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Important Papers: Codd and the Relational Model

29 Dec 2017

It’s hard to believe today, but the relational database was once the cool new kid on the block. In 2017, the relational model competes with all sorts of cutting-edge NoSQL technologies that make relational database systems seem old-fashioned and boring. Yet, 50 years ago, none of the dominant database systems were relational. Nobody had thought to structure their data that way. When the relational model did come along, it was a radical new idea that revolutionized the database world and spawned a multi-billion dollar industry.

The relational model was introduced in 1970. Edgar F. Codd, a researcher at IBM, published a paper called “A Relational Model of Data for Large Shared Data Banks.” The paper was a rewrite of a paper he had circulated internally at IBM a year earlier. The paper is unassuming; Codd does not announce in his abstract that he has discovered a brilliant new approach to storing data. He only claims to have employed a novel tool (the mathematical notion of a “relation”) to address some of the inadequacies of the prevailing database models.

In 1970, there were two schools of thought about how to structure a database: the hierarchical model and the network model. The hierarchical model was used by IBM’s Information Management System (IMS), the dominant database system at the time. The network model had been specified by a standards committee called CODASYL (which also—random tidbit—specified COBOL) and implemented by several other database system vendors. The two models were not really that different; both could be called “navigational” models. They persisted tree or graph data structures to disk using pointers to preserve the links between the data. Retrieving a record stored toward the bottom of the tree would involve first navigating through all of its ancestor records. These databases were fast (IMS is still used by many financial institutions partly for this reason, see this excellent blog post) but inflexible. Woe unto those database administrators who suddenly found themselves needing to query records from the bottom of the tree without having an obvious place to start at the top.

Codd saw this inflexibility as a symptom of a larger problem. Programs using a hierarchical or network database had to know about how the stored data was structured. Programs had to know this because they were responsible for navigating down this structure to find the information they needed. This was so true that when Charles Bachman, a major pioneer of the network model, received a Turing Award for his work in 1973, he gave a speech titled “The Programmer as Navigator.” Of course, if programs were saddled with this responsibility, then they would immediately break if the structure of the database ever changed. In the introduction to his 1970 paper, Codd motivates the search for a better model by arguing that we need “data independence,” which he defines as “the independence of application programs and terminal activities from growth in data types and changes in data representation.” The relational model, he argues, “appears to be superior in several respects to the graph or network model presently in vogue,” partly because, among other benefits, the relational model “provides a means of describing data with its natural structure only.” By this he meant that programs could safely ignore any artificial structures (like trees) imposed upon the data for storage and retrieval purposes only.

To further illustrate the problem with the navigational models, Codd devotes the first section of his paper to an example data set involving machine parts and assembly projects. This dataset, he says, could be represented in existing systems in at least five different ways. Any program \(P\) that is developed assuming one of five structures will fail when run against at least three of the other structures. The program \(P\) could instead try to figure out ahead of time which of the structures it might be dealing with, but it would be difficult to do so in this specific case and practically impossible in the general case. So, as long as the program needs to know about how the data is structured, we cannot switch to an alternative structure without breaking the program. This is a real bummer because (and this is from the abstract) “changes in data representation will often be needed as a result of changes in query, update, and report traffic and natural growth in the types of stored information.”

Codd then introduces his relational model. This model would be refined and expanded in subsequent papers: In 1971, Codd wrote about ALPHA, a SQL-like query language he created; in another 1971 paper, he introduced the first three normal forms we know and love today; and in 1972, he further developed relational algebra and relational calculus, the mathematically rigorous underpinnings of the relational model. But Codd’s 1970 paper contains the kernel of the relational idea:

The term relation is used here in its accepted mathematical sense. Given sets \(S_1, S_i, ..., S_n\) (not necessarily distinct), \(R\) is a relation on these \(n\) sets if it is a set of \(n\)-tuples each of which has its first element from \(S_1\), its second element from \(S_2\), and so on. We shall refer to \(S_j\) as the \(j\)th domain of \(R\). As defined above, \(R\) is said to have degree \(n\). Relations of degree 1 are often called unary, degree 2 binary, degree 3 ternary, and degree \(n\) n-ary.

Today, we call a relation a table, and a domain an attribute or a column. The word “table” actually appears nowhere in the paper, though Codd’s visual representations of relations (which he calls “arrays”) do resemble tables. Codd defines several more terms, some of which we continue to use and others we have replaced. He explains primary and foreign keys, as well as what he calls the “active domain,” which is the set of all distinct values that actually appear in a given domain or column. He then spends some time distinguishing between a “simple” and a “nonsimple” domain. A simple domain contains “atomic” or “nondecomposable” values, like integers. A nonsimple domain has relations as elements. The example Codd gives here is that of an employee with a salary history. The salary history is not one salary but a collection of salaries each associated with a date. So a salary history cannot be represented by a single number or string.

It’s not obvious how one could store a nonsimple domain in a multi-dimensional array, AKA a table. The temptation might be to denote the nonsimple relationship using some kind of pointer, but then we would be repeating the mistakes of the navigational models. Instead. Codd introduces normalization, which at least in the 1970 paper involves nothing more than turning nonsimple domains into simple ones. This is done by expanding the child relation so that it includes the primary key of the parent. Each tuple of the child relation references its parent using simple domains, eliminating the need for a nonsimple domain in the parent. Normalization means no pointers, sidestepping all the problems they cause in the navigational models.

At this point, anyone reading Codd’s paper would have several questions, such as “Okay, how would I actually query such a system?” Codd mentions the possibility of creating a universal sublanguage for querying relational databases from other programs, but declines to define such a language in this particular paper. He does explain, in mathematical terms, many of the fundamental operations such a language would have to support, like joins, “projection” (SELECT in SQL), and “restriction” (WHERE). The amazing thing about Codd’s 1970 paper is that, really, all the ideas are there—we’ve been writing SELECT statements and joins for almost half a century now.

Codd wraps up the paper by discussing ways in which a normalized relational database, on top of its other benefits, can reduce redundancy and improve consistency in data storage. Altogether, the paper is only 11 pages long and not that difficult of a read. I encourage you to look through it yourself. It would be another ten years before Codd’s ideas were properly implemented in a functioning system, but, when they finally were, those systems were so obviously better than previous systems that they took the world by storm.

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