Programming languages express computations in a form comprehensible to both people and machines. The syntax of a language specifies how various sorts of phrases (expressions, commands, declarations, and so forth) may be combined to form programs. But what are these phrases? What is a program made of?

The informal concept of syntax involves several distinct concepts. The surface, or concrete, syntax is concerned with how phrases are entered and displayed on a computer. The surface syntax is usually thought of as given by strings of characters from some alphabet (say, ASCII or Unicode). The structural, or abstract, syntax is concerned with the structure of phrases, specifically how they are composed from other phrases. At this level, a phrase is a tree, called an abstract syntax tree, whose nodes are operators that combine several phrases to form another phrase. The binding structure of syntax is concerned with the introduction and use of identifiers: how they are declared, and how declared identifiers can be used. At this level, phrases are abstract binding trees, which enrich abstract syntax trees with the concepts of binding and scope.

We will not concern ourselves in this book with concrete syntax but will instead consider pieces of syntax to be finite trees augmented with a means of expressing the binding and scope of identifiers within a syntax tree. To prepare the ground for the rest of the book, we define in this chapter what is a “piece of syntax” in two stages. First, we define abstract syntax trees, or ast's, which capture the hierarchical structure of a piece of syntax, while avoiding commitment to their concrete representation as a string. Second, we augment abstract syntax trees with the means of specifying the binding (declaration) and scope (range of significance) of an identifier. Such enriched forms of abstract syntax are called abstract binding trees, or abt's for short.

Several functions and relations on abt's are defined that give precise meaning to the informal ideas of binding and scope of identifiers. The concepts are infamously difficult to define properly and are the mother lode of bugs for language implementors. Consequently, precise definitions are essential, but they are also fairly technical and take some getting used to. It is probably best to skim this chapter on first reading to get the main ideas, and return to it for clarification as necessary.