10.1184/R1/6603224.v1 Yitzhak Mandelbaum Yitzhak Mandelbaum David Walker David Walker Robert Harper Robert Harper An Effective Theory of Type Refinements Carnegie Mellon University 1986 computer sciences 1986-01-01 00:00:00 Journal contribution https://kilthub.cmu.edu/articles/journal_contribution/An_Effective_Theory_of_Type_Refinements/6603224 We develop an explicit two level system that allows programmers to reason about the behavior of effectful programs. The first level is an ordinary ML-style type system, which confers standard properties on program behavior. The second level is a conservative extension of the first that uses a logic of type refinements to check more precise properties of program behavior. Our logic is a fragment of intuitionistic linear logic, which gives programmers the ability to reason locally about changes of program state. We provide a generic resource semantics for our logic as well as a sound, decidable, syntactic refinement-checking system. We also prove that refinements give rise to an optimization principle for programs. Finally, we illustrate the power of our system through a number of examples.