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

== Features ==

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

# the number of argument places, or object arity is not fixed but is enabling step by step in interoperations with other objects;
# 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;
# the self-applying of functions is allowed, i.e. any object can be applied to itself.

ACS give a sound ground for [[applicative programming language|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.<ref>{{cite journal |author-link=John Backus |first=J. |last=Backus |title=1977 Turing Award Lecture: Can Programming Be Liberated from the von Neumann Style? A Functional Style and Its Algebra of Programs |journal=Commun. ACM |volume=2 |issue=8 |pages=613–641 |date=1978 |doi=10.1145/359576.359579 |s2cid=16367522 |doi-access=free }}</ref>

== See also ==

* [[Applicative programming language]]
* [[Categorical abstract machine]]
* [[Combinatory logic]]
* [[Functional programming]]
* [[Lambda calculus]]

== References ==
<references/>

== Further reading ==

*{{citation
| editor1-first = J. Roger | editor1-last = Hindley
| editor2-first = Jonathan P. | editor2-last = Seldin
| editor1-link = J. Roger Hindley
| editor2-link = Jonathan P. Seldin
| title = To H. B. Curry: Essays on combinatory logic, lambda calculus and formalism
| publisher = [[Academic Press]]
| location=Boston, MA
| isbn = 978-0-12-349050-6
|date=September 1980
}} [This volume reflects the research program and philosophy of [[Haskell Curry|H. Curry]], one of the founders of [[computational models]] and the deductive framework for reasoning in terms of objects.]

*{{cite book |first=V.E. |last=Wolfengagen |title=Combinatory logic in programming. Computations with objects through examples and exercises |publisher=JurInfoR |edition=2nd |date=2003 |isbn=9785891581265 |citeseerx=10.1.1.62.4421 |oclc=491339472}}

{{DEFAULTSORT:Applicative Computing Systems}}
[[Category:Applicative computing systems| ]]
[[Category:Models of computation]]
[[Category:Combinatory logic]]
[[Category:Lambda calculus]]

Applicative computing systems - Revision history

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