Research and Advances

One of the most primitive parts of a formula language is its specification of input-output actions within the framework of the language. While the specification is intrinsically more complex, say, than the evaluation of an arithmetic expression, most of the difficulties associated with input-output specification arise from the fact that the desired operations have not been properly defined using the framework of a programming language. Indeed, the complexity largely disappears when a programming language is constructed to specify input-output actions. The point to be made here is that the definition of an appropriate programming language makes more rational and simpler all three phases of the input-output programming cycle: (i) source program construction, (ii) object program construction, (iii) object program execution.

The topics began with discussion of almost exclusively syntactic analysis and methods. Beginning with context-free phrase-structure languages, we considered limitations thereof to remove generative syntactic ambiguities (Floyd), and extensions thereto to introduce more context-dependence (Rose). As the conference proceeded we ran through a spectrum of considerations in which the expressions in the languages considered were examined less and less as meaningless objects (the formal, or purely syntactic approach, as in the paper by Steel) and required more and more meaningful interpretations. In other words, we became more and more involved with semantic considerations. It is clear, then, that applications of the study of mechanical languages to programming must involve semantic questions; ADD must mean something more than the concatenation of three (not two) characters. The papers beyond Session 1 were therefore discussing the mechanization of semantics, but in only one case did we hear about the formalization (and hence mechanization) of the specification of the semantics of a language (McCarthy).

This note is by way of commentary on the notions of “bounded context” of Floyd [1] and “structural connections” of Irons [2], as these notions relate to as yet unpublished researches growing out of the development of the author's Algorithmic Theory of Language [3, 4]. In the closing paragraphs of [3], the author made comments concerning further developments of the theory which would include “context dependence” and “resolution of apparent syntactic ambiguities.” The work on parsing reported here was carried out in early September, 1962 (an earlier version in March, 1962), but has not been polished or reduced to final form because, for the purpose of the total theory, parsing should not be considered separately, and the complexities of the proper treatment of the “precedence string” (which relates to semantic structure as distinct from syntactic structure of parsing) have not yet been satisfactorily resolved.