According to a recently discovered theorem, the flow graph of any program, no matter how much "spaghetti code" it contains, may be reordered in such a way that it shows a loop structure. The rearranged program has no backward branches except for loopbacks, which go to the head of some loop from somewhere within that loop. No new vertices or variables are introduced; only the order of the vertices is changed. Rearrangement may be automated, for either low-level or high-level languages. We have constructed a tool, which we call a Rearranger, to act on a description of an assembly language, followed by a program written in that language. A spaghetti-code version of depth-first search has been programmed for Intel, MPS, G3, Motorola 68000, and the IBM mainframe, and successfully rearranged for all these machines

The programming language concepts which ought to be presented in the comparative programming languages course (either graduate or undergraduate) are all covered by choosing C++, Java, Perl, and Python as the languages to be compared. These include dynamic typing, object orientation, multiple inheritance, interpreters and compilers, keyword and default parameters, generics, operator overloading, complex numbers, universal hierarchies, exceptions, and garbage collection. We describe such a course, which we have given.

The advent of the microcomputer has caused a profound change in our thinking about the teaching of programming. Up to now we have been assuming that a computer is necessarily expensive and must be shared by all students. With the appearance of time-sharing systems, many universities, including The George Washington University, purchased large numbers of terminals for student use; but students were still using a single large or mid-size computer, albeit through several terminals. It is now possible, however, to purchase an entire computer for the price of a terminal. Such a computer is necessarily limited in scope; but it can serve admirably for the teaching of programming at an elementary level, as well as handling certain more advanced tasks. About a year and a half ago, the Computer Committee of the Department of Electrical Engineering and Computer Science, of which I was the chairman, made a decision to purchase sixteen microcomputer systems for student use, primarily for the teaching of BASIC, and secondarily for assembly language and PASCAL.

For the past seven years, including three years at the University of California (Berkeley) and four years at The George Washington University, this author has taught material relating to the correctness of programs in both undergraduate and graduate courses.

A computer is a set M (the memory), a set B , a class of maps S : M → B , known as states, and a class @@@@ of maps T : @@@@ → @@@@, known as instructions. Each instruction I has an input region IR ( I ), an output region OR ( I ), and affected regions AR ( M′ , I ), for M′ ⊆ IR ( I ). For example, let I be the instruction ( CLA Y ) on the IBM 7094. If L is the location counter and AC is the accumulator, then IR ( I ) = Y ∪ L and OR ( I ) = AC ∪ L ; if M′ is the address portion of Y , then AR ( M′ , I ) is the address portion of AC . The fundamental properties of all these notions are derived, and computers are related to other models, such as sequential machines. The existence problem (how arbitrarily the input, output and affected regions of an instruction can be specified) is fully settled for countable memory M .