15-150: Principles of Functional Programming

Lecture 17: Functors, Parameterized Structures, Type Classes

A functor is a parameterized module that acts as a kind of function (not an ML function with a type, but a mathematical function). A functor takes a structure as argument and returns a new structure as result. Functors greatly facilitate hierarchical organization and code reuse in large programs. In particular, they can enable a clean separation between the details of a particular definition and a higher-level structure, allowing the implementation of "generic" algorithms that are easier to debug and maintain, and that maximize code reuse.

Key Concepts

• Functors
• Parameterized modules
• Substructures
• Code reuse
• Type Classes

The following perspective may be useful in thinking about types in a signature:

• concrete : client and implementation both know what the type is
• abstract : client does not/should not know how the type is implemented -- the details are left up to the implementation -- the client's code must work regardless of the implementation
• parameter : client supplies the type, implementation must work with whatever the client supplies

Sample Code:    using transparent ascription      using opaque ascription

Some Notes on Functors      Some more Notes on Functors

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