| Summary: | Production compilers implement optimizing transformation rules for built-in types. What justifies applying these optimizing rules is the axioms that hold for built-in types and the built-in operations supported by these types. Similar axioms also hold for user-defined types and the operations defined on them, and therefore justify a set of optimization rules that may apply to user-defined types. Production compilers, however, do not attempt to construct and apply these optimization rules to user-defined types.
Built-in types together the axioms that apply to them are instances of more general algebraic structures. So are user-defined types and their associated axioms. We use the technique of generic programming, a programming paradigm to design efficient, reusable software libraries, to identify the commonality of classes of types, whether built-in or user-defined, convey the semantics of the classes of types to compilers, design scalable and effective program analysis for them, and eventually apply optimizing rules to the operations on them.
In generic programming, algorithms and data structures are defined in terms of such algebraic structures. The same definitions are reused for many types, both built-in and user-defined. This dissertation applies generic programming to compiler analyses and transformations. Analyses and transformations are specified for general algebraic structures, and they apply to all types, both built-in and primitive types.
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