Historical Development
Denotational semantics originated in the work of Christopher Strachey and Dana Scott in the late 1960s. As originally developed by Strachey and Scott, denotational semantics provided the denotation (meaning) of a computer program as a function that mapped input into output. To give denotations to recursively defined programs, Scott proposed working with continuous functions between domains, specifically complete partial orders. As described below, work has continued in investigating appropriate denotational semantics for aspects of programming languages such as sequentiality, concurrency, non-determinism and local state.
Denotational semantics have been developed for modern programming languages that use capabilities like concurrency and exceptions, e.g., Concurrent ML, CSP, and Haskell. The semantics of these languages is compositional in that the denotation of a phrase depends on the denotations of its subphrases. For example, the meaning of the applicative expression f(E1,E2) is defined in terms of semantics of its subphrases f, E1 and E2. In a modern programming language, E1 and E2 can be evaluated concurrently and the execution of one of them might affect the other by interacting through shared objects causing their denotations to be defined in terms of each other. Also, E1 or E2 might throw an exception which could terminate the execution of the other one. The sections below describe special cases of the semantics of these modern programming languages.
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