19,439 research outputs found
On Semi-Completeness of Term Rewriting Systems
We investigate the question whether semi-completeness, i.e., weak termination plus confluence, of term rewriting systems is preserved under the normalization of right-hand sides. We give a simple counterexample showing that in general this transformation neither preserves weak termination nor (local) confluence. Moreover we present two conditions which are sufficient for the preservation of semi-completeness. In particular, we show that (almost) orthogonal systems enjoy this preservation property
Extending Context-Sensitivity in Term Rewriting
We propose a generalized version of context-sensitivity in term rewriting
based on the notion of "forbidden patterns". The basic idea is that a rewrite
step should be forbidden if the redex to be contracted has a certain shape and
appears in a certain context. This shape and context is expressed through
forbidden patterns. In particular we analyze the relationships among this novel
approach and the commonly used notion of context-sensitivity in term rewriting,
as well as the feasibility of rewriting with forbidden patterns from a
computational point of view. The latter feasibility is characterized by
demanding that restricting a rewrite relation yields an improved termination
behaviour while still being powerful enough to compute meaningful results.
Sufficient criteria for both kinds of properties in certain classes of rewrite
systems with forbidden patterns are presented
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
The Sigma-Semantics: A Comprehensive Semantics for Functional Programs
A comprehensive semantics for functional programs is presented, which generalizes the well-known call-by-value and call-by-name semantics. By permitting a separate choice between call-by value and call-by-name for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameter-passing mechanism. Thus common and distinguishing features of all instances of the sigma-semantics, especially call-by-value and call-by-name semantics, are highlighted. Furthermore, a property can be validated for all instances of the sigma-semantics by a single proof. This is employed for proving the equivalence of the given denotational (fixed-point based) and two operational (reduction based) definitions of the sigma-semantics. We present and apply means for very simple proofs of equivalence with the denotational sigma-semantics for a large class of reduction-based sigma-semantics. Our basis are simple first-order constructor-based functional programs with patterns
The Sigma-Semantics: A Comprehensive Semantics for Functional Programs
A comprehensive semantics for functional programs is presented, which generalizes the well-known call-by-value and call-by-name semantics. By permitting a separate choice between call-by value and call-by-name for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameter-passing mechanism. Thus common and distinguishing features of all instances of the sigma-semantics, especially call-by-value and call-by-name semantics, are highlighted. Furthermore, a property can be validated for all instances of the sigma-semantics by a single proof. This is employed for proving the equivalence of the given denotational (fixed-point based) and two operational (reduction based) definitions of the sigma-semantics. We present and apply means for very simple proofs of equivalence with the denotational sigma-semantics for a large class of reduction-based sigma-semantics. Our basis are simple first-order constructor-based functional programs with patterns
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