A transitive dependency is a

functional dependency In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database. In other words, a functional dependency is a constraint between two attributes in a relation. Given a relation ' ...

which holds by virtue of transitivity among various software components.

Computer programs

In a

computer program A computer program is a sequence or set of instructions in a programming language for a computer to execute. Computer programs are one component of software, which also includes documentation and other intangible components. A computer program ...

a direct dependency is functionality exported by a

library A library is a collection of materials, books or media that are accessible for use and not just for display purposes. A library provides physical (hard copies) or digital access (soft copies) materials, and may be a physical location or a vir ...

, or

API An application programming interface (API) is a way for two or more computer programs to communicate with each other. It is a type of software interface, offering a service to other pieces of software. A document or standard that describes how ...

, or any

software component Component-based software engineering (CBSE), also called component-based development (CBD), is a branch of software engineering that emphasizes the separation of concerns with respect to the wide-ranging functionality available throughout a give ...

that is referenced directly by the program itself. A transitive dependency is any dependency that is induced by the components that the program references directly. E.g. a call to a function will usually induce a transitive dependency to a library that manages the I/O to write the log message in a file. Dependencies and transitive dependencies can be resolved at different times, depending on how the

is assembled and/or executed: e.g. a

compiler In computing, a compiler is a computer program that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs tha ...

can have a link phase where the dependencies are resolved. Sometimes the build system even allows management of the transitive dependencies. Similarly, when a computer uses

services Service may refer to: Activities * Administrative service, a required part of the workload of university faculty * Civil service, the body of employees of a government * Community service, volunteer service for the benefit of a community or a p ...

, a

can depend on a service that should be started before to execute the program. A transitive dependency in such case is any other service that the service we depend directly on depends on, e.g. a

web browser A web browser is application software for accessing websites. When a user requests a web page from a particular website, the browser retrieves its files from a web server and then displays the page on the user's screen. Browsers are used o ...

depends on a Domain Name Resolution service to convert a web URL in an

IP address An Internet Protocol address (IP address) is a numerical label such as that is connected to a computer network that uses the Internet Protocol for communication.. Updated by . An IP address serves two main functions: network interface ident ...

; the DNS will depend on a networking service to access a remote name server. The Linux boot system is based on a set of configurations that ''declare'' the dependencies of the modules to be started: at boot time analyzes all the transitive dependencies to decide the execution order of each module to start.

Database Management Systems

Let A, B, and C designate three distinct (but not necessarily disjoint) sets of attributes of a relation. Suppose all three of the following conditions hold: # A → B # It is not the case that B → A # B → C Then the functional dependency A → C (which follows from 1 and 3 by the

axiom of transitivity In mathematics, a relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Each partial order as well as each equivalence relation needs to be transitive. Definition A hom ...

) is a transitive dependency. In

database normalization Database normalization or database normalisation (see spelling differences) is the process of structuring a relational database in accordance with a series of so-called normal forms in order to reduce data redundancy and improve data integrity ...

, one of the important features of

third normal form Third normal form (3NF) is a database schema design approach for relational databases which uses normalizing principles to reduce the duplication of data, avoid data anomalies, ensure referential integrity, and simplify data management. It was ...

is that it excludes certain types of transitive dependencies. E.F. Codd, the inventor of the relational model, introduced the concepts of transitive dependence and third normal form in 1971.Codd, E.F. "Further Normalization of the Data Base Relational Model." (Presented at Courant Computer Science Symposia Series 6, "Data Base Systems," New York City, May 24th-25th, 1971.) IBM Research Report RJ909 (August 31st, 1971). Republished in Randall J. Rustin (ed.), ''Data Base Systems: Courant Computer Science Symposia Series 6''. Prentice-Hall, 1972. See pages 45-51, which cover third normal form and transitive dependence.

Example

A transitive dependency occurs in the following relation: The functional dependency → applies; that is, if we know the book, we know the author's nationality. Furthermore: * → * does not → * → Therefore → {Author nationality} is a transitive dependency. Transitive dependency occurred because a non-key attribute (Author) was determining another non-key attribute (Author nationality).

Notes

Database constraints Database theory