eta conversion

(theory)In lambda-calculus, the eta conversion rule states

\\ x . f x f

provided x does not occur as a free variable in f and f is afunction. Left to right is eta reduction, right to left iseta abstraction (or eta expansion).

This conversion is only valid if bottom and \\ x . bottom areequivalent in all contexts. They are certainly equivalentwhen applied to some argument - they both fail to terminate.If we are allowed to force the evaluation of an expression inany other way, e.g. using seq in Miranda or returning afunction as the overall result of a program, then bottom and\\ x . bottom will not be equivalent.

See also observational equivalence, reduction.

单词	eta conversion
释义	eta conversion eta conversion (theory)In lambda-calculus, the eta conversion rule states \\ x . f x f provided x does not occur as a free variable in f and f is afunction. Left to right is eta reduction, right to left iseta abstraction (or eta expansion). This conversion is only valid if bottom and \\ x . bottom areequivalent in all contexts. They are certainly equivalentwhen applied to some argument - they both fail to terminate.If we are allowed to force the evaluation of an expression inany other way, e.g. using seq in Miranda or returning afunction as the overall result of a program, then bottom and\\ x . bottom will not be equivalent. See also observational equivalence, reduction.
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