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.
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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).
On context and ambiguity in parsing
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notions of “bounded context” of Floyd [1] and “structural connections” of Irons [2], as these notions relate to as yet unpublished researches growing out of the development of the author's Algorithmic Theory of Language [3, 4].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.
A programming package for some general modes of arithmetic
An interpretive programming package is described for computation with operands which may be real, complex, single or double precision, or real multiple precision. It also performs operations on matrices formed from these elements. A simple language structure is used to describe the computation.
Bounded context syntactic analysis
Certain phase structure grammars define languages in which the phrasehood and structure of a substring of a sentence may be determined by consideration of only a bounded context of the substring. It is possible to determine, for any specified bound on the number of contextual characters considered, whether a given grammar is such a bounded context grammar. Such grammars are free from syntactic ambiguity. Syntactic analysis of sentences in a bounded context language may be performed by a standard process and requires a number of operations proportional to the length of sentence analyzed.
Bounded context grammars form models for most languages used in computer programming, and many methods of syntactic analysis, including analysis by operator precedence, are special cases of bounded context analysis.
A general business-oriented language based on decision expressions
The structure of a digital computer programming language which covers a wide class of business and file processing applications is presented. Such a structure, based on identifying and incorporating into a compiler the aspects common to all processes of such class, permits writing extremely compact programs, even for comparatively complex applications, in terms of tables of control expressions which express only information characteristic of the particular application. Furthermore, local changes of a process (e.g. changes affecting only one of the output files involved) can be effected by local modifications in the program (e.g. modification of only one entry of the tables). This structure also allows for inexpensive preparation of loading-speed compilers which translate the source programs into efficient machine codes.
The approach adopted here departs from conventional mechanical language design philosophies. It stresses the structural analysis of the class of processes to be represented in the languages, as opposed to emphasizing formal (i.e., contents-independent) syntactical definitions. It relies exclusively on nonprocedural representation of processes as sets (tables) of relations between data and results (there are no control statements such as GO TO, etc.), instead of using procedure descriptions (which are one-to-one translations of flowcharts). Here an invariant pattern of procedure is identified as characteristic of the class of all batch file processes.
GIT—a heuristic program for testing pairs of directed line graphs for isomorphism
Given a pair of directed line graphs, the problem of ascertaining whether or not they are isomorphic is one for which no efficient algorithmic solution is known. Since a straightforward enumerative algorithm might require 40 years of running time on a very high speed computer in order to compare two 15-node graphs, a more sophisticated approach seems called for. The situation is similar to that prevailing in areas such as game-playing and theorem-proving, where practical algorithms are unknown (for the interesting cases), but where various practical though only partially successful techniques are available. GIT—Graph Isomorphism Tester—incorporates a variety of processes that attempt to narrow down the search for an isomorphism, or to demonstrate that none exists. No one scheme is relied upon exclusively for a solution, and the program is designed to avoid excessive computation along fruitless lines. GIT has been written in the COMIT language and successfully tested on the IBM 7090.
Floating-point arithmetic with 84-bit numbers
A classic and straightforward technique is presented which is not limited to the size or type of number representation used or multiple precision arithmetic.
A fast procedure for generating normal random variables
A technique for generating normally distributed random numbers is described. It is faster than those currently in general use and is readily applicable to both binary and decimal computers.
Use of the disk file on stretch
The paper begins by briefly describing the Stretch (IBM 7030) computer with special emphasis given to the organization and operation of its input-output equipment. Physical characteristics of the two-disk system (4,194,304 72-bit words, 8 µsec-per-word transmission rate, etc.) are noted. Timing limitations due to arm motion and disk rotation are discussed.
Applications of disk usage are discussed separately for problem programs and for systems programs such as compilers and the supervisory program. Approximately 260,000 words of disk storage are reserved for the storage of systems programs and the subroutine library. Problem programs, however, are not currently filed on the disk.
Certain programming techniques are discussed for transmitting words between disk and core storage with minimum delaying and interruption of the arithmetic unit. Dumps on disk are considered for both recovery from computer malfunction and for mathematical or physical developments during the calculation.
Computation’s development critical to our society
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