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fix


1. hematics> The href="module.php?name=Lexikon&file=search&eid=1&query=fixed point">fixed point href="module.php?name=Lexikon&file=search&eid=1&query=combinator">combinator. Called Y in href="module.php?name=Lexikon&file=search&eid=1&query=combinatory logic">combinatory logic. Fix is a href="module.php?name=Lexikon&file=search&eid=1&query=higher-order function">higher-order function which returns a fixed point of its argument (which is a function). fix :: (a -> a) -> a fix f = f (fix f) Which satisfies the equation fix f = x such that f x = x. Somewhat surprisingly, fix can be defined as the non-recursive href="module.php?name=Lexikon&file=search&eid=1&query=lambda abstraction">lambda abstraction: fix = h . ( x . h (x x)) ( x . h (x x)) Since this involves self-application, it has an {infinite type}. A function defined by f x1 .. xN = E can be expressed as f = fix ( f . x1 ... xN . E) = ( f . x1 ... xN . E) (fix ( f . x1 ... xN . E)) = let f = (fix ( f . x1 ... xN . E)) in x1 ... xN . E If f does not occur href="module.php?name=Lexikon&file=search&eid=1&query=free">free in E (i.e. it is not href="module.php?name=Lexikon&file=search&eid=1&query=recursive">recursive) then this reduces to simply f = x1 ... xN . E In the case where N = 0 and f is free in E, this defines an infinite data object, e.g. ones = fix ( ones . 1 : ones) = ( ones . 1 : ones) (fix ( ones . 1 : ones)) = 1 : (fix ( ones . 1 : ones)) = 1 : 1 : ... Fix f is also sometimes written as mu f where mu is the Greek letter or alternatively, if f = x . E, written as mu x . E. Compare href="module.php?name=Lexikon&file=search&eid=1&query=quine">quine. [href="module.php?name=Lexikon&file=search&eid=1&query=Jargon File">Jargon File] (1995-04-13) 2. href="module.php?name=Lexikon&file=search&eid=1&query=bug fix">bug fix. (1998-06-25)

In addition suitable contents:
[ href="module.php?name=Lexikon&op=content&tid=31">2 ] [ href="module.php?name=Lexikon&op=content&tid=134">= ] [ href="module.php?name=Lexikon&op=content&tid=178">abstraction ] [ href="module.php?name=Lexikon&op=content&tid=433">al ] [ href="module.php?name=Lexikon&op=content&tid=531">alt ] [ href="module.php?name=Lexikon&op=content&tid=544">am ] [ href="module.php?name=Lexikon&op=content&tid=592">an ] [ href="module.php?name=Lexikon&op=content&tid=683">app ] [ href="module.php?name=Lexikon&op=content&tid=700">application ] [ href="module.php?name=Lexikon&op=content&tid=740">ar ] [ href="module.php?name=Lexikon&op=content&tid=743">arc ] [ href="module.php?name=Lexikon&op=content&tid=759">arg ] [ href="module.php?name=Lexikon&op=content&tid=760">argument ] [ href="module.php?name=Lexikon&op=content&tid=800">as ] [ href="module.php?name=Lexikon&op=content&tid=894">at ] [ href="module.php?name=Lexikon&op=content&tid=1026">b ] [ href="module.php?name=Lexikon&op=content&tid=1177">bd ] [ href="module.php?name=Lexikon&op=content&tid=1181">be ] [ href="module.php?name=Lexikon&op=content&tid=1269">bi ] [ href="module.php?name=Lexikon&op=content&tid=1368">bj ] [ href="module.php?name=Lexikon&op=content&tid=1606">bs ] [ href="module.php?name=Lexikon&op=content&tid=1645">bug fix ] [ href="module.php?name=Lexikon&op=content&tid=1695">by ] [ href="module.php?name=Lexikon&op=content&tid=1708">C ] [ href="module.php?name=Lexikon&op=content&tid=1724">ca ] [ href="module.php?name=Lexikon&op=content&tid=1844">case ] [ href="module.php?name=Lexikon&op=content&tid=1863">cat ] [ href="module.php?name=Lexikon&op=content&tid=1896">cc ] [ href="module.php?name=Lexikon&op=content&tid=2001">ch ] [ href="module.php?name=Lexikon&op=content&tid=2247">co ] [ href="module.php?name=Lexikon&op=content&tid=2330">com ] [ href="module.php?name=Lexikon&op=content&tid=2333">combinator ] [ href="module.php?name=Lexikon&op=content&tid=2334">combinatory logic ] [ href="module.php?name=Lexikon&op=content&tid=2900">cu ] [ href="module.php?name=Lexikon&op=content&tid=3006">data ] [ href="module.php?name=Lexikon&op=content&tid=3151">de ] [ href="module.php?name=Lexikon&op=content&tid=3565">do ] [ href="module.php?name=Lexikon&op=content&tid=3752">du ] [ href="module.php?name=Lexikon&op=content&tid=3834">E ] [ href="module.php?name=Lexikon&op=content&tid=3865">ec ] [ href="module.php?name=Lexikon&op=content&tid=3896">ed ] [ href="module.php?name=Lexikon&op=content&tid=3923">edu ] [ href="module.php?name=Lexikon&op=content&tid=3929">ee ] [ href="module.php?name=Lexikon&op=content&tid=4148">er ] [ href="module.php?name=Lexikon&op=content&tid=4171">es ] [ href="module.php?name=Lexikon&op=content&tid=4199">et ] [ href="module.php?name=Lexikon&op=content&tid=4497">fi ] [ href="module.php?name=Lexikon&op=content&tid=4520">file ] [ href="module.php?name=Lexikon&op=content&tid=4559">finite ] [ href="module.php?name=Lexikon&op=content&tid=4597">fixed point ] [ href="module.php?name=Lexikon&op=content&tid=4828">fr ] [ href="module.php?name=Lexikon&op=content&tid=4859">free ] [ href="module.php?name=Lexikon&op=content&tid=4940">function ] [ href="module.php?name=Lexikon&op=content&tid=4983">G ] [ href="module.php?name=Lexikon&op=content&tid=5134">gh ] [ href="module.php?name=Lexikon&op=content&tid=5141">gi ] [ href="module.php?name=Lexikon&op=content&tid=5171">gl ] [ href="module.php?name=Lexikon&op=content&tid=5403">gu ] [ href="module.php?name=Lexikon&op=content&tid=5434">h ] [ href="module.php?name=Lexikon&op=content&tid=5540">hat ] [ href="module.php?name=Lexikon&op=content&tid=5635">higher-order function ] [ href="module.php?name=Lexikon&op=content&tid=5768">hr ] [ href="module.php?name=Lexikon&op=content&tid=5931">id ] [ href="module.php?name=Lexikon&op=content&tid=5956">ie ] [ href="module.php?name=Lexikon&op=content&tid=6013">il ] [ href="module.php?name=Lexikon&op=content&tid=6064">in ] [ href="module.php?name=Lexikon&op=content&tid=6068">inc ] [ href="module.php?name=Lexikon&op=content&tid=6103">infinite ] [ href="module.php?name=Lexikon&op=content&tid=6194">int ] [ href="module.php?name=Lexikon&op=content&tid=6413">io ] [ href="module.php?name=Lexikon&op=content&tid=6482">is ] [ href="module.php?name=Lexikon&op=content&tid=6558">it ] [ href="module.php?name=Lexikon&op=content&tid=6589">J ] [ href="module.php?name=Lexikon&op=content&tid=6620">Jargon File ] [ href="module.php?name=Lexikon&op=content&tid=6918">la ] [ href="module.php?name=Lexikon&op=content&tid=6938">lambda abstraction ] [ href="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ href="module.php?name=Lexikon&op=content&tid=7107">li ] [ href="module.php?name=Lexikon&op=content&tid=7399">ls ] [ href="module.php?name=Lexikon&op=content&tid=7410">lt ] [ href="module.php?name=Lexikon&op=content&tid=7437">lv ] [ href="module.php?name=Lexikon&op=content&tid=7441">ly ] [ href="module.php?name=Lexikon&op=content&tid=7463">ma ] [ href="module.php?name=Lexikon&op=content&tid=8032">mo ] [ href="module.php?name=Lexikon&op=content&tid=8040">mod ] [ href="module.php?name=Lexikon&op=content&tid=8079">module ] [ href="module.php?name=Lexikon&op=content&tid=8167">mp ] [ href="module.php?name=Lexikon&op=content&tid=8258">mu ] [ href="module.php?name=Lexikon&op=content&tid=8384">N ] [ href="module.php?name=Lexikon&op=content&tid=8386">na ] [ href="module.php?name=Lexikon&op=content&tid=8460">nc ] [ href="module.php?name=Lexikon&op=content&tid=8472">ne ] [ href="module.php?name=Lexikon&op=content&tid=8622">nf ] [ href="module.php?name=Lexikon&op=content&tid=8627">ng ] [ href="module.php?name=Lexikon&op=content&tid=8630">ni ] [ href="module.php?name=Lexikon&op=content&tid=8675">no ] [ href="module.php?name=Lexikon&op=content&tid=8760">ns ] [ href="module.php?name=Lexikon&op=content&tid=8838">object ] [ href="module.php?name=Lexikon&op=content&tid=8964">om ] [ href="module.php?name=Lexikon&op=content&tid=9204">pa ] [ href="module.php?name=Lexikon&op=content&tid=9457">pe ] [ href="module.php?name=Lexikon&op=content&tid=9550">ph ] [ href="module.php?name=Lexikon&op=content&tid=9651">pl ] [ href="module.php?name=Lexikon&op=content&tid=9738">ply ] [ href="module.php?name=Lexikon&op=content&tid=9762">point ] [ href="module.php?name=Lexikon&op=content&tid=9908">pr ] [ href="module.php?name=Lexikon&op=content&tid=10253">query ] [ href="module.php?name=Lexikon&op=content&tid=10272">quine ] [ href="module.php?name=Lexikon&op=content&tid=10364">rc ] [ href="module.php?name=Lexikon&op=content&tid=10385">re ] [ href="module.php?name=Lexikon&op=content&tid=10433">recursive ] [ href="module.php?name=Lexikon&op=content&tid=10918">S ] [ href="module.php?name=Lexikon&op=content&tid=10922">sa ] [ href="module.php?name=Lexikon&op=content&tid=11150">se ] [ href="module.php?name=Lexikon&op=content&tid=11376">si ] [ href="module.php?name=Lexikon&op=content&tid=11651">so ] [ href="module.php?name=Lexikon&op=content&tid=11934">st ] [ href="module.php?name=Lexikon&op=content&tid=12133">su ] [ href="module.php?name=Lexikon&op=content&tid=12359">T ] [ href="module.php?name=Lexikon&op=content&tid=12588">th ] [ href="module.php?name=Lexikon&op=content&tid=12721">to ] [ href="module.php?name=Lexikon&op=content&tid=12787">tr ] [ href="module.php?name=Lexikon&op=content&tid=12896">tt ] [ href="module.php?name=Lexikon&op=content&tid=12970">type ] [ href="module.php?name=Lexikon&op=content&tid=12986">ua ] [ href="module.php?name=Lexikon&op=content&tid=13008">ug ] [ href="module.php?name=Lexikon&op=content&tid=13030">um ] [ href="module.php?name=Lexikon&op=content&tid=13310">ve ] [ href="module.php?name=Lexikon&op=content&tid=14024">Y ]






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