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". (1995-02-03)

In addition suitable contents:
[ 2 ] [ = ] [ al ] [ am ] [ an ] [ ar ] [ arc ] [ arg ] [ argument ] [ as ] [ at ] [ B ] [ b ] [ be ] [ bo ] [ bot ] [ bottom ] [ C ] [ ch ] [ D ] [ de ] [ denotational semantics ] [ du ] [ E ] [ ed ] [ er ] [ es ] [ et ] [ fi ] [ file ] [ fo ] [ for ] [ function ] [ gu ] [ h ] [ hr ] [ id ] [ il ] [ in ] [ input ] [ io ] [ is ] [ it ] [ LaTeX ] [ Lex ] [ li ] [ ma ] [ man ] [ mo ] [ mod ] [ module ] [ na ] [ nc ] [ ne ] [ no ] [ np ] [ om ] [ op ] [ pa ] [ pe ] [ perp ] [ ph ] [ pr ] [ query ] [ rc ] [ re ] [ rw ] [ se ] [ semantics ] [ set ] [ si ] [ sit ] [ su ] [ T ] [ ] [ th ] [ to ] [ total function ] [ tt ] [ type ] [ um ] [ up ] [ X ]