Programming language specification
A programming language specification can take several forms, including the following:
- An explicit definition of the syntax and semantics of the language. While syntax is commonly specified using a formal grammar, semantic definitions may be written in natural language (e.g., the approach taken for the C language), or a formal semantics (e.g., the Standard MLand Scheme specifications).
- A description of the behavior of a translator for the language (e.g., the C++ and Fortran). The syntax and semantics of the language has to be inferred from this description, which may be written in natural or a formal language.
- A model implementation, sometimes written in the language being specified (e.g., the Prolog). The syntax and semantics of the language are explicit in the behavior of the model implementation.
The Syntax of a programming language is usually described using a combination of the following two components:
- a regular expression describing its lexemes, and
- a context-free grammar which describes how lexemes may be combined to form a syntactically correct program.
Formulating a rigorous semantics of a large, complex, practical programming language is a daunting task even for experienced specialists, and the resulting specification can be difficult for anyone but experts to understand. The following are some of the ways in which programming language semantics can be described; all languages use at least one of these description methods, and some languages combine more than one
- Natural language: Description by human natural language.
- Formal semantics: Description by mathematics.
- Reference implementations: Description by computer program
- Test suites: Description by examples of programs and their expected behaviors. While few language specifications start off in this form, the evolution of some language specifications has been influenced by the semantics of a test suite (e.g. in the past the specification of Ada has been modified to match the behavior of the Ada Conformity Assessment Test Suite).
Most widely used languages are specified using natural language descriptions of their semantics. This description usually takes the form of a reference manual for the language. These manuals can run to hundreds of pages, e.g., the print version of The Java Language Specification, 3rd Ed. is 596 pages long.
The imprecision of natural language as a vehicle for describing programming language semantics can lead to problems with interpreting the specification. For example, the semantics of Java threads were specified in English, and it was later discovered that the specification did not provide adequate guidance for implementors.
Formal semantics are grounded in mathematics. As a result, they can be more precise and less ambiguous than semantics given in natural language. However, supplemental natural language descriptions of the semantics are often included to aid understanding of the formal definitions. For example, The ISO Standard for Modula-2 contains both a formal and a natural language definition on opposing pages.
Programming languages whose semantics are described formally can reap many benefits. For example:
- Formal semantics enable mathematical proofs of program correctness;
- Formal semantics facilitate the design of type systems, and proofs about the soundness of those type systems;
- Formal semantics can establish unambiguous and uniform standards for implementations of a language.
Automatic tool support can help to realize some of these benefits. For example, an automated theorem prover or theorem checker can increase a programmer's (or language designer's) confidence in the correctness of proofs about programs (or the language itself). The power and scalability of these tools varies widely: full formal verification is computationally intensive, rarely scales beyond programs containing a few hundred lines and may require considerable manual assistance from a programmer; more lightweight tools such as model checkers require fewer resources and have been used on programs containing tens of thousands of lines; many compilers apply static type checks to any program they compile.
A reference implementation is a single implementation of a programming language that is designated as authoritative. The behavior of this implementation is held to define the proper behavior of a program written in the language. This approach has several attractive properties. First, it is precise, and requires no human interpretation: disputes as to the meaning of a program can be settled simply by executing the program on the reference implementation (provided that the implementation behaves deterministically for that program).
On the other hand, defining language semantics through a reference implementation also has several potential drawbacks. Chief among them is that it conflates limitations of the reference implementation with properties of the language. For example, if the reference implementation has a bug, then that bug must be considered to be an authoritative behavior. Another drawback is that programs written in this language may rely on quirks in the reference implementation, hindering portability across different implementations.
Nevertheless, several languages have successfully used the reference implementation approach. For example, the Perl interpreter is considered to define the authoritative behavior of Perl programs. In the case of Perl, the Open Source model of software distribution has contributed to the fact that nobody has ever produced another implementation of the language, so the issues involved in using a reference implementation to define the language semantics are moot.
Defining the semantics of a programming language in terms of a test suite involves writing a number of example programs in the language, and then describing how those programs ought to behave — perhaps by writing down their correct outputs. The programs, plus their outputs, are called the "test suite" of the language. Any correct language implementation must then produce exactly the correct outputs on the test suite programs.
The chief advantage of this approach to semantic description is that it is easy to determine whether a language implementation passes a test suite. The user can simply execute all the programs in the test suite, and compare the outputs to the desired outputs. However, when used by itself, the test suite approach has major drawbacks as well. For example, users want to run their own programs, which are not part of the test suite; indeed, a language implementation that could only run the programs in its test suite would be largely useless. But a test suite does not, by itself, describe how the language implementation should behave on any program not in the test suite; determining that behavior requires some extrapolation on the implementor's part, and different implementors may disagree. In addition, it is difficult to use a test suite to test behavior that is intended or allowed to be nondeterministic.
Therefore, in common practice, test suites are used only in combination with one of the other language specification techniques, such as a natural language description or a reference implementation.
A few examples of official or draft language specifications:
- Milner, R.; M. Tofte, R. Harper and D. MacQueen. (1997). The Definition of Standard ML (Revised). MIT Press. ISBN 0-262-63181-4.
- Kelsey, Richard; William Clinger and Jonathan Rees (February 1998). "Section 7.2 Formal semantics". Revised5 Report on the Algorithmic Language Scheme. Retrieved 2006-06-09.
- Jones, D. (2008). Forms of language specification. Retrieved 2012-06-23.
- William Pugh. The Java Memory Model is Fatally Flawed. Concurrency: Practice and Experience 12(6):445-455, August 2000