x . f x fprovided x does not occur as a free variableThis conversion is only valid if "> in f and f is a function. Left to right is eta reduction, right to left is eta abstraction (or eta expansion).This conversion is only valid if bottom and x . bottom are equivalent in all contexts. They are certainly equivalent when applied to some argument - they both fail to terminate. If we are allowed to force the evaluation of an expression in any other way, e.g. using {seq} in Miranda or returning a function as the overall result of a program, then bottom and See also "> x . bottom will not be equivalent.See also observational equivalence, reduction.reduction.……"> eta conversion : FOLDOC
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eta conversion : FOLDOC
eta conversion
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 a function. Left to right is eta reduction, right to left is eta abstraction (or eta expansion).
This conversion is only valid if
bottom and x . bottom are equivalent in all contexts. They are certainly equivalent when applied to some argument - they both fail to terminate. If we are allowed to force the evaluation of an expression in any other way, e.g. using {seq} in Miranda or returning a function as the overall result of a program, then bottom and x . bottom will not be equivalent.
See also
observational equivalence, reduction.

reduction.



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