154. object BVComp extends IndexedBVOp
  155. object BVConcat extends IndexedBVOp
  156. object BVExtract extends IndexedBVOp
  157. object SignedBVSort

    Object to create and recognise modulo sorts representing signed bit-vectors.

  158. object UnsignedBVSort

    Object to create and recognise modulo sorts representing unsigned bit-vectors.

  159. object ZeroExtend extends IndexedBVOp

Deprecated Value Members

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

    (Since version 9)

Inherited from Theory

Inherited from AnyRef

Inherited from Any

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