Abstract

The rewriting calculus is a rule construction and application framework. As such it embeds in a uniform way term rewriting and lambda-calculus. Since rule application is an explicit object of the calculus, it allows us also to handle the set of results explicitly. We present a simply typed version of the rewriting calculus. With a good choice of the type system, we show that the calculus is type preserving and terminating, i.e. veries the subject reduction and strong normalization properties. 1 Introduction The rewriting calculus [CK99a,CK99b] is a general framework handling explicitly the three notions of rule formation, rule application and rule application result. The rule formation constructor is denoted ! and given two terms like x+ s(y) and s(x +y) it allows us to built the rewrite rule x+ s(y) ! s(x +y). Applying the previous rewrite rule to the top position of the sum 3 + 2 is performed using the application operator denoted [ ]( ) (where 3 is an abbreviation for s(s(s(0)))...

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