Generic Programming of Reusable, High Performance Container Types using Automatic Type Hierarchy Inference and Bidirectional Antichain Typing

Abstract: We introduce a new compile-time notion of type subsumption based on type simulation. We show how to apply this static subsumption relation to support a more intuitive, object oriented approach to generic programming of reusable, high performance container types. As a first step towards an efficient implementation of the resulting type system in a compiler we present a novel algorithm for bidirectional type inference over arbitrary syntax graphs. The algorithm uses the new static type subsumption relation to compress the data that has to be stored for each node in the typeflow graph. During typeflow analysis this means that the set of types for a given node can be symbolically represented using antichains instead of using bitvectors or some other explicit set representation. This results in a typing algorithm that is both flexible and precise and shows good performance on representative instances.