ONT Re: Program Semantics
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| Algebraic Approaches to Program Semantics
| Part 1. Denotational Semantics of Control
| Chapter 1. An Introduction to Denotational Semantics
|
| 1.1. Syntax and Semantics (cont.)
|
| 'Operational semantics' is the most intuitive for beginners with
| some programming experience, being the form of semantics described
| in most programming manuals. To provide an operational semantics for
| a programming language, one invents an "abstract computer" and describes
| how programs "run" on this computer. Usually, the semantics prescribes how
| the syntactic form of a program is to be interpreted as a (data-dependent)
| sequence of instructions. Input data are then transformed as the program
| is run in sequence, instruction by instruction, branching and looping back
| on the basis of tests on current values of data.
|
| By contrast to operational semantics which traces all intermediate states
| in a computation, 'denotational semantics' focuses on input/output behavior
| and ignores the intermediate states. Operational semantics provides more
| information on how to implement a programming language as long as the
| implementation environment resembles that of the abstract computer.
| For example, an operational semantics in which every computation is
| described as a serial sequence of state changes would be somewhat
| at odds with an implementation on a pipeline architecture which
| maximizes parallel computation. An objective of denotational
| semantics is to avoid worry about details of implementation.
|
| A challenge posed by denotational semantics is to invent
| mathematical frameworks permitting the description of
| repetitive programming constructs (i.e., "loops")
| without explicit reference to intermediate states.
| The "partially additive semantics" of Section 1.5
| introduces a power-series representation for
| computed functions which, in part, expresses
| programming constructs in terms of operations
| that manipulate power series. Other approaches
| to denotational semantics, to be discussed
| in Part 2, use partially ordered sets
| and metric spaces for their
| mathematical underpinnings.
|
| Manes & Arbib, AAPS, pages 3-4.
|
| Ernest G. Manes & Michael A. Arbib,
|'Algebraic Approaches to Program Semantics',
| Springer-Verlag, New York, NY, 1986.
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