696 research outputs found
State space c-reductions for concurrent systems in rewriting logic
We present c-reductions, a state space reduction technique.
The rough idea is to exploit some equivalence relation on states (possibly capturing system regularities) that preserves behavioral properties, and explore the induced quotient system. This is done by means of a canonizer
function, which maps each state into a (non necessarily unique) canonical representative of its equivalence class. The approach exploits the expressiveness of rewriting logic and its realization in Maude to enjoy several advantages over similar approaches: exibility and simplicity in
the definition of the reductions (supporting not only traditional symmetry reductions, but also name reuse and name abstraction); reasoning support for checking and proving correctness of the reductions; and automatization
of the reduction infrastructure via Maude's meta-programming
features. The approach has been validated over a set of representative case studies, exhibiting comparable results with respect to other tools
Mechanising syntax with binders in Coq
Mechanising binders in general-purpose proof assistants such as Coq is cumbersome and difficult. Yet binders, substitutions, and instantiation of terms with substitutions are a critical ingredient of many programming languages. Any practicable mechanisation of the meta-theory of the latter hence requires a lean formalisation of the former. We investigate the topic from three angles: First, we realise formal systems with binders based on both pure and scoped de Bruijn algebras together with basic syntactic rewriting lemmas and automation. We automate this process in a compiler called Autosubst; our final tool supports many-sorted, variadic, and modular syntax. Second, we justify our choice of realisation and mechanise a proof of convergence of the sigma calculus, a calculus of explicit substitutions that is complete for equality of the de Bruijn algebra corresponding to the lambda calculus. Third, to demonstrate the practical usefulness of our approach, we provide concise, transparent, and accessible mechanised proofs for a variety of case studies refined to de Bruijn substitutions.Die Mechanisierung von Bindern in universellen Beweisassistenten wie Coq ist arbeitsaufwƤndig und schwierig. Binder, Substitutionen und die Instantiierung von Substitutionen sind jedoch kritischer Bestandteil
vieler Programmiersprachen. Deshalb setzt eine praktikable Mechanisierung der Metatheorie von Programmiersprachen eine elegante Formalisierung von Bindern voraus. Wir nƤhern uns dem Thema aus drei Richtungen an:
Zuerst realisieren wir formale Systeme mit Bindern mit Hilfe von reinen und indizierten de Bruijn Algebren, zusammen mit grundlegenden syntaktischen Gleichungen und Automatisierung. Wir automatisieren diesen Prozess in
einem Kompilierer namens Autosubst. Unser finaler Kompilierer unterstĆ¼tzt Sortenlogik, variadische Syntax und modulare Syntax. Zweitens rechtfertigen wir unsere ReprƤsentation und mechanisieren einen Beweis der Konvergenz
des SP-KalkĆ¼ls, einem KalkĆ¼l expliziter Substitutionen der bezĆ¼glich der Gleichheit der puren de Bruijn Algebra des -KalkĆ¼ls vollstƤndig ist. Drittens entwickeln wir kurze, transparente und leicht zugƤngliche mechanisierte
Beweise fĆ¼r diverse Fallstudien, die wir an de Bruijn Substitutionen angepasst haben. Wir weisen so die praktische Anwendbarkeit unseres Ansatzes nach
Ten virtues of structured graphs
This paper extends the invited talk by the first author about the virtues
of structured graphs. The motivation behind the talk and this paper relies on our
experience on the development of ADR, a formal approach for the design of styleconformant,
reconfigurable software systems. ADR is based on hierarchical graphs
with interfaces and it has been conceived in the attempt of reconciling software architectures
and process calculi by means of graphical methods. We have tried to
write an ADR agnostic paper where we raise some drawbacks of flat, unstructured
graphs for the design and analysis of software systems and we argue that hierarchical,
structured graphs can alleviate such drawbacks
Towards a complete transformational toolkit for compilers
PIM is an equational logic designed to function as a ``transformational toolkit'' for compilers and other programming tools that analyze and manipulate imperative languages.It has been applied to such problems as program slicing, symbolic evaluation, conditional constant propagation, and dependence analysis.PIM consists of the untyped lambda calculus extended with an algebraic data type that characterizes the behavior of lazy stores and generalized conditionals.A graph form of PIM terms is by design closely related to several intermediate representations commonly used in optimizing compilers. In this paper, we show that PIM's core algebraic component, PIM, possesses a complete equational axiomatization (under the assumption of certain reasonable restrictions on term formation). This has the practical consequence of guaranteeing that every semantics-preserving transformation on a program representable in PIM can be derived by application of PIM rules. We systematically derive the complete PIM logic as the culmination of a sequence of increasingly powerful equational systems starting from a straightforward ``interpreter'' for closed PIM terms. This work is an intermediate step in a larger program to develop a set of well-founded tools for manipulation of imperative programs by compilers and other systems that perform program analysis
A complete transformational toolkit for compilers
In an earlier paper, one of the present authors presented a preliminary account of an equational logic called PIM. PIM is intended to function as a 'transformational toolkit' to be used by compilers and analysis tools for imperative languages, and has been applied to such problems as program slicing, symbolic evaluation, conditional constant propagation, and dependence analysis. PIM consists of the untyped lambda calculus extended with an algebraic rewriting system that characterizes the behavior of lazy stores and generalized conditionals. A major question left open in the earlier paper was whether there existed a complete equational axiomatization of PIM's semantics. In this paper, we answer this question in the affirmative for PIM's core algebraic component, PIMt, under the assumption of certain reasonable restrictions on term formation. We systematically derive the complete PIM logic as the culmination of a sequence of increasingly powerful equational systems starting from a straightforward 'interpreter' for closed PIM terms
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