Simple Lambda-Calculus Model of Programming Languages

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. We present a simple correspondence between a large subset of Algol 60 language and lambda-calculus. With the aid of this correspondence, a program can be translated into a single lambda-expression. In general, the representation of a program is specified by means of a system of simultaneous conversion relations among the representations of the program constituents. High-level programming language features are treated directly, not in terms of the representations of machine-level operations. The model includes input-output in such a way that when the representation of a (convergent) program is applied to the input item representations, the resulting combination reduces to a tuple of the representations of the output items. This model does not introduce any imperative notions into the calculus; the descriptive programming constructs, such as expressions, and the imperative ones, such as assignments and jumps, are translated alike into pure lambda-expressions. The applicability of the model to the problems of proving program equivalence and correctness is illustrated by means of simple examples.