Categorical abstract machine: Difference between revisions
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It is based on techniques of the [[applicative computing systems|applicative computing]]. |
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| ⚫ | The '''categorical abstract machine''' ('''CAM''') is a [[model of computation]] for programs<ref>''Cousineau G., Curien P.-L., Mauny M.'' The categorical abstract machine. — LNCS, 201, Functional programming languages computer architecture.-- 1985, pp.~50-64.</ref> that preserves the abilities of applicative, functional, or compositional style. It is based on the techniques of [[applicative computing systems|applicative computing]]. |
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| ⚫ | One of the implementation approaches to functional languages is given by the machinery based on [[ |
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== Overview == |
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The notion of categorical abstract machine, or CAM arose in the mid-1980s and in computer science takes a place of a kind of ''[[theory of computation]] for programmers''. |
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The notion of the categorical abstract machine arose in the mid-1980s. It took its place in computer science as a kind of [[theory of computation]] for programmers, represented by [[Cartesian closed category]] and embedded into the [[combinatory logic]]. CAM is a transparent and sound mathematical representation for the languages of functional programming. The machine code can be optimized using the equational form of a theory of computation. Using CAM, the various mechanisms of computation such as [[recursion]] or [[lazy evaluation]] can be emulated as well as parameter passing, such as [[call by name]], [[call by value]], and so on. In theory, CAM preserves{{how|date=December 2015}} all the advantages of object approach towards programming or computing. |
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The main current implementation is OCaml, which added class inheritance and dynamic method dispatch to [[Caml]] the Categorical Abstract Machine Language. Both are variants of MetaLanguage [[ML (programming language)|ML]], and all three languages implement [[type inference]]. |
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== de Bruijn’s notation == |
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== Implementation == |
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'''De Bruijn’s notation''' is the method of replacement for bound variables (formal parameters) which overcomes the bounding collision when substituting the formal parameters by the actual ones. This method is used in a code compiling phase for CAM. This kind of replacing the bound variables can be mentioned as “de Bruijn’s encoding” and is vital in using the calculi of [[lambda calculus | lambda-conversion]] on the same rights as the calculi of [[combinatory logic]]. |
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| ⚫ | One of the implementation approaches to functional languages is given by the machinery based on [[Supercombinator| supercombinators]], or an SK-machine, by D. Turner. The notion of CAM gives an alternative approach. The structure of CAM consists of syntactic, semantic, and computational constituents. Syntax is based on [[Nicolaas Govert de Bruijn | de Bruijn’s]] [[ De Bruijn notation | notation]], which overcomes the difficulties of using bound variables. The evaluations are similar to those of [[Peter J. Landin | P. Landin’s]] [[SECD machine]]. With this coverage, CAM gives a sound ground for syntax, semantics, and [[theory of computation]]. This comprehension arises as being influenced by the functional style of programming. |
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== See also == |
== See also == |
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*[[Combinatory logic]] |
*[[Combinatory logic]] |
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*[[Typed lambda calculus]] |
*[[Typed lambda calculus]] |
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* [[Currying]] |
* [[Currying]] |
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* [[Caml]] |
* [[Caml]] |
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== References == |
== References == |
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{{reflist}} |
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<references/> |
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== Further reading == |
== Further reading == |
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* Wolfengagen, V.E. ''[http://www.wolfengagen.mephi.ru/papers/Wolfengagen_CLP-2003(En).pdf Combinatory Logic in Programming]: Computations with Objects through Examples and Exercises''. |
* Wolfengagen, V.E. ''[https://web.archive.org/web/20070128222953/http://www.wolfengagen.mephi.ru/papers/Wolfengagen_CLP-2003(En).pdf Combinatory Logic in Programming]: Computations with Objects through Examples and Exercises''. 2nd ed. M.: "Center JurInfoR" Ltd., 2003. x+337 с. {{ISBN|5-89158-101-9}}. |
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[[Category:Implementation of functional programming languages]] |
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[[Category:Models of computation]] |
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[[Category:Applicative computing systems]] |
[[Category:Applicative computing systems]] |
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[[Category:Combinatory logic]] |
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[[ru:Категориальная абстрактная машина]] |
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[[uk:Категорiальна абстрактна машина]] |
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Latest revision as of 14:41, 10 May 2022
 | This article needs additional citations for verification. (December 2012) |
The categorical abstract machine (CAM) is a model of computation for programs[1] that preserves the abilities of applicative, functional, or compositional style. It is based on the techniques of applicative computing.
Overview
[edit]The notion of the categorical abstract machine arose in the mid-1980s. It took its place in computer science as a kind of theory of computation for programmers, represented by Cartesian closed category and embedded into the combinatory logic. CAM is a transparent and sound mathematical representation for the languages of functional programming. The machine code can be optimized using the equational form of a theory of computation. Using CAM, the various mechanisms of computation such as recursion or lazy evaluation can be emulated as well as parameter passing, such as call by name, call by value, and so on. In theory, CAM preserves[how?] all the advantages of object approach towards programming or computing.
The main current implementation is OCaml, which added class inheritance and dynamic method dispatch to Caml the Categorical Abstract Machine Language. Both are variants of MetaLanguage ML, and all three languages implement type inference.
Implementation
[edit]One of the implementation approaches to functional languages is given by the machinery based on supercombinators, or an SK-machine, by D. Turner. The notion of CAM gives an alternative approach. The structure of CAM consists of syntactic, semantic, and computational constituents. Syntax is based on de Bruijn’s notation, which overcomes the difficulties of using bound variables. The evaluations are similar to those of P. Landin’s SECD machine. With this coverage, CAM gives a sound ground for syntax, semantics, and theory of computation. This comprehension arises as being influenced by the functional style of programming.
See also
[edit]References
[edit]- ^ Cousineau G., Curien P.-L., Mauny M. The categorical abstract machine. — LNCS, 201, Functional programming languages computer architecture.-- 1985, pp.~50-64.
Further reading
[edit]- Wolfengagen, V.E. Combinatory Logic in Programming: Computations with Objects through Examples and Exercises. 2nd ed. M.: "Center JurInfoR" Ltd., 2003. x+337 с. ISBN 5-89158-101-9.