Semantics of context-free languages

Abstract

ABSTRACT"Meaning" may be assigned to a string in a context-free language by defining "attributes" of the symbols in a derivation tree for that string. The attributes can be defined by functions associated with each production in the grammar. This paper examines the implications of this process when some of the attributes are "synthesized", i.e., defined solely in terms of attributes of the descendants of the corresponding nonterminal symbol, while other attributes are "inherited", i.e., defined in terms of attributes of the ancestors of the nonterminal symbol. An algorithm is given which detects when such semantic rules could possibly lead to circular definition of some attributes. An example is given of a simple programming language defined with both inherited and synthesized attributes, and the method of definition is compared to other techniques for formal specification of semantics which have appeared in the literature.A simple technique for specifying the "meaning" of languages defined by context-free grammars is introduced in Section 1 of this paper, and its basic mathematical properties are investigated in Sections 2 and 3. An example which indicates how the technique can be applied to the formal definition of programming languages is described in Section 4, and finally, Section 5 contains a somewhat biased comparison of the present method to other known techniques for semantic definition. The discussion in this paper is oriented primarily towards programming languages, but the same methods appear to be relevant also in the study of natural languages.

The genesis of attribute grammars

“…And there was a blackboard at hand, with plenty of chalk. So I marched up to the board and started to write down a definition of a language very much like what later became Turingol [15]. I have no idea if what I said made any sense to the students, since I must have had to go back and erase a lot of things before getting them right; and I doubt that anybody took notes that day.…”

“…Although the conference record lists me as one of the participants [39], the truth is that I spent almost the whole time sitting on the beach outside the conference hotel writing a paper about "semantics of context-free languages" [15]. That paper explained everything I knew (or thought I knew) about attribute grammars.…”

“…So that's the story of my paper [15], which was effectively written in Ithaca, Stanford, Grenoble, and Santa Barbara. (The published paper [15] says 'Received 15 November 1967'; that must be a misprint for December.)…”

“…(The published paper [15] says 'Received 15 November 1967'; that must be a misprint for December.) I've presented this background information in some detail because it suggests that research institutes may not be the best places to do research.…”

“…A student residence, now visible behind the tree, was built here about 1980.) It is clear from reading [18] that I was still unaware of the serious error in the circularity test of [15] when I wrote the new paper. Indeed, I returned the galley proofs of [18] to the printer on July 28; then on August 6, I received a letter from Stein Krogdahl in Norway, containing an elegantly presented counterexample to my circularity algorithm.…”