196 research outputs found
POPLMark reloaded: Mechanizing proofs by logical relations
We propose a new collection of benchmark problems in mechanizing the metatheory of programming languages, in order to compare and push the state of the art of proof assistants. In particular, we focus on proofs using logical relations (LRs) and propose establishing strong normalization of a simply typed calculus with a proof by Kripke-style LRs as a benchmark. We give a modern view of this well-understood problem by formulating our LR on well-typed terms. Using this case study, we share some of the lessons learned tackling this problem in different dependently typed proof environments. In particular, we consider the mechanization in Beluga, a proof environment that supports higher-order abstract syntax encodings and contrast it to the development and strategies used in general-purpose proof assistants such as Coq and Agda. The goal of this paper is to engage the community in discussions on what support in proof environments is needed to truly bring mechanized metatheory to the masses and engage said community in the crafting of future benchmarks
αCheck: a mechanized metatheory model-checker
The problem of mechanically formalizing and proving metatheoretic properties
of programming language calculi, type systems, operational semantics, and
related formal systems has received considerable attention recently. However,
the dual problem of searching for errors in such formalizations has attracted
comparatively little attention. In this article, we present Check, a
bounded model-checker for metatheoretic properties of formal systems specified
using nominal logic. In contrast to the current state of the art for metatheory
verification, our approach is fully automatic, does not require expertise in
theorem proving on the part of the user, and produces counterexamples in the
case that a flaw is detected. We present two implementations of this technique,
one based on negation-as-failure and one based on negation elimination, along
with experimental results showing that these techniques are fast enough to be
used interactively to debug systems as they are developed.Comment: Under consideration for publication in Theory and Practice of Logic
Programming (TPLP
Mechanized semantics
The goal of this lecture is to show how modern theorem provers---in this
case, the Coq proof assistant---can be used to mechanize the specification of
programming languages and their semantics, and to reason over individual
programs and over generic program transformations, as typically found in
compilers. The topics covered include: operational semantics (small-step,
big-step, definitional interpreters); a simple form of denotational semantics;
axiomatic semantics and Hoare logic; generation of verification conditions,
with application to program proof; compilation to virtual machine code and its
proof of correctness; an example of an optimizing program transformation (dead
code elimination) and its proof of correctness
Formal Component-Based Semantics
One of the proposed solutions for improving the scalability of semantics of
programming languages is Component-Based Semantics, introduced by Peter D.
Mosses. It is expected that this framework can also be used effectively for
modular meta theoretic reasoning. This paper presents a formalization of
Component-Based Semantics in the theorem prover Coq. It is based on Modular
SOS, a variant of SOS, and makes essential use of dependent types, while
profiting from type classes. This formalization constitutes a contribution
towards modular meta theoretic formalizations in theorem provers. As a small
example, a modular proof of determinism of a mini-language is developed.Comment: In Proceedings SOS 2011, arXiv:1108.279
Q# as a Quantum Algorithmic Language
Q# is a standalone domain-specific programming language from Microsoft for
writing and running quantum programs. Like most industrial languages, it was
designed without a formal specification, which can naturally lead to ambiguity
in its interpretation. We aim to provide a formal language definition for Q#,
placing the language on a solid mathematical foundation and enabling further
evolution of its design and type system. This paper presents -Q#, an
idealized version of Q# that illustrates how we may view Q# as a quantum Algol
(algorithmic language). We show the safety properties enforced by
-Q#'s type system and present its equational semantics based on a
fully complete algebraic theory by Staton.Comment: In Proceedings QPL 2022, arXiv:2311.0837
Mechanized semantics for the Clight subset of the C language
This article presents the formal semantics of a large subset of the C
language called Clight. Clight includes pointer arithmetic, "struct" and
"union" types, C loops and structured "switch" statements. Clight is the source
language of the CompCert verified compiler. The formal semantics of Clight is a
big-step operational semantics that observes both terminating and diverging
executions and produces traces of input/output events. The formal semantics of
Clight is mechanized using the Coq proof assistant. In addition to the
semantics of Clight, this article describes its integration in the CompCert
verified compiler and several ways by which the semantics was validated.Comment: Journal of Automated Reasoning (2009
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