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The expression returned by the lambda function can be assigned to a variable and used in the code at multiple places. >>> add = lambda a : a + a >>> add ( 20 ) 40 Another example would be sorting items in a list by the name of their class (in Python, everything has a class):
The term closure is often used as a synonym for anonymous function, though strictly, an anonymous function is a function literal without a name, while a closure is an instance of a function, a value, whose non-local variables have been bound either to values or to storage locations (depending on the language; see the lexical environment section below).
However it does not demonstrate the soundness of lambda calculus for deduction, as the eta reduction used in lambda lifting is the step that introduces cardinality problems into the lambda calculus, because it removes the value from the variable, without first checking that there is only one value that satisfies the conditions on the variable ...
The examples 1 and 2 denote different terms, differing only in where the parentheses are placed. They have different meanings: example 1 is a function definition, while example 2 is a function application. The lambda variable x is a placeholder in both examples. Here, example 1 defines a function .
In the lambda calculus, which only uses functions of a single variable, this can be done via the Y combinator. First make the higher-order function of two variables be a function of a single variable, which directly returns a function, by currying:
In this case particular lambda terms (which define functions) are considered as values. "Running" (beta reducing) the fixed-point combinator on the encoding gives a lambda term for the result which may then be interpreted as fixed-point value. Alternately, a function may be considered as a lambda term defined purely in lambda calculus.
The variable b is needed here to meet Java's requirement that variables referenced from within a lambda expression be effectively final. This is an inefficient program because this implementation of lazy integers does not memoize the result of previous calls to eval. It also involves considerable autoboxing and unboxing.
These rules reverse the conversion described above. They convert from a let expression to a lambda expression, without altering the structure. Not all let expressions may be converted using these rules. The rules assume that the expressions are already arranged as if they had been generated by de-lambda. - [, =] =- [, =.