Packages

trait Func[W <: Term with Subs[W], +U <: Term with Subs[U]] extends FuncLike[W, U] with Subs[Func[W, U]]

a function (pure, not dependent), i.e., a term in a function type, has a codomain and a fixed type for the domain.

Linear Supertypes
FuncLike[W, U], (W) => U, Term, Subs[Func[W, U]], AnyRef, Any
Known Subclasses
CnstFunc, Composition, FuncDefn, RecFn, IndRecFunc, LambdaFixed, NamedFunc, RecFn, RecFn, RecFunc, RecFn, SymbolicFunc, RecFn, RecFn, Factorize, Quotient, Funcs, RecursiveDefinition, DataCons, Empty, Rec, PlusExtendedFunction, ExtendedFunction, ExtendedFunction, SimpleExtendedFunction, AddLiteral, AddTerm, AdditiveMorphism, Homomorphism, multLiteral, multTerm, prod, sum, MultLiteral, MultTerm, inv, mul
Type Hierarchy
Ordering
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  2. By Inheritance
Inherited
  1. Func
  2. FuncLike
  3. Function1
  4. Term
  5. Subs
  6. AnyRef
  7. 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

Type Members

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

Abstract Value Members

  1. abstract def act(arg: W): U

    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
    Func → FuncLike
  2. abstract val codom: Typ[U]

    codomain

  3. abstract val dom: Typ[W]

    domain

    domain

    Definition Classes
    Func → FuncLike
  4. abstract def newobj: Func[W, U] with Subs[Func[W, U]]

    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
    Subs
  5. abstract def subs(x: Term, y: Term): Func[W, U]

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    Func → FuncLike → Subs
  6. abstract val typ: Typ[Func[W, U]]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    Func → FuncLike → Term

Concrete 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 Func[W, U] toany2stringadd[Func[W, U]] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Func[W, U], B)
    Implicit
    This member is added by an implicit conversion from Func[W, U] toArrowAssoc[Func[W, U]] performed by method ArrowAssoc in scala.Predef.This conversion will take place only if U is a subclass of Option[Nothing] (U <: Option[Nothing]).
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. def :->[V <: Term with Subs[V]](that: V): Func[Func[W, U], 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 Func[W, U] toRichTerm[Func[W, U]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  6. def :~>[V <: Term with Subs[V]](that: V): FuncLike[Func[W, U], 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 Func[W, U] toRichTerm[Func[W, U]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  7. def =:=(rhs: Func[W, U]): IdentityTyp[Func[W, U]]

    equality type 'term = rhs'

    equality type 'term = rhs'

    Implicit
    This member is added by an implicit conversion from Func[W, U] toRichTerm[Func[W, U]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  8. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  9. def andThen[A](g: (U) => A): (W) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  10. def apply(arg: W): U

    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
  11. def applyUnchecked(arg: W): U
    Definition Classes
    FuncLike
  12. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  13. def canApply(arg: W): 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
  14. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  15. def compose[A](g: (A) => W): (A) => U
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  16. val depcodom: (W) => Typ[U]
    Definition Classes
    Func → FuncLike
  17. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  18. def ensuring(cond: (Func[W, U]) => Boolean, msg: => Any): Func[W, U]
    Implicit
    This member is added by an implicit conversion from Func[W, U] toEnsuring[Func[W, U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: (Func[W, U]) => Boolean): Func[W, U]
    Implicit
    This member is added by an implicit conversion from Func[W, U] toEnsuring[Func[W, U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. def ensuring(cond: Boolean, msg: => Any): Func[W, U]
    Implicit
    This member is added by an implicit conversion from Func[W, U] toEnsuring[Func[W, U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: Boolean): Func[W, U]
    Implicit
    This member is added by an implicit conversion from Func[W, U] toEnsuring[Func[W, U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  23. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  24. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Func[W, U] toStringFormat[Func[W, U]] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  25. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  26. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  27. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  28. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  29. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  30. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  31. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  32. def refl: Refl[Func[W, U]]

    reflexivity term refl : term = term

    reflexivity term refl : term = term

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

    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
  34. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  35. def toString(): String
    Definition Classes
    Function1 → AnyRef → Any
  36. def unlift: PartialFunction[W, B]
    Implicit
    This member is added by an implicit conversion from Func[W, U] toUnliftOps[W, B] performed by method UnliftOps in scala.Function1.This conversion will take place only if U is a subclass of Option[B] (U <: Option[B]).
    Definition Classes
    UnliftOps
  37. 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
  38. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  39. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  40. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated
  2. def →[B](y: B): (Func[W, U], B)
    Implicit
    This member is added by an implicit conversion from Func[W, U] toArrowAssoc[Func[W, U]] performed by method ArrowAssoc in scala.Predef.This conversion will take place only if U is a subclass of Option[Nothing] (U <: Option[Nothing]).
    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 FuncLike[W, U]

Inherited from (W) => U

Inherited from Term

Inherited from Subs[Func[W, U]]

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion UnliftOps fromFunc[W, U] to UnliftOps[W, B]

Inherited by implicit conversion RichTerm fromFunc[W, U] to RichTerm[Func[W, U]]

Inherited by implicit conversion any2stringadd fromFunc[W, U] to any2stringadd[Func[W, U]]

Inherited by implicit conversion StringFormat fromFunc[W, U] to StringFormat[Func[W, U]]

Inherited by implicit conversion Ensuring fromFunc[W, U] to Ensuring[Func[W, U]]

Inherited by implicit conversion ArrowAssoc fromFunc[W, U] to ArrowAssoc[Func[W, U]]

Ungrouped