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.
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[ey-tuh-see, ee-tuh-] /ˈeɪ təˈsi, ˈi tə-/ noun, Physics. 1. a neutral meson having a mass 5832 times that of the electron and a mean lifetime of approximately 3.1 × 10 -22 seconds. eta-c particle (ā’tə-sē’, ē’tə-) An electrically neutral meson having a mass 5,832 times that of the electron and a mean lifetime of approximately […]
/ɛˈtɪərɪəʊ/ noun 1. an aggregate fruit, as one consisting of drupes (raspberry) or achenes (traveller’s joy)
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[ey-tah-zhair, ey-tuh-; French ey-ta-zher] /ˌeɪ tɑˈʒɛər, ˌeɪ tə-; French eɪ taˈʒɛr/ noun, plural étagères [ey-tah-zhairz, ey-tuh-; French ey-ta-zher] /ˌeɪ tɑˈʒɛərz, ˌeɪ tə-; French eɪ taˈʒɛr/ (Show IPA) 1. a stand with a series of open shelves for small objects, bric-a-brac, etc. /etaʒɛr/ noun 1. a stand with open shelves for displaying ornaments, etc n. 1858, […]