World Library  
Flag as Inappropriate
Email this Article

Applicative computing systems

Article Id: WHEBN0016957829
Reproduction Date:

Title: Applicative computing systems  
Author: World Heritage Encyclopedia
Language: English
Subject: Lambda calculus, Applicative computing systems, Applicative Universal Grammar, Combinatory logic
Collection:
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Applicative computing systems

Applicative computing systems, or ACS are the systems of object calculi founded on combinatory logic and lambda calculus.[1] The only essential notion which is under consideration in these systems is the representation of object. In combinatory logic the only metaoperator is application in a sense of applying one object to other. In lambda calculus two metaoperators are used: application – the same as in combinatory logic, and functional abstraction which binds the only variable in one object.

Features of ACS

The objects generated in these systems are the functional entities with the following features:

  1. the number of argument places, or object arity is not fixed but is enabling step by step in interoperations with other objects;
  2. in a process of generating the compound object one of its counterparts—function, -- is applied to other one—argument, -- but in other contexts they can change their roles, i.e. functions and arguments are considered on the equal rights;
  3. the self-applying of functions is allowed, i.e. any object can be applied to itself.

ACS give a sound ground for applicative approach to programming.

Research challenge

Applicative computing systems' lack of storage and history sensitivity is the basic reason they have not provided a foundation for computer design. Moreover, most applicative systems employ the substitution operation of the lambda calculus as their basic operation. This operation is one of virtually unlimited power, but its complete and efficient realization presents great difficulties to the machine designer.[2]

See also

References

  1. ^ Wolfengagen V.E. Methods and means for computations with objects. Applicative Computational Systems. — M.: JurInfoR Ltd., «Center JurInfoR», 2004. — xvi+789 pp. ISBN 5-89158-100-0.
  2. ^ 1977 Turing Award Lecture: Backus J. Can Programming Be Liberated from the von Neumann Style? A Functional Style and Its Algebra of Programs. – Comm. of the ACM, Vol. 2, No 8, 1978. -- pp. 613-641

Further reading

  • [This volume reflects the research program and philosophy of H. Curry, one of the founders of computational models and the deductive framework for reasoning in terms of objects.]
  • Wolfengagen, V.E. Combinatory logic in programming. Computations with objects through examples and exercises. -- 2-nd ed. -- M.: "Center JurInfoR" Ltd., 2003. -- x+337 с. ISBN 5-89158-101-9.
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.