Ur/Web: A Simple Model for Programming the Web

The World Wide Web has evolved gradually from a document delivery platform to an architecture for distributed programming. This largely unplanned evolution is apparent in the set of interconnected languages and protocols that any Web application must manage. This paper presents Ur/Web, a domain-specific, statically typed functional programming language with a much simpler model for programming modern Web applications. Ur/Web's model is unified, where programs in a single programming language are compiled to other "Web standards" languages as needed; modular, supporting novel kinds of encapsulation of Web-specific state; and exposes simple concurrency, where programmers can reason about distributed, multithreaded applications via a mix of transactions and cooperative preemption. We give a tutorial introduction to the main features of Ur/Web, formalize the basic programming model with operational semantics, and discuss the language implementation and the production Web applications that use it.National Science Foundation (U.S.) (Grant CCF-1217501

Compositional Computational Reflection

Current work on computational reflection is single-minded; each reflective procedure is written with a specific application or scope in mind. Composition of these reflective procedures is done by a proof- generating tactic language such as Ltac. This composition, however, comes at the cost of both larger proof terms and redundant preprocessing. In this work, we propose a methodology for writing composable reflective procedures that solve many small tasks in a single invocation. The key technical insights are techniques for reasoning semantically about extensible syntax in intensional type theory. Our techniques make it possible to compose sound procedures and write generic procedures parametrized by lemmas mimicking Coq’s support for hint databases.Engineering and Applied Science

Accelerating Verified-Compiler Development with a Verified Rewriting Engine

Compilers are a prime target for formal verification, since compiler bugs invalidate higher-level correctness guarantees, but compiler changes may become more labor-intensive to implement, if they must come with proof patches. One appealing approach is to present compilers as sets of algebraic rewrite rules, which a generic engine can apply efficiently. Now each rewrite rule can be proved separately, with no need to revisit past proofs for other parts of the compiler. We present the first realization of this idea, in the form of a framework for the Coq proof assistant. Our new Coq command takes normal proved theorems and combines them automatically into fast compilers with proofs. We applied our framework to improve the Fiat Cryptography toolchain for generating cryptographic arithmetic, producing an extracted command-line compiler that is about 1000$\times$ faster while actually featuring simpler compiler-specific proofs.Comment: 13th International Conference on Interactive Theorem Proving (ITP 2022

Fiat: Deductive Synthesis of Abstract Data Types in a Proof Assistant

We present Fiat, a library for the Coq proof assistant supporting refinement of declarative specifications into efficient functional programs with a high degree of automation. Each refinement process leaves a proof trail, checkable by the normal Coq kernel, justifying its soundness. We focus on the synthesis of abstract data types that package methods with private data. We demonstrate the utility of our framework by applying it to the synthesis of query structures--abstract data types with SQL-like query and insert operations. Fiat includes a library for writing specifications of query structures in SQL-inspired notation, expressing operations over relations (tables) in terms of mathematical sets. This library includes a suite of tactics for automating the refinement of specifications into efficient, correct- by-construction OCaml code. Using these tactics, a programmer can generate such an implementation completely automatically by only specifying the equivalent of SQL indexes, data structures capturing useful views of the abstract data. Throughout we speculate on the new programming modularity possibilities enabled by an automated refinement system with proved-correct rules. “Every block of stone has a statue inside it and it is the task of the sculptor to discover it.”--MichelangeloNational Science Foundation (U.S.) (NSF grant CCF-1253229)United States. Defense Advanced Research Projects Agency (DARPA, agreement number FA8750-12-2- 0293

The End of History? Using a Proof Assistant to Replace Language Design with Library Design

Functionality of software systems has exploded in part because of advances in programming-language support for packaging reusable functionality as libraries. Developers benefit from the uniformity that comes of exposing many interfaces in the same language, as opposed to stringing together hodgepodges of command-line tools. Domain-specific languages may be viewed as an evolution of the power of reusable interfaces, when those interfaces become so flexible as to deserve to be called programming languages. However, common approaches to domain-specific languages give up many of the hard-won advantages of library-building in a rich common language, and even the traditional approach poses significant challenges in learning new APIs. We suggest that instead of continuing to develop new domain-specific languages, our community should embrace library-based ecosystems within very expressive languages that mix programming and theorem proving. Our prototype framework Fiat, a library for the Coq proof assistant, turns languages into easily comprehensible libraries via the key idea of modularizing functionality and performance away from each other, the former via macros that desugar into higher-order logic and the latter via optimization scripts that derive efficient code from logical programs

Effective Interactive Proofs for Higher-Order Imperative Programs

We present a new approach for constructing and verifying higher-order, imperative programs using the Coq proof assistant. We build on the past work on the Ynot system, which is based on Hoare Type Theory. That original system was a proof of concept, where every program verification was accomplished via laborious manual proofs, with much code devoted to uninteresting low-level details. In this paper, we present a re-implementation of Ynot which makes it possible to implement fully-verified, higher-order imperative programs with reasonable proof burden. At the same time, our new system is implemented entirely in Coq source files, showcasing the versatility of that proof assistant as a platform for research on language design and verification. Both versions of the system have been evaluated with case studies in the verification of imperative data structures, such as hash tables with higher-order iterators. The verification burden in our new system is reduced by at least an order of magnitude compared to the old system, by replacing manual proof with automation. The core of the automation is a simplification procedure for implications in higher-order separation logic, with hooks that allow programmers to add domain-specific simplification rules. We argue for the effectiveness of our infrastructure by verifying a number of data structures and a packrat parser, and we compare to similar efforts within other projects. Compared to competing approaches to data structure verification, our system includes much less code that must be trusted; namely, about a hundred lines of Coq code defining a program logic. All of our theorems and decision procedures have or build machine-checkable correctness proofs from first principles, removing opportunities for tool bugs to create faulty verifications.Engineering and Applied Science

Omnisemantics: Smooth Handling of Nondeterminism

This paper gives an in-depth presentation of the omni-big-step and omni-small-step styles of semantic judgments. These styles describe operational semantics by relating starting states to sets of outcomes rather than to individual outcomes. A single derivation of these semantics for a particular starting state and program describes all possible nondeterministic executions (hence the name "omni"), whereas in traditional small-step and big-step semantics, each derivation only talks about one single execution. This restructuring allows for straightforward modeling of languages featuring both nondeterminism and undefined behavior. Specifically, omnisemantics inherently assert safety, i.e. they guarantee that none of the execution branches gets stuck, while traditional semantics need either a separate judgment or additional error markers to specify safety in the presence of nondeterminism.Omnisemantics can be understood as an inductively defined weakest-precondition semantics (or more generally, predicate-transformer semantics) that does not involve invariants for loops and recursion, but instead uses unrolling rules like in traditional small-step and big-step semantics. Omnisemantics have already been used in the past, but we believe that it has been under-appreciated and that it deserves a well-motivated, extensive and pedagogical presentation of its benefits. We also explore several novel aspects associated with these semantics, in particular their use in type-soundness proofs for lambda calculi, partial-correctness reasoning, and forward proofs of compiler correctness for terminating but potentially nondeterministic programs being compiled to nondeterministic target languages. All results in this paper are formalized in Coq

C4: Verified Transactional Objects

A framework for Verified Transactional Objects in Coq. - Formalization of concurrent objects, linearizability, strict serializability, and associated proof techniques. - Verified linearizable concurrent hash map - Verified strictly serializable TML - Verified strictly serializable transaction-predicated ma