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The names "lambda abstraction", "lambda function", and "lambda expression" refer to the notation of function abstraction in lambda calculus, where the usual function f (x) = M would be written (λx. M), and where M is an expression that uses x. Compare to the Python syntax of lambda x: M.
A lambda calculus function (or term) is an implementation of a mathematical function. In the lambda calculus there are a number of combinators (implementations) that satisfy the mathematical definition of a fixed-point combinator.
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.
In mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following: . takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure),
Lambda expression may refer to: Lambda expression in computer programming, also called an anonymous function , is a defined function not bound to an identifier. Lambda expression in lambda calculus , a formal system in mathematical logic and computer science for expressing computation by way of variable binding and substitution.
The substitution operator is also used. The expression [:=] means substitute every occurrence of G in L by S and return the expression. The definition used is extended to cover the substitution of expressions, from the definition given on the Lambda calculus page. The matching of expressions should compare expressions for alpha equivalence ...
The lambda calculus, developed in the 1930s by Alonzo Church, is a formal system of computation built from function application. In 1937 Alan Turing proved that the lambda calculus and Turing machines are equivalent models of computation, [37] showing that the lambda calculus is Turing complete. Lambda calculus forms the basis of all functional ...
The substitution operator is used extensively. The expression [:=] means substitute every occurrence of G in L by S and return the expression. The definition used is extended to cover the substitution of expressions, from the definition given on the Lambda calculus page. The matching of expressions should compare expressions for alpha ...