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 :-> ythis creates a new variable to avoid name collisions.
- Note
that this construction gives a runtime error if the type of
ydepends onx.
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- LambdaFixed
- Serializable
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- Func
- LambdaLike
- FuncLike
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- Any
- by UnliftOps
- by RichTerm
- by any2stringadd
- by StringFormat
- by Ensuring
- by ArrowAssoc
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- Public
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Instance Constructors
- new LambdaFixed(variable: X, value: Y)
Type Members
- type Cod = Y
- Definition Classes
- LambdaLike
- type D = X
- Definition Classes
- LambdaLike
- abstract type Obj <: FuncLike[X, Y]
- Definition Classes
- FuncLike
Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##: Int
- Definition Classes
- AnyRef → Any
- def +(other: String): String
- Implicit
- This member is added by an implicit conversion from LambdaFixed[X, Y] toany2stringadd[LambdaFixed[X, Y]] performed by method any2stringadd in scala.Predef.
- Definition Classes
- any2stringadd
- def ->[B](y: B): (LambdaFixed[X, Y], B)
- Implicit
- This member is added by an implicit conversion from LambdaFixed[X, Y] toArrowAssoc[LambdaFixed[X, Y]] performed by method ArrowAssoc in scala.Predef.This conversion will take place only if Y is a subclass of Option[Nothing] (Y <: Option[Nothing]).
- Definition Classes
- ArrowAssoc
- Annotations
- @inline()
- 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
- 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
- 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
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- 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
- def andThen[A](g: (Y) => A): (X) => A
- Definition Classes
- Function1
- Annotations
- @unspecialized()
- def andthen[Z <: Term with Subs[Z]](f: (Y) => Z): LambdaTerm[X, Z]
- Definition Classes
- LambdaLike
- 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.
- def applyUnchecked(arg: X): Y
- Definition Classes
- FuncLike
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- 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
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
- val codom: Typ[Y]
codomain
codomain
- Definition Classes
- LambdaFixed → Func
- def compose[A](g: (A) => X): (A) => Y
- Definition Classes
- Function1
- Annotations
- @unspecialized()
- val dep: Boolean
- Definition Classes
- LambdaFixed → LambdaLike
- val depcodom: (X) => Typ[Y]
- def dependsOn(that: Term): Boolean
returns whether
thisdepends onthatreturns whether
thisdepends onthat- Definition Classes
- Term
- lazy val dom: Typ[X]
domain
domain
- Definition Classes
- LambdaFixed → Func → LambdaLike → FuncLike
- def ensuring(cond: (LambdaFixed[X, Y]) => Boolean, msg: => Any): LambdaFixed[X, Y]
- Implicit
- This member is added by an implicit conversion from LambdaFixed[X, Y] toEnsuring[LambdaFixed[X, Y]] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- def ensuring(cond: (LambdaFixed[X, Y]) => Boolean): LambdaFixed[X, Y]
- Implicit
- This member is added by an implicit conversion from LambdaFixed[X, Y] toEnsuring[LambdaFixed[X, Y]] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- def ensuring(cond: Boolean, msg: => Any): LambdaFixed[X, Y]
- Implicit
- This member is added by an implicit conversion from LambdaFixed[X, Y] toEnsuring[LambdaFixed[X, Y]] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- def ensuring(cond: Boolean): LambdaFixed[X, Y]
- Implicit
- This member is added by an implicit conversion from LambdaFixed[X, Y] toEnsuring[LambdaFixed[X, Y]] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(that: Any): Boolean
- Definition Classes
- LambdaLike → AnyRef → Any
- def formatted(fmtstr: String): String
- Implicit
- This member is added by an implicit conversion from LambdaFixed[X, Y] toStringFormat[LambdaFixed[X, Y]] performed by method StringFormat in scala.Predef.
- Definition Classes
- StringFormat
- Annotations
- @inline()
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- lazy val hashCode: Int
- Definition Classes
- LambdaLike → AnyRef → Any
- def indepOf(that: Term): Boolean
returns whether
thisis independent ofthat.returns whether
thisis independent ofthat.- Definition Classes
- Term
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- 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
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def productElementNames: Iterator[String]
- Definition Classes
- Product
- def refl: Refl[LambdaFixed[X, Y]]
reflexivity term
refl : term = termreflexivity 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
- 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
- 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
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def toString(): String
- Definition Classes
- LambdaLike → Function1 → AnyRef → Any
- 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
- 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
- def usesVar(t: Term): Boolean
returns whether the variable
tis used as a variable in a lambda definition.returns whether the variable
tis used as a variable in a lambda definition.- Definition Classes
- LambdaLike → Term
- val value: Y
the value
yin the lambda definitionx mapsto ythe value
yin the lambda definitionx mapsto y- Definition Classes
- LambdaFixed → LambdaLike
- val variable: X
the variable
xin the lambda definitionx \mapsto ythe variable
xin the lambda definitionx \mapsto y- Definition Classes
- LambdaFixed → LambdaLike
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
Deprecated Value Members
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable]) @Deprecated
- Deprecated
- def →[B](y: B): (LambdaFixed[X, Y], B)
- Implicit
- This member is added by an implicit conversion from LambdaFixed[X, Y] toArrowAssoc[LambdaFixed[X, Y]] performed by method ArrowAssoc in scala.Predef.This conversion will take place only if Y is a subclass of Option[Nothing] (Y <: 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.