Executable Refinement Types

This dissertation introduces executable refinement types, which refine structural types by semi-decidable predicates, and establishes their metatheory and accompanying implementation techniques. These results are useful for undecidable type systems in general. Particular contributions include: (1) Type soundness and a logical relation for extensional equivalence for executable refinement types (though type checking is undecidable); (2) hybrid type checking for executable refinement types, which blends static and dynamic checks in a novel way, in some sense performing better statically than any decidable approximation; (3) a type reconstruction algorithm - reconstruction is decidable even though type checking is not, when suitably redefined to apply to undecidable type systems; (4) a novel use of existential types with dependent types to ensure that the language of logical formulae is closed under type checking (5) a prototype implementation, Sage, of executable refinement types such that all dynamic errors are communicated back to the compiler and are thenceforth static errors.Comment: Ph.D. dissertation. Accepted by the University of California, Santa Cruz, in March 2014. 278 pages (295 including frontmatter

A verification framework suitable for proving large language translations

Previously, researchers established some frameworks, such as Morpheus, to specify a compiler translation in a small language and prove the semantic preservation property of the translation in the language under the assumption of sequential consistency. Based on the Morpheus specification language, we extend the verification framework to prove the compiler translation semantic preservation property in a large real-world programming language with a real-world weak concurrency model. The framework combines four different pieces. First, we specify a complete semantics of the K framework and a translation from K to Isabelle as our basis for defining language specifications and proving properties about the specifications. Second, we define a complete operational semantics of LLVM in K, named K-LLVM, including the specifications of all instructions and intrinsic functions in LLVM, as well as the concurrency model of LLVM. Third, to verify the correctness of the K-LLVM operational model, we create an axiomatic model, named Hybrid Axiomatic Timed Relaxed Concurrency Model (HATRMM). The creation of HATRMM is to bridge the traditional C++ candidate execution models and the K-LLVM operational concurrency model. Finally, to enhance our framework to prove the semantic preservation property in a relaxed memory model, we define a new simulation framework, named Per Location Simulation (PLS). PLS is suitable for proving semantic preservation property in a relaxed memory model