1,708 research outputs found
Reversible Computation in Term Rewriting
Essentially, in a reversible programming language, for each forward
computation from state to state , there exists a constructive method to
go backwards from state to state . Besides its theoretical interest,
reversible computation is a fundamental concept which is relevant in many
different areas like cellular automata, bidirectional program transformation,
or quantum computing, to name a few.
In this work, we focus on term rewriting, a computation model that underlies
most rule-based programming languages. In general, term rewriting is not
reversible, even for injective functions; namely, given a rewrite step , we do not always have a decidable method to get from
. Here, we introduce a conservative extension of term rewriting that
becomes reversible. Furthermore, we also define two transformations,
injectivization and inversion, to make a rewrite system reversible using
standard term rewriting. We illustrate the usefulness of our transformations in
the context of bidirectional program transformation.Comment: To appear in the Journal of Logical and Algebraic Methods in
Programmin
Soundness of Unravelings for Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity
Unravelings are transformations from a conditional term rewriting system
(CTRS, for short) over an original signature into an unconditional term
rewriting systems (TRS, for short) over an extended signature. They are not
sound w.r.t. reduction for every CTRS, while they are complete w.r.t.
reduction. Here, soundness w.r.t. reduction means that every reduction sequence
of the corresponding unraveled TRS, of which the initial and end terms are over
the original signature, can be simulated by the reduction of the original CTRS.
In this paper, we show that an optimized variant of Ohlebusch's unraveling for
a deterministic CTRS is sound w.r.t. reduction if the corresponding unraveled
TRS is left-linear or both right-linear and non-erasing. We also show that
soundness of the variant implies that of Ohlebusch's unraveling. Finally, we
show that soundness of Ohlebusch's unraveling is the weakest in soundness of
the other unravelings and a transformation, proposed by Serbanuta and Rosu, for
(normal) deterministic CTRSs, i.e., soundness of them respectively implies that
of Ohlebusch's unraveling.Comment: 49 pages, 1 table, publication in Special Issue: Selected papers of
the "22nd International Conference on Rewriting Techniques and Applications
(RTA'11)
Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems
Transforming conditional term rewrite systems (CTRSs) into unconditional systems (TRSs) is a common approach to analyze properties of CTRSs via the simpler framework of unconditional rewriting. In the past many different transformations have been introduced for this purpose. One class of transformations, so-called unravelings, have been analyzed extensively in the past.
In this paper we provide an overview on another class of transformations that we call structure-preserving transformations. In these transformations the structure of the conditional rule, in particular their left-hand side is preserved in contrast to unravelings. We provide an overview of transformations of this type and define a new transformation that improves previous approaches
Translating logic programs into conditional rewriting systems
In this paper a translation from a subclass of logic programs consisting of the simply moded logic programs into rewriting systems is defined. In these rewriting systems conditions and explicit substitutions may be present. We argue that our translation is more natural than previously studied ones and establish a result showing its correctness
Conditional Complexity
We propose a notion of complexity for oriented conditional term rewrite systems. This notion is realistic in the sense that it measures not only successful computations but also partial computations that result in a failed rule application. A transformation to unconditional context-sensitive rewrite systems is
presented which reflects this complexity notion, as well as a technique to derive runtime and derivational complexity bounds for the latter
Soundness of Unravelings for Deterministic Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity
Unravelings are transformations from a conditional term rewriting
system (CTRS, for short) over an original signature into an
unconditional term rewriting systems (TRS, for short) over an extended
signature. They are not sound for every CTRS w.r.t. reduction, while
they are complete w.r.t. reduction. Here, soundness w.r.t. reduction
means that every reduction sequence of the corresponding unraveled
TRS, of which the initial and end terms are over the original
signature, can be simulated by the reduction of the original CTRS. In
this paper, we show that an optimized variant of Ohlebusch\u27s
unraveling for deterministic CTRSs is sound w.r.t. reduction if the
corresponding unraveled TRSs are left-linear or both right-linear and
non-erasing. We also show that soundness of the variant implies that
of Ohlebusch\u27s unraveling
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