The LaTeX Case Study

The LaTeX Case Study: Issues in the development of open-source software over the long-term

This research, published in 2007 in the Review of Network Economics [*] traces the history of TeX, the open source typesetting program. TeX was an early and very successful open source project that imposed its standards in a particularly competitive environment and inspired many advances in the typesetting industry. Developed over three decades, TeX came into competition with a variety of open source and proprietary alternatives. I identify a range of issues that arise in the development of open-source software over the long-term. I argue that open source developers derive direct and indirect network externalities from the use of their software by others. They must therefore consider non-developers’ needs to make their software more attractive to a broader audience and more competitive with proprietary alternatives.

1. Introduction

This paper offers an analysis of the competition between open source (OS) and proprietary software systems through a study of the long-term development dynamics of the TeX typesetting software.[1] The TeX project was launched in 1978 under an open source license, long before other better known OS projects such as Linux. This case study thus draws on a long history.

In this article, I focus on the dynamics of competition between OS and proprietary typesetting software. I analyze the multi-period strategies by which they borrowed from each other, complemented each other and reacted to advances on the competing side. A variety of developers developed applications, proprietary or otherwise, for TeX, an open source typesetting platform. On one side, users chose whether to adopt TeX as their typesetting platform, or competing proprietary platforms, and if they chose TeX, also chose what specific applications to use. On the other side, developers chose whether to develop for the TeX platform or for another platform, and if they chose TeX, chose under what license they would release their contributions. This depended on the nature of the application they wished to develop. It also depended on the presence of and ease of access to other development platforms in the proprietary world. Decisions of users and developers were complementary: the diffusion of TeX was closely dependent on the dynamics of its development and on the technological changes that happened outside of the TeX world. OS developers and users recognized this; they formed coalitions and took strategic decisions to influence the direction of the development of TeX.

This paper illustrates a simple basic hypothesis: while OS developers improve open source software (OSS) for their own purposes, in order to better fulfil their needs, they also derive benefits from the use of their software by others (network externalities). This encourages them to broaden the software’s user base by providing features that may be of no direct use to themselves or that may be low on their own priority lists. For example, they work to facilitate the initiation into the use of the software, or to make the software more accessible and easy to use. They also want to maximize the benefit of network externalities by agreeing on and following a variety of standards in the development, licensing and maintenance of their contributions to the software. They want the software to behave the same way on any user’s machine, they want new contributions to fit guidelines so they can be integrated seamlessly into the software distribution and they want this “official” software distribution to be used by all. Those objectives are only achieved by agreeing with others on how the software should behave and by coordinating the ensuing development efforts with other developers. Developers have to balance their need for independence in their development decisions with the need to coordinate with other developers and they have to be receptive to the needs of users. OS developers also have to take account of the proprietary offering and negotiate the positioning of their software in the market in order to maintain or increase their user base. Not only do they have to think in strategic terms but they also have to impose a level of discipline and a sense of direction onto the development of the software, which is more difficult. This is the purpose of OSS organizations. Those organizations provide a platform where users can express their needs and where developers can express their ideas and goals. Users and developers make sense together of the software’s position in its development area and negotiate development objectives. This process give rise to complex organizational dynamics whereby developers position themselves, form coalitions, try to convince others by appealing to shared interests or the common good, etc.

The basic hypothesis according to which developers and users consider network effects in their development and consumption decisions is used to explain a number of patterns in the development of the TeX development platform. The next section is an analysis of the existing literature on the topic.

2. Literature review

This paper is a study of the competition in the provision of a potentially excludable but non-rival good, software. When a good is non-excludable, then it is generally assumed it has to be publicly provided. If it is made excludable, by putting it under copyright for example, then it is assumed it is privately supplied in the same way as most standard goods. However, the situation in the software industry is different: some software is provided under open source licenses,[2] while some other software is provided under proprietary licenses. This is a mixed industry where for-profits and nonprofits coexist (Kuan, 2001). Open source software is privately provided through voluntary contributions (Bergstrom, 1986). OSS organizations differ from other nonprofits in that OSS production is not usually publicly subsidized, it does not rely in any significant way on private donations for its development, and its provision is not directed by the State or any other formal institutions or interest group. Open source projects are the result of the work of individually motivated developers and it is difficult for any institution to direct their development.

This paper extends the literature on public goods in the specific context of open source provision by examining the dynamics of the private provision of a public good in a competitive setting. How does an OS organization react to competition, both from other OS projects and from proprietary projects? How does an open source organization adapt to changes in its market environment? How do commercial organizations adapt to the presence of OS competition? Will each type of organization specialize in specific areas of software development? Will they serve different types of customers or develop different software parts? Are there exchanges and synergies between each type of organization?

I will build on the existing literature on OS methods of production, which deals principally with (1) the organization of development and (2) the incentives of OS developers. I will then be able to present (3) the literature on competition between OS and proprietary organizations.

2.1 Organization:

Far from being the “bazaar” evoked in Raymond (2001), open source development is hierarchic and subject to peer review. Small groups of developers contribute most of the “core” code. Other developers provide support for specific systems or functionalities while some other volunteers provide user support and help maintain the infrastructure of the project (Mockus, 2005; and Lakhani, 2002).[3]

Development is done module by module in an incremental way, with each module a relatively independent part of the complete software. Work is thus fragmented to the individual or small team level, with limited need for central coordination (Krogh, 2003a). Central coordination is done by the lead developers, who also contribute the most to the software’s development (see, for example, Kogut, 2001, Table 3) and are able to influence its course (see, for example, Bezroukov, 1999 on the role of the leader and conflicts between developers).

2.2 Incentives

A developer who develops software that is under OS licensing terms has two sets of motives (Lakhani, 2005). One set of motives is own-use or own-enjoyment; she wants to develop software that she needs or enjoys developing (Hippel, 2005). The other set of motives is to get others to use her software, or software based on the code she developed. It may be that the software benefits from network effects (the more people use it, the higher is its utility, as is the case, for example, with communication software); or that she derives prestige and reputation from its success (Lerner, 2002); or that she expects users to convert into developers who will then improve the software, contribute their expertise and knowledge and provide peer review (Krogh, 2003a); or that she is an altruist or her effort is sponsored by a governmental entity or a foundation with altruistic goals.[4] Finally, it may be that developers who work in teams come to identify with the group, its welfare and its objectives (Hertel, 2003). Early users then become advocates for their software and help its diffusion (Dalle, 2003).

Organizational factors and individual incentives combine in such a way as to allow some predictions on the likely outcomes of OSS development processes. User-developers who arrange to produce a good for themselves (Kuan, 2002) are precursors whose needs anticipate others’ (Hippel, 1994; and Hippel, 1998). They focus on developing novel functionality rather than improving existing products. They develop software that is more flexible and offers better control of its internal working than what proprietary software can offer. OS developers develop software in those areas in which the proprietary offering is unsatisfactory and they group along common needs (Franke, 2003). This commonality of aims facilitates coordination among developers.

2.3 Competition

OSS has made significant inroads in many areas of software development, from servers (Apache) and mail management systems (Sendmail) to operating systems (Linux), browsers (Mozilla) and typesetting engines (TeX). However, some argue quite reasonably that OSS is not used by the average user because it is difficult to install, use, maintain and update, because it is of lower quality or offers less functionality than proprietary software or finally because OS development is too unruly and undirected to provide the stability and support users’ need (Nichols, 2003).

The problem that is most often evoked in the economic literature, however, is that of free-riding which leads to a tragedy of the commons where no one develops and all use low-quality free software. The problem worsens as OSS becomes more popular; it can lead experienced developers to quit (Foray, 2001; see also Foray, 2007) or to develop proprietary versions of OSS. That last option is indeed available if software is under the liberal Berkeley Software Distribution (BSD) license rather than the more restrictive General Public License (GPL) (Gaudeul, 2005).

In the following, I consider three different hypotheses: (1) OSS would mean the end of proprietary software because of it is available for free; (2) proprietary software would subsist as a complement to OSS because OSS is not fit for all uses or for all users; and (3) proprietary developers would maintain their position vis-à-vis OSS because they keep a strategic advantage over OS developers. This paper complements the existing literature by showing how OS developers also develop strategies to compete with proprietary software.

Consider in the first instance the hypothesis according to which, everything else being equal, OSS means the end of proprietary software. The logic is simple: consumers prefer using a free product to a paying one. OSS thus reduces profits for proprietary firms and deters investment in software production and thus innovation, leading to a standstill in software development (Schmidt, 2003). Bitzer (2006) argues otherwise; case studies of the markets for operating systems, servers and web browsers show that increasing competition by OSS tends to accelerate the pace of innovation. Krogh (2003b) argues that OSS breeds a new and more efficient “private-collective” innovation model. Rather than disappear, proprietary firms adopt a range of for-profit strategies in the exploitation of OSS – examples are offered by Koenig (2004) for such companies as Oracle, IBM, HP or Red Hat. Proprietary firms develop and sell OS-related products and support services, or they launch OS products and encourage the development of a community of OS developers that improve them (Bonaccorsi, 2004; see also Wichmann, 2002). Proprietary firms encourage and support OSS when doing so promotes their preferred standard,[5] or when it allows them to gain some control of the OS standard and influence its development (a strategy followed by IBM with Linux and by Sun Microsystems with Java) (Mustonen, 2005; see also Mustonen, 2003).

A second strand of literature thus argues how OS and proprietary software can cohabit. This is, for example, because OSS is developed by developers for the benefit of developers, whose purpose and need are different from those of the average user. Notably, OSS is developed specifically for those who are not satisfied with the proprietary offering so that by design, OSS is not fit for use by the majority of users who use proprietary software. Bessen (2004) argues that pre-packaged proprietary software addresses common uses with limited feature sets while OSS targets users with more specialized and complex needs. Nichols (2003) points out how developers differ from most users in their preferences in terms of user interface. For example, developers prefer command-line-based interfaces with many shortcuts that allow direct access to the basic functions of the software. Users prefer the more intuitive WYSIWYG interfaces that automate frequently used tasks but are less flexible.

This leads a third strand of literature to point out that proprietary developers keep a strategic advantage over OSS. This is through their ability to coordinate strategy and development in a market oriented way. Proprietary developers benefit from their ability to direct the work of others in a centralized way according to a well-defined and enforceable strategy (Herbsleb, 2003 or Yamauchi, 2000). Proprietary developers may exploit network effects strategically, subsidizing the first users to build a user base and then exploiting the late comers (Casadesus-Masanell, 2003). The proprietary developers attract developers to their development platform by cross-subsidizing developers with revenues from users or vice versa (Economides, 2006). This type of cross-subsidy, as well as other strategies that require financial means, such as advertising, is not available to OS developers as OSS generates only limited income streams. Proprietary developers are also able to differentiate in specific ways from OSS (Bitzer, 2004). They may identify new needs and devise targeted development strategies to address those needs. Proprietary developers may address the needs of a niche portion of the market if they are latecomers on a market where OSS is already present. Proprietary developers may use OS code or adopt OS standards to get a head start into specific development areas (Gaudeul, 2006). They may also hire OS developers away from OS development by offering them high wages, a strategy that may be at work if one considers such OS developers as Linux’s Linus Torvalds or Sendmail’s Eric Allman who did go on to work for proprietary outfits (Mustonen, 2003).[6] Some companies such as (allegedly) Microsoft, may use a range of other strategies to counter the emergence of OSS. They may use scare tactics underlining the fact OSS is “unsupported”.[7] They may also lower their prices for those consumers who are most likely to be attracted by OSS. Administrations thus get preferential deals and less developed countries get Windows XP Starter Edition, a lower cost lesser quality version of Windows XP.

In this paper, I analyse the strategies, successful or otherwise, by which OS developers try to establish themselves in the market. As in Dalle (2003), much depends on the initial momentum gained from proselytizing by early users and on the ability of open source developers to organize efficient development processes (possibly with the help of ancillary business firms). There is a constant tension between coordinated development on a standard that brings high direct (for consumers) and indirect (for developers) network externalities in the long-term, and fragmented development that faster addresses a wider range of needs, though at the expense of coherence in development.

This paper is introduced by a presentation of the TeX software and of the actors and institutions that influenced its development. The development of the software is analyzed over time, which leads to a discussion of how TeX positioned itself in its environment. The main body of the paper deals with the strategic motives behind the evolution of the development of OS and proprietary software in the typesetting software industry since the emergence of TeX. Information on the project’s development was gathered from interviews with participants in the development of the TeX typesetting system, with administrators of the TeX User Groups (TUG) and with maintainers of the project’s organizational infrastructure. Other sources include the TUG’s journal (TUGBoat), the TUG’s website (, the websites of the many national TeX users’ group, the websites of projects associated to TeX, and also the TeX related newsgroups. Several others sources were used to gain a better understanding of the typesetting software industry and of its evolution over time.

3. TeX, the software and its history

TeX is a computerized typesetting system. A TeX file contains both the text to be published and instructions on how to format it for an output (dvi, ps, pdf, html, or xml files). That output may be distributed in digital or paper form. TeX is used by authors, typesetters and publishers for a wide variety of tasks. TeX became the standard submission format for most mathematical journals and is commonly used for scientific papers; TeX is widely used in the publishing industry for the communication of printed work between authors, editors, and printers; TeX is frequently used as a back-end application in publishing, taking as input documents typeset in various mark-up languages (HTML, XML, TeX) and outputting documents in various rendering formats for printers or for the web. Typesetters whose needs are not fulfilled by a proprietary offering, those who cannot afford proprietary tools and those with very specialized needs appreciate the flexibility, versatility and free availability of TeX systems. Finally, the TeX info format, based on TeX, is the official documentation format of the Free Software Foundation (FSF).

TeX is a medium size software project; not as big as an operating system like GNU/Linux, but still a whole typesetting system with many interdependent modules. From statistics on the popularity of the project (Table 1, Appendix 7.1), gathered from several sources, TeX could be compared in size to Sendmail, the OS mail management software, or to QuarkXPress, a dominant proprietary typesetting software. It is, however, certainly less popular than mainstream word processing software, be they open source or proprietary. The initial version of TeX (1979) gained about 100 to 1,000 users, the second version (1982) had about 10,000 users while TeX was used by more than one million by the time its third version was released in 1990.[8] TeX is widely available as it was ported to the Linux, Mac and Windows platforms, among others. The extent of the diffusion of TeX is reflected in the steady increase in the number of requests for support in TeX -related newsgroups, up to 4,500 posts per month in 2000 across newsgroups devoted to TeX in English, German and French.[9] The creation of Local User Groups (LUG) across the world is another testimony to the popularity of TeX and the wide involvement of users in its promotion and development. There were about 6,500 active members in a dozen national TeX user groups across the world in the early 2000s.[10]

The TeX project was started by Donald E. Knuth in the late 70s at Stanford University.[11] In a first phase (1978-1985), development was heavily centred around Donald Knuth at Stanford University. This was when the core of the program was developed.[12]

In a second phase (mid-80s), core development was complemented by the development of TeX sub-routines, that is, sequences of TeX commands that eased access to TeX’s functionalities.[13] A number of packages were developed in a rather decentralized way, leading to many replications in the development of similar features. Several different distributions of TeX competed on the market, each maintained by different persons and distributed under different licenses: freeware, OS, proprietary.

The LaTeX package rapidly became the most widely adopted. In the third phase (late 80s, early 90s), priority was given to the development of tools and systems that made the TeX system easier to use and develop.[14] Development became better coordinated thanks to the creation of coding banks (software packages repositories) and to the creation of a standard way of classifying those packages into the repository (directory structure).

The TeX User Groups worked to improve usability by making TeX systems available as a complete set of inter-related TeX packages – the TeX Live distribution, structured along a standard (the TeX Directory Structure) and available on a common repository (the Comprehensive TeX Archive Network). There were efforts also in developing programs for easy access to the various TeX programs and commands (interfaces). This was, thus, a stage of rationalization and of integration.

The fourth and present stage (90s to present) was characterized by a return to decentralization. The need for a central dedicated coordination system became less urgent as Web-based tools made it possible to efficiently coordinate OS projects in a decentralized way. The software came to be used in a wider variety of countries and by a wider variety of people. The software also came to be called upon for the fulfilment of needs that the original developers had not anticipated and that the standard TeX software could not respond to adequately. This was when there were several attempts at remodelling the core of TeX along new lines, with various levels of success.[15] A stable TeX distribution of reference (TeX Live), used by most but developed and maintained only by a few, now coexists with a variety of specialized applications based on TeX, where most of the development effort is concentrated.

The licensing of TeX systems is complex. The core of TeX, tex.web, is copyrighted by D.E. Knuth, and no changes are permitted, although of course concepts used in the program may be re-used. “TeX: the program” is in the public domain, although the use of the name “TeX” is restricted to exact copies of Knuth’s software systems. Most programs that have added up to “TeX: the program” – are licensed under the LaTeX Project Public License (‘LPPL’). The LPPL can best be described as a BSD license. This means developers can develop closed-source proprietary versions of the software. However, the LPPL is slightly more restrictive than the BSD: any change to a file must be renamed and distributed with the original version. This is meant to guarantee the integrity of the TeX system: a user should always have the choice between the standard version of a file and its modified version. This means any user is guaranteed access to the exact same program as any other user and can thus output the exact same result from a .tex file as that other user. Finally, many of the binaries in TeX distributions are licensed under the GPL.

The next part goes further into an analysis of the dynamics of TeX’s development but the argument can be summarized as follows: the growth of TeX’s user base came with a progressive diminution in the dynamism of the software’s development; the weight of legacy users undermined attempts to adapt TeX to new uses, technologies and standards. There was then a certain amount of diversification in different projects that addressed ancillary needs. From competing projects addressing the same needs emerged a few clear winners. Those were gathered and combined by developers and users into a distribution,[16] under the leadership of the TeX User Groups. Proprietary developers identified specific gaps in the OS offering and developed proprietary improvements on TeX, provided WYSIWYG interfaces and add-ons or simply provided support in the use of the software. While some of those proprietary products did draw some users away from OS TeX and its community, they also often provided the non-programmer a first step in the use of TeX and thus broadened its audience. A variety of new independently developed proprietary software and standards then threatened the survival of TeX. TeX developers had to adapt to and adopt those new standards to keep TeX up-to-date with changing technologies and standards in the typesetting industry. However, not all developers agreed on how to do so, which weakened the coherence of the TeX project. Different engines, packages and distributions appeared and users came to adopt the ones that responded best to the different specific new needs that were brought about by the evolution of the typesetting software industry. This fragmentation of user constituencies limited the incentives for developers to coordinate and maintain compatibility, which threatened further the coherence of the TeX project.

4. Competition with proprietary software

4.1 A map of the industry

TeX had to face intense competition from an array of competitors, from simple word processing software to professional publishing software. First aimed at professional typesetters, TeX’s superior quality (better fonts, better hyphenations and justification algorithms, better rules for letter spacing) drove out less advanced proprietary competition from which it borrowed many ideas and features as well (Script (1970), Roff (1971), Scribe (1978)). It also replaced in-house proprietary typesetting systems such as the one that was used by the American Mathematical Society for mathematical typesetting.

TeX’s code was then integrated into proprietary offerings. Distributions such as pcTeX (1985), MicroTeX (1985), TrueTeX and Y&Y (1991) provide(d) TeX systems that were pre-packaged and easy to install. Environments such as TeXtures (1989) for the Mac or Scientific Workplace (1994) for Windows provide(d) user interfaces. Extensions such as vTeX added functionalities to open source TeX systems. Some companies provided additional font packages and printer drivers for TeX systems.

With the exception of Scientific Word and PCTeX, TeX-based proprietary competition did not maintain itself over the long-term as OS versions caught up with it. Distributions such as TeX Live (1996) and MikTeX (1996) eased the installation and management of TeX distributions, and some projects such as LyX (1999) or TeXmacs (2002) developed WYSIWYG interfaces to TeX.

Independently developed proprietary software was more serious competition: it was easier to learn and came with superior interfaces and took a large part of the market. This occurred in a two pronged attack: some proprietary systems fulfilled the needs of those professional typesetters who needed easy-to-learn standardized software (Framemaker (1986), Quark’s QuarkXPress (1987)). Some others satisfied the needs of those users who merely needed simple and easy-to-use text processors (Corel’s WordPerfect (1982), Microsoft’s Word (1984)).[17] Proprietary software that was developed independently from TeX thus came to replace TeX in its less specialized, general typesetting functionalities.

Typesetting standards and technologies evolved as well. Adobe’s pdf technology (1993) was generally adopted as a document rendering format, replacing TeX’s DVI, and the TeX mark-up language was replaced by new OS markup languages (SGML (1986), XML (1998), MathML (1999), XHTML (2000)).

Development at that stage was mainly influenced by the emergence of those open typesetting and document rendering standards. pdfTeX (1996) was developed to output pdf documents from TeX. TeX was one of the first high-end typesetting programs to be adapted to handle new mark-up languages such as XML (XMLTeX, 2000).

In the end, TeX kept those users who could not afford proprietary typesetting software (users in emerging countries, students), those people who needed its unique mathematical capabilities (academics) and those typesetters who valued the flexibility OSS offers to devise their own specialized versions of TeX. Many typesetters kept using TeX as a back-end to handle documents typeset in a variety of typesetting languages. Development focused on specialized applications such as Ω (1994) for rare script and ancient documents with complex, multi-lingual typesetting or ConTeXt (1994) for interactive educational material. There was also a drive to develop user friendly interfaces for TeX (LyX (1999), TeXmacs (2002), XeMTeX (2003)), following a trend towards improving OS usability; cf. for example, the emergence of open source word processors such as OpenOffice (2002) or Abiword (2000).[18]

development tex

Figure 1: The development of TeX over time: Dominance, squeeze and fragmentation.

Figure 1 illustrates the above paragraph. The three phases in the relation of TeX to its competition are outlined (dominance, squeeze and fragmentation) and the main actors in each phase are represented. Represented at the top are high-end applications for typesetting and publishing, and at the bottom are common applications for the end user (word processors). The right hand side illustrates the fragmentation in the development of high-end TeX applications, as well as the development of integrated TeX systems and interfaces for the end user.

The next sections offer an analysis of the evolution of TeX with respect to its proprietary competition, and is divided in four parts, broadly along chronological lines.

4.2 Network externalities and OS development goals

How effective the OS organization was in getting work coordinated was largely dependent on the anticipated benefit of doing so. This was linked in the minds of developers not only to how effective coordination could be in achieving technical aims, but also to whether those aims would make (La)TeX more competitive vs. its proprietary alternatives. They thus considered the interests of users, as well as their own, in the choice of what features to develop and whether to participate in collaborative work instead of each working on their own.

The consideration of user needs was important to TeX developers for all the reasons evoked in section 2.2, but also more specifically because TeX developers believe in the superiority of TeX as a standard and in the desirability of all using one standard to facilitate communication of typeset material in the scientific community. Developers wanted (La)TeX to keep a high market share in some domains – mathematical typesetting foremost among those. From the beginning, the development of TeX was user oriented and attracted active interest from users.

The user organizations’ dynamism was highest when (La)TeX was under the highest threat of losing market share to its alternatives (1990s). The TUGboat, official journal of the TeX community, collected users’ initiatives and outlined the problems they encountered. Several programmatic papers outlining goals and priorities for the development of TeX were published in the TUGboat and presented at TUG conferences.[19] This was when OS developers worked on interfaces, distributions and a rationalization of development so as to keep their user base. Development then had to become ever more efficiently led – with the use of better coordination tools, the building of central code repositories and the writing of procedures to submit new codes.

Lesson 1: User orientation: OS developers that are motivated, at least in part, by the popularity of their software see competition from proprietary software as a stir for the development of features they would otherwise find useless. Competition encourages developers to participate in collective development, to make their software accessible, to promote it actively and to respond to users’ needs and queries.

4.3 Open source inertia

There was some inertia in this response to competition, however. TeX’s development was dominated by the original set of users of the software, which meant new or potential new users found it difficult to influence the dynamics of the software’s development. TeX’s license forbade different versions of TeX from calling themselves TeX. This meant there was only one version of TeX which was controlled by its original developer, D.E. Knuth. The same pattern was repeated in the case of LaTeX, the dominant set of TeX macros. First controlled by its original developer, Leslie Lamport, its control was then transferred to a group of developers, the LaTeX3 team. This tight control made it difficult for outsiders to influence the development of new versions of TeX or LaTeX.[20]

The user groups had an ambiguous influence on development, both encouraging better coordination between developers and discouraging development into new areas which would have required adaptation by “legacy” users. One of the TUG’s main early sponsors was the American Mathematical Society, which saw in TeX an archival format. It thus wanted to promote backward compatibility, that is, all new versions of TeX had to be able to process all TeX documents that were typeset in the past. The TUGs encouraged projects that were of interest to existing users, such as extensions of the software’s core, compatibility with alternative standards (PDF, HTML, XML), rationalization of the TeX distributions, or standardization of the most popular packages. It did not get involved in specialized projects that were of interest only to a few of the existing users or that could lead to problems of compatibility between versions of TeX. The TUG wanted to protect their constituency; a change attracting some users had to be balanced against the risk of alienating some established users.

Lesson 2: Inertia: Institutionalized tight control by relatively closed development teams and the conservative influence of established users combine to make changes in OSS difficult. This is not all for the worse, as it promotes stability and continuity in development. However, this slows down the response to technological shocks (new standards, new concepts).

This meant there was a fall in the membership and contributions to the original US TUG in the 90s (see figure 2); existing users, satisfied with TeX, stopped contributing to its development, and few new members joined. On the other hand, European user groups such as the NLG (Netherland) and Dante (Germany) that were more responsive to the needs of new users became very dynamic and worked to encourage the adoption of TeX in their respective countries.[21]

development tug

Figure 2: TUG revenues and membership by year: 1982-2000

The inertia from having to keep on serving established users translated into tensions between TeX developers and a tendency for new developers to start their own projects, leading to a progressive fragmentation in the development effort. Fragmentation (forking) was due to initiatives by users whose needs were not accommodated by the (La)TeX development teams. While this forking weakened the position of TeX as a standard and diverted developers from the main strand of development, it also adapted TeX to the needs of a wider variety of users, thus contributing to the popularity of TeX. On the proprietary side, there was a switch from entrepreneurs borrowing from TeX to them developing software independently.

Lesson 3: Fragmentation: Faced with the resulting obsolescence of their software, developers find it difficult to agree on needed changes because any change threatens at least some users or can weaken the influence of at least one development group. This leads to dissensions so that development coherence is threatened. Inertia in the development of OSS leads to the fragmentation of its user base and of its development groups. Developers start independent projects and each project attracts a part of the existing user base.

4.4 Proprietary responsiveness

As explained above, the TUG encouraged the diffusion of new TeX developments to a broad audience and prevented unnecessary replication in the development of new features. However, it cared mostly about existing users and improving the existing software, not necessarily finding new domains of application or increasing TeX’s market share. OS developers frequently anticipated the need for some features but quite often, however, their needs were too specialized and were of no interest to the common user, while on the other hand, what would have been interesting for the common user was of no interest to them. For example, they were not interested in a graphical user interface as they were already comfortable with the TeX language and there was considerable reluctance in considering the needs of Windows users.[22] TeX developers also lacked the means or the will to conduct radical restructuring of TeX; a project such as the New Typesetting System (NTS), whereby TeX users’ groups financed the development of a successor to TeX, was not successful. Successful projects, such as pdfTeX, developed only through small extensions of TeX and focused on practical typesetting problems.

All this meant that proprietary developers were often first to spot new market opportunities and act on them. Proprietary development, in contrast to OS development, was directed toward providing new functionalities so as to attract new segments of the user population, at the expense sometimes of improving existing functionalities that were of use to their existing partially locked-in users. Commercial developers focused, for example, on making a coherent whole from OS development efforts or filling in its missing features. Commercial software found a relative advantage in facilitating the use of TeX by adding a user interface and porting TeX to non-Unix platforms. They did relatively little work in improving the core functionalities of TeX. Proprietary software based on TeX was frequently able to offer new and original features that were in demand but outside of the realm of interest of existing TeX users. TeXtures catered to the Mac users, PCTeX catered (and still caters) to the PC users, Y&Y provided sets of proprietary font outlines, Scientific Workplace integrates a computation software (Maple and then MuPAD).

One can wonder at this point why proprietary developers did not get involved in the development of TeX itself but rather concentrated on its marketing. In this, TeX indeed differs from other OS projects where proprietary involvement took other forms (support, development, patches and add-ins). This difference was probably due to the nature of TeX’s license (the LPPL, which is similar to the BSD license and allows for proprietary exploitation of the code), to the fact TeX was relatively easy to market as-is, as it was designed for use by a wide public of end-users with no required programming background, and to the fact that most changes in TeX could be handled without touching its core programming. Another factor was the stability of TeX over time and its status as a standard. This encouraged its take-up by commercial companies that then made TeX available to a wider public.

Lesson 4: Privatization: Proprietary developers take advantage of a certain amount of inertia in OS development to offer their own solutions to the problems faced by the OS community. Unimpeded by a responsibility to established users and motivated by profits, proprietary developers offer their own private “OS solutions”, targeted at those users who are outside of the area of interest of OS developers. In doing so, they patch OS deficiencies and help make OSS more accessible.

4.5 Open source catch-up

While proprietary developers were more responsive to users’ needs, this was only a transitory advantage as competition triggered a reaction by TeX developers and encouraged them to address user needs. TeX was made available in a complete easy-to-install distribution, integrated new font sets and also came to offer pdf format output. TeX Live, the OS distribution of TeX, and user interfaces such as the shareware WinEdt or the freeware WinShell spelled the end of many proprietary versions of TeX. Only these proprietary software that included features that the OS community was not able to develop, such as the WYSIWYG equation editor of Scientific Workplace and its integration of the Maple computation program, were able to survive.[23]

The fate of those entrepreneurs who chose to borrow from TeX and that of others who chose to innovate independently of OS development differed markedly. Entrepreneurs who borrowed from TeX saved on development cost and, as TeX was already established, could offer users of their proprietary product the benefit of being able to use an established standard. Proprietary products that were based on OSS often served as a Trojan horse for open source products. The enhanced diffusion of TeX, thanks to its better marketed and more accessible proprietary versions, helped to promote its standard. Users of the proprietary versions of TeX, which TeX would not have reached if it had been distributed only in its OS version, switched to OS TeX when the premium offered by proprietary versions weakened. Most firms that based their strategies on offering augmented versions of TeX were driven off the market when the OS TeX distribution caught up with them in terms of ease of use and functionalities. Commercial developers who did not differentiate from TeX, those who developed niche products in areas which OS development neglected or those who supplied easier access to the newest developments in TeX only gained a fleeting competitive advantage. Those entrepreneur who developed software independently from TeX, on the other hand, faced more expenses in development and had more difficulties establishing themselves but they were not threatened by every advance in TeX’s open source development, eschewed TeX’s technological limitations and did not depend on the continued development of TeX for their own survival.

Lesson 5: Catching-up: OS developers catch up with proprietary solutions that use OSS. Proprietary leadership encourages them to develop missing applications, develop compatibility with newly established standards and make OSS more accessible to the end user. Proprietary developers then face a choice between using OS code and building a fragile lead over OSS developers or incurring high development costs by developing software independently and establishing their own user base.

5. Conclusion

The open source TeX typesetting program was developed over three decades and came into competition with a variety of open source and proprietary alternatives. TeX was an early and very successful open source project that imposed its standards in a particularly competitive environment and inspired many advances in the typesetting industry. TeX’s rather unique success in a domain applications for the end user that is usually reserved for proprietary software gives it a status as a role model for the OS projects that want to attain success beyond the rarefied world of current users of OSS.

A strong user base increased the value of the software through direct and indirect network effects. Direct, demand-side network effects were particularly strong for TeX, a standard format for document exchange, while indirect, production-side network effects were strong as users could relatively easily convert into developers who then contributed themselves to the improvements in the software.

The TUG, staffed by volunteers, used members’ contributions to finance and encourage development of a more complete and accessible TeX distribution as well as a more user-friendly interface. This made TeX more attractive to a broader audience and more competitive vs. proprietary alternatives. The resulting wider use of TeX, in turn, increased the benefit of network effects to existing developers and users.

Network effects motivated developers to consider users’ needs. However, those users were those in their own constituency – be it defined as the group of early developers, as early users of TeX, as academics or as specialized typesetters. This situation gave the opportunity for commercial software developers to offer typesetting software for other types of users.

Over time, as commercial software came to offer increasingly high typesetting standards, TeX lost a part of its user base. Compatibility with its standard thus became less valuable. Those OS developers who previously had to abide by the TeX standards for fear of losing compatibility of their systems with the main strand of TeX development were no longer so reluctant to launch their own versions of TeX, extending its capabilities to, for example, multilingual typesetting or educational publishing.

Network externalities thus played an important role in the dynamics of TeX’s development, imposing coherence in times of dominance, leading to fragmentation in times of weakness.

In this article, I focused on the competitive dynamics in the development of the  system. Further work would examine the ecology of this OSS project: how did the various projects within TeX compete, how was a constant level of commitment obtained from developers, what were the specific coordination/management skills that successful project leaders within TeX possessed? The TeX experience certainly is a fertile ground for further research into the dynamics of community wide efforts in the development of a public good.

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7. Appendix

7.1 Popularity estimates for TeX

TeX vs. other OS projects
  Website Page Rank Back Links Word Count Alexa Rank
TeX 8 1,740 52,700,000 42,363
Apache 9 106,000 125,000,000 535
Mozilla 10 238,000 110,000,000 541
Linux 9 23,700 355,000,000 12,276
Sendmail 8 1,650 16,600,000 46,147
TeX vs. other typesetting and word processing software
  Website Page Rank Back Links Word Count Alexa Rank
TeX 8 1,740 52,700,000 42,363
QuarkXPress 8 1,660 5,570,000 27,403
InDesign 9 5,730 11,200,000 100
Microsoft Word 8 6,780 182,000,000 16
OpenOffice 8 49,200 31,200,000 2408

Table 1: TeX vs. its peer groups

Methodology: The name of the software was typed into Google’s search box. The number of websites mentioning the software (word count) was collected. The first website in Google’s list of results was selected. The number of websites linking back to that website (back-links) and its page rank was collected. The page rank is a complex function of the number of back-links that determines a website’s rank in Google’s list of results. It ranges from 0 to 10, on which scale higher is better. The website’s Alexa Rank, determined by the number of visitors to the website and their comments was also collected (where lower is better).

In case the software name used common words, the relevance of the search results was assessed by checking that the 10th page of results on Google contained a reasonable concentration of references to the software under study. If not, a more precise keyword was chosen.

7.2 TeX sub-projects

Name Object Category Lead Developer Inception
TeX Mathematical typesetting Core Donald Knuth 1978
PlainTeX Basic macros Macros Donald Knuth 1978
AMS-TeX Macros for AMS journals Macros Michael Spivak 1981
LaTeX General purpose TeX macros Macros Leslie Lamport 1983
BiBTeX Bibliographies Extension Oren Patashnik 1984
MakeIndex Indexes Extension Pehong Chen 1987
NFSS Easy access to a complete selection of fonts System Frank Mittelbach and Rainer Schöpf 1989
CTAN Online repository of TeX packages System CTAN team 1990
PSTricks Figures and graphs Extension Timothy Van Zandt 1993
4AllTeX Plug and Play TeX distribution for MSDOS PCs Distribution Netherland LUG 1993
WinEdt Shareware Interface Interface Aleksander Simonic 1993
Multilingual typesetting Core Yannis Haralambous and John Plaice 1994
LaTeX2ε Extension of LaTeX Macros LaTeX team 1994
ConTeXt Macros for educational publishing Macros Hans Hagen 1994
TDS Directory structure System TUG Working Group 1994
teTeX TeX distribution for Unix Distribution Thomas Esser 1994
pdfTeX pdf output Extension Hàn Thế Thành 1996
TeXLive Official distribution Distribution TUG and LUGs 1996
MikTeX Distribution for Windows systems Distribution Christian Schenk 1996
ε-TeX Updating TeX Core Peter Breitenlohner 1997
NTS Rewriting TeX Core Karel Skoupý 1998
fpTeX Windows version of teTeX Distribution Fabrice Popineau 1998
Winshell Freeware interface Interface Ingo de Boer 1998
LyX WYSIWYM (what you see is what you mean) interface Interface Matthias Ettrich 1999
TeXshop TeX previewer for Mac OS X Interface Richard Koch 2000
Preview-LaTeX Instant previewing of documents Interface David Kastrup 2001
TeXmacs WYSIWYW (what you see is what you want) interface Interface Joris van der Hoeven 2002
XeMTeX TeX system for the education sector and public administrations Distribution Marie-Louise Chaix and Fabrice Popineau 2003
XeTeX TeX with Mac OS X and Unicode Core Jonathan Kew 2004

Table 2:  sub-projects by year of inception and development category

The list of projects in table 2 is not comprehensive. A more complete list of contributors is given below. Categories include core, macros, distribution and interface development. Additional categories are systems development, which are improvements in the accessibility and structure of  systems and extensions, which are programs extending the capabilities of  without changing its core.

ε-TeX: Peter Breitenlohner and Phil Taylor.

CTAN team: Rainer Schöpf, Joachim Schrod, Sebastian Rahtz, George Greenwade, Robin Fairbairns, Jim Hefferon.

LaTeX3 team: Johannes Braams, David Carlisle, Robin Fairbairns, Frank Mittelbach, Chris Rowley, Rainer Schöpf, Thomas Lotze, Morten Høgholm, and Javier Bezos. Previous members: Denys Duchier, Alan Jeffrey, Michael Downes.

TeX Live/Collection coordinators: Sebastian Rahtz, Karl Berry, Staszek Wawrykiewicz, Manfred Lotz.

ConTeXt: Hans Hagen, Taco Hoekwater, Patrick Gundlach, Adam Lindsay and others.

pdfTeX: Hàn Thế Thành, Martin Schröeder, Hartmut Henkel, Taco Hoekwater, Hans Hagen, Heiko Oberdiek.

7.3 Chronology

See tables 3 and 4. Development is divided into three areas: core, macro, and others (organization, distributions and interfaces). Competitors are divided into four types: independently developed software, OS or proprietary, and software inspired by TeX, open source or proprietary. Freeware and shareware are classified as proprietary.

Development of TeX
  1970-1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989
Core TeX 1.0 in Sail DVI format TeX 2.0 in Pascal TeX2C: TeX in C TeX 3.0
Macro Plain TeX AMS- TeX LaTeX BibTeX makeindex LaTeX3 team
Organization (O), distributions (D) and Interface (I) TUG (O) NFSS (O)
Evolution in the software environment
  1970-1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989
Independent proprietary Script by IBM (70), Roff by Bell Labs (71) Corel Word Perfect Microsoft Word Pagemaker, Adobe Postscript Framemaker, Ventura, 3B2 QuarkXPress MS Word for Windows
Independent OS SGML
Inspired proprietary PCTeX, MicroTeX TeXtures
Inspired OS

Table 3: Chronology of the development of TeX and of its competitive environment from 1970 to 1989

Development of TeX
  1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Core Web2C PdfTeX ε-TeX NTS XeTeX
Macro PSTricks LaTeX2ε, ConTeXt XMLTeX JadeTeX (SGML)
Organization (O), distributions (D) and Interface (I) CTAN (O) 4AllTeX (D) TDS (O), teTeX (D) MikTeX (D), TeX Live (D) fpTeX (D) LPPL (O) TeXshop (MacOS) (I) preview-LaTeX (Unix) (I) Debian guidelines XeMTeX (Windows) (I)
Evolution in the software environment
  1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Independent proprietary pdf by Adobe InDesign by Adobe
Independent OS Groff (roff for GNU) HTML XML, Corel Wordperfect for Linux MathML XHTML, Abiword OpenOffice
Inspired proprietary Y&Y Scientific Word WinEdt WinShell
Inspired OS Lyrix LyX TeXMacs

Table 4: Chronology of the development of TeX and of its competitive environment from 1990 to 2003

8. Footnotes

[*] Gaudeul, A. (2007). Do open source developers respond to competition? The LaTeX case study. Review of Network Economics, 6(2), I would like to thank William Adams, Jacques André, Nelson Beebe, Barbara Beeton, Karl Berry, Lance Carnes, Thomas Esser, David Fuchs, Bernard Gaulle, Hans Hagen, Yannis Haralambous, Jim Hefferon, David Kastrup, Donald Knuth, Leslie Lamport, Wendy McKay, Barry MacKichan, B. Mahesh, Frank Mittelbach, Oren Patashnik, Simon Pepping, John Plaice, Fabrice Popineau, Sebastian Rahtz, Denis Roegel, Chris Rowley, Joachim Schröd, Karel Skoupý, Hàn Thế Thành and all other participants in the (La)TeX project whom I met and interviewed. Special thanks are due to Hans Hagen for his help in editing this paper. I would also like to thank Jacques Crémer, Bruno Jullien, Jean Tirole and Hal Varian for their advice, and an anonymous referee for helpful comments. The support of the CNRS and of the ESRC Centre for Competition Policy is gratefully acknowledged. All errors and omissions are mine.

[1] TeX is the core of the typesetting program while most users of TeX use the LaTeX set of TeX macros. Both the terms TeX and (La)TeX are used to designate the whole of the project.

[2] OS developers keep the copyright over their contributions to an OS project, but are limited in its use; it can be asserted only to prevent others from using their contribution without acknowledgment (Berkeley licenses (BSD)) or from using it as part of proprietary software (GNU Public License (GPL)).

[3] Fitzgerald, 2001; Fitzgerald, 2002; and Krogh, 2003b introduce special issues on this topic.

[4] An altruist is happy to develop software that is freely modifiable, with specifications that are open and that is free. Those developers who are employed by a firm to work on OSS have more pragmatic motives (Bonaccorsi, 2004; see also Hann, 2004).

[5] A strategy followed by Adobe, for example, which encouraged the development of pdfTeX, a version of TeX that produces pdf output.

[6] Lerner (2002) argues indeed that OS developers wish to signal their ability to firms by contributing to OSS development.

[7] FUD tactics (fear, uncertainty, and doubt), compare with for example, the Halloween documents that underline responses to open source emergence that were considered by Microsoft (

[8] Estimates provided by TeX administrators.

[9] From its creation in early 1990, posts to comp.text.tex peaked to 2,000 per month in 1994. As postings to the English-speaking newsgroup reached a plateau, posts to newsgroups in other languages grew. The German de.comp.text.tex started in 1996 and equalled the English group by 2000, while the French fr.comp.text.tex which started earlier (1994) received 500 messages per month by 2000 (figure 2, p.139 in Gaudeul, 2003). TeX newsgroups are primarily user and not developer oriented as developers communicate through mailing lists. By way of comparison, a popular Linux newsgroup such as comp.os.linux.misc was created in 1993 and received about 5,000 posts per month in 2000.

[10] The first TeX user group was established in the US in 1980 and now counts 1,800 members. It was followed by several LUG, first in Western Europe and then in Eastern Europe and Asia: Netherlands (1988, 300 members), Germany (1989, 2,000 members), France (1989, 500 members), the UK (1992, 150 members), Poland (1993, 300 members), the Czech Republic (1995, 400 members), India (1997, 100 members) and China (1999, 700 members).

[11] Table 2, Appendix 7.2 lists the most important TeX sub-projects, ranked by their date of first release.

[12] The core of TeX went through three versions, TeX 1.0 in 1978, TeX 2.0 in 1982 and TeX 3.0 in 1989, each a progressively smaller marginal improvement on the other. By 1990 then, the development of TeX was essentially stopped and by the mid-90s, limitations in TeX became more apparent. Various projects to extend the capabilities of TeX emerged: Ω (1994) for multilingual typesetting, pdfTeX (1996) for pdf rendering, ε-TeX (1997) and the “New Typesetting System” (NTS) (1998) that made TeX more flexible. ε-TeX is now the standard TeX extension while pdfTeX is currently the most popular TeX package.

[13]Early sets of macros such as plain-TeX (1978) and AMS-TeX (1981) were soon replaced by LaTeX (1983-1985). LaTeX’s development was taken over by the LaTeX3 team (1989), a group development effort that led to the release of LaTeX2ε (1994), while a set of macros for educational publishing was developed (ConTeXt, 1994). The suite of programs became more complex and the number of programs linked to it rose. The programs came to fit increasingly specialized needs: programs to generate bibliographies (BibTeX, 1984) and indexes (makeindex, 1987) or to draw figures (PSTricks, 1992) were developed. In Europe, local user groups initiated adaptations of macro packages to non-American typesetting traditions; TeX the program was adapted to deal with 8 bit input needed for non English languages (TeX 3.0, 1989)

[14] In that third phase, the TUG (1980), along with LUGs, set up a common repository for TeX packages (CTAN, 1990) and a standard way of organising all the TeX -related files on a computer system (TDS, 1994). Several other initiatives gave coherence to TeX systems, such as the NFSS (1989) that allowed easier access to the wide variety of fonts that had been developed over time. Complete distributions were made available. TeX Live (1996), the OS LaTeX distribution based on teTeX for UNIX distribution (1994), was translated into fpTeX for Windows Distributions (1998), a distribution that competed with the independently developed MikTeX Windows distribution (1996). Interfaces were also developed, the most popular being now the freeware WinShell (1998) which competed with the earlier shareware WinEdt (1993). Finally, the LPPL, a formalization of existing TeX license agreements, was imposed on most packages in a LaTeX distribution (1999). That license was adapted to the Debian Linux OS guidelines (2002) so as to facilitate the inclusion of the TeX system into Linux distributions. Routines to translate TeX in various alternative typesetting mark-up languages (html, xml, sgml …) and convert its output into various document formats (bitmap, postscript, pdf …) were developed. User interfaces became more sophisticated.

[15] Ω (1994), pdfTeX (1996), ε-TeX (1997) or NTS (1998), see note 12.

[16]A software distribution is a collection of software, already compiled and configured, that when installed on a computer constitutes an entire self-contained software system.

[17]Some of those companies (Arbortext (1982) or 3B2 (1986) for mathematical typesetting) borrowed parts of TeX. TeX’s conception principles, line breaking algorithm or syntax were widely copied. TeX’s equation editor was integrated in MS’s Word (1984) and TeX’s hyphenation and justification algorithm was used in Adobe’s InDesign (2000).

[18] Some proprietary firms, such as Corel and its Wordperfect (1998), made their word processors open source, in the same type of reaction to Microsoft’s dominance as that of Netscape vs. Explorer. Whether that type of software can really be considered open source is debatable, as there is generally little subsequent involvement by OS developers in those projects.

[19] For example, Mittelbach (1997) set out the program for the reworking of LaTeX by the LaTeX3 project team. The Netherland Local User Group (NTG, 1998) called for more cooperative development efforts in the reworking of TeX. Flynn (2001) set priorities for the broadening of TeX’s user base. Beebe (2004) advocated the adoption of the new OS mark-up languages rather than TeX’s native language. The debate over whether TeX should develop Windows-like, WYSIWYG interfaces was particularly heated (Cottrell, 1999).

[20] On the other hand, it did ensure coherence in the development of (La)TeX, which made TeX more stable and less difficult to maintain on one’s computer. One can notice that the release of new versions of TeX packages is a lot less frequent and more controlled than what is usually portrayed for a “typical” OS project; there were only three successive versions of TeX; the TeX Live distribution is distributed only annually to a wider public; more generally, development in teams tends to be rather secretive with potential new releases being the subject of much anticipation, as in the proprietary world. Much of this can be explained by the wish expressed by both Donald Knuth (Knuth, 1991) and the LaTeX3 team (LaTeX3, 1997) that TeX and LaTeX be typesetting standards. This meant that changes have to go through a long approval process and are released only once one has made sure they work well within existing TeX distributions.

[21] The European Local User Groups were instrumental in making TeX more accessible to the users. A group of volunteers at Aston University in the UK established a central repository for TeX code from which it was possible to download the latest developments in the TeX system via the Net. This group inspired the development of a package classification system, the TeX Directory Structure, which served as the model for TeX distribution everywhere. The Aston initiative led to the creation of the CTAN archives in 1990. Another seminal initiative came from the Netherlands Local User Group which developed 4AllTeX in 1993. 4AllTeX was a TeX distribution on a CD that was intended for an end user with no programming background. It was a precursor and an inspiration for the development of TeX Live.

[22] TeX Live was always considered to be a superset of the Unix teTeX distribution. Changes in that Unix distribution always took precedence over changes in the fpTeX distribution for Windows, which led to this later distribution being abandoned.

[23] While OS interfaces improved over time, they never became as aesthetically pleasing, complete or ergonomically efficient as that of competing proprietary WYSIWYG text editors such as Microsoft’s Word, of competing proprietary typesetting software such as Quark, or of some software based on  such as Scientific Workplace. The main interfaces were the freeware WinEdt (1993) and the OS WinShell (1998) but they required knowledge of the TeX syntax and commands. Some developers tried to go further and develop WYSIWYG interfaces based on their own implementations of TeX (LyX (1999), TeXMacs (2002)). This disconnected them from the main branch in the development of TeX. There were, therefore, individual OS initiatives trying to adopt the middle ground (TeXshop (2000) for Mac Operating Systems, preview-LaTeX (2001) for Unix OS or XeMTeX (2003) for Windows OS). Those interfaces could be used on top of the standard TeX distributions.