EXTENSIONAL EQUALITY
\ɛkstˈɛnʃənə͡l iːkwˈɒlɪti], \ɛkstˈɛnʃənəl iːkwˈɒlɪti], \ɛ_k_s_t_ˈɛ_n_ʃ_ə_n_əl iː_k_w_ˈɒ_l_ɪ_t_i]\
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(Or extensionality). Functions, f and g are extensionallyequal if and only iff x = g x for all x.where "=" means both expressions fail to terminate (under somegiven reduction strategy) or they both terminate with thesame basic value.Two functions may be extensionally equal but notinter-convertible (neither is reducible to the other). E.g.\ x . x+x and \ x . 2*x. See also observationalequivalence, referential transparency.
By Denis Howe
