5. Language Design Considerations
SCHEME is a lexically scoped ("full-funarg") dialect of LISP, and so is an applicative language which conforms to the spirit of the lambda-calculus. [Church] We divide the definition of the SCHEME language into two parts: the environment and control constructs, and the data manipulation primitives. Examples of the former are LAMBDA-expressions, combinations, and IF; examples of the latter are CONS, CAR, EQ, and PLUS. Note that we can conceive of a version of SCHEME which did not have CONS, for example, and more generally did not have S-expressions in its data domain. Such a version would still have the same environment and control constructs, and so would hold the same theoretical interest for our purposes here. (Such a version, however, would be less convenient for purposes of writing a meta-circular description of the language, however!)
By the "spirit of lambda-calculus" we mean the essential properties of the axioms obeyed by lambda-calculus expressions. Among these are the rules of alpha-conversion and beta-conversion. The first intuitively implies that we can uniformly rename a function parameter and all references to it without altering the meaning of the function. An important corollary to this is that we can in fact effectively locate all the references. The second implies that in a situation where a known function is being called with known argument expressions, we may substitute an argument expression for a parameter reference within the body of the function (provided no naming conflicts result, and that certain restrictions involving side effects are met). Both of these operations are of importance to an optimizing compiler. Another property which follows indirectly is that of tail-recursion. This property is exploited in expressing iteration in terms of applicative constructs, and is discussed in some detail in
