Automatically Solving Simultaneous Type Equations for Type Difference Transformations That Redesign Code

This paper introduces a generalization of programming data types called Context Qualified Types (or CQ Types for short). CQ Types are a superset of programming language data types. They incorporate design features or contexts that fall outside of the programming data type domain (e.g., a planned program scope). CQ Types are functionally related to other CQ Types (and eventually to conventional data types) such that a differencing operation defined on two related types will produce a program transformation that will convert a computational instance (i.e., code) of the first type into a computational instance of the second type. Large grain abstract relationships between design contexts may be expressed as simultaneous type equations. Solving these equations, given some starting code instances, produces transformations that redesign the code from one design context (e.g., a payload context) to a different design context (e.g., a “hole” within a design framework from a reusable library).