Scala Compiler2.13.2 < Back
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# Packages

-  package root

  The Scala compiler and reflection APIs.

  The Scala compiler and reflection APIs.

  Definition Classes
    root
-  package scala
  Definition Classes
    root
-  package tools
  Definition Classes
    scala
-  package nsc
  Definition Classes
    tools
-  package transform
  Definition Classes
    nsc
-  package patmat
  Definition Classes
    transform
-  trait Solving extends Logic

  Solve pattern matcher exhaustivity problem via DPLL.

  Solve pattern matcher exhaustivity problem via DPLL.

  Definition Classes
    patmat
- CNF
- PropositionalLogic
- Solver
- debug

t

scala.tools.nsc.transform.patmat.Solving

# CNF

###

#### trait CNF extends PropositionalLogic

Source
  Solving.scala

Linear Supertypes
Solving.PropositionalLogic, AnyRef, Any
Known Subclasses
OptimizingMatchTranslator, Solver
Type Hierarchy
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Ordering

1. Alphabetic
2. By Inheritance

Inherited

1. CNF
2. PropositionalLogic
3. AnyRef
4. Any

Implicitly

1. by any2stringadd
2. by StringFormat
3. by Ensuring
4. by ArrowAssoc

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Visibility

1. Public
2. Protected

### Type Members

1.  trait AbsVar extends AnyRef
   Definition Classes
     PropositionalLogic
2.  final case class And(ops: Set[Prop]) extends Prop with Product with Serializable
   Definition Classes
     PropositionalLogic
3.  final case class AtMostOne(ops: List[Sym]) extends Prop with Product with Serializable
   Definition Classes
     PropositionalLogic
4.  final case class Eq(p: Var, q: Const) extends Prop with Product with Serializable
   Definition Classes
     PropositionalLogic
5.  final case class Not(a: Prop) extends Prop with Product with Serializable
   Definition Classes
     PropositionalLogic
6.  final case class Or(ops: Set[Prop]) extends Prop with Product with Serializable
   Definition Classes
     PropositionalLogic
7.  class Prop extends AnyRef
   Definition Classes
     PropositionalLogic
8.  trait PropMap extends AnyRef
   Definition Classes
     PropositionalLogic
9.  trait PropTraverser extends AnyRef
   Definition Classes
     PropositionalLogic
10.  final case class Solution(model: Model, unassigned: List[Sym]) extends Product with Serializable
    Definition Classes
      PropositionalLogic
11.  final class Sym extends Prop
    Definition Classes
      PropositionalLogic
12.  trait TypeConstExtractor extends AnyRef
    Definition Classes
      PropositionalLogic
13.  trait ValueConstExtractor extends AnyRef
    Definition Classes
      PropositionalLogic
14.  trait VarExtractor extends AnyRef
    Definition Classes
      PropositionalLogic
15.  class AlreadyInCNF extends AnyRef
16.  type Clause = Set[Lit]
17.  type Cnf = Array[Clause]

    Conjunctive normal form (of a Boolean formula).

    Conjunctive normal form (of a Boolean formula). A formula in this form is amenable to a SAT solver (i.e., solver that decides satisfiability of a formula).

18.  trait CnfBuilder extends AnyRef
19.  abstract type Const
    Definition Classes
      PropositionalLogic
20.  type Model = Map[Sym, Boolean]
    Definition Classes
      PropositionalLogic
21.  final case class Solvable(cnf: Cnf, symbolMapping: SymbolMapping) extends Product with Serializable
22.  class SymbolMapping extends AnyRef
23.  class TransformToCnf extends CnfBuilder

    Plaisted transformation: used for conversion of a propositional formula into conjunctive normal form (CNF) (input format for SAT solver).

    Plaisted transformation: used for conversion of a propositional formula into conjunctive normal form (CNF) (input format for SAT solver). A simple conversion into CNF via Shannon expansion would also be possible but it's worst-case complexity is exponential (in the number of variables) and thus even simple problems could become untractable. The Plaisted transformation results in an _equisatisfiable_ CNF-formula (it generates auxiliary variables) but runs with linear complexity. The common known Tseitin transformation uses bi-implication, whereas the Plaisted transformation uses implication only, thus the resulting CNF formula has (on average) only half of the clauses of a Tseitin transformation. The Plaisted transformation uses the polarities of sub-expressions to figure out which part of the bi-implication can be omitted. However, if all sub-expressions have positive polarity (e.g., after transformation into negation normal form) then the conversion is rather simple and the pseudo-normalization via NNF increases chances only one side of the bi-implication is needed.

24.  abstract type Tree
    Definition Classes
      PropositionalLogic
25.  abstract type Type
    Definition Classes
      PropositionalLogic
26.  abstract type TypeConst <: Const
    Definition Classes
      PropositionalLogic
27.  abstract type ValueConst <: Const
    Definition Classes
      PropositionalLogic
28.  abstract type Var <: AbsVar
    Definition Classes
      PropositionalLogic

### Abstract Value Members

1.  abstract val EmptyModel: Model
   Definition Classes
     PropositionalLogic
2.  abstract val NoModel: Model
   Definition Classes
     PropositionalLogic
3.  abstract val NullConst: Const
   Definition Classes
     PropositionalLogic
4.  abstract def TypeConst: TypeConstExtractor
   Definition Classes
     PropositionalLogic
5.  abstract def ValueConst: ValueConstExtractor
   Definition Classes
     PropositionalLogic
6.  abstract val Var: VarExtractor
   Definition Classes
     PropositionalLogic
7.  abstract def cnfString(f: Array[Clause]): String
8.  abstract def findAllModelsFor(solvable: Solvable, sym: Global.Symbol = NoSymbol): List[Solution]
   Definition Classes
     PropositionalLogic
9.  abstract def findModelFor(solvable: Solvable): Model
   Definition Classes
     PropositionalLogic
10.  abstract def prepareNewAnalysis(): Unit
    Definition Classes
      PropositionalLogic
11.  abstract def reportWarning(message: String): Unit
    Definition Classes
      PropositionalLogic
12.  abstract def uncheckedWarning(pos: Global.Position, msg: String, site: Global.Symbol): Unit
    Definition Classes
      PropositionalLogic

### Concrete Value Members

1.  object AnalysisBudget
   Definition Classes
     PropositionalLogic
2.  object And extends java.io.Serializable
   Definition Classes
     PropositionalLogic
3.  case object False extends Prop with Product with Serializable
   Definition Classes
     PropositionalLogic
4.  object Or extends java.io.Serializable
   Definition Classes
     PropositionalLogic
5.  object Sym
   Definition Classes
     PropositionalLogic
6.  case object True extends Prop with Product with Serializable
   Definition Classes
     PropositionalLogic
7.  final def !=(arg0: Any): Boolean
   Definition Classes
     AnyRef → Any
8.  final def ##: Int
   Definition Classes
     AnyRef → Any
9.  def +(other: String): String
   Implicit
     This member is added by an implicit conversion from CNF toany2stringadd[CNF] performed by method any2stringadd in scala.Predef.
   Definition Classes
     any2stringadd
10.  def ->[B](y: B): (CNF, B)
    Implicit
      This member is added by an implicit conversion from CNF toArrowAssoc[CNF] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
      ArrowAssoc
    Annotations
      @inline()
11.  def /\(props: Iterable[Prop]): Product with Prop with java.io.Serializable
    Definition Classes
      PropositionalLogic
12.  final def ==(arg0: Any): Boolean
    Definition Classes
      AnyRef → Any
13.  val ArrayOfFalse: Array[Clause]
14.  val NoClauses: Array[Clause]
15.  def \/(props: Iterable[Prop]): Product with Prop with java.io.Serializable
    Definition Classes
      PropositionalLogic
16.  final def asInstanceOf[T0]: T0
    Definition Classes
      Any
17.  def clause(ls: IterableOnce[Lit]): Clause
18.  def clause(l: Lit, l2: Lit, ls: Lit*): Clause
19.  def clause(l: Lit, l2: Lit): Clause
20.  def clause(l: Lit): Clause
21.  def clause(): Clause
22.  def clone(): AnyRef
    Attributes
      protected[lang]
    Definition Classes
      AnyRef
    Annotations
      @throws(classOf[java.lang.CloneNotSupportedException]) @native()
23.  def ensuring(cond: (CNF) => Boolean, msg: => Any): CNF
    Implicit
      This member is added by an implicit conversion from CNF toEnsuring[CNF] performed by method Ensuring in scala.Predef.
    Definition Classes
      Ensuring
24.  def ensuring(cond: (CNF) => Boolean): CNF
    Implicit
      This member is added by an implicit conversion from CNF toEnsuring[CNF] performed by method Ensuring in scala.Predef.
    Definition Classes
      Ensuring
25.  def ensuring(cond: Boolean, msg: => Any): CNF
    Implicit
      This member is added by an implicit conversion from CNF toEnsuring[CNF] performed by method Ensuring in scala.Predef.
    Definition Classes
      Ensuring
26.  def ensuring(cond: Boolean): CNF
    Implicit
      This member is added by an implicit conversion from CNF toEnsuring[CNF] performed by method Ensuring in scala.Predef.
    Definition Classes
      Ensuring
27.  final def eq(arg0: AnyRef): Boolean
    Definition Classes
      AnyRef
28.  def eqFreePropToSolvable(p: Prop): Solvable
    Definition Classes
      CNF → PropositionalLogic
29.  def equals(arg0: AnyRef): Boolean
    Definition Classes
      AnyRef → Any
30.  def finalize(): Unit
    Attributes
      protected[lang]
    Definition Classes
      AnyRef
    Annotations
      @throws(classOf[java.lang.Throwable])
31.  def formatted(fmtstr: String): String
    Implicit
      This member is added by an implicit conversion from CNF toStringFormat[CNF] performed by method StringFormat in scala.Predef.
    Definition Classes
      StringFormat
    Annotations
      @inline()
32.  def gatherSymbols(p: Prop): Set[Sym]
    Definition Classes
      PropositionalLogic
33.  def gatherVariables(p: Prop): Set[Var]
    Definition Classes
      PropositionalLogic
34.  final def getClass(): Class[_ <: AnyRef]
    Definition Classes
      AnyRef → Any
    Annotations
      @native()
35.  def hashCode(): Int
    Definition Classes
      AnyRef → Any
    Annotations
      @native()
36.  final def isInstanceOf[T0]: Boolean
    Definition Classes
      Any
37.  final def ne(arg0: AnyRef): Boolean
    Definition Classes
      AnyRef
38.  final def notify(): Unit
    Definition Classes
      AnyRef
    Annotations
      @native()
39.  final def notifyAll(): Unit
    Definition Classes
      AnyRef
    Annotations
      @native()
40.  def propToSolvable(p: Prop): Solvable
    Definition Classes
      PropositionalLogic
41.  def removeVarEq(props: List[Prop], modelNull: Boolean = false): (Prop, List[Prop])
    Definition Classes
      PropositionalLogic
42.  def simplify(f: Prop): Prop

    Simplifies propositional formula according to the following rules: - eliminate double negation (avoids unnecessary Tseitin variables) - flatten trees of same connectives (avoids unnecessary Tseitin variables) - removes constants and connectives that are in fact constant because of their operands - eliminates duplicate operands - convert formula into NNF: all sub-expressions have a positive polarity which makes them amenable for the subsequent Plaisted transformation and increases chances to figure out that the formula is already in CNF

    Simplifies propositional formula according to the following rules: - eliminate double negation (avoids unnecessary Tseitin variables) - flatten trees of same connectives (avoids unnecessary Tseitin variables) - removes constants and connectives that are in fact constant because of their operands - eliminates duplicate operands - convert formula into NNF: all sub-expressions have a positive polarity which makes them amenable for the subsequent Plaisted transformation and increases chances to figure out that the formula is already in CNF

    Complexity: DFS over formula tree

    See http://www.decision-procedures.org/slides/propositional_logic-2x3.pdf

    Definition Classes
      PropositionalLogic
43.  final def synchronized[T0](arg0: => T0): T0
    Definition Classes
      AnyRef
44.  def toString(): String
    Definition Classes
      AnyRef → Any
45.  final def wait(): Unit
    Definition Classes
      AnyRef
    Annotations
      @throws(classOf[java.lang.InterruptedException])
46.  final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
      AnyRef
    Annotations
      @throws(classOf[java.lang.InterruptedException])
47.  final def wait(arg0: Long): Unit
    Definition Classes
      AnyRef
    Annotations
      @throws(classOf[java.lang.InterruptedException]) @native()

### Deprecated Value Members

1.  def →[B](y: B): (CNF, B)
   Implicit
     This member is added by an implicit conversion from CNF toArrowAssoc[CNF] performed by method ArrowAssoc in scala.Predef.
   Definition Classes
     ArrowAssoc
   Annotations
     @deprecated
   Deprecated

     (Since version 2.13.0) Use `->` instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.

### Inherited from Solving.PropositionalLogic

### Inherited from AnyRef

### Inherited from Any

### Inherited by implicit conversion any2stringadd fromCNF to any2stringadd[CNF]

### Inherited by implicit conversion StringFormat fromCNF to StringFormat[CNF]

### Inherited by implicit conversion Ensuring fromCNF to Ensuring[CNF]

### Inherited by implicit conversion ArrowAssoc fromCNF to ArrowAssoc[CNF]

### Ungrouped