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Compact Normalisation Trace via Lazy Rewriting
, 2001
"... Innermost strategies are usually used in compiling term rewriting systems (TRSs) since they allow to eciently build result terms in a bottomup fashion. However, innermost strategies do not always give the shortest normalising derivation. In many cases, using an appropriate laziness annotation on th ..."
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Innermost strategies are usually used in compiling term rewriting systems (TRSs) since they allow to eciently build result terms in a bottomup fashion. However, innermost strategies do not always give the shortest normalising derivation. In many cases, using an appropriate laziness annotation on the arguments of function symbols, we evaluate lazy arguments only if it is necessary and hence, get a shorter derivation to normal forms while avoiding nonterminating reductions. We provide in this work a transformation of annotated TRSs, that allows to compute normal forms using an innermost strategy and to extract lazy derivations in the original TRS from normalising derivations in the transformed TRS. We apply our result to improve the eciency of equational reasoning in the Coq proof assistant using ELAN as an external rewriting engine.
Verifying an Infinite Systolic Algorithm using ThirdOrder Algebraic Methods
"... We consider using thirdorder algebraic methods to specify and equationally verify an infinite systolic algorithm for convolution. The detailed case study we present provides an interesting insight into the use of thirdorder algebra as a formal framework for developing families of computing systems ..."
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We consider using thirdorder algebraic methods to specify and equationally verify an infinite systolic algorithm for convolution. The detailed case study we present provides an interesting insight into the use of thirdorder algebra as a formal framework for developing families of computing systems. We consider using purely equational reasoning in our verification proofs and in particular, using the rule of free variable induction. We conclude by considering how our verification proofs can be automated using rewriting techniques.
Algebraic Prototyping Tools for Petri Nets with Time
, 2002
"... Rewriting logic (RL) is an extension of standard algebraic specification techniques which uses rewrite rules to model the dynamic behaviour of a system. In this paper we consider using RL and the associated support tool Elan as an environment for specifying, rapidly prototyping and analysing Petri n ..."
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Rewriting logic (RL) is an extension of standard algebraic specification techniques which uses rewrite rules to model the dynamic behaviour of a system. In this paper we consider using RL and the associated support tool Elan as an environment for specifying, rapidly prototyping and analysing Petri nets with time. Our flexible approach allows the wide range of possible time extensions presented in the literature to be investigated and thus overcomes one of the major drawbacks of the current hardwired tools. We demonstrate our ideas by considering two different time extensions: time Petri nets in which transitions are associated with a firing interval and timed Petri nets in which a firing delay is associated with transitions. In each case we demonstrate the flexibility of our approach by examining a range of semantic choices detailed in the literature.