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Lexikon


lambda-calculus


ematics> (Normally written with a Greek letter lambda). A branch of mathematical logic developed by ef="module.php?name=Lexikon&file=search&eid=1&query=Alonzo Church">Alonzo Church in the late 1930s and early 1940s, dealing with the application of ef="module.php?name=Lexikon&file=search&eid=1&query=functions">functions to their arguments. The ef="module.php?name=Lexikon&file=search&eid=1&query=pure lambda-calculus">pure lambda-calculus contains no constants - neither numbers nor mathematical functions such as plus - and is untyped. It consists only of ef="module.php?name=Lexikon&file=search&eid=1&query=lambda abstraction">lambda abstractions (functions), variables and applications of one function to another. All entities must therefore be represented as functions. For example, the natural number N can be represented as the function which applies its first argument to its second N times (ef="module.php?name=Lexikon&file=search&eid=1&query=Church integer">Church integer N). Church invented lambda-calculus in order to set up a foundational project restricting mathematics to quantities with "ef="module.php?name=Lexikon&file=search&eid=1&query=effective procedures">effective procedures". Unfortunately, the resulting system admits ef="module.php?name=Lexikon&file=search&eid=1&query=Russell' s paradox">Russell' s paradox in a particularly nasty way Church couldn' t see any way to get rid of it, and gave the project up. Most ef="module.php?name=Lexikon&file=search&eid=1&query=functional programming">functional programming languages are equivalent to lambda-calculus extended with constants and types. ef="module.php?name=Lexikon&file=search&eid=1&query=Lisp">Lisp uses a variant of lambda notation for defining functions but only its ef="module.php?name=Lexikon&file=search&eid=1&query=purely functional">purely functional subset is really equivalent to lambda-calculus. See ef="module.php?name=Lexikon&file=search&eid=1&query=reduction">reduction. (1995-04-13)

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=134">= ] [ ef="module.php?name=Lexikon&op=content&tid=178">abstraction ] [ ef="module.php?name=Lexikon&op=content&tid=262">ad ] [ ef="module.php?name=Lexikon&op=content&tid=396">ag ] [ ef="module.php?name=Lexikon&op=content&tid=411">ai ] [ ef="module.php?name=Lexikon&op=content&tid=433">al ] [ ef="module.php?name=Lexikon&op=content&tid=515">Alonzo Church ] [ 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=996">av ] [ 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=1535">br ] [ ef="module.php?name=Lexikon&op=content&tid=1550">branch ] [ ef="module.php?name=Lexikon&op=content&tid=1606">bs ] [ 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=1863">cat ] [ ef="module.php?name=Lexikon&op=content&tid=2000">Ch ] [ ef="module.php?name=Lexikon&op=content&tid=2001">ch ] [ ef="module.php?name=Lexikon&op=content&tid=2096">Church integer ] [ ef="module.php?name=Lexikon&op=content&tid=2247">co ] [ ef="module.php?name=Lexikon&op=content&tid=2545">con ] [ ef="module.php?name=Lexikon&op=content&tid=2606">cons ] [ ef="module.php?name=Lexikon&op=content&tid=2900">cu ] [ ef="module.php?name=Lexikon&op=content&tid=3151">de ] [ ef="module.php?name=Lexikon&op=content&tid=3546">dm ] [ 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=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=3946">eg ] [ 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=4319">extend ] [ 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=4700">fo ] [ ef="module.php?name=Lexikon&op=content&tid=4727">for ] [ ef="module.php?name=Lexikon&op=content&tid=4801">foundation ] [ ef="module.php?name=Lexikon&op=content&tid=4940">function ] [ ef="module.php?name=Lexikon&op=content&tid=4941">functional ] [ ef="module.php?name=Lexikon&op=content&tid=4946">functional program ] [ ef="module.php?name=Lexikon&op=content&tid=4947">functional programming ] [ ef="module.php?name=Lexikon&op=content&tid=4983">G ] [ ef="module.php?name=Lexikon&op=content&tid=4989">ga ] [ ef="module.php?name=Lexikon&op=content&tid=5057">ge ] [ ef="module.php?name=Lexikon&op=content&tid=5141">gi ] [ ef="module.php?name=Lexikon&op=content&tid=5291">gr ] [ 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=5768">hr ] [ ef="module.php?name=Lexikon&op=content&tid=5791">hu ] [ 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=6194">int ] [ ef="module.php?name=Lexikon&op=content&tid=6196">integer ] [ ef="module.php?name=Lexikon&op=content&tid=6413">io ] [ ef="module.php?name=Lexikon&op=content&tid=6449">ir ] [ 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=6918">la ] [ ef="module.php?name=Lexikon&op=content&tid=6938">lambda abstraction ] [ ef="module.php?name=Lexikon&op=content&tid=6950">language ] [ ef="module.php?name=Lexikon&op=content&tid=7014">lc ] [ ef="module.php?name=Lexikon&op=content&tid=7023">ld ] [ 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=7203">Lisp ] [ ef="module.php?name=Lexikon&op=content&tid=7410">lt ] [ ef="module.php?name=Lexikon&op=content&tid=7415">lu ] [ ef="module.php?name=Lexikon&op=content&tid=7441">ly ] [ ef="module.php?name=Lexikon&op=content&tid=7457">M ] [ ef="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ef="module.php?name=Lexikon&op=content&tid=7579">mall ] [ ef="module.php?name=Lexikon&op=content&tid=8019">mm ] [ 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=8449">natural number ] [ 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=8660">nl ] [ 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=8787">nu ] [ ef="module.php?name=Lexikon&op=content&tid=8799">numbers ] [ ef="module.php?name=Lexikon&op=content&tid=8819">nz ] [ ef="module.php?name=Lexikon&op=content&tid=9014">op ] [ ef="module.php?name=Lexikon&op=content&tid=9204">pa ] [ ef="module.php?name=Lexikon&op=content&tid=9270">paradox ] [ 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=9736">plus ] [ ef="module.php?name=Lexikon&op=content&tid=9908">pr ] [ ef="module.php?name=Lexikon&op=content&tid=9994">procedure ] [ ef="module.php?name=Lexikon&op=content&tid=10023">program ] [ ef="module.php?name=Lexikon&op=content&tid=10042">programming ] [ ef="module.php?name=Lexikon&op=content&tid=10178">pure lambda-calculus ] [ ef="module.php?name=Lexikon&op=content&tid=10253">query ] [ 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=10390">real ] [ ef="module.php?name=Lexikon&op=content&tid=10453">reduction ] [ ef="module.php?name=Lexikon&op=content&tid=10754">rl ] [ ef="module.php?name=Lexikon&op=content&tid=10767">ro ] [ ef="module.php?name=Lexikon&op=content&tid=10907">Russell ] [ ef="module.php?name=Lexikon&op=content&tid=10918">S ] [ ef="module.php?name=Lexikon&op=content&tid=11150">se ] [ ef="module.php?name=Lexikon&op=content&tid=11281">set ] [ ef="module.php?name=Lexikon&op=content&tid=11376">si ] [ ef="module.php?name=Lexikon&op=content&tid=11934">st ] [ ef="module.php?name=Lexikon&op=content&tid=12090">strict ] [ ef="module.php?name=Lexikon&op=content&tid=12133">su ] [ ef="module.php?name=Lexikon&op=content&tid=12246">sy ] [ ef="module.php?name=Lexikon&op=content&tid=12312">system ] [ 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=13030">um ] [ ef="module.php?name=Lexikon&op=content&tid=13141">untyped ] [ ef="module.php?name=Lexikon&op=content&tid=13146">up ] [ ef="module.php?name=Lexikon&op=content&tid=13175">us ] [ ef="module.php?name=Lexikon&op=content&tid=13252">va ] [ ef="module.php?name=Lexikon&op=content&tid=13274">var ] [ ef="module.php?name=Lexikon&op=content&tid=13275">variable ] [ ef="module.php?name=Lexikon&op=content&tid=13310">ve ]






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