15,266 research outputs found
Theorem proving support in programming language semantics
We describe several views of the semantics of a simple programming language
as formal documents in the calculus of inductive constructions that can be
verified by the Coq proof system. Covered aspects are natural semantics,
denotational semantics, axiomatic semantics, and abstract interpretation.
Descriptions as recursive functions are also provided whenever suitable, thus
yielding a a verification condition generator and a static analyser that can be
run inside the theorem prover for use in reflective proofs. Extraction of an
interpreter from the denotational semantics is also described. All different
aspects are formally proved sound with respect to the natural semantics
specification.Comment: Propos\'e pour publication dans l'ouvrage \`a la m\'emoire de Gilles
Kah
Experimental Evaluation of Formal Software Development Using Dependently Typed Languages
We will evaluate three dependently typed languages,
and their supporting tools and libraries, by implementing the
same tasks in each language. One task will demonstrate the basic
dependent type support of each language, the other task will
show how to do basic imperative programming combined with
theorem proving, to ensure both resource safety and functional
correctness.info:eu-repo/semantics/publishedVersio
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
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
Privatization-Safe Transactional Memories
Transactional memory (TM) facilitates the development of concurrent applications by letting the programmer designate certain code blocks as atomic. Programmers using a TM often would like to access the same data both inside and outside transactions, and would prefer their programs to have a strongly atomic semantics, which allows transactions to be viewed as executing atomically with respect to non-transactional accesses. Since guaranteeing such semantics for arbitrary programs is prohibitively expensive, researchers have suggested guaranteeing it only for certain data-race free (DRF) programs, particularly those that follow the privatization idiom: from some point on, threads agree that a given object can be accessed non-transactionally.
In this paper we show that a variant of Transactional DRF (TDRF) by Dalessandro et al. is appropriate for a class of privatization-safe TMs, which allow using privatization idioms. We prove that, if such a TM satisfies a condition we call privatization-safe opacity and a program using the TM is TDRF under strongly atomic semantics, then the program indeed has such semantics. We also present a method for proving privatization-safe opacity that reduces proving this generalization to proving the usual opacity, and apply the method to a TM based on two-phase locking and a privatization-safe version of TL2. Finally, we establish the inherent cost of privatization-safety: we prove that a TM cannot be progressive and have invisible reads if it guarantees strongly atomic semantics for TDRF programs
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
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