A function which is not defined for all arguments of its input type. E.g.
f(x) = 1/x if x /= 0.
The opposite of a total function. In denotational semantics, a partial function
f : D -> C
may be represented as a total function
ft : D’ -> lift(C)
where D’ is a superset of D and
ft x = f x if x in D ft x = bottom otherwise
where lift(C) = C U bottom. Bottom (LaTeX \perp) denotes “undefined”.
[pahr-shuh-lahyz] /ˈpɑr ʃəˌlaɪz/ verb (used with object), partialized, partializing. 1. to bias.
[pahr-shee-al-i-tee, pahr-shal-] /ˌpɑr ʃiˈæl ɪ ti, pɑrˈʃæl-/ noun, plural partialities. 1. the state or character of being . 2. a favorable bias or prejudice: the partiality of parents for their own children. 3. a special fondness, preference, or liking (usually followed by to or for): a partiality for country living. /ˌpɑːʃɪˈælɪtɪ/ noun (pl) -ties 1. […]
/ˈpærɪtʃ; ˈpɑːr-/ noun 1. a Scot word for porridge
[par-is] /ˈpær ɪs/ noun 1. a U.S. Marine Corps base, recruit depot, and training station in SE South Carolina, SW of Beaufort and S of Port Royal Island.