Gradual refinement: blending pattern matching with data abstraction

TL;DR: This work proposes an approach to abstract datatypes based on a right-invertible language RINV--every function has a right (or pre-) inverse, and shows how this new design is able to permit a smooth incremental transition from programs with algebraic datatype and pattern matching, to ones with proper encapsulation, while maintaining simple and sound reasoning.

Abstract: Pattern matching is advantageous for understanding and reasoning about function definitions, but it tends to tightly couple the interface and implementation of a datatype. Significant effort has been invested in tackling this loss of modularity; however, decoupling patterns from concrete representations while maintaining soundness of reasoning has been a challenge. Inspired by the development of invertible programming, we propose an approach to abstract datatypes based on a right-invertible language RINV--every function has a right (or pre-) inverse. We show how this new design is able to permit a smooth incremental transition from programs with algebraic datatypes and pattern matching, to ones with proper encapsulation (implemented as abstract datatypes), while maintaining simple and sound reasoning.