Dynamic Term Rewriting Calculus is a new computation model proposed by the authors for the purpose of formal description and verification of algorithms treating Term Rewriting Systems. The computation of DTRC is basically term rewriting. The characteristic features of DTRC are dynamic change of rewriting rules during computation and hierarchical declaration of not only function symbols and variables but also rewriting rules. These features allow us to program metacomputation of TRSs in DTRC, that is , we can implement in DTRC in a natural way those algorithms which manipulate term rewriting systems as well as those procedures which verify such algorithms. In this paper, we give a formal description of DTRC. We then show some results on confluence property of DTRC.

Dynamic Term Rewriting Calculus (DTRC) is a new computation model aiming at formal description and verification of algorithms treating Term Rewriting Systems (TRSs). In this paper, we show that we can use DTRC to mechanize explicit induction for proving an inductive theorem, that is, we can translate the statements of base and induction steps for proving by induction into a DTRC term. The translation reduces the proof of the statements into the evaluation of the corresponding DTRC term.