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Lambda calculus - Lambda calculus and programming languages | | Lambda calculus - Lambda calculus and programming languages: Encyclopedia II - Lambda calculus - Lambda calculus and programming languages | | Most programming languages are equivalent to the lambda calculus extended with some additional programming language constructs. The classical work where this viewpoint was put forward was Peter Landin's "A Correspondence between ALGOL 60 and Church's Lambda-notation", published in CACM in 1965. The key point is that the lambda calculus expresses the kind of procedural abstraction and application useful for any programming language. Prominently, functional programming languages are basically the lambda calculus with some constants and datatyp ...
See also:Lambda calculus, Lambda calculus - History, Lambda calculus - Informal description, Lambda calculus - Formal definition, Lambda calculus - α-conversion, Lambda calculus - β-reduction, Lambda calculus - η-conversion, Lambda calculus - Arithmetic in lambda calculus, Lambda calculus - Logic and predicates, Lambda calculus - Recursion, Lambda calculus - Computable functions and lambda calculus, Lambda calculus - Undecidability of equivalence, Lambda calculus - Lambda calculus and programming languages | | | Lambda calculus, Lambda calculus - Arithmetic in lambda calculus, Lambda calculus - Computable functions and lambda calculus, Lambda calculus - Formal definition, Lambda calculus - History, Lambda calculus - Informal description, Lambda calculus - Lambda calculus and programming languages, Lambda calculus - Logic and predicates, Lambda calculus - Recursion, Lambda calculus - Undecidability of equivalence, Lambda calculus - α-conversion, Lambda calculus - β-reduction, Lambda calculus - η-conversion, SKI combinator calculus, H.P. Barendregt's Lambda cube, Jean-Yves Girard's System F, Thierry Coquand's calculus of constructions, Typed lambda calculus, Curry-Howard isomorphism, Anonymous recursion, Unlambda | | |
| | | Lambda calculus: Encyclopedia II - Lambda calculus - Lambda calculus and programming languages
Lambda calculus - Lambda calculus and programming languages
Most programming languages are equivalent to the lambda calculus extended with some additional programming language constructs. The classical work where this viewpoint was put forward was Peter Landin's "A Correspondence between ALGOL 60 and Church's Lambda-notation", published in CACM in 1965. The key point is that the lambda calculus expresses the kind of procedural abstraction and application useful for any programming language. Prominently, functional programming languages are basically the lambda calculus with some constants and datatypes added. Lisp uses a variant of lambda notation for defining functions, but only its purely functional subset is really equivalent to lambda calculus.
Actually implementing the lambda calculus on a computer involves treating "functions" as first-class objects, which turns out to be rather difficult to accomplish using stack-based computer languages. This is known as the Funarg problem.
Theory of the lambda calculus says that lambda calculus computations can always be carried out sequentially, not that they must be carried out sequentially. The lambda calculus is suitable for expressing some kinds of parallelism, e.g., the parallel evaluation of the arguments of a procedure. However the lambda calculus does not in general implement concurrency, e.g., a shared financial account that is updated concurrently. On the other hand concurrent computation as in the Actor model and Process calculi can perform the parallelism of the lambda calculus. The difference between parallelism in the lambda calculus and concurrency in Actors is reflected in that the Actor model has unbounded nondeterminism whereas the nondeterministic lambda calculus has bounded nondeterminism.
Other related archives1930s, Actor model, Alonzo Church, Anonymous recursion, BNF, Church numerals, Church-Rosser theorem, Church-Turing thesis, Curry-Howard isomorphism, Entscheidungsproblem, Funarg problem, Gödel number, Gödel numbering, Gödel's first incompleteness theorem, H.P. Barendregt, Jean-Yves Girard, Lambda cube, Lisp, Process calculi, Recursion, Russell's paradox, SKI combinator calculus, Stephen Cole Kleene, System F, Turing machine, Typed lambda calculus, Unlambda, Y combinator, algorithm, calculus of constructions, combinator, combinatory logic, computability, computable function, computer science, concurrency, constants, context-free grammar, countably infinite, currying, datatypes, equivalence relation, extensionality, factorial, formal system, function, functional programming languages, halting problem, higher-order function, if and only if, iff, induction, left associative, natural numbers, parallelism, programming languages, recursion, set, typed lambda calculi, unbounded nondeterminism, undecidability, up to
 Adapted from the Wikipedia article "Lambda calculus and programming languages", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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