In type theory, a discipline within mathematical logic, containers are abstractions which permit various "collection types", such as lists and trees, to be represented in a uniform way. A (unary) container is defined by a type of shapes S and a type family of positions P, indexed by S. The extension of a container is a family of dependent pairs consisting of a shape (of type S) and a function from positions of that shape to the element type.
In type theory, a discipline within mathematical logic, containers are abstractions which permit various "collection types", such as lists and trees, to be represented in a uniform way. A (unary) container is defined by a type of shapes S and a type family of positions P, indexed by S. The extension of a container is a family of dependent pairs consisting of a shape (of type S) and a function from positions of that shape to the element type.
Source: Wikipedia "Container (type theory)" · CC BY-SA 4.0
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