A de Bruijn notation for higher - order rewriting ( Extended
نویسندگان
چکیده
We propose a formalism for higher-order rewriting in de Bruijn notation. This notation not only is used for terms (as usually done in the literature) but also for metaterms, which are the syntactical objects used to express general higher-order rewrite systems. We give formal translations from higher-order rewriting with names to higher-order rewriting with de Bruijn indices, and vice-versa. These translations can be viewed as an interface in programming languages based on higher-order rewrite systems, and they are also used to show some properties, namely, that both formalisms are operationally equivalent, and that connuence is preserved when translating one formalism into the other.
منابع مشابه
A de Bruijn Notation for Higher-Order Rewriting
We propose a formalism for higher-order rewriting in de Bruijn notation. This notation not only is used for terms (as usually done in the literature) but also for metaterms, which are the syntactical objects used to express general higher-order rewrite systems. We give formal translations from higher-order rewriting with names to higher-order rewriting with de Bruijn indices, and vice-versa. Th...
متن کاملRecognizability of Redexes for Higher-Order Rewrite Systems
It is known that the set of all redexes for a left-linear term rewriting system is recognizable by a tree automaton, which means that we can construct a tree automaton that accepts redexes. The present paper extends this result to Nipkow’s higher-order rewrite systems, in which every left-hand side is a linear fully-extended pattern. A naive extension of the first-order method causes the automa...
متن کاملReviewing the Classical and the de Bruijn Notation for [lambda]-calculus and Pure Type Systems
This article is a brief review of the type-free -calculus and its basic rewriting notions, and of the pure type system framework which generalises many type systems. Both the type-free -calculus and the pure type systems are presented using variable names and de Bruijn indices. Using the presentation of the -calculus with de Bruijn indices, we illustrate how a calculus of explicit substitutions...
متن کاملHigher-order Abstract Syntax in Type Theory
We develop a general tool to formalize and reason about languages expressed using higher-order abstract syntax in a proof-tool based on type theory (Coq). A language is specified by its signature, which consists of sets of sort and operation names and typing rules. These rules prescribe the sorts and bindings of each operation. An algebra of terms is associated to a signature, using de Bruijn n...
متن کاملSwapping: a natural bridge between named and indexed explicit substitution calculi
This article is devoted to the presentation of λ rex, an explicit substitution calculus with de Bruijn indexes and a simple notation. By being isomorphic to λex – a recent formalism with variable names –, λ rex accomplishes simulation of β -reduction (Sim), preservation of β -strong normalization (PSN) and meta-confluence (MC), among other desirable properties. Our calculus is based on a novel ...
متن کامل