45 research outputs found
Dynamic Dependency Pairs for Algebraic Functional Systems
We extend the higher-order termination method of dynamic dependency pairs to
Algebraic Functional Systems (AFSs). In this setting, simply typed lambda-terms
with algebraic reduction and separate {\beta}-steps are considered. For
left-linear AFSs, the method is shown to be complete. For so-called local AFSs
we define a variation of usable rules and an extension of argument filterings.
All these techniques have been implemented in the higher-order termination tool
WANDA
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
On normalisation
Using a characterisation of strongly normalising -terms, we give new and simple proofs of the following: all developments and superdevelopments are finite, a certain rewrite strategy is perpetual, a certain rewrite strategy is maximal and thus perpetual, simply typed -calculus is strongly normalising
On normalisation
Using a characterisation of strongly normalising -terms, we give new and simple proofs of the following: all developments and superdevelopments are finite, a certain rewrite strategy is perpetual, a certain rewrite strategy is maximal and thus perpetual, simply typed -calculus is strongly normalising
Weak orthogonality implies confluence: the higher-order case
In this paper we prove confluence for weakly orthogonal Higher-Order Rewriting Systems. This generalises all the known `confluence by orthogonality' results
Weak orthogonality implies confluence : the higher-order case
In this paper we prove confluence for weakly orthogonal Higher-Order Rewriting Systems. This generalises all the known `confluence by orthogonality' results
On the Existence of Universal Finite or Pushdown Automata
We investigate the (non)-existence of universal automata for some classes of
automata, such as finite automata and pushdown automata, and in particular the
influence of the representation and encoding function. An alternative approach,
using transition systems, is presented too.Comment: In Proceedings DCM 2011, arXiv:1207.6821. Sadly, Manfred Kudlek
passed away June 18, 2012, before publication of this pape
Completeness of algebraic CPS simulations
The algebraic lambda calculus and the linear algebraic lambda calculus are
two extensions of the classical lambda calculus with linear combinations of
terms. They arise independently in distinct contexts: the former is a fragment
of the differential lambda calculus, the latter is a candidate lambda calculus
for quantum computation. They differ in the handling of application arguments
and algebraic rules. The two languages can simulate each other using an
algebraic extension of the well-known call-by-value and call-by-name CPS
translations. These simulations are sound, in that they preserve reductions. In
this paper, we prove that the simulations are actually complete, strengthening
the connection between the two languages.Comment: In Proceedings DCM 2011, arXiv:1207.682