کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4950012 | 1440354 | 2017 | 18 صفحه PDF | دانلود رایگان |

A formalisation of soundness of the notion of α-equivalence in nominal abstract syntax modulo associative (A) and associative-commutative (AC) equational theories is described. Initially, the notion of α-equivalence is specified based on a so called “weak” nominal relation as suggested by Urban in his nominal development in Isabelle/HOL. Then, it is formalised in Coq that this equality is indeed an equivalence relation. After that, general α-equivalence with A and AC function symbols is specified and formally proved to be an equivalence relation. As corollaries, the soundness α-equivalence modulo A and modulo AC is obtained. Finally, an algorithm for checking α-equivalence modulo A and AC is proposed. General α-equivalence problems are log-linearly solved while AC and the combination of A and AC α-equivalence problems have the same complexity as standard first-order approaches. This development is a first step towards verification of nominal matching, unification and narrowing algorithms modulo equational theories in general.
Journal: Electronic Notes in Theoretical Computer Science - Volume 332, 11 June 2017, Pages 21-38