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Author MacLennan, B. J.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Modes ♦ Extensible languages ♦ Data types ♦ Data structures ♦ Formal systems ♦ Description languages ♦ Correctness ♦ Formal description ♦ Models of computation ♦ Axioms ♦ Semantics ♦ Formal language definition ♦ Lambda-calculus
Abstract A formal system is presented which abstracts the notions of data item, function, and relation. It is argued that the system is more suitable than set theory (or its derivatives) for the concise and accurate description of program semantics. It is shown how the system can be used to build composite data types out of simpler ones with the operations of rowing, structuring, and uniting. It is also demonstrated that completely new primitive types can be introduced into languages through the mechanism of singleton data types.Both deterministic and nondeterministic functions are shown to be definable in the system. It is described how the local environment can be modeled as a data item and how imperative statements can be considered functions on the environment. The nature of recursive functions is briefly discussed, and a technique is presented by which they can be introduced into the system. The technique is contrasted with the use of the paradoxical combinator, Y. The questions of local and global environments and of various modes of function calling and parameter passing are touched upon.The theory is applied to the proof of several elementary theorems concerning the semantics of the assignment, conditional, and iterative statements.An appendix is included which presents in detail the formal system governing webs and fen, the abstractions used informally in the body of the paper.
Description Affiliation: Florida State Univ. (MacLennan, B. J.)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 16
Issue Number 8
Page Count 7
Starting Page 468
Ending Page 474


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Source: ACM Digital Library