Packages

class Substitution extends PreSubstitution

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. PreSubstitution
  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. All

Instance Constructors

  1. new Substitution(map: Map[Var, Expr], typeMap: Map[TVar, Ty] = Map())

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. def +(v: TVar, t: Ty): PreSubstitution
    Definition Classes
    PreSubstitution
  4. def +(v: Var, t: Expr): PreSubstitution
    Definition Classes
    PreSubstitution
  5. 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()
  6. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  7. 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.

  8. def asFOLSubstitution: FOLSubstitution
    Definition Classes
    PreSubstitution
  9. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  10. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate() @throws( ... )
  11. def compose(that: Substitution): Substitution

    Compose two substitutions such that (a compose b)(x) == a(b(x)).

  12. def domain: Set[Var]
    Definition Classes
    PreSubstitution
  13. 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
  14. 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
  15. 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
  16. 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
  17. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  18. def equals(a: Any): Boolean
    Definition Classes
    PreSubstitution → AnyRef → Any
  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
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  21. def hashCode(): Int
    Definition Classes
    PreSubstitution → AnyRef → Any
  22. def isEmpty: Boolean
    Definition Classes
    PreSubstitution
  23. def isIdentity: Boolean
    Definition Classes
    PreSubstitution
  24. def isInjective(dom: Set[Var]): Boolean
  25. def isInjectiveOnDomain: Boolean
  26. def isInjectiveRenaming: Boolean
    Definition Classes
    PreSubstitution
  27. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  28. def isRenaming: Boolean
    Definition Classes
    PreSubstitution
  29. val map: Map[Var, Expr]
    Definition Classes
    PreSubstitution
  30. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  31. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  32. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  33. def range: Set[Var]
    Definition Classes
    PreSubstitution
  34. def restrict(newDomain: Iterable[Var]): Substitution
  35. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  36. def toString(): String
    Definition Classes
    PreSubstitution → AnyRef → Any
  37. def toSubstitution: Substitution
    Definition Classes
    PreSubstitution
  38. val typeMap: Map[TVar, Ty]
    Definition Classes
    PreSubstitution
  39. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  40. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  41. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  42. 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

Shadowed Implicit Value Members

  1. 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.
    Shadowing
    This implicitly inherited member is shadowed by one or more members in this class.
    To access this member you can use a type ascription:
    (substitution: any2stringadd[Substitution]).+(other)
    Definition Classes
    any2stringadd

Deprecated Value Members

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

    (Since version ) see corresponding Javadoc for more information.

Inherited from PreSubstitution

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