object FreeGroup extends SymbolicGroup[Word]
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Type Members
- type LocalTerm = RepTerm[Word]
- Definition Classes
- SymbolicGroup
- type Obj = RepTerm[Word]
scala type of objects with this HoTT-type (refining
U) - type Op = Func[LocalTerm, Func[LocalTerm, LocalTerm]]
- Definition Classes
- SymbolicGroup
- case class MultLiteral(a: A) extends Func[LocalTerm, LocalTerm] with MiscAppln with Product with Serializable
- Definition Classes
- SymbolicGroup
- case class MultTerm(a: LocalTerm) extends Func[LocalTerm, LocalTerm] with MiscAppln with Product with Serializable
- Definition Classes
- SymbolicGroup
Value Members
- object Elem
Pattern for element of the given type.
Pattern for element of the given type.
- Definition Classes
- Typ
- def !:(term: Term): RepTerm[Word]
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
- def &&[UU >: RepTerm[Word] <: 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
- def &:[UU >: RepTerm[Word] <: Term with Subs[UU], V <: Term with Subs[V]](variable: V): SigmaTyp[V, UU]
- Definition Classes
- Typ
- def ++[UU >: Typ[RepTerm[Word]] <: 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
- def ->:[W <: Term with Subs[W], UU >: RepTerm[Word] <: Term with Subs[UU]](that: Typ[W]): FuncTyp[W, UU]
function type:
this -> thatfunction type:
this -> that- Definition Classes
- Typ
- def ::(name: String): RepTerm[Word]
symbolic object with given name
symbolic object with given name
- Definition Classes
- Typ
- def Var(implicit factory: NameFactory): RepTerm[Word]
new variable from a factory.
new variable from a factory.
- Definition Classes
- Typ
- def dependsOn(that: Term): Boolean
returns whether
thisdepends onthatreturns whether
thisdepends onthat- Definition Classes
- Term
- val e: RepTerm[Word]
- Definition Classes
- SymbolicGroup
- val g: RepTerm[Word]
- Definition Classes
- SymbolicGroup
- val group: Group[Word]
- Definition Classes
- SymbolicGroup
- implicit val groupStructure: Group[LocalTerm]
- Definition Classes
- SymbolicGroup
- val h: RepTerm[Word]
- Definition Classes
- SymbolicGroup
- def indepOf(that: Term): Boolean
returns whether
thisis independent ofthat.returns whether
thisis independent ofthat.- Definition Classes
- Term
- val lm: Func[RepTerm[Word], Func[RepTerm[Word], RepTerm[Word]]]
- Definition Classes
- SymbolicGroup
- def newobj: Typ[RepTerm[Word]]
A new object with the same type, to be used in place of a variable to avoid name clashes.
- def obj: RepTerm[Word]
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
- val power: Func[RepTerm[Word], Func[NatRing.LocalTerm, RepTerm[Word]]]
- Definition Classes
- SymbolicGroup
- implicit val rep: ScalaRep[RepTerm[Word], Word]
- Definition Classes
- ScalaTyp
- def replace(x: Term, y: Term): Typ[RepTerm[Word]] with Subs[Typ[RepTerm[Word]]]
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
- val rm: Func[RepTerm[Word], Func[RepTerm[Word], RepTerm[Word]]]
- Definition Classes
- SymbolicGroup
- def subs(x: Term, y: Term): Typ[RepTerm[Word]]
substitute x by y recursively in
this. - def sym(implicit name: Name): RepTerm[Word]
shortcut for symbolic object
shortcut for symbolic object
- Definition Classes
- Typ
- def symbObj(name: AnySym): RepTerm[Word] with Subs[RepTerm[Word]]
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
- def toString(): String
- Definition Classes
- FreeGroup → AnyRef → Any
- val typ: ScalaTypUniv[Word]
type of a type is a universe.
- lazy val typlevel: Int
- Definition Classes
- Typ
- 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
- Term
- def variable(name: AnySym): RepTerm[Word]
A symbolic object with this HoTT type, and with scala-type Obj
- def word(s: String): LocalTerm with Subs[LocalTerm]
- def ||[UU >: RepTerm[Word] <: 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
- def ~>:[UU >: RepTerm[Word] <: Term with Subs[UU], V <: Term with Subs[V]](variable: V): GenFuncTyp[V, UU]
dependent function type (Pi-Type) define by a lambda:
thisdepends on thevariable, which hence gives a type family; note that a new variable is created and substituted inthisto avoid name clashes.dependent function type (Pi-Type) define by a lambda:
thisdepends on thevariable, which hence gives a type family; note that a new variable is created and substituted inthisto avoid name clashes.- Definition Classes
- Typ
- object Comb
- Definition Classes
- SymbolicGroup
- object Literal extends ScalaSym[LocalTerm, A]
- Definition Classes
- SymbolicGroup
- object Theorems
- Definition Classes
- SymbolicGroup
- case object inv extends Func[LocalTerm, LocalTerm] with Product with Serializable
- Definition Classes
- SymbolicGroup
- case object mul extends Func[LocalTerm, Func[LocalTerm, LocalTerm]] with Product with Serializable
- Definition Classes
- SymbolicGroup