Combining First Order Algebraic Rewriting Systems, Recursion and Extensional Lambda Calculi

It is well known that connuence and strong normalization are preserved when combining left-linear algebraic rewriting systems with the simply typed lambda calculus. It is equally well known that connuence fails when adding either the usual extensional rule for , or recursion together with the usual contraction rule for surjective pairing. We show that connuence and normalization are modular properties for the combination of left-linear algebraic rewriting systems with typed lambda calculi enriched with expansive extensional rules for and surjective pairing. For that, we use a translation technique allowing to simulate expansions without expansion rules. We also show that connuence is maintained in a modular way when adding xpoints. This result is also obtained by a simple translation technique allowing to simulate bounded recursion with reduction.