Implementing first-order rewriting with constructor systems

Partial Inversion of Constructor Term Rewriting Systems

Partial-inversion compilers generate programs which compute some unknown inputs of given programs from a given output and the rest of inputs whose values are already given. In this paper, we propose a partial-inversion compiler of constructor term rewriting systems. The compiler automatically generates a conditional term rewriting system, and then unravels it to an unconditional system. To impr...

Rewriting Calculus with Fixpoints: Untyped and First-Order Systems

The rewriting calculus, also called ρ-calculus, is a framework embedding λ-calculus and rewriting capabilities, by allowing abstraction not only on variables but also on patterns. The higher-order mechanisms of the λ-calculus and the pattern matching facilities of the rewriting are then both available at the same level. Many type systems for the λ-calculus can be generalized to the ρ-calculus: ...

Relating Meseguer’s Rewriting Logic with the Constructor-Based Rewriting Logic

From Higher-Order to First-Order Rewriting

We show how higher-order rewriting may be encoded into rst-order rewriting modulo an equational theory E. We obtain a characterization of the class of higher-order rewriting systems which can be encoded by rst-order rewriting modulo an empty theory (that is, E = ;). This class includes of course the-calculus. Our technique does not rely on a particular substitution calculus but on a set of abst...

Lifting Term Rewriting Derivations in Constructor Systems by Using Generators

Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation starting from an instance of an expression can be ‘lifted’ to a narrowing derivation, whenever the substitution employed is normalized. In this paper we adapt the...