57,140 research outputs found
Transformations of Logic Programs with Goals as Arguments
We consider a simple extension of logic programming where variables may range
over goals and goals may be arguments of predicates. In this language we can
write logic programs which use goals as data. We give practical evidence that,
by exploiting this capability when transforming programs, we can improve
program efficiency.
We propose a set of program transformation rules which extend the familiar
unfolding and folding rules and allow us to manipulate clauses with goals which
occur as arguments of predicates. In order to prove the correctness of these
transformation rules, we formally define the operational semantics of our
extended logic programming language. This semantics is a simple variant of
LD-resolution. When suitable conditions are satisfied this semantics agrees
with LD-resolution and, thus, the programs written in our extended language can
be run by ordinary Prolog systems.
Our transformation rules are shown to preserve the operational semantics and
termination.Comment: 51 pages. Full version of a paper that will appear in Theory and
Practice of Logic Programming, Cambridge University Press, U
A criterion for separating process calculi
We introduce a new criterion, replacement freeness, to discern the relative
expressiveness of process calculi. Intuitively, a calculus is strongly
replacement free if replacing, within an enclosing context, a process that
cannot perform any visible action by an arbitrary process never inhibits the
capability of the resulting process to perform a visible action. We prove that
there exists no compositional and interaction sensitive encoding of a not
strongly replacement free calculus into any strongly replacement free one. We
then define a weaker version of replacement freeness, by only considering
replacement of closed processes, and prove that, if we additionally require the
encoding to preserve name independence, it is not even possible to encode a non
replacement free calculus into a weakly replacement free one. As a consequence
of our encodability results, we get that many calculi equipped with priority
are not replacement free and hence are not encodable into mainstream calculi
like CCS and pi-calculus, that instead are strongly replacement free. We also
prove that variants of pi-calculus with match among names, pattern matching or
polyadic synchronization are only weakly replacement free, hence they are
separated both from process calculi with priority and from mainstream calculi.Comment: In Proceedings EXPRESS'10, arXiv:1011.601
Reasoning on Schemata of Formulae
A logic is presented for reasoning on iterated sequences of formulae over
some given base language. The considered sequences, or "schemata", are defined
inductively, on some algebraic structure (for instance the natural numbers, the
lists, the trees etc.). A proof procedure is proposed to relate the
satisfiability problem for schemata to that of finite disjunctions of base
formulae. It is shown that this procedure is sound, complete and terminating,
hence the basic computational properties of the base language can be carried
over to schemata
Well-definedness of Streams by Transformation and Termination
Streams are infinite sequences over a given data type. A stream specification
is a set of equations intended to define a stream. We propose a transformation
from such a stream specification to a term rewriting system (TRS) in such a way
that termination of the resulting TRS implies that the stream specification is
well-defined, that is, admits a unique solution. As a consequence, proving
well-definedness of several interesting stream specifications can be done fully
automatically using present powerful tools for proving TRS termination. In
order to increase the power of this approach, we investigate transformations
that preserve semantics and well-definedness. We give examples for which the
above mentioned technique applies for the ransformed specification while it
fails for the original one
Theories of termination of the contract of employment: the Scylla and Charybidis
The principles governing the termination of a contract of employment are problematic. Decisions both in Australia and England continue to reveal an unresolved dilemma between the 'automatic' and 'elective' theories of termination, the outcome of which can have important practical consequences. It is argued that the courts are not consistent in their application of these theories, and that each lacks coherence. For example, neither properly accommodates the principle that a readiness and willingness to work provides consideration for wages. Accordingly, the general rule that a wrongfully dismissed employee is only entitled to damages representing the value of wages not earned during the contractual notice period needs to be reconsidered. This article proposes that an exclusive reliance on either theory will be misconceived. It is further argued that terms of the contract end according to different rules depending on their nature, and that these rules recognise a role for public policy
Modularity of Convergence and Strong Convergence in Infinitary Rewriting
Properties of Term Rewriting Systems are called modular iff they are
preserved under (and reflected by) disjoint union, i.e. when combining two Term
Rewriting Systems with disjoint signatures. Convergence is the property of
Infinitary Term Rewriting Systems that all reduction sequences converge to a
limit. Strong Convergence requires in addition that redex positions in a
reduction sequence move arbitrarily deep. In this paper it is shown that both
Convergence and Strong Convergence are modular properties of non-collapsing
Infinitary Term Rewriting Systems, provided (for convergence) that the term
metrics are granular. This generalises known modularity results beyond metric
\infty
Rewriting and Well-Definedness within a Proof System
Term rewriting has a significant presence in various areas, not least in
automated theorem proving where it is used as a proof technique. Many theorem
provers employ specialised proof tactics for rewriting. This results in an
interleaving between deduction and computation (i.e., rewriting) steps. If the
logic of reasoning supports partial functions, it is necessary that rewriting
copes with potentially ill-defined terms. In this paper, we provide a basis for
integrating rewriting with a deductive proof system that deals with
well-definedness. The definitions and theorems presented in this paper are the
theoretical foundations for an extensible rewriting-based prover that has been
implemented for the set theoretical formalism Event-B.Comment: In Proceedings PAR 2010, arXiv:1012.455
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