Functional Big-step Semantics

When doing an interactive proof about a piece of software, it is important that the underlying programming language’s semantics does not make the proof unnecessarily difficult or unwieldy. Both smallstep and big-step semantics are commonly used, and the latter is typically given by an inductively defined relation. In this paper, we consider an alternative: using a recursive function akin to an interpreter for the language. The advantages include a better induction theorem, less duplication, accessibility to ordinary functional programmers, and the ease of doing symbolic simulation in proofs via rewriting. We believe that this style of semantics is well suited for compiler verification, including proofs of divergence preservation. We do not claim the invention of this style of semantics: our contribution here is to clarify its value, and to explain how it supports several language features that might appear to require a relational or small-step approach. We illustrate the technique on a simple imperative language with C-like for-loops and a break statement, and compare it to a variety of other approaches. We also provide ML and lambda-calculus based examples to illustrate its generality

Synthesis of Recursive ADT Transformations from Reusable Templates

Recent work has proposed a promising approach to improving scalability of program synthesis by allowing the user to supply a syntactic template that constrains the space of potential programs. Unfortunately, creating templates often requires nontrivial effort from the user, which impedes the usability of the synthesizer. We present a solution to this problem in the context of recursive transformations on algebraic data-types. Our approach relies on polymorphic synthesis constructs: a small but powerful extension to the language of syntactic templates, which makes it possible to define a program space in a concise and highly reusable manner, while at the same time retains the scalability benefits of conventional templates. This approach enables end-users to reuse predefined templates from a library for a wide variety of problems with little effort. The paper also describes a novel optimization that further improves the performance and scalability of the system. We evaluated the approach on a set of benchmarks that most notably includes desugaring functions for lambda calculus, which force the synthesizer to discover Church encodings for pairs and boolean operations

Shared-Environment Call-by-Need

Call-by-need semantics formalize the wisdom that work should be done at most once. It frees programmers to focus more on the correctness of their code, and less on the operational details. Because of this property, programmers of lazy functional languages rely heavily on their compiler to both preserve correctness and generate high-performance code for high level abstractions. In this dissertation I present a novel technique for compiling call-by-need semantics by using shared environments to share results of computation. I show how the approach enables a compiler that generates high-performance code, while staying simple enough to lend itself to formal reasoning. The dissertation is divided into three main contributions. First, I present an abstract machine, the \ce machine, which formalizes the approach. Second, I show that it can be implemented as a native code compiler with encouraging performance results. Finally, I present a verified compiler, implemented in the Coq proof assistant, demonstrating how the simplicity of the approach enables formal verification