Class/Object

at.logic.gapt.expr

Substitution

Related Docs: object Substitution | package expr

Permalink

class Substitution extends AnyRef

A substitution is a mapping from variables to lambda-expressions which differs from the identity on finitely many variables. Therefore: 1) each variable is mapped to only one lambda expression 2) the order of the variable-mappings is irrelevant 3) all variable-mappings are applied simultaneously to a term i.e. {x |-> y, y |-> a}x = y and not a.

As the lambda calculus contains variable binders, substitution can only be defined up to alpha-equivalence. When applying a substitution, bound variables are renamed if needed.

Source
substitution.scala
Linear Supertypes
Known Subclasses
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Substitution
  2. AnyRef
  3. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Instance Constructors

  1. new Substitution(map: Map[Var, LambdaExpression])

    Permalink

Value Members

  1. final def !=(arg0: Any): Boolean

    Permalink
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

    Permalink
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String

    Permalink
    Implicit information
    This member is added by an implicit conversion from Substitution to any2stringadd[Substitution] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Substitution, B)

    Permalink
    Implicit information
    This member is added by an implicit conversion from Substitution to ArrowAssoc[Substitution] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean

    Permalink
    Definition Classes
    AnyRef → Any
  6. def apply[T, U](x: T)(implicit ev: Substitutable[Substitution, T, U]): U

    Permalink

    Applies this substitution to an object.

    Applies this substitution to an object.

    T

    The type of x.

    U

    The type of x substituted.

    x

    The object to be substituted.

    ev

    Testifies that applying a Substitution to an element of type T will result in an element of type U.

  7. def asFOLSubstitution: FOLSubstitution

    Permalink
  8. final def asInstanceOf[T0]: T0

    Permalink
    Definition Classes
    Any
  9. def clone(): AnyRef

    Permalink
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  10. def compose(sub: Substitution): Substitution

    Permalink
  11. def domain: Set[Var]

    Permalink
  12. def ensuring(cond: (Substitution) ⇒ Boolean, msg: ⇒ Any): Substitution

    Permalink
    Implicit information
    This member is added by an implicit conversion from Substitution to Ensuring[Substitution] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. def ensuring(cond: (Substitution) ⇒ Boolean): Substitution

    Permalink
    Implicit information
    This member is added by an implicit conversion from Substitution to Ensuring[Substitution] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. def ensuring(cond: Boolean, msg: ⇒ Any): Substitution

    Permalink
    Implicit information
    This member is added by an implicit conversion from Substitution to Ensuring[Substitution] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  15. def ensuring(cond: Boolean): Substitution

    Permalink
    Implicit information
    This member is added by an implicit conversion from Substitution to Ensuring[Substitution] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  16. final def eq(arg0: AnyRef): Boolean

    Permalink
    Definition Classes
    AnyRef
  17. def equals(a: Any): Boolean

    Permalink
    Definition Classes
    Substitution → AnyRef → Any
  18. def finalize(): Unit

    Permalink
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  19. def formatted(fmtstr: String): String

    Permalink
    Implicit information
    This member is added by an implicit conversion from Substitution to StringFormat[Substitution] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  20. final def getClass(): Class[_]

    Permalink
    Definition Classes
    AnyRef → Any
  21. def hashCode(): Int

    Permalink
    Definition Classes
    Substitution → AnyRef → Any
  22. def isIdentity: Boolean

    Permalink
  23. def isInjectiveRenaming: Boolean

    Permalink
  24. final def isInstanceOf[T0]: Boolean

    Permalink
    Definition Classes
    Any
  25. def isRenaming: Boolean

    Permalink
  26. val map: Map[Var, LambdaExpression]

    Permalink
  27. final def ne(arg0: AnyRef): Boolean

    Permalink
    Definition Classes
    AnyRef
  28. final def notify(): Unit

    Permalink
    Definition Classes
    AnyRef
  29. final def notifyAll(): Unit

    Permalink
    Definition Classes
    AnyRef
  30. def range: Set[Var]

    Permalink
  31. def restrict(newDomain: Iterable[Var]): Substitution

    Permalink
  32. final def synchronized[T0](arg0: ⇒ T0): T0

    Permalink
    Definition Classes
    AnyRef
  33. def toString(): String

    Permalink
    Definition Classes
    Substitution → AnyRef → Any
  34. final def wait(): Unit

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

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

    Permalink
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  37. def [B](y: B): (Substitution, B)

    Permalink
    Implicit information
    This member is added by an implicit conversion from Substitution to ArrowAssoc[Substitution] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from Substitution to any2stringadd[Substitution]

Inherited by implicit conversion StringFormat from Substitution to StringFormat[Substitution]

Inherited by implicit conversion Ensuring from Substitution to Ensuring[Substitution]

Inherited by implicit conversion ArrowAssoc from Substitution to ArrowAssoc[Substitution]

Ungrouped