15-851 Project Report: Refinement Type Inference using Abstract Interpretation

Typing checking is an efficient way to catch simple errors. Refinement types [3] are invented to take advantage of type systems in specifying more program properties and verifying them through type checking. In [3, 2], a method to use rectype declaration has been proposed to specify regular tree grammar based invariants. Datatype lattices are then derived from rectype declarations. An algorithm based on abstract interpretation [1] is used to infer refinement types. Abstract interpretation [1] is a program analysis techniques. Abstract domain is defined for a program, and the program’s execution on the concrete domain is approximated by operations on this abstract domain. Most often, results on the abstract domain are safe simulations of the actual execution. In this project, two refinement type inference algorithms based on abstract interpretation are described. one without intersection types and one with principal intersection types. In Section 2, a dialect of Mini-ML with type annotations to function arguments is defined, which is our source language. In Section 3, a simple refinement type inference algorithm is outlined, where there are no intersection types, thus expressions do not have principal types. In Section 4, a full-blown refinement type inference algorithm as is described in [2] is outlined. Experimental comparisons of these two algorithms are discussed in Section 5. Section 6 concludes the report with some future work.