TRX: A Formally Verified Parser Interpreter

Parsing is an important problem in computer science and yet surprisingly little attention has been devoted to its formal verification. In this paper, we present TRX: a parser interpreter formally developed in the proof assistant Coq, capable of producing formally correct parsers. We are using parsing expression grammars (PEGs), a formalism essentially representing recursive descent parsing, which we consider an attractive alternative to context-free grammars (CFGs). From this formalization we can extract a parser for an arbitrary PEG grammar with the warranty of total correctness, i.e., the resulting parser is terminating and correct with respect to its grammar and the semantics of PEGs; both properties formally proven in Coq.Comment: 26 pages, LMC

Action semantics in retrospect

This paper is a themed account of the action semantics project, which Peter Mosses has led since the 1980s. It explains his motivations for developing action semantics, the inspirations behind its design, and the foundations of action semantics based on unified algebras. It goes on to outline some applications of action semantics to describe real programming languages, and some efforts to implement programming languages using action semantics directed compiler generation. It concludes by outlining more recent developments and reflecting on the success of the action semantics project

Meta-F*: Proof Automation with SMT, Tactics, and Metaprograms

We introduce Meta-F*, a tactics and metaprogramming framework for the F* program verifier. The main novelty of Meta-F* is allowing the use of tactics and metaprogramming to discharge assertions not solvable by SMT, or to just simplify them into well-behaved SMT fragments. Plus, Meta-F* can be used to generate verified code automatically. Meta-F* is implemented as an F* effect, which, given the powerful effect system of F*, heavily increases code reuse and even enables the lightweight verification of metaprograms. Metaprograms can be either interpreted, or compiled to efficient native code that can be dynamically loaded into the F* type-checker and can interoperate with interpreted code. Evaluation on realistic case studies shows that Meta-F* provides substantial gains in proof development, efficiency, and robustness.Comment: Full version of ESOP'19 pape

Memoizing a monadic mixin DSL

Modular extensibility is a highly desirable property of a domain-specific language (DSL): the ability to add new features without affecting the implementation of existing features. Functional mixins (also known as open recursion) are very suitable for this purpose. We study the use of mixins in Haskell for a modular DSL for search heuristics used in systematic solvers for combinatorial problems, that generate optimized C++ code from a high-level specification. We show how to apply memoization techniques to tackle performance issues and code explosion due to the high recursion inherent to the semantics of combinatorial search. As such heuristics are conventionally implemented as highly entangled imperative algorithms, our Haskell mixins are monadic. Memoization of monadic components causes further complications for us to deal with

Multi-dimensional Type Theory: Rules, Categories, and Combinators for Syntax and Semantics

We investigate the possibility of modelling the syntax and semantics of natural language by constraints, or rules, imposed by the multi-dimensional type theory Nabla. The only multiplicity we explicitly consider is two, namely one dimension for the syntax and one dimension for the semantics, but the general perspective is important. For example, issues of pragmatics could be handled as additional dimensions. One of the main problems addressed is the rather complicated repertoire of operations that exists besides the notion of categories in traditional Montague grammar. For the syntax we use a categorial grammar along the lines of Lambek. For the semantics we use so-called lexical and logical combinators inspired by work in natural logic. Nabla provides a concise interpretation and a sequent calculus as the basis for implementations.Comment: 20 page