Frameworks for Reasoning about Syntax that Utilize Quotation and Evaluation

TL;DR

This paper introduces a formal structure called a syntax framework to model reasoning about syntax and semantics of interpreted languages, integrating quotation and evaluation mechanisms.

Contribution

It formalizes the concept of syntax frameworks, enabling systematic reasoning about syntax and semantics, and discusses how to incorporate quotation and evaluation into languages.

Findings

Defines a mathematical structure for syntax reasoning

Provides examples of syntax frameworks

Clarifies the integration of quotation and evaluation

Abstract

It is often useful, if not necessary, to reason about the syntactic structure of an expression in an interpreted language (i.e., a language with a semantics). This paper introduces a mathematical structure called a syntax framework that is intended to be an abstract model of a system for reasoning about the syntax of an interpreted language. Like many concrete systems for reasoning about syntax, a syntax framework contains a mapping of expressions in the interpreted language to syntactic values that represent the syntactic structures of the expressions; a language for reasoning about the syntactic values; a mechanism called quotation to refer to the syntactic value of an expression; and a mechanism called evaluation to refer to the value of the expression represented by a syntactic value. A syntax framework provides a basis for integrating reasoning about the syntax of the expressions with reasoning about what the expressions mean. The notion of a syntax framework is used to discuss how quotation and evaluation can be built into a language and to define what quasiquotation is. Several examples of syntax frameworks are presented.