object NatRing extends SymbolicCRing[SafeLong] with ExstInducStrucs
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Type Members
- case class Induc[U <: Term with Subs[U]](typFamily: Func[Nat, Typ[U]], init: U, g: FuncLike[Nat, Func[U, U]]) extends InducFuncLike[Nat, U] with Subs[Induc[U]] with Product with Serializable
- type LocalTerm = RepTerm[SafeLong]
- Definition Classes
- SymbolicCRing
- type Nat = RepTerm[SafeLong]
- type Op = Func[LocalTerm, Func[LocalTerm, LocalTerm]]
- Definition Classes
- SymbolicCRing
- case class Rec[U <: Term with Subs[U]](init: U, g: Func[Nat, Func[U, U]]) extends RecFunc[Nat, U] with Product with Serializable
- case class AddLiteral(a: A) extends Func[LocalTerm, LocalTerm] with MiscAppln with Product with Serializable
- Definition Classes
- SymbolicCRing
- case class AddTerm(x: LocalTerm) extends Func[LocalTerm, LocalTerm] with MiscAppln with Product with Serializable
returns function x + _ where x is not a literal and is indecomposable under sum
returns function x + _ where x is not a literal and is indecomposable under sum
- Definition Classes
- SymbolicCRing
- case class AdditiveMorphism[U <: LocalTerm with Subs[U]](base: Func[LocalTerm, U], op: (U, U) => U) extends Func[LocalTerm, LocalTerm] with Product with Serializable
- Definition Classes
- SymbolicCRing
- case class PiTerm(multElems: Map[LocalTerm, Int]) extends LocalTerm with FoldedTerm[LocalTerm] with Product with Serializable
A product of terms in normal form, i.e., * none of the terms is a sum * we have either at least two terms or a single term with exponent not 1, * no exponent is 0.
A product of terms in normal form, i.e., * none of the terms is a sum * we have either at least two terms or a single term with exponent not 1, * no exponent is 0.
- Definition Classes
- SymbolicCRing
- case class SigmaTerm(elems: Set[LocalTerm]) extends LocalTerm with FoldedTerm[LocalTerm] with Product with Serializable
- Definition Classes
- SymbolicCRing
- case class multLiteral(b: A) extends Func[LocalTerm, LocalTerm] with MiscAppln with Product with Serializable
- Definition Classes
- SymbolicCRing
- case class multTerm(x: LocalTerm) extends Func[LocalTerm, LocalTerm] with MiscAppln with Product with Serializable
- Definition Classes
- SymbolicCRing
Value Members
- val NatTyp: LocalTyp.type
- val constants: Vector[Term]
- Definition Classes
- NatRing → ExstInducStrucs
- lazy val context: Context
- implicit val cringStructure: CRing[LocalTerm]
- Definition Classes
- SymbolicCRing
- val divides: FuncLike[LocalTerm, FuncLike[LocalTerm, SigmaTyp[LocalTerm, Equality[LocalTerm]]]]
- Definition Classes
- SymbolicCRing
- lazy val exstInducDefn: ExstInducDefn
- def findDifference(x: Nat, y: Nat): Option[Nat]
- def findDifferenceFlip(x: Nat, y: Nat): Option[Nat]
- def findDivisibility(x: Nat, y: Nat): Option[AbsPair[Nat, Equality[Nat]]]
- def findFactor(x: Nat, y: Nat): Option[Nat]
- def findLEQ(x: Nat, y: Nat): Option[AbsPair[Nat, Equality[Nat]]]
- def funcSum(f: (LocalTerm) => LocalTerm, g: (LocalTerm) => LocalTerm): Func[LocalTerm, LocalTerm]
- Definition Classes
- SymbolicCRing
- def incl[A](r: SymbolicCRing[A])(implicit arg0: CRing[A]): Func[Nat, LocalTerm]
- def induc[U <: Term with Subs[U]](typFamily: Func[Nat, Typ[U]]): Func[U, Func[FuncLike[Nat, Func[U, U]], FuncLike[Nat, U]]]
- def inducOpt(dom: Term, cod: Term): Option[Term]
- Definition Classes
- NatRing → ExstInducStrucs
- implicit def intLiteral(n: Int): Nat
- val leq: FuncLike[Nat, FuncLike[Nat, SigmaTyp[Nat, Equality[Nat]]]]
- lazy val minusone: LocalTerm
- Definition Classes
- SymbolicCRing
- def negate(x: LocalTerm): LocalTerm
- Definition Classes
- SymbolicCRing
- final def posPower(x: LocalTerm, n: Int, accum: LocalTerm = Literal(one)): LocalTerm
- Definition Classes
- SymbolicCRing
- Annotations
- @tailrec()
- def power(x: LocalTerm, n: Int): LocalTerm
returns power of x by n, in generality an error for negative n; should be overridden in fields, where negative powers are meaningful
returns power of x by n, in generality an error for negative n; should be overridden in fields, where negative powers are meaningful
- Definition Classes
- SymbolicCRing
- lazy val predicate: (SafeLong) => Boolean
- Definition Classes
- NatRing → SymbolicCRing
- def rec[U <: Term with Subs[U]](codom: Typ[U]): Func[U, Func[Func[Nat, Func[U, U]], Func[Nat, U]]]
- def recDefn[U <: Term with Subs[U]](n: SafeLong, formal: U, h: (SafeLong) => (U) => U): U
- def recOpt[C <: Term with Subs[C]](dom: Term, cod: Typ[C]): Option[Term]
- Definition Classes
- NatRing → ExstInducStrucs
- lazy val reciprocal: Func[LocalTerm, LocalTerm]
- Definition Classes
- SymbolicCRing
- val reciprocalOpt: Option[Func[LocalTerm, LocalTerm]]
override this in fields
override this in fields
- Definition Classes
- SymbolicCRing
- val ring: Ring[SafeLong]
- Definition Classes
- SymbolicCRing
- def subs(x: Term, y: Term): ExstInducStrucs
- Definition Classes
- NatRing → ExstInducStrucs
- val succ: Func[Nat, Nat]
- def toString(): String
- Definition Classes
- NatRing → AnyRef → Any
- val two: SafeLong
- Definition Classes
- SymbolicCRing
- val x: Nat
- val zero: Nat
- def ||(that: ExstInducStrucs): OrElse
- Definition Classes
- ExstInducStrucs
- object DIV
- object Induc extends Serializable
- object LEQ
- object Comb
- Definition Classes
- SymbolicCRing
- object LitProd
matching, building for formal product with a literal
matching, building for formal product with a literal
- Definition Classes
- SymbolicCRing
- object Literal extends ScalaSym[LocalTerm, A]
- Definition Classes
- SymbolicCRing
- object LiteralSum
- Definition Classes
- SymbolicCRing
- object LocalTyp extends ScalaTyp[A]
- Definition Classes
- SymbolicCRing
- object PiTerm extends Serializable
- Definition Classes
- SymbolicCRing
- object Reciprocal
- Definition Classes
- SymbolicCRing
- object SigmaTerm extends Serializable
- Definition Classes
- SymbolicCRing
- case object prod extends Func[LocalTerm, Func[LocalTerm, LocalTerm]] with Product with Serializable
- Definition Classes
- SymbolicCRing
- case object sum extends Func[LocalTerm, Func[LocalTerm, LocalTerm]] with Product with Serializable
- Definition Classes
- SymbolicCRing