The central theme of this book is that the structure of a computation on a data type reflects the structure of the data type. This is true in two senses:

• Any homomorphism on a data type is intimately related to the algebraic structure of its codomain; which can be exploited in the search for programs, and

• The evaluation of any homomorphism can follow the structure of its argument; which can be exploited in computing programs.

Structured data types and the homomorphisms on them, called catamorphisms, form a programming model for parallel computation that has many attractive properties.

There is a desperate need for a model of parallel computation that can decouple software from hardware. This decoupling occurs in two dimensions: decoupling the rate of change of parallel hardware (high) from that of parallel software (low, if it is to be economic); and decoupling the variety of parallel hardware from a single, architecture-independent version of the software.

Such a model is hard to find because the requirements are mutually in tension. A model must be opaque enough to hide target architectures and the complexity of parallel execution, while providing a semantic framework that is rich enough to allow software development. At the same time, it must be partly translucent so that the costs of programs can be visible during development, to allow intelligent choices between algorithms.