18,658 research outputs found
Proving termination of evaluation for System F with control operators
We present new proofs of termination of evaluation in reduction semantics
(i.e., a small-step operational semantics with explicit representation of
evaluation contexts) for System F with control operators. We introduce a
modified version of Girard's proof method based on reducibility candidates,
where the reducibility predicates are defined on values and on evaluation
contexts as prescribed by the reduction semantics format. We address both
abortive control operators (callcc) and delimited-control operators (shift and
reset) for which we introduce novel polymorphic type systems, and we consider
both the call-by-value and call-by-name evaluation strategies.Comment: In Proceedings COS 2013, arXiv:1309.092
Termination of rewriting strategies: a generic approach
We propose a generic termination proof method for rewriting under strategies,
based on an explicit induction on the termination property. Rewriting trees on
ground terms are modeled by proof trees, generated by alternatively applying
narrowing and abstracting steps. The induction principle is applied through the
abstraction mechanism, where terms are replaced by variables representing any
of their normal forms. The induction ordering is not given a priori, but
defined with ordering constraints, incrementally set during the proof.
Abstraction constraints can be used to control the narrowing mechanism, well
known to easily diverge. The generic method is then instantiated for the
innermost, outermost and local strategies.Comment: 49 page
Efficient Solving of Quantified Inequality Constraints over the Real Numbers
Let a quantified inequality constraint over the reals be a formula in the
first-order predicate language over the structure of the real numbers, where
the allowed predicate symbols are and . Solving such constraints is
an undecidable problem when allowing function symbols such or . In
the paper we give an algorithm that terminates with a solution for all, except
for very special, pathological inputs. We ensure the practical efficiency of
this algorithm by employing constraint programming techniques
Efficient CTL Verification via Horn Constraints Solving
The use of temporal logics has long been recognised as a fundamental approach
to the formal specification and verification of reactive systems. In this
paper, we take on the problem of automatically verifying a temporal property,
given by a CTL formula, for a given (possibly infinite-state) program. We
propose a method based on encoding the problem as a set of Horn constraints.
The method takes a program, modeled as a transition system, and a property
given by a CTL formula as input. It first generates a set of forall-exists
quantified Horn constraints and well-foundedness constraints by exploiting the
syntactic structure of the CTL formula. Then, the generated set of constraints
are solved by applying an off-the-shelf Horn constraints solving engine. The
program is said to satisfy the property if and only if the generated set of
constraints has a solution. We demonstrate the practical promises of the method
by applying it on a set of challenging examples. Although our method is based
on a generic Horn constraint solving engine, it is able to outperform
state-of-art methods specialised for CTL verification.Comment: In Proceedings HCVS2016, arXiv:1607.0403
Logical relations for coherence of effect subtyping
A coercion semantics of a programming language with subtyping is typically
defined on typing derivations rather than on typing judgments. To avoid
semantic ambiguity, such a semantics is expected to be coherent, i.e.,
independent of the typing derivation for a given typing judgment. In this
article we present heterogeneous, biorthogonal, step-indexed logical relations
for establishing the coherence of coercion semantics of programming languages
with subtyping. To illustrate the effectiveness of the proof method, we develop
a proof of coherence of a type-directed, selective CPS translation from a typed
call-by-value lambda calculus with delimited continuations and control-effect
subtyping. The article is accompanied by a Coq formalization that relies on a
novel shallow embedding of a logic for reasoning about step-indexing
Invariant Generation through Strategy Iteration in Succinctly Represented Control Flow Graphs
We consider the problem of computing numerical invariants of programs, for
instance bounds on the values of numerical program variables. More
specifically, we study the problem of performing static analysis by abstract
interpretation using template linear constraint domains. Such invariants can be
obtained by Kleene iterations that are, in order to guarantee termination,
accelerated by widening operators. In many cases, however, applying this form
of extrapolation leads to invariants that are weaker than the strongest
inductive invariant that can be expressed within the abstract domain in use.
Another well-known source of imprecision of traditional abstract interpretation
techniques stems from their use of join operators at merge nodes in the control
flow graph. The mentioned weaknesses may prevent these methods from proving
safety properties. The technique we develop in this article addresses both of
these issues: contrary to Kleene iterations accelerated by widening operators,
it is guaranteed to yield the strongest inductive invariant that can be
expressed within the template linear constraint domain in use. It also eschews
join operators by distinguishing all paths of loop-free code segments. Formally
speaking, our technique computes the least fixpoint within a given template
linear constraint domain of a transition relation that is succinctly expressed
as an existentially quantified linear real arithmetic formula. In contrast to
previously published techniques that rely on quantifier elimination, our
algorithm is proved to have optimal complexity: we prove that the decision
problem associated with our fixpoint problem is in the second level of the
polynomial-time hierarchy.Comment: 35 pages, conference version published at ESOP 2011, this version is
a CoRR version of our submission to Logical Methods in Computer Scienc
Faithful (meta-)encodings of programmable strategies into term rewriting systems
Rewriting is a formalism widely used in computer science and mathematical
logic. When using rewriting as a programming or modeling paradigm, the rewrite
rules describe the transformations one wants to operate and rewriting
strategies are used to con- trol their application. The operational semantics
of these strategies are generally accepted and approaches for analyzing the
termination of specific strategies have been studied. We propose in this paper
a generic encoding of classic control and traversal strategies used in rewrite
based languages such as Maude, Stratego and Tom into a plain term rewriting
system. The encoding is proven sound and complete and, as a direct consequence,
estab- lished termination methods used for term rewriting systems can be
applied to analyze the termination of strategy controlled term rewriting
systems. We show that the encoding of strategies into term rewriting systems
can be easily adapted to handle many-sorted signa- tures and we use a
meta-level representation of terms to reduce the size of the encodings. The
corresponding implementation in Tom generates term rewriting systems compatible
with the syntax of termination tools such as AProVE and TTT2, tools which
turned out to be very effective in (dis)proving the termination of the
generated term rewriting systems. The approach can also be seen as a generic
strategy compiler which can be integrated into languages providing pattern
matching primitives; experiments in Tom show that applying our encoding leads
to performances comparable to the native Tom strategies
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