Rewriting Modulo in Deduction Modulo
We study the termination of rewriting modulo a set of equations in the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In a previous work, we defined general syntactic conditions based on the notion of computability closure for ensuring the termination of the combination of rewriting and β-reduction.
Here, we show that this result is preserved when considering rewriting modulo a set of equations if the equivalence classes generated by these equations are finite, the equations are linear and satisfy general syntactic conditions also based on the notion of computability closure. This includes equations like associativity and commutativity and provides an original treatment of termination modulo equations.
KeywordsInduction Hypothesis Transitive Closure Predicate Symbol Critical Pair Lambda Calculus
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