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.
@cite_13: The report gives a complete defining description of the international algorithmic language Algol 60. This is a language suitable for expressing a large class of numerical processes in a form suitably concise for direct automatic translation into the language of programmed automatic computers.
Types were originally invented as simple names for sets of values that form part of a programming language @cite_13 . As programming languages grew more sophisticated in keeping up with the complexity of the problems they were employed to solve, types evolved into more than simple sets of values and became an object of study in and of itself.