Relating Nominal and Higher-order Abstract Syntax Specifications

Nominal abstract syntax and higher-order abstract syntax provide a means for describing binding structure which is higher-level than traditional techniques. These approaches have spawned two different communities which have developed along similar lines but with subtle differences that make them difficult to relate. The nominal abstract syntax community has devices like names, freshness, name-abstractions with variable capture, and the new-quantifier, whereas the higher-order abstract syntax community has devices like lambda-binders, lambda-conversion, raising, and the nabla-quantifier. This paper aims to unify these communities and provide a concrete correspondence between their different devices. In particular, we develop a semantics-preserving translation from alpha-Prolog, a nominal abstract syntax based logic programming language, to G-, a higher-order abstract syntax based logic programming language. We also discuss higher-order judgments, a common and powerful tool for specifications with higher-order abstract syntax, and we show how these can be incorporated into G-. This establishes G- as a language with the power of higher-order abstract syntax, the fine-grained variable control of nominal specifications, and the desirable properties of higher-order judgments.Comment: To appear in PPDP 201

A Language Description is More than a Metamodel

Within the context of (software) language engineering, language descriptions are considered first class citizens. One of the ways to describe languages is by means of a metamodel, which represents the abstract syntax of the language. Unfortunately, in this process many language engineers forget the fact that a language also needs a concrete syntax and a semantics. In this paper I argue that neither of these can be discarded from a language description. In a good language description the abstract syntax is the central element, which functions as pivot between concrete syntax and semantics. Furthermore, both concrete syntax and semantics should be described in a well-defined formalism

Syntax for free: representing syntax with binding using parametricity

We show that, in a parametric model of polymorphism, the type ∀ α. ((α → α) → α) → (α → α → α) → α is isomorphic to closed de Bruijn terms. That is, the type of closed higher-order abstract syntax terms is isomorphic to a concrete representation. To demonstrate the proof we have constructed a model of parametric polymorphism inside the Coq proof assistant. The proof of the theorem requires parametricity over Kripke relations. We also investigate some variants of this representation

Free relative constructions in OT syntax

This paper is part of a research project on OT Syntax and the typology of the free relative (FR) construction. It concentrates on the details of an OT analysis and some of its consequences for OT syntax. I will not present a general discussion of the phenomenon and the many controversial issues it is famous for in generative syntax