Formal semantics of programming languages

Formal semantics of programming languages

In theoretical computer science, formal semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages and models of computation.

The formal semantics of a language is given by a mathematical model that describes the possible computations described by the language.

There are many approaches to formal semantics; these approaches belong to three major classes:

* Denotational semantics, whereby each phrase in the language is translated into a "denotation", i.e. a phrase in some other language. Denotational semantics loosely corresponds to compilation, although the "target language" is usually a mathematical formalism rather than another computer language. For example, denotational semantics of functional languages often translates the language into domain theory;
* Operational semantics, whereby the execution of the language is described directly (rather than by translation). Operational semantics loosely corresponds to interpretation, although again the "implementation language" of the interpreter is generally a mathematical formalism. Operational semantics may define an abstract machine (such as the SECD machine), and give meaning to phrases by describing the transitions they induce on states of the machine. Alternatively, as with the pure lambda calculus, operational semantics can be defined via syntactic transformations on phrases of the language itself;
* Axiomatic semantics, whereby one gives meaning to phrases by describing the "logical axioms" that apply to them. Axiomatic semantics makes no distinction between a phrase's meaning and the logical formulas that describe it; its meaning "is" exactly what can be proven about it in some logic. The canonical example of axiomatic semantics is Hoare logic.

The distinctions between the three broad classes of approaches can sometimes be blurry, but all known approaches to formal semantics use the above techniques, or some combination thereof.

Apart from the choice between denotational, operational, or axiomatic approaches, most variation in formal semantic systems arises from the choice of supporting mathematical formalism.

Some variations of formal semantics include the following:
* Action semantics is an approach that tries to modularize denotational semantics, splitting the formalization process in two layers (macro and microsemantics) and predefining three semantic entities (actions, data and yielders) to simplify the specification;
* Attribute grammars define systems that systematically compute "metadata" (called "attributes") for the various cases of the language's syntax. Attribute grammars can be understood as a denotational semantics where the target language is simply the original language enriched with attribute annotations. Aside from formal semantics, attribute grammars have also been used for code generation in compilers, and to augment regular or context-free grammars with context-sensitive conditions;
* Categorical (or "functorial") semantics uses category theory as the core mathematical formalism;
* Concurrency semantics is a catch-all term for any formal semantics that describes concurrent computations. Historically important concurrent formalisms have included the Actor model and process calculi;
* Game semantics uses a metaphor inspired by game theory.

For a variety of reasons, one might wish to describe the relationships between different formal semantics. For example:
*One might wish to prove that a particular operational semantics for a language satisfies the logical formulas of an axiomatic semantics for that language. Such a proof demonstrates that it is "sound" to reason about a particular (operational) "interpretation strategy" using a particular (axiomatic) "proof system".
*Given a single language, one might define a "high-level" abstract machine and a "low-level" abstract machine for the language, such that the latter contains more primitive operations than the former. One might then wish to prove that an operational semantics over the high-level machine is related by a bisimulation with the semantics over the low-level machine. Such a proof demonstrates that the low-level machine "faithfully implements" the high-level machine.One can sometimes relate multiple semantics through abstractions via the theory of abstract interpretation.

The field of formal semantics encompasses all of the following:
*the definition of semantic models,
*the relations between different semantic models,
*the relations between different approaches to meaning, and
*the relation between computation and the underlying mathematical structures from fields such as logic, set theory, model theory, category theory, etc.

It has close links with other areas of computer science such as programming language design, type theory, compilers and interpreters, program verification and model checking.

External links

* [ Semantics with Applications]


* Carl Gunter. "Semantics of Programming Languages". MIT Press, 1992. (ISBN 0-262-07143-6)
* Robert Harper. "Practical Foundations for Programming Languages". Working draft, 2006. ( [ online] , as PDF)
* Shriram Krishnamurthi. "Programming Languages: Application and Interpretation". ( [ online] , as PDF)
* John C. Reynolds. "Theories of Programming Languages". Cambridge University Press, 1998. (ISBN 0-521-59414-6)
* Glynn Winskel. "The Formal Semantics of Programming Languages: An Introduction". MIT Press, 1993 (paperback ISBN 0-262-73103-7)

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Formal semantics — See also Formal semantics of programming languages. Formal semantics is the study of the semantics, or interpretations, of formal languages. A formal language can be defined apart from any interpretation of it. This is done by designating a set… …   Wikipedia

  • Comparison of programming languages — Programming language comparisons General comparison Basic syntax Basic instructions Arrays Associative arrays String operations …   Wikipedia

  • Programming language — lists Alphabetical Categorical Chronological Generational A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that… …   Wikipedia

  • Semantics — is the study of meaning in communication. The word derives from Greek σημαντικός ( semantikos ), significant , [cite web|url= bin/ptext?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3D%2393797|title=Semantikos, Henry… …   Wikipedia

  • Formal verification — In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods… …   Wikipedia

  • Programming language theory — (commonly known as PLT) is a branch of computer science that deals with the design, implementation, analysis, characterization, and classification of programming languages and programming language features. It is a multi disciplinary field, both… …   Wikipedia

  • Programming language specification — A programming language specification is an artifact that defines a programming language so that users and implementors can agree on what programs in that language mean.A programming language specification can take several forms, including the… …   Wikipedia

  • Formal grammar — In formal semantics, computer science and linguistics, a formal grammar (also called formation rules) is a precise description of a formal language ndash; that is, of a set of strings over some alphabet. In other words, a grammar describes which… …   Wikipedia

  • Semantics encoding — A semantics encoding is a translation between formal languages. For programmers, the most familiar form of encoding is the compilation of a programming language into machine code or byte code. Conversion between document formats are also forms of …   Wikipedia

  • Formal methods — In computer science and software engineering, formal methods are particular kind of mathematically based techniques for the specification, development and verification of software and hardware systems.cite web|author=R. W. Butler|title=What is… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.