Programming Languages and Lambda Calculi

These are the basic thoughts that should go into the preface. It is not a final version. In a series of papers in the mid-1960's, Landin expounded two important observations about programming languages. First, he argued that all programming languages share a basic set of facilities for specifying computation but differ in their choice of data and data primitives. The set of common facilities contains names, procedures, applications, exception mechanisms, mutable data structures, and possibly other forms of non-local control. Languages for numerical applications typically include several forms of numerical constants and large sets of numerical primitives, while those for string manipulation typically offer efficient string matching and manipulation primitives. Second, he urged that programmers and implementors alike should think of a programming language as an advanced, symbolic form of arithmetic and algebra. Since all of us are used to calculating with numbers, booleans, and even more complex data structures from our days in kindergarten and highschool, it should be easy to calculate with programs too. Program evaluation, many forms of program editing, program transformations, and optimizations are just different, more elaborate forms of calculation. Instead of simple arithmetic expressions, such calculations deal with programs and pieces of programs. Landin defined the programming language Iswim. The basis of his design was Church's λ-calculus. Church had proposed the λ-calculus as a calculus of functions 1. Given Landin's insight on the central role of procedures as a facility common to all languages, the λ-calculus was a natural starting point. However, to support basic data and related primitives as well as assignments and control constructs, Landin extended the λ-calculus with appropriate constructions. He specified the semantics of the extended language with an abstract machine because he did not know how to extend the equational theory of the λ-calculus to a theory for the complete programming language. Indeed, it turned out that the λ-calculus does not even explain the semantics of the pure functional sub-language because Iswim always evaluates the arguments to a procedure. Thus, Landin did not accomplish what he had set out to do, namely, to define the idealized core of all programming languages and an equational calculus that defines its semantics. Starting with Plotkin's work on the relationship of abstract machines to equational 1 With the goal of understanding all of mathematics based on this calculus 5 6 CONTENTS calculi in the mid-1970's, the gap in Landin's work has been filled …