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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.
A constructive decision procedure for equalities modulo AC
"... this paper an optimised constructive decision procedure for AC equalities based on the syntacticness of AC theories. The original motivation for it comes from our work [5] to incorporate term rewriting into the Coq proof assistant [3] using ELAN [7]. The main idea is to perform term rewriting in ELA ..."
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this paper an optimised constructive decision procedure for AC equalities based on the syntacticness of AC theories. The original motivation for it comes from our work [5] to incorporate term rewriting into the Coq proof assistant [3] using ELAN [7]. The main idea is to perform term rewriting in ELAN and to only use Coq for checking purpose. When considering AC rewriting, proof checking requires an ecient method to prove AC equality in Coq using two axioms of associativity and commutativity or possibly a nite set of equalities derived from them