Re: CODASYL-like databases

> The innovative aspect was that before RM, there was no
> direct relationship between mathematical concepts and database
> management.

Not exactly.

Assuming RM is a reference to Codd's seminal work ("A Relational Model of Data for Large Data Banks", 1970), you need only look at the papers he cited to find an earlier paper that showed the relationship between mathematics and database management.

David L. Childs taught mathematics at the University of Michigan and Codd cited his work. Here's the abstract for a March 1968 paper by Childs:

DESCRIPTION OF A SET-THEORETIC DATA STRUCTURE A set-theoretic data structure (STDS) is virtually a 'floating' or pointer-free structure allowing quicker access, less storage, and greater flexibility than fixed or rigid structures that rely heavily on internal pointers or hash-coding, such as 'associative or relational structures,' 'list structures,' 'ring structures,' etc. An STDS relies on set-theoretic operations to do the work usually allocated to internal pointers. A question in an STDS will be a set-theoretic expression. Each set in an STDS is completely independent of every other set, allowing modification of any set without perturbation of the rest of the structure; while fixed structures resist creation, destruction, or changes in data. An STDS is essentially a meta-structure, allowing a question to 'dictate' the structure or data-flow. A question establishes which sets are to be accessed and which operations are to be performed within and between these sets. In an STDS there are as many 'structures' as there are combinations of set-theoretic operations; and the addition, deletion, or change of data has no effect on set-theoretic operations, hence no effect on the 'dictated structures.' Thus in a floating structure like an STDS the question directs the structure, instead of being subservient to it.

And there's also ARPA-funded research described in this August 1968 research paper presented to the IFIP Congress 1968. Note the INTRODUCTION below.

"Childs, D. L., Feasibility of a Set-Theoretic Data Structure: A General Structure Based on a Reconstituted Definition of Relation"

ABSTRACT This paper is motivated by an assumption that many problems dealing with arbitrarily related data can be expedited on a digital computer by a storage structure which allows rapid execution of operations within and between sets of datum names. In order for such a structure to be feasible, two problems must be considered: 1. the structure should be general enough that the sets involved may be unrestricted, thus allowing sets of sets of sets...; sets of ordered pairs, ordered triples...; sets of variable length n-tuples, n-tuples of arbitrary sets; etc.; 2. the set-operations should be general in nature, allowing any of the usual set theory operations between sets as described above, with the assurance that these operations will be executed rapidly. A sufficient condition for the latter is the existence of a well-ordering relation on the union of the participating sets. These problems are resolved in this paper with the introduction of the concept of a 'complex,' which has an additional feature of allowing a natural extension of properties of binary relations to properties of general relations.

TABLE OF CONTENTS Page

ABSTRACT............................................ I.
INTRODUCTION..................................
II. COMPLEXES.................................... 5
III. EXTENSION OF SET OPERATIONS TO COMPLEXES...... 9
IV. ORDERED PAIR DEFINED BY A COMPLEX............. 11
V. FUNCTIONS..................................... 13
VI. DEVELOPMENT OF AN N-TUPLE..................... 14
VII. RECONSTITUTED DEFINITION OF RELATION.......... 18
VIII. TAU-ORDERING............................ 21
IX. EXTENDED OPERATIONS FOR RELATIONS............. 28
X. EXAMPLES.................................. 31
XI. CONCLUSION............................... 33
DEFINED SYMBOLS..................................... 35
REFERENCES.......................................... 37

I. INTRODUCTION The overall goal, of which this paper is a part, is the development of a machine-independent data structure allowing rapid processing of data related by arbitrary assignment such as: the contents of a telephone book, library files, census reports, family lineage, networks, etc. Data which are non-intrinsically related have to be expressed (stored) in such a way as to define the way in which they are related before any data structure is applicable. Since any relation can be expressed in set theory as a set of ordered pairs and since set theory provides a wealth of operations for dealing with relations, a set-theoretic data structure appears worth investigation. Received on Sat Apr 05 2008 - 02:32:51 CEST