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

Flag-based big-step semantics

Structural operational semantic specifications come in different styles: small-step and big-step. A problem with the big-step style is that specifying divergence and abrupt termination gives rise to annoying duplication. We present a novel approach to representing divergence and abrupt termination in big-step semantics using status flags. This avoids the duplication problem, and uses fewer rules and premises for representing divergence than previous approaches in the literature

Declassification of Faceted Values in JavaScript

This research addresses the issues with protecting sensitive information at the language level using information flow control mechanisms (IFC). Most of the IFC mechanisms face the challenge of releasing sensitive information in a restricted or limited manner. This research uses faceted values, an IFC mechanism that has shown promising flexibility for downgrading the confidential information in a secure manner, also called declassification. In this project, we introduce the concept of first-class labels to simplify the declassification of faceted values. To validate the utility of our approach we show how the combination of faceted values and first-class labels can build various declassification mechanisms

Constraint Generation for the Jeeves Privacy Language

Our goal is to present a completed, semantic formalization of the Jeeves privacy language evaluation engine, based on the original Jeeves constraint semantics defined by Yang et al at POPL12, but sufficiently strong to support a first complete implementation thereof. Specifically, we present and implement a syntactically and semantically completed concrete syntax for Jeeves that meets the example criteria given in the paper. We also present and implement the associated translation to J, but here formulated by a completed and decompositional operational semantic formulation. Finally, we present an enhanced and decompositional, non-substitutional operational semantic formulation and implementation of the J evaluation engine (the dynamic semantics) with privacy constraints. In particular, we show how implementing the constraints can be defined as a monad, and evaluation can be defined as monadic operation on the constraint environment. The implementations are all completed in Haskell, utilizing its almost one-to-one capability to transparently reflect the underlying semantic reasoning when formalized this way. In practice, we have applied the "literate" program facility of Haskell to this report, a feature that enables the source LATEX to also serve as the source code for the implementation (skipping the report-parts as comment regions). The implementation is published as a github project

Determiner spreading as DP-predication

Determiner Spreading (DS) occurs in adjectivally modified nominal phrases comprising more than one definite article, a phenomenon that has received considerable attention and has been extensively described in Greek. This paper discusses the syntactic properties of DS in detail and argues that DS structures are both arguments and predication configurations involving two DPs. This account successfully captures the word-order facts and the distinctive interpretation of DS, while also laying the groundwork towards unifying it with other structures linking two DPs in a predicative relation

Pretty-Big-Step Semantics

International audienceIn spite of the popularity of small-step semantics, big-step semantics remain used by many researchers. However, big-step semantics suffer from a serious duplication problem, which appears as soon as the semantics account for exceptions and/or divergence. In particular, many premises need to be copy-pasted across several evaluation rules. This duplication problem, which is particularly visible when scaling up to full-blown languages, results in formal definitions growing far bigger than necessary. Moreover, it leads to unsatisfactory redundancy in proofs. In this paper, we address the problem by introducing pretty-big-step semantics. Pretty-big-step semantics preserve the spirit of big-step semantics, in the sense that terms are directly related to their results, but they eliminate the duplication associated with big-step semantics

On Computational Small Steps and Big Steps: Refocusing for Outermost Reduction

We study the relationship between small-step semantics, big-step semantics and abstract machines, for programming languages that employ an outermost reduction strategy, i.e., languages where reductions near the root of the abstract syntax tree are performed before reductions near the leaves.In particular, we investigate how Biernacka and Danvy's syntactic correspondence and Reynolds's functional correspondence can be applied to inter-derive semantic specifications for such languages.The main contribution of this dissertation is three-fold:First, we identify that backward overlapping reduction rules in the small-step semantics cause the refocusing step of the syntactic correspondence to be inapplicable.Second, we propose two solutions to overcome this in-applicability: backtracking and rule generalization.Third, we show how these solutions affect the other transformations of the two correspondences.Other contributions include the application of the syntactic and functional correspondences to Boolean normalization.In particular, we show how to systematically derive a spectrum of normalization functions for negational and conjunctive normalization