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This section gives an overview of Scheme’s semantics. A detailed informal semantics is the subject of chapters Basic concepts through Standard procedures. For reference purposes, Formal semantics provides a formal semantics of Scheme.
Scheme is a statically scoped programming language. After macros are expanded, each use of a variable is associated with a lexically apparent binding of that variable.
Scheme is a dynamically typed language. Types are associated with values (also called objects) rather than with variables. Statically typed languages, by contrast, associate types with variables and expressions as well as with values.
All objects created in the course of a Scheme computation, including procedures and continuations, have unlimited extent. No Scheme object is ever destroyed. The reason that implementations of Scheme do not (usually!) run out of storage is that they are permitted to reclaim the storage occupied by an object if they can prove that the object cannot possibly matter to any future computation. Implementations of Scheme are required to be properly tail-recursive. This allows the execution of an iterative computation in constant space, even if the iterative computation is described by a syntactically recursive procedure. Thus with a properly tail-recursive implementation, iteration can be expressed using the ordinary procedure-call mechanics, so that special iteration constructs are useful only as syntactic sugar. See Proper tail recursion.
Scheme procedures are objects in their own right. Procedures can be created dynamically, stored in data structures, returned as results of procedures, and so on. One distinguishing feature of Scheme is that continuations, which in most other languages only operate behind the scenes, also have “first-class” status. Continuations are useful for implementing a wide variety of advanced control constructs, including non-local exits, backtracking, and coroutines. See Control features.
Arguments to Scheme procedures are always passed by value, which means that the actual argument expressions are evaluated before the procedure gains control, regardless of whether the procedure needs the result of the evaluation. Scheme’s model of arithmetic is designed to remain as independent as possible of the particular ways in which numbers are represented within a computer. In Scheme, every integer is a rational number, every rational is a real, and every real is a complex number. Thus the distinction between integer and real arithmetic, so important to many programming languages, does not appear in Scheme. In its place is a distinction between exact arithmetic, which corresponds to the mathematical ideal, and inexact arithmetic on approximations. Exact arithmetic is not limited to integers.
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