Denotational Semantics

As a concept, denonational semantics was first proposed by Christopher Strachey and Dana Scott¹. As originally developed, denotational semantics provided the denotation (i.e. meaning) of a computer program as a function that mapped input into output. More generally, denotational semantics is concerned with finding mathematical objects that represent what programs do.

Denotational sematics is not very useful for those trying to learn a new language. However, denotational semantics are very useful for automatic compiler generation. While it is hard to write out a denotational sematics definition for a language, once done done it is possible to automatically generate a compiler for the language.

For more information:

"Denotational Semantics" (PDF), chapter 9 of Formal Syntax and Sematics of Programming Languages: A Laboratory Based Approach by Kenneth Slonneger and Barry L. Kurtz, Addison-Wesley, 1995.
Denotational Semantics: A Methodology for Language Development by David Schmidt, 1997 (full text available on-line in zipped PDF format)
Denotational Semantics - course notes by Grant Malcom, The University of Liverpool

Reference:
1. "Toward a Mathematical Semantics for Computer Languages" by Dana Scott and Christopher Strachey. Programming Research Group Technical Monograph PRG-6, Oxford Univ. Computing Lab., 1971.