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Lexikon


fix


1. ematics> The ef="module.php?name=Lexikon&file=search&eid=1&query=fixed point">fixed point ef="module.php?name=Lexikon&file=search&eid=1&query=combinator">combinator. Called Y in ef="module.php?name=Lexikon&file=search&eid=1&query=combinatory logic">combinatory logic. Fix is a ef="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 ef="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 ef="module.php?name=Lexikon&file=search&eid=1&query=free">free in e (i.e. it is not ef="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 ef="module.php?name=Lexikon&file=search&eid=1&query=quine">quine. [ef="module.php?name=Lexikon&file=search&eid=1&query=Jargon File">Jargon File] (1995-04-13) 2. ef="module.php?name=Lexikon&file=search&eid=1&query=bug fix">bug fix. (1998-06-25)

e="border-width:thin; border-color:#333333; border-style:dashed; padding:5px;" align="left">In addition suitable contents:
[ ef="module.php?name=Lexikon&op=content&tid=31">2 ] [ ef="module.php?name=Lexikon&op=content&tid=134">= ] [ ef="module.php?name=Lexikon&op=content&tid=178">abstraction ] [ ef="module.php?name=Lexikon&op=content&tid=433">al ] [ ef="module.php?name=Lexikon&op=content&tid=531">alt ] [ ef="module.php?name=Lexikon&op=content&tid=544">am ] [ ef="module.php?name=Lexikon&op=content&tid=592">an ] [ ef="module.php?name=Lexikon&op=content&tid=683">app ] [ ef="module.php?name=Lexikon&op=content&tid=700">application ] [ ef="module.php?name=Lexikon&op=content&tid=740">ar ] [ ef="module.php?name=Lexikon&op=content&tid=743">arc ] [ ef="module.php?name=Lexikon&op=content&tid=759">arg ] [ ef="module.php?name=Lexikon&op=content&tid=760">argument ] [ ef="module.php?name=Lexikon&op=content&tid=800">as ] [ ef="module.php?name=Lexikon&op=content&tid=894">at ] [ ef="module.php?name=Lexikon&op=content&tid=1026">b ] [ ef="module.php?name=Lexikon&op=content&tid=1177">bd ] [ ef="module.php?name=Lexikon&op=content&tid=1181">be ] [ ef="module.php?name=Lexikon&op=content&tid=1269">bi ] [ ef="module.php?name=Lexikon&op=content&tid=1368">bj ] [ ef="module.php?name=Lexikon&op=content&tid=1606">bs ] [ ef="module.php?name=Lexikon&op=content&tid=1645">bug fix ] [ ef="module.php?name=Lexikon&op=content&tid=1695">by ] [ ef="module.php?name=Lexikon&op=content&tid=1708">C ] [ ef="module.php?name=Lexikon&op=content&tid=1724">ca ] [ ef="module.php?name=Lexikon&op=content&tid=1844">case ] [ ef="module.php?name=Lexikon&op=content&tid=1863">cat ] [ ef="module.php?name=Lexikon&op=content&tid=1896">cc ] [ ef="module.php?name=Lexikon&op=content&tid=2001">ch ] [ ef="module.php?name=Lexikon&op=content&tid=2247">co ] [ ef="module.php?name=Lexikon&op=content&tid=2330">com ] [ ef="module.php?name=Lexikon&op=content&tid=2333">combinator ] [ ef="module.php?name=Lexikon&op=content&tid=2334">combinatory logic ] [ ef="module.php?name=Lexikon&op=content&tid=2900">cu ] [ ef="module.php?name=Lexikon&op=content&tid=3006">data ] [ ef="module.php?name=Lexikon&op=content&tid=3151">de ] [ ef="module.php?name=Lexikon&op=content&tid=3565">do ] [ ef="module.php?name=Lexikon&op=content&tid=3752">du ] [ ef="module.php?name=Lexikon&op=content&tid=3834">e ] [ ef="module.php?name=Lexikon&op=content&tid=3865">ec ] [ ef="module.php?name=Lexikon&op=content&tid=3896">ed ] [ ef="module.php?name=Lexikon&op=content&tid=3923">edu ] [ ef="module.php?name=Lexikon&op=content&tid=3929">ee ] [ ef="module.php?name=Lexikon&op=content&tid=4148">er ] [ ef="module.php?name=Lexikon&op=content&tid=4171">es ] [ ef="module.php?name=Lexikon&op=content&tid=4199">et ] [ ef="module.php?name=Lexikon&op=content&tid=4497">fi ] [ ef="module.php?name=Lexikon&op=content&tid=4520">file ] [ ef="module.php?name=Lexikon&op=content&tid=4559">finite ] [ ef="module.php?name=Lexikon&op=content&tid=4597">fixed point ] [ ef="module.php?name=Lexikon&op=content&tid=4828">fr ] [ ef="module.php?name=Lexikon&op=content&tid=4859">free ] [ ef="module.php?name=Lexikon&op=content&tid=4940">function ] [ ef="module.php?name=Lexikon&op=content&tid=4983">G ] [ ef="module.php?name=Lexikon&op=content&tid=5134">gh ] [ ef="module.php?name=Lexikon&op=content&tid=5141">gi ] [ ef="module.php?name=Lexikon&op=content&tid=5171">gl ] [ ef="module.php?name=Lexikon&op=content&tid=5403">gu ] [ ef="module.php?name=Lexikon&op=content&tid=5434">h ] [ ef="module.php?name=Lexikon&op=content&tid=5540">hat ] [ ef="module.php?name=Lexikon&op=content&tid=5635">higher-order function ] [ ef="module.php?name=Lexikon&op=content&tid=5768">hr ] [ ef="module.php?name=Lexikon&op=content&tid=5931">id ] [ ef="module.php?name=Lexikon&op=content&tid=5956">ie ] [ ef="module.php?name=Lexikon&op=content&tid=6013">il ] [ ef="module.php?name=Lexikon&op=content&tid=6064">in ] [ ef="module.php?name=Lexikon&op=content&tid=6068">inc ] [ ef="module.php?name=Lexikon&op=content&tid=6103">infinite ] [ ef="module.php?name=Lexikon&op=content&tid=6194">int ] [ ef="module.php?name=Lexikon&op=content&tid=6413">io ] [ ef="module.php?name=Lexikon&op=content&tid=6482">is ] [ ef="module.php?name=Lexikon&op=content&tid=6558">it ] [ ef="module.php?name=Lexikon&op=content&tid=6589">J ] [ ef="module.php?name=Lexikon&op=content&tid=6620">Jargon File ] [ ef="module.php?name=Lexikon&op=content&tid=6918">la ] [ ef="module.php?name=Lexikon&op=content&tid=6938">lambda abstraction ] [ ef="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ ef="module.php?name=Lexikon&op=content&tid=7107">li ] [ ef="module.php?name=Lexikon&op=content&tid=7399">ls ] [ ef="module.php?name=Lexikon&op=content&tid=7410">lt ] [ ef="module.php?name=Lexikon&op=content&tid=7437">lv ] [ ef="module.php?name=Lexikon&op=content&tid=7441">ly ] [ ef="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ef="module.php?name=Lexikon&op=content&tid=8032">mo ] [ ef="module.php?name=Lexikon&op=content&tid=8040">mod ] [ ef="module.php?name=Lexikon&op=content&tid=8079">module ] [ ef="module.php?name=Lexikon&op=content&tid=8167">mp ] [ ef="module.php?name=Lexikon&op=content&tid=8258">mu ] [ ef="module.php?name=Lexikon&op=content&tid=8384">N ] [ ef="module.php?name=Lexikon&op=content&tid=8386">na ] [ ef="module.php?name=Lexikon&op=content&tid=8460">nc ] [ ef="module.php?name=Lexikon&op=content&tid=8472">ne ] [ ef="module.php?name=Lexikon&op=content&tid=8622">nf ] [ ef="module.php?name=Lexikon&op=content&tid=8627">ng ] [ ef="module.php?name=Lexikon&op=content&tid=8630">ni ] [ ef="module.php?name=Lexikon&op=content&tid=8675">no ] [ ef="module.php?name=Lexikon&op=content&tid=8760">ns ] [ ef="module.php?name=Lexikon&op=content&tid=8838">object ] [ ef="module.php?name=Lexikon&op=content&tid=8964">om ] [ ef="module.php?name=Lexikon&op=content&tid=9204">pa ] [ ef="module.php?name=Lexikon&op=content&tid=9457">pe ] [ ef="module.php?name=Lexikon&op=content&tid=9550">ph ] [ ef="module.php?name=Lexikon&op=content&tid=9651">pl ] [ ef="module.php?name=Lexikon&op=content&tid=9738">ply ] [ ef="module.php?name=Lexikon&op=content&tid=9762">point ] [ ef="module.php?name=Lexikon&op=content&tid=9908">pr ] [ ef="module.php?name=Lexikon&op=content&tid=10253">query ] [ ef="module.php?name=Lexikon&op=content&tid=10272">quine ] [ ef="module.php?name=Lexikon&op=content&tid=10364">rc ] [ ef="module.php?name=Lexikon&op=content&tid=10385">re ] [ ef="module.php?name=Lexikon&op=content&tid=10433">recursive ] [ ef="module.php?name=Lexikon&op=content&tid=10918">S ] [ ef="module.php?name=Lexikon&op=content&tid=10922">sa ] [ ef="module.php?name=Lexikon&op=content&tid=11150">se ] [ ef="module.php?name=Lexikon&op=content&tid=11376">si ] [ ef="module.php?name=Lexikon&op=content&tid=11651">so ] [ ef="module.php?name=Lexikon&op=content&tid=11934">st ] [ ef="module.php?name=Lexikon&op=content&tid=12133">su ] [ ef="module.php?name=Lexikon&op=content&tid=12359">T ] [ ef="module.php?name=Lexikon&op=content&tid=12588">th ] [ ef="module.php?name=Lexikon&op=content&tid=12721">to ] [ ef="module.php?name=Lexikon&op=content&tid=12787">tr ] [ ef="module.php?name=Lexikon&op=content&tid=12896">tt ] [ ef="module.php?name=Lexikon&op=content&tid=12970">type ] [ ef="module.php?name=Lexikon&op=content&tid=12986">ua ] [ ef="module.php?name=Lexikon&op=content&tid=13008">ug ] [ ef="module.php?name=Lexikon&op=content&tid=13030">um ] [ ef="module.php?name=Lexikon&op=content&tid=13310">ve ] [ ef="module.php?name=Lexikon&op=content&tid=14024">Y ]






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