Scheme

Scheme is the ultimate stage in the evolution of the Lisp family of programming languages. Lisp and Fortran, originally developed at about the same time in the late 1950's, were the first two widely used and studied "high level" computer programming languages. Prior to their appearance, programming was exclusively done using assembly language or by entering binary machine code directly using all those quaint switches, knobs and dials visible on 50's vintage computers.

Lisp and Fortran take fundamentally different approaches to language design. Fortran was intended to appeal directly to engineers familiar with the branches of mathematics used in the applied sciences and with the kind of structured design documentation used in electrical engineering and similar eminently practical endeavors. The majority of popular programming languages to this day owe a lot of their syntactical and semantic conventions to Fortran.

Lisp was intended to be as a direct an embodiment of Church's Lambda Calculus as can be achieved in the real world. Scheme comes the closest of all Lisp dialects to achieving that aim. For that reason alone, any programmer who wishes to understand something about the origin of the very concept of "programming language" would do well to learn Scheme.

For example, to represent what Church would have a written on a chalk board at UCLA as \(\lambda x.+ \hskip0.25em x \hskip0.25em 1\) (yes, he preferred prefix notation) as a Scheme expression, one writes (lambda (x) (+ x 1)) (and, yes, Lisp syntax introduces a lot of parentheses even though the ability to do without them is one of the motivations for prefix notation in the first place). Both expressions represent a function which adds 1 to its argument, \(x\). The first as a mathematical formula and the second as a compilable, executable snippet of source code. The primary semantic difference between them is that \(\lambda x.+ \hskip0.25em x \hskip0.25em 1\), being a mathematical formula, has no theoretical limit on the magnitude of \(x\) while (lambda (x) (+ x 1)) is limited by the magnitude of the bignum data type on a given machine with a given amount of heap space allocated to the process running the Scheme program.

The following descriptions of particular Scheme features will make the most sense if you already know at least one Lisp dialect, such as Common Lisp. A complete tutorial on Lisp in general or Scheme in particular is (currently) beyond the scope of these pages.

Kirk Rader

Scheme