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
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Inherited
  1. Substitution
  2. AnyRef
  3. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
  2. All

Instance Constructors

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

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    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)
    Implicit
    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
    Definition Classes
    AnyRef → Any
  6. def apply[T, U](x: T)(implicit ev: Substitutable[Substitution, T, U]): U

    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
  8. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  9. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  10. def compose(sub: Substitution): Substitution
  11. def domain: Set[Var]
  12. def ensuring(cond: (Substitution) ⇒ Boolean, msg: ⇒ Any): Substitution
    Implicit
    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
    Implicit
    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
    Implicit
    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
    Implicit
    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
    Definition Classes
    AnyRef
  17. def equals(a: Any): Boolean
    Definition Classes
    Substitution → AnyRef → Any
  18. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  19. def formatted(fmtstr: String): String
    Implicit
    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[_]
    Definition Classes
    AnyRef → Any
  21. def hashCode(): Int
    Definition Classes
    Substitution → AnyRef → Any
  22. def isIdentity: Boolean
  23. def isInjective(dom: Set[Var]): Boolean
  24. def isInjectiveOnDomain: Boolean
  25. def isInjectiveRenaming: Boolean
  26. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  27. def isRenaming: Boolean
  28. val map: Map[Var, LambdaExpression]
  29. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  30. final def notify(): Unit
    Definition Classes
    AnyRef
  31. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  32. def range: Set[Var]
  33. def restrict(newDomain: Iterable[Var]): Substitution
  34. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  35. def toString(): String
    Definition Classes
    Substitution → AnyRef → Any
  36. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  37. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  38. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  39. def [B](y: B): (Substitution, B)
    Implicit
    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