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OCaml is a language of the ML family that inherits a lot from several decades of research in type theory, language design, and implementation of functional languages. Moreover, the language is quite mature, its compiler produces efficient code and comes with a large set of general purpose as well as domain-specific libraries. Thus, OCaml is well-suited for teaching and academic projects, and is simultaneously used in the industry, in particular in several high-tech software companies.

This document is a multi-dimensional presentation of the OCaml language that combines an informal and intuitive approach to the language with a rigorous definition and a formal semantics of a large subset of the language, including ML. All along this presentation, we explain the underlying design principles, highlight the numerous interactions between various facets of the language, and emphasize the close relationship between theory and practice.

Indeed, theory and practice should often cross their paths. Sometimes, the theory is deliberately weakened to keep the practice simple. Conversely, several related features may suggest a generalization and be merged, leading to a more expressive and regular design. We hope that the reader will follow us in this attempt of putting a little theory into practice or, conversely, of rebuilding bits of theory from practical examples and intuitions. However, we maintain that the underlying mathematics should always remain simple.

The introspection of OCaml is made even more meaningful by the fact that the language is boot-strapped, that is, its compilation chain is written in OCaml itself, and only parts of the runtime are written in C. Hence, some of the implementation notes, in particular those on typechecking, could be scaled up to be actually very close to the typechecker of OCaml itself.

The material presented here is divided into three categories. On the practical side, the course contains a short presentation of OCaml. Although this presentation is not at all exhaustive and certainly not a reference manual for the language, it is a self-contained introduction to the language: all facets of the language are covered; however, most of the details are omitted. A sample of programming exercises with different levels of difficulty have been included, and for most of them, solutions can be found in Appendix C. The knowledge and the practice of at least one dialect of ML may help getting the most from the other aspects. This is not mandatory though, and beginners can learn their first steps in OCaml by starting with Appendix A. Conversely, advanced OCaml programmers can learn from the inlined OCaml implementations of some of the algorithms. Implementation notes can always be skipped, at least in a first reading when the core of OCaml is not mastered yet —other parts never depend on them. However, we left implementation notes as well as some more advanced exercises inlined in the text to emphasize the closeness of the implementation to the formalization. Moreover, this permits to people who already know the OCaml language, to read all material continuously, making it altogether a more advanced course.

On the theoretical side —the mathematics remain rather elementary, we give a formal definition of a large subset of the OCaml language, including its dynamic and static semantics, and soundness results relating them. The proofs, however, are omitted. We also describe type inference in detail. Indeed, this is one of the most specific facets of ML.

A lot of the material actually lies in between theory and practice: we put an emphasis on the design principles, the modularity of the language constructs (their presentation is often incremental), as well as their dependencies. Some constructions that are theoretically independent end up being complementary in practice, so that one can hardly go without the other: it is often their combination that provides both flexibility and expressive power.

The document is organized in four parts (see the road maps in figure 1). Each of the first three parts addresses a different layer of OCaml: the core language (Chapters 1 and 2), objects and classes (Chapter 3), and modules (Chapter 4); the last part (Chapter 5) focuses on the combination of objects and modules, and discusses a few perspectives. The style of presentation is different for each part. While the introduction of the core language is more formal and more complete, the emphasis is put on typechecking for the Chapter on objects and classes, the presentation of the modules system remains informal, and the last part is mostly based on examples. This is a deliberate choice, due to the limited space, but also based on the relative importance of the different parts and interest of their formalization. We then refer to other works for a more formal presentation or simply for further reading, both at the end of each Chapter for rather technical references, and at the end of the manuscript, Page ?? for a more general overview of related work.

This document is thus addressed to a wide audience. With several entry points, it can be read in parts or following different directions (see the road maps in figure 1). People interested in the semantics of programming languages may read Chapters 1 and 2 only. Conversely, people interested in the object-oriented layer of OCaml may skip these Chapters and start at Chapter 3. Beginners or people interested mostly in learning the programming language may start with appendix A, then grab examples and exercises in the first Chapters, and end with the Chapters on objects and modules; they can always come back to the first Chapters after mastering programming in OCaml, and attack the implementation of a typechecker as a project, either following or ignoring the relevant implementation notes.

Programming languages

are rigorous but incomplete approximations of the language of mathematics. General purpose languages are Turing complete. That is, they allow to write all algorithms. (Thus, termination and many other useful properties of programs are undecidable.) However, programming languages are not all equivalent, since they differ by their ability to describe certain kinds of algorithms succinctly. This leads to an —endless?— research for new programming structures that are more expressive and allow shorter and safer descriptions of algorithms. Of course, expressiveness is not the ultimate goal. In particular, the safety of program execution should not be given up for expressiveness. We usually limit ourselves to a relatively small subset of programs that are well-typed and guaranteed to run safely. We also search for a small set of simple, essential, and orthogonal constructs.

Learning programming languages

Learning a programming language is a combination of understanding the language constructs and practicing. Certainly, a programming language should have a clear semantics, whether it is given formally, ie. using mathematical notation, as for Standard ML [51], or informally, using words, as for OCaml. Understanding the semantics and design principles, is a prerequisite to good programming habits, but good programming is also the result of practicing. Thus, using the manual, the tutorials, and on-line helps is normal practice. One may quickly learn all functions of the core library, but even fluent programmers may sometimes have to check specifications of some standard-library functions that are not so frequently used.

Copying (good) examples may save time at any stage of programming. This includes cut and paste from solutions to exercises, especially at the beginning. Sharing experience with others may also be helpful: the first problems you face are likely to be “Frequently Asked Questions” and the libraries you miss may already be available electronically in the “OCaml hump”. For books on ML see “Further reading”, Page ??.

A brief history of OCaml

The current definition and implementation of the OCaml language is the result of continuous and still ongoing research over the last two decades. The OCaml language belongs to the ML family. The language ML was invented in 1975 by Robin Milner to serve as a “meta-language”, ie. a control language or a scripting language, for programming proof-search strategies in the LCF proof assistant. The language quickly appeared to be a full-fledged programming language. The first implementations of ML were realized around 1981 in Lisp. Soon, several dialects of ML appeared: Standard ML at Edinburgh, Caml at INRIA, Standard ML of New-Jersey, Lazy ML developed at Chalmers, or Haskell at Glasgow. The two last dialects slightly differ from the previous ones by relying on a lazy evaluation strategy (they are called lazy languages) while all others have a strict evaluation strategy (and are called strict languages). Traditional languages, such as C, Pascal, Ada are also strict languages. Standard ML and Caml are relatively close to one another. The main differences are their implementations and their superficial —sometimes annoying— syntactic differences. Another minor difference is their module systems. However, SML does not have an object layer.

Continuing the history of Caml, Xavier Leroy and Damien Doligez designed a new implementation in 1990 called Caml-Light, freeing the previous implementation from too many experimental high-level features, and more importantly, from the old Le_Lisp back-end.

The addition of a native-code compiler and a powerful module system in 1995 and of the object and class layer in 1996 made OCaml a very mature and attractive programming language. The language is still under development: for instance, in 2000, labeled and optional arguments on the one hand and anonymous variants on the other hand were added to the language by Jacques Garrigue.

In the last decade, other dialects of ML have also evolved independently. Hereafter, we use the name ML to refer to features of the core language that are common to most dialects and we speak of OCaml, mostly in the examples, to refer to this particular implementation. Most of the examples, except those with object and classes, could easily be translated to Standard ML. However, only few of them could be straightforwardly translated to Haskell, mainly because of both languages have different evaluation strategy, but also due to many other differences in their designs.

Resemblances and differences in a few key words

All dialects of ML are functional. That is, functions are taken seriously. In particular, they are first-class values: they can be arguments to other functions and returned as results. All dialects of ML are also strongly typed. This implies that well-typed programs cannot go wrong. By this, we mean that assuming no compiler bugs, programs will never execute erroneous access to memory nor other kind of abnormal execution step and programs that do not loop will always terminate normally. Of course, this does not ensure that the program executes what the programmer had in mind!

Another common property to all dialects of ML is type inference, that is, types of expressions are optional and are inferred by the system. As most modern languages, ML has automatic memory management, as well.

Additionally, the language OCaml is not purely functional: imperative programming with mutable values and side effects is also possible. OCaml is also object-oriented (aside from prototype designs, OCaml is still the only object-oriented dialect of ML). OCaml also features a powerful module system inspired by the one of Standard ML.


Many thanks to Jacques Garrigue, Xavier Leroy, and Brian Rogoff for their careful reading of parts of the notes.

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