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IE<T>

As explained in Fabulous Adventures in Data Structures and Algorithms

IE<T> is a simplified generic interface whose type parameter T occurs only in output positions.

IE<T> is a simplified generic interface for traversing values. It exposes T only as the readable Current result, so the type parameter occupies an output position. section 7.2

abstract class Animal : Object {}
class Giraffe : Animal {}
class Tiger : Animal {}

These classes establish the assignment-compatibility hierarchy: Giraffe and Tiger both relate to Animal and Object, but not to each other. section 7.2

interface IE<T> 
{ 
    T Current { get; } 
    bool MoveNext(); 
}

The interface combines a Current result of type T with MoveNext, making its producer-like shape explicit. section 7.2

Covariant assignment

Without covariance, assigning IE<Giraffe> to IE<Animal> is rejected. Marking the interface as IE<out T> makes that assignment valid because consumers receive values but do not supply T values. section 7.2

interface IE<out T> 
{ 
    T Current { get; } 
    bool MoveNext(); 
}

The out modifier records the variance rule directly in the interface declaration. section 7.2

Mapping every type T to IE<T> preserves the assignment structure, suggesting a covariant endofunctor. Making that construction an endofunctor requires infinitely many nested constructed types. section 7.2

How Fabulous Adventures in Data Structures and Algorithms covers it

How deep it goes
Develops the interface, variance rule, type mapping, and infinite nesting, but stops short of broader implementation details.
Examples
Uses Animal, Giraffe, and Tiger types plus assignments between IE<Giraffe> and IE<Animal>.
What it assumes
Assumes familiarity with C# generics, interfaces, inheritance, and assignment compatibility; introduces the category-theoretic endofunctor connection.
What you can do after
Evaluate covariance by checking whether a generic type parameter appears only in output positions.
How it connects
Connects generic interfaces with covariance, assignment compatibility, posetal categories, and endofunctors.

This explainer was generated by Manning's knowledge graph from the text of Fabulous Adventures in Data Structures and Algorithms. The section links point to the parts of the book it draws on.