Packages

  • package root
    Definition Classes
    root
  • package provingground

    This is work towards automated theorem proving based on learning, using homotopy type theory (HoTT) as foundations and natural language processing.

    This is work towards automated theorem proving based on learning, using homotopy type theory (HoTT) as foundations and natural language processing.

    The implementation of homotopy type theory is split into:

    • the object HoTT with terms, types, functions and dependent functions, pairs etc
    • the package induction with general inductive types and recursion/induction on these.

    The learning package has the code for learning.

    Scala code, including the spire library, is integrated with homotopy type theory in the scalahott package

    We have implemented a functor based approach to translation in the translation package, used for nlp as well as serialization and parsing.

    The library package is contains basic structures implemented in HoTT.

    Definition Classes
    root
  • package induction

    Much of the richness of HoTT is in the definitions of Inductive types (and their indexed counterparts) and of (dependent) functions on these by recursion and induction These are implemented using several layers of recursive definitions and diagonals (i.e., fixed points).

    Much of the richness of HoTT is in the definitions of Inductive types (and their indexed counterparts) and of (dependent) functions on these by recursion and induction These are implemented using several layers of recursive definitions and diagonals (i.e., fixed points). In HoTT, recursion and induction are applications of (dependent) functions rec_W,X and ind_W, Xs to the definition data.

    It is useful to capture information regarding inductive types and the recursion and induction functions in scala types. Our implementation is designed to do this.

    Inductive Type Definitions

    Inductive types are specified by introduction rules. Each introduction rule is specified in ConstructorShape (without specifying the type) and ConstructorTL including the specific type. The full definition is in ConstructorSeqTL.

    Recursion and Induction functions

    These are defined recursively, first for each introduction rule and then for the inductive type as a whole. A subtlety is that the scala type of the rec_W,X and induc_W, Xs functions depends on the scala type of the codomain X (or family Xs). To make these types visible, some type level calculations using implicits are done, giving traits ConstructorPatternMap and ConstructorSeqMap that have recursive definition of the recursion and induction functions, the former for the case of a single introduction rule. Traits ConstructorSeqMapper and ConstructorPatternMapper provide the lifts.

    Indexed Versions

    There are indexed versions of all these definitions, to work with indexed inductive type families.

    Definition Classes
    provingground
  • package coarse

    an earlier implementation of induction, without clean separation of codomain scala types; use induction instead

    an earlier implementation of induction, without clean separation of codomain scala types; use induction instead

    Definition Classes
    induction
  • BaseConstructorTypes
  • Constructor
  • ConstructorDefn
  • ConstructorPattern
  • ConstructorSeq
  • ConstructorTyp
  • Curry
  • FmlyPtn
  • Implicits
  • IndexedConstructorPatterns
  • InductiveTyp
  • InductiveTypDefinition
  • IterFuncPattern

class IndexedConstructorPatterns[C <: Term with Subs[C], H <: Term with Subs[H], F <: Term with Subs[F]] extends AnyRef

Self Type
IndexedConstructorPatterns[C, H, F]
Linear Supertypes
AnyRef, Any
Type Hierarchy
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Inherited
  1. IndexedConstructorPatterns
  2. AnyRef
  3. 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 IndexedConstructorPatterns(typFmlyPtn: FmlyPtn[H, C, F])

Type Members

  1. case class CnstDepFuncPtn[TT <: Term with Subs[TT], U <: Term with Subs[U], V <: Term with Subs[V], VV <: Term with Subs[VV], W <: Term with Subs[W]](tail: Typ[TT], headfibre: (TT) => iConstructorPattern[U] { ... /* 2 definitions in type refinement */ }) extends RecursiveiConstructorPattern[TT, U, FuncLike[TT, U]] with Product with Serializable
  2. case class CnstFncPtn[TT <: Term with Subs[TT], HC <: Term with Subs[HC]](tail: Typ[TT], head: iConstructorPattern[HC]) extends RecursiveiConstructorPattern[TT, HC, Func[TT, HC]] with Product with Serializable
  3. type Cod = C
  4. type DI = IterDepFunc
  5. case class DepFuncPtn[U <: Term with Subs[U], V <: Term with Subs[V], VV <: Term with Subs[VV], W <: Term with Subs[W], TF <: Term with Subs[TF]](tail: IterFuncPtn[H, C, TF], tailIndex: Ind, index: Ind, headfibre: (TF) => iConstructorPattern[U] { ... /* 2 definitions in type refinement */ }) extends RecursiveiConstructorPattern[TF, U, FuncLike[TF, U]] with Product with Serializable
  6. case class Family(W: F) extends Product with Serializable
  7. case class FuncPtn[TF <: Term with Subs[TF], HC <: Term with Subs[HC]](tail: IterFuncPtn[H, C, TF], tailIndex: Ind, head: iConstructorPattern[HC]) extends RecursiveiConstructorPattern[TF, HC, Func[TF, HC]] with Product with Serializable
  8. type I = IterFunc
  9. type IT = IterTypFunc
  10. type Ind = ArgType
  11. case class PartialiConstructorSeq[FF <: Term with Subs[FF]](head: iConstructorTyp[FF], tail: iConstructorSeq) extends Product with Serializable
  12. sealed trait RecursiveiConstructorPattern[ArgT <: Term with Subs[ArgT], HeadT <: Term with Subs[HeadT], CT <: FuncLike[ArgT, HeadT] with Subs[CT]] extends iConstructorPattern[CT]

    Functional extension of a type pattern

  13. trait iConstructor extends AnyRef

    Constructor for an inductive type, with given scala type and poly-pattern of this type.

    Constructor for an inductive type, with given scala type and poly-pattern of this type.

    abstraction of ConstructorDefn mainly to allow different type parameters.

  14. case class iConstructorDefn[U <: Term with Subs[U]](pattern: iConstructorPattern[U], cons: U, W: F) extends iConstructor with Product with Serializable

    a constructor given by its parameters.

    a constructor given by its parameters.

    U

    scala type of polypattern.

    pattern

    poly-pattern for the constructor.

    cons

    constructor function.

  15. sealed trait iConstructorPattern[Cnstr <: Term with Subs[Cnstr]] extends AnyRef
  16. sealed trait iConstructorSeq extends AnyRef
  17. case class iConstructorTyp[Cnstr <: Term with Subs[Cnstr]](pattern: iConstructorPattern[Cnstr], fmly: FamilyType) extends Product with Serializable

    iConstructor pattern with type, for convenient building.

  18. case class iW(index: Ind) extends iConstructorPattern[H] with Product with Serializable

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 IndexedConstructorPatterns[C, H, F] toany2stringadd[IndexedConstructorPatterns[C, H, F]] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (IndexedConstructorPatterns[C, H, F], B)
    Implicit
    This member is added by an implicit conversion from IndexedConstructorPatterns[C, H, F] toArrowAssoc[IndexedConstructorPatterns[C, H, F]] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  7. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  8. def ensuring(cond: (IndexedConstructorPatterns[C, H, F]) => Boolean, msg: => Any): IndexedConstructorPatterns[C, H, F]
    Implicit
    This member is added by an implicit conversion from IndexedConstructorPatterns[C, H, F] toEnsuring[IndexedConstructorPatterns[C, H, F]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  9. def ensuring(cond: (IndexedConstructorPatterns[C, H, F]) => Boolean): IndexedConstructorPatterns[C, H, F]
    Implicit
    This member is added by an implicit conversion from IndexedConstructorPatterns[C, H, F] toEnsuring[IndexedConstructorPatterns[C, H, F]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  10. def ensuring(cond: Boolean, msg: => Any): IndexedConstructorPatterns[C, H, F]
    Implicit
    This member is added by an implicit conversion from IndexedConstructorPatterns[C, H, F] toEnsuring[IndexedConstructorPatterns[C, H, F]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  11. def ensuring(cond: Boolean): IndexedConstructorPatterns[C, H, F]
    Implicit
    This member is added by an implicit conversion from IndexedConstructorPatterns[C, H, F] toEnsuring[IndexedConstructorPatterns[C, H, F]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  13. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  14. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from IndexedConstructorPatterns[C, H, F] toStringFormat[IndexedConstructorPatterns[C, H, F]] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  15. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  16. def getTotalArg(typ: Typ[Term], fmly: F): ArgType
  17. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  18. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  19. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  20. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  21. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  22. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  23. def toString(): String
    Definition Classes
    AnyRef → Any
  24. def totalArg(typ: Term, fmly: F, accum: Term = Star): Term
  25. val typFmlyPtn: FmlyPtn[H, C, F]
  26. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  27. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  28. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  29. object iConstructor
  30. object iConstructorSeq
  31. object iConstructorTyp extends 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): (IndexedConstructorPatterns[C, H, F], B)
    Implicit
    This member is added by an implicit conversion from IndexedConstructorPatterns[C, H, F] toArrowAssoc[IndexedConstructorPatterns[C, H, F]] 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 AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromIndexedConstructorPatterns[C, H, F] to any2stringadd[IndexedConstructorPatterns[C, H, F]]

Inherited by implicit conversion StringFormat fromIndexedConstructorPatterns[C, H, F] to StringFormat[IndexedConstructorPatterns[C, H, F]]

Inherited by implicit conversion Ensuring fromIndexedConstructorPatterns[C, H, F] to Ensuring[IndexedConstructorPatterns[C, H, F]]

Inherited by implicit conversion ArrowAssoc fromIndexedConstructorPatterns[C, H, F] to ArrowAssoc[IndexedConstructorPatterns[C, H, F]]

Ungrouped