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
Linear Supertypes
PreSubstitution, AnyRef, Any
Known Subclasses
FOLSubstitution
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
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. Protected

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 toArrowAssoc[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(v: Var): Expr
    Definition Classes
    Substitution → PreSubstitution
  8. 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.

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

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

  13. def domain: Set[Var]
    Definition Classes
    PreSubstitution
  14. def ensuring(cond: (Substitution) => Boolean, msg: => Any): Substitution
    Implicit
    This member is added by an implicit conversion from Substitution toEnsuring[Substitution] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  15. def ensuring(cond: (Substitution) => Boolean): Substitution
    Implicit
    This member is added by an implicit conversion from Substitution toEnsuring[Substitution] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  16. def ensuring(cond: Boolean, msg: => Any): Substitution
    Implicit
    This member is added by an implicit conversion from Substitution toEnsuring[Substitution] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  17. def ensuring(cond: Boolean): Substitution
    Implicit
    This member is added by an implicit conversion from Substitution toEnsuring[Substitution] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  18. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  19. def equals(a: Any): Boolean
    Definition Classes
    PreSubstitution → AnyRef → Any
  20. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  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() @IntrinsicCandidate()
  32. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  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(classOf[java.lang.InterruptedException])
  40. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  41. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

Shadowed Implicit Value Members

  1. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from Substitution toany2stringadd[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[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated
  2. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Substitution toStringFormat[Substitution] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @deprecated @inline()
    Deprecated

    (Since version 2.12.16) Use formatString.format(value) instead of value.formatted(formatString), or use the f"" string interpolator. In Java 15 and later, formatted resolves to the new method in String which has reversed parameters.

  3. def →[B](y: B): (Substitution, B)
    Implicit
    This member is added by an implicit conversion from Substitution toArrowAssoc[Substitution] 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 PreSubstitution

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromSubstitution to any2stringadd[Substitution]

Inherited by implicit conversion StringFormat fromSubstitution to StringFormat[Substitution]

Inherited by implicit conversion Ensuring fromSubstitution to Ensuring[Substitution]

Inherited by implicit conversion ArrowAssoc fromSubstitution to ArrowAssoc[Substitution]

Ungrouped