Packages

case class Composition[U <: Term with Subs[U], V <: Term with Subs[V], W <: Term with Subs[W]](f: Func[V, W], g: Func[U, V]) extends Func[U, W] with Subs[Composition[U, V, W]] with Product with Serializable

Linear Supertypes
Serializable, Product, Equals, Func[U, W], FuncLike[U, W], (U) => W, Term, Subs[Composition[U, V, W]], AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Composition
  2. Serializable
  3. Product
  4. Equals
  5. Func
  6. FuncLike
  7. Function1
  8. Term
  9. Subs
  10. AnyRef
  11. Any
Implicitly
  1. by UnliftOps
  2. by RichTerm
  3. by any2stringadd
  4. by StringFormat
  5. by Ensuring
  6. by ArrowAssoc
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new Composition(f: Func[V, W], g: Func[U, V])

Type Members

  1. abstract type Obj <: FuncLike[U, W]
    Definition Classes
    FuncLike

Value Members

  1. def :->[V <: Term with Subs[V]](that: V): Func[Composition[U, V, W], 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 Composition[U, V, W] toRichTerm[Composition[U, V, W]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  2. def :~>[V <: Term with Subs[V]](that: V): FuncLike[Composition[U, V, W], 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 Composition[U, V, W] toRichTerm[Composition[U, V, W]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  3. def =:=(rhs: Composition[U, V, W]): IdentityTyp[Composition[U, V, W]]

    equality type 'term = rhs'

    equality type 'term = rhs'

    Implicit
    This member is added by an implicit conversion from Composition[U, V, W] toRichTerm[Composition[U, V, W]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  4. def act(a: U): W

    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
    Composition → Func → FuncLike
  5. def andThen[A](g: (W) => A): (U) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  6. def apply(arg: U): W

    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
  7. def applyUnchecked(arg: U): W
    Definition Classes
    FuncLike
  8. def canApply(arg: U): 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
    FuncLike
  9. val codom: Typ[W]

    codomain

    codomain

    Definition Classes
    Composition → Func
  10. def compose[A](g: (A) => U): (A) => W
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  11. val depcodom: (U) => Typ[W]
    Definition Classes
    Func → FuncLike
  12. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  13. val dom: Typ[U]

    domain

    domain

    Definition Classes
    Composition → Func → FuncLike
  14. val f: Func[V, W]
  15. val g: Func[U, V]
  16. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  17. def newobj: Nothing

    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
    Composition → Subs
  18. def productElementNames: Iterator[String]
    Definition Classes
    Product
  19. def refl: Refl[Composition[U, V, W]]

    reflexivity term refl : term = term

    reflexivity term refl : term = term

    Implicit
    This member is added by an implicit conversion from Composition[U, V, W] toRichTerm[Composition[U, V, W]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  20. def replace(x: Term, y: Term): Composition[U, V, W] with Subs[Composition[U, V, W]]

    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
  21. def subs(x: Term, y: Term): Composition[U, V, W]

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    Composition → Func → FuncLike → Subs
  22. def toString(): String
    Definition Classes
    Function1 → AnyRef → Any
  23. val typ: FuncTyp[U, W]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    Composition → Func → FuncLike → Term
  24. def unlift: PartialFunction[U, B]
    Implicit
    This member is added by an implicit conversion from Composition[U, V, W] toUnliftOps[U, B] performed by method UnliftOps in scala.Function1.This conversion will take place only if W is a subclass of Option[B] (W <: Option[B]).
    Definition Classes
    UnliftOps
  25. 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
    Term