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This paper introduces ctrees, a monad for modeling nondeterministic, recursive, and impure programs in Coq. Inspired by Xia et al.'s itrees, this novel data structure embeds computations into coinductive trees with three kind of nodes: external events, and two variants of nondeterministic branching. This apparent redundancy allows us to provide shallow embedding of denotational models with internal choice in the style of CCS, while recovering an inductive LTS view of the computation. ctrees inherit a vast collection of bisimulation and refinement tools, with respect to which we establish a rich equational theory. We connect ctrees to the itree infrastructure by showing how a monad morphism embedding the former into the latter permits to use ctrees to implement nondeterministic effects. We demonstrate the utility of ctrees by using them to model concurrency semantics in two case studies: CCS and cooperative multithreading.

Monadic computations built by interpreting, or handling , operations of a free monad are a compelling formalism for modeling language semantics and defining the behaviors of effectful systems. The resulting layered semantics offer the promise of modular reasoning principles based on the equational theory of the underlying monads. However, there are a number of obstacles to using such layered interpreters in practice. With more layers comes more boilerplate and glue code needed to define the monads and interpreters involved. That overhead is compounded by the need to define and justify the relational reasoning principles that characterize the equivalences at each layer. This paper addresses these problems by significantly extending the capabilities of the Coq interaction trees (ITrees) library, which supports layered monadic interpreters. We characterize a rich class of interpretable monads ---obtained by applying monad transformers to ITrees---and show how to generically lift interpreters through them. We also introduce a corresponding framework for relational reasoning about "equivalence of monads up to a relation R". This collection of typeclasses, instances, new reasoning principles, and tactics greatly generalizes the existing theory of the ITree library, eliminating large amounts of unwieldy boilerplate code and dramatically simplifying proofs.

We present the first formal verification of a networked server implemented in C. Interaction trees, a general structure for representing reactive computations, are used to tie together disparate verification and testing tools (Coq, VST, and QuickChick) and to axiomatize the behavior of the operating system on which the server runs (CertiKOS). The main theorem connects a specification of acceptable server behaviors, written in a straightforward "one client at a time" style, with the CompCert semantics of the C program. The variability introduced by low-level buffering of messages and interleaving of multiple TCP connections is captured using network refinement, a variant of observational refinement., 13 pages + references

Bidirectional transformations between different data representations occur frequently in modern software systems. They appear as serializers and deserializers, as database views and view updaters, and more. Manually building bidirectional transformations---by writing two separate functions that are intended to be inverses---is tedious and error prone. A better approach is to use a domain-specific language in which both directions can be written as a single expression. However, these domain-specific languages can be difficult to program in, requiring programmers to manage fiddly details while working in a complex type system. To solve this, we present Optician, a tool for type-directed synthesis of bijective string transformers. The inputs to Optician are two ordinary regular expressions representing two data formats and a few concrete examples for disambiguation. The output is a well-typed program in Boomerang (a bidirectional language based on the theory of lenses). The main technical challenge involves navigating the vast program search space efficiently enough. Unlike most prior work on type-directed synthesis, our system operates in the context of a language with a rich equivalence relation on types (the theory of regular expressions). We synthesize terms of a equivalent language and convert those generated terms into our lens language. We prove the correctness of our synthesis algorithm. We also demonstrate empirically that our new language changes the synthesis problem from one that admits intractable solutions to one that admits highly efficient solutions. We evaluate Optician on a benchmark suite of 39 examples including both microbenchmarks and realistic examples derived from other data management systems including Flash Fill, a tool for synthesizing string transformations in spreadsheets, and Augeas, a tool for bidirectional processing of Linux system configuration files., 127 Pages, Extended Version with Appendix

We introduce our efforts within the project ‘The science of deep specification’ to work out the key formal underpinnings of industrial-scale formal specifications of software and hardware components, anticipating a world where large verified systems are routinely built out of smaller verified components that are also used by many other projects. We identify an important class of specification that has already been used in a few experiments that connect strong component-correctness theorems across the work of different teams. To help popularize the unique advantages of that style, we dub itdeep specification, and we say that it encompasses specifications that arerich,two-sided,formalandlive(terms that we define in the article). Our core team is developing a proof-of-concept system (based on the Coq proof assistant) whose specification and verification work is divided across largely decoupled subteams at our four institutions, encompassing hardware microarchitecture, compilers, operating systems and applications, along with cross-cutting principles and tools for effective specification. We also aim to catalyse interest in the approach, not just by basic researchers but also by users in industry.This article is part of the themed issue ‘Verified trustworthy software systems’.

In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite models, one based on finite sets and the other on finite vector spaces. The first model is shown to be fully complete with respect to the operational semantics of the language, while the second model is not. We then develop an algebraic extension of the finite lambda calculus and study two operational semantics: a call-by-name and a call-by-value. These operational semantics are matched with their corresponding natural denotational semantics based on finite vector spaces. The relationship between the various semantics is analyzed, and several examples based on Church numerals are presented.

This paper presents an embedded security sublanguage for enforcing information-flow policies in the standard Haskell programming language. The sublanguage provides useful information-flow control mechanisms including dynamic security lattices, run-time code privileges and declassification all without modifying the base language. This design avoids the redundant work of producing new languages, lowers the threshold for adopting security-typed languages, and also provides great flexibility and modularity for using security-policy frameworks.The embedded security sublanguage is designed using a standard combinator interface called arrows. Computations constructed in the sublanguage have static and explicit control-flow components, making it possible to implement information-flow control using static-analysis techniques at run time, while providing strong security guarantees. This paper presents a formal proof that our embedded sublanguage provides noninterference, a concrete Haskell implementation and an example application demonstrating the proposed techniques.11This paper is an expanded version of an earlier paper that appeared in IEEE CSFW (Li and Zdancewic, 2006 [4]).

We introduce a Hoare-style logic for probabilistic programs, called VPHL , that has been formally verified in the Coq proof assistant. VPHL features propositional, rather than additive, assertions and a simple set of rules for reasoning about these assertions using the standard axioms of probability theory. VPHL 's assertions are partial correctness assertions , meaning that their conclusions are dependent upon (deterministic) program termination. The underlying simple probabilistic imperative language, PrImp , includes a probabilistic toss operator, probabilistic guards and potentially-non-terminating while loops.

International audience; Necula [2000] and Tristan et al. [2011] established that symbolic execution combined with rewriting is effective in validating the code produced by state-of-the-art compilers applying various optimizations. In the meantime, Tristan and Leroy [2008] used formally-verified symbolic execution to certify the schedules produced by untrusted oracles-optimizing pipeline usage-within the CompCert compiler. Alas, their formally-verified checker had exponential complexity and was thus never integrated into mainline CompCert. Recently, Six et al. [2020] solved this performance issue with formally-verified hash-consing within the symbolic execution. Our paper extends these approaches to superblocks (where instructions move across branches) and enables translation validation of instruction rewritings (changing instructions for "better" ones) modulo register liveness (e.g. with introduction of "fresh" registers): a significant step forward for certifying compilers from symbolic executions.