Adequate encodings are a powerful programming tool, which eliminate whole classes of program bugs: they ensure that a program cannot generate ill-formed data, because such data is not part of the representation; and they also ensure that a program is well-defined, meaning that it cannot have different behaviors on different representations of the same piece of data. Unfortunately, it has proven difficult to define adequate encodings of programming languages themselves. Such encodings would be very useful in language processing tools such as interpreters, compilers, model-checking tools, etc., as these systems are often difficult to get correct. The key problem in representing programming languages is in encoding binding constructs; previous approaches have serious limitations in either the operations they allow or the correcness guarantees they make. In this paper, we introduce a new library for Haskell that allows the user to define and use higher-order encodings, a powerful technique for representing bindings. Our library allows straightforward recursion on bindings using pattern-matching, which is not possible in previous approaches. We then demonstrate our library on a medium-sized example, lambda-lifting, showing how our library can be used to make strong correctness guarantees at compile time.

Multi-stage programming (MSP) provides a disciplined approach to run-time code generation. In the purely functional setting, it has been shown how MSP can be used to reduce the overhead of abstractions, allowing clean, maintainable code without paying performance penalties. Unfortunately, MSP is difficult to combine with imperative features, which are prevalent in mainstream languages. The central difficulty is scope extrusion, wherein free variables can inadvertently be moved outside the scopes of their binders. This paper proposes a new approach to combining MSP with imperative features that occupies a "sweet spot" in the design space in terms of how well useful MSP applications can be expressed and how easy it is for programmers to understand. The key insight is that escapes (or "anti-quotes") must be weakly separable from the rest of the code, i.e. the computational effects occurring inside an escape that are visible outside the escape are guaranteed to not contain code. To demonstrate the feasibility of this approach, we formalize a type system based on Lightweight Java which we prove sound, and we also provide an implementation, called Mint, to validate both the expressivity of the type system and the effect of staging on the performance of Java programs.

In this paper a language-based approach to functionally correct imperative programming is proposed. The approach is based on a programming language called RSP1, which combines dependent types, general recursion, and imperative features in a type-safe way, while preserving decidability of type checking. The methodology used is that of internal verification, where programs manipulate programmer-supplied proofs explicitly as data. The fundamental technical idea of RSP1 is to identify problematic operations as impure, and keep them out of dependent types. The resulting language is powerful enough to verify statically non-trivial properties of imperative and functional programs. The paper presents the ideas through the examples of statically verified merge sort, statically verified imperative binary search trees, and statically verified directed acyclic graphs.