ConjunctiveNormalForm

Helper functions that perform computations with Boolean formulas while keeping them in the conjunctive normal form.

A Boolean formula in CNF is represented by a list of lists of an arbitrary type T. For instance, the Boolean formula (a || b) && (c || d || e) is represented as

List( List(a, b), List(c, d, e) )

These helper methods will compute disjunction, conjunction, and negation of Boolean formulas in CNF, outputting the results also in CNF. Simplifications are performed only in so far as to remove exact duplicate terms or clauses such as a || a or (a || b) && (a || b).

The type T represents primitive Boolean terms that cannot be further simplified or factored to CNF. These terms could be represented by expression trees or in another way; the CNF computations do not depend on the representation of terms.

Note that negation such as ! a is considered to be a primitive term. Negation of a conjunction or disjunction, such as ! (a || b), can be simplified to CNF.

Linear Supertypes

AnyRef, Any

Type Members

type CNF[T] = List[List[T]]

Value Members

final def !=(arg0: Any): Boolean

Definition Classes
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final def ##(): Int

Definition Classes
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final def ==(arg0: Any): Boolean

Definition Classes
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final def asInstanceOf[T0]: T0

Definition Classes
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def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
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Annotations
@throws( ... )
def conjunction[T](a: CNF[T], b: CNF[T]): CNF[T]

Compute a && b where a and b are Boolean formulas in CNF.
Compute a && b where a and b are Boolean formulas in CNF.
T
Type of primitive Boolean terms.
a
A Boolean formula in CNF.
b
A Boolean formula in CNF.
returns
The resulting Boolean formula in CNF.
def disjunction[T](a: CNF[T], b: CNF[T]): CNF[T]

Compute a || b where a and b are Boolean formulas in CNF.
Compute a || b where a and b are Boolean formulas in CNF.
T
Type of primitive Boolean terms.
a
A Boolean formula in CNF.
b
A Boolean formula in CNF.
returns
The resulting Boolean formula in CNF.
def disjunctionOneClause[T](a: List[T], b: CNF[T]): CNF[T]

Compute a || b where a is a single "clause", i.e.
Compute a || b where a is a single "clause", i.e. a disjunction of primitive Boolean terms, and b is a Boolean formula in CNF.
T
Type of primitive Boolean terms.
a
A list of primitive Boolean terms. This list represents a single disjunction clause, e.g. List(a, b, c) represents a || b || c.
b
A Boolean formula in CNF.
returns
The resulting Boolean formula in CNF.
def disjunctionOneTerm[T](a: T, b: CNF[T]): CNF[T]

Compute a || b where a is a single Boolean term and b is a Boolean formula in CNF.
Compute a || b where a is a single Boolean term and b is a Boolean formula in CNF.
T
Type of primitive Boolean terms.
a
Primitive Boolean term that cannot be simplified; does not contain disjunctions or conjunctions.
b
A Boolean formula in CNF.
returns
The resulting Boolean formula in CNF.
final def eq(arg0: AnyRef): Boolean

Definition Classes
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def equals(arg0: Any): Boolean

Definition Classes
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def falseConstant[T]: CNF[T]

Represents the constant false value in CNF.
def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
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Annotations
@throws( classOf[java.lang.Throwable] )
final def getClass(): Class[_]

Definition Classes
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def hashCode(): Int

Definition Classes
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final def isInstanceOf[T0]: Boolean

Definition Classes
Any
final def ne(arg0: AnyRef): Boolean

Definition Classes
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def negation[T](negateOneTerm: (T) ⇒ T)(a: CNF[T]): CNF[T]

Compute ! a where a is a Boolean formula in CNF.
Compute ! a where a is a Boolean formula in CNF.
T
Type of primitive Boolean terms.
negateOneTerm
A function that describes the transformation of a primitive term under negation. For instance, negateOneTerm(a) should return ! a in the term's appropriate representation.
a
A Boolean formula in CNF.
returns
The resulting Boolean formula in CNF.
final def notify(): Unit

Definition Classes
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final def notifyAll(): Unit

Definition Classes
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def oneTerm[T](a: T): CNF[T]

Injects a single primitive term into a CNF.
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
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def toString(): String

Definition Classes
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def trueConstant[T]: CNF[T]

Represents the constant true value in CNF.
final def wait(): Unit

Definition Classes
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Annotations
@throws( ... )
final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
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Annotations
@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
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Annotations
@throws( ... )

Related Doc: package util

object ConjunctiveNormalForm

Type Members

type CNF[T] = List[List[T]]

Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

final def asInstanceOf[T0]: T0

def clone(): AnyRef

def conjunction[T](a: CNF[T], b: CNF[T]): CNF[T]

def disjunction[T](a: CNF[T], b: CNF[T]): CNF[T]

def disjunctionOneClause[T](a: List[T], b: CNF[T]): CNF[T]

def disjunctionOneTerm[T](a: T, b: CNF[T]): CNF[T]

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def falseConstant[T]: CNF[T]

def finalize(): Unit

final def getClass(): Class[_]

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

final def ne(arg0: AnyRef): Boolean

def negation[T](negateOneTerm: (T) ⇒ T)(a: CNF[T]): CNF[T]

final def notify(): Unit

final def notifyAll(): Unit

def oneTerm[T](a: T): CNF[T]

final def synchronized[T0](arg0: ⇒ T0): T0

def toString(): String

def trueConstant[T]: CNF[T]

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit

Inherited from AnyRef

Inherited from Any

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