Packages

class SymbolicGroup[A] extends ScalaTyp[A]

Self Type
SymbolicGroup[A]
Linear Supertypes
ScalaTyp[A], Typ[RepTerm[A]], Term, Subs[Typ[RepTerm[A]]], AnyRef, Any
Known Subclasses
FreeGroup
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. SymbolicGroup
  2. ScalaTyp
  3. Typ
  4. Term
  5. Subs
  6. AnyRef
  7. 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 SymbolicGroup()(implicit arg0: Group[A])

Type Members

  1. type LocalTerm = RepTerm[A]
  2. case class MultLiteral(a: A) extends Func[LocalTerm, LocalTerm] with MiscAppln with Product with Serializable
  3. case class MultTerm(a: LocalTerm) extends Func[LocalTerm, LocalTerm] with MiscAppln with Product with Serializable
  4. type Obj = RepTerm[A]

    scala type of objects with this HoTT-type (refining U)

    scala type of objects with this HoTT-type (refining U)

    Definition Classes
    ScalaTyp → Typ
  5. type Op = Func[LocalTerm, Func[LocalTerm, LocalTerm]]

Value Members

  1. object Elem

    Pattern for element of the given type.

    Pattern for element of the given type.

    Definition Classes
    Typ
  2. def !:(term: Term): RepTerm[A]

    checks term is of this type and returns it; useful for documentation.

    checks term is of this type and returns it; useful for documentation.

    Definition Classes
    Typ
  3. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. final def ##: Int
    Definition Classes
    AnyRef → Any
  5. def &&[UU >: RepTerm[A] <: Term with Subs[UU], V <: Term with Subs[V]](that: Typ[V]): ProdTyp[UU, V]

    returns product type, mainly to use for "and" for structures

    returns product type, mainly to use for "and" for structures

    Definition Classes
    Typ
  6. def &:[UU >: RepTerm[A] <: Term with Subs[UU], V <: Term with Subs[V]](variable: V): SigmaTyp[V, UU]
    Definition Classes
    Typ
  7. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from SymbolicGroup[A] toany2stringadd[SymbolicGroup[A]] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  8. def ++[UU >: Typ[RepTerm[A]] <: Typ[Term] with Subs[UU], VV <: Term with Subs[VV], V <: Typ[VV] with Subs[V]](those: V): SigmaTyp[UU, VV]

    returns Sigma-Type, mainly to use as "such that", for example a group type is this with product etc.

    returns Sigma-Type, mainly to use as "such that", for example a group type is this with product etc. dependent on this.

    Definition Classes
    Typ
  9. def ->[B](y: B): (SymbolicGroup[A], B)
    Implicit
    This member is added by an implicit conversion from SymbolicGroup[A] toArrowAssoc[SymbolicGroup[A]] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  10. def ->:[W <: Term with Subs[W], UU >: RepTerm[A] <: Term with Subs[UU]](that: Typ[W]): FuncTyp[W, UU]

    function type: this -> that

    function type: this -> that

    Definition Classes
    Typ
  11. def ::(name: String): RepTerm[A]

    symbolic object with given name

    symbolic object with given name

    Definition Classes
    Typ
  12. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  13. def Var(implicit factory: NameFactory): RepTerm[A]

    new variable from a factory.

    new variable from a factory.

    Definition Classes
    Typ
  14. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  15. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  16. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  17. val e: RepTerm[A]
  18. def ensuring(cond: (SymbolicGroup[A]) => Boolean, msg: => Any): SymbolicGroup[A]
    Implicit
    This member is added by an implicit conversion from SymbolicGroup[A] toEnsuring[SymbolicGroup[A]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: (SymbolicGroup[A]) => Boolean): SymbolicGroup[A]
    Implicit
    This member is added by an implicit conversion from SymbolicGroup[A] toEnsuring[SymbolicGroup[A]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. def ensuring(cond: Boolean, msg: => Any): SymbolicGroup[A]
    Implicit
    This member is added by an implicit conversion from SymbolicGroup[A] toEnsuring[SymbolicGroup[A]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: Boolean): SymbolicGroup[A]
    Implicit
    This member is added by an implicit conversion from SymbolicGroup[A] toEnsuring[SymbolicGroup[A]] 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 SymbolicGroup[A] toStringFormat[SymbolicGroup[A]] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  25. val g: RepTerm[A]
  26. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  27. val group: Group[A]
  28. implicit val groupStructure: Group[LocalTerm]
  29. val h: RepTerm[A]
  30. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  31. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  32. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  33. val lm: Func[RepTerm[A], Func[RepTerm[A], RepTerm[A]]]
  34. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  35. def newobj: Typ[RepTerm[A]]

    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
    ScalaTyp → Subs
  36. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  37. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  38. def obj: RepTerm[A]

    factory for producing objects of the given type.

    factory for producing objects of the given type. can use {{innervar}} if one wants name unchanged.

    Definition Classes
    Typ
  39. val power: Func[RepTerm[A], Func[NatRing.LocalTerm, RepTerm[A]]]
  40. implicit val rep: ScalaRep[RepTerm[A], A]
    Definition Classes
    ScalaTyp
  41. def replace(x: Term, y: Term): Typ[RepTerm[A]] with Subs[Typ[RepTerm[A]]]

    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
  42. val rm: Func[RepTerm[A], Func[RepTerm[A], RepTerm[A]]]
  43. def subs(x: Term, y: Term): Typ[RepTerm[A]]

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    ScalaTyp → Subs
  44. def sym(implicit name: Name): RepTerm[A]

    shortcut for symbolic object

    shortcut for symbolic object

    Definition Classes
    Typ
  45. def symbObj(name: AnySym): RepTerm[A] with Subs[RepTerm[A]]

    A symbolic object with this HoTT type, and with scala-type Obj

    A symbolic object with this HoTT type, and with scala-type Obj

    Definition Classes
    Typ
  46. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  47. def toString(): String
    Definition Classes
    AnyRef → Any
  48. val typ: ScalaTypUniv[A]

    type of a type is a universe.

    type of a type is a universe.

    Definition Classes
    ScalaTyp → Typ → Term
  49. lazy val typlevel: Int
    Definition Classes
    Typ
  50. 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
  51. def variable(name: AnySym): RepTerm[A]

    A symbolic object with this HoTT type, and with scala-type Obj

    A symbolic object with this HoTT type, and with scala-type Obj

    Definition Classes
    ScalaTyp → Typ
  52. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  53. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  54. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  55. def ||[UU >: RepTerm[A] <: Term with Subs[UU], V <: Term with Subs[V]](that: Typ[V]): PlusTyp[UU, V]

    returns coproduct type, mainly to use for "or".

    returns coproduct type, mainly to use for "or".

    Definition Classes
    Typ
  56. def ~>:[UU >: RepTerm[A] <: Term with Subs[UU], V <: Term with Subs[V]](variable: V): GenFuncTyp[V, UU]

    dependent function type (Pi-Type) define by a lambda: this depends on the variable, which hence gives a type family; note that a new variable is created and substituted in this to avoid name clashes.

    dependent function type (Pi-Type) define by a lambda: this depends on the variable, which hence gives a type family; note that a new variable is created and substituted in this to avoid name clashes.

    Definition Classes
    Typ
  57. object Comb
  58. object Literal extends ScalaSym[LocalTerm, A]
  59. object Theorems
  60. case object inv extends Func[LocalTerm, LocalTerm] with Product with Serializable
  61. case object mul extends Func[LocalTerm, Func[LocalTerm, LocalTerm]] with Product with Serializable

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): (SymbolicGroup[A], B)
    Implicit
    This member is added by an implicit conversion from SymbolicGroup[A] toArrowAssoc[SymbolicGroup[A]] 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 ScalaTyp[A]

Inherited from Typ[RepTerm[A]]

Inherited from Term

Inherited from Subs[Typ[RepTerm[A]]]

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromSymbolicGroup[A] to any2stringadd[SymbolicGroup[A]]

Inherited by implicit conversion StringFormat fromSymbolicGroup[A] to StringFormat[SymbolicGroup[A]]

Inherited by implicit conversion Ensuring fromSymbolicGroup[A] to Ensuring[SymbolicGroup[A]]

Inherited by implicit conversion ArrowAssoc fromSymbolicGroup[A] to ArrowAssoc[SymbolicGroup[A]]

Ungrouped