We present an extension of the Hindley-Milner type system that supports a generous class of type constructors called functors, and provide a parametrically polymorphic algorithm for their mapping, i.e. for applying a function to each datum appearing in a value of constructed type. The algorithm comes from shape theory, which provides a uniform method for locating data within a shape. The resulting system is Church-Rosser and strongly normalising, and supports type inference.
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