We now embark on a tour of the technology by which languages are established in terms of other languages. Metalinguistic abstraction — establishing new languages — plays an important role in all branches of engineering design. It is particularly important to computer programming, because in programming not only can we formulate new languages but we can also implement these languages by constructing interpreters. An interpreter for a programming language is a function that, when applied to an expression of the language, performs the actions required to evaluate that expression.

We will first define an interpreter for a language that is a limited subset of Scheme, called Calculator. Then, we will develop a sketch of an interpreter for Scheme as a whole. The interpreter we create will be complete in the sense that it will allow us to write fully general programs in Scheme. To do so, it will implement the same environment model of evaluation that we introduced for Python programs in Chapter 1.

Many of the examples in this section are contained in the companion Scheme-Syntax Calculator example, as they are too complex to fit naturally in the format of this text.