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Arithmetic if is an unstructured control statement, and is not used in structured programming. In practice it has been observed that most arithmetic IF statements reference the following statement with one or two of the labels. This was the only conditional control statement in the original implementation of Fortran on the IBM 704 computer. On ...
The example in the previous section used unformalized, natural-language reasoning. Curry's paradox also occurs in some varieties of formal logic.In this context, it shows that if we assume there is a formal sentence (X → Y), where X itself is equivalent to (X → Y), then we can prove Y with a formal proof.
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 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.
Calling f with a regular function argument first applies this function to the value 2, then returns 3. However, when f is passed to call/cc (as in the last line of the example), applying the parameter (the continuation) to 2 forces execution of the program to jump to the point where call/cc was called, and causes call/cc to return the value 2.
A lambda abstraction represents a function without a name. This is a source of the inconsistency in the definition of a lambda abstraction. However lambda abstractions may be composed to represent a function with a name. In this form the inconsistency is removed. The lambda term, (.) (.)
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 term syntactic sugar was coined by Peter J. Landin in 1964 to describe the surface syntax of a simple ALGOL-like programming language which was defined semantically in terms of the applicative expressions of lambda calculus, [1] [2] centered on lexically replacing λ with "where".