Packages

case class LambdaFixed[X <: Term with Subs[X], Y <: Term with Subs[Y]](variable: X, value: Y) extends LambdaLike[X, Y] with Func[X, Y] with Subs[LambdaFixed[X, Y]] with Product with Serializable

lambda which is known to be pure, i.e., have fixed codomain; this is reflected in its scala class; one should usually not use the constructor of this case class, instead use the function lambda or the syntactic sugar for this, e.g. 

val f = x :-> y

this creates a new variable to avoid name collisions.

Note

that this construction gives a runtime error if the type of y depends on x.

Linear Supertypes
Serializable, Product, Equals, Func[X, Y], LambdaLike[X, Y], FuncLike[X, Y], (X) => Y, Term, Subs[LambdaFixed[X, Y]], AnyRef, Any
Type Hierarchy
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Inherited
  1. LambdaFixed
  2. Serializable
  3. Product
  4. Equals
  5. Func
  6. LambdaLike
  7. FuncLike
  8. Function1
  9. Term
  10. Subs
  11. AnyRef
  12. Any
Implicitly
  1. by UnliftOps
  2. by RichTerm
  3. by any2stringadd
  4. by StringFormat
  5. by Ensuring
  6. by ArrowAssoc
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Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new LambdaFixed(variable: X, value: Y)

Type Members

  1. type Cod = Y
    Definition Classes
    LambdaLike
  2. type D = X
    Definition Classes
    LambdaLike
  3. abstract type Obj <: FuncLike[X, Y]
    Definition Classes
    FuncLike

Value Members

  1. def :->[V <: Term with Subs[V]](that: V): Func[LambdaFixed[X, Y], V]

    constructor for (pure) lambda functions, see lmbda

    constructor for (pure) lambda functions, see lmbda

    Implicit
    This member is added by an implicit conversion from LambdaFixed[X, Y] toRichTerm[LambdaFixed[X, Y]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  2. def :~>[V <: Term with Subs[V]](that: V): FuncLike[LambdaFixed[X, Y], V]

    constructor for (in general dependent) lambda functions, see lambda

    constructor for (in general dependent) lambda functions, see lambda

    Implicit
    This member is added by an implicit conversion from LambdaFixed[X, Y] toRichTerm[LambdaFixed[X, Y]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  3. def =:=(rhs: LambdaFixed[X, Y]): IdentityTyp[LambdaFixed[X, Y]]

    equality type 'term = rhs'

    equality type 'term = rhs'

    Implicit
    This member is added by an implicit conversion from LambdaFixed[X, Y] toRichTerm[LambdaFixed[X, Y]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  4. def act(arg: X): Y

    the action of the function to define: define this method, but use apply.

    the action of the function to define: define this method, but use apply.

    Definition Classes
    LambdaLike → FuncLike
  5. def andThen[A](g: (Y) => A): (X) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  6. def andthen[Z <: Term with Subs[Z]](f: (Y) => Z): LambdaTerm[X, Z]
    Definition Classes
    LambdaLike
  7. def apply(arg: X): Y

    application of the function: use this but define the act method; checks HoTT-type of argument is in the domain and throws exception if it fails.

    application of the function: use this but define the act method; checks HoTT-type of argument is in the domain and throws exception if it fails.

    Definition Classes
    FuncLike → Function1
  8. def applyUnchecked(arg: X): Y
    Definition Classes
    FuncLike
  9. def canApply(arg: X): Boolean

    checks if application is valid; can override to allow for example resizing universes

    checks if application is valid; can override to allow for example resizing universes

    arg

    the argument

    returns

    whether the argument has the correct type.

    Definition Classes
    LambdaLike → FuncLike
  10. val codom: Typ[Y]

    codomain

    codomain

    Definition Classes
    LambdaFixed → Func
  11. def compose[A](g: (A) => X): (A) => Y
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  12. val dep: Boolean
    Definition Classes
    LambdaFixed → LambdaLike
  13. val depcodom: (X) => Typ[Y]
    Definition Classes
    Func → FuncLike
  14. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  15. lazy val dom: Typ[X]

    domain

    domain

    Definition Classes
    LambdaFixed → Func → LambdaLike → FuncLike
  16. def equals(that: Any): Boolean
    Definition Classes
    LambdaLike → AnyRef → Any
  17. lazy val hashCode: Int
    Definition Classes
    LambdaLike → AnyRef → Any
  18. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  19. def newobj: LambdaFixed[X, Y]

    A new object with the same type, to be used in place of a variable to avoid name clashes.

    A new object with the same type, to be used in place of a variable to avoid name clashes. Should throw exception when invoked for constants.

    Definition Classes
    LambdaFixed → Subs
  20. def productElementNames: Iterator[String]
    Definition Classes
    Product
  21. def refl: Refl[LambdaFixed[X, Y]]

    reflexivity term refl : term = term

    reflexivity term refl : term = term

    Implicit
    This member is added by an implicit conversion from LambdaFixed[X, Y] toRichTerm[LambdaFixed[X, Y]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  22. def replace(x: Term, y: Term): LambdaFixed[X, Y] with Subs[LambdaFixed[X, Y]]

    refine substitution so if x and y are both of certain forms such as pairs or formal applications, components are substituted.

    refine substitution so if x and y are both of certain forms such as pairs or formal applications, components are substituted.

    Definition Classes
    Subs
  23. def subs(x: Term, y: Term): LambdaFixed[X, Y]

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    LambdaFixed → Func → LambdaLike → FuncLike → Subs
  24. def toString(): String
    Definition Classes
    LambdaLike → Function1 → AnyRef → Any
  25. lazy val typ: FuncTyp[X, Y]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    LambdaFixed → Func → LambdaLike → FuncLike → Term
  26. def unlift: PartialFunction[X, B]
    Implicit
    This member is added by an implicit conversion from LambdaFixed[X, Y] toUnliftOps[X, B] performed by method UnliftOps in scala.Function1.This conversion will take place only if Y is a subclass of Option[B] (Y <: Option[B]).
    Definition Classes
    UnliftOps
  27. def usesVar(t: Term): Boolean

    returns whether the variable t is used as a variable in a lambda definition.

    returns whether the variable t is used as a variable in a lambda definition.

    Definition Classes
    LambdaLike → Term
  28. val value: Y

    the value y in the lambda definition x mapsto y

    the value y in the lambda definition x mapsto y

    Definition Classes
    LambdaFixed → LambdaLike
  29. val variable: X

    the variable x in the lambda definition x \mapsto y

    the variable x in the lambda definition x \mapsto y

    Definition Classes
    LambdaFixed → LambdaLike