A method and a system for first, expressing relationships between design contexts as a set of simultaneous parameterized type equations and then, automatically solving those type equations to produce type difference transformations that automatically convert code from one design context to a different design context. For example, a set of solution transforms might redesign code from a simple image convolution expression within a specification context to a set of thread based, parallelized expressions of the convolution designed to fit the “holes” within a design framework from a reusable library. The type equations are expressed in terms a generalization of programming data types (called Context Qualified Types or CQ Types) that may have embedded variable parameters. In addition to programming data type information, CQ Types incorporate design features or concepts that fall outside of the programming data type domain (e.g., a planned program scope or a design skeleton).