From Higher-Order to First-Order Rewriting
نویسندگان
چکیده
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 abstract properties to be veriied by the substitution calculus used in the translation.
منابع مشابه
A Transformation System Combining Partial Evaluation with Term Rewriting
This paper presents a new approach to optimizing functional programs based on combining partial evaluation and rewriting. Programs are composed of higher-order primitives. Partial evaluation is used to eliminate higher-order functions. First-order rewriting is used to process the transformation. Laws about the higher-order primitives that are relevant for the optimizations are automatically ext...
متن کاملA Transformation System Combining Partial Evaluation
This paper presents a new approach to optimizing functional programs based on combining partial evaluation and rewriting. Programs are composed of higher-order primitives. Partial evaluation is used to eliminate higher-order functions. First-order rewriting is used to process the transformation. Laws about the higher-order primitives that are relevant for the optimizations are automatically ext...
متن کاملar X iv : 1 50 2 . 04 65 3 v 1 [ cs . F L ] 1 6 Fe b 20 15 Rewriting Higher - Order Stack Trees ⋆
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for monadic second order logic (respectively first order logic with a reachability predicate) is decidable on such graphs. We unify both models by introducing the ...
متن کاملHigher-Order Rewriting via Conditional First-Order Rewriting in the Open Calculus of Constructions
Although higher-order rewrite systems (HRS) seem to have a first-order flavor, the direct translation into first-order rewrite systems, using e.g. explicit substitutions, is by no means trivial. In this paper, we explore a two-stage approach, by showing how higher-order pattern rewrite systems, and in fact a somewhat more general class, can be expressed by conditional first-order rewriting in t...
متن کاملHigher - Order ( Non - ) Modularity Claus
We show that, contrary to the situation in first-order term rewriting, almost none of the usual properties of rewriting are modular for higher-order rewriting, irrespective of the higher-order rewriting format. We show that for the particular format of simply typed applicative term rewriting systems modularity of confluence, normalization, and termination can be recovered by imposing suitable l...
متن کامل