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sealed trait ConstructorPatternMap[Cod <: Term with Subs[Cod], ConstructorType <: Term with Subs[ConstructorType], H <: Term with Subs[H], RecDataType <: Term with Subs[RecDataType], InducDataType <: Term with Subs[InducDataType]] extends AnyRef

Introduction rule for an inductive type, as in ConstructorShape with the scala type of the codomain specified; hence the scala type of the recurion and induction types are determined. The definitions of recursion and induction functions for the case matching the introduction rule are the abstract methods recDefCase and inducDefCase.

Cod

the scala type of the codomain.

ConstructorType

the scala type of the introduction rule

H

the scala type of terms of an inductive type that can have this constructor.

RecDataType

type of data for recursive definitions for the case corresponding to this introduction rule.

InducDataType

type of data for inductive definitions for the case corresponding to this introduction rule. this is used indirectly through ConstructorSeqTL

Self Type
ConstructorPatternMap[Cod, ConstructorType, H, RecDataType, InducDataType]
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Abstract Value Members

  1. abstract def codFromData(d: RecDataType): Typ[Cod]
  2. abstract def inducDataTyp(w: Typ[H], xs: Func[H, Typ[Cod]])(cons: ConstructorType): Typ[InducDataType]

    domain containing the induction data for the constructor, i.e., the HoTT type of the induction data.

  3. abstract def inducDefCase(cons: ConstructorType, data: InducDataType, f: => FuncLike[H, Cod]): (H) => Option[Cod]

    given a term, matches to see if this is the image of a given (quasi)-constructor, with this constructor pattern.

    given a term, matches to see if this is the image of a given (quasi)-constructor, with this constructor pattern. optionally returns simplification (if the term matches).

    cons

    constructor, actually quasi-constructor, with which to match.

    data

    definition data for the image of the constructor.

    f

    the function being defined inductively, to be used recursively in definition.

  4. abstract def recDataTyp(w: Typ[H], x: Typ[Cod]): Typ[RecDataType]

    domain containing the recursion data for the constructor, i.e., the HoTT type of recursion data.

  5. abstract def recDefCase(cons: ConstructorType, data: RecDataType, f: => Func[H, Cod]): (H) => Option[Cod]

    given a term, matches to see if this is the image of a given (quasi)-constructor, with this constructor pattern.

    given a term, matches to see if this is the image of a given (quasi)-constructor, with this constructor pattern. optionally returns simplification (if the term matches), determined by the recursion data.

    cons

    constructor, actually quasi-constructor, with which to match.

    data

    definition data for the image of the constructor.

    f

    the function being defined recursively, to be used recursively in definition.

  6. abstract def subs(x: Term, y: Term): ConstructorPatternMap[Cod, ConstructorType, H, RecDataType, InducDataType]
  7. abstract val univLevel: Int